This training and consultancy activity helps member states of the European Union and the European Centre for Modern Languages (ECML) of the Council of Europe ensure access to quality education and helps bridge the attainment gap between these learners and non-migrant pupils. The initiative draws on a wide range of successful ECML projects and resources which focus on inclusive, plurilingual and intercultural approaches. The workshops offer tailored support to different educational stakeholders, including teachers, teacher educators, administrators and school leaders, on how best to develop learners' competences in the language/s of schooling, whilst valuing all children's home languages and drawing on these languages as a rich resource for learning.
The workshops will offer support on how to value children's home languages as well as on how to draw on these languages as a rich resource for learning.
The long-term objective of the initiative is that learners with a migrant background are better integrated into national education systems, leading to better educational achievement, which in turn will contribute to improved self-esteem, better employment prospects and a more cohesive society.
Support materials will be developed and adapted, by drawing on key ECML tools and resources, to meet the needs of specific contexts.
a dedicated section on the ECML website outlining key resources for multilingual classrooms.
Training activites can be conducted in English, French or German.
Online Seminar 2017: "Supporting multilingual classrooms"
"Teachers and school leaders from 12 different schools from all over Portugal attended the Council of Europe workshop Supporting Multilingual Classrooms (SMC) on 21 and 22 February 2019. The Lisbon workshop, part of a series being held in a number of member states, has been hosted by the Ministry of Education (DGAE).
During the last years the number of multilingual classes in Portugal has increased continuously. Some of the teachers attending the workshop come from schools where up to 50% of the student population speak at least one language other than Portuguese at home.
At the workshop, participants explored tools that support both second language development and the promotion of a better understanding of learners' specific needs. Creating an inclusive school environment in which all languages, including all home languages, are valued was an important theme. Participants discussed how multilingualism in their schools can become an asset, and how a whole school approach to supporting it can be developed.
This intercultural approach examines how learners' home languages and cultures can be taken account of when planning classes, how links can be established between home languages and the language of schooling, and how the knowledge and experience that learners, parents and community groups bring to Portuguese education and society can be harnessed.
At the end of the workshop the 12 participating schools decided, supported by the representatives of the Ministry of Education (DGAE), to build a network for mutual support. All tools and materials from the workshop will be used in the participating schools. In this way the workshop results can contribute to the teaching and learning of languages in Portuguese schools.
ECML project website: Supporting multilingual classrooms – EU-ECML cooperation agreement 2018-2019 "Innovative methodologies and assessment in language learning"
That the ECML experts were willing and able to adapt the type of workshop and inputs they led at the events in Scotland made a huge difference in terms of encouraging teachers to attend, as we currently have a national shortage of teachers and difficulty in finding supply teachers. In order that as many teachers as possible could attend, the experts tailored their inputs into two x 1 day events, the second day a repeat of the first.
Despite the challenge of truncating a two-day workshop, the team put together a highly effective, engaging and impressive event which received 100% positive feedback from the participants.
As an observer of each day's proceedings, I saw how engaged the teachers were throughout each day; they appreciated the opportunity to share practice , as well as learn about methodologies to enhance their own pedagogy. There is possibly a gap in provision in Scotland of relevant, up-to-date training for teachers who are tasked with integrating learners with limited or no English into their classrooms, as well as training which equips teachers with approaches on how to ensure that migrant children's home language(s) are recognised and respected. This ECML workshop has helped to open up a debate on how we provide support for our school-age 'New Scots'.
The ECML experts were knowledgeable, approachable and highly professional - they thoroughly deserve the very positive feedback they have received from the Scottish participants!
ECML project website: Supporting multilingual classrooms – EU-ECML cooperation agreement 2017-2018 "Innovative methodologies and assessment in language learning"
ECML colloquium "Teacher education for linguistic diversity: the contribution of the ECML" (Graz, Austria, 13-14 December 2017) – Register online now!
With the increasingly diverse linguistic and cultural composition of classrooms around Europe, this topic has become a central issue in language education.
This one and a half day event will bring together several renowned experts in the field of pluralistic and pluricultural approaches to discuss progress that has been made in this field in recent years, giving special emphasis to how projects initiated under the auspices of the ECML have supported the development and expansion of this important area.
The event takes place in cooperation with the European Commission, within the framework of the EC-ECML "Innovative methodologies and assessment in language learning" joint action and in particular its "Supporting multilingual classrooms" initiative.
Costs: no attendance fee; participants will be expected to cover their own travel and subsistence costs.
Registration: 50 places in total will be available and these will be allotted strictly on a first-come, first-served basis.
Linguistic and cultural diversity is now the norm in European classrooms. What does this mean for teachers, both language teachers and teachers of other subjects? How can teachers adapt their methodology to ensure that this linguistic and cultural capital becomes a rich resource for learning? This seminar aimed to encourage teachers to question their own beliefs as they discover for themselves the answers to these questions and the wide range of free resources developed by the European Centre for Modern Languages of the Council of Europe (ECML) in support of an inclusive, plurilingual and intercultural approach to teaching and learning.
A recording of the seminar involving Sarah Breslin, Executive Director of the ECML, and Terry Lamb, Co-coordinator of the ECML-EC Training and consultancy activity "Supporting multilingual classrooms" is now available on YouTube.


View all the upcoming Weddings events taking place throughout Renfrewshire below or use the calendar to find events taking place on a specific month or date.
Braw Brides return to Saint Lukes on Monday 29th April with their Wedding Band Showcase to help you plan your perfect big day!
Join Carbon Copy at Blackfriars in Glasgow's Merchant City for some live music, a chat and a complimentary glass of fizz or soft drink at their free wedding showcase!
Bohemia return to the West End with their Fairytale Bespoke Vintage Wedding Fair at the Hilton Grosvenor on Sunday 15th September!
The Ayrshire Wedding Exhibition on Sunday 29th September will give you the opportunity to meet some of Ayrshire's finest wedding suppliers all under one roof at Trump Turnberry!


text:
Is the Orion Nebula as fiery as it looks?
by Gemma Lavender, 19 May 2014
The temperatures in this cradle of young stars might surprise you
This shot of the Orion Nebula, captured by the NASA/ESA's Hubble Space Telescope is one of the most detailed astronomical images ever produced
It's a winter sky gem for many amateur astronomers and the go-to target for the naked eye, binoculars and telescopes. Located some 1,344 light years away in the constellation of Orion, the Orion Nebula (M42) is a place where stars are born, a stellar nursery displayed in great volumes of gas and dust, clutching its young open star cluster – the Trapezium – to its heart.
The dramatic new image, captured by the European Southern Observatory-operated Atacama Pathfinder Experiment (APEX) in Chile, is a shot of this stunning diffuse nebula that's seldom seen: a fiery ribbon, glowing in a hue of oranges plays up the light coming from grains of interstellar dust.
You would be forgiven in thinking that this region, which can be seen extending from the luminous centre of M42, is a place of high temperatures but this shot – revealed in a submillimetre-wavelength glow and showing light that's undetectable to the human eye – is a very cold place. In fact, the hottest places in the nebula sizzle in an icy blue.
Swathes of dust have been manipulated by strong stellar winds, blown out by the atmosphere of the nebula's stars and giving the clouds their shape. These wavelengths have allowed astronomers to discover unusual objects lurking in this region of the universe, including fifteen protostars – an early phase in star formation – which pop out as brilliant points of light.
Image Credit: ESO
Tags: APEX, Atacama Pathfinder Experiment, Dust, ESO, gas, Icy Blue, M42, Nebula, Orion, Protostars, stars, Trapezium

redpajama_set_name: RedPajamaCommonCrawl


More Than a Walk on the Beach is a plainspoken and frank account of life as a U.S. Ambassador living abroad.
The unlikely (note the connection to Krista and Mary's co-authored book) journey begins when President George W. Bush phones Krista's mom, Mary E. Kramer, former President of the Iowa Senate, to invite her to serve as the U.S. Ambassador to Barbados and the Eastern Caribbean. The story unveils the process a U.S. diplomat must go through, as well as Mary's opinions on that lengthy – and sometimes frustrating – road to ambassadorship.
Along the way, Mary relates her often humorous and entertaining experiences in dealing with dignitaries, foreign cultures, and the U.S. Government. More importantly, through her firsthand accounts of personal distress after witnessing the aftermath of Hurricane Ivan, to the delicate balancing act needed in order to maintain foreign relations, Mary shares her guiding wisdom, common sense and inspiration to a sometimes chaotic profession.
Connect with us to buy your personally signed copy/copies.


This has been a record-breaking opening month for entries in our third annual Travel Story Competition. If you haven't read them all yet, please take a few minutes to catch up with the entries here.
It is a real pleasure to welcome our latest entrant, Alison Ripley Cubitt, who is another newcomer to our travel writing competitions. I'm sure you will really enjoy her story Snakes on a Plane, which you can read here.
Alison Ripley Cubitt is a multi-genre author who co-writes thrillers (with Sean Cubitt) as Lambert Nagle. She loves walking and horsing around in Jane Austen country. For fifteen years she worked in TV production. She wishes she'd heeded the advice about never working with children and animals. One of her jobs at Walt Disney was to chaperone Chip and Dale on a filming trip to Norway. The chipmunks behaved so badly on tour they ended up on the front page of every national newspaper.
A warm welcome to Angie Clifford, who is a newcomer to our travel writing competitions. In fact, Angie tells me that she's never entered a competition before, so this is a real honour. I hope you enjoy her story Miracle at Lourdes as much as I have. You can read it here.
I married in 1970, aged 19, my only dream at the time was to own my own home, and be a perfect wife. I had not the first clue about life then, however, Jerry and I had some chemistry between us, and with the arrogance of youth I envisaged a wonderful future.
Together, we have four children and five grandchildren, so far! I've tried my hand at many things, including starting my own catering company in my late 40's. I'm a passionate reader, my favourite gender of book being, memoirs, biography, and autobiography. I love to cook, read, write, and swim.
Jerry and I retired to Spain in 2013, and we now spend our retirement gliding seamlessly between those two countries.
Welcome back to Philippa Hawley. You may remember her entry from last year's competition,  'God! Help me stay alive, among this deadly love'. If you missed it you can read it here, before enjoying Philippa's latest entry, Tocca il cielo.
It is wonderful to be able to feature another great travel story entry from Nancy McBride. You may remember that Nancy came second overall in last year's competition with FAIRIES-Do they exist? If you haven't read it yet then you can catch up with her story here, before reading Nancy's new entry AIN'T LION.
Being present to interpret my life and to allow it to "happen" is my shtick. I've travelled. I've fallen. I'm a disaster. I'm a survivor. I've ruminated. I've worked. I've loved. I've raised kids. I blurt art. Life's a story happening.
There are just 7 days left to enter this month's Travel Story competition.
We have already had ten fantastic entries from some amazing authors and writers.
If you want some inspiration read their stories here.
There is a cash prize of $50 for this month's best story. There will also be prizes for the Top 3 featured entries after the overall competition closes at the end of July 2017.
It's time for another treat. Welcome back to Robyn Boswell, whose entry last year Weathering the Storm was widely appreciated. You can catch up with it here.
Enjoy Robyn's new entry A Comedy of Errors in Kuranda here.
I live in the beautiful far north of New Zealand surrounded by beaches and forests. My family have lived here since the earliest days of settlement in New Zealand.
I recently retired and am enjoying a new lease of life. I wanted to travel since I was six and my great aunt worked as a stewardess on cruise ships around the world. I've been lucky enough to spend 13 months travelling in Europe and the UK, 17 trips to the USA, 3 months camping in the Australian Outback and various trips through the South Pacific and Asia. A last I have time to travel again and am enjoying having the time to rediscover my own beautiful country and am looking forward to once again venturing further afield. 30 years after this incident on our 'Aussie Safari', I am soon heading on a cruise which will take me to Cairns and I have pre-booked the train trip to Kuranda – at last!
I have chronicled my trips through scrapbooking and journal writing so my memories are always with me.
A big welcome back to Mike Cavanagh, who was our June winner in last year's Travel Story competition. If you haven't read A Once Upon A Time True Story then check it out here. I hope you enjoy Mike's new story In Control as much as I have. Read it here.
Mike Cavanagh is now in his sixties and has no idea how he got here. He lives with his wife, Julie, and two black cats in Bateman's Bay, NSW. The house he and Julie live in is quirky and in need of regular maintenance, as are its owners. Mike's passions are writing, playing guitar, composing music, and, as Julie will only too readily tell you, playing too many role-playing games on PC.
Amy Bovaird taught English as a Second Language (ESL) abroad and in the United States for many years. She lives with a dual disability—progressive vision and hearing loss due to Usher Syndrome. Amy is an accomplished public speaker on a variety of topics based on her life experiences and continues to educate and inspire others through her writing and speaking.
Amy is the author of Mobility Matters and Cane Confessions: The Lighter Side to Mobility.
She blogs about the challenges she faces as she loses more vision and hearing and manages to find humor around almost every corner.
A very warm welcome to Susan Mellsopp, another newcomer to our travel writing competitions. Thank you so much Susan for your very touching story In Flanders Fields. To read her entry, please click here.
Susan Mellsopp is a recently retired Archivist and accessible transport researcher. She has written all her life but is now able to indulge in her passion full time.
She lives in New Zealand with her retired guide dog Chocolat and working dog Jay. Susan also loves to travel, reads voraciously, enjoys cooking and classical music.
This story is a shorter version of one which was placed highly commended in the Cathay Pacific Travel Media Awards in 2012.
It is a great pleasure to feature the latest entry in our 2017 Travel Story Competition. This story is from well-known author Patricia Steele, who is another newcomer to our travel writing competitions. Many thanks for taking part Patricia.
Patricia's entry is an excerpt from her memoir A Roundabout Passage to Venice and you can read it here.
Patricia says, I'm a west coast girl that moved to the east coast and back again. Twice. My imagination has always been etched in music, color and rose-colored glasses. I've had crazy characters and stories banging and fluttering around in my head, dying to get out, since I was old enough to hold a pen. I'm a fan of historical fiction filled with adventure and romance. And I'm addicted to genealogy! My sense of humor runs a little rampant at times, I'm no stranger to laughter, and I love a good anticipation scene. I am proud to state that The Girl Immigrant, the first novel in my Spanish Pearls Series, is being whisked off my shelves. The second book in the series, Silván Leaves, is now available. My next project is a memoir titled, Fairydust to Daffodils about my daughter and her fight with Cystic Fibrosis.


text:
Home » INSTALL Welcomes New Members to its Floorcovering Network
Breaking Flooring NewsTalkFloor News
INSTALL Welcomes New Members to its Floorcovering Network
KEYWORDS Flooring industry / partnership
International Standards & Training Alliance continues to raise the bar in quality and reliability by offering the flooring industry's most endorsed and specified training program. INSTALL Warranty Contractors (IWCs) and INSTALL Alliance Partners lay the foundation for INSTALL's continued success.
Upon meeting its exacting requirements, INSTALL provides a Warranty on Labor for all carpeting, resilient flooring, wood flooring and floor prep work completed by IWCs, helping to assure clients that every job is professional and yields exceptional results. In addition, INSTALL Alliance Partners work side by side with INSTALL to bring technical expertise and the best product training to the flooring industry. Most recently, INSTALL welcomes three new IWCs and one new Alliance Partner to its organization.
INSTALL Warranty Contractor (IWC)
Becoming an INSTALL Warranty Contractor (IWC) is the highest level of certification offered by INSTALL, which provides an additional, extended, free, non-proprietary and third-party installation warranty to every job completed by the contractor.
Three impressive companies will join the IWC network. Each company had to be nominated and complete a rigorous review to achieve this status. These new IWCs must maintain financial reliability, an impressive performance history and employ only floorcovering mechanics that have earned INSTALL certifications carpet, resilient, substrate preparation or hardwood.
- Integrity Interiors, Inc.: As a service-oriented contractor, quality and teamwork are important to Integrity Interiors, Inc. As an IWC, the company continues to build upon those principles by ensuring high-quality, skilled professionals work on all its flooring projects, large or small.
- Flooring Systems, Inc.: Serving clients for 25 years, the company offers all types of commercial flooring for new builds or renovations. They travel and complete projects across the continental U.S. and with commercial offices in Springfield, Kansas City, and St. Louis, MO, they are the leader for carpet reclamation and recycling, having kept over 10 million pounds of carpet out of landfills for more than a decade.
- National Decor Inc.: One of Ottawa, Canada's most experienced commercial flooring contractors, National Decor Inc. stalls carpet tile, broadloom pattern carpet, resilient, thin porcelain tile, sports surfaces, hardwood, rubber and more, while solving flooring challenges for businesses and industries including education, hospitality and healthcare.
Over the last five years, INSTALL has been standing behind every IWC and has underwritten $1 billion in flooring installations without a single claim filed, proving that INSTALL training is vital to the continued success of the industry. The INSTALL warranty is completely free and goes above and beyond the manufacturer's warranty.
New INSTALL Alliance Partner
Becoming an Alliance Partner provides the opportunity to deliver specialized training to installers. This allows installers to be trained in the latest technologies and provides peace of mind to manufacturers that its products will be installed correctly every time. INSTALL is partnered with top mills and manufacturers, including its newest partner Parador.
· Parador: A design industry leader that specializes in large commercial, institutional and multi-unit projects, Parador has a diverse knowledge of premium, sustainable floor coverings made in Europe, including wood, alternative resilient surfaces and more. The company's wood products are free from harmful VOCs and come from third-party-certified plantation forests, allowing for reforestation. Plus, its products meet Europe's GUT certification and are certified under TUV and CRA's NA Green Label Plus.
"INSTALL's alliance, comprised of hundreds of contractors, thousands of flooring installers, and hundreds of flooring manufacturers enables us all to share the common goal of delivering work we can all take pride in," said John T. McGrath Jr., executive director of INSTALL.
INSTALL Inducts Five New Members to its Floorcovering Alliance
INSTALL welcomes seven new members
Decorative Surface Solutions Group Welcomes New Members
CRI Welcomes New Board Members at Annual Meeting; Honors Awards Recipients
National Institute of Certified Floorcovering Inspectors
American Floorcovering Alliance Inc.


In this research, we examine how the number of mobile organic clicks changes when advertisers significantly change their mobile ad spend. This continues the line of research of search ads pause by applying it to the mobile platform. We utilize a statistical model to estimate the fraction of clicks that can be attributed to mobile search advertising. A metastudy of 327 advertisers reveals that 88% of ad clicks are incremental, in the sense that the visits to the advertiser's site would not have occurred without the mobile ad campaigns.


text:
Q: Can we specify maximum absolute GPU memory usage Tensorflow allows to specify the maximum fractional GPU memory used by the process:
import tensorflow as tf
import keras
gpu_options = tf.GPUOptions(per_process_gpu_memory_fraction=0.2)
sess = tf.Session(config=tf.ConfigProto(gpu_options=gpu_options))
keras.backend.set_session(sess)

Using the above, my code ends up consuming around 2203MB/7982MB GPU RAM.
NOTE: 2203MB is more than 20% of 7982.
Now my code ends up executing on various different GPUs at times. And percentage gpu usage doesn't work well across them (since diff GPU has different amount of RAM)
Is there a possibility to specify the maximum GPU memory fraction to be used in absolute terms, instead of relative terms?
Looking for something like (per_process_gpu_memory_inmb:
# Looking for something like `per_process_gpu_memory_inmb` option
gpu_options = tf.GPUOptions(per_process_gpu_memory_inmb=2203)
sess = tf.Session(config=tf.ConfigProto(gpu_options=gpu_options))
keras.backend.set_session(sess)

A: Sure! You can create a virtual GPU device with hard-coded memory size:
gpus = tf.config.experimental.list_physical_devices('GPU')
if gpus:
  # Restrict TensorFlow to only allocate 2203 MB of memory on the first GPU
  try:
    tf.config.experimental.set_virtual_device_configuration(
        gpus[0],
        [tf.config.experimental.VirtualDeviceConfiguration(memory_limit=2203)]) # limit in megabytes
    logical_gpus = tf.config.experimental.list_logical_devices('GPU')
    print(len(gpus), "Physical GPUs,", len(logical_gpus), "Logical GPUs")
  except RuntimeError as e:
    # Virtual devices must be set before GPUs have been initialized
    print(e)

redpajama_set_name: RedPajamaStackExchange


text:
'Deadwood: The Movie' Behind-the-Scenes Video Takes You Back to HBO's Western
Posted on Friday, May 10th, 2019 by Chris Evangelista
Ready to saddle up and head back to Deadwood? After 13 years of waiting, viewers will have the chance to return to HBO's poetically vulgar Western with Deadwood: The Movie. In anticipation of the impending debut, HBO has released a new behind-the-scenes video that checks in with the cast on set, discussing how excited and emotional they all are to slip back into character.
Dead The Movie Behind the Scenes
I don't know about you, but I've been eagerly awaiting my return to Deadwood for more than a decade. It remains one of my all-time-favorite shows – on HBO or any network, for that matter. And while I always held out hope that we'd get to see the wrap-up movie that creator David Milch teased so many years ago, I wasn't holding my breath. As time ticked on, it grew more and more unlikely that the increasingly busy cast could be rounded up to mosey on back to the set.
But the seemingly impossible happened, and practically the entire original cast has returned for Deadwood: The Movie. The above video takes you behind the scenes with the cast. "To be back, more than a decade later, is really just as good as it gets," star Timothy Olyphant says. "This is the best project I've ever been a part of," adds John Hawkes. "To be back here…it's emotional." Emotional is certainly the right word. I'm getting a little teary-eyed just watching this, and realizing I'll be able to spend time with these characters again after so many years.
The movie picks up years ten after the season 3 finale, with the town of Deadwood bracing for South Dakota's impending statehood. "The town's maturing and becoming part of the Union and what that event sets in motion, in a very personal way for the people that it brings in town and what ensues," executive producer Carolyn Strauss said previously. "The toll of time has not just struck Deadwood and the characters, but all the people making it as well." Per the official synopsis, "Former rivalries are reignited, alliances are tested and old wounds reopened as all are left to navigate the inevitable changes that modernity and time have wrought."
Deadwood: The Movie, starring Ian McShane, Timothy Olyphant, Molly Parker, Paula Malcomson, John Hawkes, Anna Gunn, Dayton Callie, Brad Dourif, Robin Weigert, William Sanderson, Kim Dickens, Gerald McRaney, Sean Bridgers, W. Earl Brown and Keone Young, premieres on HBO Friday, May 31. Look for our review soon.
2019 Television Critics Association Awards Love 'Fleabag' Quite a Bit, But HBO Wins Big Too
'Deadwood: The Movie': Molly Parker Talks Alma's Return, Addiction, and David Milch [Interview]
W. Earl Brown Reveals the Backstory Behind that Infamous 'Deadwood' Season 3 Fight [Interview]
Robin Weigert Talks Becoming Calamity Jane, Dealing With Cancellation and Returning for 'Deadwood: The Movie' [Interview]
Behind the Scenes Footage, HBO, Video Clips, Western, deadwood, Deadwood: The Movie


FTC halts another phantom debt collection scheme – San Bernardino American News celebtates 50 Years!
The fraudulent scheme bilked millions of dollars from consumers for debts they did not owe. At the FTC's request, a federal court has temporarily halted the operation and frozen its assets. This action is part of the FTC's continuing crackdown on abusive and phantom debt collectors.
Don't let debt collectors – real or phony – scare you. Know your legal rights, so you can spot when something isn't right. By law, debt collectors have to send you a validation notice in writing, within five days of contacting you. If they don't, that's a red flag. And if a debt collector threatens, harasses or intimidates you to pay a debt, that's illegal, too.
If you, or someone you know, has gotten a suspicious debt collection call, report it to the FTC. We've stopped a lot of bad debt collectors. Help us stop more.


Here is my first attempt to share my own recipe version of an easy PINAKBET!!!
Many of us are not familiar with measurements, so in my recipes I will give basic measurement/sizes (hints) for all of us, and learn from what ingredient (maybe) is lacking or too much.
Step 4 – Add onion until it becomes transparent.
Before hand, I have prepared my chosen meat or poultry or seafood that I would like to mix with this recipe. Often times, pinakbet is mixed with pork or chicken… but in this recipe I chose mixed seafood.
I washed it once or twice and boil it to a hot water, once they are totally boiled I have kept its soup to be used later.
Step 5 – Add the mixed seafood (and a little black pepper), sauté.
Step 6 – Once the seafood is a little cooked, add the mixed vegetables, sauté.
Step 7 – Add the soup of the seafood that we set aside earlier and mix.
Keep it for at least 2-3 minutes.
Step 8 – Add 1 – 2 spoons of shrimp paste to taste.
You may add salt and pepper according to your taste and mix.
Tip : Half cooked vegetables are known to be healthier as many people said… so try not to overcooked them!


text:
\section{Introduction}

The hunt for the Higgs boson is performed with great enthusiasm both
at the Fermilab Tevatron and at the CERN Large Hadron Collider (LHC).
The Higgs boson constitutes the last missing piece in the Standard Model
(SM) of particle physics and could explain the generation of mass terms
in the Lagrange density. The latter is also true in many extensions
of the SM, such as supersymmetry.

In the recent years many higher order corrections to production and
decay of the Higgs boson have been computed.
The leading order (LO) and the next-to-leading order (NLO)
  corrections to the production cross section in gluon fusion
  have been considered in Refs.
  ~\cite{Georgi:1977gs,Djouadi:1991tka,Dawson:1990zj,Spira:1995rr}.
The most recent
computations within the SM that appeared in the end of
2009~\cite{Harlander:2009mq,Pak:2009dg,Harlander:2010my}
describe the Higgs boson production in gluon fusion at the
next-to-next-to-leading order (NNLO) taking the finite top
quark mass into account. An important outcome of these
papers is the justification to use the effective theory (built for
the infinite top quark mass) for the evaluation of the cross
section as it was done in
Refs.~\cite{Harlander:2002wh,Anastasiou:2002yz,Ravindran:2003um}.
As long as one restricts the analysis to the top quark/squark sector
it is suggestive that this conclusion also holds for the Minimal
Supersymmetric Standard Model (MSSM) since the corresponding
calculation would have a similar structure.
At NLO this has been demonstrated in
Refs.~\cite{Harlander:2004tp,Anastasiou:2008rm}. In this paper we
assume that it also holds at NNLO in situation when all
supersymmetric particles are heavier than the top quark.
Note that we explicitly exclude the bottom quark/squark sector from our
consideration since in that case the effective-theory approach as presented
in this paper is not applicable.\footnote{See, e.g.,
Refs.~\cite{Degrassi:2010eu,Harlander:2010wr} where the bottom
quark/squark sector is discussed at NLO in detail.}
Thus, our results only apply to
small and moderate values of $\tan\beta$, the ratio
of the vacuum expectation values of the two Higgs doublets,
where the contribution of the bottom quark/squark sector is numerically negligible.

The supersymmetric NLO correction to the gluon fusion process has
been considered in various papers. In
Refs.~\cite{Harlander:2003bb,Harlander:2004tp} the Higgs boson production cross
section and the decay rate have been computed in the effective theory
framework and thus apply to Higgs boson masses less than about
200~GeV. The results have been confirmed by a (numerical) calculation
in the full theory~\cite{Anastasiou:2008rm} (see also
Refs.~\cite{Degrassi:2008zj,Muhlleitner:2010nm}). It should be mentioned
that the squark contribution has been considered separately in
Refs.~\cite{Bonciani:2007ex,Muhlleitner:2006wx}. Furthermore, an
estimate of the NNLO supersymmetric corrections was presented in
Ref.~\cite{Harlander:2003kf} (see also Ref.~\cite{Harlander:2004tp})
assuming that the NNLO corrections to the
matching coefficient in the MSSM and the SM are numerically of the same order.

In this paper we consider the strong interaction part of the MSSM and evaluate
the total production cross section of an intermediate mass Higgs boson
in the process of gluon fusion. As motivated above, we employ the effective
theory obtained in the formal limit where all supersymmetric particles
and the top quark are infinitely heavy, which leads to the Lagrange density
\begin{eqnarray}
  {\cal L}_{Y,\rm eff} &=& -\frac{\phi^0}{v^0} C_1^0 {\cal O}_1^0
  + {\cal L}_{QCD}^{(5)}
  \,,
  \label{eq::leff}
\end{eqnarray}
with
\begin{eqnarray}
  {\cal O}_1^0 &=& \frac{1}{4} G_{\mu\nu}^0 G^{0,\mu\nu}\,.
\end{eqnarray}
$C_1^0$ is the coefficient function containing the remnant
contributions of the heavy particles and ${\cal O}_1^0$ is the effective
operator. ${\cal L}_{QCD}^{(5)}$ is the QCD Lagrange density
with five active flavours.
In our case $\phi^0$ denotes the light CP-even Higgs
boson of the MSSM. $G_{\mu\nu}^0$ is the gluonic field strength
tensor of the standard five-flavour QCD and the superscript ``0''
indicates bare quantities.  Note that
the renormalization of $\phi^0/v^0$ is of higher order in the
electromagnetic coupling constant.

The renormalization of ${\cal O}_1^0$ is discussed
in detail in Refs.~\cite{Spiridonov:1984br,Chetyrkin:1997un}.
For completeness we reproduce here the renormalization constant
which in the $\overline{\rm MS}$ scheme is given by
\begin{eqnarray}
  {\cal O}_1 = Z_{11}\,{\cal O}_1^0\,,\qquad
  Z_{11} = \left(1 - \frac{\pi}{\alpha_s}\frac{\beta^{(5)}}{\epsilon}\right)^{-1}\,,
  \label{eq::c1ren}
\end{eqnarray}
where $d=4-2\epsilon$ is the space-time dimension and
$\beta^{(5)}=\beta^{(5)}(\alpha_s)$ is the $\beta$ function of the standard
five-flavour QCD with $\beta^{(5)} =
-(\alpha_s^{(5)}/\pi)^2\beta_0^{(5)}+\ldots$
and $\beta_0^{(n_l)}=11/4-n_l/6$.
Since $C_1^0 {\cal O}_1^0 = C_1 {\cal O}_1$, the coefficient
function is renormalized with $1/Z_{11}$.

Following Ref.~\cite{Chetyrkin:1996ke}, we slightly
redefine the coefficient function and the operator in order to have
objects which are separately renormalization group invariant.
Introducing
\begin{eqnarray}
  {\cal O}_g &=& B^{(5)} {\cal O}_1 \,,\nonumber\\
  C_g &=& \frac{1}{B^{(5)}} C_1\,,
  \label{eq::B5}
\end{eqnarray}
with
\begin{eqnarray}
  B^{(5)} &=& -\frac{\pi^2 \beta^{(5)}}{\beta_0^{(5)}\alpha_s^{(5)}}
  \,,
\end{eqnarray}
we may choose independently the ``soft'' and the ``hard''
renormalization scales. Our following analysis of the Higgs
production cross section takes advantage of
those properties of ${\cal O}_g$ and $C_g$.
Note that the LO piece of $C_g$ is not proportional to $\alpha_s$.

In this paper we consider the strongly interacting part of the MSSM and assume
for simplicity the degenerate supersymmetric mass spectrum. The evaluation of
the coefficient functions is performed within Dimensional Reduction
({\tt DRED})~\cite{Siegel:1979wq} where we follow
Refs.~\cite{Harlander:2009mn,Kant:2010tf} for the practical
implementation.

The remainder of the paper is organized as follows: in the following
section we briefly revisit the SM and in particular discuss the effect of
$B^{(5)}$ introduced above. We furthermore evaluate the SM coefficient
function within {\tt DRED} which is a useful preparation for the SUSY
QCD calculation.
Next, in Section~\ref{sec::mssm} we discuss
the three-loop calculation of the MSSM coefficient function
which is used in Section~\ref{sec::xsec} to compute the cross
section to NNLO. Section~\ref{sec::concl} contains the summary and conclusions.

\section{\label{sec::sm}Revisiting the SM}

As mentioned in the Introduction, the gluon fusion process has been discussed
extensively in the literature. The purpose of this section is twofold: on the
one hand we want to discuss the effect of $B^{(5)}$ introduced in
Eq.~(\ref{eq::B5}) on the numerical predictions, on the other hand we
repeat the SM calculation in the framework of {\tt DRED} as a preparation for
the calculation in the supersymmetric theory.

\subsection{Separation of hard and soft scales}

The SM coefficient function expressed in terms of the
on-shell top quark mass and the five-flavour strong coupling
reads\footnote{Here and in the following we suppress the $\mu$-dependence
  of $\alpha_s$. If not stated otherwise we have
  $\alpha_s\equiv\alpha_s(\mu)$. The same is true for the $\overline{\rm DR}$
  mass parameters $m_t$ and $m_{\rm susy}$ introduced in
  Section~\ref{sec::mssm}.}\cite{Chetyrkin:1997un,Steinhauser:2002rq} (see
also Ref.\cite{Kramer:1996iq}):
\begin{eqnarray}
  C_1^{\rm SM} &=& -\frac{1}{3} \frac{\alpha_s^{(5)}}{\pi} \Bigg\{
    1 + \frac{\alpha_s^{(5)}}{\pi} \frac{11}{4}
    \nonumber \\
    &&\mbox{}+ \left(\frac{\alpha_s^{(5)}}{\pi}\right)^2
    \left[\frac{2777}{288} + \frac{19}{16}\ln\frac{\mu^2}{M_t^2}
      + n_l \left(- \frac{67}{96} + \frac{1}{3}\ln\frac{\mu^2}{M_t^2}\right)
      \right]
  \Bigg\}\,,
  \label{eq::C1SM}
\end{eqnarray}
where $n_l=5$ is the number of massless quarks.

In Fig.~\ref{fig::xsecsm}(a) we show the production cross section
$\sigma(pp\to H+X)$ for the LHC with the center-of-mass energy of 14~TeV
at LO, NLO and NNLO for $M_t=173.3$~GeV~\cite{:1900yx},
computed with MSTW08~\cite{Martin:2009iq} parton distribution function (PDF)
set.

The chosen PDFs fix the values of $\alpha_s^{(5)}(M_Z)$ to LO, NLO and NNLO
accuracy used as the starting point in order to obtain the strong
coupling for the other choices of the renormalization scale.
The bands are obtained by varying the renormalization and factorization
scales $\mu_r = \mu_f = \mu$ between $M_H/4$ and
$M_H$~\cite{Anastasiou:2008tj,Grazzini:2010zc}\footnote{For the other
opinions concerning the scale variation see Ref.~\cite{Baglio:2010um}.}
with $\mu=M_H/2$ as central value.
For comparison we present the NNLO result computed with ABKM09
PDFs~\cite{Alekhin:2009ni} (the dashed line). It is remarkable that the
difference in the central values for the different PDFs is comparable to the
uncertainty due to the scale variation.

\begin{figure}[t]
  \centering
  \begin{tabular}{c}
    \includegraphics[width=0.75\linewidth]{figs/sm_mh_lhc.eps}
    \\ (a) \\[-1em]
    \includegraphics[width=0.75\linewidth]{figs/ra_mus_lhc.eps}
    \\ (b)
  \end{tabular}
  \caption[]{\label{fig::xsecsm}
    (a) The SM cross section as a function of $M_H$.
    The LO, NLO, and NNLO results are represented by the lower, middle
    (coarse filling) and the upper bands, respectively. Band width
    is due to simultaneous variation of renormalization and factorization
    scales. The dashed line corresponds to the NNLO prediction using ABKM09.
    (b) Ratio $R=\sigma(\mu_s,M_t)/\sigma(\mu_s,\mu_s)$ for $M_H=120$~GeV
    as a function of $\mu_s$. Dotted, dashed (barely visible) and solid lines
    correspond to LO, NLO and NNLO, respectively.
    }
\end{figure}

The three-loop term of Eq.~(\ref{eq::C1SM}) contains the
logarithm $\ln(\mu^2/M_t^2)$ which can potentially lead to numerically
big effects if the scale $\mu$ assumes very small or very large values.
With the help of $C_g$ and ${\cal O}_g$ introduced in Eq.~(\ref{eq::B5})
we may introduce separate scales $\mu_h$ and $\mu_s$
for the hard and the soft parts of the cross section
$\sigma=\sigma(\mu_s,\mu_h)$. The dangerous logarithms can
then be avoided by choosing $\mu_h \sim M_t$ which is the natural
scale for the coefficient function, and varying $\mu_s$ around $M_H/2$
as done above. Note that for $\mu_s=\mu_h$ the quantity $B^{(5)}$ drops
out of the analysis.

In Fig.~\ref{fig::xsecsm}(b) we plot the ratio
$R=\sigma(\mu_s,M_t)/\sigma(\mu_s,\mu_s)$ for $M_H=120$~GeV.
In the numerator the hard scale is kept fixed while in
the denominator we use the common
approach~\cite{Harlander:2002wh,Anastasiou:2002yz,Ravindran:2003um}
and identify the scales as in Fig.~\ref{fig::xsecsm}(a).
At LO $R=1$ by construction. The NLO corrections (dashed curve which is hardly
visible) are quite small and amount to less than $\pm 2\%$ which is only
slightly modified after inclusion of the NNLO results (solid line).
From these considerations we conclude that the resummation of
$\ln(\mu^2/M_t^2)$ terms has only a small numerical effect.
On the other hand, the framework of
Eq.~(\ref{eq::B5}) is quite useful in the context of supersymmetric
corrections discussed below since it allows to fix the hard scale $\mu_h$
and vary $\mu_s$.

\subsection{\label{sub::SMDRED}$C_1^{\rm SM}$ in {\tt DRED}}

Whereas {\tt DRED} is the preferable framework for the two- and three-loop
calculations in a supersymmetric theory, in the SM the application of {\tt DRED}
introduces several so-called evanescent couplings which can make practical
calculations quite tedious. This has been discussed extensively in the
literature (see, e.g.,
Refs.~\cite{Jack:1993ws,Jack:1994bn,Harlander:2006rj,Harlander:2006xq,Jack:2007ni}).
Nevertheless, for our purpose it is useful to evaluate the QCD corrections to
the matching coefficient using {\tt DRED} since there are several new features
which also apply to the MSSM.

We implement {\tt DRED} with the help of the so-called $\varepsilon$
scalars. They have mass dimension $(4-d)$ and complement the
$d$-dimensional gluon field so that the gauge fields and the fermions
have exactly four degrees of freedom.
In a practical calculation the $\varepsilon$ scalars induce new Feynman
rules (see, e.g., Ref.~\cite{Kant:2009zza})
which (in non-supersymmetric theories) involve new couplings
that have to be renormalized independently from the gauge coupling.

In our matching calculation it is convenient to define $C_1^{\rm SM}$
in such a way that the effective theory is
built from the five-flavour QCD fields regularized with {\tt DREG}. As a consequence,
we have to integrate the $\varepsilon$ scalar field out together with the top
quark in order to guarantee the transition from {\tt DRED} to {\tt DREG} in
the matching procedure.
This means that formally $M_\varepsilon\not=0$ and even
$M_\varepsilon\gg M_H$ since the latter is identical to zero for the matching
calculation. In the end, we take the limit $M_\varepsilon\to 0$ in agreement with
our renormalization condition (see below).

We evaluate the matching coefficient in the limit
$M_t\gg M_\varepsilon\not=0$ and apply the rules of asymptotic expansion together
with a naive expansion in the external momenta in order to project out the
Lorentz structure of the Higgs-gluon-gluon vertex (see the following section for
details).
Consequently, there are (sub-)diagrams which contain only
$\varepsilon$ scalars as massive particles.
Due to the dimension of the underlying integrals they lead to
terms proportional to $M_\varepsilon^{-2}$ and $M_\varepsilon^{-4}$
in the sum of the bare diagrams. Thus it is
necessary to keep positive powers in $M_\varepsilon$ in counterterms
entering the calculation.

The top quark mass and the strong coupling need to be renormalized
at two-loop order. Furthermore, one has to make sure
that the external gluon fields of the full and the effective theory
Green functions are identical.
There are two operators involved in the renormalization procedure which
deserve additional attention: the $\varepsilon$-scalar mass and the
coupling of the Higgs boson to $\varepsilon$ scalars. The corresponding
part of the Lagrange density is
\begin{eqnarray}
  {\cal L}_\varepsilon &=&
  -\frac{1}{2}\left(M_\varepsilon^0\right)^2 \varepsilon^{0,a}_\sigma\varepsilon^{0,a}_\sigma
  - \frac{\phi^0}{v^0} \left(\Lambda_\varepsilon^0\right)^2
  \varepsilon^{0,a}_\sigma\varepsilon^{0,a}_\sigma
  + \ldots
  \,.
  \label{eq::Lep}
\end{eqnarray}
As mentioned above, we keep $M_\varepsilon \ne 0$ for the
matching procedure, however, in the final expression for $C_1^{\rm SM}$ we
require that the on-shell $M_\varepsilon$ vanishes.
This leads to the well-known counterterm
(see, e.g., Refs.~\cite{Marquard:2007uj,Kant:2010tf})
which we need to one-loop accuracy. For our purposes we have to
keep the terms proportional to $M_\varepsilon^2$ and restore
the dependence on all evanescent couplings.

The second term in Eq.~(\ref{eq::Lep}) is
not present at tree-level, however, quantum corrections induce such a
structure~\cite{Anastasiou:2008rm}. We require that the
renormalized parameter $\Lambda_\varepsilon$ vanishes since we
want to avoid a non-zero coupling between the Higgs boson and the
unphysical $\varepsilon$ scalars. As a consequence of this condition,
we have to introduce
a non-zero bare coupling of the Higgs boson to $\varepsilon$ scalars.
Furthermore, in the counterterm contribution to
$\Lambda_\varepsilon$ we only have to keep terms not
proportional to $\Lambda_\varepsilon$.
We refrain from listing the explicit results which become
quite lengthy due to the evanescent couplings.

It is an important check of our calculation that the
negative powers in $M_\varepsilon$ cancel after
the renormalization of $\Lambda_\varepsilon$ and $M_\varepsilon$.

Our final result for the coefficient function reads:
\begin{align}
 C_1^{\overline{\text{DR}}}=& -\frac{\alpha_s^{\overline{\text{DR}}}}{3\pi}\Bigg\{
   1
  +\frac{\alpha_s^{\overline{\text{DR}}}}{\pi} \bigg(
          \frac{5}{2}
         -\frac{1}{6}l_t
   \bigg)
  +\frac{\alpha_s^{\overline{\text{DR}}}\alpha_e}{\pi^2}\bigg(
       \frac{7}{36}
      +n_l\frac{1}{12}
   \bigg)\nonumber\\
  & +\left(\frac{\alpha_s^{\overline{\text{DR}}}}{\pi}\right)^2\Bigg[
      \frac{2065}{288}
      -\frac{5}{48} l_t
      +\frac{1}{36}l_t^2
      -n_l\bigg(
      \frac{67}{96}
     -\frac{1}{3}l_t
   \bigg)
   \Bigg]
  \Bigg\}
  \,,
  \label{eq::C1DR_QCD}
\end{align}
where $l_{\rm t}=\ln[\mu^2/(m_t(\mu^2))^2]$, $\alpha_s^{\overline{\rm DR}}$
is the strong coupling with six
active flavours in the $\overline{\rm DR}$ scheme and $\alpha_e$ is
the evanescent coupling originating from the $\varepsilon$
scalar-quark vertex. Note that the evanescent coupling stemming from the
four-$\varepsilon$-vertex cancels in Eq.~(\ref{eq::C1DR_QCD}).

The transition to the five-flavour QCD is achieved with the help of
\begin{align}
\alpha_s^{\overline{\rm DR}}=&\,\, \alpha_s^{(5)}\zeta_{\alpha_s}^{-1}
   \,,
  \nonumber\\
  \zeta_{\alpha_s}^{-1} =&\,\,
  1
  + \frac{\alpha_s^{(5)}}{\pi}
  \left[\frac{1}{4}+ \frac{1}{6}l_{\rm t} + \epsilon\left(\frac{1}{4}l_{\varepsilon}+\frac{1}{12}l_{\rm t}^2 + \frac{1}{12}\zeta_2\right)\right]\nonumber\\
  &+ \left(\frac{\alpha_s^{(5)}}{\pi}\right)^2
  \left(\frac{11}{9} + \frac{13}{24}l_{\rm t} + \frac{1}{36}l_{\rm t}^2\right)
  -\frac{\alpha_s^{(5)}\alpha_e}{\pi^2}\left(\frac{7}{36}+n_l\frac{1}{12}\right)
  \,.
  \label{eq::zetag_QCD}
\end{align}
From Eqs.~(\ref{eq::C1DR_QCD}) and~(\ref{eq::zetag_QCD})
we recover $C_1^{\rm SM}$ of Eq.~(\ref{eq::C1SM})\footnote{Note that the
  functional form of Eq.~(\ref{eq::C1SM}) is independent from the quark
  mass definition.} which
is a welcome cross check on all individual steps of our calculation,
in particular on the counterterms originating from
  Eq.~(\ref{eq::Lep}). In the next section the same framework is applied
  to the MSSM.

\section{\label{sec::mssm}Coefficient function in the MSSM to three loops}

In this section we describe the evaluation of the coefficient function $C_1$
of Eq.~(\ref{eq::leff}) within the strong sector of the MSSM. Note that the operator
${\cal O}_1$ contains the effective interaction of two, three or four
gluons with the Higgs boson and we are free to choose any
corresponding Green functions in order to extract $C_1$. We
decided to consider the two-gluon-Higgs boson amplitude since
it involves fewer diagrams. We need to keep the two gluon momenta
different until the Lorentz structure of $O_1$ responsible for
the two-gluon coupling is projected out.

At one-, two- and three-loop order 10, 671 and 49632 Feynman
diagrams have to be considered. Some typical diagrams are shown
in Fig.~\ref{fig::diags}.
In addition to the particles of
supersymmetric QCD we also have the $\varepsilon$ scalar.
Higgs boson couplings to the light quarks and the corresponding
squarks are omitted. Furthermore, we neglect the contribution of the
Higgs boson-squark coupling suppressed by $M_Z^2/m_t^2$ (for
the Feynman rules see, e.g., Appendix~A of Ref.~\cite{Harlander:2004tp}).

\begin{figure}[t]
  \centering
  \includegraphics[width=\linewidth]{figs/dias.eps}
  \caption[]{\label{fig::diags}Sample diagrams contributing to
    $C_1$ at one, two and three loops.
    The symbols $t$, $\tilde{t}_i$, $g$, $\tilde{g}$, $h^0$ and
    $\varepsilon$ denote top quarks, top squarks, gluons, gluinos,
    Higgs bosons and $\varepsilon$ scalars, respectively.
    }
\end{figure}

Our calculation is based on a chain of programs designed to minimize
the manual input. First, we generate all the Feynman diagrams with
{\tt QGRAF}~\cite{Nogueira:1991ex}, then transform the
output to {\tt FORM}~\cite{Vermaseren:2000nd} notation
with the help of {\tt q2e} and apply asymptotic expansion
(see, e.g., Ref.~\cite{Smirnov:2002pj})
using {\tt exp}~\cite{Harlander:1997zb,Seidensticker:1999bb}.

Due to the gauge invariance the Higgs-gluon-gluon coupling has the form
\begin{eqnarray}
  {\cal A}^{\mu\nu,ab} &=& A \,\, \delta^{ab}
  \left(g^{\mu\nu}q_1\cdot q_2 - q_1^\nu q_2^\mu\right)\,,
\end{eqnarray}
where $A$ is a scalar function depending on $M_H^2=2q_1\cdot q_2$, $M_t^2$,
$\mu^2$, and the mass parameters of SUSY QCD. $q_1$ and $q_2$ are the
outgoing momenta of the gluons with polarization vectors $\varepsilon^\mu(q_1)$
and $\varepsilon^\nu(q_2)$ and colour indices $a$ and $b$.
We begin by convoluting the vertex Feynman diagrams with the projector
\begin{eqnarray}
  P^{ab}_{\mu\nu}(q_1,q_2) &=&
  \delta^{ab}
  \frac{q_1\cdot q_2 g_{\mu \nu}
    -q_{1\mu} q_{2\nu}
    -q_{1\nu} q_{2\mu}}
       {8(d-2)(q_1\cdot q_2)^2}
  \,,
  \label{eq::proj}
\end{eqnarray}
so that only scalar integrals remain.
After the Taylor expansion to the linear order in $q_1$ and $q_2$
the factor $(q_1\cdot q_2)^2$ in the denominator of Eq.~(\ref{eq::proj})
cancels and both momenta can be set to zero.
Finally, we evaluate vacuum integrals which (after the asymptotic
expansion) only contain a single scale. This is done using the package
{\tt MATAD}~\cite{Steinhauser:2000ry}.

Due to the transverse structure of the Higgs-gluon-gluon amplitude
${\cal A}^{\mu\nu,ab}$
an alternative projector to Eq.~(\ref{eq::proj}) can be applied
to obtain $C_1$:
\begin{eqnarray}
  \tilde{P}^{ab}_{\mu\nu}(q_1,q_2) &=&
  \delta^{ab}
  \frac{q_1\cdot q_2 g_{\mu \nu}
    -(d-1)q_{1\mu} q_{2\nu}
    -q_{1\nu} q_{2\mu}}
       {8(d-2)(q_1\cdot q_2)^2}
  \,.
  \label{eq::proj2}
\end{eqnarray}
We have checked that in both cases we obtain the same result.

One may consider different hierarchies between the mass scales
involved in this calculation.
As the first choice, we identify all supersymmetric masses with
$m_{\rm susy}$ and thus have two expansion parameters, $x_{ts} = m_t/m_{\rm susy}$
and $x_{\varepsilon t}=M_{\varepsilon}/m_t$.
At three-loop order we have computed terms through
${\cal O}\left(x_{ts}^6\right)$ and ${\cal O}\left(x_{\varepsilon t}^0\right)$.
As a cross-check, we performed a similar calculation where the top quark
mass and $m_{\rm susy}$ were identified from the very beginning.
Comparing the latter result to the former expansion in $x_{ts}$ evaluated at
$x_{ts} = 1$ we find agreement to within a few per cent, which
serves as a convergence test of our results.

We choose to renormalize all parameters in the
$\overline{\rm DR}$ scheme~\cite{Siegel:1979wq}. In particular, we need
the counterterms for
$\alpha_s$, the top quark, and the top squark masses
to two-loop, and the gluino and other squark mass
counterterms to one-loop order. Furthermore, the
counterterm for the mixing angle $\theta_t$ between the top squarks
is also required to the two-loop order. Although $\theta_t$ is zero in our
approximation, its renormalization in the non-degenerate one- and
two-loop expressions leads to non-zero contributions at three-loop
level. The corresponding counterterm can either be obtained from
the exact one- and two-loop result for
$C_1$~\cite{Harlander:2004tp}, or (as done in this paper) via expansion
in the mass difference between the two top squarks. Note that the
same effect is also present in the
three-loop calculation of the Higgs boson mass within the MSSM, as
discussed in Ref.~\cite{Harlander:2008ju,Kant:2010tf}.
All necessary counterterms can be found in the Appendix of
Ref.~\cite{Kant:2010tf} except for the decoupling constant relating
the gluon field in the SUSY-QCD to that in the five-flavour QCD, given by
\begin{align}
\zeta_3^0=&  1
   +\frac{\alpha_s^{(\text{SQCD})}}{\pi}
 \Bigg\{
     \frac{1}{\epsilon}
     \bigg(
         \frac{3}{4}
       + \frac{n_l}{12}
     \bigg)
   + \frac{1}{4}
   + \frac{7}{12}l_{\text{susy}}
   + \frac{1}{6}l_t
   + n_l\frac{1}{12}l_{\text{susy}}\nonumber\\
 & + \epsilon
 \Bigg[
 \frac{1}{4}l_{\varepsilon}
  + \frac{7}{24}l_{\text{susy}}^2
  + \frac{1}{12}l_t^2
  + \frac{3 \zeta_2}{8}
  + n_l
 \bigg(
  \frac{1}{24}l_{\text{susy}}^2
    + \frac{\zeta_2}{24}
  \bigg)
  \Bigg]
  \Bigg\}\nonumber\\
 & +\left(\frac{\alpha_s^{(\text{SQCD})}}{\pi}\right)^2
    \Bigg\{
 \frac{1}{\epsilon^2}
     \bigg(
   - \frac{69}{64}
   + n_l\frac{13}{192}
  + n_l^2\frac{1}{48}
  \bigg)\nonumber\\
  & +\frac{1}{\epsilon}
    \Bigg[
     \frac{421}{384}
    - \frac{49}{96} l_{\text{susy}}
    - \frac{7}{48} l_t
    + n_l
  \bigg(
     - \frac{25}{384}
     + \frac{7}{96} l_{\text{susy}}
     + \frac{1}{24}l_t
   \bigg)
    + n_l^2\frac{1}{48}l_{\text{susy}}
 \Bigg]\nonumber\\
 & + \frac{1535}{2304}
  - \frac{7}{32} l_{\varepsilon}
   + \frac{53}{192} l_{\text{susy}}
   + \frac{7}{96} l_{\text{susy}}^2
   + \frac{29}{96} l_t
   + \frac{1}{48}l_t^2
   - \frac{21 \zeta_2}{64}\nonumber\\
 & + n_l
 \bigg(
    \frac{97}{2304}
   + \frac{1}{16}l_{\varepsilon}
   - \frac{67}{576} l_{\text{susy}}
   + \frac{1}{12}l_{\text{susy}}^2
   + \frac{1}{48}l_t^2
   + \frac{11 \zeta_2}{192}
 \bigg)\nonumber\\
 & + n_l^2
 \bigg(
 \frac{1}{96}l_{\text{susy}}^2
   + \frac{\zeta_2}{96}
 \bigg)
   + x_{ts}^2
 \bigg(
   -\frac{1}{432}
   - \frac{13}{72} l_{\text{susy}}
   + \frac{5}{72} l_t
 \bigg)
 \Bigg\}
 + {\cal O}\left(x_{ts}^4\right)\,,
\label{eq::zeta30}
\end{align}
where $l_{\rm susy}=\ln[\mu^2/(m_{\rm susy}(\mu^2))^2]$ and
$\alpha_s^{\rm (SQCD)}$ denotes the $\overline{\mbox{DR}}$ coupling
where all particles of the theory contribute to the running.
In Eq.~(\ref{eq::zeta30}) $n_l=5$ counts the number of massless quarks and
at the same time the number of squark flavours different from top squarks.
Similarly to the SM case in Section~\ref{sub::SMDRED}, we keep $M_\varepsilon \ne 0$
in the intermediate steps
in order to match to the effective theory of Eq.~(\ref{eq::leff}).
Thus, $M_\varepsilon$ and the
coupling $\Lambda_\varepsilon$ (cf. Eq.~(\ref{eq::Lep})) have to be renormalized
with the help of the counterterms
\begin{eqnarray}
  \left(M^0_{\varepsilon}\right)^2 &=&
  M_{\varepsilon}^2 +
  \frac{\alpha_s^{\rm(SQCD)}}{\pi}
  \Bigg\{m_t^2\left(\frac{1}{2\epsilon}+\frac{1}{2}+\frac{1}{2}l_{\rm t}\right)
    + M_{\varepsilon}^2\Bigg[
      \frac{8 - n_l}{4\epsilon}
    + \frac{9}{2}
    + 3l_{\varepsilon}
    - \frac{3}{4}l_{\rm susy}
    - \frac{1}{4}l_{\rm t}
    \nonumber\\&&\mbox{}
    + \left(-\frac{1}{2} - \frac{1}{4}l_{\varepsilon}\right)n_l
    \Bigg]
    + m_{\rm susy}^2
    \left[1 + l_{\rm susy} + \frac{2 - nl}{2\epsilon}
    + \left(-\frac{1}{2} - \frac{1}{2}l_{\rm susy}\right)n_l
    \right]
    \Bigg\}
    \,,
    \nonumber\\
\end{eqnarray}
with $l_{\varepsilon}=\ln[\mu^2/M_\varepsilon^2]$, and
\begin{align}
\left(\Lambda_\varepsilon^0\right)^2 - \Lambda_\varepsilon^2=&\,\,\delta \Lambda_{\varepsilon}^2
\nonumber\\
=&-2m_t^2\frac{c_\alpha}{s_{\beta}}
                            \Bigg\{
                                      \frac{\alpha_s^{(\text{SQCD})}}{\pi}
                                      \Bigg[
                                               \frac{1}{2}l_{\text{susy}}
                                             -  \frac{1}{2}l_t
                                             + \epsilon
                                               \bigg(
                                                      \frac{1}{4}l_{\text{susy}}^2
                                                     - \frac{1}{4}l_t^2
                                               \bigg)
                                       \Bigg]\nonumber\\
                                  & + \left(\frac{\alpha_s^{(\text{SQCD})}}{\pi}\right)^2
                                      \Bigg[
                                              \frac{1}{\epsilon}
                                               \bigg(
                                                      -l_{\text{susy}}
                                                      +l_t
                                                      +n_l
                                                       \Big(
                                                              \frac{1}{8}l_{\text{susy}}
                                                            - \frac{1}{8}l_t
                                                       \Big)
                                               \bigg)\nonumber\\
                                       &     + \frac{1}{3}
                                             + \frac{23}{12} l_{\text{susy}}
                                             - \frac{1}{8}l_{\text{susy}}^2
                                             - \frac{23}{12} l_t
                                             - \frac{1}{12}l_{\text{susy}} l_t
                                             + \frac{5}{24} l_t^2
                                             + n_l
                                               \bigg(
                                                       \frac{1}{16}l_{\text{susy}}^2
                                                     - \frac{1}{16}l_t^2
                                               \bigg)\nonumber\\
                                      &
                                             + x_{ts} x_{\mu t}
                                               \bigg(
                                                      t_{\alpha}
                                                     +\frac{1}{t_{\beta}}
                                               \bigg)
                                               \bigg(
                                                       \frac{11}{12}
                                                     + \frac{1}{6}l_{\text{susy}}
                                                     + \frac{1}{6}l_t
                                               \bigg)
                                               + x_{ts}^2
                                               \bigg(
                                                       -\frac{359}{216}
                                                       +\frac{19}{72} l_{\text{susy}}
                                                       -\frac{67}{72} l_t
                                               \bigg)
                                      \Bigg]
                            \Bigg\}
                            \nonumber\\&
                            + {\cal O}(x_{ts}^4)
                            + {\cal O}(x_{ts}^3 x_{\mu t})
                            \,,
\label{eq::Lambda_ep_SQCD}
\end{align}
where $c_\alpha=\cos\alpha$, $s_\beta=\sin\beta$,
$t_\alpha=\tan\alpha$, $t_\beta=\tan\beta$ and $x_{\mu t}=\mu_{\text{susy}}/m_t$.
Here $\alpha$ is the
mixing angle between the weak and the mass eigenstates of the neutral
scalar Higgs bosons, $\tan\beta$ is the ratio of the vacuum expectation values
of the two Higgs doublets, and $\mu_{\rm susy}$ is the Higgs-Higgsino
bilinear coupling from the super potential.
Note that the counterterm for $\Lambda_\varepsilon$
and the three-loop vertex diagrams have been evaluated
assuming the same hierarchy of the top quark and the top squark masses.
Let us mention that the counterterm in
Eq.~(\ref{eq::Lambda_ep_SQCD}) is finite at one-loop order and only
contains a single pole at two loops whereas the corresponding
expression in QCD has a single and a double pole, respectively.

In the first step we obtain $C_1$ in terms of $\alpha_s^{\rm (SQCD)}$.
It is, however, more convenient to express the final result in terms of
the five-flavour coupling in the $\overline{\rm MS}$ scheme
$\alpha_s^{(5)} = \alpha_s^{(5),\overline{\rm MS}}$.
The relation establishing this transition is as follows:
\begin{eqnarray}
  \alpha_s^{(5)} &=& \zeta_{\alpha_s} \alpha_s^{\rm (SQCD)}
  \,.
  \label{eq::zetaas}
\end{eqnarray}
Two-loop corrections to the decoupling constant $\zeta_{\alpha_s}$
within supersymmetric QCD have been computed in
Refs.~\cite{Harlander:2005wm,Bauer:2008bj,Bednyakov:2007vm}. Since
$\zeta_{\alpha_s}$ in Eq.~(\ref{eq::zetaas}) combines the decoupling of the
heavy particles and the transition from $\overline{\rm DR}$ to
$\overline{\rm MS}$, we present the explicit result
in the limit of equal supersymmetric masses:
\begin{eqnarray}
  \zeta_{\alpha_s} &=& 1
  + \frac{\alpha_s^{\rm (SQCD)}}{\pi}\left(
  -\frac{1}{4} - \frac{7}{12}l_{\rm susy} - \frac{1}{6}l_{\rm t}
  - n_l\frac{1}{12}l_{\rm susy}
  \right)
  + \left(\frac{\alpha_s^{\rm (SQCD)}}{\pi}\right)^2
  \Bigg[
    \frac{77}{288}
    \nonumber\\&&\mbox{}
    - \frac{5}{8}l_{\rm susy}
    + \frac{49}{144}l_{\rm susy}^2
    - \frac{3}{8}l_{\rm t}
    + \frac{7}{36}l_{\rm susy}l_{\rm t}
    + \frac{1}{36}l_{\rm t}^2
    + n_l \Bigg(
    \frac{23}{144}
    - \frac{1}{72}l_{\rm susy}
    + \frac{7}{72}l_{\rm susy}^2
    \nonumber\\&&\mbox{}
    + \frac{1}{36}l_{\rm susy}l_{\rm t}
    \Bigg)
    + n_l^2\frac{1}{144}l_{\rm susy}^2
    + \left(\frac{1}{432} + \frac{13}{72}l_{\rm susy}
    - \frac{5}{72}l_{\rm t}\right)x_{ts}^2
    \Bigg]
    + {\cal O}(x_{ts}^4)
    \,.
\end{eqnarray}
All occurring mass parameters and the top squark mixing angle have been renormalized in the
$\overline{\mbox{DR}}$ scheme.

Finally, we present the coefficient function $C_1$ expressed in terms
of $\overline{\mbox{DR}}$ masses in the full theory, expanded in
$\alpha_s^{(5)}$:
\begin{eqnarray}
  C_1^{\overline{\rm DR}} &=&
  -\frac{\alpha_s^{(5)}}{3\pi}\frac{c_\alpha}{s_\beta}
  \Bigg\{
  1 + \frac{x_{ts}^2}{2}
  + \frac{\alpha_s^{(5)}}{\pi}\Bigg[
  \frac{11}{4} - \frac{1}{3}\left(t_\alpha +
    \frac{1}{t_\beta}\right)\frac{\mu_{\rm susy}}{\msusy}
  + \left(\frac{23}{12} + \frac{5}{12}l_{\rm susy}
    \right.\nonumber\\&&\left.\mbox{}
    -\frac{5}{12}l_{\rm t}\right)x_{ts}^2
  \Bigg]
  + \left(\frac{\alpha_s^{(5)}}{\pi}\right)^2
  \Bigg[
  \frac{2777}{288} + \frac{19}{16}l_{\rm t} + \left(-\frac{67}{96} +
    \frac{1}{3}l_{\rm t}\right)n_l
  \nonumber\\&&\mbox{}
  + \left(-\frac{85}{54} - \frac{85}{108}l_{\rm susy} -
    \frac{1}{18}l_{\rm t}  + \left(-\frac{1}{18} +
      \frac{1}{12}l_{\rm susy}\right)n_l
  \right)\left(t_\alpha+\frac{1}{t_\beta}\right)\frac{\mu_{\rm susy}}{\msusy}
  \nonumber\\&&\mbox{}
  + \Bigg(
  \frac{30779857}{648000} - \frac{6029}{10800}l_{\rm susy}
  - \frac{475}{288}l_{\rm susy}^2 - \frac{20407}{10800}l_{\rm t}
  + \frac{26}{45}l_{\rm susy}l_{\rm t} - \frac{377}{1440}l_{\rm t}^2
  \nonumber\\&&\mbox{}
  - \frac{15971}{576}\zeta_3
  + \left(
    - \frac{3910697}{216000}
    + \frac{63}{4}\zeta_3
    + \frac{3307}{4800}l_{\rm susy}
    + \frac{131}{576}l_{\rm susy}^2
    + \frac{5113}{14400}l_{\rm t}
    \right.\nonumber\\&&\left.\mbox{}
    - \frac{101}{1440}l_{\rm susy}l_{\rm t}
    + \frac{3}{320}l_{\rm t}^2
  \right) n_l
  \Bigg)
  x_{ts}^2
  \Bigg]
  \Bigg\}
  + {\cal O}\left(x_{ts}^4\right)
  + {\cal O}\left(\xmusx_{ts}^2\right)
  \,.
  \label{eq::C1DR}
\end{eqnarray}
The analytic expression including ${\cal O}(x_{ts}^6)$ and ${\cal O}(\xmusx_{ts}^4)$ is available
on request from the authors.
It is noteworthy that in the limit $m_{\rm susy}\to\infty$ we recover exactly
the SM result of Eq.~(\ref{eq::C1SM}).

\section{\label{sec::xsec}Higgs boson production at NNLO}

In this section we discuss the numerical effect of the corrections presented
above. The effective-theory parts in the MSSM and the SM are identical,
and thus we can borrow the framework of Ref.~\cite{Pak:2009dg}. In addition,
we incorporate the factor $B^{(5)}$ (in the $\overline{\rm MS}$
scheme) as discussed in the Introduction.

On the full-theory side we consider the renormalization group invariant
combination $C_g=C_1/B^{(5)}$
where both $C_1$ and $B^{(5)}$ are parameterized with the five-flavour
strong coupling in the $\overline{\rm MS}$ scheme.
For the numerical evaluation of $C_1^{\overline{\rm DR}}$ we fix
the (hard) renormalization scale at the on-shell top quark mass value,
i.e. $\mu_h=M_t$, which means that the $\overline{\rm DR}$ mass parameters in
Eq.~(\ref{eq::C1DR}) have to be interpreted as $m_{\rm susy}(M_t)$ and
$m_t(M_t)$.
Any variation of $\mu_h$ leads to a non-degenerate supersymmetric spectrum
and thus renders Eq.~(\ref{eq::C1DR}) not applicable.
As shown in
Section~\ref{sec::sm} (Fig.~\ref{fig::xsecsm}(b)), the variation of
$\mu_h$ only leads to a very small effect and thus we keep it fixed.

Following the common practice, we write the hadronic cross section
for the individual channels as\footnote{The subscripts $hk$ mark the partons
  in the initial state. Below we sum over all possibilities.}
\begin{eqnarray}
  \sigma_{hk}(s) &=& \sigma_0 C_g^2 \Sigma_{hk}(s)
  \,,
  \label{eq::sigma_hk}
\end{eqnarray}
where $hk\in\{gg,qg,q\bar{q},qq,qq^\prime\}$ ($q$ and $q^\prime$ denote
different light quark flavours) and
$\sigma_0$ contains the exact dependence on the heavy masses at the
LO. In the SM this is only the top quark mass, while in the MSSM
also the top squark masses $m_{\tilde{t}_1} = m_{\tilde{t}_2} = m_{\rm susy}$
must be taken into account\footnote{The terms of order $M_W^2/m_t^2$ are not
displayed but are accounted for in the numerical evaluation.}:
\begin{eqnarray}
  \sigma_0 &=&\left| \frac{c_\alpha}{s_\beta} \left\{
      \frac{3}{2}\tau_t \left[1 + (1-\tau_t)\right] f(\tau_t)
      - \frac{m_t^2}{2 m_{\rm susy}^2} 3 \tau_s \left[1 - \tau_s f(\tau_s)\right]
    \right\} + {\cal O}\left(\frac{M_W^2}{m_t^2}\right) \right|^2\,.
\end{eqnarray}
where $\tau_t = 4 m_t^2/M_H^2$, $\tau_s = 4 m_{\rm susy}^2/M_H^2$ and
\begin{equation}
  f(t) =
  \left\{\begin{array}{cl}
      \arcsin^2(1/\sqrt{t}), & t \ge 1\,, \\
      - \frac{1}{4} \left(\ln\frac{1 + \sqrt{1-t}}{1 - \sqrt{1-t}} - i\pi \right)^2,
      & t < 0\,.
    \end{array}
  \right.
\end{equation}

The quantity $\Sigma_{hk}(s)$ in Eq.~(\ref{eq::sigma_hk}), expanded in
$\alpha_s^{(5)}(\mu_s)$, contains the convolutions of the PDFs with
the $n$-loop ($n=0,1,2$) effective-theory partonic cross sections.
In the SM, such effective theory approach provides an excellent
approximation at NNLO~\cite{Harlander:2009mq,Pak:2009dg,Harlander:2010my}.
Once the LO cross section which depends on $\alpha_s^{(5)}(\mu_s)$ is
factored out, we are left with a product of the residual hard coefficient
depending on $\alpha_s^{(5)}(\mu_h)$ and the
remaining part of $\Sigma_{hk}(s)$ which is parameterized in terms of
$\alpha_s^{(5)}(\mu_s)$.
We expand these factors and consistently discard higher orders in
the strong coupling, decomposing the hadronic cross section into
the LO, NLO and NNLO pieces. Introducing
\begin{eqnarray}
  C_g &=& 1 + \frac{\alpha_s^{(5)}(\mu_h)}{\pi} c_g^{(1)}
  + \left(\frac{\alpha_s^{(5)}(\mu_h)}{\pi}\right)^2
  c_g^{(2)}
  + \ldots
  \,,\nonumber\\
  \Sigma &=& \Sigma^{(0)} + \frac{\alpha_s^{(5)}(\mu_s)}{\pi} \Sigma^{(1)}
  + \left(\frac{\alpha_s^{(5)}(\mu_s)}{\pi}\right)^2 \Sigma^{(2)}
  + \ldots  \,,
\end{eqnarray}
we write the production cross section as
\begin{eqnarray}
  \sigma^{\rm NNLO} &=& \sigma_0
  \Bigg\{\Sigma^{(0)}
    + \frac{\alpha_s^{(5)}(\mu_s)}{\pi}\Sigma^{(1)}
    + \frac{\alpha_s^{(5)}(\mu_h)}{\pi}2c_g^{(1)}\Sigma^{(0)}
    + \left(\frac{\alpha_s^{(5)}(\mu_s)}{\pi}\right)^2\Sigma^{(2)}
    \nonumber\\&&\mbox{}
    + \frac{\alpha_s^{(5)}(\mu_s)}{\pi}\frac{\alpha_s^{(5)}(\mu_h)}{\pi}
    2c_g^{(1)}\Sigma^{(1)}
    + \left(\frac{\alpha_s^{(5)}(\mu_h)}{\pi}\right)^2
    \left[(c_g^{(1)})^2+2c_g^{(2)}\right]\Sigma^{(0)}
    + \ldots
    \Bigg\}
    \,,
    \nonumber\\
\end{eqnarray}
where superscripts on $c_g$ or $\Sigma$ denote the loop order of the
corresponding quantity.

As input for the numerical evaluation we use the on-shell top
quark mass $M_t=173.3$~GeV~\cite{:1900yx} and convert it to the
$\overline{\rm DR}$ scheme using two-loop
SUSY-QCD corrections~\cite{Martin:2005ch}.
By default we use
LO, NLO and NNLO PDFs by MSTW2008 collaboration~\cite{Martin:2009iq}.
The choice of the PDFs determines the values of $\alpha_s^{(5)}(M_Z)$
at the considered order. Using the appropriate $\overline{\rm MS}$ beta
function, we then derive $\alpha_s^{(5)}(\mu_s)$ and $\alpha_s^{(5)}(\mu_h)$.

\begin{figure}[t]
  \centering
  \begin{tabular}{c}
    \includegraphics[width=0.9\linewidth]{figs/mssm_msusy_lhc_degen.eps}
  \end{tabular}
  \caption[]{\label{fig::degen_xsec}
    LO (lower), NLO (middle)
    and NNLO (upper curves) Higgs production cross section as a function of
    $m_{\rm susy}$.
    The solid and dashed lines correspond to the MSSM and SM, respectively.
    }
\end{figure}

In Fig.~\ref{fig::degen_xsec} we show the total cross section as a
function of a common supersymmetric mass scale $m_{\rm susy}$ up to
NNLO with $\tan\beta=5$, $\mu_{\rm susy}=200$~GeV,
vanishing mixing angle for the top squarks and a pseudoscalar Higgs boson
mass $M_{A}=1$~TeV. The Higgs boson mass is computed with the help
of the program {\tt H3m}~\cite{Kant:2010tf} as a function of $m_{\rm susy}$
to three-loop accuracy.
In the range of $m_{\rm susy}$ varying between 250~GeV and
2~TeV $M_H$ assumes values between 92~GeV and 117~GeV. Although
experimentally excluded if the SM limits on $M_H$ are assumed, we show the
curves for illustration in the mentioned region for $m_{\rm susy}$.
The mixing angle $\alpha$
is relatively stable so that $\frac{\cos\alpha}{\sin\beta}\approx 0.99$.
The SM results are shown with the dashed lines. They develop
$m_{\rm susy}$ dependence since we identify the SM Higgs boson mass with
the MSSM value. Note that for $m_{\rm susy} \lsim 1500$~GeV the
corresponding Higgs boson masses are excluded by LEP~\cite{PDG}.
Nevertheless we continue the dashed curves to $m_{\rm susy}=250$~GeV to have a
comparison with the MSSM curves.

One observes that for the large values of
$m_{\rm susy}$ the MSSM curves approach the SM result
whereas for $m_{\rm susy}\lsim 400-500$~GeV a significant enhancement
of the MSSM cross section is observed.

In order to determine the effect of higher order corrections
it is convenient to define the so-called $K$-factor as the ratio
of the higher order cross section and the Born cross section
with the soft scale fixed at $\mu_s^2=(M_H/2)^2$,
\begin{eqnarray}
  K^{\rm HO} &=& \frac{\sigma^{\rm HO}(\mu_s)}{\sigma^{\rm LO}(\mu_s=M_H/2)}
  \,.
  \label{eq::Kdef}
\end{eqnarray}

The values of the $K$-factor corresponding to Fig.~\ref{fig::degen_xsec}
vary only slightly with $m_{\rm susy}$ and are
$K^{\rm NLO} \approx 1.5$, $K^{\rm NNLO} \approx 1.8$,
very close to their SM counterparts.

We refrain from discussing the renormalization scale dependence since it is
essentially inherited from the SM corrections discussed in
Section~\ref{sec::sm}.

\begin{figure}[t]
  \centering
  \begin{tabular}{c}
    \includegraphics[width=0.9\linewidth]{figs/mssm_ma_lhc_nomix.eps}
  \end{tabular}
  \caption[]{\label{fig::nomix_xsec}
    LO (lower), NLO (middle)
    and NNLO (upper curves) Higgs production cross section for the
    ``no-mixing'' scenario as a function of $M_A$.
    The solid and dashed lines correspond to the MSSM and SM, respectively.
    }
\end{figure}

Our following scenario is based on the so-called ``no-mixing'' scheme
as defined in Ref.~\cite{Carena:2002qg}. Keeping
$\tan\beta = 5$ fixed, we vary $M_A$, the mass of the pseudoscalar
Higgs boson, between 200~GeV and 1~TeV, and compute the scalar Higgs
mass and the supersymmetric particle masses with
SOFTSUSY~\cite{Allanach:2001kg}. Averaging the masses of squark, stop and gluino,
we obtain $m_{\text{susy}}\approx 1970$~GeV. In Fig.~\ref{fig::nomix_xsec} we
present the cross section
computed in this scenario. Here the Higgs boson mass varies
from 114~GeV to 117~GeV, and that  affects the SM cross section
(the dashed lines). Compared to the previous plot, the variation of
$\alpha$ is more pronounced, reaching $\frac{\cos\alpha}{\sin\beta}\approx 0.95$
at the left boundary, while for the larger values of $M_A$ this ratio
approaches 1.
The genuine supersymmetric corrections (arising from terms of ${\cal
  O}(1/m_{\rm susy})$ in Eq.~(\ref{eq::C1DR})) are small.
Again, the $K$-factors are very stable in the whole
range of $M_A$ and are $K^{\rm NLO} = 1.6$ and $K^{\rm NNLO} = 1.9$.

\section{\label{sec::concl}Conclusions}

In this letter we have computed supersymmetric NNLO SUSY-QCD corrections
arising from the top quark/squark sector
to the matching coefficient determining the Higgs-gluon coupling in the
effective theory.
Regularization was done in {\tt DRED} with the help of the
so-called $\varepsilon$ scalars which made the matching
to the five-flavour QCD very delicate.
In particular, we had to renormalize the mass of the $\varepsilon$ scalar and
its coupling to the Higgs boson at one- and two-loop orders, respectively.

The approximation investigated in this paper, assuming zero mixing in
the stop sector, produces significant effects only when $m_{\rm susy}$
is small, $\ll 1$~TeV. However, the effect of zero mixing on
Higgs mass together with the current experimental bounds on this mass
exclude this possibility. We expect that a more general result,
allowing for a large mixing angle, will not be so severely constrained,
and enhancement of the cross section by as much as 50\% (as in the
left side of  Fig.~\ref{fig::degen_xsec}) may be allowed.

Analyzing the higher order corrections, in the MSSM we observe
the same pattern as in the SM: large NLO corrections which further
increase at NNLO.
For $m_{\rm susy}\gsim 1$~TeV the genuine supersymmetric
corrections are suppressed and the difference from the SM is mainly due to the
factor $\frac{\cos\alpha}{\sin\beta}$ in Eq.~(\ref{eq::C1DR}).
However, the MSSM $K$-factors are very similar to their SM counterparts.
This confirms the estimate of Ref.~\cite{Harlander:2003kf} based on
the complete NLO corrections to the matching coefficient and
the NNLO calculation in the effective theory.

Our calculation has been performed in the limit of degenerate supersymmetric
masses. In order to explore all interesting regions of the supersymmetric
parameter space it would be necessary to relax this restriction. Since a
three-loop calculation with many different mass scales is currently not
feasible it is more promising to employ a strategy based on asymptotic
expansions which has been applied successfully to predict the lightest
MSSM Higgs boson mass in Ref.~\cite{Kant:2010tf}.

\section*{Acknowledgements}

This work was supported by the DFG through the SFB/TR~9 ``Computational
Particle Physics'' and the Graduiertenkolleg ``Hochenergiephysik und
Teilchenastrophysik''.

redpajama_set_name: RedPajamaArXiv


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Other opportunities to connect with the postdoctoral community.
The NPA Annual Conference is the largest national conference and networking event dedicated to the postdoctoral community. Conference attendees - postdoctoral scholars, administrators, faculty, and representatives from disciplinary societies, industry, and corporations - are provided with the opportunity to gather and enhance their professional development and leadership skills. There are several opportunities for sponsorship that will allow corporations, institutions, associations, and societies to connect with postdocs in a meaningful way. Visit this page for a full conference prospectus.
Tailored, annual packages of multiple marketing opportunities are available for maximum exposure. Please contact the NPA for assistance.
The NPA welcomes advertisements that promote resources geared towards postdocs but reserves the right to edit content for an appropriate message in regards to the NPA's mission. Images must be in .GIF. .JPG, .JPEG, or .PNG format. Images will link to a landing page of the advertiser's selection.
Although we are a nonprofit organization, your sponsorship of an advertisement may or may not be fully tax-deductible depending on the content of the ad and to the extent allowed by the IRS rules and regulations.
For more information on any of our advertising opportunities, please contact Amy N. Wilson, Office & Marketing Manager at awilson@nationalpostdoc.org or (301) 984-4800.
The NPA serves approximately 210 Sustaining Members and more than 14,000 individual members, making advertising with the NPA a unique opportunity to reach a targeted market of institutions and postdocs to promote resources and services geared toward that population.


Use these online calculators to evaluate options and scenarios for principal, interest rates, term and payments. For current Stearns Bank rates and product information, consult with a Stearns Bank representative.
The break even analysis calculator is designed to demonstrate how many units of your product must be sold to make a profit.
Use this calculator to estimate your debt service coverage with a new commercial loan.
Use this calculator to look at a variety of possible loans. Change your monthly payment, loan amount, interest rate or term.


Council crews have been sweeping roads, clearing gullies and checking known flooding hotspots in preparation for the heavy rain expected to hit Plymouth tonight and tomorrow night.
Rain is currently forecast from around 11pm tonight until 10am, with another band of rain from around 6pm tomorrow.
Teams are working throughout the day and night and are on standby to respond to any issues.
Severe flooding should be reported as soon as possible on 01752 668000. Less urgent issues like blocked gullies can be reported via our website.


A Beach Villa Four Bedroom Villa is located at 29 Calypso Drive, Lagoons in Montego Bay in 810 m from the centre.
Tourists can take advantage of a huge range of services: internet services, car lot, tennis court, well-equipped private beach, equipped gym, wheelchair friendly. You can pay using these types of bank cards: American Express, Visa, Mastercard, Discover, UnionPay credit card.
There is only one room type - villa. Lodgers at the hotel have facilities such as air conditioning, refrigerator, free toiletries, microwave, flat-screen tv, computer, coffee machine.
You will enjoy a pool view from your window. Accommodation also provides unique facilities for guests: patio, private pool.
This villa has a dishwasher, kitchen and toaster.


Protest. Photo courtesy of Ana Carolina Fernandes.
Ana Carolina Fernandes is a Brazilian photojournalist and documentary photographer. After training and working at some of Brazil's largest newspapers, she decided to begin working as a freelance photographer. Since then, she has photographed everything from protests at some of Brazil's most delicate political moments, to Rio de Janeiro's transgender community, to the city of Havana, Cuba. Fernandes spoke to Brazil reports about her passion for photography, photojournalism and the role it plays within Brazilian mainstream media.
"I was always interested in photography…Cinema, images and journalism always played a large role in my family. My father owned a newspaper during the military dictatorship, my mother always put films on the projector in our house, my grandfather used to dub cinema, so the medium of images was always very present. At the age of 13 I first realised I was really interested when I was given a better camera. I used to take photos on family holidays.
What do you like most about the photo as a medium? What is special about it?
What do you most try to capture in your photography?
To what extent is it important for you to see beyond a particular editorial stance and tell a different narrative through your photojournalism?
So, do you believe in social media as the future of photojournalism?
Do you think that the Brazilian mainstream media reinforces certain race and gender stereotypes? Was your work with Rio's transgender community an expression of this?
Many people have commented on the racial stereotypes enforced by the media after the assassination of city councillor Marielle Franco, do you think photojournalism plays an important role in making Brazilian media less 'white'?
Photojournalism is sometimes very dangerous: does this ever dissuade you from doing your job?
Havana, Cuba's only official gay beach. Photo courtesy of Ana Carolina Fernandes.
Cuban Boxer. Photo courtesy of Ana Carolina Fernandes.
Carnival. Photo courtesy of Ana Carolina Fernandes.
International Women's Day. Photo courtesy of Ana Carolina Fernandes.
New York. Photo courtesy of Ana Carolina Fernandes.
Transvestite on beach in Rio. Photo courtesy of Ana Carolina Fernandes.
Ana Carolina Fernandes plans to be on the streets again photographing the run up to this year's presidential elections in Brazil. Follow her on Instagram to keep up to date with her work.


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Harbor Beach farm selling direct to consumer
Looking to rid public concerns about coronavirus impact on food supply
By Sara Eisinger, sara.eisinger@hearstnp.com
The family of Prime Land Farm is selling beef directly to their customers
Barbara Ann SiemenShow MoreShow Less
HURON COUNTY — Some are beginning to feel threatened that the global coronavirus pandemic might impact future food supply. Darrin and Barbara Siemen of Prime Land Farm in Harbor Beach want to reassure area residents that they are in good hands.
The Siemen's are selling meat directly to those who are interested and have begun advertising via Facebook.
"With many processing plants being shut down right now due to coronoavirus, and the uncertainty of future food availability, we thought this was a good way to ensure people we know have access to beef," Barbara posted.
The Siemen's have been farming for four generations, beginning with Darrin's great-grandfather. Along with his wife, children and employees the farm continues today. Everyone works hard to supply the market with a little bit of everything — beef, milk, sugar beets, corn, wheat, etc.
"We don't have the option to take a week off," Darrin said. "We are planting and the cattle need milking. When something like this happens, people are thankful for the food. We have to continue on."
Due to COVID-19, the agriculture market has seen a significant decline. Farmers are putting in long hours but not seeing profit.
"Our last paycheck was 35% less on milk than it should've been," Darrin said. "That's well below cost of production. It is scary and not farm specific. It's everybody. I am nervous about bills and how fast markets will come up."
Darrin revealed that his farm applied for a small business loan, but he anticipated the money would be used to supplement employee payroll.
"My crew has not even considered not coming to work," Darrin said.
He discussed the U.S. Department of Agriculture's $19 billion Coronavirus Food Assistance Program, created to provide relief to farmers nationwide.
"The amount of money we are losing is so high that even though the stimulus bill sounds good, it won't do much," Darrin said. "We've already gone four or five years with low prices."
In order to help their farm and community, the Siemen's are prepared to sell direct. The problem is that most people have been conditioned to going to the grocery store and buying only what they need for that specific day or week.
"We are getting a lot of inquiry, but it's a large quantity at one time and people aren't used to that," Darrin said. "It is cheaper than the store, but people will struggle to come up with the money upfront. They are used to budgeting for the week's groceries, not a large amount. But they wouldn't have to pay for a long time."
The Siemen's have received a lot of great feedback from customers, including those who didn't even realize that most farmers sell produce direct.
"Everyone loves the idea, love that we do it," Darrin said. "People don't realize that it's available all the time. Farmers will sell a lot directly, but the interest just isn't there."
The Siemen's take their meat to a professional butcher for processing to be sold as quarter, half or whole.
"A half of beef is 400 pounds of meat," Darrin said. "Instead of four steaks to grill you'll have 400 pounds. A quarter is 200 pounds. I think once people get the meat they won't go back."
He explained how the meat goes from the farm and straight to processing, where it is stored in a freezer for fourteen days.
"You cannot get fresher," Darrin said.
Darrin went on to share his concerns for everybody in the nation, believing that society's "if you want it you want it now" mindset might need to shift some.
"People just have to budget for something like this," Darrin said.
Darrin Siemen can be contacted through Facebook Messenger with any questions. The phone number to Prime Land Farm is 989-550-6120.
By Sara Eisinger