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3 September 2012 11:16am
By EXSS
Bittersweet Victory For Oman At Act 5, Cardiff
A bitter sweet end to Act 5, Cardiff for the two Omani teams
© Lloyd Images
Extreme Sailing Series - Act 5
Cardiff, Great Britain
The pressure mounted on the final day of the Extreme Sailing Series Act 5 in Cardiff, and it was more than apparent out on Cardiff Bay.
Leigh McMillan helming The Wave, Muscat was in the hunt for his fourth straight win, to match the Alinghi record set in 2008, and things were generally going his way until the fourth race of today. A penalty at the start of that race for infringing the leeward boats put McMillan at the back of the nine-boat fleet. In a single moment, the door opened even wider for their stable-mates Oman Air, skippered by US sailor Morgan Larson, and Austria's Red Bull Sailing Team to get back in the frame. Two races later Oman Air went into the lead by just 2 points leaving McMillan and Hagara on equal points.
Going into the final double-points race, all eyes were on the two Omani teams and the Austrians. Morgan Larson ensured his team got the best start, McMillan was also fast off the start line but for Hagara it was a false start - the team's hopes of their first 2012 Act win were over as the fleet sailed away. "We tried to win the Act here and we had a good chance," said Hagara. "We were leading on the first two days, but then on the third day we had a bad day, no good starts at all so we had to fight all the way then we had a false start in the last race today. We had a chance to win, but the OCS was really hard."
It was the ever-improving Danish team SAP Extreme Sailing who enjoyed the glory of winning the final race, but the Oman Air crew had done enough. Finishing in 2nd place cemented their spot at the top of the podium for the second time this season after winning the inaugural Act in Muscat, Oman, and denying The Wave, Muscat their fourth straight win. "Our level of sailing was high enough to win all week, but somebody just always had a little better day than us, especially The Wave, Muscat," said Morgan Larson. "You know, those guys are so good. They are a real challenge for us, but as it got lighter and shiftier, I think that worked to our advantage a little bit - it really was anybody's race. We just got on a roll for the last few races. To win here is fantastic. It is a testament to the Series and the competitors that there were five teams in for the win on the last race."
The win here for Oman Air also move Larson's team up into second place on the Overall 2012 leaderboard behind The Wave, Muscat. "It was really hard today, but I think we made it hard for ourselves," said McMillan. "We weren't executing the starts and the wind was a lot lighter today, so the holes were more aggressive than usual and we struggled to adapt to the situation. We can't beat ourselves up too much, second is still good for the Overall scores."
GAC Pindar, helmed by Andrew Walsh supported by US Olympian Anna Tunnicliffe calling tactics, had sailed brilliantly throughout this Act putting the British team within touching distance of their first podium finish this season, but a penalty in the penultimate race ruined their chances and the team finished in 4th overall just 3 points off Red Bull Sailing Team.
The French team of Groupe Edmond de Rothschild will leave Cardiff empty-handed and frustrated that their pre-season status as favourites is not bearing fruit on the water, although they retain 4th in the Overall 2012 rankings. Ernesto Bertarelli's Swiss team on Alinghi mixed it up enough to keep the leaderboard close going into the final day, finally finishing in 7th just 3 points off 5th placed SAP Extreme Sailing Team.
The local entry of Team Wales, skippered by young talent Dave Evans, had the support of the 35,000-strong crowd that crammed into the best vantage points around Cardiff Bay over the 4 days. "We experienced the crowds for the first time at the Games during the medal race and that was pretty insane with like 5000 people on the hill shouting at us," said 470 Olympic silver medalist Hannah Mills who crewed on Team Wales. "But it was wicked here - all round the Bay and everywhere you went there were people shouting and screaming, it was really cool."
Next stop on the Extreme Sailing Series will be Act 7 in Nice, France. OC Sport, the organisers of the award-winning Extreme Sailing Series, have been forced to cancel Act 6 in Trapani, Sicily, that was due to start in just 10 days time as the Province of Trapani and the regional government of Sicily failed to execute their financial and operational obligations necessary to host the event.
Extreme Sailing Series 2012 Act 5, Cardiff, Wales, UK standings after Day 4, 32 races (2.9.12)
Position / Team / Points
1. Oman Air (OMA), Morgan Larson 199 points
2. The Wave, Muscat (OMA), Leigh McMillan 188 points
3. Red Bull Sailing Team (AUT), Roman Hagara 181 points
4. GAC Pindar (GBR), Andrew Walsh 178 points
5. SAP Extreme Sailing Team (DEN), Jes Gram-Hansen 174 points
6. Groupe Edmond de Rothschild (FRA), Pierre Pennec 173.3 points
7. Alinghi (SUI), Ernesto Bertarelli 167 points
8. ZouLou (FRA), Erik Maris 124 points
9. Team Wales, Dave Evans 104 points
Extreme Sailing Series 2012 Overall Series Results after Act 5, Cardiff
1. The Wave, Muscat 48 points
2. Oman Air 41 points
3. Red Bull Sailing Team 41 points
4. Groupe Edmond de Rothschild 36 points
5. GAC Pindar 29 points
6. SAP Extreme Sailing Team 24 points
7. Alinghi 22 points
8. ZouLou 19 points


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Kazimierz Michał Andrzej Elżanowski (ur. 4 marca 1832 w Warszawie, zm. 29 listopada 1904 w Petersburgu) – polski generał infanterii armii carskiej (awansowany w 1893).Kawaler orderów

Był synem Juliana asesora Trybunału województwa mazowieckiego i Franciszki Barbary Szczanieckiej. Pochowany na cmentarzu Powązkowskim w Warszawie (kwatera 11-6-22/23).

Jego córką była Emilia Elżanowska.

Przypisy

Urodzeni w 1832
Ludzie urodzeni w Warszawie
Polacy – generałowie Imperium Rosyjskiego
Pochowani na cmentarzu Powązkowskim w Warszawie
Zmarli w 1904

redpajama_set_name: RedPajamaWikipedia


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Extend your spring walks into overnight adventures by stopping off in a mountain bothy.
This feature was first published in the Spring 2018 issue of The Great Outdoors.
As we publish this, winter is still very much in charge in most British mountain areas. Read this notice about winter conditions before planning your walk.
Always follow the Bothy Code.
There's a choice of two bothies on this scenic circular, which tackles the High Stile Ridge on the first day and returns via Fleetwith Pike. Stay in the remote Warnscale Head bothy, or continue a little further to reach the recently refurbed Dubs Hut. Fancy a real challenge? An alternative return route takes in Green Gable, Pillar and Ennerdale Forest.
Hidden away above the far-flung Grwyne Fawr Reservoir is a tiny but idyllic bothy, bearing the same name. Walk in from Llanbedr near Crickhowell, following the Beacons Way and then branching off along the ridge that overlooks the Mynydd Du Forest. The return route takes in some of the area's loftiest peaks, including 809m Waun Fach and Pen y Gadair at 800m.
The undulating path between Elgol and Loch Coruisk must be one of Britain's most beautiful coastal walks. Getting there and back in a day is challenging – but luckily there's a stunning bothying spot on the golden sands of Camasunary Bay. Loop around Loch Coruisk and drink in stunning views of the Black Cuillin before returning via the same route.
The highest bothy in England, Greg's Hut makes a great overnight stop either for an Eden Valley circuit or a longer, linear walk along the Pennine Way. This route begins in Garrigill and loops up to the Way via Tyne Head and Great Dun Fell. Drop down off Cross Fell and spend the night in the bothy before following the route of Wainwright's A Pennine Journey back to Garrigill.
The Dulyn bothy is a great starting point for peak-bagging in the Carneddau – but it's justifiably popular, so come prepared to share. This route winds in to the bothy from Cwm Eigiau, summiting Foel Fras, Carnedd Gwenllian and Carnedd Llewelyn the following day in a grand figure-of-eight.
Tackle Scotland's remotest Munros from a base at Shenavall. The walk-in alone is over four miles, so you'll need to plan at least one overnight to complete this classic circuit. Summit ticks include the Munros of Sgurr Ban, Beinn Tarsuinn and Ruadh Stac Mor as well as the Corbett Beinn a' Chlaidheimh.
Extend Wainwright's Bannisdale Horseshoe to spend the night at remote Mosedale Cottage in the Shap Fells. The high point is 664m Tarn Crag, but the route's real appeal is the wild, pathless terrain and the solitude. Wainwrights to bag in this corner of the Lakes include Whiteside Pike, Todd Fell and White Howe.
Restored in 2017 from a ruined shack, Flittingford is one of England's newest bothies. Walk in from Falstone for the night, then spend the next day tramping the shady tracks of Kielder Forest in a loop around Sidwood, Highfield and High Hawkhope.
Legend has it that the Thieves' Road between Nethy Bridge and Glen More was a favourite route of cattle reivers. Stay at Ryvoan Bothy, using it as the base for a there-and-back ascent of 810m Meall a' Bhuachaille the next day. Then catch a bus from Glen More back to Aviemore or Nethy Bridge.
Bag four Munros on this strenuous linear walk, which links train stations at Tarbet and Ardlui. Three of the 'Arrochar Alps' – Beinn Narnain, Beinn Ime and Ben Vane – can be done in a day, and a stay at brand new Abyssinia bothy in Glen Kinglas will allow you to tackle Beinn Vorlich into the bargain.


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Jacobs agreed that millennials face a lot of headwinds now. But he claimed that one of the key reasons to of invest in MILN is that millennials' earnings are expected to quadruple in the coming years.
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Aphnaeus caffer är en fjärilsart som beskrevs av Henry Trimen 1868. Aphnaeus caffer ingår i släktet Aphnaeus och familjen juvelvingar. Inga underarter finns listade i Catalogue of Life.

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caffer


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Professionals who understand the immense importance of an accelerated online Master's in Management Information Systems degree will also understand how vital the field is to businesses both in the public and private sector. After all, with the rise of the Internet, companies are moving their business operations to more sustainable and more secure networks online. As technology continues to play a more significant role in society, it follows that any advancements in the field would serve to better build businesses and companies, which is precisely what management information systems do.
However, there is a shortage of professionals who have the necessary educational background. This is perhaps because there aren't many accelerated online programs that are dedicated to management information systems. As time goes on, however, more and more programs that offer flexibility regarding term schedules and accelerated formats have made it easier for students to earn a master's in around a year, all while continuing to work in their current position. The following 15 programs would be great choices for any professional interested in a graduate education.
To compile this ranking, research was conducted using the National Center for Education Statistics and its publicly available database, the College Navigator. By searching for online Master's in Information Systems, an initial pool of 50 schools was discovered. From there, the list was narrowed down; this was done by comparing different factors, such as time to degree completion timetables and tuition rates. The final 15 schools, which can be found below, were selected based on their in-state graduate tuition rates.
Ranking Low-Cost Accelerated Master's in Management Information Systems
15. National University
Online Master of Science in Management Information Systems
The online MS in MIS from National University is available entirely online.
National University offers students the chance to earn an accelerated master's online in management information systems degree that is designed specifically to provide professionals with the necessary skills and knowledge to prepare them to become leaders in the field. This degree is conferred 100 percent online and focuses on the quarter credit unit model; courses are delivered asynchronously and synchronously with an average term length of 12 weeks. This degree is comprehensive and covers advanced concepts and theories within the field. Students can expect to complete 54 quarter credit units, a master's research project, and a comprehensive written and oral exam. Sample courses include Systems Analysis and Design, Human and Computer Interaction, and Strategic Decision Systems.
14. Colorado State University
Online Master of Computer Information Systems (MCIS)
The online Master of Computer Information Systems from CSU requires 33 credit hours of coursework.
The one year master's in management information systems online program at Colorado State University is one that is perfect for professionals who are interested in finding employment in the IT field regardless of their previous work or education experience. Students will have the option to study full-time or part-time; regardless of their study schedule, all students will complete this degree 100 percent online. This program focuses on software development, applications for business, and systems integration. The degree has a solid, comprehensive core curriculum but does allow students to take on free electives to strengthen their understanding of one particular area of the field. Students can expect to complete 33 credit hours of coursework, a capstone project, and a comprehensive written and oral exam. Sample courses include Agile Management and Product Development, Business Visual Application Development, and E-Business Application Technologies.
13. The University of Oregon
Online Master of Science in Applied Information Management
The online MS in Applied Information Management from the University of Oregon offers courses either asynchronously or synchronously.
The University of Oregon confers an accelerated online Master's in Management Information Systems that are perfect for mid-service professionals who are interested in advancing in their careers, whether with their current employers or at a new organization. The school's curriculum has a stated focus on information design, applied research, and business management. It is a degree that is geared towards developing the skill and knowledge that an IT professional will require in leadership positions. This program is conferred entirely online, and courses are delivered as either asynchronous or synchronous courses. Students will also find that courses are offered on a seven-week, eight-week, or 10-week term format. This degree requires 36 credit hours of coursework, an applied research project, and a comprehensive written and oral exam. Sample courses include Information and Communications Security, Organizational Behavior, and Project Management for Information Technology.
12. Webster University
Online Master of Arts in Information Technology Management
The online MA in Information Technology Management requires 36 credit hours of coursework.
Students at Webster University will find that the accelerated online Master's in Management Information Systems available here is one of the best in the country. This degree was designed for mid-service IT professionals who currently hold or will hold mid-management positions. The curriculum focuses on the skills and foundational knowledge necessary for professionals who will be holding a supervisory role within an organization or business. The curriculum focuses on information systems projects, security systems, and management skills. All courses are available online as asynchronous courses; the program does not require any on-campus residencies. Students can expect to complete 36 credit hours of coursework, a final project in information technology management, and a comprehensive written exam. Sample courses include Procurement and Contract Management for Information Technology, Information and Communications Systems and Networks, and Basic Finance for Managers.
11. Florida Institute of Technology
Online Master of Science in Management and Information Systems
The online MS in Information Technology and Database Administration requires 33 credit hours of coursework.
Florida Institute of Technology provides students with a one year online Master's in Management Information Systems degree that focuses on management theory, information systems security protocols, and organizational behavior. Students who take on this degree will be prepared to become mid-level managers and supervisors in the IT world and will find themselves in high demand in business settings. This program can be pursued as an entirely online option or as a hybrid program. Regardless of program option, all courses are taught by the same professors who teach the courses on campus. Online courses are synchronous, and live participation is required. Students will be able to finish this degree within one year with full-time, year-round study. The degree requires 33 credit hours of coursework, a final capstone project, and a comprehensive written and oral exam for graduation. Sample courses include Leadership Theory and Effective Management, Telecommunications Systems Management, and Advanced Management Information Systems.
10. Concordia University in Wisconsin
Online Master of Business Administration in Management Information Systems
The online MBA in MIS from Concordia University in Wisconsin is delivered 100 percent online.
Students who are interested in melding their business acumen with a strong affordable accelerated Master's in Management Information Systems online degree are well served at Concordia University in Wisconsin. This degree provides students with a Master of Business Administration that focuses on information systems management, a degree that is perfect for in-service professionals who are currently working in the private or public sectors. This degree does not have set start date, so students are encouraged to apply and enroll whenever they are ready. Courses are delivered 100 percent online and as asynchronous offerings, meaning that students get to choose how and when they study. Because this degree is business-minded, students are expected to complete an MBA core as well as an MIS core. Students can also expect to complete 39 credit hours of coursework, a capstone project, and a comprehensive written and oral exam; there is an internship available, but this is optional. Sample courses include Oracle Java Fundamentals and Programming, Systems Analysis and Design, and Oracle Academy Database Design and Programming.
9. Embry-Riddle Aeronautical University
The online MS in MIS from Embry-Riddle Aeronautical University can be completed in 18 months.
The online Master's in Management Information systems that is available at Embry-Riddle Aeronautical University has become one of the most in-demand offerings available in the country. This degree is housed in the school's worldwide virtual hub, making it available to students both here in the country and abroad. The program and its curriculum have a stated focus on management principles and skills along with understanding information systems and how technology continues to advance these systems. There are three specializations that are available with this degree, including Business Intelligence and Analytics, Information Systems Project Management, and Information Security and Assurance. This program was designed to be completed online and through asynchronous and synchronous courses that are offered on a 10-week term schedule. As a self-directed program, students are expected to keep pace with curriculum as well as keep track of their program requirements so that they graduate in a good amount of time; currently, the average time to completion for this degree is around 18 months. Students will be expected to complete 30 credit hours, a research project, and a comprehensive written exam. Sample courses include Information Analytics and Visualization in Decision making, Knowledge Management: Quality Management for the IS Enterprise, and Data and Information Modeling and Management.
8. Bellevue University
Bellevue, Nebraska
Online Master of Science in Management of Information Systems Degree
The online MS in MIS from Bellevue University requires 36 credit hours of coursework
Bellevue University confers an affordable accelerated online Master's in Management Information Systems degree that is a perfect fit for information systems managers who are in need of an advanced degree for their career. This program is accredited by the Global Accreditation Center for Project Management. There are five concentrations for this program: business administration, business analytics, cybersecurity, information security management, and information technology project management. These specializations may also be earned as stand-alone certificates, and in some cases, these specializations can help students pave a pathway forward towards licensure. This is a comprehensive program that is offered 100 percent online through asynchronous and synchronous courses; students who study full-time can complete this degree in less than 18 months. Students can expect to complete 36 credit hours of coursework, an integrated capstone project, and a comprehensive written and oral exam. Sample courses include Project Communications Management and Leadership, Information Technology Project Management, and Project Management in Global and Virtual Workplaces.
7. Liberty University
Online Master of Science in Information Technology
The online MS in Information Technology from Liberty University offers eight start dates throughout the year.
Students at Liberty University have the chance to pursue their dream of becoming an IT professional. This school confers a 12-month online Master's in Management information systems that are perfect for pre-service or early service professionals. The program is delivered entirely online through Liberty University's virtual school through asynchronous courses. The program has eight different start dates throughout the year and courses are all offered in the eight-week format, making it possible for students to complete all of the necessary requirements in one year. This degree also comes with two specializations: Network Design and Security as well as Software Design and Management. Students can expect to complete 36 credit hours of coursework, an integrated capstone project, and a comprehensive written and oral exam. Sample courses include Telecommunications and Network Security, Network Architecture and Design, and Software Development Management.
6. Florida State University
The online MS in MIS from FSU requires 33 credit hours of coursework.
Florida State University offers students the chance to earn an accelerated online master's degree in management information systems that will provide students with an exceptional background in the field. This program was specifically designed for mid-service professionals that have at least three years of work experience in MIS; this degree is not a great choice for professionals who have little to no work or education experience in the field. This program can be earned as either a 100 percent online program or a hybrid program; all online courses are asynchronous and students follow the traditional academic term schedule. This degree will require 33 credit hours of coursework, a capstone project, and a comprehensive written and oral exam. Sample courses include Knowledge Management and Business Intelligence, Social and Organization Issues in Management Information Systems, and Corporate Information Security.
5. The University of Massachusetts at Lowell
Lowell, Massachusetts
The online MS in Information Technology from the University of Massachusetts at Lowell requires 30 credit hours of coursework.
The accelerated online Master's in Management Information Systems available from the University of Massachusetts at Lowell is an incredible degree that is technology-focused and based. This program has been approved by both the National Security Agency and the United States Department of Homeland Security as a National Program of Academic Excellence in Cyber Defense Research. This program is offered wholly online, and there is never a need to take residency on campus. This program can also be completed in as little as one year, provided that the student has completed the prerequisite courses before starting their degree. Students will find that the degree offers a great deal of flexibility; there are four core areas that courses must originate, but the choices are endless. This degree requires 30 credit hours of coursework and a comprehensive written and oral exam. Sample courses include Designing and Building a Cybersecurity Program, Managing Large Data Sets, and Large Scale Application Deployment.
4. The University of Maryland at University College
Online Master of Science in Management with a Specialization in Information Systems and Services
The online MS in Management from the University of Maryland University College can be completed in 18 months.
The University of Maryland at University College offers an accelerated online Master's in Management Information Systems that can be completed in as little as 18 months. This degree is available both as a 100 percent online degree or as a blended format degree. Students will find that all online courses are delivered synchronously and in a 10-week format. The curriculum was designed by industry experts and scholars, ensuring that the plan of study is always up-to-date with the latest trends and issues in the industry. Students can expect to complete 36 credit hours of coursework, a capstone project, and a comprehensive written and oral exam. Sample courses include Financial Decision Making for Managers, Decision Support Systems and Expert Systems, and Information Technology, the CIO, and Organizational Transformation.
3. Minot State University
Minot, North Dakota
Online Master of Science in Information Systems (MSIS)
The online MS in Information Systems from Minot State University is available entirely online.
Students at Minot State University are offered an exceptional 12-month master's online in management information systems degree. This program is open to all MIS professionals who have an educational background in the field or who have two or more years of experience in the workplace. This degree incorporates new and emerging technologies into its curriculum, ensuring that students understand how the theories and concepts used in the field actually work in the real world. This is a 100 percent online degree that offers both asynchronous and synchronous courses on an eight-week term schedule. Students can expect to complete 30 credit hours of coursework, a capstone project including a real-world case study, and a comprehensive written and oral exam. Sample courses include Database Management and Administration, Business Network Systems Management, and Foundations of Information Assurance and Security.
2. Mississippi State University
Mississippi State, Mississippi
Online Master of Science in Information Systems
The online MS in Information Systems from MSU requires 33 credit hours of coursework.
Mississippi State University offers an accredited, accelerated online Master's in Management Information Systems that is currently ranked by U.S. News and World Report. This degree is available to all students, regardless of their education or work experience; however, students with no prior background in information systems management will be required to take some prerequisite courses that will be available online. This degree is offered 100 percent online through the school's virtual portal; courses are delivered asynchronously with no set log-in times and on the traditional academic term schedule. Students will be expected to complete 33 credit hours of coursework, a capstone project or integrated research project, and a comprehensive written and oral exam. Sample courses include Business Network Systems Management, Managing Large Data Sets, and Advanced Management Information Systems.
1. Western Governors University
Online Master of Business Administration in Information Technology Management
The online MBA in IT Management from Western Governors University can be completed in one year of study.
Western Governors University offers students the chance to earn an accelerated online Master's in Management Information Systems that are combined with a master of business administration. For students who require a combined degree such as this, WGU provides the best of both worlds. This degree is conferred 100 percent online with asynchronous and synchronous courses available on the traditional academic term schedule. Students will also find that it is possible for them to complete their degree requirements in just over a year if they study full-time. This degree was built to showcase how business and technology, specifically information systems, work hand-in-hand. Students can expect to complete 36 credit hours of coursework, a capstone project, and a comprehensive written and oral exam. Sample courses include Global Economics for Managers, Managing Organizations and Leading People, and Accounting for Decision Makers.
What are the Career Options for an Accelerated Online Master's in Management Information Systems Degree?
Computer Systems Analyst
Computer and Information Systems Manager
Application Analyst
IT Technical Support Officer
Information Systems Supervisor
Management Consultant
How Much Can You Earn in This Field?
MIS professionals can earn anywhere between $81,000 to $135,000 as a yearly salary. This range accounts for positions that range from analyst to manager, work experience and education level, different endorsements and credentials that can be used in the field, and more. It does not account for bonuses or additional forms of compensation. Professionals will do well to remember that the lowest part of this range focuses on professionals who only have a bachelor's degree in the field.
What are the Various Disciplines of Management Information Systems?
The first and foremost apparent discipline in this field is that of technology, specifically computer science and engineering. The field is quite broad, however, and while management information systems speak directly to the field's impact on business, it still covers a lot of disciplines. Everything from software development to application integration to big data and machine learning can be found in the field. Other disciplines include computer security, network architecture, databases, and more.
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In our case we are gonna use Express.js. Express.js is a Node.js web framework based on Sinatra. It's very easy to start with it and that's the reason why I'm gonna use it.
Jade. It's a Node.js template engine 'heavily influenced by Haml' that help us to write HTML5 code in a efficient and smart way. We are writting our HTML5 pages using this template engine. What we are going to do is create a layout from where other pages are going to inherit some configuration.
Less. It's a dynamic stylesheet language that provides us a way to create CSS3 very easily. With it you can use some concepts like variables, inheritance or mixins in your CSS3. There are some other dynamic stylesheet languages out there like SaSS or Stylus (you cand find a nice comparison here).
In order to build our application we need some data. Our data sources will be Twitter and Yahoo API, and for that purpose we are going to call to their REST API.
Get search. We are interested in getting tweets regarding some topic we can search for. You have to add a query parameter to the URL in order to look for specifics tweets within Twitter.
Get users/show. We need to indicate to the user_id parameter the user's id from who we want to extract some information such location or screen name.
Yahoo Geoplanet. We are use the Yahoo Geoplanet API to get latitude and longitude from a specified city in the world. The only thing we are going to need is saying the city from we want to know its coordinates.
To use the Twitter API we don't need to posses a developer key, but we have some limitations in the users/show services (we are restricted to use more than 150 request per hour). In the case of the Yahoo API we need to sign up in order to get a valid App identifier.
Well, so we want to develop our application and test it in our local enviroment and after that we want to deploy it to the cloud. I've choosen some PaaS in order to upload it.
Heroku. Heroku is a PaaS (Platform as a Service) that is built to upload your application to the cloud. Besides that it gives us many services (NoSQL, Message Queue services and so on) to make our applications better. You need to sign up to get an account. Fortunately, there is a special account where you can upload your application for free.
Cloud Foundry: Cloud Foundry is a PaaS created by VMWare quite similar to Heroku. It has support for several development stacks (JEE, Ruby or Node.js). As with Heroku it gives you some services (not as many than with Heroku) to your application. You can sign up for a free acount here.
Amazon Web Services. Both Heroku and Cloud Foundry can be consider PaaS, but with AWS we are talking about Iaas (Infrastructure as a Service). With AWS you have a machine (an instance) where you can install, deploy or use any stuff you like (a node.js application in our case). Althought, it's quite easy to start with Heroku or Cloud Foundry than AWS I want to try AWS because it's the base from some PaaS (Heroku uses AWS for example). We are using Amazon Elastic Compute Cloud (Amazon EC2) to deploy our application to the Cloud.
A few words about the project.
The project is quite simple. We want a simple HTML5 page with a text field and a search button. We write a work in the text field and we will look for tweets relating to that word in Twitter. Besides that we will show some extra information of it and use leaflet to present it. Easy, isn`t it?. I'll explain in the next write up how to develop it.


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text:
\section{\label{intro}Introduction}
Transverse single-spin asymmmetries (SSA) can provide crucial information on the three-dimensional structure of hadrons and have hence been a subject of increasing interest in the past two decades. While such asymmetries have been observed since the mid-70s in the hadroproduction of pions, i.e., $p^\uparrow p\to\pi+X$ ~\cite{Dick:1975ty, Klem:1976ui, Dragoset:1978gg}, the past few years have provided a large amount of high quality data on SSAs in a wide variety of processes such as $p^\uparrow p\to\pi+X$, $p^\uparrow p\to K^\pm+X$, $p^\uparrow p\to J/\psi+X$, $lp^\uparrow\to\pi+X$, $lp^\uparrow\to K+X$ etc., (see Refs.~\cite{DAlesio:2007bjf, Barone:2010zz} for reviews on the subject). A theoretical approach based on factorisation in terms of a hard-part and transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation function (FFs) has been formally established for processes which have  two scales: a hard, high energy scale such as the virtuality of the photon in the Drell-Yan process and a relatively soft scale of the order of $\Lambda_\text{QCD}$, such as the transverse momentum of the Drell-Yan lepton-pair. Another approach based on factorisation in terms of twist-3 parton correlators has been shown to be valid for the description of SSAs in processes with a single hard scale such as the transverse momentum of a pion in hadronic collisions.

Despite the absence of a formal proof, a lot of work has been done on a TMD description of single hard-scale processes under the assumption of factorisation, in what is generally referred to as the generalised parton model (GPM) approach. This approach has been quite succesful in describing unpolarised cross-sections in the hadroproduction of pions~\cite{DAlesio:2004eso}. The leading-order (LO) GPM is able to describe (upto a K-factor) experimental data on pion production in high energy hadron-hadron collisions better than either the LO or the NLO collinear pQCD. It is also able to provide a good description of data on SSA in $p^\uparrow p\to \pi+X$ at widely different c.o.m energies~\cite{DAlesio:2007bjf}. One of the important transverse-momentum-dependent distributions which can lead to SSAs is the Sivers distribution~\cite{Sivers:1989cc, Sivers:1990fh}, which encodes the correlation between the azimuthal anisotropy in the distribution of an unpolarised parton and the spin of its parent hadron. This anisotropy in the parton's transverse momentum distribution can lead to an azimuthal anisotropy in the distribution of the inclusive final state, i.e., a SSA. Fits of the $u$ and $d$ quark Sivers functions (QSF) obtained using data on $A_N(p^\uparrow p\to \pi+X)$ at E704 ($\sqrt{s}=19.4$ GeV), do a good job of describing the main features of the asymmetry observed at STAR ($\sqrt{s}=200$ GeV)~\cite{DAlesio:2007bjf}. While the quark Sivers functions have been widely studied over the years, the gluon Sivers function (GSF) still remains poorly understood.

A first indirect estimate of the gluon Sivers function in a GPM framework was obtained in Ref.~\cite{DAlesio:2015fwo}. The analysis consisted of fitting the GSF to midrapidity data on SSA in pion production at RHIC. In this analysis, the quark contribution to the SSA was calculated using quark Sivers functions (QSF) as extracted from semi-inclusive deep inelastic scattering data. The GSF fits obtained by this analysis predict asymmetries much smaller than allowed by the positivity bound on the GSF, viz. twice the unpolarised TMD gluon distribution. On the other hand, a recent study of large-$p_T$ hadron pair production in COMPASS indicates a substantial negative gluon Sivers asymmetry for both proton and deuteron targets~\cite{Adolph:2017pgv}. Since large-$p_T$ hadron pairs are produced through the photon-gluon fusion, this process is indeed sensitive to the GSF. However the final state also receives contributions from the QCD Compton process, which is quark initiated.  Hence an extraction of the GSF using large-$p_T$ hadron production is contaminated by the quark contributions to the SSA and would therefore depend on the extent to which these different processes can be separated in a data sample. With this being the first significant evidence for a non-zero GSF, it is important to study processes such as closed and open charm production which probe the gluon channel cleanly and directly.

In this work, using a GPM approach, we study the low-virtuality leptoproduction ($Q^2\approx0$) of open-charm as a possible probe of the poorly understood gluon Sivers function (GSF). At the leading-order (LO) of this process, the production of open-charm happens only via photon-gluon fusion (PGF), making it a direct probe of the gluon content of the proton. The GPM study of open-charm production as a probe of the gluon Sivers function was first proposed in Ref.~\cite{Anselmino:2004nk} for the process $p^\uparrow p\to D^0+X$. In that study they considered two extreme scenarios for the GSF: zero and maximal. The term `maximal' here refers to the Sivers function with its positivity bound of twice the unpolarised TMD ($|\Delta^Nf_{i/p^\uparrow}(x,\mathbf{k}_\perp)|/2f_{i/p}(x,\mathbf{k}_\perp)\leq1$), saturated for all values of $x$ --- we shall refer to this as the `saturated' Sivers function henceforth. Their study indicated that a measurement of SSA at RHIC for this process can give a direct indication of a nonzero gluon Sivers function. Further in Ref.~\cite{Godbole:2016tvq} we caculated the SSA for the same process (open charm hadroproduction) using the fits of Ref.~\cite{DAlesio:2015fwo} and found that these fits predict sizeable, measurable asymmetries.

The low-virtuality leptoproduction of $J/\psi$ has also been suggested as a probe of the GSF~\cite{Godbole:2012bx,Godbole:2013bca, Godbole:2014tha}. However, leptoproduction of open-charm may have some more advantages over the above mentioned processes. Firstly, unlike the case with $p^\uparrow p\to D^0+X$, one need not worry about possible factorisation breaking initial state interactions. $p^\uparrow l\to D^0+X$ would have the same initial/final state interactions as SIDIS, for which TMD factorisation has been established. A study of SSA in this process might therefore complement studies of SSA in SIDIS and $lp^\uparrow\to h+X$~\cite{DAlesio:2017nrd, DAlesio:2017jdm} by providing an additional handle on the gluon Sivers function. Secondly, open-charm production is free from dependence on production model, as is the case with closed-charm~\cite{Yuan:2008vn}.

We therefore consider the process $lp^\uparrow\to D^0+X$ in the low-virtuality regime in a GPM framework and see how it could serve as a probe of the GSF at both the COMPASS experiment and a future Electron-Ion Collider (EIC). While present data on open-charm production in COMPASS is limited due to statistics, the proposed Electron-Ion Collider~\cite{Accardi:2012qut} would have a significantly higher luminosity and should be able to provide better data on open/closed charm production. For both experiments, we present estimates for the maximum magnitude of SSA as obtained using the saturated GSF, and also the expected values of SSA obtained using the fits of Ref.~\cite{DAlesio:2015fwo}.

In section II, we give the expressions for the relevant quantities in the GPM framework. In section III, we give parametrisations for the different TMDs used, and in section IV, we discuss results for both the COMPASS and the EIC kinematics.

\section{The GPM Formalism}
In this work, we are concerned with the single-spin asymmetry in the low-virtuality leptoproduction of open charm,
\begin{equation}
A_N=\frac{d\sigma^\uparrow-d\sigma^\downarrow}{d\sigma^\uparrow+d\sigma^\downarrow}
\label{SSA}
\end{equation}
where $d\sigma^{\uparrow( \downarrow)}$ is the invariant differential cross-section for the process $p^{\uparrow(\downarrow)} l\to D+X$ with the spin of the transversely polarised proton being aligned in the $\uparrow$($\downarrow$) direction with respect to the production plane. Here, $\uparrow$ would be the $+y$ direction in a frame where the polarised proton is moving along the $+z$ direction and the meson is produced in the $xz$ plane. Note that this is the convention for collider experiments (such as EIC). In case of fixed target experiments (such as COMPASS), by convention, the polarised proton would be considered to be moving along the $-z$ direction with everything else remaining the same (cf.~Fig.~\ref{conventions}).

Following the treatment of open-charm hadroproduction~\cite{Anselmino:2004nk}, we can write the denominator and numerator of Eq.~1 as,
\begin{eqnarray}
d\sigma ^\uparrow + d\sigma ^\downarrow &=&
\frac{E_D \, d\sigma^{p^\uparrow l \to DX}} {d^{3} \mbox{\boldmath $p$}_D} +
\frac{E_D \, d\sigma^{p^\downarrow l \to DX}} {d^{3} \mbox{\boldmath $p$}_D}
= 2 \, \frac{E_D \, d\sigma^{pl \to DX}} {d^{3} \mbox{\boldmath $p$}_D}
\label{denominator}\\
&& \hspace*{-3.0cm} = \>
2\int dx_g \, dx_\gamma  \, dz \, d^2 \mathbf{k}_{\perp g} \, d^2 \mathbf{k}_{\perp \gamma} \,
d^3 \mathbf{k}_{D} \,
\delta (\mathbf{k}_{D} \cdot \hat{\mbox{\boldmath $p$}}_c) \,
\delta (\hat s +\hat t +\hat u - 2m_c^2) \>
{\mathcal C}(x_g,x_\gamma,z,\mathbf{k}_D) \nonumber \\
&& \hspace*{-3.0cm} \times ~
f_{g/p}(x_g,\mathbf{k}_{\perp g}) \>  f_{\gamma/l}(x_\gamma,
\mathbf{k}_{\perp \gamma}) \>
\frac{d \hat{\sigma}^{g\gamma \to c \bar c}}
{d\hat t}(x_g, x_\gamma, \mathbf{k}_{\perp g}, \mathbf{k}_{\perp \gamma}, \mathbf{k}_D) \>
 D_{D/c}(z,\mathbf{k}_D) \> \nonumber
\end{eqnarray}
and
\begin{eqnarray}
d\sigma ^\uparrow - d\sigma ^\downarrow &=&
\frac{E_D \, d\sigma^{p^\uparrow l  \to DX}} {d^{3} \mbox{\boldmath $p$}_D} -
\frac{E_D \, d\sigma^{p^\downarrow l\to DX}} {d^{3} \mbox{\boldmath $p$}_D}
\label{numerator}\\
&& \hspace*{-3.0cm} = \>
\int dx_g \, dx_\gamma  \, dz \, d^2 \mathbf{k}_{\perp g} \, d^2 \mathbf{k}_{\perp \gamma} \,
d^3 \mathbf{k}_{D} \,
\delta (\mathbf{k}_{D} \cdot \hat{\mbox{\boldmath $p$}}_c) \,
\delta (\hat s +\hat t +\hat u - 2m_c^2) \>
{\mathcal C}(x_g,x_\gamma,z,\mathbf{k}_D) \nonumber \\
&& \hspace*{-3.0cm} \times~
 \Delta ^N f_{g/p^\uparrow}(x_g,\mathbf{k}_{\perp g}) \>  f_{\gamma/l}(x_\gamma,
\mathbf{k}_{\perp \gamma}) \>
\frac{d \hat{\sigma}^{g\gamma \to c \bar c}}
{d\hat t}(x_g, x_\gamma, \mathbf{k}_{\perp g}, \mathbf{k}_{\perp \gamma}, \mathbf{k}_D) \>
 D_{D/c}(z,\mathbf{k}_D). \> \nonumber
\end{eqnarray}
In the above expressions, $x_{g(\gamma)}$ is the light-cone momentum fraction of the incoming gluon (photon) with the $z$-axis along the parent proton (lepton) direction, $z=p_D^+/p_c^+$ is the light-cone momentum fraction of the $D$-meson with the $z$-axis along the fragmenting charm quark direction, $\mathbf{k}_{g(\gamma)}$ is the intrinsic transverse momentum of the gluon (photon) with respect to the parent particle direction, $\mathbf{k}_D$ is the transverse momentum with which the meson fragments from the charm quark, $\hat\mbox{\boldmath $p$}$ is the unit vector along the heavy quark direction, $m_c$ is the charm quark mass, and $\hat{s}$, $\that$ and $\hat{u}$ are the Mandelstam variables for the photon-gluon fusion process $\gamma g\to c\bar{c}$.

$\Delta^Nf_{g/p^\uparrow}(x,\mathbf{k}_\perp)$ and $f_{g/p}(x,\mathbf{k}_\perp)$ stand for the gluon Sivers function and unpolarised TMD respectively. $f_{\gamma/l}(x,\mbox{$\mathbf{k}_\perp$})$ is the transverse-momentum-dependent distribution of quasi-real photons in an unpolarised lepton, and $D_{D/c}(z,\mathbf{k}_D)$ is the transverse-momentum-dependent fragmentation function. We will discuss the functional forms for all these distributions in Sec. III.

As mentioned earlier, the Sivers function, $\Delta^Nf_{i/p^\uparrow}(x,k_\perp;Q)$ describes the azimuthal anisotropy in the transverse momentum distribution of an unpolarised parton in transversely polarised hadron, and we have
\begin{eqnarray}
f_{i/h^\uparrow}(x,\mathbf{k}_\perp,\mathbf{S};Q)&=&f_{i/h}(x,k_\perp;Q)+\frac{1}{2}\Delta^N f_{i/h^\uparrow}(x,k_\perp;Q)\frac{\epsilon_{ab}k_\perp^a S^b}{k_\perp}\nonumber \\
&=&f_{i/h}(x,k_\perp;Q)+\frac{1}{2}\Delta^N f_{i/h^\uparrow}(x,k_\perp;Q)\cos\phi_{\perp}
\label{Sivers}
\end{eqnarray}
where $\mathbf{k}_\perp=k_\perp(\cos\phi_\perp, \sin\phi_\perp)$. In a generalised parton model (GPM) description of this process, the only possible source of an asymmetry would be a non-zero gluon Sivers function. Since photon-gluon fusion results in unpolarised final state quarks, there cannot be any contribution from the Collins effect, which would require transversely polarised final state quarks.

The partonic cross-section for photon-gluon fusion into a heavy quark pair is given by~\cite{Babcock:1977fi},
\begin{eqnarray}
\frac{d\hat{\sigma}^{g\gamma \to c \bar c}}{d\hat t}&=&\frac{4\pi}{8\times9}~\frac{\alpha_\text{em}\alpha_s}{ \hat{s}^{2}(\that-m_c^2)^{2}(\hat{u}-m_c^2)^{2}}[-(\that-\hat{u})^4-4\hat{s}(\that+\hat{u})(\that-\hat{u})^2
\\ \nonumber &-&4\hat{s}^2\left((\that-\hat{u})^2+2(\that+\hat{u})^2\right)-12\hat{s}^3(\that+\hat{u})-3\hat{s}^4]
\end{eqnarray}
where the Mandelstam variables are defined in the usual way,
\begin{equation}
\hat s = (P_g+P_\gamma)^2;\> \hat t = (P_g-P_c)^2;\>\hat u = (P_\gamma-P_c)^2.
\end{equation}
The factor ${\mathcal C}(x_g,x_\gamma,z,\mathbf{k}_D)$ in Eqs.~2 and 3 contains the parton flux and the Jacobian relating the partonic phase-space to the mesonic phase-space. It is give by,
\begin{equation}
{\mathcal C}(x_g,x_\gamma,z,\mathbf{k}_D)=\frac{\hat s}{\pi z^2}\,\frac{\hat s}{x_g x_\gamma s}\,
\frac{ \left( E_D+\sqrt{\mathbf{p}_D^2 - \mathbf{k}_{\perp D}^2} \right)^2}
{4(\mathbf{p}_D^2 - \mathbf{k}_{\perp D}^2)} \,
\left[1- \frac{z^2 m_c^2}
{ \left( E_D+\sqrt{\mathbf{p}_D^2 - \mathbf{k}_{\perp D}^2} \right)^2}\right]^2
\end{equation}
The on-shell condition $\hat{s}+\that+\hat{u}=2m_c^2$ in Eqs.~2 and 3, gives a quartic equation in $z$. $z$ can then be fixed by using this equation as shown in  Ref.~\cite{Godbole:2016tvq}.

The delta function $\delta (\mathbf{k}_{D} \cdot \hat{\mbox{\boldmath $p$}}_c)$ in Eqs.~2 and 3 ensures that the region of integration for $\mathbf{k}_D$ is confined to the two-dimensional plane perpendicular to the direction of the charm quark i.e.,
\begin{equation}
\int d^3\mathbf{k}_D~\delta (\mathbf{k}_{D} \cdot \hat{\mbox{\boldmath $p$}}_c)D_{D/c}(z,\mathbf{k}_D)...=\int d^2\mathbf{k}_{\perp D}D_{D/c}(z,\mathbf{k}_{\perp D})...
\end{equation}
where $\mathbf{k}_{\perp D}$ represents values of transverse momenta on the allowed plane.

An outline of the treatment of the parton level kinematics and the TMD fragmentation is given in Appendix A.

\section{Parametrisation of the TMDs}
Since we give predictions using the GSF fits of Ref.~\cite{DAlesio:2015fwo}, for consistency we have to use the unpolarised gluon TMD and Sivers function used therein. We use standard factorised Gaussian form for the unpolarised gluon TMD,
\begin{equation}
f_{g/p}(x,k_\perp;Q)=f_{g/p}(x,Q)\frac{1}{\pi\langle k_\perp^2\rangle}e^{-k_\perp^2/\langle k_\perp^2\rangle}
\end{equation}
with $\langle k_\perp^2\rangle=0.25\text{ GeV}^2$.

For the photon distribution $f_{\gamma/l}(x,\mathbf{k}_\perp)$, we consider two cases:
\begin{enumerate}
\item The Weizsacker-Williams distribution of quasi-real photons with a Gaussian transverse momentum spread~\cite{Godbole:2012bx,Godbole:2013bca, Godbole:2014tha},
\begin{equation}
f_{\gamma/l}(x_\gamma,\mathbf{k}_{\perp \gamma};s)=f_{\gamma/l}(x_\gamma,s)\frac{1}{\pi\langle k_{\perp\gamma}^2\rangle}e^{-k_{\perp g}^2/\langle k_{\perp\gamma}^2\rangle}\hspace*{0.5cm}\text{(Gaussian WW)}
\end{equation}
where the Weizsacker-Williams distribution is given by~\cite{Brodsky:1971ud, Terazawa:1973tb,Kniehl:1990iv},
\begin{equation}
f_{\gamma/l}(x_\gamma,s)=\frac{\alpha_\text{em}}{\pi}\left(
\frac{1+(1-x_\gamma)^2}{x_\gamma}\left[\log\frac{\sqrt{s}}{2m_l}-\frac{1}{2}\right
\right)
\end{equation}
and the width of the Gaussian is $\langle k_{\perp\gamma}^2\rangle=0.1$ GeV$^2$.
\item The leading order result for the TMD distribution of photons in a lepton from Ref.~\cite{Bacchetta:2015qka},
\begin{equation}
f_{\gamma/l}(x_\gamma,\mathbf{k}_{\perp \gamma})=\frac{\alpha_\text{em}}{2\pi^2}\frac{\mathbf{k}^2_{\perp\gamma}\left[1+(1-x_\gamma)^2\right]+m^2x_\gamma^4}{x_\gamma\left[\mathbf{k}^2_{\perp\gamma}+m^2x_\gamma^2\right]^2}\hspace*{0.5cm}\text{(Photon TMD)}
\end{equation}
where $m$ is the mass of the lepton.
\end{enumerate}
The first choice, which we will refer to as Gaussian WW, was used in earlier studies of low-virtuality leptoproduction by us~ \cite{Godbole:2012bx,Godbole:2013bca, Godbole:2014tha} (and also in an analysis of low-$Q^2$ contributions to $ep^\uparrow\to h+X$~\cite{DAlesio:2017nrd}, but without the Gaussian spread) when first-principles result for the photon TMD distribution was not available. The second choice, which we will refer to as Photon TMD, is the first analytical result available in literature for the transverse-momentum-dependent distribution of photons in a lepton~\cite{Bacchetta:2015qka}. Here we present results using both choices for completeness.

As with the unpolarised densities, we take the transverse-momentum-dependence of the FF to be Gaussian,
\begin{equation}
D_{D/c}(z,\mathbf{k}_{D})=D_{D/c}(z)\frac{1}{\pi\langle k^2_{\perp D}\rangle}e^{-k_D^2/\langle k^2_{\perp D}\rangle}
\end{equation}
with $\langle k^2_{\perp D}\rangle=0.25$ GeV$^2$.

The gluon Sivers function is parametrised as follows~\cite{DAlesio:2015fwo},
\begin{equation}
\Delta ^N f_{g/p^\uparrow}(x,k_{\perp};Q)=2\mathcal{N}_g(x)f_{g/p}(x,Q)\frac{\sqrt{2e}}{\pi}\sqrt{\frac{1-\rho}{\rho}}k_\perp \frac{e^{-k^2_\perp/\rho\langle k^2_\perp\rangle}}{\langle k^2_\perp\rangle^{3/2}}
\end{equation}
with $0<\rho<1$. $\mathcal{N}_g(x)$ parametrises the $x$-dependence of the GSF and is generally written as
\begin{equation}
\mathcal{N}_g(x)=N_gx^{\alpha_g}(1-x)^{\beta_g}\frac{(\alpha_g+\beta_g)^{\alpha_g+\beta_g}}{\alpha_g^{\alpha_g}\beta_g^{\beta_g}}
\end{equation}
It must obey $|\mathcal{N}_g(x)|<1$ in order for the Sivers function to satisfy the positivity bound,
\begin{equation}
\frac{|\Delta^Nf_{g/p^\uparrow}(x,\mathbf{k}_\perp)|}{2f_{g/p}(x,\mathbf{k}_\perp)}\leq 1\>\forall \>x, \mathbf{k}_\perp.
\end{equation}

\begin{table}[t]
\centering
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
SIDIS1 & \multicolumn{2}{l|}{$N_g=0.65$} & $\alpha_g=2.8$ & $\beta_g=2.8$ & $\rho=0.687$ & \multirow{2}{*}{$\langle k^2_\perp\rangle=0.25$ GeV$^2$} \\ \cline{1-6}
SIDIS2 & \multicolumn{2}{l|}{$N_g=0.05$} & $\alpha_g=0.8$ & $\beta_g=1.4$ & $\rho=0.576$ &                                                        \\ \cline{1-7}
\end{tabular}
\caption{Parameters of the GSF fits from Ref.~\cite{DAlesio:2015fwo}.}
\label{SIDIS-gluon-fits}
\end{table}

In this work, for the predictions we consider two options for the gluon Sivers function:
\begin{enumerate}
\item the Sivers function with the positivity bound saturated, i.e., $\mathcal{N}_g(x)=1$ and $\rho=2/3$.
\item the SIDIS1 and SIDIS2 extractions of the Sivers function from Ref.~\cite{DAlesio:2015fwo}.
\end{enumerate}

As mentioned in the introduction, we will refer to the first choice as the `saturated' Sivers function. It would give an upper bound on the asymmetry for a fixed width $\langle k^2_\perp\rangle$. The parameter $\rho$ is set to $2/3$ in order to maximize the first $k_\perp$-moment of the Sivers function, following Ref.~\cite{DAlesio:2010sag}. It must be kept in mind though, that this cannot be treated as giving an absolute upper bound on $A_N$ --- an increased width $\langle k^2_\perp\rangle$, for a fixed value of $\rho$, naturally would result in an increased asymmetry since the effects of the parton transverse momenta are more pronounced.

The SIDIS1 and SIDIS2 GSFs from Ref.~\cite{DAlesio:2015fwo} are the first (and so far, only) available extractions of the GSF in a GPM framework. They were obtained by fitting to PHENIX data on $A_N$ in inclusive pion production in the midrapidity region at RHIC. The QSFs used in these extractions, also labelled SIDIS1 and SIDIS2 respectively, were fit to data on semi-inclusive deep inelastic scattering. The SIDIS1 QSF set~\cite{Anselmino:2005ea} (which was used in the extraction of the SIDIS1 GSF) was fitted to data on pion production in HERMES and positive hadron production in COMPASS with fragmentation functions by Kretzer~\cite{Kretzer:2000yf}. It contains only the $u$ and $d$ quark Sivers functions since the data was not sensitive to sea quark contributions. The SIDIS2 QSF set~\cite{Anselmino:2008sga} was fitted to flavour segregated data on pion and kaon production from HERMES and COMPASS and hence included sea quark Sivers functions as well. It used fragmentation functions by de Florian, Sassot and Stratmann (DSS)~\cite{deFlorian:2007aj}.

Both QSF sets give a good description of their respective SIDIS data sets. Furthermore both the GSFs (taken along with their associated QSF sets) describe the data on $A_N$ in midrapidity pion production equally well. Despite this the two fits show very different $x$-dependencies, with SIDIS1 being larger in the moderate-$x$ region and SIDIS2 being larger in the low-$x$ region. The values of the parameters of the two GSF fits are given in Table I.

\section{Results}

In this section we present results on the unpolarised cross-section and SSA for COMPASS and EIC kinematics. Before going into the  results, we should first make a note on the differing kinematic conventions of the two experiments: As COMPASS is a fixed target experiment, by convention the lepton is taken to be along the $+z$ direction. This means that, in the definition of $A_N$ in Eq.~1, keeping the conventions for proton spin direction and production plane the same, positive $x_F$ and $\eta$ correspond to the backward hemisphere of the proton, whereas negative $x_F$ and $\eta$ correspond to the forward hemisphere of the proton. Note that this convention differs from that adopted Sec.~II where, following the RHIC convention, the {\it proton} is taken to be moving along the $+z$ direction. Since EIC, like RHIC, is also a collider experiment, we shall use the same convention for it. In the interest of clarity, the conventions used for the two experiments are illustrated in Fig.~\ref{conventions}.

\begin{figure}[h]
\begin{center}
\includegraphics[width=0.45\linewidth]{COMPASS.pdf}
\includegraphics[width=0.45\linewidth]{EIC.pdf}
\caption{Kinematics for COMPASS (left) and EIC (right). $\vec{P}_N$ is the proton momentum  and $\vec{S}$ is its spin orientation. $\vec{P}_l$ is the lepton momentum. The $D$-meson momentum, $\vec{P}_D$ is taken to be on the $x\text{--}z$ plane.}
\label{conventions}
\end{center}
\end{figure}

Please note that since we are interested in quasi-real photoproduction, we have put a cut, $Q^2<1$ GeV$^2$, where $Q^2=-(P_l-P_{l'})^2$ is the photon virtuality. This was motivated by the COMPASS antitagging cuts.  In regions of large photon transverse momenta, the lepton-photon vertex becomes $hard$ and the photon becomes off-shell. Hence one cannot use hard-parts defined for on-shell initial and final states.  The cut on the photon virtuality $Q^2$ can be implemented by considering its relation to $k_{\perp\gamma}$ and $x_\gamma$, $Q^2=k_{\perp\gamma}^2\left(1+\frac{x_\gamma}{1-x_\gamma}\right)$. In this work, all results associated with both COMPASS as well as EIC were obtained with the $Q^2<1$ GeV$^2$ cut. When using the Gaussian WW approximation, this cut does not make a huge difference since the steeply falling  $k_{\perp\gamma}$-dependence for $k_{\perp\gamma}>\sqrt{\langle k_{\perp\gamma}^2\rangle}$ prevents large contributions from regions of large virtuality. However, this is not the case with the Photon TMD as it has a much longer tail due to its $1/k_{\perp\gamma}^2$ dependence. One must also note here that the opposite is true in the low-$k_{\perp\gamma}$ region. At low $k_{\perp\gamma}$ the Photon TMD falls off very sharply with increasing ${k}_{\perp\gamma}$ whereas the Gaussian WW approximation, by virtue of being a Gaussian, has a  flat $k_T$-dependence at very low $k_T$.

The numerical results were obtained using the GRV98LO set for the collinear gluon density and for the collinear part of the FF, the LO parametrisation of the $c\to D^0$ fragmentation function by Kniehl and Kramer~\cite{Kniehl:2006mw} was used. The QCD scale was chosen to be $Q^2=m_D^2+P_T^2$.

\subsection{COMPASS}
The COMPASS experiment is a fixed target experiment involving a 160 GeV muon beam colliding on a proton target with a centre of mass energy $\sqrt{s}=17.4$ GeV. The COMPASS spectrometer covers hadrons in the $l\text{-}p$ c.o.m frame pseudorapidity range $-0.1<\eta_h<2.4$ and detects $D^0$ mesons through their $D^0\to K^-\pi^+$ decay mode. The geometry of the detector allows a proper reconstruction of the $D^0$'s produced only in the backward hemisphere of the proton and hence we restrict our analysis to the $x_F, ~\eta>0$ region.

\begin{figure}[t]
\begin{center}
\vspace*{-2cm}
\includegraphics[width=\linewidth]{COMPASS_logcs_combined.pdf}
\vspace*{-2cm}
\caption{Unpolarized cross-section at COMPASS as a function of $x_F$ (at fixed $P_T$, left panel) and $P_T$ (at fixed $\eta$, right panel).}
\label{COMPlogcs}
\end{center}
\end{figure}

In Fig.~\ref{COMPlogcs}, we show results for the unpolarised invariant cross-section using both the Gaussian WW approximation and the Photon TMD with the $Q^2<1$ GeV$^2$ cut. We show the cross-section as a function of $x_F$ at fixed $P_T=1$ GeV (left panel) and as a function of $P_T$ at a fixed pseudorapidity $\eta=1$ (right panel). At a fixed $P_T$, the cross-sections obtained with both the Gaussian WW and Photon TMD vary by two orders of magnitude in the region $0<x_F<0.8$. The Photon TMD result is generally smaller than the Gaussian WW result by 30-40\%, except at very large $x_F$ where both become comparable. At fixed pseudorapidity, for both choices of the photon density, the cross-section decreases by three orders of magnitude with increasing $P_T$ in the range $0.5<P_T<3.0$ GeV. The cross-section obtained with the Photon TMD is smaller by roughly 30-40\% over the entinre $P_T$ range.  For a larger value of the width of unpolarised gluon TMD, viz. $\langle k_\perp^2\rangle=1$ GeV$^2$ instead of 0.25 GeV$^2$, the cross-section at fixed $P_T$ is not affected much whereas, the cross-section at fixed pseudorapidity spreads out in $P_T$ somewhat --- becoming smaller by 6\% at $P_T=0.5$ GeV and larger by 40\% at $P_T=3$ GeV --- as one would expect. Overall, cross-section estimates for COMPASS are not very sensitive to the unpolarised gluon TMD width. Varying the width of the TMD FF in the range $0<\langle k^2_{\perp D}\rangle<0.25$ GeV$^2$ also does not have any significant effect on the cross-section.

\begin{figure}[t]
\begin{center}
\vspace*{-2cm}
\includegraphics[width=\linewidth]{COMPASS_satAN_combined.pdf}
\vspace*{-2cm}
\caption{SSA with saturated GSF at COMPASS as a function of $x_F$ (at fixed $P_T$, left panel) and $P_T$ (at fixed $\eta$, right panel).}
\label{COMPsatAN}
\end{center}
\end{figure}

Fig.~\ref{COMPsatAN} shows estimates for the maximal value of the magnitude of the asymmetry $|A^\text{max}_N|$, obtained by using the saturated gluon Sivers function viz., $\mathcal{N}_g(x)=1$, $\rho=2/3$. The results are presented  as a function of $x_F$ at fixed $P_T=1$ GeV (left panel) and as a function of $P_T$ at a fixed pseudorapidity $\eta=1$ (right panel). At fixed $P_T$, estimates of $|A^\text{max}_N|$  range from a minimum of about 12\% at $x_F\approx0.2-0.3$ to upto 24\% at $x_F=0.8$. At fixed  $\eta$, $|A^\text{max}_N|$ shows a general increase with the meson transverse momentum, ranging from around $8\%$ at $P_T=0.5$ GeV to $24\%$ at $P_T=3$ GeV. Both the Gaussian WW distribution and the Photon TMD give similar results with the former being slightly smaller at low $x_F$/$P_T$ and vice versa.

\begin{figure}[t]
\begin{center}
\vspace*{-1cm}
\includegraphics[width=\linewidth]{COMPASS_sidis_combined.pdf}
\vspace*{-2cm}
\caption{SSA from GSF fits of Ref.~\cite{DAlesio:2015fwo} at COMPASS as a function of $x_F$ (at fixed $P_T$, left panel) and $P_T$ (at fixed $\eta$, right panel).}
\label{COMPsidisAN}
\end{center}
\end{figure}

Fig.~\ref{COMPsidisAN} shows the asymmetries obtained using the SIDIS1 and SIDIS2 fits~\cite{DAlesio:2015fwo}. As was the case with the saturated asymmetry, the results obtained with the Gaussian WW approximation and Photon TMD are generally similar, with the former being slightly smaller at low $x_F$/$P_T$ and vice versa. Both fits give asymmetry predictions much smaller than allowed by the positivity bound with SIDIS2 giving significantly smaller asymmetries than SIDIS1. This is because the kinematic regions we consider probe the region $0.08<x_g<0.5$, where SIDIS2 is much smaller than SIDIS1, as can be seen from the numbers in Table~\ref{SIDIS-gluon-fits}. At fixed $P_T$, SIDIS1 gives a peak asymmetry of $4.2\%$ at $x_F=0$ and SIDIS2 gives a peak asymmetry of $0.8\%$ at $x_F=0.8$. At fixed $\eta=1$, SIDIS1 gives a peak asymmetry of $7\%$ and SIDIS2 gives a peak asymmetry of almost $1\%$, both at $P_T=3.0$ GeV. We have verified that changes in the width of the TMD FF in the range $0<\langle k^2_{\perp D}\rangle<0.25$ GeV$^2$ do not alter the results for either SIDIS1 or SIDIS2 substantially and the general features of the $A_N$ predictions stay the same.

\subsection{EIC}

\begin{figure}[t]
\begin{center}
\vspace*{-2cm}
\includegraphics[width=\linewidth]{EIC_logcs_combined.pdf}
\vspace*{-2cm}
\caption{Unpolarized cross-section at EIC as a function of $x_F$ (at fixed $P_T$, left panel) and $P_T$ (at fixed $\eta$, right panel).}
\label{EIClogcs}
\end{center}
\end{figure}

The Electron-Ion Collider (EIC) is a proposed experiment with colliding electron and proton/ion beams, with the possibility of both being polarised. It is meant to be capable of attaining high luminosities, with a centre of mass energy of upto 140 GeV in the $ep$ configuration.

In Fig.~\ref{EIClogcs}, we show results for the unpolarised invariant cross-section using both the Gaussian WW approximation and the Photon TMD with the same $Q^2<1$ GeV$^2$ cut as used for COMPASS. We show the cross-section as a function of $x_F$ at fixed $P_T=1.5$ GeV (left panel) and as a function of $P_T$ at a fixed pseudorapidity $\eta=3$ (right panel). At fixed $P_T$, in the forward region, the cross-section decreases with increasing $x_F$ by more than six orders of magnitude in the range $0<x_F<0.7$. In contrast, in the backward region, the decrease in the cross-section with increasing $|x_F|$, is only around one order of magnitude. This is because, for $x_F<0$ the gluon density is being probed in the small-$x$ region and both the Weiszacker-Williams distribution and the Photon TMD are being probed in the moderate-to-large-$x$ region. In the small-$x$ region the gluon density rises faster with decreasing $x$ than both photon distributions, which behave as $1/x$. Further, in the moderate-to-large-$x$ region, the photon distributions fall much less steeply with increasing $x$ than the gluon density. These two effects combine to give the widely differing behaviour of the cross-section in the backward and forward regions. In the forward region ($x_F,\eta>0$), both the Photon TMD and the Gaussian WW approximation give almost identical results, whereas in the backward region the Photon TMD gives slightly smaller results for moderate values of negative $x_F$. This is similar to what was observed at COMPASS. At fixed $\eta$, the cross-section decreases with increasing $P_T$ by four orders of magnitude in the range $0.5<P_T<3.0$ GeV. With a larger value of the unpolarised TMD width $\langle k_\perp^2\rangle=1.0$ GeV$^2$, the cross-section at fixed $P_T$ is found to be unaffected in the forward region, but shows a decrease in the backward region of about $40\%$ on average. The increase in the $P_T$-spread of the cross-section is also observed at fixed $\eta$, but the effect is very small. The cross-section is also found to be insensitive to changes in the width of the fragmentation function in the range $0<\langle k_{\perp D}^2\rangle<0.25$ GeV$^2$.
\begin{figure}[t]
\begin{center}
\vspace*{-2cm}
\includegraphics[width=\linewidth]{EIC_satAN_combined.pdf}
\vspace*{-2cm}
\caption{SSA with saturated GSF at EIC as a function of $x_F$ (at fixed $P_T$, left panel) and $P_T$ (at fixed $\eta$, right panel).}
\label{EICsatAN}
\end{center}
\end{figure}

In Fig.~\ref{EICsatAN}, we show estimates for the maximal value of the magnitude of the asymmetry $|A_N^\text{max}|$ obtained by using the saturated gluon Sivers function, as a function of $x_F$ at fixed $P_T=1.5$ GeV (left panel) and as a function of $P_T$ at fixed pseudorapidity $\eta=3$ (right panel). With the fairly large centre of mass energy of the EIC, we find that the general features of $|A^\text{max}_N|$ are similar to what was obtained for proton-proton collisions at RHIC~\cite{Anselmino:2004nk,Godbole:2016tvq}.  At fixed $\eta=3$, for the Photon TMD, the asymmetry peaks at $21\%$ at $P_T=2$ GeV. At fixed $P_T$, large asymmetries are allowed in the forward region, with estimates being upto almost 25\% at $x_F=0.8$. Overall, in the forward region ($x_F,\eta>0$) the Photon TMD gives results that are upto 18\% larger than the what is obtained with the Gaussian WW approximation. This difference can be understood qualitatively, from the much smaller values of $k_{\perp\gamma}$ contributing to production in the case of the Photon TMD and the resultant change in the values of $x_g$, $k_{\perp g}$ and $x_\gamma$ which contribute for a given $P_T$ and $x_F$.   As is the case for calculations at RHIC energy and kinematics~\cite{Anselmino:2004nk,Godbole:2016tvq}, the asymmetry is suppressed in the backward hemisphere of the proton ($x_F<0$). This is because, in the backward region, the hard-part $d\sigma/d\that$ depends very weakly on the azimuthal angle of the gluon transverse momentum $\phi_{\perp g}$. This weak dependence, along with the $\cos\phi_{\perp g}$ term that is present in the Sivers function (see Eq.~\ref{Sivers}) leads to a suppression when the azimuthal angle is integrated over. The same has been observed in Ref.~\cite{Anselmino:2004nk}. It must be mentioned however, that this feature is energy dependent and the suppression is weaker at lower centre of mass energies. This can be seen from the large values of $|A^\text{max}_N|$ at $x_F\gtrsim0.3$ for COMPASS shown in Fig.~\ref{COMPsatAN}.

\begin{figure}[t]
\begin{center}
\vspace*{-2cm}
\includegraphics[width=\linewidth]{EIC_sidis_combined.pdf}
\vspace*{-2cm}
\caption{SSA from GSF fits of Ref.~\cite{DAlesio:2015fwo} at EIC as a function of $x_F$ (at fixed $P_T$, left panel) and $P_T$ (at fixed $\eta$, right panel).}
\label{EICsidisAN}
\end{center}
\end{figure}

Fig.~\ref{EICsidisAN} shows the asymmetries obtained using the SIDIS1 and SIDIS2 fits~\cite{DAlesio:2015fwo}. As was the case for COMPASS kinematics, both fits give asymmetries much smaller than allowed by the positivity bound, with SIDIS1 giving the larger results of the two. As was found at COMPASS energy, the Photon TMD gives results that are a few percent larger than those obtained using the Gaussian WW approximation.  At fixed $P_T$, in the forward region, SIDIS1 gives a peak asymmetry of 13\% at $x_F=0.4$ and SIDIS2 gives a peak asymmetry of $0.8\%$ at $x_F=0.3$. In the backward region $x_F<0$, $D$ production gets contributions mainly from from $x_g<0.08$, where SIDIS2 is larger than SIDIS1. However the overall values of both fits in this region are very small. Combined with the azimuthal suppression, this makes the asymmetries from both fits almost negligible. At fixed pseudorapidity, SIDIS1 gives a peak asymmetry of around 11.5\% at $P_T=2.5$ GeV and SIDIS2 gives a peak asymmetry of around $0.8\%$ at $P_T=1.6\text{-}2.2$ GeV.

\subsection{Single-Spin Asymmetry in open-charm decay muons}

So far we have considered the SSA in terms of the $D$-meson kinematics. It would also be interesting to consider the SSA in terms of the kinematics of the decay muons. A detector such as the proposed ePHENIX~\cite{Adare:2014aaa} would be able to study open heavy flavour production through the leptonic decay channels. With this in mind, we consider the semileptonic decay of the $D$'s in order to obtain the SSA for the decay muons, ${A^\mu_N}$,
\begin{equation}
A^\mu_N=\frac{d\sigma^{P^\uparrow l\to D+X\to\mu+X'}-d\sigma^{P^\downarrow l\to D+X\to\mu+X'}}{d\sigma^{P^\uparrow l\to D+X\to\mu+X'}+d\sigma^{P^\downarrow l\to D+X\to\mu+X'}}
\end{equation}
where $d\sigma^{P~l\to D+X\to\mu+X'}$ is the Lorentz-invariant inclusive decay-muon cross-section,
\begin{equation*}
d\sigma^{P~l\to D+X\to\mu+X'} 	\equiv E_\mu \frac{d\sigma^{P~l\to D+X\to\mu+X'}}{d^3\mbox{\boldmath $p$}_\mu}.
\end{equation*}
In keeping with the conventions for the $D$-meson asymmetry defined in Eq~1, we take the muon to be produced in the $xz$ plane with the proton moving along the $+z$ direction and its spin parallel or antiparallel to the $y$-axis. Using the narrow width approximation, the expression for the Lorentz-invariant decay-muon cross-section can be written for a general $n$-body decay channel as follows:
\begin{eqnarray}
\hspace*{-0.2
cm}
E_\mu \frac{d\sigma^{P~l\to D+X\to\mu+X'}}{d^3\mbox{\boldmath $p$}_\mu}&=&\int\frac{d^3\mbox{\boldmath $p$}_D}{E_D}\left( E_D\frac{d^3\sigma^{P~l\to D+X}}{d^3\mbox{\boldmath $p$}_D}\right)\frac{1}{2(2\pi)^3 E_D~\Gamma^\text{total}}\left(\prod_{i=1}^{n-1}\frac{d^3\mbox{\boldmath $p$}_{x_i}}{(2\pi)^32E_{x_i}}\right)\\  \nonumber
&&\hspace*{-4cm}\times|\mathcal{M}^{D^0\to \mu^++x_1+...+x_{n-1}}|^2(2\pi)^4\delta^4\left(P_D-P_\mu-\sum P_{x_i}\right)\times \text{BR}
\label{woo}
\end{eqnarray}
where the $x_i$ are the $n-1$ decay products produced along with the muon. $\Gamma^\text{total}$ is the total decay width of the $D$-meson and BR stands for the branching ratio for the considered $n$-body decay channel. The above expression consists of the meson production cross-section, the decay matrix element and a phase-space integral over all the decay products except the muon. It makes use of the fact that the decay of a scalar meson can be treated as independent of its production, allowing a factorised form involving the meson cross-section convoluted with the differential decay rate. This can be shown to be true by using the narrow width approximation.

To account for all possible open-charmed meson decays in to muons through all possible channels would be a complex task. To simplify things, we make the following assumptions: First, we consider only the decay of the $D^0$ to muons. Muons can also be produced through the decay of other charmed mesons states but we do not consider those decays here. For the $D^0$ we consider the two major semileptonic decay channels, $D^0\to K^-\mu^+\nu_\mu$ which as a branching ratio of 3.33\% and $D^0\to K^*(892)^-\mu^+\nu_\mu$ which has a branching ratio of 1.92\%. Second, in the calculation of the three-body decays, we set the decay matrix elements $|\mathcal{M}^{D^0\to K^-\mu^+\bar\nu_\mu}|$ and $|\mathcal{M}^{D^0\to K^{*-}\mu^+\bar\nu_\mu}|$ to 1, and only account for the phase-space kinematics. In Eq.~\ref{woo}, the momentum  $\mbox{\boldmath $p$}_D$ must be integrated over the entire region of phase-space from which a $D$-meson can decay to produce a muon of given momentum $\mbox{\boldmath $p$}_\mu$. The derivation of the closed form expression for decay-muon invariant cross-section, $E_\mu \frac{d\sigma^{P~l\to D+X\to\mu+X'}}{d^3\mbox{\boldmath $p$}_\mu}$ and the integration limits for the momentum of the $D$-meson, $\mbox{\boldmath $p$}_D$ is given in Appendix B.

\begin{figure}[t]
\begin{center}
\vspace*{-2cm}
\includegraphics[width=1.05\linewidth]{EIC_inclusive_muon_combined.pdf}
\vspace*{-2cm}
\caption{Cross-section (left panel) and SSA (right panel) for decay-muons.}
\label{EICsatANdecay}
\end{center}
\end{figure}

The results for the decay-muon invariant cross-section and SSA, $A^\mu_N$ are presented in Fig.~\ref{EICsatANdecay}. The asymmetry is shown for the case of the saturated GSF and the SIDIS1 and SIDIS2~\cite{DAlesio:2015fwo} fits. $A^\mu_N$ is presented as a function of ${x_F}_\mu\equiv 2{P_L}_\mu/\sqrt{s}$, with the muon transverse momentum ${P_T}_\mu=1.5$ GeV. It appears that an azimuthal anisotropy in $D$ production would be retained significantly in the decay-muons. The general dependence of the $A^\mu_N$ on ${x_F}_\mu$ is similar to the dependence of the $D$-meson SSA on $x_F$. As with the $D$-meson,  the muon SSA is also suppressed in the backward hemisphere. Peak values of the $A^\mu_N$ are close to those obtained for the meson: With the Gaussian WW approximation and SIDIS1 GSF, $A^\mu_N$  has a peak value of 11\% at ${x_F}_\mu=0.3$ whereas $A_N$ has a peak value of almost 12\% at $x_F=0.4$. With the SIDIS2 GSF, $A^\mu_N$ has a peak value of 0.75\% at ${x_F}_\mu=0.23$ whereas $A_N$ has a peak value of 0.8\% at $x_F=0.3$.

\section{Conclusions}

In this work, we have presented results for SSA in the low-virtuality leptoproduction of open-charm at both COMPASS and a future Electron-Ion Collider. We find that an asymmetry of upto around 25\% is allowed by the saturated gluon Sivers function at both COMPASS and EIC. We also find that, for EIC kinematics, the asymmetry is significantly retained in the distribution of the decay muons. In calculating the asymmetry we used two different forms for the TMD distribution of quasi-real photons in the lepton. The first was the Weizsacker-Williams distribution with a Gaussian transverse-momentum spread (Gaussian WW) and the second was the LO analytical result for the TMD distribution of photons in a lepton (Photon TMD) from Ref.~\cite{Bacchetta:2015qka}. At COMPASS energy the two forms give similar results, whereas at EIC energy, the Photon TMD gives slightly larger asymmetries in the forward region. The differences in the result for the two distributions can be attributed to the interplay of different $k_{\perp\gamma}$, $x_\gamma$, $x_g$ and and ${k}_{\perp g}$ values that get sampled in the two cases for a given value of $x_F$/$\eta$ and $P_T$.

The two GSF fits of Ref.~\cite{DAlesio:2015fwo} for which we give predictions, were extracted from data on midrapidity pion production at RHIC. As mentioned earlier, the two differ in the flavour structure of the QSFs used as well as the light quark fragmentation functions used in the extraction. SIDIS1 was obtained using an extraction of the QSFs~\cite{Anselmino:2005ea} that included only the $u$ and $d$ flavours and used fragmentation functions by Kretzer~\cite{Kretzer:2000yf}. SIDIS2 was obtained using an extraction of the QSFs that also included sea quarks~\cite{Anselmino:2008sga} and used more recent fragmentation functions by de Florian, Sassot and Stratmann~\cite{deFlorian:2007aj}. While both the GSF fits, taken along with their associated QSF sets, describe the input data on SSA in midrapidity pion production equally well, they have widely differing $x$-dependencies. This indicates that pion production in the midrapidity region at RHIC is only weakly sensitive to the gluon Sivers function.

In this work,  we find that the low-virtuality leptoproduction of open-charm, which probes the gluon content of the proton directly, is able to discriminate well between these two fits. Thus we see that this process offers a good probe of the gluon Sivers function and can be of help in a global extraction of the Sivers function in a generalised parton model framework. In general, at COMPASS and in the forward region of EIC, SIDIS2 gives small, but non-negligible asymmetry predictions on the level of significant fractions of a percent, whereas SIDIS1 predicts larger asymmetries of the order of a few percent.  This indicates that the leptoproduction of open-charm could be a vital probe in constraining the gluon Sivers function, and also in testing the validity of the GPM framework.

\section{Acknowledgements}

R.M.G. wishes to acknowledge support from the Department of Science and
Technology, India under Grant No. SR/S2/JCB-64/2007 under the J.C. Bose Fellowship scheme.  A.M would like to thank the Department of Science and Technology, India for financial support under Grant No.EMR/2014/0000486. A.M would also like to thank the Theory Division, CERN, Switzerland for their kind hospitality.

\section{Appendix}
\subsection{Treatment of GPM kinematics}
In this work, we have considered inclusive single-particle leptoproduction in the low virtuality regime. This allows us to handle the process in terms of a TMD distribution of quasi-real photons in a lepton, not unlike a TMD distribution of partons in a hadron. The treatment of parton kinematics here is thus similar to the treatment of transverse-momentum-dependent parton kinematics for inclusive single-particle hadroproduction, which can be found in quite a few places~\cite{Feynman:1977yr,Contogouris:1978kh} including Ref.~\cite{DAlesio:2004eso}, where heavy meson final states have been considered.

 The momenta of the proton, lepton and the $D$-meson can be written in the $p\text{--}l$ centre of mass frame as,
\begin{equation}
 P_P=\frac{\sqrt{s}}{2}(1,0,0,1), P_l=\frac{\sqrt{s}}{2}(1,0,0,-1)\text{ and } P_D=(E_D,P_T,0,P_L)
\end{equation}
where the masses of the proton and lepton have been neglected.

The gluon and the quasi-real photon carry light-cone momentum fractions $x_g=P_g^+/P_P^+$, $x_\gamma=P_\gamma^-/P_l^-$ and transverse momenta $\mathbf{k}_g$ and $\mathbf{k}_\gamma$ respectively. Their momenta are given by,
\begin{eqnarray}
P_g&=x_g\frac{\sqrt{s}}{2}\left(1+\frac{k_{\perp g}^2}{x_g^2 s},\frac{2k_{\perp g}}{x_g\sqrt{s}}\cos\phi_{\perp g},\frac{2k_{\perp g}}{x_g\sqrt{s}}\sin\phi_{\perp g},1-\frac{k_{\perp g}^2}{x_g^2 s}\right)
\\\nonumber
P_\gamma&=x_\gamma\frac{\sqrt{s}}{2}\left(1+\frac{k_{\perp \gamma}^2}{x_\gamma^2 s},\frac{2k_{\perp \gamma}}{x_\gamma\sqrt{s}}\cos\phi_{\perp\gamma},\frac{2k_{\perp \gamma}}{x_\gamma\sqrt{s}}\sin\phi_{\perp\gamma},-1+\frac{k_{\perp \gamma}^2}{x_\gamma^2 s}\right)
\end{eqnarray}
where $\phi_{\perp g}$ and $\phi_{\perp\gamma}$ are the azimuthal angles of gluon and photon transverse momenta.

The heavy quark is produced through photon-gluon fusion $g\gamma\rightarrow c\bar{c}$ and then fragments into the heavy meson. The momentum of the heavy quark is described by $z$, the light-cone momentum fraction of the heavy meson and $\mathbf{k}_D$, the transverse momentum of the meson with respect to direction of heavy quark. In a choice of coordinates where the heavy quark momentum, $p_c$ is along the $z$-axis, the $D$-meson momentum can be written as
\begin{equation}
P_D=(E_D,0,0,|\mathbf{p}_D - \mathbf{k}_D|) +  (0,\mathbf{k}_D)
\end{equation}
where the first term on the right is the component along the heavy quark direction and the second term is the component transverse to it. Here, $\mathbf{k}_D$ is simply $(k_{D_x},k_{D_y},0)=(\mathbf{k}_{D_\perp},0)$. In the lab coordinates however, $\mathbf{k}_D$ can have all three components non-zero and is specified as,
\begin{equation}
\mathbf{k}_D=k_D(\sin\theta\cos\phi,\sin\theta\sin\phi,\cos\theta) \text{, with } |\mathbf{k}_D|=|\mathbf{k}_{D_\perp}|
\end{equation}
and the orthogonality condition $\mathbf{k}_D.\mathbf{p}_c=0$ ensures that $\mathbf{k}_D$ lies in a plane perpendicular to $\mathbf{p}_c$. The light-cone momentum fraction $z$ is given by,
\begin{equation}
z=\frac{P_D^+}{P_c^+}=\frac{E_D+|\mathbf{p}_D-\mathbf{k}_D|}{E_c+|\mathbf{p}_c|}=\frac{E_D+\sqrt{\mathbf{p}_D^2-\mathbf{k}_D^2}}{E_c+\sqrt{E_c^2-m_c^2}}
\label{light-cone-z}
\end{equation}
This gives us the expression for the energy of the heavy quark,
\begin{equation}
E_c=\frac{m_c^2+\left((E_D+\sqrt{\mathbf{p}_D^2-\mathbf{k}_D^2})/z\right)^2}{2\left((E_D+\sqrt{\mathbf{p}_D^2-\mathbf{k}_D^2})/z\right)}.
\label{energy-relation}
\end{equation}
The expression for $\mathbf{p}_c$ can be obtained from the fact that it is collinear with $\mathbf{p}_D - \mathbf{k}_D$ and that the unit vector constructed out of both must therefore be equal,
\begin{equation}
\mathbf{p}_c=\sqrt{E_c^2-m_c^2}\frac{\mathbf{p}_D-\mathbf{k}_D}{|\mathbf{p}_D-\mathbf{k}_D|}.
\label{momentum-relation}
\end{equation}
Eqs. \ref{energy-relation} and \ref{momentum-relation} relate the energy and momentum of the observed $D$-meson with that of the fragmenting heavy quark for given values of $k_D$ and $z$.

The term $d^3 \mathbf{k}_D \,
\delta (\mathbf{k}_D \cdot \hat{\mathbf{p}}_c)$ in Eqs. (\ref{denominator}) and (\ref{numerator}) ensures that the $\mathbf{k}_D$ integration is only over momenta transverse to the fragmenting parton:
\begin{equation}
d^2\mathbf{k}_{D_\perp}=d^3 \mathbf{k}_D \,
\delta (\mathbf{k}_D \cdot \hat{\mathbf{p}}_c)=dk_D\text{ }k_D\text{ }d\theta \text{ }d\phi\frac{|\mathbf{p}_D-\mathbf{k}_D|}{P_T\sin\phi_1}\left[\delta(\phi-\phi_1)+\delta(\phi-(2\pi-\phi_1))\right]
\end{equation}
where,
\begin{equation}
\cos \phi_1=\frac{k_D-P_L\cos\theta}{P_T\sin\theta}
\end{equation}
Limits on $k_D$ can be obtained by requiring $|\cos \phi_1|\leq1$,
\begin{equation}
\text{max}\left[P_L\cos\theta-P_T\sin\theta,0\right]\leq k_D\leq\text{max}\left[P_L\cos\theta+P_T\sin\theta,0\right].
\end{equation}

Furthermore, the inclusion of intrinsic transverse momenta in the kinematics calls for the following constraints: a) the energy of the incoming parton should not be greater than that of its parent particle, $E_{g(\gamma)}\leq E_{p(l)}$ and, b) the energy of the $D$-meson should not be greater than the energy of the heavy quark $E_D\leq E_c$. The first leads to the following bound on the transverse momenta of the incoming partons,
\begin{equation}
k_{\perp g(\gamma)}<\sqrt{s}~\min[x_{g(\gamma)}, \sqrt{x_{g(\gamma)}(1-x_{g(\gamma)})}].
\end{equation}
The second constraint, $E_D\leq E_c$ is inherently fulfilled by Eq.~\ref{energy-relation}. However, this alone does not ensure that the heavy quark is more energetic than the $D$-meson in the photon-gluon c.o.m frame.  By demanding $E_c>E_D$ in the $\gamma\text{--}g$ c.o.m frame, we get a lower bound on $\hat{s}$,
\begin{equation}
\hat{s}\geq2P_D.(P_\gamma+P_g).
\end{equation}
In our earlier work on open charm production (Ref.~\cite {Godbole:2016tvq}) we had not implemented this bound in our calculations. We find that the inclusion of this bound significantly improves the convergence of the integral  in the close vincinity of $x_F=0$.

\subsection{Derivation of Lorentz-invariant decay-muon cross-section}
With the decay matrix element set to unity, the three body decay width can be written as follows,
\begin{eqnarray}
\Gamma(D\to x_1,x_ 2, \mu)=\frac{1}{2m_D}\frac{1}{(2\pi)^5}\int\frac{d^3\mbox{\boldmath $p$}_\mu}{2E_\mu}~\pi\left(\frac{s-m_{x_1}^2}{s}\right)
\label{diff}
\end{eqnarray}
where $s=(p_{x_1}+p_{x_2})^2=(p_D-p_\mu)^2$ is a Lorentz-invariant quantity. Here, $x_1$ and $x_2$ are the decay products produced along with the $\mu$. We take $x_1$ to be $K^-$ or $K^{*-}$ and $x_2$ to be $\bar\nu_\mu$. Here we consider the muon to be massless. Since we know the decay factorises, we can write the production and decay as a convolution,
\begin{equation}
\sigma^{P~l\to D+X\to\mu+X'}=\int d\sigma^{P~l\to D+X}\ast\frac{d\Gamma}{\Gamma^\text{total}}\times\text{BR}
\end{equation}
where $d\Gamma$ is the decay-width for an infinitesimal muon momentum region $d^3\mbox{\boldmath $p$}_\mu$. Then using Eq.~\ref{diff} we finally have,
\begin{equation}
E_\mu \frac{d\sigma^{P~l\to D+X\to\mu+X'}}{d^3\mbox{\boldmath $p$}_\mu}=\int\frac{d^3\mbox{\boldmath $p$}_D}{E_D}\left( E_D\frac{d^3\sigma^{P~l\to D+X}}{d^3\mbox{\boldmath $p$}_D}\right)\frac{\pi}{4E_D(2\pi)^5}\times\left(\frac{s-m_1^2}{s}\right)\frac{1}{\Gamma^\text{total}}\times\text{BR}.
\end{equation}

The allowed phase-space region for $\mbox{\boldmath $p$}_D$ can be obtained determined by considering the decay in the rest frame of the $D$-meson. In it, one can see that the allowed values of muon energy lie in the range $0<E^\text{D com}_\mu<(m_D^2-m_K^2)/2m_D$, where $m_K$ is the mass of the kaon. This constraint on the muon energy in the rest frame of the $D$, can be translated into the following constraint on the the Lorentz-invariant quantity constructed from the $D$-meson and muon four-momenta:
\begin{equation}
m_K^2\leq s=(P_D-P_\mu)^2\leq m_D^2
\label{ineq}
\end{equation}
The expression for $s$ in terms of the momenta involved is,
\begin{eqnarray}
s=(P_D-P_\mu)^2=(E_D-E_\mu)^2-P_T^2-P_{T\mu}^2+2P_T P_{T\mu} \cos\phi_{P_T}-(P_L-P_{L\mu})^2
\label{sexp}
\end{eqnarray}
where we have assumed that the muon is massless and is in the $xz$-plane, $\vec{P}_{T\mu}=(P_{T\mu},0)$. Here $P_{T\mu}$ and $P_{L\mu}$ are the $x$ and $z$ components of the muon momentum respectively. The lower inequality in Eq.~\ref{ineq} can be cast as follows:
\begin{equation}
\cos\phi_{P_T} \geq \frac{2(E_D E_\mu-P_LP_{L\mu})-(m_D^2-m_K^2)}{2P_TP_{T\mu}} (\equiv Y).
\end{equation}
We will call the quantity on the right hand side of the above expression, $Y$. This gives us a constraint on the angle of the $D$-meson transverse momentum,
\begin{equation}
-\cos^{-1}Y\leq\phi_{P_T}\leq\cos^{-1}Y
\end{equation}
Naturally, we also require $Y\leq 1$, since the lower bound on a cosine term can't be greater than 1. Demanding this gives us upper and lower limits on $P_L$:
\begin{eqnarray}
P_L^\text{max}&=&\frac{1}{2P_{T\mu}^2}[P_{L\mu}(m_D^2-m_K^2+2P_TP_{T\mu})  \nonumber \\
&+&
\sqrt{
E_\mu^2 \left(
(m_D^2-m_K^2)^2+2P_{T\mu}(P_T(m_D^2-2m_K^2)-m_D^2P_{T\mu})
\right)
}
]
\end{eqnarray}
\begin{eqnarray}
P_L^\text{min}&=&\frac{1}{2P_{T\mu}^2}[P_{L\mu}(m_D^2-m_K^2+2P_TP_{T\mu})  \nonumber \\
&-&
\sqrt{
E_\mu^2 \left(
(m_D^2-m_K^2)^2+2P_{T\mu}(P_T(m_D^2-2m_K^2)-m_D^2P_{T\mu})
\right)
}
]
\end{eqnarray}
Demanding $Y\leq 1$ also gives us a lower bound on $P_T$:
\begin{equation}
P_T^\text{min}=\max[0,\frac{4m_D^2P_{T\mu}^2-(m_D^2-m_K^2)^2}{4(m_D^2-m_K^2)P_{T\mu}}]
\end{equation}

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