text:
Pet Brands / Himalaya
Himalaya Digyton Drops For Dog & Cat - 30 ml
Himalaya Digyton Plus For Dog & Cat - 100 ml
Himalaya Erina Coat Cleanser For Dog - 450 ml
Himalaya is a well-known brand when it comes to pharmaceuticals; this health care giant is known to produce quality drugs without the use of any harmful chemicals. Their USP is that they use all Ayurveda products that are completely safe to use and do not have any additional chemicals.
Himalaya has created a name for itself in the human medicine genre and is known to have developed various supplements and medicines that source the ingredients from Ayurveda, which is found in abundance in nature.
The Himalaya Drug company was founded somewhere in 1930 by M. Manal, his aim was to bring Ayurveda into the contemporary medicine form. He wanted to bring the 5,000 year old form of medicine to modern society. The medicines were manufactured selecting various indigenous herbs and formulations, which draws its inspiration from various ayurvedic texts written all through history. It was after much research that he developed various drugs and therapies for humans. These combined the goodness of Ayurveda with modern technology.
Himalaya Drug Company has been based on the pillar of performing research in nature to identify the appropriate ingredient, which will have therapeutic qualities. They have been the pioneers when it comes to developing modern medicines with the help of age old secrets of Ayurveda. The company uses 9001:2000 cutting edge technologies to develop pharmaceutical grade ayurvedic products. The herbal care company has been even awarded a certification for the same in 2003.
Ever since the conception of the organization, Himalaya has developed safe and innovative remedies that can help people to develop and lead healthier lives. In fact Himalaya products have been endorsed by over 2,50,000 doctors and has become a globally renowned brand that is present and prescribed in over 89 countries of the world.
This pharmaceutical brand extended its range to the animal health care segment as well. They bring in expertise to the animal care segment and developed natural drugs and therapies for all pets as well, which includes cats and dogs.
The organization boasts of a vast range of pet health products, this includes well researched and safe products that help to alleviate the suffering of the animals. The medicines will help to improve the health of your pet and increase the productivity as well with a wide range of supplements, which have been specially formulated for your pets.
Around the world there is a widespread discontent for the presence of chemical contaminants in various dairy and poultry products, taking its cue from this the Himalaya Drug Company produces quality ayurvedic drugs and therapies for animal health care.
Himalaya Drug Company launched an entire range of pet health care products for the commercial livestock in July 1998. The products have been especially formulated to help animals live a safe and healthy life and also produce a range of supplements to improve their health. The resultant output is that there is a healthy livestock and the animal products are absolutely safe for all human consumption.
After this in 2000, Himalaya introduced a range of product for companions that are the pets. There is a wide range of medicines and supplements available for dogs and cats as well.
Buy Online Himalaya Pet Health Products at Best Online Pet Store India


text:
Car dealership flies the flag
Andy Keeble
Published: 9:00 AM May 25, 2012
Giant window display in the spirt of the jubilee.
A BARNSTAPLE car dealership is flying the flag in preparation for what promises to be a red-white-and-blue-themed great British summer.
Staff at Taw Ford are embracing the spirit of the Queen's Diamond Jubilee and the London Olympics with a giant Union Jack motif at the Victoria Road showroom.
The striking window display, designed by local firm The Sign Shop, is already proving to be a real head-turner.
Mark Brend said: "With the jubilee and the Olympics coming up it's going to be a summer to celebrate and Taw Ford is joining the party.
"The window looks very spectacular and we've already had quite a few customers comment on it."
Taw Ford is also offering motorists the chance to drive away with a special limited edition white Ford KA Edge - complete with Union flag decal on the roof.
"It's a one-off and will look great on the road," said Mr Brend.

redpajama_set_name: RedPajamaCommonCrawl


text:
SpongeBob Pantaloni Pătrați, cunoscut și ca Buretele Bob Pantaloni Pătrați sau simplu SpongeBob (în engleză SpongeBob SquarePants), este un serial de animație creat de educatorul în știință marină și animatorul Stephen Hillenburg pentru Nickelodeon. Serialul urmărește aventurile personajului eponim și prietenilor lui acvatici în orașul marin fictiv Bikini Bottom. Al cincilea cel mai lung serial american de animație, popularitatea sa mare l-a făcut intr-o franciză media. Este cel mai urmărit serial pe Nickelodeon și cea mai profitabilă proprietate pentru Paramount Consumer Products, generând peste 13 miliarde de $ în venituri de marfă în 2019.

Multe dintre ideile serialului au originat în The Intertidal Zone, o bandă desenată educativă nepublicată creată de Hillenburg în 1989 cu scopul de a educa studenții despre viața acvatică. El a început să dezvolte serialul în 1996, iar în 1997 un episod pilot de 7 minute a fost prezentat la Nickelodeon. Executivii canalului au vrut ca SpongeBob să fie un copil, dar Hillenburg a preferat ca el să fie un personaj adult. El era gata să abandoneze serialul, dar în cele din urmă a compromis creând personajul Doamna Puff și școala ei de navigat ca SpongeBob să frecventeze o școală ca un adult.

Nickelodeon a difuzat o avanpremieră pentru serial în Statele Unite pe 31 mai 1999, după difuzarea ediției din 1999 a Kids' Choice Awards. Premiera oficială a avut loc pe 17 iulie 1999. A devenit enorm de popular din al doilea sezon, și apoi a fost primit cu laude în toată lumea. Al treisprezecelea sezon a început în octombrie 2020, iar pe 24 martie 2022 serialul a fost reînnoit pentru un al paisprezecelea sezon. Serialul a inspirat trei filme, Burețelul Bob și Coroana Regelui Neptun (2004), SpongeBob: Aventuri pe uscat (2015) și SpongeBob: Misiune de salvare (2020). Două seriale spin-off, Tabăra Coral: Cu SpongeBob mini-marini și Un show cu Patrick Stea, au debutat în 2021. Din februarie 2022, patru filme sunt plănuite: trei filme spin-off de personaje pentru Paramount+ și un nou film cinematografic cu SpongeBob.

SpongeBob Pantaloni Pătrați a fost premiat cu o mulțime de premii, incluzând șase Premii Annie, opt Premii Golden Reel, patru Premii Emmy, 19 Premii Kids' Choice Awards și două Premii BAFTA pentru Copii. Un muzical pe Broadway bazat pe serial a început în 2017 cu laude din partea criticilor.

În România, serialul a fost difuzat pe canalele de televiziune PRO TV, Boom Smarty și Kanal D, iar în prezent serialul se difuzează pe canalele de televiziune Nickelodeon, Nicktoons și Comedy Central.

Istorie
Nickelodeon a ținut o previzualizare pentru seria din Statele Unite pe 1 mai 1999, în urma emisiunii televizate a Premiilor Kids 'Choice 1999. Seria a avut premiera în mod oficial pe 17 iulie 1999. A primit recunoaștere critică la nivel mondial încă de la premieră și a câștigat o popularitate enormă până în al doilea sezon. Un film de lung metraj, Filmul SpongeBob SquarePants, a fost lansat în teatre pe 19 noiembrie 2004, iar un sequel a fost lansat pe 6 februarie 2015. În anul 2017 serialul a început să difuzeze sezonul al unsprezecelea și a fost reînnoită pentru un sezon al doisprezecelea.

Serialul a câștigat o varietate de premii, printre care șase premii Annie, opt premii Golden Reel, patru premii Emmy, 15 premii pentru copii și două premii BAFTA pentru copii. În ciuda popularității pe scară largă, seria a fost implicată în mai multe controverse publice, printre care una care se axa pe speculații asupra orientării sexuale a SpongeBob. În anul 2011, o specie nouă de ciuperci descrisă, Spongiforma squarepantsii, a fost numită după personajul titlului de desene animate. Un muzical de pe Broadway, bazat pe serialul deschisă în anul 2017, la aprecierea critică.

Personaje
SpongeBob Pantaloni Pătrați (en. SpongeBob SquarePants) - Este un burete care trăiește pe Fundul Mării într-o casă făcută dintr-un ananas și muncește la Krusty Krab.
Patrick Stea (en. Patrick Star) - Este amicul prostovan al lui SpongeBob, cu care își petrece majoritatea timpului. El locuiește sub o rocă și e vecin cu SpongeBob.
Calamar Tentacule (en. Squidward Tentacles) - Este o caracatiță morocănoasă. El este vecinul lui SpongeBob Pantaloni Pătrați și Patrick și care este mereu enervat de ei doi. El lucrează la Krusty Krab, deși nu-i place slujba sa.
Eugene Krabs (en. Eugene H. Krabs) - Este un crab zgârcit care deține Krusty Krab și e șeful lui SpongeBob și al lui Calamar. A inventat formula celui mai apreciat burger din mare.
Perla Krabs (en. Pearl Krabs) - Este fiica lui Krabs care este o balenă.
Sheldon Plankton (en. Sheldon J. Plankton) - Este rivalul lui Krabs care deține restaurantul Găleata cu Scoici (Chum Bucket) și încearcă să fure formula secretă de Turtițe Krabby.
Karen Plankton - Este soția computer a lui Plankton.
Sandy Veveriță (en. Sandy Cheeks) - Este o veveriță, prietenă cu SpongeBob și Patrick, care și-a construit o capsulă plină cu aer, ca să trăiască în ocean.
Doamna Puff (en. Mrs. Puff) - Este profesoara de la școala de navigat. Ea este morocănoasă și nu-i place să-l vadă pe SpongeBob.
Gary - Este animăluțul de companie al lui SpongeBob. El este un melc.
Omul Sirenă și Băiatul Scoică (en. Mermaid Man and Barnacle Boy) - sunt doi super-eroi pensionari care au avut propriul lor serial TV cu super-eroi și răufăcători, ei luptând în realitate împotriva răului.
Homarul Larry (en. Larry the Lobster) - Este un homar și cel mai musculos și mai puternic din ocean.

Episoade

Referințe și note

Legături externe

Nickelodeon
Seriale de televiziune americane
Seriale de televiziune după care s-au făcut piese de teatru

redpajama_set_name: RedPajamaWikipedia


Where marketers come to grow.
You've carefully picked out your brand colors, fonts, shapes and more. Maybe you've even had a logo designed to spec.
And at first, it's easy to stand behind your brand. You like the choices you've made. You feel the elements you've selected accurately reflect your business and the market you're looking to serve.
But something strange happens. After a while, you begin to feel bored with your brand identity.
You see your competitors update their website design and suddenly your fresh logo looks outdated by comparison.
Is it time to follow suit and call upon a graphic designer to whip up a new design? Don't be so hasty. It's best to think of your branding like a marriage commitment and here's why.
Your logo signifies the relationship that exists between you and your customers.
Your customers have come to identify with your branding. When you change it without warning, and without asking for feedback, they could feel confused or betrayed.
Your logo is seen by your customers everywhere. They see it on your flyers and brochures, your website, your products, your packaging and so on. They become familiar with it and begin to identify your product or service with it.
It's easy to think of your logo as being yours, but as you build your customer base, it becomes theirs.
Just like in a marriage, your life is not your own anymore. It belongs equally to your partner.
When you're single, you answer to yourself. When you're married, you need to involve your partner in important decisions.
In early 2011, Starbucks announced a change to their logo, removing the words "Starbucks" and "coffee" from it. Fans were in an outrage.
Many businesses make decisions about their branding and marketing without first talking to their audience.
Do you know what makes your company unique? Your most loyal customers do, so survey them and ask for their opinion before making unwarranted changes to your brand.
The truth is the market changes every day.
Businesses sometimes feel the need to adapt based on shifts they see in the market.
It is a good idea to stay up-to-date with changes in your industry and the needs of your customer.
But if you adapted your branding every time you saw something new coming, you would be endlessly reworking your identity.
When the market changes, does what you stand for as a company change? Do your values change?
It shouldn't. Therefore, your brand doesn't need to change every time the market does.
In marriage, many things will change around you and your partner, but your consistency with each other and your values make your bond strong. Wanting to change on every whim can drive each of you crazy.
In marriage, change is important, but you look for ways to help each other without compromising yourself.
If you want to shift with the market, create new products and services to serve your customers. You don't need to change your brand.
What do you value you most? Your values should guide your branding, not the other way around.
Marriage is not so much about monetary costs, but you are investing your entire future with another person. It's obviously important to focus on the key aspects of marriage to make it successful. If each person goes into the marriage with a different vision it can require a huge use of time to realign things so both are on the same page.
How much does rebranding cost? This depends a lot on the size of your company, but according to HiveMind Studios, the average B2B company spends about 5% of revenues on marketing. In that context, the average rebranding initiative costs about 10% to 20% of the marketing budget.
In a business that makes $15 million and whose marketing budget is $750,000, the cost of rebranding would be anywhere from $75,000 to $150,000.
Rebranding initiatives can require a lot of capital and manpower – resources that could be better spent on new products and services to fill the gaps in your offers.
Creating new offers can also increase your revenue. Rebranding will just increase your expenses, and unless there's a good reason to rebrand, it will not do much to grow your business.
Marriage is one of the most important commitments people make in life. Successful marriages possess certain key elements like proper self analysis and communication with your future partner.
For a business, creating a brand identity is similar to a marriage.
Once your brand is cemented in the minds of the people you're serving, changing it carries certain risks.
Customers that used to identify with you may not want to buy from you anymore.
Customers who used to rely on your products and services may become confused about who you are. They may not recognize your business as being the same one that previously served them.
Additionally, you may receive an outpouring of negative feedback. This can be a publicity nightmare.
Remember to think of your branding like a marriage. Once you've made a commitment to it, you must uphold that commitment for the sake of your businesses.
Is there a branding challenge you're trying to address? Schedule your free 60-minute marketing conversation now.
© 2019 Palmer Ad Agency - All Rights Reserved.


On the 2nd day of Christmas Sassy Mama gave to me … an absolutely adorable mummy-and-me wardrobe from Glitter Glam worth $250!
As a mama, matching outfits with your daughter is just the cutest! Just think, how many times has your little girl wanted to dress up just like mama and wear your shoes, your lipstick, or even your perfume? The bond between mummy and daughter is so strong, and what better way to express this than with mother-daughter mini-me fashion?
Local label Glitter Glam and their child spinoff Mary Had A Little Lamb have together pioneered matching mama-and-mini-me fashion in Singapore. The collection of mummy-daughter fashion is full of trendy and absolutely darling designs sure to make for some amusing and sweet photo ops!
Sassy Mama is giving one lucky mama the chance to win a complete and matching set of mother-and-child outfits from the Glitter Glam x Mary Had A Little Lamb collection!
Time to get this giveaway all wrapped up!
Remember mamas, you've got to be in it to win it! So simply drop your (and your friends') details in the form below to enter. Simple!
You only have to enter once for your chance to win any one of the amazing prizes over the entire giveaway period, so start crossing those fingers for the next 12 days!


text:
Q: Image can't upgrade in CI PHP I using CI for build my website and i have some issue with my code, my profile page can't change image for profile. This is my code

*

*Controller
public function edit()
{
  $data['title'] = 'Edit Profile';
  $data['user'] = $this->db->get_where('user', ['email' => $this->session->userdata('email')])->row_array();

  $this->form_validation->set_rules('name', 'Full Name', 'required|trim');

  if ($this->form_validation->run() == false) {
    $this->load->view('templates/header', $data);
    $this->load->view('templates/sidebar', $data);
    $this->load->view('templates/topbar', $data);
    $this->load->view('user/edit', $data);
    $this->load->view('templates/footer');
  } else {
    $name = $this->input->post('name');
    $email = $this->input->post('email');

    // cek jika gambar yang akan diubah

    $upload_image = $_FILES['image']['name'];

    if ($upload_image) {
      $config['allowed_types'] = 'gif|jpg|png';
      $config['max_size']      = '2048';
      $config['upload_path']   = './assets/img/profile/';

      $this->load->library('upload', $config);

      if ($this->upload->do_upload('image')) {
        $new_image = $this->upload->data('file_name');
        $this->db->set('image', $new_image);
      } else {
        echo $this->upload->display_errors();
      }
    }

    $this->db->set('name', $name);
    $this->db->where('email', $email);
    $this->db->update('user');

    $this->session->set_flashdata('message', '
Your profile has been updated
');
    redirect('user');

*View

Picture

            <img src="<?= base_url('assets/img/profile/') . $user['image']; ?>" class="img-thumbnail">

              <input type="file" class="custom-file-input" id="image" name="image">
              Choose file

What should I do to solved this issue?

redpajama_set_name: RedPajamaStackExchange


text:
ALT Main Site
#ALTC Blog
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#altc blog editors
ALT News
Chief Executive's Reports
Special Interest Group updates
Research (RLT)
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altc2011
The 2011 and 2012 ALT Conferences
By the time this report is available, ALT-C 2011 will be upon us, having absorbed the lion's share of the ALT staff team's efforts in recent weeks. Alongside this, we are working out the overall focus and shape of the 2012 conference, which will take place in Manchester between 11 and 13 September, and which will be chaired by a "troika" of Jonathan Drori, Sarah Sherman, and Julie Voce. We will announce full details of the conference on 8 September at which time we will also be inviting expressions of interest in membership of the ALT-C 2012 Programme Committee, with a substantial proportion of those involved in the 2011 committee being given the option of continuing their membership for a further year.
HE White Paper and the HEFCE's new Strategy Statement
The HE White Paper and HEFCE's "Opportunity, choice and excellence in higher education" [PDF] were published earlier this month. The White Paper is largely silent on technology in learning (its focus is much more on the long term shape of the HE system in England). In contrast, the HEFCE Strategy Statement has a couple of helpful references to learning technology, with one of six HEFCE objectives for learning and teaching being: "To support the continuous improvement of teaching, learning and assessment, diverse forms and modes of provision, the effective utilisation of learning technologies and the increased accessibility and use of open educational resources." ALT will be responding formally to the consultation questions for the White Paper, and, by arrangement with HEFCE, we will also be summarising briefly for HEFCE our perspectives on "the effective utilisation of learning technologies" consideration by HEFCE as it develops its business plan later this year.
Election of two new Trustees
ALT is governed by a board of 13 trustees, nine of whom are elected by the membership as a whole, with three vacancies filled each year. This year there has been one nomination for the role of vice-chair (who will become chair in 2012 and president in 2013): This candidate will be declared elected unopposed at the ALT Annual General Meeting on 7 September in Leeds. There have been four nominations for the two vacancies as trustees. We have engaged Electoral Reform Services to run an online ballot of the membership to choose the two new trustees. The four candidates are: Alastair Clark (NIACE), Lesley Diack (Robert Gordon University), Matt Lingard (LSE) and Stuart Sutherland (National College for School Leadership). All ordinary and certified individual members, and the representatives of all organisational and sponsoring members, will be sent voting instructions on ALT's behalf from ERS, by email, during August. The closing date for voting will be 1 September 2011. Please use your vote.
Vacancies on our four operational committees
We have some vacancies on each of our four operational committees (Further Education, Membership Services, Publications, and Research), for an initial three year term, with effect from autumn 2011. Becoming a member of one of these committees is a good and reasonably "low-hurdle" way to get involved in ALT. Membership is open to non-members – although anyone appointed to a committee who is not already an ordinary or certified member of ALT is expected to join before taking up their role. Current memberships are shown here http://www.alt.ac.uk/about-alt/who-we-are/operational-committees. You can express an interest from the ALT website. The closing date for expressions of interest is 9 September 2011.
An honour for ALT founder member and ambassador Wendy Hall
We are proud to announce that Wendy Hall, who is a founder member of ALT and who is now one of our three ambassadors has just been honoured (with Manuel Castells, Vint Cerf, David Clark, Joi Ito and Niklas Zennström) with a Lifetime Achievement Award from the Oxford Internet Institute in recognition of her significant contributions to the development of web technologies and web science research.
Seb Schmoller
If you enjoyed reading this article we invite you to join the Association for Learning Technology (ALT) as an individual member, and to encourage your own organisation to join ALT as an organisational or sponsoring member.
ITN Productions Industry News and the Association for Learning Technology (ALT) co-production. Find out more
AmplifyFE Project at the VocTeach Symposium
Learning Technologist…and what is next? The impact of the Covid-19 pandemic in the opportunities for career progression
Transforming TEL support during a pandemic
Developing accessible network simulation software for the visually impaired
A new team's adventure in Digital Learning (James McDonald, Edel Gallagher)
The Question of 'Disruptive Technologies': some heretical thoughts
The Self Organised Learning Environment (SOLE) School Support Pack
Some pros and cons of 'track-changes' feedback on work returned to students electronically
Social media in education: ethical concerns
Learning about Hospital Ward Rounds with 360-Degree Video
ALT Latest
Measuring the correlation between digital media usage and students' perceived writing ability: Are they related? January 15, 2021
Two groups separated by a shared goal: how academic managers and lecturers have embraced the introduction of digital technologies in UK Higher Education January 15, 2021
Use of augmented reality (AR) to aid bioscience education and enrich student experience January 15, 2021
OERxDOMAINS Conference 2021 - Call for Proposals January 14, 2021
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Is it time to ask for the guidance of a North Canaan, CT, tax preparation provider that also delivers IRS help services? At Riccardelli Accounting, we offer the insights you need to keep your tax bill the lowest allowed by law. Tiny issues can blow up quickly, so talk to our preparers and help ensure your filings are all in proper order.
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The annual Goat Days Festival is a Millington tradition and takes place the second full weekend in September each year. Bigger and better than ever, Goat Days kicks off with the World's Greatest Goat Parade at 5:30 PM on Friday and the family fun continues non-stop until the end at 10:00 PM on Saturday. Tractor pulls, antique tractor show, equestrian events, car show and swap meet, KCBS Championship BBQ Contest, Arts & Crafts, games and rides, fishing rodeo, horseshoe and corn hole tournaments, battle of the bands, incredible food, live music and goats, goats and MORE GOATS!
Benefiting many charitable organization, Goat Days is presented by the City of Millington in memory of the event founder, W. S. "Babe" Howard, sponsored by Republic Services, Carey's Body Shop, Ritter Communications, Homer Skelton Ford and Homer Skelton Chrysler, Dodge, Jeep.
$5 per car load, festival admission FREE.


Suvari is a very good and affordable choice for a family blue cruise. Captain Sahin is a super host and an experienced captain. He and his crew will do their best to make Your holiday a great memory of beautiful bays, and wonderful meals.


"V" front neckline with sheer tank straps, while the back is a sheer bateau neckline with a plunging "V" satin back neckline. The entire sheer build-up is heavily beaded and embroidered with beaded trim along the entire empire waist. This fitted sleek satin a-line gown has matching satin buttons from the nape of the neck to the end of the train. A side zipper makes is easy to wear this elegant gown and maintains the beautiful beading and embroidery on this stunning gown.


text:
\section{Introduction}
Ultraperipheral relativistic heavy ion collisions can explore several
aspects of particle and nuclear physics and have been extensively
discussed in the literature (for a small sample of references, see
e.g. \cite{Jackson, Bertulani:1988,Cahn:1990jk,Baur:1990fx,KN99,
Bertulani:1999cq,Goncalves:2001vs,KNV02,Goncalves:2003is,Bertulani:2005ru,
Baltz:2007kq,AyalaFilho:2008zr,Salgado:2011wc}).
In a recent publication we explored lead-lead peripheral collisions
at energies available at the CERN Large Hadron Collider to probe gluon
distributions in nuclei \cite{Adeluyi:2011rt}. Using recent gluon
distributions from global fits to data, we investigated the
sensitivity of direct photoproduction of heavy quarks and exclusive
production of vector mesons to varying strength of gluon
modifications. This idea, originally proposed in
Ref. \cite{Goncalves:2001vs}, can be used to constrain nuclear gluon
distribution from data on production of heavy quarks and vector mesons.

In this article we extend our previous work by considering both
direct and resolved processes in the photoproduction of heavy quarks
in ultraperipheral proton-lead (pPb) and lead-lead (PbPb) collisions
at the LHC. We also consider, as an addition to the previous treatment,
exclusive production of vector mesons in pPb collisions. Our main goal
is to investigate quantitatively the extent of applicability of these
processes in constraining nuclear gluon modifications. In order to
present a self-contained report we include all relevant results and
discussions from our previous study.

The paper is organized as follows: below we briefly discuss the photon
flux generated by one of the nuclei (or proton), making reference to
several previous publications where it has been discussed in details.
Sec.~\ref{phothadupc} treats the photoprocesses considered in this
study, as well as the input nuclear and photon parton distributions.
In Sec.~\ref{res} we present the results of our calculations and a
brief comment on theoretical errors. Our conclusion is contained in
Sec.~\ref{conc}.

For a given impact
parameter ${\bf b}$, the flux of virtual photons with photon energy
$k$, ${d^3N_\gamma(k,{\bf b}) / dkd^2b} $,  is strongly dependent
on the Lorentz factor $\gamma$. At the Large Hadron Collider (LHC) at
CERN the Lorentz factor in the laboratory frame $\gamma_L$ is $7455$
for proton-proton (pp), $4690$ for proton-lead (pPb) and $2930$
for lead-lead (PbPb) collisions. The relationship between the Lorentz
contraction factor associated with the relative velocity between the
colliding nuclei, and the collider energy per nucleon, $E/A$, in GeV,
is given by $\gamma=2\gamma_L^2-1 \approx 2(1.0735E/A)^2$.
The photon flux also depends strongly on the  adiabaticity parameter
 $\zeta=kb/\gamma$ \cite{Bertulani:1988, Cahn:1990jk,Baur:1990fx}:
\begin{equation}
\frac{d^3N_\gamma(k,{\bf b})}{dkd^2b} =
\frac{Z^2\alpha \zeta^2}{\pi^2kb^2} \left[ K_1^2(\zeta) + \frac{1}{
\gamma_L^2} K_0^2(\zeta) \right] \, \, ,
\label{dpf}
\end{equation}
which drops off exponentially for $\zeta >1$, above a cutoff
energy determined  essentially by the size of the nucleus,
$E_{cutoff} \sim \gamma$MeV$/b$ (fm).

For symmetric nucleus-nucleus (AA) collisions, such as PbPb
collisions at the LHC, each nucleus can act equally as source or
target of the photon flux.
Integrating ${d^3N_\gamma(k,{\bf b}) / dkd^2b} $ over impact
parameters with the constraint of no hadronic interactions  and
accounting for the photon polarization yields the total
photon flux ${dN_\gamma^Z(k) / dk} $  given by  \cite{KN99,Baltz:2007kq},
\begin{eqnarray}
\frac{dN_\gamma^Z(k)}{dk}& =&
2 \pi \int_{2R_A}^{\infty} db \, b
\int_0^R  {dr \, r \over \pi R_A^2}
\int_0^{2\pi} d\phi  \nonumber \\
&\times& {d^3N_\gamma(k,b+r\cos \phi)\over dkd^2b} \, \, ,
\label{npf}
\end{eqnarray}
with $R_A$ the radius of the nucleus.

In the case of proton-nucleus (pA) collisions, the nucleus
acts preferentially as the source and the proton as the target,
leading predominantly to $\gamma$p processes. But there is still
a non-negligible contribution from $\gamma$A processes in which the
proton acts as the source of photons and the nucleus as the target.
Thus expressions for both types of fluxes are required for pA collisions.
The flux due to the nucleus (of charge Z) can be evaluated
analytically and is given by \cite{Bertulani:1988},
\begin{eqnarray}
\frac{dN_\gamma^Z(k)}{dk} &=&
{2Z^2 \alpha \over\pi k} \bigg[ \zeta_R^{pA}K_0(\zeta_R^{pA})
K_1(\zeta_R^{pA}) \nonumber \\
&-& {(\zeta_R^{pA})^2\over 2} \big(K_1^2(\zeta_R^{pA})-K_0^2(\zeta_R^{pA})
\big) \bigg] \, \, ,
\label{anaf}
\end{eqnarray}
with reduced adiabaticity parameter, $\zeta_R^{pA}$, given by
$\zeta_R^{pA} = k(R_p + R_A)/\gamma$ and $R_p$ the effective radius
of the proton.

The flux due to the proton is usually estimated using the dipole
formula for the electric form factor \cite{Drees:1988pp}:
\begin{eqnarray}
\frac{dN_\gamma^p(k)}{dk} &=& \frac{\alpha}{2\pi k}
\bigg[1+ \big(1-\frac{2k}{\sqrt{S_{NN}}}\big)^2\bigg]
\nonumber \\
&&\bigg(\ln{D} - \frac{11}{6} + \frac{3}{D} - \frac{3}{2D^2}
+\frac{1}{3D^3}\bigg) \, \, ,
\label{pf}
\end{eqnarray}
where
$D = 1 + [\rm 0.71 \, GeV^2/Q_{\rm min}^2]$ and the minimum momentum
transferred $Q_{\rm min}^2 = k^2/[\gamma^2(1-2k/\sqrt{S_{NN}})]$.

With the knowledge of the photon flux, any generic total photoproduction
cross section can be expressed as a convolution
of a process cross section $\sigma_{\gamma}^{X}(k)$
and the photon flux, $dN_\gamma/dk$. Thus for AA collisions
\begin{equation}
\sigma^{X}=2 \int dk \,\frac{dN_\gamma^Z(k)}{dk}\, \sigma^{\gamma A
  \rightarrow X}(k) \, \, ,
\label{tAAxs}
\end{equation}
with ${dN_\gamma^Z}/{dk}$ given by  Eq.~(\ref{npf}). The factor of $2$
accounts for the source/target symmetry present in AA collisions. In
the case of pA collisions, we have
\begin{equation}
\sigma^{X}= \int dk \bigg[\frac{dN_\gamma^Z}{dk}\, \sigma^{\gamma p
  \rightarrow X}(k)
+ \frac{dN_\gamma^p}{dk}\, \sigma^{\gamma A
  \rightarrow X}(k)\bigg] \, \, ,
\label{tpAxs}
\end{equation}
with ${dN_\gamma^Z}/{dk}$ and ${dN_\gamma^p}/{dk}$ given by
Eq.~(\ref{anaf}) and Eq.~(\ref{pf}) respectively. Relevant
expressions for the rapidity distributions for both AA and pA
collisions are given later.
\section{Photon-hadron interactions in ultraperipheral collisions}
\label{phothadupc}
\subsection{Photoproduction of heavy quarks}
From the viewpoint of a Fock space decomposition, photon
interactions with hadrons and nuclei can be classified as
direct or resolved.
In direct interactions the photon behave as a point-like
particle (``bare photon'') while in resolved interactions the
photon fluctuates into a quark-antiquark state or an even more complex
partonic configuration consisting of quarks and gluons. The cross section
for the photoproduction of a pair of heavy quarks,
$\sigma^{\gamma H\to Q\overline{Q}X}\, (k)$,
is thus a sum of both the direct and resolved
contributions,
\begin{equation}
\sigma^{\gamma H \rightarrow Q\overline{Q}X}\, (k) =
\sigma^{\gamma H \rightarrow Q\overline{Q}X}_{direct}\, (k) +
\sigma^{\gamma H \rightarrow Q\overline{Q}X}_{resolved}\, (k) .
\end{equation}
Here $H$ stands for a proton or a nucleus ($H \equiv p, A$)
and the total photoproduction cross section is obtained by convoluting
the equivalent photon flux, $dN_\gamma(k)/dk$, with
$\sigma^{\gamma H\rightarrow Q\overline{Q}X}\, (k)$, as described by
Eq.~(\ref{tAAxs}) and Eq.~(\ref{tpAxs}) for AA and pA collisions.

Let us now consider both processes in some detail.
At leading order (LO), photon-gluon fusion leading to the production of
a heavy quark pair is the only subprocess relevant to direct
photoproduction. In view of the high energies
involved, perturbative QCD is applicable, and the direct
photoproduction cross section
can be expressed as a convolution of the partonic cross section for the
subprocess $\gamma g \rightarrow Q \overline{Q}$ and the relevant
nucleon or nuclear gluon distribution:
\begin{equation}
\sigma^{\gamma H\rightarrow Q\overline{Q}X}_{direct}\, (s) =
\int dx
 \,  \sigma^{\gamma g \rightarrow Q\overline{Q}}(\hat{s}) \,
 f_{g}^{H}(x,Q^2)\,\Theta(\zeta) \, ,
\label{dppcs}
\end{equation}
with $x$ the momentum fraction carried by the gluon.
We use $m_Q$ for the mass of the heavy
quark (charm or bottom), $s=W_{\gamma H}^2$ denotes
the square of the center-of-mass energy of the photon-nucleus
(or photon-nucleon) system, $\hat{s}=W_{\gamma g}^2$ that of the
photon-gluon system, and $\zeta = \hat{s}-4m_{Q}^2$.
The gluon distribution in $H$, $f_{g}^{H}(x, Q^2)$, is evaluated at
the pQCD factorization scale $Q^2=W_{\gamma g}^2=\hat{s}$.
The function $\Theta(\zeta)$ enforces a minimum (``threshold'') value
of $x$, $x_{min}$, on the integral given by
$x_{min} = 4m_q^2/W_{\gamma H}^2$

The partonic photon-gluon fusion cross section is given
by \cite{Gluck:1978bf,JonesWyld,FriStreng78}
\begin{eqnarray}
\sigma^{\gamma g \rightarrow Q \overline{Q}} \, (\hat{s})= \frac {2\pi\,\alpha_{em}\,\alpha_s(Q^2)\,e_Q^2}
{\hat{s}} \nonumber \\
\times \left[(1+\beta -\frac{\beta^2}{2})
\ln\big[\frac{1+\nu}
{1-\nu}\big]  -(1+\beta)\, \nu\right] \,\,,
\label{plcs}
\end{eqnarray}
with $e_Q$ the electric charge of the heavy quark $Q$, $\alpha_{em}$ the
electromagnetic coupling constant,
$\beta=4\,m_Q^2/\hat{s}$, and $\nu=\sqrt{1-\beta}$.

The resolved contribution is identical to the hadroproduction of
heavy quarks, and at leading order, involves terms corresponding to
gluon-gluon and quark-antiquark subprocesses. The resolved cross
section can be written as
\begin{widetext}
\begin{equation}
\sigma^{\gamma H\rightarrow Q\overline{Q}X}_{resolved}\, (s) =
\int d\tilde{x} \left[f_{g}^{\gamma}(x_1,Q^2) f_{g}^{H}(x_2,Q^2)
 \sigma^{g g \rightarrow Q\overline{Q}}(\hat{s})
+ \sum_{q}f_{q}^{\gamma}(x_1,Q^2)[f_{q}^{H}(x_2,Q^2)+f_{\bar{q}}^{H}(x_2,Q^2)]
\sigma^{q \bar{q} \rightarrow Q\overline{Q}}(\hat{s}) \right]\Theta(\zeta)
\label{rppcs}
\end{equation}
\end{widetext}
where $d\tilde{x} \equiv dx_1 dx_2$, $f_{a}^{\gamma}(x_1,Q^2)$ ($f_{a}^{H}(x_2,Q^2)$)
is the distribution of parton $a$ with momentum fraction $x_1$
($x_2$) in a photon ($H$) respectively, $\hat{s}=x_1x_2s$
and $\zeta = \hat{s}-4m_{Q}^2$. The summation over $q$ runs over the
light flavors, i.e. $q = u,d,s$.

The partonic cross sections $\sigma^{g g \rightarrow  Q\overline{Q}}(\hat{s})$
and $\sigma^{q \bar{q} \rightarrow Q\overline{Q}}(\hat{s})$ are given
by \cite{Gluck:1977zm,Combridge:1978kx,Brock:1993sz}
\begin{eqnarray}
&& \sigma^{g g \rightarrow Q \overline{Q}} \, (\hat{s})= \frac {\pi \,\alpha_s^2(Q^2)}
{3\hat{s}} \nonumber \\
&\times&\left[(1+\beta +\frac{\beta^2}{16}) \ln(\frac{1+\nu}{1-\nu})
-(\frac{7}{4}+\frac{31}{16}\beta)\, \nu\right] \,
\label{ggcs}
\end{eqnarray}
and
\begin{eqnarray}
\sigma^{q \bar{q} \rightarrow Q \overline{Q}} \, (\hat{s})= \frac {8\pi\,\alpha_s^2(Q^2)}
{27 \hat{s}}\left[(1+\frac{\beta}{2}) \sqrt{1-\beta}\right] \,\, .
\label{qqbcs}
\end{eqnarray}
Here $\beta$ and $\nu$ are as defined previously.

It is often more enlightening to represent the
cross section in terms of rapidity, that is, to consider
rapidity distributions.
The differential cross section with respect to the rapidity
of the heavy quark pair,
$d\sigma/dy$, is related to the differential cross section
with respect to photon energy, $d\sigma/dk$, through
the relation $d\sigma/dy = kd\sigma/dk$. The rapidity
distribution can therefore be expressed as
\begin{equation}
\frac{d \sigma^{\gamma H \rightarrow Q \overline{Q}X}}{dy} =
k\, \frac{dN_\gamma(k)}{dk}\, \sigma^{\gamma H
\rightarrow Q \overline{Q}X}(k)
\label{Hqqhrap}
\end{equation}
and scales directly with the photon flux $dN_\gamma/dk$.
Thus for pA collisions, with the convention that the proton is
incident from the right and the nucleus from the left, the total
rapidity distribution is
\begin{eqnarray}
\frac{d \sigma^{pA \rightarrow Q \overline{Q}X}}{dy}&=&
\bigg[k \, \frac{dN_\gamma^Z(k)}{dk}\, \sigma^{\gamma p
\rightarrow Q \overline{Q}X}(k)\bigg]_{k=k_l} \nonumber \\
&+&\bigg[k \, \frac{dN_\gamma^p(k)}{dk}\, \sigma^{\gamma A
\rightarrow Q \overline{Q}X}(k)\bigg]_{k=k_r}
\label{pAqqhrap}
\end{eqnarray}
where $k_l$ ($k_l \propto e^{-y}$) and $k_r$ ($k_r \propto e^{y}$)
simply denote photons from the nucleus and proton respectively,
and the fluxes ${dN_\gamma^Z}/{dk}$ and ${dN_\gamma^p}/{dk}$ are given by
Eq.~(\ref{anaf}) and Eq.~(\ref{pf}). As remarked earlier, the
fluxes have support only at small values of $k$, dying out
exponentially at large $k$. Thus the first term on the right-hand side
($\gamma$p distribution) peaks at positive rapidities while the
second term ($\gamma$A distribution) peaks at negative rapidities.
Since both the fluxes and process cross sections are different,
the total distribution is manifestly asymmetric, and the $\gamma$p
term dominates due to the much larger nuclear
flux ${dN_\gamma^Z}/{dk}$.

The total rapidity distribution for AA collisions can
likewise be written as
\begin{eqnarray}
\frac{d \sigma^{AA \rightarrow Q \overline{Q}X}}{dy}&=&
\bigg[k \, \frac{dN_\gamma^Z(k)}{dk}\, \sigma^{\gamma p
\rightarrow Q \overline{Q}X}(k)\bigg]_{k=k_l} \nonumber \\
&+&\bigg[k \, \frac{dN_\gamma^Z(k)}{dk}\, \sigma^{\gamma A
\rightarrow Q \overline{Q}X}(k)\bigg]_{k=k_r}
\label{AAqqhrap}
\end{eqnarray}
with $k_l$ ($k_r$) simply denoting photons from the nucleus
incident from the left (right) and the flux ${dN_\gamma^Z}/{dk}$
given by Eq.~(\ref{npf}). Here the process cross sections and
the left/right fluxes are identical, thus the respective rapidity
distributions are mirror images of each other, and consequently the
total distribution is symmetric about midrapidity ($y=0$).

\subsection{Exclusive production of vector mesons}
The cross section for the exclusive elastic photoproduction of a
vector meson $V$ on $H$ ($H \equiv p, A$) can be written as
\begin{equation}
\sigma^{\gamma H \rightarrow VH} (k) = \left.  \frac{d \sigma^{\gamma
H \rightarrow VH}}{dt} \right| _{t=0}  \int dt | F_H(t) |^{2} ,
\label{eepvm}
\end{equation}
where $d \sigma^{\gamma A \rightarrow VA}/ dt|_{t=0}$ is the forward
scattering amplitude and
$F_H(t)$ is the form factor. The dynamical
information is encoded in the forward scattering amplitude while
the momentum transfer of the elastic scattering is determined by the
form factor, which is, in general, dependent on the spatial attributes
of the target $H$.

There have been studies of the photoproduction of $J/\Psi$ and
$\Upsilon$ in ultraperipheral collisions at LHC (see for instance \cite{KN99,
Goncalves:2001vs,Baltz:2007kq,
strikman_plb,per4,ivanov_kop,vicmag_prd2008,AyalaFilho:2008zr,
strikman_jhep,klein_prl,vicmag_prc}).
In this work we use the simple amplitude calculated from leading order
two-gluon exchange in perturbative QCD \cite{Ryskin,Brodsky:1994kf}
and corrected for other
relevant effects (such as relativistic corrections, inclusion of the
real part of the scattering amplitude, next-to-leading order NLO
effects, etc, see for instance \cite{Ryskin:1995hz,Frankfurt:1997fj}) through a
phenomenological multiplicative correction factor $\zeta_V$.

For elastic photoproduction on protons, the corrected LO
scattering amplitude can be written as
\begin{equation}
\left.  \frac{d \sigma^{\gamma p \rightarrow Vp}}{dt} \right| _{t=0} =
\zeta_V \frac{16\pi^3 \alpha_{s} ^{2} \, \Gamma_{ee}}{3 \alpha M_{V} ^{5}}
\left[  x g_p(x,Q^{2}) \right] ^{2} .
\label{epvm_p}
\end{equation}
Here, $M_V$ is the mass of the vector meson ($J/\Psi$ and
$\Upsilon(1s)$ in the present study), $x = M_V^2/W_{\gamma p}^2$ is the fraction of the nucleon momentum carried by the
gluons, and $g_p(x,Q^{2})$ is the gluon distribution in a proton,
evaluated at a momentum transfer $Q^{2} = (M_{V}/2)^{2}$.
$\Gamma_{ee}$ is the leptonic decay width and $\alpha_s$
($\alpha$) the strong (electromagnetic) coupling constant.
Eq.~\ref{epvm_p} is easily generalized to the nuclear case,
\begin{equation}
\left.  \frac{d \sigma^{\gamma A \rightarrow VA}}{dt} \right| _{t=0} =
\zeta_V \frac{16\pi^3 \alpha_{s} ^{2} \, \Gamma_{ee}}{3 \alpha M_{V} ^{5}}
\left[  x g_A(x,Q^{2}) \right] ^{2} ,
\label{epvm_A}
\end{equation}
where $g_A(x,Q^{2}) = g_p(x,Q^{2}) \times R_g^A(x,Q^{2})$ is the
nuclear gluon distribution and $ R_g^A(x,Q^{2})$ the gluon modification.

The correction factor $\zeta_V$ is estimated by constraining the
calculated cross sections for elastic vector meson photoproduction on protons,
$\sigma^{\gamma p \rightarrow Vp}(W_{\gamma p})$, to reasonably
reproduce the photoproduction data from HERA: \cite{Adloff:2000vm}
for $J/\Psi$ and
\cite{Adloff:2000vm,Breitweg:1998ki,Chekanov:2009zz} for $\Upsilon
(1s)$. Further details can be found in \cite{Adeluyi:2011rt}.
In contrast to photoproduction of heavy quarks, the quadratic
dependence of the cross section on the gluon distribution
has the significant implication of making exclusive vector
meson production a very sensitive probe of nuclear gluon
modifications.

We now discuss the momentum-squared transferred dependence ($t$-dependence)
of the cross section. For a proton the standard practice
is to parametrize the $t$-dependence in the form of a rapidly
decreasing exponential function, $e^{b|t|}$, where $b$ is referred to
as the slope parameter. Integrating this function with respect to
$t$ gives a multiplicative factor $1/b$ with units GeV$^{2}$.
In the case of a nucleus, the nuclear form factor $F_A(t)$ is given
by the Fourier transform of the nuclear density distribution:
$F_A(t) = \int d^3r \, \rho_A(r) \, e^{i{\bf q} \cdot {\bf r}}$,
where $q$ is the momentum transferred.
For a heavy nucleus it is customary to model the density
distribution as a Woods-Saxon distribution with parameters from
electron scattering, $\rho_A(r)= \rho_0 /[1 + e^{[(r-R_{A})/d]}]$,
with central density $\rho_0$, radius $R_{A}$ and skin depth $d$.
For $^{208}$Pb in use at the LHC,
$\rho_0 = 0.16$/fm$^{3}$, $R_{A} = 1.2 A^{1/3}$ fm, and $d =
0.549$ fm \cite{DeJager:1974dg}.

For the proton the photonucleon cross section
$\sigma^{\gamma p \rightarrow Vp} (k)$ is obtained through
\begin{equation}
\sigma^{\gamma p \rightarrow Vp} (k) = \frac{1}{b}\, \frac{d\sigma^{\gamma p\rightarrow
Vp}}{dt}\bigg|_{t=0}
\end{equation}
with slope parameter $b$. In the present study we employ $b = 4.5$ GeV$^{-2}$.
The photonuclear cross section is given by
\begin{equation}
\sigma^{\gamma A\rightarrow VA}(k) = \frac{d\sigma^{\gamma A\rightarrow
VA}}{dt}\bigg|_{t=0} \int_{t_{min}(k)}^\infty dt |F(t)|^2
\end{equation}
Here $t_{min}(k)=(M_v^2/4k\gamma_{L})^2$, as is appropriate for narrow
resonances \cite{klein_prl}.
The total cross sections for pA and AA collisions are obtained
by a convolution of
$\sigma^{\gamma p \rightarrow Vp} (k)$ and $\sigma^{\gamma  A\rightarrow VA}(k)$
with the relevant photon flux as described by
Eq.~(\ref{tpAxs}) and Eq.~(\ref{tAAxs}) respectively.

The photon energy, $k$, is related to the rapidity of the vector
meson $y$ by $k= (M_{V}/2) \exp(y)$.
Thus, as in the case of photoproduction of heavy quarks,
the differential cross section with respect to rapidity is given by
${d \sigma^{\gamma H \rightarrow VH}}/{dy} =
( k {dN_\gamma(k)}/{dk}) \sigma^{\gamma H \rightarrow VH}(k)$, and
the corresponding expressions for rapidity distributions
in pA and AA collisions are of the forms given by
Eq.~(\ref{pAqqhrap}) and Eq.~(\ref{AAqqhrap}) respectively.
The symmetry attributes of the distributions are also similar.

\subsection{Parton distributions in nuclei and photons}
We now turn to the consideration of the parton distributions (PDs) relevant to
the processes considered in the present study. As mentioned earlier,
the direct contribution to the photoproduction of heavy quarks is
dependent solely on the gluon distributions in protons and nuclei,
same as for the elastic photoproduction of vector mesons. The
resolved contribution, on the other hand, requires the distributions
of light quarks and antiquarks and gluons in photons, protons and
nuclei. Thus in addition to the usual requirement of nucleon and
nuclear parton distributions (nPDs), there is also the need for the
relatively poorly known parton distributions in photons ($\gamma$PDs), thereby
increasing the level of the theoretical uncertainties in the
calculation of photoproduction of heavy quarks. Although the direct
contribution is dominant, this dominance does not vitiate the need to
have a good control on the resolved contribution, especially for
$b\bar{b}$ production where the resolved components are quite sizable.

Let us first discuss nuclear parton distributions. It is rather well-known
that the distributions of partons (i.e. quarks and gluons) in
nuclei are quite different from the distributions in free nucleons,
that is, they are ``modified'' by the complex, many-body effects in the
nucleus. These nuclear effects are usually
parametrized in terms of "nuclear modifications" $R_{a}^A(x,Q^2)$
which in general depend on the parton specie ($a$), the nucleus ($A$),
momentum fraction $x$ and scale $Q^2$.
The nuclear effects can be categorized based on different intervals in $x$.
At small values of $x$ ($x \lesssim 0.04$), we have the phenomenon
generally referred to as shadowing. This is a depletion, in the sense
that in this interval, the distribution of a parton $a$ in the nucleus
is smaller compared to the corresponding distribution in a free
proton, i.e. $R_a^A < 1$. Antishadowing, which is an
enhancement ($R_a^A > 1$), occurs in the range $0.04 \lesssim x \lesssim
0.3$. Another depletion, the classic EMC effect \cite{Aubert:1983xm}, is
present in the interval $0.3 \lesssim x \lesssim 0.8$, while for
$x > 0.8$, the Fermi motion region, we have another enhancement.
It is important to note that although both shadowing and
the EMC effect (antishadowing and Fermi motion) correspond to
depletion (enhancement), the physical principles and mechanisms
governing these phenomena are quite different. Further details can be
found in \cite{Geesaman:1995yd,Piller:1999wx,Armesto:2006ph,Kolhinen:2005az}
With the knowledge of $R_{a}^A(x,Q^2)$, nuclear parton distributions
can be expressed as a convolution of free nucleon parton distributions
and nuclear modifications, i.e.
$f_a^A(x,Q^2) = f_a(x,Q^2) \otimes R_{a}^A(x,Q^2)$.

While the determination of quark and antiquark distributions in
nucleons and nuclei is in general a nontrivial task, that of gluons
is even more problematic. Gluons are electrically neutral, and
thus their distributions cannot be extracted directly from
Deeply Inelastic Scattering (DIS) and Drell-Yan (DY) processes
which account for the major part of the data used in global fits.
Their distributions are in general inferred from sum
rules and the $Q^2$ evolution of sea quarks distributions.
The situation is even worse in the nuclear case: the
available data is much less than for nucleons, and there is the added
complication of a mass dependence. It is therefore not unusual for
nuclear gluon distributions from different global fits to differ
significantly, especially in the magnitude of the various nuclear
effects (shadowing, antishadowing, etc). This is especially obvious
at low $Q^2$ (i.e. around their initial starting scales) since
evolution to high $Q^2$ tends to lessen the differences.
Earlier global analyses
\cite{Eskola:1998df,deFlorian:2003qf,Shad_HKN,Hirai:2007sx} relied
heavily on fixed-target nuclear deep-inelastic scattering
(DIS) and Drell-Yan (DY) lepton-pair production.
Incorporation of data on inclusive hadron production in deuteron-gold
collisions has been implemented in \cite{Eskola:2008ca,Eskola:2009uj},
and neutrino-iron data in \cite{Schienbein:2009kk,Stavreva:2010mw,
Kovarik:2010uv}. We should also mention
the approach in \cite{Frankfurt:2003zd,Frankfurt:2011cs} utilizing the Gribov
picture of shadowing. Despite all these advances the nuclear gluon
distribution is still currently the least constrained aspect of global fits to
nuclear parton distributions, as significant uncertainties still persist at
both small and large $x$.

Four recent nucleon and nuclear parton distributions are utilized in
the present study. For the proton we use the Martin-Stirling-Thorne-Watts
(MSTW08) parton distributions \cite{Martin:2009iq} which are
available up to next-to-next-to-leading order (NNLO).
In the nuclear case we use three nuclear modification sets.
Two sets are by  Eskola, Paukunnen, and Salgado, namely EPS08 and EPS09
\cite{Eskola:2008ca,Eskola:2009uj}.
The third is the Hirai-Kumano-Nagai (HKN07) distributions
\cite{Hirai:2007sx}. While EPS08 is only to leading order (LO),
both EPS09 and HKN07 are available up to next-to-leading order (NLO).
The distributions from MSTW08 serve two purposes:
as the free nucleon distributions used in conjunction with
nuclear modifications, and also as a ``special'' nuclear
distribution in the absence of nuclear effects. The latter case is
particularly useful for highlighting the influence of the various
nuclear effects on observables.

It is instructive to compare the characteristics of the gluon
distributions from the four aforementioned sets based on the strength
of their nuclear modifications. In Fig.~\ref{fig:RgPb_Mjpsi} we show
the nuclear modifications for gluons in Pb, $R_g^Pb(x,Q^2)$ from
EPS08, EPS09, and HKN07 at the factorization scale $Q^2 =
M_{J/\Psi}^2$, appropriate for the elastic photoproduction of the $J/\Psi$
meson. As already stated, one can view the MSTW08 gluon distribution
as a nuclear gluon distribution in the limit of zero nuclear effects
( $R_a^A = 1$).
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=8.75cm, height=8.5cm, angle=270]{RgPb_Mv.ps}
\end{center}
\caption[...]{(Color online) Nuclear gluon modifications in Pb,
 $R_{g}^{Pb}(x,Q^2 = M_{J/\Psi}^2)$, from EPS08 (dashed line),
 EPS09 (solid line), and HKN07 (dash-dotted line) respectively.}
\label{fig:RgPb_Mjpsi}
\end{figure}
At this scale, HKN07 has a rather weak gluon shadowing which extends
well into the antishadowing region, no antishadowing and
gluon EMC effect, and an early onset of Fermi motion.
EPS09 exhibits a moderately strong shadowing, and appreciable
antishadowing and EMC effect, with a quite strong Fermi motion.
Nuclear modifications are strongest in EPS08: an especially strong
shadowing, and substantial antishadowing, EMC, and Fermi motion.
Thus in terms of shadowing we have
a progression from zero effects to weak effects, moderate
(intermediate) effects, then to strong effects as one progresses from
MSTW08 to EPS08. The issue of uncertainties in parton distributions
is becoming increasingly important especially in relation to
precision tests of QCD. Discussions on uncertainties in
nuclear parton distributions can be found in \cite{Hirai:2007sx,Eskola:2009uj}.

Parton distributions in photons ($\gamma$PDs) are derived from experimentally
determined photon structure function $F_2^{\gamma}(x,Q^2)$, in conjunction
with appreciable theoretical inputs. These inputs, which are
necessary in implementing the parametrizations of photon parton
distributions from the structure function, account in part for
some of the observable differences in the available photon
parton distribution sets. Another source of differences is in the
choice and scope of experimental data from which $F_2^{\gamma}$ is
extracted. At present there is an appreciable number of photon parton
distribution sets available, both at leading and next-to-leading orders
\cite{Duke:1982bj,Drees:1984cx,Abramowicz:1991yb,Hagiwara:1994ag,
Gluck:1991ee,Gluck:1994tv,Gluck:1991jc,Gordon:1996pm,Gordon:1991tk,
Schuler:1996fc,Schuler:1995fk,Aurenche:1994in,Aurenche:1992sb,Cornet:2002iy,
Cornet:2004ng,Cornet:2004nb}. It should be noted that
unlike in the case of a nucleon, there are no valence quarks
present in the photon; therefore antiquark distributions are the
same as quark distributions. Furthermore, there are no sum rules
governing the gluon content; thus the gluon distribution is
almost totally unconstrained. The gluon distribution contributes to
$F_2^{\gamma}(x,Q^2)$ majorly through the $\gamma^*g \to q\bar{q}$
channel, which has significant numerical support only at small $x$.

In light of the relatively poor situation especially in the gluon
sector, we use three different photon parton distribution sets in the
present study. The rationale for this will become clear when we
present results for the resolved component in heavy quark
production. Two sets are relatively older and have been in common
use: the Gluck-Reya-Vogt (GRV) set \cite{Gluck:1991jc} and that
by Schuler and Sjostrand (SaS1d) \cite{Schuler:1995fk}.
The third set, the Cornet-Jankowski-Krawczyck (CJK2)
set \cite{Cornet:2004ng}, is more recent and has facility to estimate
error on a calculated quantity due to the uncertainties in the input photon
parton distributions. In Fig.~\ref{photpdf3d} we show the parton
distributions from these three sets for the light (u,d,s) quarks and gluon.
\begin{figure}[!htb]
\includegraphics[width=8.75cm, height=9.25cm, angle=270]{photondst.ps}
\caption[...]{(Color online) Parton distributions in the photon
for light quarks (u,d,s) and gluons at $Q^2 = 10$ GeV$^2$
for three distribution sets:  CJK2 (solid line) \cite{Cornet:2004ng},
GRV (dashed line) \cite{Gluck:1991jc}, and SaS1d (dash-dotted line)
\cite{Schuler:1995fk} respectively. For better visuality the down
quark distributions have been enhanced by a factor of $5/3$, the strange quark
distributions by $5/2$, and the gluon distributions by $1/14$.}
\label{photpdf3d}
\end{figure}

The up quark is the best constrained component of photon parton
distributions, and even in this case there are clear differences
between the three sets. This is also the case for the down quark.
Only for the strange quark distribution is there good agreement
between the three sets. But these differences pale in comparison
with that of gluons where the differences between the sets are quite
significant almost across the whole $x$ interval, with CJK2 having
the largest magnitude while SaS1d has the lowest, with the GRV
somewhat intermediate. For the LO resolved contribution to heavy
quark photoproduction, the two competing partonic subprocesses are
the $gg \to Q\bar{Q}$ and $q\bar{q} \to Q\bar{Q}$, and it thus to be
expected that significant differences will arise in the resolved cross
sections whenever the $gg \to Q\bar{Q}$ component is appreciable.

\section{Results}
\label{res}
We now discuss the results of our calculations for both the inclusive
photoproduction of heavy quarks ($c\bar{c}$ and $b\bar{b}$) and the
exclusive elastic production of vector mesons ($J/\Psi$ and
$\Upsilon(1s)$) in pPb ($\sqrt{s_{NN}}=8.8$ TeV) and PbPb
($\sqrt{s_{NN}}=5.5$ TeV) collisions at the LHC.
We take $m_c = 1.4$ GeV and $m_b = 4.75$ GeV for
consistency with the MSTW08 parton distributions, and
$m_{J/\Psi} = 3.097$ GeV and $m_{\Upsilon} = 9.46$ GeV respectively.
The strong coupling constant $\alpha_{s}(Q^{2})$, needed for the
calculations, is evaluated to one loop at the scale $Q^{2}$
using the evolution code contained in the MSTW08 package.
Two comments pertaining to the results on photoproduction of heavy quarks
are in order: first, due to the relative smallness of nuclear effects
in heavy quark photoproduction, especially for pPb collisions, we
have, for visual purposes, left out the results from the HKN07
distributions. In general the HKN07 values are intermediate between
those of EPS09 and MSTW08. Second, while we have used three sets of
photon parton distributions in the calculations, we show only the
rapidity distribution plots using the GRV set, since the GRV results
are consistently somewhat intermediate between those from CJK2 and
SaS1d distributions.

\subsection{Heavy Quarks in pA and AA Collisions}
\subsubsection{Open charm}
In Table~\ref{cccbarpA} we present the cross sections for both
direct and resolved $c\bar{c}$ production in ultraperipheral
pPb collisions at the LHC, using the previously-described
nucleon/nuclear and photon parton distributions. Due to the
large disparity in the magnitude of the photon fluxes from the
proton and the nucleus (Pb), it is a common practice to neglect
the photonuclear ($\gamma$Pb) contribution to the total cross
section. Another simplification is the neglect of the resolved
contribution which is relatively small in comparison with the
dominant direct contribution. Since both the $\gamma$Pb and resolved
contributions are dependent on nuclear and photon parton
distributions, the results presented in
Table~\ref{cccbarpA} afford a good handle in determining the
degree of validity of the above approximations for the rather
significantly different attributes of the distributions utilized
in the present study.
\begin{table}[!htb]
\caption{Cross sections for photoproduction of
$c\bar{c}$ in ultraperipheral pPb collisions at the LHC. All
cross sections are in microbarns ($\mu$b).}
\begin{tabular}[c]{|l| l c c| c c| c c c c|}
\hline
       &&PDF            && Direct       &&&& Resolved & \\
\cline{7-10}
        &&                &&             && SaS1d   && GRV      & CJK   \\
\hline
$\gamma$p &&MSTW08          && 5570      && 692   && 1157   & 1418  \\
\hline
         &&MSTW08          && 607       && 114   && 195    & 228   \\
$\gamma$A &&EPS08           && 376       && 94    && 162    & 185  \\
         &&EPS09	    && 471       && 102   && 175    & 202  \\
\hline
\end{tabular}
\label{cccbarpA}
\end{table}

We first consider the photonuclear part. The $\gamma$Pb
contribution to the total cross section is approximately $10.6\%$ for
MSTW08 (no nuclear modifications), $8.8\%$ for EPS09 (
moderate gluon shadowing), and $7.4\%$ for EPS08 (strong
gluon shadowing), almost totally independent of the choice of
photon parton distribution set. The resolved contribution, on
the other hand, while depending strongly on the choice of
photon parton distributions, has an even more negligible dependence
on the choice of nuclear parton distributions. For the SaS1d
distribution, the resolved component is approximately $12\%$
while it is approximately $18\%$ for the GRV distribution, and
$21\%$ for the CJK2 set. As is to be expected about $96\%$ of the
resolved component stems from $\gamma$p while about $90\%$ of the
$\gamma$Pb contribution derives from the direct component.
Overall the sensitivity to nuclear modifications (dominantly shadowing) is
rather small: the no-modification (MSTW08) total cross section is
reduced by approximately $4\%$ and $2\%$ by the modifications in
EPS08 and EPS09 respectively.

\begin{figure}[!htb]
\begin{center}
\includegraphics[width=8.5cm, height=8.5cm, angle=270]{pphqpArap_cc_t.ps}
\end{center}
\caption[...]{(Color online) Rapidity distributions of $c\bar{c}$
photoproduction in pPb collisions at the LHC using the GRV photon
parton distributions. Left panel: $\gamma$p and $\gamma$Pb
contributions to total rapidity distributions. Dotted line depicts
the $\gamma$p contribution while the dashed (MSTW08), solid
(EPS09), and dash-dotted (EPS08) lines correspond to $\gamma$Pb
contributions with no shadowing, moderate shadowing, and strong
shadowing respectively. Right panel: total rapidity distributions
(sum of $\gamma$p and $\gamma$Pb contributions).}
\label{fig:pphqpArapcc}
\end{figure}

In Fig.~\ref{fig:pphqpArapcc} we show the corresponding rapidity
distributions for $c\bar{c}$ production using the GRV photon parton
distributions.
The left panel depicts the distributions separately for both $\gamma$p
and $\gamma$Pb contributions while the right panel shows the total
distributions, i.e. the sum of both contributions. As is apparent
from the left panel, the $\gamma$p contribution is dominant at all
rapidities except for $y \lesssim -5$. In line with our convention,
the $\gamma$p contribution peaks at positive rapidities while
the $\gamma$Pb distributions peak at negative rapidities, and the
asymmetric nature of the total distributions is clearly exhibited.
Despite the smallness of the $\gamma$Pb contribution, the effects of nuclear
modifications are still slightly manifested in the total rapidity
distributions shown in the right panel. It is interesting to note that
the sensitivity to nuclear effects is significantly enhanced when
one considers the ratio of the total rapidity distribution at a
specific negative rapidity ($-y_1$), and the rapidity distribution
at the equivalent positive rapidity ($+y_1$), somewhat reminiscent
of pseudorapidity asymmetry in deuteron-gold collisions. The MSTW08
ratio for $y=-3,3$ is reduced by about $9\%$ and $5\%$ by the
modifications in EPS08 and EPS09 respectively, while for $y=-4,4$
the reductions amount to $15\%$ and $10\%$, and $23\%$ and $14\%$
respectively for $y=-5,5$. Thus the rapidity asymmetry ratio in the
interval $-5 \le y \le 4, 4 \le y \le 5$ exhibits appreciable
sensitivity to nuclear effects.

We now discuss the corresponding case of $c\bar{c}$ production in
ultraperipheral PbPb collisions, and in Table~\ref{cccbarAA} we show the
cross sections (in mb) for both direct and resolved contributions.
\begin{table}[!htb]
\caption{Cross sections for photoproduction of
$c\bar{c}$ in ultraperipheral PbPb collisions at the LHC. All
cross sections are in millibarns (mb).}
\begin{tabular}[c]{|l|c c c| c c c c c c |}
\hline
 PDF            && Direct              &&&&& Resolved && \\
\cline{5-10}
                &&             &&& SaS1d   && GRV      && CJK   \\
\hline
MSTW08          && 1167     &&& 110   && 180    && 226  \\
EPS08           && 890       &&& 99    && 165    && 207  \\
EPS09	        && 1002      &&& 101   && 169    && 213  \\
\hline
\end{tabular}
\label{cccbarAA}
\end{table}

The sensitivity to nuclear modifications (dominantly shadowing) is
more significant here than in pPb collisions. Thus considering
the direct contribution which is the dominant part, the
modification-free (MSTW08) cross section is reduced by approximately
$24\%$ by the rather strong nuclear shadowing present in EPS08, and by
about $14\%$ in the case of EPS09. With the inclusion of the resolved
component, the reductions are around $22\%$ and $13\%$ respectively,
and vary only slightly with the choice of photon parton distribution.

The resolved contribution exhibits a mild dependence on nuclear
modifications and a much stronger sensitivity to photon parton
distribution. Thus in the case of SaS1d the resolved component
is $8.6\%$ of the total cross section for MSTW08, $10\%$ for
EPS08, and $9.2\%$ for EPS09. For GRV, the contributions are
$13.4\%$, $15.6\%$, and $14.4\%$ respectively. The CJK2 values
are the largest: $16.2\%$, $18.9\%$, and $17.5\%$ respectively.

The rapidity distributions for $c\bar{c}$ production in
ultraperipheral PbPb collisions are shown in Fig.~\ref{thqrapcc},
and are manifestly symmetric about midrapidity ($y = 0$).
The sensitivity to nuclear modifications is more transparent here than
in total cross sections.
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=8.5cm, height=8.5cm, angle=270]{ccraptAA.ps}
\end{center}
\caption[...]{(Color online) Total rapidity distributions of the
  photoproduction of $c\bar{c}$ in PbPb collisions at the LHC using
  the GRV photon parton distributions. Dashed
  line depicts result using the MSTW08 gluon distribution (no nuclear
  modifications). Solid and dash-dotted lines are results
  from nuclear-modified gluon distributions from EPS09 and EPS08
  respectively.}
\label{thqrapcc}
\end{figure}
Shadowing is the dominant nuclear effect for $-3 < y < 3$, and the rapidity
distributions in this region reproduce the observed trend of
gluon shadowing strength exhibited in  Fig.~\ref{fig:RgPb_Mjpsi}.
MSTW08 with its zero gluon shadowing gives the largest rapidity
distribution while EPS08, with its strong gluon shadowing, gives the
smallest. Due to strong flux suppression, shadowing is most markedly
apparent for the rapidity range $-2 \lesssim y \lesssim 2$.
This range therefore provides a good window to discriminate among
different gluon shadowing scenarios.

The rapidity intervals  $3 < y < 6$
corresponds to $x_{min}$ in the antishadowing region (deep shadowing)
for right (left) incident photons and vice versa for $-6 < y < -3$.
Due to the photon flux suppression
in the deep shadowing region, the rapidity distributions are
sensitive mainly to  antishadowing in addition to both EMC effect and
Fermi motion. Since both EPS08 and EPS09 have substantial
antishadowing, their rapidity distributions reflect this,
being slightly larger than those from MSTW08. The
discriminatory power here is not as appreciable as in the shadowing
case though, due largely to the smallness of the distributions.

For both rapidity ranges $y < -6$ and $y > 6$, $x_{min} > 0.2$ and the
relevant contributing nuclear effects are the EMC and Fermi motion
since the contribution from antishadowing is small, and that from
shadowing practically nonexistent by virtue of flux suppression.
Both EPS08 and EPS09 nuclear
modifications exhibit EMC effect and Fermi motion, and the destructive
interference from both effects render their rapidity distributions to
practically coincide with that from MSTW08.
\subsubsection{Open bottom}
We now discuss our results for total cross sections and
rapidity distributions for $b\bar{b}$ production.
In Table~\ref{cbbbarpA} we present the cross sections for both
direct and resolved $b\bar{b}$ production in ultraperipheral
pPb collisions at the LHC. In parallel with the treatment of
$c\bar{c}$ production, we determine the relative importance
of $\gamma$Pb and resolved contributions to the total $b\bar{b}$
production cross sections.
\begin{table}[!h]
\caption{Cross sections for photoproduction of
$b\bar{b}$ in ultraperipheral pPb collisions at the LHC. All
cross sections are in nanobarns (nb).}
\begin{tabular}[c]{|l| l c c| c c| c c c c|}
\hline
       &&PDF            && Direct       &&&& Resolved & \\
\cline{7-10}
        &&                &&             && SaS1d   && GRV      & CJK   \\
\hline
$\gamma$p &&MSTW08        && 36512      && 8641   && 12178   & 14977  \\
\hline
         &&MSTW08          && 5084       && 2061   && 3032    & 3663  \\
$\gamma$A &&EPS08          && 3972       && 1886    && 2808    & 3389  \\
         &&EPS09	   && 4409      && 1936   && 2874   & 3477  \\
\hline
\end{tabular}
\label{cbbbarpA}
\end{table}
For MSTW08 (no nuclear modifications) the $\gamma$Pb
contribution to the total cross section is approximately $14\%$,
$13\%$ for EPS09 ( moderate gluon shadowing), and $12\%$ for
EPS08 (strong gluon shadowing), with little dependence on the choice of
photon parton distribution set. It is thus apparent that while the
photonuclear contribution is relatively more significant here than in
$c\bar{c}$ production the effect of nuclear shadowing is less.
The resolved contribution again depends significantly
on the choice of photon parton distribution, and exhibits negligible dependence
on the choice of nuclear parton distribution. For the SaS1d
distribution, the resolved component is approximately $21\%$
while it is approximately $27\%$ for the GRV distribution, and
$30\%$ for the CJK2 set. These values are larger than the
corresponding ones for $c\bar{c}$ production, and thus serve to
underscore the relatively higher importance of the resolved component
in $b\bar{b}$ photoproduction.
As noted above, the sensitivity to nuclear modifications
(dominantly shadowing) is very small: the no-modification (MSTW08)
total cross section is reduced by approximately $2.4\%$ and $1.5\%$
by the modifications in EPS08 and EPS09 respectively. Thus with its
appreciably large resolved component and weak sensitivity to nuclear
effects, it is tempting to speculate that $b\bar{b}$ photoproduction
could be of some use in constraining photon parton distributions.
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=8.5cm, height=8.5cm, angle=270]{pphqpArap_bb_t.ps}
\end{center}
\caption[...]{(Color online) Rapidity distributions of $b\bar{b}$
photoproduction in pPb collisions at the LHC using the GRV photon
parton distributions. Left panel: $\gamma$p and $\gamma$Pb
contributions to total rapidity distributions. Dotted line depicts
the $\gamma$p contribution while the dashed (MSTW08), solid
(EPS09), and dash-dotted (EPS09) lines correspond to $\gamma$Pb
contributions with no shadowing, moderate shadowing, and strong
shadowing respectively. Right panel: total rapidity distributions
(sum of $\gamma$p and $\gamma$Pb contributions).}
\label{fig:pphqpArapbb}
\end{figure}

In Fig.~\ref{fig:pphqpArapbb} we show the corresponding rapidity
distributions for $b\bar{b}$ production using the GRV photon parton
distributions.
The left panel depicts the distributions separately for both $\gamma$p
and $\gamma$Pb contributions while the right panel shows the total
distributions, being the sum of both contributions. As is apparent
from the left panel, the $\gamma$p contribution is dominant at all
rapidities except for $y \lesssim -4$. As in $c\bar{c}$ production
the $\gamma$p contribution peaks at positive rapidities while
the $\gamma$Pb distributions peak at negative rapidities, and the
asymmetric nature of the total distributions is clearly manifested.
Due to the smallness of the nuclear effects, the total rapidity
distributions shown in the right panel almost overlap for the
different nuclear parton distributions considered in the present
study. Similar to $c\bar{c}$ production, the rapidity asymmetry
ratio exhibits appreciable sensitivity to nuclear effects around
$y=-4,4$: the MSTW08 ratio is reduced by $19\%$ and $6\%$ respectively
by the modifications in EPS08 and EPS09.

Let us now consider the corresponding case of $b\bar{b}$ production in
ultraperipheral PbPb collisions. In Table~\ref{cbbbarAA} we show the
cross sections (in $\mu$b) for both direct and resolved contributions.
\begin{table}[!htb]
\caption{Cross sections for photoproduction of
$b\bar{b}$ in ultraperipheral PbPb collisions at the LHC. All
cross sections are in microbarns ($\mu$b).}
\begin{tabular}[c]{|l|c c c| c c c c c c |}
\hline
 PDF            && Direct              &&&&& Resolved && \\
\cline{5-10}
                &&             &&& SaS1d   && GRV      && CJK   \\
\hline
MSTW08          && 6227      &&& 1076   && 1468    && 1800  \\
EPS08           && 5812       &&& 982    && 1378    && 1734  \\
EPS09	        && 5992      &&& 969   && 1357    && 1708  \\
\hline
\end{tabular}
\label{cbbbarAA}
\end{table}

The sensitivity to nuclear modifications, while more appreciable here
than in pPb collisions, is significantly less than for the equivalent
$c\bar{c}$ production.
The modification-free (MSTW08) cross section is reduced
$7\%$ by the modifications in EPS08, and
about $5\%$ in the case of EPS09.
The resolved contribution is almost independent of nuclear
modifications but exhibits a strong sensitivity to photon parton
distribution. Thus the resolved component
is approximately $15\%$ of the total cross section for SaS1d, $19\%$
for GRV, and about $23\%$ for CJK2. Again, these values indicate that
the resolved component is relatively more significant in $b\bar{b}$
as compared to $c\bar{c}$ photoproduction.

In Fig.~\ref{fig:hqrapbb} we show the rapidity distribution for $b\bar{b}$
in ultraperipheral PbPb collisions at the LHC.
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=8.5cm, height=8.5cm, angle=270]{bbraptAA.ps}
\end{center}
\caption[...]{(Color online) Total rapidity distributions of $b\bar{b}$
  photoproduction in PbPb collisions at the LHC using the GRV photon
  parton distributions. Dashed
  line depicts result using the MSTW08 gluon distribution (no nuclear
  modifications). Solid and dash-dotted lines are results
  from nuclear-modified distributions from EPS09 and EPS08 respectively.}
\label{fig:hqrapbb}
\end{figure}
Shadowing dominates in the rapidity interval $-2 < y < 2$ and is
most clearly manifested in the rapidity window $-1 < y < 1$. Thus
this interval presents the best sensitivity to shadowing effects
in $b\bar{b}$ production. Although less marked, the progression
of rapidity distribution with relative shadowing strength follows the
trend observed in $c\bar{c}$ production: MSTW08 still gives the
largest distribution while EPS08 gives the smallest.
As in the case of $c\bar{c}$ production, there is a slight
manifestation of the influence of antishadowing around
$y = -3$ and $y = 3$. The distributions practically overlap
for $y < -4$ and $y > 4$; thus overall, the interval
$-1 \lesssim y \lesssim 1$ seems to afford the best sensitivity to
nuclear effects, in this case primarily shadowing. A detailed
treatment of $b\bar{b}$ production at the LHC with emphasis on
the $x$ dependence can be found in \cite{Strikman:2005yv}.
\subsection{Vector Mesons in pA and AA Collisions}
\subsubsection{$J/\Psi$}
We now present our results on elastic photoproduction of the $J/\Psi$
and $\Upsilon(1s)$ in the framework of a corrected leading-order
two-gluon exchange formalism in QCD. Here the nuclear effect
(shadowing) is quite sizable; we therefore also display explicitly results
from the HKN07 distribution set.

In Table~\ref{tjpsipPb} we present the components and total cross
sections for the elastic photoproduction of  $J/\Psi$ in
ultraperipheral pPb collisions at the LHC. As expected the $\gamma$p
contribution is dominant, with the $\gamma$Pb contribution decreasing
in size with increasing severity of gluon shadowing.
\begin{table}[!htb]
\caption{Cross sections (in $\mu$b) for elastic photoproduction of
 $J/\Psi$ in ultraperipheral pPb collisions at the LHC. Second
and third columns are the contributions from $\gamma$p and
$\gamma$Pb respectively for different distributions. The sums of the
two contributions are presented in the fourth column.}
\begin{tabular}[c]{|l|ccc c c c c c c c| c c c c}
\hline
    &             && $\gamma$p    &&& $\gamma$A    &&& Total & \\
\hline
MSTW08&           && 167.3        &&& 23.6         &&& 190.9 & \\
EPS08&            &&              &&& 2.2          &&& 169.5 & \\
EPS09&	         &&              &&& 8.5          &&& 175.8  & \\
HKN07&            &&              &&& 15.4         &&& 182.7  & \\
\hline
\end{tabular}
\label{tjpsipPb}
\end{table}

The contribution of the $\gamma$Pb component to the total cross
section ranges from a high of about $12\%$ for MSTW08 (no gluon shadowing)
to a low of $1.3\%$ for EPS08 (strong gluon shadowing), in
accordance with the trend displayed in Fig.~\ref{fig:RgPb_Mjpsi}. This
trend is replicated in the degree of shadowing reflected in the total
cross section: the no-shadowing (MSTW08) cross section is reduced by
about $11\%$ by the shadowing in EPS08, $8\%$ in EPS09, and $4\%$ in
HKN07 respectively.

Fig.~\ref{jpsirappPb} shows the rapidity distributions for both
$\gamma$p and $\gamma$Pb components and their sums. The distributions
are manifestly asymmetric, with the dominant $\gamma$p component
peaking at positive rapidities while the subdominant $\gamma$Pb
contributions peak at negative rapidities.
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=8.5cm, height=8.5cm, angle=270]{epvmpArap_jpsi.ps}
\end{center}
\caption[...]{(Color online) Rapidity distributions of exclusive
photoproduction of $J/\Psi$ in pPb collisions at the LHC.
Left panel: $\gamma$p and $\gamma$Pb
contributions to total rapidity distributions. Dotted line depicts
the $\gamma$p contribution while the dashed (MSTW08), dash-double-
dotted (HKN07), solid
(EPS09), and dash-dotted (EPS08) lines correspond to $\gamma$Pb
contributions with no shadowing, weak shadowing, moderate shadowing,
and strong shadowing respectively. Right panel: total rapidity distributions
(sum of $\gamma$p and $\gamma$Pb contributions).}
\label{jpsirappPb}
\end{figure}
The $\gamma$Pb distributions exhibit clearly the influence of
gluon shadowing, especially in the narrow rapidity window
$-3 \lesssim y \lesssim 1$ where the differences mimic the
relative strength of gluon shadowing in the respective nuclear
parton distribution. Although the $\gamma$p contribution
is dominant for practically all rapidities, these $\gamma$Pb
distributions with the exception of EPS08 are appreciable enough
in the said rapidity range such that the total rapidity distributions
show the same tendency as that of the $\gamma$Pb component in the
designated rapidity window.
Thus it seems feasible that a consideration of $J/\Psi$ production
in pPb collisions in this rapidity interval offers some potential
in constraining gluon shadowing.

We now turn to $J/\Psi$ production in utraperipheral PbPb collisions
at the LHC and in Table~\ref{tjpsiPbPb} we present the total cross
sections from the different parton distributions. The differences in
the predicted cross sections are extremely clear cut, and thus this
process can serve as an excellent probe of gluon shadowing as well as
a good discriminator of the different gluon shadowing templates
considered in the current study.
\begin{table}[!htb]
\caption{Total cross sections (in mb) for elastic photoproduction of
 $J/\Psi$ in ultraperipheral PbPb collisions at the LHC.}
\begin{tabular}[c]{|lc|c|c c c}
\hline
PDF                 && Cross Section \\
\hline
MSTW08              && 74 \\
EPS08               && 10 \\
EPS09	            && 29 \\
HKN07               && 49 \\
\hline
\end{tabular}
\label{tjpsiPbPb}
\end{table}

It is instructive to consider the remarkable effect that the
quadratic gluon dependence has on the cross
sections (and also on the rapidity distributions). Thus the
no shadowing cross section is reduced by approximately $87\%$
by the strong shadowing in EPS08, and by about $61\%$ by the
relatively moderate shadowing in EPS09. Even the rather weak
gluon shadowing present in HKN07 is responsible for reducing the
cross section by about $34\%$.

The constraining potential of the $J/\Psi$ elastic production
process is more clearly exhibited when rapidity distributions are
considered. To this end we display the corresponding rapidity
distributions in  Fig.~\ref{jpsirapPbPb} for the four different
gluon shadowing scenarios.

\begin{figure}[!htb]
\begin{center}
\includegraphics[width=8.5cm, height=8.5cm, angle=270]{jpsiraptgcn.ps}
\end{center}
\caption[...]{(Color online) Total rapidity distributions of exclusive
  photoproduction of $J/\Psi$ in PbPb collisions at the LHC. Dashed
  line depicts result using the MSTW08 gluon distribution (no nuclear
  modifications). Solid, dash-dotted, and dash-double-dotted lines are results
  from nuclear-modified gluon distributions from EPS09, EPS08, and
  HKN07 parton distributions respectively.}
\label{jpsirapPbPb}
\end{figure}
Shadowing is the relevant nuclear effect in the rapidity interval
$-3 < y < 3$ and unsurprisingly, the rapidity distributions mimic
the behavior in the shadowing region of Fig.~\ref{fig:RgPb_Mjpsi}.
The largest rapidity distribution is given by MSTW08, followed by
HKN07, and EPS09. The smallest is by EPS08 due to its strong gluon
shadowing. The rapidity window $-2 < y < 2$ manifestly depicts the
significant distinction between the various gluon distributions
arising from the quadratic dependence. Antishadowing manifests
in the intervals $-5 < y < -4$ and $4 < y < 5$; the effect though
is quite slight.

\subsubsection{$\Upsilon(1s)$}
We now discuss our results for elastic production of {$\Upsilon(1s)$
in ultraperipheral pPb and PbPb collisions. The ensuing treatment
parallels closely that of $J/\Psi$ in many respects due to the same
underlying production mechanism.

In Table~\ref{tupsipPb} we present the components and total cross
sections for the elastic photoproduction of  $\Upsilon$ in
ultraperipheral pPb collisions at the LHC. While the $\gamma$p
contribution is still dominant, the $\gamma$Pb contributions
from the different gluon distributions are markedly significant,
and exhibit the trend of decreasing magnitude with increasing
strength of gluon shadowing.

\begin{table}[!htb]
\caption{Total cross sections (in nb) for elastic photoproduction of
 $\Upsilon$ in ultraperipheral pPb collisions at the LHC. Second
and third columns are the contributions from $\gamma$p and
$\gamma$Pb respectively for different distributions. The sums of the
two contributions are presented in the fourth column.}
\begin{tabular}[c]{|l|ccc c c c c c c c| c c c c}
\hline
    &             && $\gamma$p    &&& $\gamma$A    &&& Total & \\
\hline
MSTW08&           && 390        &&& 219         &&& 609 & \\
EPS08&            &&              &&& 84          &&& 474 & \\
EPS09&	         &&              &&& 130          &&& 520  & \\
HKN07&            &&              &&& 161         &&& 551  & \\
\hline
\end{tabular}
\label{tupsipPb}
\end{table}

The contribution of the $\gamma$Pb component to the total cross
section is $36\%$ for MSTW08 (no gluon shadowing), $29\%$ for HKN07
(weak gluon shadowing), $25\%$ for EPS09 (moderate gluon shadowing),
and $18\%$ for EPS08 (strong gluon shadowing). This gradation accords
with the trend observed in Fig.~\ref{fig:RgPb_Mjpsi}, which is also
replicated in the degree of shadowing reflected in the total
cross section: the no-shadowing (MSTW08) cross section is reduced by
about $22\%$ by the shadowing in EPS08, $15\%$ in EPS09, and $10\%$ in
HKN07 respectively. This appreciable magnitude of the effect of shadowing
seems to indicate that $\Upsilon$ photoproduction cross section
in ultraperipheral pPb collisions offers some promising potential in
constraining nuclear gluon shadowing.

In Fig.~\ref{upsirappPb} we show the rapidity distributions for both
$\gamma$p and $\gamma$Pb components (left panel )and the total
(right panel). As usual the distributions are asymmetric, with the
dominant $\gamma$p component peaking at positive rapidities while the
subdominant $\gamma$Pb contributions peak at negative rapidities
according to the convention adopted in the present study.
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=8.5cm, height=8.5cm, angle=270]{epvmpArap_upsi.ps}
\end{center}
\caption[...]{(Color online) Rapidity distributions of exclusive
photoproduction of $\Upsilon(1s)$ in pPb collisions at the LHC.
Left panel: $\gamma$p and $\gamma$Pb
contributions to total rapidity distributions. Dotted line depicts
the $\gamma$p contribution while the dashed (MSTW08), dash-double-
dotted (HKN07), solid
(EPS09), and dash-dotted (EPS08) lines correspond to $\gamma$Pb
contributions with no shadowing, weak shadowing, moderate shadowing,
and strong shadowing respectively. Right panel: total rapidity distributions
(sum of $\gamma$p and $\gamma$Pb contributions).}
\label{upsirappPb}
\end{figure}

Let us consider the left panel. The $\gamma$Pb component distributions here,
relative to that of $\gamma$p, are more appreciable than for $J\Psi$
production. In fact, for $-5 \lesssim y \lesssim -2$ these
distributions are larger than the $\gamma$p distribution, and around
their peaks at $y \sim -2.7$ they reflect quite distinctly the effect
of the varying shadowing strength in the gluon distributions used.
Thus in the rapidity interval $-4 \lesssim y \lesssim -1$ the
total distributions in the right panel show good sensitivity to
gluon shadowing, and therefore afford good potential for constraining
purposes.

We now turn to $\Upsilon$ production in ultraperipheral PbPb collisions
at the LHC. In Table~\ref{tupsiPbPb} we present the total cross
sections from the different gluon distributions.
\begin{table}[!htb]
\caption{Total cross sections (in $\mu$b) for elastic photoproduction of
 $\Upsilon(1s)$ in ultraperipheral PbPb collisions at the LHC.}
\begin{tabular}[c]{|lc|c| c c c}
\hline
PDF                 && Cross Section  \\
\hline
MSTW08              && 189  \\
EPS08               && 99  \\
EPS09	            && 130  \\
HKN07               && 146 \\
\hline
\end{tabular}
\label{tupsiPbPb}
\end{table}

Although not quite as dramatic as in the case of $J\Psi$ here also
one can see the effect on the cross sections of the
quadratic dependence on gluon distribution. The MSTW08
(no-shadowing) cross section is reduced by approximately $48\%$
by the strong shadowing in EPS08, by about $31\%$ by the
relatively moderate shadowing in EPS09, and by $23\%$ by the rather weak
gluon shadowing present in HKN07. Thus a consideration of the cross
section can serve as a good probe of gluon shadowing as well as
an efficient discriminator of the different gluon shadowing scenarios
considered in the current study.

In order to further exhibit the constraining potentials of $\Upsilon$
photoproduction we display the rapidity distributions in
Fig.~\ref{upsirapPbPb} for the four different gluon shadowing scenarios.

\begin{figure}[!htb]
\begin{center}
\includegraphics[width=8.5cm, height=8.5cm, angle=270]{upsiraptg.ps}
\end{center}
\caption[...]{(Color online) Total rapidity distributions of exclusive
  photoproduction of $\Upsilon(1s)$ in PbPb collisions at the LHC in the
  modified hard sphere density distribution approximation. Dashed
  line depicts result using the MSTW08 gluon distribution (no nuclear
  modifications). Solid, dash-dotted, and dash-double-dotted lines are results
  from nuclear-modified gluon distributions from EPS09, EPS08, and
  HKN07 parton distributions respectively.}
\label{upsirapPbPb}
\end{figure}
Shadowing remains the relevant nuclear modification for practically
the entire rapidity range shown in the figure, and is markedly
manifested in the interval $-2 < y < 2$. Thus rapidity distribution
in this interval should be a good discriminator of gluon shadowing strength.

\subsection{Theoretical errors and uncertainties in parton distributions}
 From a consideration of the general structure of the quantities
(cross sections and rapidity distributions) considered in this study,
three major sources of theoretical errors can be readily identified:
\begin{itemize}
\item accuracy of the relevant expressions for the photon flux,
\item higher-order corrections (neglect of terms greater than
leading order in the case of photoproduction of heavy quarks, the
accuracy of mopping up higher-order corrections with data from HERA
in the case of production of $J/\Psi$ and $\Upsilon$),
\item uncertainties in the parton distributions.
\end{itemize}
Here we give a brief qualitative comment on the third, i.e. the
effects of uncertainties in parton distributions on our calculations.
Let us first consider uncertainties in nuclear parton distributions (nPDs).
This relevant for the dominant direct contribution in photoproduction
of heavy quarks and elastic production of vector mesons.
Both HKN07 \cite{Hirai:2007sx} and EPS09 \cite{Eskola:2009uj} have
facilities for estimating error in the determination of a
nPDs-dependent quantity like the cross section
due to the uncertainties in the nuclear parton distributions.
The HKN07 set achieves this through the availability of a set of
gradient functions while EPS09 has thirty error sets to be used in
conjunction with free proton parton distributions error sets.

For technical reasons we have not computed errors on cross sections
using either of these two sets. Since this is a continuation of our
earlier study, we have maintained the usage of the MSTW08 set for the
free proton parton distributions while the EPS09 error evaluation
is better handled with the CTEQ sets \cite{Pumplin:2002vw} of nucleon parton
distributions. In the case of HKN07 we have
used the nuclear modifications in our calculations whereas the
gradient terms are for the parton distributions proper. We thus
advocate that the spread in the results involving the nuclear
parton distributions be taken as loosely indicative of the effect of
the uncertainties in the nuclear PDs.

We now consider the resolved component of photoproduction of heavy
quarks where photon parton distributions are required. Among the
available sets of photon parton distributions, only the CJK set has
the facility to compute errors from uncertainties in photon PDs in
terms of a tolerance parameter $T$ \cite{Cornet:2004ng,Jankowski:2003mt},
with the CJK2 uncertainty bands generated with $T=5$.
Thus, in principle, one needs only the CJK2 best
fit and the associated error sets in order to compute the errors in
the resolved contribution due to uncertainties in $\gamma$PDs. The
problem here is that the SaS1d distributions seems to lie consistently
outside the CJK2 parton distributions error bands (further details can
be found in \cite{Jankowski:2003mt}).
A reflection of this trend can be seen in our
results for the resolved component where the CJK2 values are
consistently about a factor of two greater than the SaS1d values.
As a test we have used the CJK2 error sets in conjunction
with EPS09 to evaluate the uncertainty on the $c\bar{c}$ resolved
cross section in PbPb collisions, with the result
$\sigma^{res}_{CJK2} = 212.6 \pm 10.7\,T$ mb. The corresponding cross
sections using SaS1d and GRV are $\sigma^{res}_{SaS1d} = 101.1$ mb and
$\sigma^{res}_{GRV} = 169.3$ mb respectively.
Thus the GRV result is already within the error limits of the CJK for
$T \simeq 4$ whereas one needs $T \simeq 10.4$ in order to accommodate
the SaS1d result. In view of this situation and since we have no
cogent reason to exclude the SaS1d distributions, we have presented results
from all three sets of $\gamma$PDs and adopt the viewpoint espoused
above that the spread in results should be taken rather loosely as an
indicator of the effects of the uncertainties in the  $\gamma$PDs.
\section{Conclusions}
\label{conc}
In the present study we have considered photoproduction of
heavy quarks ($c\bar{c}$ and $b\bar{b}$) and elastic photoproduction
of vector mesons ($J/\Psi$ and $\Upsilon(1s)$) in ultraperipheral
proton-lead (pPb) and lead-lead (PbPb) collisions at LHC.
Both the dominant direct component in photoproduction of heavy
quarks and elastic production of heavy mesons are dependent on nuclear gluon
distributions, and could therefore be potentially useful in constraining
modifications such as shadowing and antishadowing in nuclear
gluon distributions. The resolved component in photoproduction of
heavy quarks depends on the distributions of light quarks and
gluons in both photons and nuclei. Different sets of both nuclear and
photon parton distributions with different attributes have been utilized.

In photoproduction of heavy quarks the parton distribution dependence is
linear and different modifications are superimposed due to the
integration over the momentum fraction $x$. Despite these limitations,
both cross sections and rapidity distributions for $c\bar{c}$ in PbPb
collisions manifest appreciable sensitivity to
shadowing around midrapidity and a slight sensitivity to antishadowing
at more forward and backward rapidities. Thus $c\bar{c}$
photoproduction offers good constraining potential for shadowing, and
a somewhat less potential for antishadowing. Although photoproduction of
$b\bar{b}$ is less sensitive to modifications than $c\bar{c}$, the
influence of shadowing is evident around midrapidity, and it thus
offers some constraining ability for shadowing. While both $c\bar{c}$ and
$b\bar{b}$ total photoproduction cross sections and rapidity
distributions in pPb collisions show little sensitivity
to nuclear modifications, the rapidity asymmetry ratios in some select
intervals do exhibit significant sensitivity. The resolved components are
appreciable, especially for $b\bar{b}$ and are heavily dependent on
the choice of $\gamma$PDs. Thus it seems feasible that they could be
of some use in constraining photon parton distributions.

The outlook for constraining gluon shadowing is even better in
the case of vector meson production.
Here the quadratic dependence on gluon modifications makes elastic
photoproduction of vector mesons particularly attractive for
constraining purposes. The cross sections and rapidity
distributions for both $J/\Psi$ and $\Upsilon(1s)$ photoproduction
in PbPb collisions exhibit very good sensitivity to gluon shadowing.
Thus both offer remarkable potential in constraining the shadowing
component of nuclear gluon distributions. This is also true for
$\Upsilon$ production and to a lesser extent $J\Psi$ production
in pPb collisions.

\bigskip

We acknowledge support by the US Department of Energy grant  DE-FG02-08ER41533  and the Research Corporation.

redpajama_set_name: RedPajamaArXiv


text:
Homechevron_rightWorldchevron_rightMinister among 10...
date_range 21 Feb 2015 10:02 AM GMT
Minister among 10 killed in Somalia explosions
Mogadishu: At least 10 people, including senior government officials, were killed and several others injured in explosions that rocked a hotel in Somalia's capital Mogadishu Friday, police and witnesses said.
Mohamed Yusuf, spokesman for the Somali ministry of national security, said the bomb killed several people, including two parliament members.
Police and eyewitnesses said loud explosions were heard at the Central Hotel, usually frequented by politicians and foreigners.
The officials were meeting in the hotel, including the deputy prime minister who reportedly suffered a slight wound in the attack.
A female suicide bomber carried out a deadly attack at the hotel, former lawmaker Salad Ali Jelle told Xinhua news agency.
Jelle said the female attacker blew herself up at a mosque inside the hotel at noon when occupants were preparing for Friday prayers.
"Among those killed are minister for seaports, deputy mayor of Mogadishu and a parliament member," said a police officer who declined to be named.
He said the country's minister for aviation and a lawmaker were among those wounded during the explosions.
The Al Shabaab terrorist group has claimed responsibility for the attack via its online radio station. Police said they were investigating the incident.
Rescue operations were underway and the exact number of casualties was still unclear, while police at the scene told Xinhua that they have so far confirmed 10 deaths. An earlier Xinhua report had put the toll at 20.
The attack came amid an ongoing police counter-insurgency operation which killed one Al Shabaab militant and led to the arrest of several others. Police had reported that some of the militants had escaped and were being pursued.