text:
Tag: European Court of Human Rights
Excerpt: Rights of Child Detainees
November 20, 2020 November 20, 2020 parichayteamLeave a comment
The following post is an excerpt from the upcoming report 'Securing Citizenship' on India's legal obligations towards precarious citizens and stateless persons authored by the Centre for Public Interest Law, JGLS and Faculty of Law, Université Catholique de Lille. The Report reviews and comments on the key contemporary legal issues pertaining to citizenship and statelessness in India. Divided into three chapters – Citizenship Status, Detention and Socio-Economic Rights – the Report presents recommendations to strengthen the existing legal framework. This excerpt is the last in a three-part series of excerpts from the report. The previous excerpts on legal recognition of the status of statelessness and the framework of socio-economic rights of non-nationals can be found here and here. The entire Report will be published in the final week of November, and the schedule of events can be found here.
IV. RIGHTS OF CHILD DETAINEES
All the rights and prohibitions against detention established and elaborated above apply in the case of children. However, given their special and vulnerable condition, children enjoy additional standards of protection. This section begins with an argument against detaining children on the premise that such detention violates international law pertaining to child rights. Moreover, the state can deploy less intrusive measures in dealing with children. However, given that children may be under detention at present, this section details the rights of such child detainees to be ensured by the state.
The situation of children detained in Assam is worrisome. There is a lack of clarity about the number of children that are currently in detention; however, their presence in detention centres is a confirmed fact. A recent affirmation is found in the application filed before the Supreme Court seeking the release of declared foreigners in the detention centres in light of the COVID-19 outbreak. The application mentions the increased vulnerability of the detainees, which includes elderly people and children living in crowded conditions. There were 31 children in detention centres as per available information. The conditions of these detention centres pose debilitating effects on mental health, without adequate treatment and opportunities for education and recreation. The impact of this situation on children is exponentially greater and liable to pose severe harm to their health.
Detention of children should not take place in principle
As per international law and Indian statutes, detention of children should not take place. The Central Government's submission before the Supreme Court in the ongoing case of Assam Public Works is a welcome development, stating that children of parents declared as citizens in the NRC shall not be sent to detention centres and shall not be separated from their parents. The absolute prohibition of detention also applies to 'foundlings' as a particularly vulnerable category of children. It is argued that children should qualify for protection under the Juvenile Justice Act, 2015 ('JJ Act') as 'Children in Need of Care and Protection' ('CNCP'). This section addresses the categories of children who are vulnerable and need protection. This section also seeks to establish safeguards that necessitate compliance when dealing with children in detention.
A.1 Principle of 'Best Interests of the Child'
Detention of children for the purpose of deportation is a flagrant and unjustified breach of the fundamental principle of best interests of the child protected by Article 3 of the CRC. India is a party to the convention and has incorporated the principle in Chapter II of the JJ Act. As stated by the CRC Committee, the best interests principle is satisfied by the strong prohibition of detention of children since such deprivations of liberty have an extraordinarily adverse impact on the child's well-being and development. This prohibition particularly must be enforced if the child is detained on the sole basis of their or her parent's migration status.
While the lack of data is deplorable with regard to the age of the children currently detained in Assam, it is extremely likely that all categories of children and more specifically the most vulnerable ones, such as unaccompanied and young children, are in detention. In light of these elements, India is obligated to cease its current practice of detaining children in detention centres. All the children currently in detention must be immediately released as per international law and Indian law on the issue.
A.2 Detained children as 'Children in Need of Care and Protection' under the JJ Act
The Juvenile Justice (Care And Protection Of Children) Act, 2015 1 (4) Notwithstanding anything contained in any other law for the time being in force, the provisions of this Act shall apply to all matters concerning children in need of care and protection and children in conflict with law, including — (i) apprehension, detention, prosecution, penalty or imprisonment, rehabilitation and social re-integration of children in conflict with law; (ii) procedures and decisions or orders relating to rehabilitation, adoption, re-integration, and restoration of children in need of care and protection. 2 (14) "child in need of care and protection" means a child — (i) who is found without any home or settled place of abode and without any ostensible means of subsistence; or (vii) who is missing or run away child, or whose parents cannot be found after making reasonable inquiry in such manner as may be prescribed;
The Object of the Act includes the making of comprehensive provisions for all children in consonance with the standards prescribed in the CRC. Therefore, the JJ Act can be used to operationalise India's international obligations to address the vulnerabilities of both stateless children and children at risk of statelessness.
The scope of the term CNCP encompasses the broad categories of children who are at the risk of detention and its consequent negative impact. Section 2(14)(i) of the JJ Act refers to a child who is found without any home or settled place of abode and without any ostensible means of subsistence. This can cover children whose parents are in detention, who are stateless or are suspected of being foreign nationals. Such children would qualify for protection under the JJ Act. Further, Section 2(14)(vii) extends the scope of CNCP to foundlings i.e. children 'whose parents cannot be found after making reasonable inquiry in such manner as may be prescribed'. [A foundling is a child of unknown parentage found abandoned within the territory of a state.] This argument is further corroborated by the view taken by Justice Lokur on the scope of the definition of CNCP, stating that the term must be given a broad interpretation. This means stateless children as well as children at the risk of statelessness qualify for protection under the JJ Act.
A.3 Conclusion and recommendations
The CRC and the JJ Act extend a large set of protections to these vulnerable children. The state must conform with best interests of children as mentioned in the JJ Act, keeping in line with international law. Detention of children for removal shall never take place, irrespective of the citizenship status of their parents.
Release all children in detention in Assam as well as stateless children in detention in India as per international law and Indian law. NGOs shall be allowed unimpeded access to detention centres in Assam to ensure that no children remain in detention.
Children at the risk of statelessness and currently in detention should be presented before the district Child Welfare Committee for drawing up protection plans on a case-by-case basis, bearing in mind the best interests of the child.
Develop alternatives to detention for stateless children and their families. Non-custodial, community-based alternatives shall be prioritised.
Rights of children in detention
As argued above, despite the prohibition of arbitrary detention of children, there is evidence indicating that children remain in detention in Assam due to their precarious citizenship. This section responds to rights of children in detention until they are released as per international law and Indian law on the issue.
Right Indian context European context Recommendations
Right to family unity (if parents are also being detained) Children below 6 years of age are kept alongside their mothers in the detention centre. There is no clarity on circumstances of children over 6 years of age. Families in detention must be provided with separate accommodation to ensure their privacy. Best practice: In Belgium, children accompanied by their parents are, in principle, not detained but transferred to return houses or to an open reception centre which are adequate, child-friendly alternatives to detention. Conduct an assessment on the compliance of the detention measure with the best interest of the child as per the family unity principle. Develop more alternatives to detention for stateless children to avoid the disruption of family unity, such as reception centres.
Right to education at an off-site facility The Supreme Court hasheld that India is obligated to provide free and compulsory education to all children between 6 and 14 years. The court has clarified the vast scope of Article 21A of the Constitution, referring to India's participation in the drafting of the UDHR as well as the ratification of the CRC. Issue: lack of data regarding any educational opportunity for children in detention in Assam. EU member states must provide minors, whose removal has been postponed, with access to a basic education system, depending on the length of their stay. Best practice: Czech Republic allows migrant children to attend schools at the local elementary school outside the detention facilities. The ECtHR also requires the classes to be free as a bar against discrimination on the immigration and nationality status. Children must have access to an education system where they are taught by qualified teachers through programmes integrated in India's education system, regardless of the length of their stay in detention facilities.They must benefit from free classes to avoid any discrimination.Education should be provided outside of detention facilities in line with the best interests of the child.
Right to recreation and play Article 31, CRC + Best Interests of the Child. Issue: lack of data concerning children's access to leisure activities in detention in Assam. This right is protected in Europe but suffers from poor and uneven implementation in the region. Best practice: In Lithuania, children may participate in recreational activities in one of the country's detention centres. Ensure recreational activities in which children facing statelessness can meet local children and young people through NGOs or social workers.Sensitise the public with information on the significance of this right for children.Guarantee access without discrimination on the child's legal status.
Right to medical treatment There is an obligation to provide access to health care services to all children. The state must ensure satisfactory health conditions and health-related education. Issue: lack of information on the health conditions of children. Necessary healthcare must be provided, at least with regards to emergency care and to essential treatment of illness and serious mental disorders. First challenge: the consent of unaccompanied children to medical treatment (rigorous assessment of the age and maturity of the child by Finland, the Netherlands, Slovenia and Spain). Second challenge: lack of paediatricians and mental health specialists Best practice: In Poland, children benefit from regular visits from paediatricians in the centre. In Portugal, children may benefit from psychological services to help them deal with anxiety, stress, depression, etc. and can also be referred to the hospital or psychiatric services if necessary. Ensure that the consultations are conducted in a child-friendly manner and are respectful of the child's right to confidentiality.Organise regular visits by medical professionals from outside the facilities.Provide children information about available mental health services. Conduct medical screenings of newly arrived stateless children identifying potential issues, both physical and mental, that need care.Ensure a rigorous assessment of the child's free and deliberate consent to medical treatment.
Posted in FeaturesTagged Article 21, child rights, Citizenship, Citizenship Act 1955, European Court of Human Rights, Foreigners Tribunals, NRC, Statelessness, Supreme Court
Excerpt: Framework of Socio-Economic Rights for Non-Nationals
November 19, 2020 November 20, 2020 parichayteam1 Comment
The following post is an excerpt from the upcoming report 'Securing Citizenship' on India's legal obligations towards precarious citizens and stateless persons authored by the Centre for Public Interest Law, JGLS and Faculty of Law, Université Catholique de Lille. The Report reviews and comments on the key contemporary legal issues pertaining to citizenship and statelessness in India. Divided into three chapters – Citizenship Status, Detention and Socio-Economic Rights – the Report presents recommendations to strengthen the existing legal framework. This excerpt is the second in a three-part series of excerpts from the report. The previous excerpt on legal recognition of the status of statelessness can be found here. The next excerpt will cover 'Rights of Child Detainees'. The entire Report will be published in the final week of November, and the schedule of events can be found here.
Socio-Economic Frameworks
B.1 International law obligations
As previously mentioned, this report acknowledges the fact that Indian citizens themselves are routinely deprived of these rights in practice. However, despite this unfortunate reality, a State has a legal and moral duty to provide access to fundamental entitlements to all individuals in its territory, regardless of their nationality. These fundamental entitlements refer to social and economic protection which includes access to healthcare, the right to housing and sanitation, the right to education and the right to work and employment, among others.
In international law, Article 25 of the UDHR covers a vast range of rights, including access to adequate water, food, clothing, housing, medical care and other social protections. This 'minimum threshold' for a standard of living is applicable to all persons and is certainly not conditional on citizenship. Based on the principles of equality and non-discrimination, the rights espoused in Article 25 of the UDHR provide the core grounding to the more specific articulations of socio-economic rights in the International Covenant on Economic, Social and Cultural Rights ('ICESCR'). The vast majority of human rights are applicable to everyone, regardless of nationality or immigration status (including stateless persons) as confirmed by General Comment No. 15 and 31. Specifically, in relation to socio-economic rights, the Committee for Economic, Social, and Cultural Rights ('CESCR') in 2009 clarified the interpretation and applicability of ICESCR, stating that the Covenant rights apply to 'everyone including non-nationals, such as refugees, asylum-seekers, stateless persons, migrant workers and victims of international trafficking, regardless of legal status and documentation'. This unequivocally clarifies that socio-economic rights recognised in international law are positively enforceable or applicable to all persons, including non-citizens, stateless persons and precarious citizens, regardless of their citizenship status.
Article 25 of the UDHR Everyone has the right to a standard of living adequate for the health and well-being of himself and of his family, including food, clothing, housing and medical care and necessary social services, and the right to security in the event of unemployment, sickness, disability, widowhood, old age or other lack of livelihood in circumstances beyond his control.Motherhood and childhood are entitled to special care and assistance. All children, whether born in or out of wedlock, shall enjoy the same social protection.
The 1954 Convention is the sole treaty framework that directly prescribes standards of treatment of stateless persons to be implemented by states. While India is not yet a signatory to this pertinent treaty, many of its provisions are now either customary international law, or at the very least offer important approaches relating to the protection of stateless persons that can serve as a useful model, as stated in the UNHCR Statelessness Handbook. The 1954 Convention provides a broad framework of civil, economic, social and cultural rights that must be granted to stateless persons. The broad categories include welfare rights to rationing, housing, public education, public relief, labour legislation, social security, access to identity documentation and gainful employment (wage earning, self-employment, access to liberal professions), among others.
B.2 Lessons from protection frameworks for non-nationals
India does not have a comprehensive policy governing refugees that have fled to India or for stateless persons and their protections. The Indian government's approach towards different precarious citizens of other nationalities and stateless persons has been varied. The Tibetan community and those refugees recognised by (and registered with) the UNHCR serve as two distinct examples. Though the legal, social and political positions of these two communities are clearly distinguishable, their access to socio-economic rights present a blueprint of the rights that could and should be made available to stateless persons. Much like stateless persons, refugees find themselves at the risk of sliding further on the slippery slope of citizenship. Therefore, it is appropriate to refer to the Indian refugee framework and approaches to inform our recommendations for stateless persons and precarious citizens. The nexus between the two frameworks can also be observed from the fact that the 1954 Convention and the 1951 Refugee Convention have a shared drafting history where the former is largely modelled on the provisions of the latter.
An important caveat, however, is that the status of the Tibetan community is not a completely transposable model to stateless individuals, as Tibetans are specifically recognised and protected by the Indian Government. Depending on when they arrived in India (after the Dalai Lama's 'flight into exile' in 1959) they possess stateless identity certificates, are considered 'temporary refugees in India', or fall into the category of 'Long Term Stay'. On the other hand, the refugees who are recognised and registered by the UNHCR, such as the Afghans, Somalians and certain Burmese groups, are 'entitled to an assessment for a Refugee Certificate; a visa if granted a certificate, though often shorter-term; and the possibility of naturalisation, but this depends on irregular and opaque criteria'. Their access to socio-economic rights, therefore, is dependent on and varies according to their specific contexts and the kind of documentation they have. The UNHCR works with a number of implementing partners, such as Don Bosco and the Development and Justice Initiative ('DAJI') to facilitate support and access to these rights. Don Bosco particularly focuses on assisting vulnerable refugee children. It provides them with support in the form of 'rescue operations, short-stay homes, home reparation, institutional rehabilitation, child protection mechanisms, advocacy, education skill trainings, accompaniment and foster care'. Nonetheless, despite the variations in the terminology and categorisation of the legal status of precarious citizens in India, the refugee framework illustrates the crucial socio-economic rights that have been made available to non-citizen communities, as outlined below.
Right Measures by Government of India/UNHCR for Tibetans Measures by Government of India for Rohingya refugees
Healthcare Access to facilities in settlement colonies, administered by the Central Tibetal Administration.Access to Indian hospitals but ineligible for state healthcare subsidies available to citizens. In principle, they have equal access to Primary Health Centres. However, reports persist of Rohingyas being denied treatment due to lack of Indian documentation. Prescription medicines are expensive and inaccessible.Limited coverage by Anganwadis for maternal, neonatal, and early childhood care.
Food and Nutrition Access to PDS rations. Dependent upon rations supplied by UNHCR/local NGOs.Limited access to Anganwadis in certain states for infant nutritional requirements.
Shelter, Housing, Sanitation Tibetan refugee settlements, established in the 1960s on Government land and administered through officers appointed by the Tibetan Government-in-Exile. Lease agreements signed with the Central Tibetan Relief Committee. The majority live in clusters of shanties, with shared toilets and water facilities. Wastewater from toilets flows out into open drains; some are forced to manually collect and dispose of faeces. Access to clean drinking water remains erratic, dependent upon sympathetic local residents.
Education Tibetan secondary and high schools.Access to higher education in Indian colleges and universities. Eligible for Government scholarships. Children under age 14 technically have access to primary schools under the RTE Act, but implementation is erratic – admissions denied due to lack of documentation.When allowed to attend local schools, they are barred from the midday meal scheme.
Employment Non-interference with employment. Seasonal sweater selling, agriculture, and small enterprises are their primary sources of income.Eligible for trade licenses in nursing, teaching, chartered accountancy, medicine, and engineering as per Tibetan Rehabilitation Policy, 2014.Not eligible for government jobs. Common sources of livelihood are rag-picking, construction work, sanitation work, and various kinds of unskilled labour in the informal sector. This work is precarious and makes for a very unstable source of income.
Posted in FeaturesTagged Article 21, Citizenship, Citizenship Act 1955, European Court of Human Rights, Naturalisation, Passport Rules 1980, Passports Act 1967, Statelessness, Supreme Court
Excerpt: Legal Recognition of Status of Statelessness in India
November 18, 2020 November 19, 2020 parichayteam2 Comments
The following post is an excerpt from the upcoming report 'Securing Citizenship' on India's legal obligations towards precarious citizens and stateless persons authored by the Centre for Public Interest Law, JGLS and Faculty of Law, Université Catholique de Lille. The Report reviews and comments on the key contemporary legal issues pertaining to citizenship and statelessness in India. Divided into three chapters – Citizenship Status, Detention and Socio-Economic Rights – the Report presents recommendations to strengthen the existing legal framework. This excerpt is the first in a three-part series of excerpts from the report. The next two excerpts will cover 'Rights of Child Detainees', and 'Socio-Economic Rights of Stateless Persons'. The entire Report will be published in the final week of November, and the schedule of events can be found here.
II. LEGAL RECOGNITION OF STATELESSNESS IN INDIA
A. Recognition of Status
Statelessness poses a moral and normative challenge to the legitimacy of the international state system. In simpler terms, since the world is comprehensively divided between nation states, then every person should be able to claim citizenship and its attendant rights somewhere. Yet, thousands of people around the world face barriers in claiming citizenship rights in any nation because of several aggravating factors.
There are several stateless groups in India who either arrived or were born in India as stateless persons, such as the Tibetans and the Rohingyas. This section pertains to these stateless persons in Indian territory whose citizenship was not deprived as a result of any action of the Indian state. They have no avenues of return to their country of nationality as a result of their statelessness i.e. their state does not accept them as nationals. Thus, they are prohibited from exercising their right to return. In this situation, they cannot be deported and continue to reside in India as subjects of a legal framework which does not formally recognise their status.
A close reading of the Indian domestic law framework governing the status of non-citizens [the Constitution (Articles 5 – 11); the Citizenship Act, 1955 (Sections 2, 3, 6, 6A, 6B, 10); the Foreigners Act, 1946 (Sections 2, 3, 8, 9); and the Passports Act, 1967 (Section 4)] reveals that the definitional categories determining the legal status of an individual are inadequate for guaranteeing the rights of stateless persons. The use of the terms 'illegal migrant', 'foreigner', and 'citizen', as distinct and oppositional categories, operates on the implicit assumption that the person whose status is to be ascertained must be in possession of at least one nationality, even if that nationality is not Indian. None of these terms can be used interchangeably for a stateless person; the Acts simply do not define or acknowledge the phenomenon of statelessness.
International law on the right to nationality of every individual along with the obligation on the state to prevent and reduce statelessness commands states to naturalise all stateless persons in their territory. Hence, it is imperative that the Indian state recognise stateless persons formally and issue identity certificates to them, thereby ensuring recognition of their equal legal personhood for them to avail their rights. These certificates will ensure that their special situation would be addressed. The only pieces of legislation that recognise the status of stateless persons are the Passports Rules, 1980, framed under the Passports Act, 1967, which grant the MEA the power to issue certificates of identity. However, the duty of the state under international law, constitutional law and human rights law (as argued above) does not end with issuing certificates of identity. India must grant them nationality in accordance with international law obligations to ensure that they can enjoy their right to nationality.
As emphasised in previous sections, the lack of legal status is a direct infringement of an individual's right to a dignified life under Article 21 of the Indian Constitution. In a juridical framework, a dignified existence can only be secured through recognition as an individual member of the civic community, which in turn forms the foundation for the free exercise of bodily integrity, autonomy, and self-determination. In Sheikh Abdul Aziz, the Delhi High Court recognised this urgency of determining the legal status of the petitioner. The Court excoriated the Central Government for its inaction in issuing a stateless certificate to the petitioner after nationality determination had failed, particularly after he had been confined in detention for an additional seven years, well beyond his initial sentence under Section 14 of the Foreigners Act. It understood that the issuance of a stateless certificate, under Rule 4 of the Passports Rules, 1980, and the subsequent granting of a Long-Term Visa ('LTV'), were essential for the petitioner's release from detention, and enabling his right to a dignified existence upon Indian soil. In National Human Rights Commission (Chakma case), the Supreme Court held that eligible stateless individuals, like the Chakmas in Arunachal Pradesh, have constitutional and statutory rights to be considered for Indian citizenship. Local administrative officers cannot refuse to act upon Chakma individuals' applications under Section 5 of the Citizenship Act to the Central Government. The Court also held that the state is obliged to protect Chakmas from eviction and threats of assault even while their citizenship applications are pending. These cases indicate Indian courts' proactive approach in reducing indeterminacy of status for individuals, assuring the terms of their membership in the civic community.
For stateless persons in India, international law necessitates that the burden is always upon the Indian state to fairly and expeditiously determine legal status for such persons. As we have argued at length above, the state's sovereign prerogative in citizenship matters is implicitly circumscribed by international law and human rights standards. Therefore, it is the state's obligation to establish whether they are recognised nationals of any other country. If the state fails in establishing that, they must be naturalised i.e. granted Indian nationality.
It is also important to note that statelessness should not operate as an impediment to an eventual path to Indian citizenship. The naturalisation of stateless persons within the ambit of India's existing citizenship laws has precedent: the Delhi High Court in Namgyal Dolkar ordered the MEA to issue an Indian passport to the petitioner who, despite holding a stateless identity certificate and being born to two Tibetan refugees, was eligible for Indian citizenship by birth under Section 3 (1)(a) of the Citizenship Act.
The significance of naturalising stateless persons residing in a State was recently followed by the ECtHR as well. In Sudita Keita, the applicant had arrived in Hungary in 2002. He was subsequently recognised as a stateless person after the local courts recognised that the burden on the applicant to prove lawful stay was contrary to Hungary's international law obligations relating to statelessness. Furthermore, in the case at hand, the ECtHR held that the stateless applicant had been left in a vulnerable position for 15 years without access to an effective and accessible naturalisation procedure. With reference to international law on statelessness, the Court highlighted that his situation had resulted in grave difficulties in access to healthcare and employment and violated his right to private and family life.
This report further argues that the stateless persons should be automatically naturalised (i.e. grant of nationality) since any formal requirements in this regard would place an undue burden upon them. Such a process would fail to recognise the underlying discrimination and lack of access to documents. This is visible in the Sri Lankan experience with grant of nationality as elaborated in Section I.C.1 of this chapter in the full report.
Hence, it is only through naturalisation that stateless persons can access the full extent of their rights. Their exceptionally vulnerable situation and international law obligations demands that the state shall automatically recognise them as citizens.
Posted in FeaturesTagged Article 21, Citizenship, Citizenship Act, Citizenship Act 1955, Delhi High Court, European Court of Human Rights, Foreigners Act 1946, Naturalisation, Passport Rules 1980, Passports Act 1967, Statelessness, Supreme Court


As summer gives way to autumn, Melbourne, Florida, residents are preparing to enjoy more comfortable temperatures and relief from summer's high humidity. However, the fall season can still bring some occasional warm days that call for the comfort of air conditioning. By changing your HVAC system's air filter and weatherizing your home's doors and windows, you can keep your air conditioner operating at peak efficiency this fall.
When a member of your Rockledge, Florida, household suffers from allergies, you want to reduce sources of allergy triggers in the home while still maintaining a comfortable space for all members of the family. Through regular HVAC maintenance and proper ventilation, you can get the perfect balance between home cooling and allergy trigger reduction.


This article analyzes the social standing of artists and architects during the Mamluk period. It shows that the majority had a rather modest status. Those few who achieved social recognition had to transform themselves intellectually and socially to move beyond the confines of small-time artisanal limitations. They had to become something else, in addition to being artists and architects, before they could be acknowledged. This, however, is not a specifically Mamluk attitude. All medieval cultures shared it. Our modern expectations are retroactively and anachronistically inflated by the unprecedented phenomenon of Renaissance Italy, when architects and artists became the model humanists.


text:
Home COVID-19 COVID-19 forces changes to Catholic Mass in T&T
COVID-19 forces changes to Catholic Mass in T&T
The Roman Catholic Church of the Archdiocese of Port of Spain says effective immediately, the new full precautionary measures must be followed at all Catholic Masses and Services (Image copyright Archdiocese of Port of Spain)
Changes to the way local Catholics are to conduct themselves and interact with each other and the clergy have been issued by the Archdiocese of Port of Spain, in its latest official statement on COVID-19.
The changes, which reduce or eliminate physical contact among parishioners and clergy, go into effect immediately.
The full text of the statement from the Archdiocese, follows…
With the confirmation that the government of T&T is escalating their policy on COVID-19, the Roman Catholic Church of the Archdiocese of Port of Spain is now updating their guidelines.
Effective immediately, until further notice, full precautionary measures must be followed at all Catholic Masses and Services:
Holy Communion will be distributed only in the hand (not on the tongue)
No distribution of the Precious Blood
At the exchange of the Sign of the Peace, no handshakes are to be given (make a small bow instead)
No holy water will be provided for use in public spaces
Ministers who distribute communion must sanitise hands before and after distribution
Sanitise or wash hands with soap before and after church and after leaving church restroom
Cough or sneeze into a flexed elbow or tissue, then throw tissue into a closed bin
Seek medical assistance and stay isolated if you exhibit any flu-like symptoms
The Archdiocese of Port of Spain continues to pray fervently for and join in solidarity with those impacted by or working to treat COVID-19.
You are urged to keep abreast of any further updates on the Archdiocese's position on this matter via facebook.com/catholictt
Archdiocese of Port of Spain
Catholic Masses and Services
no handshakes
Previous articleWHO says coronavirus is deadlier than the flu
Next articleFour in court charged with sexual offences against children

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: ScriptReference path set to jquery-1.4.1 conflicts with jquery-1.8.2 - based fancybox I am working on an ASP.NET web application and it has a page using a master page. The master page has the <asp:ContentPlaceHolder ID="HeadContent"> block on top of the call for the fancy box. The fancy box calls to to jquery-1.8.2.min.js and jquery.fancybox.js?v=2.1.3. Now the page (listing.aspx) using the master page has this code block within the HeadContent ContentPlaceHolder:
<asp:ScriptManagerProxy ID="ScriptManagerProxy1" runat="server">
  <Scripts>
    <asp:ScriptReference Path="~/Scripts/jquery-1.4.1.min.js" />
  </Scripts>
</asp:ScriptManagerProxy>

This is used for the continuous scrolling function for listing.aspx.
On other pages using the master page, the fancybox works fine, but when viewing listing.aspx, it does not recognize the functions of the fancybox anymore. I have tried searching for answers and have tried referencing jquery-1.8.2.min.js too. It does not work. When I tried moving the HeaderContent ContentPlaceHOlder within the master page below the calls to the fancybox, the continuous scrolling would not work. I'm so stumped. Really need your help. THanks.

redpajama_set_name: RedPajamaStackExchange


I'm Ella, a third-year student studying Spanish and German at the University of Exeter. Learning another language can open up many pathways for a student, allowing them to learn about and adapt to new cultures. Being able to communicate well with someone is, in my opinion, the most important skill you can have, however, often teaching in schools focuses on writing, reading and listening. In my sessions I will give the students a chance to speak in the language they're studying, so that they feel comfortable using it in real life situations. I found exams, personally, very stressful when I was at school, especially GCSEs, as in a short period of time I had to sit 25 exams, which I believed would make or break my life. Retrospectively, I now can see that although exams are important, what is more important is finding enjoyment within subjects. Within my tutor sessions I hope to be able to help my students have some fun with languages, as well as figure out which subjects are for them. At university I am part of many societies, including MUN and Maths Society. I am very glad I joined Maths Society when I started University, as I had worried that I would no longer be able to pursue my interest in Maths after school and joining MUN has really helped with my confidence as it requires public speaking. Hopefully, through my tutoring I will be able to improve the self-confidence of my students, as I think that self-belief is key in achieving the results you want.
I think in terms of language tuition it is important to know what specifics a student is struggling with and to cater the sessions to focus on resolving them. However, I will always make sure to incorporate elements of speaking into every session as I believe this is not covered enough within schools. I think it is important to set goals and therefore I will set work for outside of the lessons. This work will consist of an exercise, that won't take too much time as I understand that students have to balance all the work set from school too. In the next session we will then discuss this exercise going through any mistakes and figuring out why they were made. It's not something to stress about, only a way to measure improvement and to help the student figure out what they're finding difficult. I am also a fan of using games in order to promote learning and as I have taught in schools before I will incorporate some of the resources I have found effective. I will start each of my tutorials asking the student if there is any homework they have been set which they have questions about or any concepts they are struggling with, if so I will aim to resolve these questions and if not then I will provide activities which relate to the point in the syllabus that they're currently at. I hope I will be able to discover which learning methods are effective for each individual and be able to adapt my sessions to work with this.
A Free Video Meeting is a great next step. Just ask Ella below!
Hi Ella, I'm looking for a tutor. Are you available for a Free Video Meeting? I'd like to find out more about how you work. I'm looking forward to your reply!


AUSTIN, Texas, October 23, 2012 – Caringo, the leading provider of object storage software, today announced that Truliant Federal Credit Union is using CAStor® for the long-term storage of business-critical files including call center audio, video, check images, ATM receipts and email archives. CAStor provides Truliant with the ability to create a massively scalable pool of storage on the company's choice of commodity x86 server hardware with high performance and instant accessibility regardless of capacity or file count. Additionally, CAStor enabled Truliant to reduce its storage footprint and costs by 42 percent, allowing for the elimination of dedicated power distribution and network switches.
Truliant Federal Credit Union has 22 member financial centers in four states with 190,000 members and $1.5 billion in assets. Truliant has been leveraging the benefits of object storage since 2005 to efficiently store, manage and access the millions of rich media files, ranging in size from a few KBs to a few hundred MBs, used daily in the line of business.
With the need to replace its original, aging object storage devices, Truliant began evaluating current solutions. Truliant selected the Caringo Object Storage Platform powered by CAStor because of its ability to install on any standard server hardware, plug-and-play throughput with no downtime or impact to applications, and 'set it and forget it' ease of maintenance.
Caringo software gives enterprises everything they need to deliver private cloud storage or cloud storage as a service. The solution combines efficient object storage technology with elastic content protection, intelligent and automatic distribution and centralized management under a global namespace on your choice of commodity hardware. The result is a secure and compliant unified pool of storage that can expand or contract capacity and object count to meet any operational or business requirements – all at cloud economics and secure in your datacenter.


With timely and critical information, each themed issue of BioSupply Trends Quarterly (BSTQ) covers topics ranging from product breakthroughs, industry insights and innovations, news on the latest clinical trials, accessibility and service and safety concerns. Reach the audience that has the power to purchase your products.
Rates are exclusive of agency fees.
Dimensions to be provided upon request.
Please submit your ad as High-Resolution (minimum 300 dpi) PDF files in CMYK format, with all fonts embedded.
Computer-to-plate, web-offset on 70# gloss book stock (text) and 100# coated cover stock (cover). Perfect bound. CMYK process.
Colors must be converted to CMYK process. Total density should not exceed 300%. We recommend a color proof accompany your ad. We cannot assume responsibility for digital ads supplied without a color proof.
We cannot guarantee the legibility of reversed type under 10pt.


Your opinion matters. Leave A Review Or Edit This Listing for Least Of These, Inc..
Pantry Details, hours, photos, information: Least Of These, Inc.
Open Monday, Wednesday and Friday from 8 am until 1pm, and the first Wednesday of the month from 4-6:30pm for working families. Families may come for food and clothing assistance once a month. Hygiene and cleaning supplies are given out 5 times a year.
No appointment necessary for your first visit. Bring socials for all members of the household, current utility bill with Christian County address and a photo i.d.
We always need more information on our pantries. If you know of any details, volunteer information, website, hours or more description information about Least Of These, Inc. please add a comment (below the map on this page), with information. We will then display this for all visitors on this page.
Locate Least Of These, Inc.


The coordination chemistry of vanadium has drawn enormous research interest owing to promising insulin-mimetic, appetite-suppressing and anti- hypertensive effects displayed by vanadium complexes. The biological relevence of vanadium regarding the essensiality, distribution and toxicity in +4 and +5 oxidation states has been abundantly established. Of the numerous ligands known to form vanadium complexes, hydroxamaic acids ( naturally occurring or syntheic ) consititute an important family of organic bioligands with NHOH moiety as constituent of antibiotic and antifuingal agents , food additives, tumor inhibitors and growth factors because of their low toxicities. The biological and medicinal impotrance of hydroxamic acids owing to their pharmacological, pathological and toxicological properties is well-documented. The powerful biological activity of hydroxamic acids is related to their ability to form stable metal chelates. In view of the biological importance of vanadium and hydroxamic acids, new oxovanadium (IV) hydroxamate complexes derived from 4-nitrocinnamo and nicotinohydroxamic acids have been synthesized. The newly synthesized complexes have been structurally characterized by physicochemical ,spectral (IR, UV-Vis, ESR, Mass ) and electrochemical studies. As the development of effective antimicrobial drugs is a matter of great concern, the antimicrobial activities of newly synthesized complexes have been evaluated against some pathogenic bacteria as E.coli, S.aureus, S.typhi, S. paratyphi, S.epidermidis and K.pneumoniae and fungi such as C.albicans, A.niger and F.oxysporum by minimum inhibitory concentration method. The complexes exhibited promising antimicrobial activity relative to standard drug compounds. Cytotoxicity of complexes was studied on mamalian transformed cell line Hep2C, a derivative of human cervix carcinoma HeLa cells by means of MTT assay. The detailed results will be presented.


text:
You are here: Home > Test API > Publications
Henry Clay, Kentuckian
August 2, 2020 /in 1958 April Lida Mayo
https://filsonhistorical.org/wp-content/uploads/filson-logo.png 0 0 Jennie Cole https://filsonhistorical.org/wp-content/uploads/filson-logo.png Jennie Cole2020-08-02 15:01:582020-08-02 15:01:58Henry Clay, Kentuckian
A Twenty-Five-Minute Speech on Clark
August 2, 2020 /in 1941 July
https://filsonhistorical.org/wp-content/uploads/filson-logo.png 0 0 Jennie Cole https://filsonhistorical.org/wp-content/uploads/filson-logo.png Jennie Cole2020-08-02 15:01:162020-08-02 15:01:16A Twenty-Five-Minute Speech on Clark
George Rogers Clark, A Biographical Sketch
August 2, 2020 /in 1941 July Hambleton Tapp
https://filsonhistorical.org/wp-content/uploads/filson-logo.png 0 0 Jennie Cole https://filsonhistorical.org/wp-content/uploads/filson-logo.png Jennie Cole2020-08-02 15:00:372020-08-02 15:00:37George Rogers Clark, A Biographical Sketch
John Graham of Virginia and Kentucky, 1765-1835
August 2, 2020 /in 1939 April Willard Rouse Jillson
https://filsonhistorical.org/wp-content/uploads/filson-logo.png 0 0 Jennie Cole https://filsonhistorical.org/wp-content/uploads/filson-logo.png Jennie Cole2020-08-02 14:59:572020-08-02 14:59:57John Graham of Virginia and Kentucky, 1765-1835
Letters by Rafinesque to Dr. Short in The Filson Club Archives
August 2, 2020 /in 1938 October Samuel E. Perkins III
https://filsonhistorical.org/wp-content/uploads/filson-logo.png 0 0 Jennie Cole https://filsonhistorical.org/wp-content/uploads/filson-logo.png Jennie Cole2020-08-02 14:59:182020-08-02 14:59:18Letters by Rafinesque to Dr. Short in The Filson Club Archives
Review of Temple Bodley's Our First Great West
https://filsonhistorical.org/wp-content/uploads/filson-logo.png 0 0 Jennie Cole https://filsonhistorical.org/wp-content/uploads/filson-logo.png Jennie Cole2020-08-02 14:58:132020-08-02 14:58:13Review of Temple Bodley's Our First Great West
Reprint of The Filson Club Program of June 25, 1937, The Lincoln Pilgrimage
August 2, 2020 /in 1937 July R. C. Ballard Thruston, Thomas C. Fisher
https://filsonhistorical.org/wp-content/uploads/filson-logo.png 0 0 Jennie Cole https://filsonhistorical.org/wp-content/uploads/filson-logo.png Jennie Cole2020-08-02 14:57:262020-08-02 14:57:26Reprint of The Filson Club Program of June 25, 1937, The Lincoln Pilgrimage
The Lincolns in Jefferson County
August 2, 2020 /in 1937 July R. C. Ballard Thruston
https://filsonhistorical.org/wp-content/uploads/filson-logo.png 0 0 Jennie Cole https://filsonhistorical.org/wp-content/uploads/filson-logo.png Jennie Cole2020-08-02 14:56:342020-08-02 14:56:34The Lincolns in Jefferson County
The Tragedy of the Lewis Brothers
August 2, 2020 /in 1936 October Otto A. Rothert
https://filsonhistorical.org/wp-content/uploads/filson-logo.png 0 0 Jennie Cole https://filsonhistorical.org/wp-content/uploads/filson-logo.png Jennie Cole2020-08-02 14:55:472020-08-02 14:55:47The Tragedy of the Lewis Brothers
The Grave of General George Rogers Clark
August 2, 2020 /in 1936 October R. C. Ballard Thruston
https://filsonhistorical.org/wp-content/uploads/filson-logo.png 0 0 Jennie Cole https://filsonhistorical.org/wp-content/uploads/filson-logo.png Jennie Cole2020-08-02 14:54:572020-08-02 14:54:57The Grave of General George Rogers Clark


Dainty and darling, these diamond stud earrings are a smart everyday look. Created in 14K white gold, each earring houses a shimmering diamond solitaire in a traditional four-prong basket setting. Radiant with 1/10 ct. t.w. of diamonds and finished with a polished shine, these post earrings secure comfortably with screw backs.


Peter H. Byers, MD is a medical Geneticist and Professor of Pathology and Medicine at the University of Washington. He received an undergraduate degree in anthropology from Reed College in Portland, Oregon and medical training at Case Western University in Cleveland, Ohio. He trained in internal medicine at UCSF before completing three years as a research associate at the National Institute of Dental Research, National Institutes of Health where he worked with George R. Martin to examine collagen biosynthesis and structure. He moved to the University of Washington for a fellowship in Medical Genetics and at the same time worked with Paul Bornstein in Biochemistry to begin to identify the underlying bases of heritable connective tissue disorders including forms of Ehlers-Danlos syndrome and osteogenesis imperfecta. His contributions to understanding these disorders range from the identification of mosaicism as a factor in variation in clinical severity of heritable disorders as well as an explanation for birth of affected siblings to unaffected parents, to studies of natural history of several genetic conditions.


text:
\section{Introduction}
In this era constraints on Dark Matter models are being synthesized from multiple experiments.   There has been much recent work in collider physics, focusing on Dark Matter (DM) models, which include both UV complete theories and Effective Field Theory (EFT) scenarios.  The same models studied in collider physics imply detectable signatures from Dark Matter annihilation in space.  Due to gauge invariance or other theoretical considerations, many of these models, both EFTs and simplified models, predict couplings between Dark Matter and multiple species of Standard Model particles. Thus, Dark Matter may be produced in many correlated final state channels at colliders, and may have multiple final state annihilation channels in space, which would contribute to total detectable photon or positron flux for satellite experiments.

In this work we explore the indirect detection bounds from Fermi-LAT dwarf spheroidal galaxies \cite{Ackermann:2013yva} on models where Dark Matter annihilates into multiple final state channels.  These bounds are among the tightest constraints on DM models.  We study several EFT models with dimensions 6  and 7 effective operators. We choose operators which lead to unsuppressed DM annihilation rates in indirect detection processes, and  which  are being simultaneously studied in  DM production processes at LHC. The dimension 6 operators we study are those which couple Dark Matter to third generation fermions pairs.  The dimension 7 operators we consider are vector boson portals where there DM couples to multiple pairs of SM gauge bosons.

The use of effective operators allows a great degree of model independence for Dark Matter studies, while capturing some of the important kinematic features of Dark Matter processes \cite{Goodman:2010yf,Goodman:2010ku,Goodman:2010qn}.  For some models which are completed by loops, EFT based calculations have so far provided the best means for study at colliders. The limits of the effective operator paradigm are becoming more clear for collider analyses.   In particular, UV completions of models with low scale messenger portals are less probe-able by colliders, and models with low scale effective operator cut-offs may not be sensible at collider energies \cite{Papucci:2014iwa,Busoni:2013lha,Busoni:2014sya,Abdallah:2015ter}.  However, we expect that EFT analyses are reliable at the scale of indirect detection where the center of mass energy of the annihilation process is the same order as the dark matter particle mass itself.  We expect that the EFT treatment is valid down to much lower scales, perhaps for mediator sectors in range of 10's of GeV, as opposed to colliders where mediators of some hundred GeV to just under a TeV  may not be appropriate.

We will visualize the bounds we set in two slices of the total parameter space, the plane of fixed DM annihilation rate, and the plane of effect operator coefficients where the total annihilation rate varies.  For the regions of fixed annihilation rates, we will use the constraints to produce a 2-D visualization of the bounds on a triangle, a technique familiar from collider physics \cite{Anandakrishnan:2014pva}.  We also compare bounds set with the dwarf limits to those set by collider constraints, and discuss the validity limits of EFTs for both cases.

The format of this paper is as follows, in Section I we will discuss dwarf constraints on photon flux from dark matter annihilations.  In Section II we will analyze constraints on models with non-interfering final state annihilations and present triangular visualizations of parameter space.  In Section III we will analyze a popular set of vector boson portal models with interfering final state channels.  Section IV presents results along with collider constraints and discusses EFT validity.  Section V concludes.

\section{Indirect Detection from Dwarf Spheroidal Galaxies}
Dwarf spheroidal galaxies provide some of the tightest constraints on photon flux originating from dark matter annihilation as they are believed to contain a substantial dark matter component \cite{Mateo:1998wg,McConnachie:2012vd}.   This combined with their low astrophysical background makes them a good laboratory to search for dark matter.  As no significant excess in the photon spectrum has been observed from dwarf data, we use upper bounds on photon flux obtained from Fermi-LAT data \cite{Ackermann:2013yva} to place constraints on dark matter mass and couplings in the scenarios discussed in the introduction.

The photon flux $(\text{photons cm}^{-2} \text{ s}^{-1})$ at the earth expected from annihilation of dark matter in the area of interest is given by
\begin{equation}
\Phi_{\gamma}=\frac{1}{4\pi}
\sum_{\substack{f}}
\frac{\vev{\sigma v}_{f}}{2m_{\chi}^{2}}\int_{E_{\text{min}}}^{E_{\text{max}}}\left(\frac{dN_{\gamma}}{dE_{\gamma}}\right)_{f}dE_{\gamma} J.
\label{eq:gflux}
\end{equation}
Where the J-factor $(\text{GeV}^2\text{cm}^{-5})$ is the line of sight integral of the dark matter density $\rho$, integrated over a solid angle, $\Delta\Omega$
\begin{equation}
J=\int_{\Delta \Omega}\int_{l.o.s}\rho^{2}(\bold{r})dl d\Omega^{\prime}.
\end{equation}
The additional terms in Eq. \ref{eq:gflux} are dependent on the particle properties of the dark matter.  Here, $dN_f/dE$ is the differential photon energy spectrum per annihilation to final state f, $\vev{\sigma v}_f$ is the thermally averaged DM annihilation cross section and $m_\chi$ is the dark matter mass.

The Fermi-LAT collaboration has presented dark matter constraints from observation of 25 dwarf spheroidal galaxies \cite{Ackermann:2013yva}.  Of these 25 Milky Way satellites, 15 were used to place constraints on annihilation cross sections of dark matter particles with masses between 2GeV and 10TeV into various standard model channels.  These annihilation constraints were derived assuming that the dark matter annihilates primarily to a single standard model channel.  This is not realistic when considering most  UV completions of Dark Matter models, even ones that are quite simple.  Here we discuss obtaining bounds on dark matter mass and annihilation cross sections assuming annihilation into multiple channels.

The bin by bin integrated $\gamma$-ray energy flux upper limits at $95\%$ CL for each of the 25 dwarf galaxies was presented in \cite{Ackermann:2013yva}.  The J-factor for dwarfs is determined through dynamical modeling of their star densities and velocity dispersion profiles; we use J-factors presented in \cite{Ackermann:2013yva}.  For a conservative limit we perform a very simple combination of six dwarfs with the highest J-factors.   The limit in each bin is obtained from  the dwarf which gives the strongest $95\%$ CL upper limit on $\gamma$-ray flux scaled by the J-factor.  The combined limits are shown in Fig. \ref{fig:CombinedDLimits}.
\begin{figure}[tbh-]
\centering
\includegraphics[scale=0.7]{bestdwarflims.pdf}
\caption{Combined $95\%$ upper bounds on photon energy flux scaled by J-factor from 6 of largest J-factor dwarf spheroidal galaxies.}
\label{fig:CombinedDLimits}
\end{figure}

We note that the Fermi-LAT collaboration has obtained its own combined dwarf limits on photon flux from DM annihilation.  However, these limits assumed  DM annihilation into one and only one visible channel at a time.  Since our goal in this work is to analyze models that may have multiple final state annihilations we have forgone use of Fermi's combination, though in future analyses,  stronger bounds than ours may be obtained in each bin by "stacking" the total signal from all dwarves and subtracting a summed astrophysical background.

We calculate the expected $\vev{\sigma v}_{f}$ for each kinematically accessible annihilation channel, and obtain the differential gamma ray spectra for annihilation channels from the Mathematica code PPPC 4 DM ID \cite{Cirelli:2010xx,Ciafaloni:2010ti}. As an example, we show the spectrum for several relevant SM pair annihilation channels for a $100$GeV mass dark matter particle in Fig. \ref{fig:DMSpectrum100} below.  Here, the dimensionless parameter x is the gamma ray energy scaled by the dark matter mass.
\begin{figure}[tbh-]
\centering
\includegraphics[scale=0.7]{gammaspectrum_100.pdf}
\caption{Gamma ray spectrum from DM annihilation into various channels for a $100$GeV DM fermion.}
\label{fig:DMSpectrum100}
\end{figure}
Analysis of many models requires calculation of differential gamma ray spectra from particles produced in non-symmetric pairs, for example, in the analysis of models of section IV we have calculated the differential spectrum of the Z$\gamma$  final state.   Limits are obtained by binned comparison of total expected flux from all DM annihilations to our combined upper bounds.

\section{Models with Independent Annihilation Channels}
We will now discuss the method of constraining the parameter space of models with multiple independent annihilation channels.  We will first assume an effective Lagrangian which is the sum of several independent operators, each of which couples Dark Matter to \textbf{one and only one} pair of SM particles.  Therefore the Lagrangian has the form
\begin{equation}
\mathcal{L}_{\text{f}} = \Sigma_i\mathcal{O}_{i}= \Sigma_i \frac{\kappa}{\Lambda_i^n} \chi \chi X_i X_i.
\label{eq:LGeneral}
\end{equation}
Here the $\chi$ is the Dark Matter, and X is some Standard Model particle with particle index i. Any specific operator will be gauge and Lorentz invariant and will have coefficient $\kappa/\Lambda_i^n$, where the effective cut-off $\Lambda$ appears with the appropriate power to make the operator dimension 4.

The full parameter space of the EFT consists of the Dark Matter mass $m_{\chi}$ and the $i$ operator coefficients  $\kappa/\Lambda_i^n$.  Each point in this parameter space specifies a total DM annihilation rate, the specific ratios of the $i$ final state annihilation channels, and the resultant $\gamma$-ray flux. There are various slices of parameter space which can  be studied. The first one we will consider is slices of the parameter space on which the total DM annihilation rate is held constant.  Below we will show that along planes of parameter space with fixed annihilation rate, we will rule out masses and effective cut-offs below  certain scales.

\subsection{Fixed Annihilation Rate}

The total annihilation rate, $\vev{\sigma v}_{\text{tot}}$, is simply a linear sum of the thermally averaged annihilation cross sections $\vev{\sigma v}_{\mathcal{O}_i}$ to particle $X_i$ due to operator $\mathcal{O}_i$,
\begin{equation}
\vev{\sigma v}_{\text{tot}}=N\vev{\sigma v}_{\text{Th}}= \vev{{\sigma v}}_{\mathcal{O}_1}+\vev{{\sigma v}}_{\mathcal{O}_2}+ \cdots
\end{equation}

We will first fix the desired total annihilation rate.  This rate may be anything we like, for simplicity we will consider it some numerical factor times the thermal annihilation rate $N \vev{\sigma v}_{\text{Th}}$. This constraint drops us 1 dimension in parameter space; certain coefficient values $\kappa/\Lambda_i^n$ will satisfy the constraint for any specific DM mass. Having fixed the total annihilations rate, we may then determine the limits of the operator coefficients which saturate the Fermi-LAT photon-flux bounds for any given Dark Matter mass.

A natural choice for the total annihilation rate is the thermal rate.  However, in the spirit of model independence, we will show Fermi-bounds on models with various annihilation rates which will correspond to models with various non-thermal histories.  The complete theory will have to account for this history, as well as the presence (and absence) of specific operator coefficients.  We note that models where the total \emph{visible} annihilation rate is below the thermal rate can easily be saved from the prospect of over-closure by the addition of invisible DM annihilation channels which restore the total annihilation rate to thermal.  We discuss such models in the next subsection.

The rate constraint confines us to a hyper-surface in the full parameter space, however we may greatly simplify the form of this constraint by dividing out by the total rate $\vev{\sigma v}_{\text{tot}}$ .  We define the fractional annihilation rate as in \cite{Calore:2014nla} to be  $R_i=\vev{\sigma v}_{i}/\vev{\sigma v}_{\text{tot}}$, giving a constraint which is linear in the partial rates $R_i$.
\begin{equation}
R_{1}+R_{2}+R_{3}+ \cdots =1.
\label{eq:constraint1}
\end{equation}

\noindent The natural visualization for this parameter space of models with 3,4,5 annihilation channels etc. are a  triangle, tetrahedron, 4-simplex, etc.

As an example and for clarity of discussion we will analyze a simple model where DM may annihilate to multiple independent channels.  We choose an EFT model where dark matter couples to the third generation of fermions via  dimension 6 operators;
\begin{equation}
\mathcal{L}_{\text{f}} =\frac{\kappa_t}{\Lambda_t^2}\chi \Gamma \overline{\chi} t \Gamma \overline{t}+\frac{\kappa_b}{\Lambda_b^2}\chi \Gamma \overline{\chi} b \Gamma \overline{b} + \frac{\kappa_{\tau}}{\Lambda_{\tau}^2}\chi  \Gamma \overline{\chi} \tau \Gamma \overline{\tau}+  \frac{\kappa_{\nu}}{\Lambda_{\nu}^2}\chi \Gamma \overline{\chi} \nu  \Gamma \overline{\nu}.
\label{eq:LFermions}
\end{equation}

Here $\Gamma$ specifies the whether the fermionic currents are scalar, pseudo-scalar, vector etc. Under the conventions in \cite{Goodman:2010ku} they correspond to operators D1, D2, etc.  Annihilation rates will depend greatly on the Lorentz structure of the operator with operators leading to velocity and/or helicity suppression of the rate \cite{Profumo:2013hqa}.  The strongest constraints from photon-flux measurements will apply to models with operators corresponding to unsuppressed DM annihilation rates.  We have here included an annihilation into an invisible channel, specifically neutrinos.  In setting constraints for fractional annihilation rates, we may consider this channel a stand-in for annihilation into any kinematically accessible invisible channel.  The option of an invisible channel allows a total visible annihilation rate below the thermal rate while still avoiding over-closure of the universe.  Recent work, for example \cite{Falkowski:2009yz}, has shown that these annihilations may be significant in some scenarios.  The relevant annihilation diagram are shown in Fig. \ref{fig:DMToFermions}.
\vspace{0.5cm}
\begin{figure}[h]
\begin{center}
	    \begin{fmffile}{sigmav5}
	        \begin{fmfgraph*}(25,25)
                   \fmfleft{i1,i2}
                   \fmfright{o1,o2}
                   \fmfblob{.5cm}{v1}
                   \fmflabel{$\chi$}{i1}
                   \fmf{fermion}{i1,v1}
                   \fmflabel{$\bar{f}$}{o2}
                   \fmf{fermion}{v1,o2}
                   \fmflabel{$f$}{o1}
                   \fmf{fermion}{o1,v1}
                   \fmflabel{$\bar\chi$}{i2}
                   \fmf{fermion}{v1,i2}
	        \end{fmfgraph*}
	    \end{fmffile}
\end{center}
\caption{Dark matter annihilation into pairs of fermions.}
\label{fig:DMToFermions}
\end{figure}

Let us first assume that the dark matter is light and that annihilation into top pairs in kinematically forbidden.  Here, the total annihilation rate is the sum of the thermally averaged annihilation cross section into b's, $\tau$'s, and the invisible channel,
\begin{equation}
\vev{\sigma v}_{\text{tot}}=\vev{\sigma v}_{\text{b}}+\vev{\sigma v}_{\tau}+\vev{\sigma v}_{\nu}.
\end{equation}
The crucial point here is that each operator in Eq. \ref{eq:LFermions} corresponds to only one channel, thus the constraint above has the form $\propto a \left(\kappa_b/\Lambda_b^2 \right)^2+b\left(\kappa_{\tau}/\Lambda_{\tau}^2 \right)^2+c\left(\kappa_{\nu}/\Lambda_{\nu}^2 \right)^2$ (where a, b, and c depend on dark matter mass and final state particle mass) with no terms of the form $\kappa_i \kappa_j$ for $i\ne j$.  Therefore, a triangle seems the natural choice for visualization of constraints where the sides of the triangle correspond to the $R_b,R_{\tau},R_{\nu}$ axis.

We see from Eq. \ref{eq:gflux} that once the annihilation rates $\vev{\sigma v}_{\text{f}}$ are fixed, upper bound on $\gamma$-ray flux corresponds to a lower bound on dark matter mass.  To determine this mass bound we set the total annihilation cross section to a multiple of the thermal relic, $\vev{\sigma v}_{\text{tot}}=N\vev{\sigma v}_{\text{thm}}$, then for a given point in $(R_b,R_{\tau},R_{\nu})$ space find the lowest mass which gives the maximum allowed $\gamma$-ray flux determined by Fig. \ref{fig:CombinedDLimits}.  The mass limits depend on the total annihilation rate which we have fixed; as we increase the total annihilation rate, the mass bounds become stronger.

The results are given in the Fig. \ref{fig:trel} for two total annihilation rates, the thermal rate and 10 times thermal rate.  The blank spaces in the triangle correspond to a lower bound of $0$ GeV or no lower bound.  We see that the strongest bounds come from annihilation into b's while the weakest bounds come from annihilation into invisible particles as expected.

\begin{figure}[H]
\centering
\includegraphics[scale=0.4]{MassLimits_Trel_3Gen.png}
\includegraphics[scale=0.4]{MassLimits_10Trel_3Gen.png}
\caption{Lower bound on dark matter mass in GeV for annihilations into b quarks, $\tau$'s, and invisible particles for $\vev{\sigma v}_{\text{tot}} = \vev{\sigma v}_{\text{Th}}$ on left and $\vev{\sigma v}_{\text{tot}} =10\vev{\sigma v}_{\text{Th}}$ on right. }
\label{fig:trel}
\end{figure}

Here the points that form the triangle each correspond to a unique ratio of the partial annihilation rates $R_i$.  At each vertex of the triangle, a single  $R_i= 1$, that is, one channel saturates that total annihilation rate.  Along the edges of the triangle only two annihilation channels contribute to the total annihilation rate, with the third partial rate set to 0.  The form of Eqn. \ref{eq:LFermions} was satisfactory to derive a lower DM mass bound for a fixed total annihilation rate.  We will now pick a specific Lorentz structure for our operators and calculate bounds on the effective operator coefficients.  As an example, we will choose to constrain the vector current operators D5, whose annihilation rate is neither velocity nor chirality suppressed.
\begin{equation}
\mathcal{L}_{\text{f}} =\frac{\kappa_f}{\Lambda_f^2}\chi \gamma^{\mu} \overline{\chi} f \gamma_{\mu} \overline{f}
\end{equation}

Each mass that satisfies the rate constraint will correspond to specific values of the effective operator coefficient.  With total annihilation rate fixed, points of lower mass will require lower effective cut-offs to satisfy the bound.  We also plot on the triangle the lowest effective cut-off (largest operator coefficient) that satisfies the bound of total flux.  Below we show the lower limits operator coefficients $ \Lambda_i^{*} = \sqrt{\kappa_i}/\Lambda_i$ which saturate the bounds on photon flux.

\begin{figure}[H]
\centering
\includegraphics[scale=0.4]{LambdaLimitsB.png}
\includegraphics[scale=0.4]{LambdaLimitsTau.png}
\caption{Lower bound on operator coefficients $\Lambda_b^{*}$ and $\Lambda_{\tau}^{*}$ for  $\vev{\sigma v}_{\text{tot}} = \vev{\sigma v}_{\text{Th}}$ on left and $\vev{\sigma v}_{\text{tot}} =10\vev{\sigma v}_{\text{Th}}$ on right.}
\label{fig:LambdaLimitsTrel}
\end{figure}

For the thermal total annihilation rate, we see that DM annihilating into mostly b's or $\tau 's$, must be above 5-15 GeV in mass while the effective operator  cut-off scales may not be smaller than a few hundred GeV.  We point out that in our exclusion region, the effective operator paradigm appears to be justified as the effective cut-offs are well above the center of mass energy for the annihilation process.  We show similar triangles for a total annihilation  rate of 10 times the thermal rate in the appendix.

\subsection{Constraints for 4 Independent Channels}

Next we consider the case of allowing more than three annihilation channels. We now allow the dark matter mass to be larger than the top mass opening up an additional annihilation channel.  One can visualize the mass constraints on a tetrahedron where the ``vertical" axis is $R_t$, see Fig. \ref{fig:blanktetrahedron}.  Each slice of the tetrahedron would correspond to a flat triangle with constraint equations given by
\begin{eqnarray}
\vev{\sigma v}_{\text{tot}}-\vev{\sigma v}_{\text{t}}&=&\vev{\sigma v}_{\text{b}}+\vev{\sigma v}_{\tau}+\vev{\sigma v}_{\nu} \nonumber \\
\left(1-R_{t}\right)&=&R_{b}+R_{\tau}+R_{\nu}.
\label{eq:constraint2}
\end{eqnarray}
\noindent

\begin{figure}[h]
\centering
\includegraphics[trim={0 10cm 0 5cm},clip,scale=0.4]{BlankTetrahedronLabeled.pdf}
\caption{Axis labeling for tetrahedron presentation of DM mass constraints when a fourth annihilation channel is allowed.  The base corresponds to the top left of Fig. \ref{fig:30And70TopTriangle}.}
\label{fig:blanktetrahedron}
\end{figure}

\noindent In particular, the base of the tetrahedron would correspond to $R_t=0$ and the constraints shown in the top left of Fig. \ref{fig:30And70TopTriangle}.  Below we show lower bounds on dark matter mass for triangle slices where the fractional annihilation rate to tops is $R_t=0, .3 \text{ and, }.7$.  The blank areas in the triangles of Fig. \ref{fig:30And70TopTriangle} correspond to the region of parameter space where the kinematic bound is stronger then that obtained from indirect searches.
\begin{figure}[H]
\centering
\includegraphics[trim={2cm 7cm 2cm 5cm},clip,scale=0.5]{TopSlice_0ToTop.pdf}
\includegraphics[trim={2cm 7cm 2cm 5cm},clip,scale=0.5]{TopSlice_30ToTop.pdf}
\includegraphics[trim={2cm 7cm 2cm 5cm},clip,scale=0.5]{TopSlice_70ToTop.pdf}
\caption{The contours correspond to lower bounds (in GeV) on DM mass from annihilations into pairs of fermions $(tt,bb,\tau\tau,\nu\nu)$.  The total annihilation rate is set to 33 times the thermal relic for all three plots.  The left image corresponds to $R_t=0$,  the right to $R_t=.3$ and the bottom to $R_t=.7$. }
\label{fig:30And70TopTriangle}
\end{figure}

For models with each operator corresponding to independent annihilation channels, this procedure may be iterated for any number of final state annihilation channels. In the next section we will discuss bounds on the parameter space of models where there is not a one to one correspondence between operators and annihilation channels.  We first discuss the bounds on parameter space visualized on surfaces of fixed total annihilation rate.  We will then discuss the bounds on surfaces of fixed operator coefficients.

\section{Constraints in Models with Interfering Channels}

Many examples of models exist in which a single parameter or operator coefficient in the Lagrangian demands Dark Matter annihilation to multiple final state channels.  Further there may be multiple operators or parameters in the Lagrangian which contribute to annihilations into the same channel.  We will now analyze a model in which both of the previous statements are true.  We consider a popular set of effective operator models for collider and indirect studies (see, for example \cite{Chen:2013gya,Rajaraman:2012fu,Weiner:2012gm,Crivellin:2015wva,Nelson:2013pqa}), the vector boson portal models .  We will consider a set of dimension 7 operators where a pseudo-scalar Dark Matter current couples to the SM field strength tensors.
\begin{equation}
\mathcal{L}=\frac{\kappa_{1}}{\Lambda^{3}}\bar{\chi}\gamma^{5}\chi B_{\mu\nu}B^{\mu\nu}
+\frac{\kappa_{2}}{\Lambda^{3}}\bar{\chi}\gamma^{5}\chi W^{i}_{\mu\nu}W_{i}^{\mu\nu}
+\frac{\kappa_{3}}{\Lambda^{3}}\bar{\chi}\gamma^{5}\chi G^{a}_{\mu\nu}G_{a}^{\mu\nu}
\label{eq:gaugelagr}
\end{equation}
These operators are not velocity suppressed and  they may naturally arise if the dark matter  couple to the SM through loops of heavy messengers which carry SM charge \cite{Weiner:2012gm}.  Unlike the previous model discussed, gauge invariance ensures that two of the above operators contribute to multiple annihilation channels.  These two operators also have interfering contributions to the same annihilation channels.  The coefficients $\kappa_{1}/\Lambda^3$ and $\kappa_{2}/\Lambda^3$ control the coupling of dark matter to four pairs of electroweak gauge boson final states: $ZZ$, $Z\gamma$, $\gamma \gamma$, and $W^{+}W^{-}$, see the relevant diagrams in Fig. \ref{fig:DMToGauge}.
\vspace{0.5cm}
\begin{figure}[h]
\begin{center}
	    \begin{fmffile}{sigmav}
	        \begin{fmfgraph*}(25,25)
                   \fmfleft{i1,i2}
                   \fmfright{o1,o2}
                   \fmfblob{.5cm}{v1}
                   \fmflabel{$\chi$}{i1}
                   \fmf{fermion}{i1,v1}
                   \fmflabel{$\gamma$}{o2}
                   \fmf{photon}{v1,o2}
                   \fmflabel{$\gamma$}{o1}
                   \fmf{photon}{o1,v1}
                   \fmflabel{$\bar\chi$}{i2}
                   \fmf{fermion}{v1,i2}
	        \end{fmfgraph*}
	    \end{fmffile}  \hspace{0.5cm}
	    \begin{fmffile}{sigmav1}
	        \begin{fmfgraph*}(25,25)
                   \fmfleft{i1,i2}
                   \fmfright{o1,o2}
                   \fmfblob{.5cm}{v1}
                   \fmflabel{$\chi$}{i1}
                   \fmf{fermion}{i1,v1}
                   \fmflabel{$\gamma$}{o2}
                   \fmf{photon}{v1,o2}
                   \fmflabel{Z}{o1}
                   \fmf{photon}{o1,v1}
                   \fmflabel{$\bar\chi$}{i2}
                   \fmf{fermion}{v1,i2}
	        \end{fmfgraph*}
	    \end{fmffile}
\hspace{0.5cm}
	    \begin{fmffile}{sigmav2}
	        \begin{fmfgraph*}(25,25)
                   \fmfleft{i1,i2}
                   \fmfright{o1,o2}
                   \fmfblob{.5cm}{v1}
                   \fmflabel{$\chi$}{i1}
                   \fmf{fermion}{i1,v1}
                   \fmflabel{Z}{o2}
                   \fmf{photon}{v1,o2}
                   \fmflabel{Z}{o1}
                   \fmf{photon}{o1,v1}
                   \fmflabel{$\bar\chi$}{i2}
                   \fmf{fermion}{v1,i2}
	        \end{fmfgraph*}
	    \end{fmffile}
	    \hspace{0.5cm}
	    \begin{fmffile}{sigmav3}
	        \begin{fmfgraph*}(25,25)
                   \fmfleft{i1,i2}
                   \fmfright{o1,o2}
                   \fmfblob{.5cm}{v1}
                   \fmflabel{$\chi$}{i1}
                   \fmf{fermion}{i1,v1}
                   \fmflabel{$W^+$}{o2}
                   \fmf{photon}{v1,o2}
                   \fmflabel{$W^-$}{o1}
                   \fmf{photon}{o1,v1}
                   \fmflabel{$\bar\chi$}{i2}
                   \fmf{fermion}{v1,i2}
	        \end{fmfgraph*}
	    \end{fmffile}
	    \hspace{0.5cm}
	    \begin{fmffile}{sigmav4}
	        \begin{fmfgraph*}(25,25)
                   \fmfleft{i1,i2}
                   \fmfright{o1,o2}
                   \fmfblob{.5cm}{v1}
                   \fmflabel{$\chi$}{i1}
                   \fmf{fermion}{i1,v1}
                   \fmflabel{g}{o2}
                   \fmf{gluon}{v1,o2}
                   \fmflabel{g}{o1}
                   \fmf{gluon}{o1,v1}
                   \fmflabel{$\bar\chi$}{i2}
                   \fmf{fermion}{v1,i2}
	        \end{fmfgraph*}
	    \end{fmffile}
\end{center}
\caption{Dark matter annihilation into gauge bosons.}
\label{fig:DMToGauge}
\end{figure}
The thermally averaged annihilation cross section to di-boson final state is given in Eq. \ref{eq:xsecs} below.
\begin{equation}
\begin{split}
\langle\sigma v_{rel}\rangle_{WW}&=\frac{\kappa_{2}^{2}}{4 \pi \Lambda^{6}}\sqrt{1-\frac{m_{W}^{2}}{m_{\chi}^{2}}}(16m_{\chi}^{4}-16m_{W}^{2}m_{\chi}^{2}+6m_{W}^{4})\\
\langle\sigma v_{rel}\rangle_{ZZ}&=\frac{(\kappa_{1}s_{w}^{2}+\kappa_{2}c_{w}^{2})^{2}}{8 \pi \Lambda^{6}}\sqrt{1-\frac{m_{Z}^{2}}{m_{\chi}^{2}}}(16m_{\chi}^{4}-16m_{Z}^{2}m_{\chi}^{2}+6m_{Z}^{4})\\
\langle\sigma v_{rel}\rangle_{Z\gamma}&=\frac{s_{w}^{2}c_{w}^{2}(\kappa_{2}-\kappa_{1})^{2}}{ 16\pi m_{\chi}^{2}\Lambda^{6}}(4m_{\chi}^{2}-m_{Z}^{2})^{3}\\
\langle\sigma v_{rel}\rangle_{\gamma\gamma}&=\frac{4(\kappa_{1}c_{w}^{2}+\kappa_{2}s_{w}^{2})^{2}}{2\pi\Lambda^{6}}m_{\chi}^{4}\\
\langle\sigma v_{rel}\rangle_{gg}&=\frac{16\kappa_{3}^{2}}{\pi\Lambda^{6}}m_{\chi}^{4}\\
\end{split}
\label{eq:xsecs}
\end{equation}

We now explore the bounds on the parameter space of this model, the space consisting of the dark matter mass $m_{\chi}$ and the three operator coefficients. For any given point in parameter space, the total photon flux due to annihilations results from the sum the annihilations into each of the five di-boson channels.  We see that the operator with coefficient $\kappa_3/\Lambda^3$ controls the annihilation to gluons and only gluons, and therefore factorizes in the total annihilation rate as per the discussion before.  However the total rate to other di-boson pairs depends on two operator coefficients.  In this case, the total annihilation rate has the form $(k_i=\kappa_i/\Lambda^3)$

\begin{equation}
(ak_1^2 +bk_2^2)^2+ck_3^2=\vev{\sigma v}_{tot}
\end{equation}

We may again study the system by fixing the total annihilation rate as in the previous section.  Unlike the case in the previous section, the rate constraint is not linear; however for each specific dark matter mass, the couplings which saturate the annihilation rate are still constrained to lie on a 2-dimensional surface. This surface  is a triangular section of an ellipsoid.  The radii of the ellipsoid vary as the total annihilation rate is changed.  We can again present dwarf constrains on the space of operator coefficients using a simple visualization, now on an ellipsoidal surface rather than a triangle. In Fig 9, we show the ellipsoidal surfaces which satisfy the constraint that the total DM annihilation rate is 10 times the thermal rate.

We consider four different dark matter masses for which this constraint is satisfied, $m_{\chi}=10,75,150 \text{ and, } 200$ GeV.  For each DM mass, certain combinations of the operator coefficients will satisfy the rate constraint.   As the DM mass is decreased, lower cut-off scales $\Lambda$ will obey the annihilation rate constraint, just as in the previous section.  For each point on the ellipsoid, we may check if the combined photon flux from di-boson annihilations violates or satisfies the dwarf constraints.  Just as before, we find that parameter regions of low mass (hence low effective cut-off scale) are ruled out.  In our scan of Dark Matter masses, we found that there is no allowed parameter space for DM masses much below 10 GeV which also satisfies the constraint $\vev{\sigma v}_{\text{tot}} = 10 \vev{\sigma v}_{Th}$.

\begin{figure}[H]
\centering
\includegraphics[scale=0.35]{yesno1010x.pdf}
\includegraphics[scale=0.40]{yesno7510x.pdf}
\includegraphics[scale=0.40]{yesno15010x.pdf}
\includegraphics[scale=0.35]{yesno20010x.pdf}
\caption{Limits on effective operator coefficients for 10 times the thermal annihilation rate given by Fermi dwarf bounds. The axes show the value of $k_i/ \Lambda^3$.  Bounds on operators are shown for four dark matter masses, $m_{\chi}=10,75,150 \text{ and, } 200$ GeV (top left, top right, bottom left and bottom right respectively).  Red points indicate that the operator coefficient is ruled out, blue points are unconstrained.  }
\label{fig:yesno}
\end{figure}

In the  Fig. \ref{fig:yesno} plots, the red points are ruled out by the Fermi-LAT data, while the blue points are unconstrained.  As we scan through parameter space increasing the Dark Matter mass different annihilation channels open up which contribute to the total photon flux.  The first plot gives constraints for a 10 GeV dark matter particle.  At such low masses $m_{\chi} < m_Z/2$, only annihilations to gluons and photons are kinematically accessible. The photon energy $E_{\gamma}$ is equal to the DM mass $m_{\chi}$ and the operator coefficient values that yield a high di-photon annihilation rate and are ruled out.  For DM masses above half of the Z mass, the  $Z \gamma$ annihilation channel open up and starts to increase in magnitude but we see the the characteristic photon energy of the $Z\gamma$ annihilation is less than that of the photons in the $\gamma \gamma$ annihilation channel, here $E_{\gamma}= m_{\chi}\sqrt{1-4m_{\chi}^2/m_Z^2}$.  Therefore the electroweak operator coefficients in this mass region are not too strongly constrained.  For higher dark matter masses, $m_{\chi} > m_{W/Z}$, the WW and ZZ annihilation channels also open up as we see in the bottom two plots where $\m_{\chi}$ is 150 and 200 GeV respectively.

We have so far proceeded by fixing the total annihilation rate.  We will now present the same constraints in a semi-orthogonal plane of parameter space where the total DM annihilation rate is allowed to vary.  In Figs. \ref{fig:k1k2massbounds} and \ref{fig:k1k2xsecbounds}, we show the Fermi-LAT bounds in plane of operator coefficients.  For simplicity in the figures we made the redefinition,  $k_i\equiv \kappa_{i}/\Lambda^{3}$.   We now allow the coefficients $k_{1}\equiv \kappa_{1}/\Lambda^{3}$ and $k_{2}\equiv \kappa_{i}/\Lambda^{3}$ to vary freely.  Here, $k_{3}$ is determined at each point by fixing the fractional annihilation rate to gluons $R_{gg}$.  We may then scan through increasing masses and determine which points in parameter space are ruled out. Note, we are not holding $k_{3}\equiv \kappa_{3}/\Lambda^{3}$ constant; as $m_{\chi}$ is varied this parameter must be varied in order for $R_{gg}$ to remain at a fixed value.  Each point in the plot corresponds to a unique value of the three operator coefficients so each specifies a particular total annihilation rate for DM.  As in the previous section, the parameter space exclusions are derived from the upper bounds on $\gamma$ ray flux from dwarfs.  For fixed operator coefficient values, the annihilation cross section goes as $m_{\chi}^4$, so the total photon flux for each point increases goes like $m_{\chi}^2$.  We may thus put an upper bound on DM masses for fixed values of operator coefficient.

We plot upper limits on Dark Matter masses in Fig. \ref{fig:k1k2massbounds}.  The top left, top right, and bottom plots in Figs. \ref{fig:k1k2massbounds} and \ref{fig:k1k2xsecbounds} correspond to $0\%$, $30\%$, and $70\%$ annihilation rate into di-gluons respectively.  The solid, dashed, and dotted lines represent the regions where $R_{Z\gamma}$, $R_{ZZ}$, and $R_{\gamma \gamma}$ go to zero respectively.  The vanishing of each of these channels coincide with a specific choice of the couplings in Eq. \ref{eq:gaugelagr} given by
\begin{eqnarray}
\kappa_1 = \kappa_2 \Rightarrow R_{Z\gamma} =0 \nonumber \\
\kappa_2 = -\kappa_1\frac{s_w^2}{c_w^2} \Rightarrow R_{ZZ} =0 \nonumber \\
\kappa_2 = -\kappa_1\frac{c_w^2}{s_w^2} \Rightarrow R_{\gamma \gamma} = 0
\end{eqnarray}
 As one would expect, the $\gamma\gamma$ channel tends to be the most powerful in constraining annihilation rates when allowed.
As we can see in Fig. \ref{fig:k1k2massbounds}, much of the parameter space will be ruled out by the $\gamma\gamma$ channel since the limits are stringent enough that other channels do not turn on before photon lines rule them out.
\begin{figure}[H]
\centering
 \includegraphics[width=.49\columnwidth]{k1k2_0gg.png}
 \includegraphics[width=.49\columnwidth]{k1k2_30gg.png}
 \includegraphics[width=.49\columnwidth]{k1k2_70gg.png}
\caption{These contours correspond to upper bounds on $m_{\chi}$ (in GeV) from annihilation into all final states allowed from the operators in Eq. \ref{eq:gaugelagr} with $k_{i}\equiv \kappa_{i}/\Lambda^{3}$.
The amount to the $gg$ final state is fixed in each of these plots as a percentage of the total rate, 0\% (upper left), 30\% (upper right), 70\% (lower).
The solid, dashed, and dotted lines correspond to a combination of $\kappa_1$ and $\kappa_2$ which turn off the final states $Z\gamma$, $ZZ$, and $\gamma \gamma$ respectively.
}
\label{fig:k1k2massbounds}
\end{figure}

\begin{figure}[H]
\centering
\includegraphics[width=.49\columnwidth]{k1k2sigma_0gg.png}
\includegraphics[width=.49\columnwidth]{k1k2sigma_30gg.png}
\includegraphics[width=.49\columnwidth]{k1k2sigma_70gg.png}
\caption{These contours correspond to upper bounds on $\langle \sigma v \rangle_{\text{tot}}$ in units of the thermal relic, $\langle \sigma v \rangle_{\text{Th}}$, from annihilation into all final states allowed from the operators in Eq. \ref{eq:gaugelagr} with $k_{i}\equiv \kappa_{i}/\Lambda^{3}$.
The amount to the $gg$ final state is fixed in each of these plots as a percentage of the total rate, 0\% (upper left), 30\% (upper right), 70\% (lower).
The solid, dashed, and dotted lines correspond to a combination of $k_1$ and $k_2$ which turn off the final states $Z\gamma$, $ZZ$, and $\gamma \gamma$ respectively.
}
\label{fig:k1k2xsecbounds}
\end{figure}

Notice that when the operator coefficients are very small, flux bounds allow for much larger DM masses.  If we look at the region where the $\gamma\gamma$ final state is off in parameter space, we still expect annihilations into the final states with $WW/ZZ$ and $Z\gamma$  which allow for strong constraints to be placed. In Fig. \ref{fig:k1k2xsecbounds} we plot the upper bound on the total DM annihilation rate in the plane of effective operator coefficients.

\subsection{Limits of the EFT and Collider Constraints}

We will now say a few words about the maximum range of validity of the EFT for DM annihilation processes. The most natural completion of a model with a vector boson portal involves loops of heavy messenger particles which are charged under the SM gauge groups such as those found such as in \cite{Weiner:2012gm}.  For the EFT to be valid, the momentum transfer of the process should be less than twice the messenger mass. Since the square root of the c.o.m energy of the process is twice the Dark Matter mass, we get $m_{\chi} < M_{\text{mess}}$.  We assume that the loops roughly scale like $f \alpha_i g_{\chi}^2 / M_{\text{mess}}^3$  where f is some numerical factor, $M_{\text{mess}}$ a messenger mass, and $g_\chi$ the coupling of the messenger to the dark matter.  Therefore, our effective operator coefficient $k_i /\Lambda^{3}$ corresponds to $f \alpha_i g_{\chi}^2/ M_{\text{mess}}^3$.  We can then estimate the messenger masses in terms of our effective cut-off for the maximum perturbative value of the hidden sector coupling $g_{\chi}$.  We find $M_{mess}\rightarrow \Lambda\left(f \alpha_i 16\pi^2 \right)^{-1/3}.$  For EFT validity $m_{\chi}< \Lambda\left(f \alpha_i 16\pi^2 \right)^{-1/3}$.  For order 1 values of f,  the validity limits for the U(1) operator for example are roughly  $m_{\chi} < \Lambda$; in regions of parameter space where the DM mass larger than the effective cut-off, derived bounds are not reliable.

We now wish to synthesize our parameter space constraints with EFT-validity limits and with constraints from colliders.  We will first reinterpret our results given in Fig. \ref{fig:k1k2xsecbounds} in the plane of dark matter mass vs operator suppression scale for several specific combinations of operator coefficients $\kappa_1$  $\kappa_2$ and $\kappa_3$.  First, we will assume $\kappa_3=0$, that is there are no annihilation of DM into gluons.  We now have a three dimensional parameter space  of $m_{\chi},k_1/\Lambda^{3}, k_2/\Lambda^{3} $ .  Our exclusions in this parameter space from Fermi-LAT data are shown in Fig. \ref{fig:scale} for certain simple ratios of couplings $\kappa_1$ and $\kappa_2$.  The excluded regions of parameter space lay under the colored lines.  The dot and dashed lines in Fig. \ref{fig:scale} correspond to curves of constant total annihilation rate.

\begin{figure}[h]
\centerline{\includegraphics[width=.8\columnwidth]{scaleconstraints.pdf}}
\caption{Constraints from Fig. \ref{fig:k1k2xsecbounds} reconfigured for the effective cut-off vs dark matter mass plane.  The regions below the solid lines are excluded.  The dashed lines correspond to curves of constant $\vev{\sigma v}_{\text{tot}}$}
\label{fig:scale}
\end{figure}

We recall that for the operators in Eq. \ref{eq:gaugelagr} $\vev{\sigma v} \propto m_{\chi}^4/\Lambda^6$ and thus upper bounds on annihilation cross section or dark matter mass correspond to lower bounds on the suppression scale $\Lambda$. Below the solid purple line is the region of breakdown of EFT validity for the indirect annihilation process for the U(1) operator.  Below the solid brown line is the region of breakdown of EFT validity for the indirect annihilation process for the SU(2) operator.

Vector boson portal models like those in this section have been widely studied in the context of collider production.  At LHC, operators of this type will lead to the production of dark matter particle pairs in association with a single vector boson, $pp \rightarrow \chi \overline{\chi}+V$ where V is a gluon, photon, W or Z.  No mono-boson signal is currently in excess and therefore collider constraints place lower bounds on the effective operator cut-offs $\Lambda_i$ for each given dark matter mass.   Studies on mono-boson collider signatures for the pseudo-scalar DM current may be found, for example, in references \cite{Lopez:2014qja} and \cite{Nelson:2013pqa}.  In the plot below we consider the effects of the SU(2) operator only for a simple comparison of collider and indirect detection bounds.  We show our exclusion contour from combined dwarf data, along with the ATLAS constrain from the mono-W channel (given by \cite{Lopez:2014qja}) for the pseudo-scalar current operator. We have also plotted contours of constant total DM annihilation rate.

\begin{figure}[h]
\centering
\includegraphics[width=.8\columnwidth]{k2scaleconstraints.pdf}
\caption{Constraints from Fig. \ref{fig:k1k2xsecbounds} reconfigured for the effective cut-off vs Dark Matter mass plane}
\label{fig:scale}
\end{figure}

We see that following lines of constant annihilation rate we arrive at a minimum dark matter mass bound.  Following lines of constant operator coefficient we arrive at a maximum DM mass bound. The Fermi-LAT dwarf bounds are more constraining than collider analyses for DM masses above a few hundred GeV. It may be true that these bounds are more strict than collider bounds for regions of small $\Lambda$ as well. The validity of the EFT prescription for the collider bound requires that the momentum transfer $\sqrt{s} < 2 M_{\text{mess}} $.  The general procedure for collider bounds is to truncate the number of events, eliminating those where $\sqrt{s}$ is larger than 2 times the maximum messenger mass \cite{Busoni:2014sya}.  Previous collider analyses for models with D11 type gluon operators estimate that the region of maximum EFT validity limits interpretation for  cut-off scales below 350 GeV.  For these low effective cut-off scales, event rates are severely truncated \cite{Aad:2015zva}.  In our analysis for the SU(2) and U(1) operators, cut-off scales of around 500 GeV, imply messenger masses at or under roughly 1 TeV.  We generated a sample of mono-W events for the process $pp\rightarrow W \chi \overline{\chi}$ at 8 TeV c.o.m. energy using in MADGRAPH \cite{Maltoni:2002qb}. Barring any other cuts, we found that less than 10 percent of the events pass the above truncation requirement for an effective cut-off of 500 GeV and DM masses of 100 GeV.  We do not know how far under 500 GeV the collider limits hold for these operators and this is a matter for further investigation.

\section{Conclusions}
We have given indirect detection constraints derived from Fermi-LATs dwarf spheroidal galaxy data on variety of models with multiple final state annihilations of DM.  These models included dark matter portals from third generation fermions, SM vector bosons, and popular effective field theory models formally analyzed in collider physics.  We have presented constraints in model space on surfaces of fixed total annihilation rate, and in planes of freely varying effective operator coefficients.  In planes of fixed annihilation rate our bounds take the form of lower mass limits for dark matter mass/effective operator cut-off.  Our mass bounds are in the 10-100s of GeV range, and we have presented these results using a visualization on triangles and ellipsoidal sections.  We have also compared our constraints to those obtained by collider production for vector boson portal models.  In general we find that dwarf constraints overtake collider constraints for dark matter masses greater than a few hundred GeV, and in regions of low effective cut-off where there is theory break down for collider applications.  While existing results indicate that EFT validity fails under a few hundred GeV in collider studies, the exact range of maximum validity in vector boson portal models is yet to be determined. This is a course for future work.

Dwarf constraints used are among the most limiting constraints for Dark Matter models, and therefore present the best possibility of ruling out regions of Dark Matter parameter space.  We reiterate that a more sophisticated combination of dwarf data, which doesn't assume annihilation into only one channel would provide much tighter constraints on our parameter space, and this is another avenue for further work.  We also give another caveat here, we have implicitly assumed the most uncontroversial dark matter profiles for dwarf galaxies.  Assumptions of different Dark Matter profiles will lead to wiggle room in our constraints and require further study.

\section{Appendix}
We present lower limits on the effective cut-offs $\Lambda_b$ and $\Lambda_{\tau}$ for our third generation fermionic model.  We present lower limits for the fixed total DM annihilation rate $10\vev{\sigma v}_{Th}$.

\begin{figure}[H]
\centering
\includegraphics[scale=0.4]{LambdaLimitsB10.png}
\includegraphics[scale=0.4]{LambdaLimitsTau10.png}
\caption{Lower bound on operator coefficients $\Lambda_b^{*}$ and $\Lambda_{\tau}^{*}$}
\label{fig:LambdaLimits10Trel}
\end{figure}

\section{Acknowledgements}
This work was made possible with funds from DOE grant DE-SC0013529.  We would like to thank Archana Anandakrishnan, Kenny Ng, and John Beacom for input and conversations.

redpajama_set_name: RedPajamaArXiv


text:
US pullout from Syria to be done in 'prudent' way: Trump
At least nine dead in India hotel fire: official
US seeks UN draft resolution calling for Venezuela elections
Khashoggi murder: Return to KSA or face 'bullet'
60 per cent of coffee varieties under threat: Scientists
May reaches out to rivals after winning confidence vote
Trump to visit Pentagon to unveil missile defense review
'One third of UN workers sexually harassed in 2 yrs'
15 dead in Kenyan hotel attack
UK parliament rejects Brexit deal
President Donald Trump on Monday sought to end fears of an abrupt US pullout from Syria, saying the fight against the Islamic State group was not over and that withdrawal would be done in a "prudent" manner.
"We will be leaving at a proper pace while at the same time continuing to fight ISIS and doing all else that is prudent and necessary!" Trump tweeted.
The president has come under withering pressure both at home and in allied capitals after previous statements indicating that he considered the IS group vanquished and that he wanted US troops out of Syria imminently.
Trump's new statement follows a trip by his national security adviser John Bolton to Israel in which he told Prime Minister Benjamin Netanyahu on Sunday that withdrawal would not happen before "ISIS is defeated and not able to revive itself."
In a call, Trump and French President Emmanuel Macron spoke of "the commitment of the United States and France to the destruction of ISIS as well as plans for a strong, deliberate, and coordinated withdrawal of US troops from Syria," the White House said.
"They reiterated that any further use of chemical weapons in Syria must not be tolerated."
Secretary of State Mike Pompeo said he had spoken with French officials. "We'll make sure we address the concerns that they have. Everyone understands
what the United States is doing," he told reporters as he headed on a Middle East visit.
The reassurances followed a diplomatic storm caused by Trump's surprise announcement in December that appeared to signal a rapid withdrawal from Syria, where US special forces play an important role in supporting local forces fighting IS.
"We've won against ISIS," he said at the time. "We've beaten them and we've beaten them badly. We've taken back the land. And now it's time for our troops to come back home."
Allies like Britain and France warned that IS was not defeated. Questions were also raised over the fate of Kurdish groups that have done much of the fighting alongside the United States in Syria, but now fear attacks from Turkey.
The initial pullout promise also sparked outspoken opposition from within Trump's Republican party and the resignation of respected defense secretary James Mattis.
In Monday's statement, Trump complained that media coverage had skewed his original words, saying that his latest position on Syria was "no different from my original statements."
Currently, about 2,000 US forces are in the Syria, which is in the grips of a complex civil war. Most of the US soldiers are there to train local forces fighting the hardcore-Islamist IS.-AFP