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Ps4 Game Cover Maker
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A Portrait of Chinese Traders in Dakar, Senegal
Although many observers point out that China's dealings in Africa are driven by natural resources, since the mid-2000s Beijing has also shown interest in Senegal, which does not sit on major deposits of oil, gold, diamonds, or timber. This West African nation — a strategic ally for China, a reliable partner in the area of development cooperation, and above all, a promising market for selling made-in-China goods — has a rapidly growing Chinese migrant community. This article explores the growing presence of Chinese traders in Dakar's Centenaire neighborhood, investigating their backgrounds and motives for migrating. It also discusses how the decision to migrate affects their families, hometowns, and the local community in Dakar.
Now that the Senate Has Passed Landmark Immigration Legislation, All Eyes Are on the House
On June 27, the U.S. Senate passed legislation to overhaul the U.S. immigration system on a scale not seen in decades. Despite this major breakthrough, it is clear that immigration reform faces an uphill battle in the House of Representatives, where the dynamics are much different than in the Senate. This article assesses the prospects for immigration reform in the House, explores provisions of the Senate bill, the implications for U.S. immigration policy of the Supreme Court's recent ruling on the Defense of Marriage Act, and more.
Diasporas and Development in Post-Communist Eurasia
The region encompassing Central and Eastern Europe as well as the former Soviet Union is the source of a sizeable share of international migrants today, yet many of these countries' development efforts do not benefit from strong diaspora ties.
As Senate Debates Immigration Reform, CBO and New Studies Examine Effects of Immigration on Nation's Fiscal Health
As the U.S. Senate continues its debate over a bill to overhaul the nation's immigration system, the fiscal impacts associated with enactment of such legislation have emerged as a divisive issue. Following the release of an official congressional cost estimate on Tuesday, this article examines the crucial question of how immigrants' contributions to the tax base compare to the public benefits they would receive under S. 744, the Border Security, Economic Opportunity, and Immigration Modernization Act of 2013.
The Growing Linkages Between Migration and Microfinance
The expansion of access to credit through microfinance—now a multibillion-dollar sector—has resulted in profound shifts across the developing world. This article, using Cambodia as its example, discusses the ways in which households are using microcredit in coordination with migration, and addresses critical questions about who benefits from these linkages—and what vulnerabilities they might create for migrants.
Asian Women Migrants: Going the Distance, But Not Far Enough
Maruja M.B. Asis, of the Philippines Scalabrini Migration Center, maps out the obstacles and opportunities facing the swelling ranks of women migrant workers in Asia.
Gender, Religion, and Secularism Meet in Germany's Headscarf Battle
A German court has restored the job of a Muslim nursery school teacher dismissed from her post for wearing a symbol of her faith, the headscarf.
Detention Center Fires Spark Renewed Debate on Australian Refugee Program
In the wake of a string of arson fires at five Australian detention centers with large populations of asylum seekers, the government has begun new discussions about its much-debated refugee and humanitarian program.

redpajama_set_name: RedPajamaCommonCrawl


How many Americans have worked at a McDonald's?
That's right, according to Reader's Digest one in eight U.S. workers has been employed by McDonald's at some point in their careers. This list includes Rachel McAdams, Pink, Macy Gray, Jay Leno, Carl Lewis, Jeff Bezos, and Andie MacDowell. The Oxford Dictionary even has a term for being employed by the Golden Arches, "McJob", which is defined as "A low-paid job with few prospects." Hey, you have to start somewhere, might as well get a few free fries and burgers while you're at it.
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★ Genealogy Tours ★ Anniversary Tours ★ Pre-20th Century Tours ★ First World War Tours ★ Second World War Tours ★ Group Tours BATTLEFIELD STUDIES GENEALOGY RESEARCH SERVICE POCKET GUIDE APPS PRESENTATIONS HISTORY PAGES MORE ...
Second World War Books
John Broom
The Royal Army Medical Corps took part in every engagement in the Second World War. From the defeat in Norway in 1940 to the hell of Dunkirk and the fall of France, from the chaos of the retreat through Greece and Crete to the war's turning point in the vast deserts of North Africa, from deep into West and East Africa to the ferocious combat of the Burma campaign, from the intensity of D-Day and the Normandy campaign to the reverses at Arnhem and the eventual liberation of the German death camps and Far East prison camps, RAMC personnel were frequently at the heart of the action, risking their lives to provide medical support to a mobile army in a highly mechanised war.
For those taken prisoner by the enemy, maintaining the physical and psychological well-being of their fellow captives became an urgent necessity whilst for a small number of exceptionally brave and hardy souls, attachment to commando units saw them provide medical support for some of the most daring raids of the war. Nearly 3,000 RAMC doctors and orderlies were killed during the war as a result of enemy action or exposure to dangerous tropical diseases.
Using previously unpublished archival material and personal family papers, this book sheds fresh light on the experience of the regulars, volunteers and conscripts who gave expression to the motto of the RAMC: Faithful in Adversity.
The Dunkirk Perimeter and Evacuation
Jerry Murland
The latest in a series of eight Battleground Europe books that deals with the British Expeditionary Force's campaign in France and Flanders in 1940, this book covers the fierce fighting around the Dunkirk Perimeter during May and June 1940 between the retreating BEF, its French allies and the advancing Germans. It covers the area that most people in Britain associate with the fighting in France in 1940, fighting that could have resulted in the destruction of the BEF. However, a catastrophic military disaster, which could have been much worse, was avoided by the evacuation and this grievous military setback was transformed into a morale boosting symbol of the resilience of the British against a Germany that had crushed so many nations in a matter of weeks.
With over 200 black and white photographs and fourteen maps, this book covers in some detail the actions that took place around Dunkirk and Nieuport and the desperate struggle to prevent the seemingly unstoppable advance of the German Army. The evacuation of the BEF from the beaches east of Dunkirk is covered in detail from the perspective of the Royal Navy and from the standpoint of the soldier on the beaches.
Within the book are three tours, 2 driving and one walking tour. The first of the driving tours covers the whole of the Dunkirk perimeter while the second covers the Ramsgate and Dover area. The walking tour is centred around De Panne and takes those following it along the beach that saw so much of the evacuation, and into the back areas of the town where the Germans left their mark when clearing up after the British had gone.
This is an excellent companion for anyone wishing to visit the Dunkirk area.
The Germans in Normandy
Richard Hargreaves
The Allied Invasion of Europe was the greatest seaborne invasion the world has ever known and is usually told from the perspective of the victors. In this book Richard Hargreaves looks at the D-Day Invasion and Battle of Normandy from the other side and provides an account from the German perspective.
It begins with the German military preparations for the invasion. While they knew an invasion was inevitable, they didn't know where or when it would come. Those manning Hitler's mighty Atlantic Wall may have felt secure in their bunkers but they had no idea about the scale or scope that the invasion would take and the ferocity of the fighting that would follow.
It discusses the initial landings and the confusion that surrounded the first hours of the invasion, when the Allied parachute divisions jumped into France and the seaborne forces came ashore on the beaches. The establishment of the Allied bridgehead and the stalemate followed. How the Germans fought with great courage hindered by lack of supplies and overwhelming Allied control of the air. Their final collapse as the Allies finally broke out from the beachhead with Patton's Third Army in the west. The entrapment of the German Seventh Army between the pincers of the Americans advancing from the west and Montgomery's forces advancing remorseless from the north against on the hard-pressed defenders. The closing of the Falaise Gap which became the graveyard of German men and equipment.
Many will have read accounts from the Allied perspective and seen movies like 'The Longest Day' and 'Saving Private Ryan'. In this book you can read the reactions of the Germans, in their own words, and not those that an author or a screenwriter ascribes to them to enhance their story.
This is an excellent read for anyone thinking about visiting the D-Day Beaches and Normandy area.
The D-Day Landings
Philip Warner
Seventy-five years have passed since that most mighty of armadas embarked across the English Channel. With hindsight, we know that Operation OVERLORD was a resounding triumph but, at the time, the risks and stakes were immense and the outcome far from a foregone conclusion. Set against the invading force was not only a ruthless enemy in formidable defensive positions but the uncertainties of the elements.
As Bill Deedes points out in his Foreword, it was the 'ordinary man' who turned this great undertaking into a reality and Philip Warner's The D Day Landings reflects this by being a rich collection of personal accounts by just such individuals. We hear the experiences of RAF pilots who dropped the parachutists and towed the gliders; of sailors of the Royal Navy who had to negotiate minefields and other obstacles; and of a wide spectrum of soldiers. Some such as infantry, tank crews, gunners and sappers came face-to-face with the enemy while others, for example doctors and chaplains, provided vital support. Hostile fire does not distinguish between those roles any more than it does between high and junior rank. It is a fascinating privilege to share these widely diverse individuals' experiences and emotions at such a defining moment both in their lives and in the history of the world.
Today no matter how hard we try, we cannot really know what was really going on through the minds of those thousands of men who so selflessly stepped into the unknown in the pursuit of freedom. But we are unlikely to come closer than by reading this evocative book so sympathetically compiled by a man who knew the fortunes of war better than most. Each section is introduced by clear explanation of the action concerned and the text is enhanced by maps and photographs.
Arras Counter-Attack 1940
Tim Saunders
On 21 May 1940 during the ill-fated Dunkirk Campaign the British launched an operation spearheaded by two tank regiments to help secure the city of Arras. This was the only significant armoured operation mounted by the British during the campaign.
Poorly coordinated and starting badly the Matilda tanks ran into the flanks of Rommel's over extended 7th Panzer Division. With the German anti-tank guns, unable to penetrate the armour of the British tanks, Rommel's infantry fell into chaos as the Matildas plunged deep into their flank. The Germans were machinegunned and started to surrendered in large numbers but with the British infantry lagging well behind, fighting their own battles in the villages, there was no one to round them up.
Into this scene of chaos entered Rommel whose personal leadership and example started to steady his troops and organise an effective response, despite being spattered with the brains of his aide de camp. This was classic Rommel but in the aftermath, he claimed to have been attacked by five divisions.
The Arras counter-attack contributed to Hitler issuing the famous 'halt order' to his panzers that arguably did much to allow the British Army to withdraw to Dunkirk and escape total destruction.
Allied Intelligence and the Cover Up at Pointe Du Hoc
Gary Sterne
Volume 1 of this two-part work puts the reader firmly into the footsteps of the 2nd and 5th Rangers as they arrive in England in 1943. It follows them during their intensive training with the Commandos and the Royal Navy as they head towards D-Day – including cliff climbing, assault landings and the Slapton Sands 'dress rehearsal'.
The orders given to the Rangers, along with dozens of aerial reconnaissance photographs of Omaha Beach, Pointe et Raz de la Percée, Pointe du Hoc and Maisy – as well as French Resistance reports – detail the information given to the Rangers' commander Lt. Col. Rudder. Shown in chronological order and in their original format, many of the documents are still marked TOP SECRET and were only recently released after nearly 70 years.
The author fills in the gaps that many have only guessed at concerning the Rangers' real missions on D-Day, and in Volume 2 he explains why a battalion commander was removed whilst onboard ship prior to the landings, why the individual Rangers were not briefed on all of their D-Day objectives – as well as the extraordinary role that Lt. Col. Rudder played at Pointe du Hoc.
Described by US historians as 'one of the most detailed works about the D-Day Rangers ever written', this work is the culmination of four years of detailed research within the US Archives and backed up by evidence uncovered in Normandy. It is a real historical game-changer that pulls no punches as it challenges conventional studies of one of the most iconic battles of WWII.
D-Day - Cover Up at Pointe du Hoc
Gary Sterne, a keen collector of militaria and co-founder of The Armourer and Skirmish Magazines, has always been fascinated by the D-Day landings. In particular he was intrigued by the lack of precise information relating to the mystery of the 'missing guns' of Pointe du Hoc.
His research led to the finding of a map which indicated the position of an 'unknown' German gun position buried in the village of Maisy. The re-discovery of the Maisy Batteries made headline news around the world and his best-selling book Cover Up at Omaha Beach subsequently changed the history of the Omaha sector and made many start to question the Rangers' Pointe du Hoc mission. The Maisy site is now one of the major Normandy D-Day attractions.
For the first time ever this follow-up book now offers complete Rangers history for the seven months prior to D-Day and does so using period documents, many of which have only recently been released from TOP SECRET status in US Archives. The author fills in the gaps that many have only guessed at concerning the Rangers' real missions on D-Day, he explains why a battalion commander was removed hours before the landings, why the Rangers were not briefed on their actual D-Day missions and the extraordinary role that Lt. Col. Rudder played at Pointe du Hoc. This book is a historical game-changer that pulls no punches.
The Battle of the Bulge
Hitler's Final Gamble
Patrick Delaforce
By late 1944 the Allies were poised to smash the Siegfried Line and break into Germany. Supply lines were shorter thanks to the port of Antwerp. Arnhem aside, there had been a long run of victories and there was no intelligence even from ULTRA to suggest a German counter-offensive.
So the major December attack through the mountainous Ardennes by massed Panzers and infantry took the Allies totally by surprise. Fog and low cloud negated the Allies' air supremacy, English-speaking German commandos in captured jeeps created panic and withdrawal of US forces became a near rout with morale all but broken. For ten days the situation worsened and Antwerp was seriously threatened and 21st Army Group in danger of being cut off. Clear skies for the Thunderbolts and coherent counter-attacks by rapidly deployed reinforcements turned the tide in the nick of time, so preventing a catastrophic defeat for the Allies.
All this and more is graphically narrated in this fine study of a pivotal battle, that so nearly changed the course of war.
The War in Italy 1943 - 1944
John Greham & Martin Mace
Despatches in this volume include that on the Conquest of Sicily from 10 July 1942 to 17 August 1943 by Field-Marshall Viscount Alexander of Tunis; the despatch on the invasion of Sicily in July 1943, by Admiral of the Fleet Sir Andrew B. Cunningham, Commander-in-Chief, Mediterranean; despatch on naval operations in connection with the landings in the Gulf of Salerno in September 1943, by Admiral of the Fleet Sir Andrew B. Cunningham; and the despatch on operations of the Allied Armies between September 1943 and December 1944, by Field Marshal the Viscount Alexander of Tunis.
This unique collection of original documents will prove to be an invaluable resource for historians, students and all those interested in what was one of the most significant periods in British military history.
Hitler's Atlantic Wall
This highly informative book begins with an examination of the background to Germany's primary military objectives in relation to the western end of their self-styled 'Fortress Europe' including the early foundation of shore defences in northern France.
In 1941, there was a switch in emphasis of the Atlantic Wall's role from attack to defence. Beach defences became more elaborate and the Nazi-controlled Todt Organisation began a massive building programme constructing new bunkers and reinforcing existing sites, using forced labour.
Hitler appointed Rommel to formulate Germany's anti-invasion plans in early 1944. At the same time the Allies were making extensive studies of the fortifications and preparing for the challenge of overcoming this most formidable of obstacles.
Using, in many cases, previously unpublished accounts of the soldiers on the ground this book follows Britain's 79th Armoured Division, Sir Percy Hobart's 'Funnies', as they utilised their unique weaponry in support of Allied efforts to ensure the success of the invasion. The author draws on British, American, Canadian and German sources.
Visiting the Normandy Invasion Beaches and Battlefields
This book will be a valuable addition to the library of anyone looking to visit the battlefield sites, museums, memorials, and cemeteries associated with the D-Day Normandy landings.
Its target audience are those looking to plan and lead school groups and similar parties. As such it is a valuable resource for teachers and inexperienced battlefield guides making their first trip to the area. It provides realistic itineraries to the best places in the Normandy area that leaves enough flexibility to allow party leaders suitable discretion.
The author provides helpful information for each site such as its context in the War, visitor orientation, the 'narrative' (the essential facts to engage, inform and entertain), suggested activity and relevant photos and maps. There are also valuable tips for lunch breaks, free time ideas and other helpful pointers. It helps tour planners to make their visit to the D-Day Normandy landings interesting and beneficial while reducing the workload of the party leaders.
Always a Soldier But Never G.I.
A World War II Soldier's Personal Journey
Emmett T. Lang
The year was 1942 and the country was united in the fight against Germany and Japan. On the home front, all industry was mobilized for war, and the draft boards were collecting young men to join the armed forces. Emmett Lang, a naive 20-year-old, wanted to be a soldier. But even after scoring a nearly perfect score in the Army General Classification Test, he was sent to infantry basic training. Despite this inauspicious beginning, Lang decided he would do his duty and take every opportunity to make his service career as rewarding and enjoyable as possible.
This is the story of Lang's Army career, an honest account that includes letters home, divisional and regimental histories, and after-action reports - with a generous dose of humorous anecdotes. Always a Soldier But Never G.I. contains stories of the action on the front lines in Europe and Battle of the Bulge, and gives an insider's personal view of the life of a World War II soldier-the hardships, adventures, and sometimes the horrors - yet Lang's story is told with wit, humor, and a love of life that cannot be suppressed.
It is a firsthand account of the action during World War II; one that I thoroughly recommend to all those interested in this conflict.


Befriend in December, New York Metropolis accredited the nation's very first minimal wage pay floor for app-basically based drivers—a ancient victory Lyft undercut practically without prolong by appealing its implementation in courtroom. This present day, drivers received more like minded news when a spend denied Lyft's motion for an injunction that would block the minimal wage for its drivers.
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Up up to now with assertion from Lyft. Shrimp clarification in lede.


text:
Q: react native custom picker set style not working I developing a react native project.
I use react-native-custom-picker but when I try gives a Custom Picker style it's not working. my code like this below
//.. in CustomPicker.js
<CustomPicker
    placeholder={labelDefault}
    options={options}
    getLabel={item => item.label}
    optionTemplate={this.renderOption}
    selectedValue={this.props.selectedValue}
    onValueChange={this.onValueChangeCustomPicker}
    textStyle={{color:colors.dark_black,fontSize:25}}--> Here is not work
/>

renderOption() function like this
renderOption(settings) {
    const { item, getLabel } = settings
    return (
      <View style={styles.optionContainer}>
        <View style={styles.innerContainer}>
          <Text style={{ color: colors.dark_black, alignSelf: 'flex-start', fontSize: 24 }} key={item.key}>{item.label}</Text>
        </View>
      </View>
    )
  }

I know Picker style only support IOS.
What's my fault? Any idea!

A: can you try this code?
I don't know how you organized "options," but you can't work because you don't have any place to take the factors for "colors."
renderOptions:
const options = [
...
color: "black",
]
...
renderOption(settings) {
    const { item, getLabel } = settings
    return (
      <View style={styles.optionContainer}>
        <View style={styles.innerContainer}>
          <Text style={{ color: item.color, alignSelf: 'flex-start', fontSize: 25 }} key={item.key}>{item.label}</Text>
        </View>
      </View>
    )
  }

<CustomPicker
    placeholder={labelDefault}
    options={options}
    getLabel={item => item.label}
    optionTemplate={this.renderOption}
    selectedValue={this.props.selectedValue}
    onValueChange={this.onValueChangeCustomPicker}
/>

A: I checked source code and documentation if I wanna give style placeholder I should use props for field template like this.
<CustomPicker
          fieldTemplateProps={{textStyle:{color:"red",fontSize:22}}}
          placeholder={'Please select your favorite item...'}
          options={options}
          getLabel={item => item.label}
          optionTemplate={this.renderOption}
          headerTemplate={this.renderHeader}
          onValueChange={value => {
            Alert.alert('Selected Item', value ? JSON.stringify(value) : 'No item were selected!')
          }}
        />

it's worked in my project
 more detail

redpajama_set_name: RedPajamaStackExchange


text:
\section{Introduction} \indent

The production of prompt photon pairs\footnote{Usually the photons are called "prompt" if they are
coupled to the interacting quarks.} in hadronic collisions at high energies
is of great interest at present\cite{1,2,3,4,5}. It provides a major
background to searches for rare or exotic processes in both the Tevatron and the
LHC. In particular, it represents a major source of large
and irreducible background to searches for the Higgs boson in the
low mass range, where its first indications (with mass of about 125--126 GeV)
have been found very recently.
It is also a significant background to searches for a new heavy resonances\cite{6},
cascade decays of a new heavy particles\cite{7} and to searches for
some effects of physics beyond the Standard Model. For example, so called Universal Extra-Dimensions
predict non-resonant diphoton production associated with significant missing
transverse energy\cite{8,9}. Other extra-dimension models, such as
Randall-Sundrum model\cite{10}, predict the production of gravitons, which would decay
into photon pairs with a narrow width.
From another side, studies of prompt diphoton production provide
a particularly clean test of perturbative Quantum Chromodynamics (pQCD) and
soft-gluon resummation methods implemented in theoretical calculations
since the produced photons are largely insensitive to the effects of final-state hadronization,
and their energies and directions can be measured with high precision.
Therefore, it is essential to have an accurate pQCD predictions for
corresponding cross sections and related kinematical distributions.

The leading contributions to the production of prompt photon pairs at hadron collisions
are the quark-antiquark annihilation $q\bar q \to \gamma \gamma$, gluon-gluon fusion
$gg \to \gamma \gamma$ and quark-gluon scattering $qg \to \gamma \gamma q$ subprocesses.
Prompt photons may also originate from single or double fragmentation
processes of the partons produced in the hard interaction\cite{11}.
However, a photon isolation requirement which involved
in the measurements\cite{1,2,3,4,5} significantly reduces
the rate for these processes\footnote{See discussion in Section~2.}.
In the framework of standard QCD, theoretical calculations of diphoton
production cross sections have been carried out at next-to-leading order (NLO)\cite{12} and
next-to-next-to-leading-log approximation (NNLL)\cite{13}.
A fixed-order NLO pQCD calculations\cite{12} implemented by the \textsc{diphox} program
accounts fragmentation subprocesses, but the gluon-gluon fusion $gg \to \gamma \gamma$
contribution is considered only at LO.
In the NNLL calculations\cite{13} implemented by the \textsc{resbos} program
the effects of initial state soft gluon radiation in
the NLO calculations are analytically resummed to
all orders in the strong coupling constant.
Both these calculations reproduce the main features of recent Tevatron and LHC
data\cite{1,2,3,4,5}, but none of them describes all aspects of the data.
So, there is significant underestimation\cite{4} of diphoton cross sections measured by the CMS
collaboration in the regions of phase space where two photons
have an azimuthal angle difference $\Delta \phi_{\gamma \gamma} \le 2.8$.
The similar observation was made\cite{5} by the ATLAS collaboration:
more photon pairs are seen in data at low $\Delta \phi_{\gamma \gamma}$ values,
while the NLO and NNLL pQCD predictions favour a
larger back-to-back production ($\Delta \phi_{\gamma \gamma} \sim \pi$).
At the Tevatron energies, there is the same problem\cite{1,2,3} common to both NLO\cite{12} and NNLL\cite{13} pQCD
calculations in the description of events with low diphoton mass $M_{\gamma \gamma}$
or low azimuthal angle distance $\Delta \phi_{\gamma \gamma}$
(and also with moderate diphoton transverse momentum $p_T^{\gamma \gamma}$).
Such disagreement between the collinear QCD predictions and the available data indicates\cite{1,2,3,4,5}
the necessity of including higher order corrections beyond NLO.

We note, however, that an alternative description of diphoton production
at high energies can be achieved within the framework of $k_T$-factorization QCD approach\cite{14,15}.
This approach is based on famous Balitsky-Fadin-Kuraev-Lipatov (BFKL)\cite{16} or
Ciafaloni-Catani-Fiorani-Marchesini (CCFM)\cite{17} equations and
provides solid theoretical grounds for the effects of initial state gluon radiation and intrinsic
non-zero parton transverse momentum.
A detailed description and discussion of the $k_T$-factorization formalism can be
found, for example, in reviews\cite{18}. Here we would like to only mention
that the main part of high-order radiative QCD corrections is
naturally included into the leading-order $k_T$-factorization formalism.
Moreover, the soft gluon resummation formulas implemented in NNLL calculations\cite{13}
are the result of the approximate treatment of the
solutions of CCFM equation, as it was shown in\cite{19}.
The $k_T$-factorization approach has been successfully applied recently, in particular,
to describe the prompt photon and Drell-Yan pair production at HERA, Tevatron and LHC\cite{20,21,22,23,24,25}.

In the present paper we apply the $k_T$-factorization QCD approach to diphoton
production in $p\bar p$ and $pp$ collisions at high energies.
Our main goal is to give a systematic analysis of available
Tevatron data taken by the D$\emptyset$ and CDF collaborations\cite{1,2,3} and
recent LHC measurements\cite{4,5} performed by the CMS and ATLAS
collaborations.
The consideration is based on the off-shell (depending on the non-zero transverse momenta $k_T$ of
incoming quarks and gluons) production amplitudes of quark-antiquark annihilation $q\bar q \to \gamma \gamma$,
quark-gluon scattering $qg \to \gamma \gamma q$ and gluon-gluon
fusion $gg \to \gamma \gamma$ subprocesses\footnote{In the case of gluon-gluon fusion
we will neglect the transverse momenta of incoming gluons in the corresponding production amplitude
but keep true off-shell subprocess kinematics. See Section~2 for more details.}.
The unintegrated ($k_T$-dependent) quark and gluon densities in a proton
are defined by using the Kimber-Martin-Ryskin (KMR) prescription\cite{26}.
This approach is the simple formalism to construct the unintegrated parton
distributions from the known conventional ones.
We calculate total and differential diphoton production cross sections
and estimate the theoretical uncertainties of our predictions.
Special attention is put to the specific
kinematic properties of the produced photon pair which are
strongly related to the non-zero transverse momenta of initial partons.
Such investigations in the framework of $k_T$-factorization approach
are performed for the first time.

The outline of our paper is following. In Section~2 we
recall shortly the basic formulas of the $k_T$-factorization approach with a brief
review of calculation steps. In Section~3 we present the numerical results
of our calculations and a discussion. Section~4 contains our conclusions.

\section{Theoretical framework} \indent

As it was mentioned above, the leading contributions to the diphoton
production at high energies are the quark-antiquark annihilation,
quark-gluon scattering and gluon-gluon fusion subprocesses:
\begin{gather}
q(k_1) + \bar q(k_2) \to \gamma(k_3) + \gamma(k_4),\\
q(k_1) + g(k_2)\to \gamma(k_3) + \gamma(k_4) + q(k_5),\\
g(k_1) + g(k_2) \to \gamma(k_3) + \gamma(k_4),
\end{gather}

\noindent
where the four-momenta of all particles are given in parentheses.
Although last two of them are higher-order processes, their contributions are
quantitatively comparable to those from quark-antiquark annihilation in the diphoton
invariant mass range of interest, due to the significant gluon luminosity in this kinematical
region.

Let us start from the kinematics.
In the center-of-mass frame of colliding particles we can write:
\begin{equation}
p^{(1)} = {\sqrt s\over 2} (1,0,0,1),\quad p^{(2)} = {\sqrt s\over 2} (1,0,0,-1),
\end{equation}

\noindent
where $p^{(1)}$ and $p^{(2)}$ are the four-momenta of colliding protons,
$\sqrt s$ is the total energy of the process under consideration and we neglect the
masses of protons. The initial parton four-momenta in the high energy limit can be
written as follows:
\begin{equation}
k_1 = x_1 p^{(1)} + k_{1T}, \quad k_2 = x_2 p^{(2)} + k_{2T},
\end{equation}

\noindent
where $k_{1T}$ and $k_{2T}$ are their transverse four-momenta.
It is important that ${\mathbf k}_{1T}^2 = - k_{1T}^2 \neq 0$,
${\mathbf k}_{2T}^2 = - k_{2T}^2 \neq 0$. From the conservation laws we can easily obtain
the following relations for subprocesses~(1) and~(3):
\begin{equation}
{\mathbf k}_{1T} + {\mathbf k}_{2T} = {\mathbf k}_{3T} + {\mathbf k}_{4T},
\end{equation}
\begin{equation}
x_1 \sqrt s = |{\mathbf k}_{3T}| e^{y_3} + |{\mathbf k}_{4T}| e^{y_4},
\end{equation}
\begin{equation}
x_2 \sqrt s = |{\mathbf k}_{3T}| e^{-y_3} + |{\mathbf k}_{4T}| e^{-y_4},
\end{equation}

\noindent
and the similar ones for subprocess~(2):
\begin{equation}
{\mathbf k}_{1T} + {\mathbf k}_{2T} = {\mathbf k}_{3T} + {\mathbf k}_{4T} + {\mathbf k}_{5T},
\end{equation}
\begin{equation}
x_1 \sqrt s = |{\mathbf k}_{3T}| e^{y_3} + |{\mathbf k}_{4T}| e^{y_4} + m_{5T} e^{y_5},
\end{equation}
\begin{equation}
x_2 \sqrt s = |{\mathbf k}_{3T}| e^{-y_3} + |{\mathbf k}_{4T}| e^{-y_4} + m_{5T} e^{-y_5},
\end{equation}

\noindent
where $k_{3T}$, $k_{4T}$ and $k_{5T}$ are the transverse four-momenta
of corresponding particles, $y_3$, $y_4$ and $y_5$ are their center-of-mass rapidities
and $m_{5T}$ is the transverse mass of produced quark (or antiquark) having mass $m$.

The off-shell partonic amplitudes of~(1) and~(2) can be written as follows:
\begin{equation}
  \displaystyle  {\cal M}(q^*\bar q^*\to \gamma \gamma) = e^2 e_q^2 \, \epsilon_\mu(k_3) \epsilon_\nu(k_4) \, \times \atop
  \displaystyle  { \times \bar u(k_2) \left[\gamma^\nu {\hat k_1 - \hat k_3 + m \over (k_1 - k_3)^2 - m^2} \gamma^\mu +
  \displaystyle  \gamma^\mu {\hat k_1 - \hat k_4 + m \over (k_1 - k_4)^2 - m^2} \gamma^\nu \right] u(k_1) },
\end{equation}
\begin{equation}
  {\cal M}(q^*g^*\to \gamma \gamma q) =  e^2 e_q^2 \, g t^a
  \epsilon_\lambda(k_2) \epsilon_\mu(k_3) \epsilon_\nu(k_4) \sum_{i = 1}^6 {\cal F}_i^{\mu \nu \lambda},
\end{equation}
\begin{equation}
  {\cal F}_1^{\mu \nu \lambda} = \bar u(k_5) \gamma^\nu {\hat k_4 + \hat k_5 + m\over (k_4 + k_5)^2 - m^2}
  \gamma^\mu {\hat k_1 + \hat k_2 + m\over (k_1 + k_2)^2 - m^2} \gamma^\lambda u(k_1),
\end{equation}
\begin{equation}
  {\cal F}_2^{\mu \nu \lambda} = \bar u(k_5) \gamma^\mu {\hat k_3 + \hat k_5 + m\over (k_3 + k_5)^2 - m^2}
  \gamma^\nu {\hat k_1 + \hat k_2 + m\over (k_1 + k_2)^2 - m^2} \gamma^\lambda u(k_1),
\end{equation}
\begin{equation}
  {\cal F}_3^{\mu \nu \lambda} = \bar u(k_5) \gamma^\nu {\hat k_4 + \hat k_5 + m\over (k_4 + k_5)^2 - m^2}
  \gamma^\lambda {\hat k_1 - \hat k_3 + m\over (k_1 - k_3)^2 - m^2} \gamma^\mu u(k_1),
\end{equation}
\begin{equation}
  {\cal F}_4^{\mu \nu \lambda} = \bar u(k_5) \gamma^\lambda {\hat k_5 - \hat k_2 + m\over (k_5 - k_2)^2 - m^2}
  \gamma^\mu {\hat k_1 - \hat k_4 + m\over (k_1 - k_4)^2 - m^2} \gamma^\nu u(k_1),
\end{equation}
\begin{equation}
  {\cal F}_5^{\mu \nu \lambda} = \bar u(k_5) \gamma^\mu {\hat k_3 + \hat k_5 + m\over (k_3 + k_5)^2 - m^2}
  \gamma^\lambda {\hat k_1 - \hat k_4 + m\over (k_1 - k_4)^2 - m^2} \gamma^\nu u(k_1),
\end{equation}
\begin{equation}
  {\cal F}_6^{\mu \nu \lambda} = \bar u(k_5) \gamma^\lambda {\hat k_5 - \hat k_2 + m\over (k_5 - k_2)^2 - m^2}
  \gamma^\nu {\hat k_1 - \hat k_3 + m\over (k_1 - k_3)^2 - m^2} \gamma^\mu u(k_1),
\end{equation}

\noindent
where $e$ and $e_q$ are the electron and quark (fractional) electric charges, $g$ is the
strong charge, $\epsilon(k_2)$, $\epsilon(k_3)$ and $\epsilon(k_4)$ are the polarization
four-vectors of corresponding particles and $a$ is the eight-fold color index.
When we calculate the matrix elements squared, the summation on the polarizations
of produced photons is carried out by usual covariant formula:
\begin{equation}
  \sum \epsilon^\mu(k_i) \epsilon^{* \nu}(k_i) = - g^{\mu \nu},
\end{equation}

\noindent
where $i = 3, 4$. In the case of initial off-shell gluon we apply the BFKL prescription\cite{14}:
\begin{equation}
  \sum \epsilon^\mu(k_2) \epsilon^{* \nu}(k_2) = {k_{2T}^\mu k_{2T}^\nu\over {\mathbf k}_{2T}^2},
\end{equation}

\noindent
This formula converges to the usual one (20) after azimuthal angle averaging
in the $|{\mathbf k}_{2T}| \to 0$ limit.
Since we do not neglect the transverse momentum of incoming quarks,
the standard on-shell quark spin density matrix has to be replaced by a more complicated expression.
To evaluate it we will follow an approximation proposed in\cite{20}. We "extend" the original
diagram and consider the off-shell quark line as internal
line in the extended diagram. The "extended" process looks like follows: the initial on-shell
quark with four-momentum $p$ and mass $m$ radiates a quantum (say, photon or gluon) and
becomes an off-shell quark with four-momentum $k$. So, for the extended diagram squared
we can write:
\begin{equation}
  |{\cal M}|^2 \sim {\rm tr} \left[ \bar {\cal T}^\mu {\hat k + m\over k^2 - m^2} \gamma^\nu\, u(p) \bar u(p) \,
  \gamma_\nu {\hat k + m\over k^2 - m^2} {\cal T}_\mu \right],
\end{equation}

\noindent
where $\cal T$ is the rest of the original matrix element.
The expression presented between $\bar {\cal T}^\mu$ and ${\cal T}_\mu$ now plays the role
of the off-shell quark spin density matrix. Using the standard on-shell condition
$\sum u(p)\bar u(p) = \hat p + m$ and performing the Dirac algebra one obtains
in the massless limit $m \to 0$:
\begin{equation}
  |{\cal M}|^2 \sim {2\over (k^2)^2} {\rm tr} \left[ \bar {\cal T}^\mu \left( k^2 \hat p -
  2 (p \cdot k) \hat k\right) {\cal T}_\mu \right].
\end{equation}

\noindent
Now, using the Sudakov decomposition $k = x p + k_T$ (where $k_T$ is the
off-shell quark non-zero transverse four-momentum, $k^2 = k_T^2 = - {\mathbf k}_T^2$)
and neglecting the second term in the
parentheses in~(23) in the small-$x$ limit, we easily obtain:
\begin{equation}
  |{\cal M}|^2 \sim {2\over x k^2} {\rm tr} \left[ \bar {\cal T}^\mu x \hat p {\cal T}_\mu \right].
\end{equation}

\noindent
Essentially, we have neglected here the negative light-cone momentum fraction of the incoming quark.
The properly normalized off-shell spin density matrix is given by $x \hat p$, while
the factor $2/x k^2$ has to be attributed to the quark distribution function (determining its
leading behavior). With this normalization, we successfully recover the on-shell collinear
limit when $k$ is collinear with $p$.
Further calculations are straighforward and in other respects follow the standard QCD
Feynman rules. We only mention that the method of orthogonal amplitudes\cite{27} has been
applied to avoid the long output. The evaluation of traces in (12) --- (19) was
done using the algebraic manipulation system \textsc{form}\cite{28}.

The matrix element squared of gluon-gluon fusion subprocess~(3)
was calculated a long time ago in the on-shell
limit $|{\mathbf k}_{1T}| \to 0$, $|{\mathbf k}_{2T}| \to 0$.
The simple analytical expression can be found,
for example, in\cite{29}. In our phenomenological study,
we apply it with one remark: numerically, we keep the exact off-shell kinematics given by
(5) --- (8).

In according to the $k_T$-factorization theorem,
to calculate the cross section of diphoton production
one should convolute off-shell partonic cross sections
with the relevant unintegrated quark and/or gluon distributions in a proton:
\begin{equation}
  \sigma = \sum_{i,j = q,\,g} \int {\hat \sigma}_{ij}^*(x_1, x_2, {\mathbf k}_{1T}^2, {\mathbf k}_{2T}^2) \, f_i(x_1,{\mathbf k}_{1T}^2,\mu^2) f_j(x_2,{\mathbf k}_{2T}^2,\mu^2) \, dx_1 dx_2 \, d{\mathbf k}_{1T}^2 d{\mathbf k}_{2T}^2,
\end{equation}

\noindent
where ${\hat \sigma}_{ij}^*(x_1, x_2, {\mathbf k}_{1T}^2, {\mathbf k}_{2T}^2)$
is the off-shell partonic cross section and $f_i(x,{\mathbf k}_{T}^2,\mu^2)$ is the
unintegrated parton densities in a proton. The contributions from
quark-antiquark annihilation, quark-gluon scattering and gluon-gluon fusion
can be easily rewritten as follows:
\begin{equation}
  \displaystyle \sigma = \sum_{q} \int {1\over 16\pi (x_1 x_2 s)^2 } |\bar {\cal M}(q^*\bar q^* \to \gamma \gamma)|^2 \times \atop
  \displaystyle  \times f_q(x_1,{\mathbf k}_{1T}^2,\mu^2) f_q(x_2,{\mathbf k}_{2T}^2,\mu^2) d{\mathbf k}_{1T}^2
  d{\mathbf k}_{2T}^2 d{\mathbf k}_{3T}^2 dy_3 dy_4 {d\phi_1 \over 2\pi} {d\phi_2 \over 2\pi},
\end{equation}
\begin{equation}
  \displaystyle \sigma = \sum_{q} \int {1\over 256\pi^3 (x_1 x_2 s)^2 } |\bar {\cal M}(q^* g^* \to \gamma \gamma q)|^2 \times \atop
  \displaystyle  \times f_q(x_1,{\mathbf k}_{1T}^2,\mu^2) f_g(x_2,{\mathbf k}_{2T}^2,\mu^2) d{\mathbf k}_{1T}^2 d{\mathbf k}_{2T}^2 d{\mathbf k}_{3T}^2 d{\mathbf k}_{4T}^2 dy_3 dy_4 dy_5 {d\phi_1 \over 2\pi} {d\phi_2 \over 2\pi} {d\phi_3 \over 2\pi} {d\phi_4 \over 2\pi},
\end{equation}
\begin{equation}
  \displaystyle \sigma = \int {1\over 16\pi (x_1 x_2 s)^2 } |\bar {\cal M}(g g \to \gamma \gamma)|^2 \times \atop
  \displaystyle  \times f_g(x_1,{\mathbf k}_{1T}^2,\mu^2) f_g(x_2,{\mathbf k}_{2T}^2,\mu^2) d{\mathbf k}_{1T}^2
  d{\mathbf k}_{2T}^2 d{\mathbf k}_{3T}^2 dy_3 dy_4 {d\phi_1 \over 2\pi} {d\phi_2 \over 2\pi},
\end{equation}

\noindent
where $\phi_1$, $\phi_2$, $\phi_3$ and $\phi_4$ are the azimuthal angles of initial partons
and produced photons, respectively. If we average these expressions over $\phi_1$ and $\phi_2$ and
take the limit $|{\mathbf k}_{1T}| \to 0$ and  $|{\mathbf k}_{2T}| \to 0$, then we recover the
corresponding formulas in the collinear QCD factorization.

Concerning the unintegrated quark and gluon densities in
a proton, we apply the Kimber-Martin-Ryskin (KMR) approach\cite{26} to calculate them. The KMR approach is the formalism
to construct the unintegrated parton distributions from the known conventional ones.
In this approximation the unintegrated quark and gluon distributions are given by
\begin{equation}
  \displaystyle f_q(x,{\mathbf k}_T^2,\mu^2) = T_q({\mathbf k}_T^2,\mu^2) {\alpha_s({\mathbf k}_T^2)\over 2\pi} \times \atop {
  \displaystyle \times \int\limits_x^1 dz \left[P_{qq}(z) {x\over z} q\left({x\over z},{\mathbf k}_T^2\right) \Theta\left(\Delta - z\right) + P_{qg}(z) {x\over z} g\left({x\over z},{\mathbf k}_T^2\right) \right],}
\end{equation}
\begin{equation}
  \displaystyle f_g(x,{\mathbf k}_T^2,\mu^2) = T_g({\mathbf k}_T^2,\mu^2) {\alpha_s({\mathbf k}_T^2)\over 2\pi} \times \atop {
  \displaystyle \times \int\limits_x^1 dz \left[\sum_q P_{gq}(z) {x\over z} q\left({x\over z},{\mathbf k}_T^2\right) + P_{gg}(z) {x\over z} g\left({x\over z},{\mathbf k}_T^2\right)\Theta\left(\Delta - z\right) \right],}
\end{equation}

\noindent
where $P_{ab}(z)$ are the usual unregulated LO DGLAP splitting
functions. The theta functions which appears
in~(29) and~(30) imply the angular-ordering constraint $\Delta = \mu/(\mu + |{\mathbf k}_T|)$
specifically to the last evolution step to regulate the soft gluon
singularities.
Numerically, for the input we have used leading-order parton densities $xq(x,\mu^2)$ and
$xg(x,\mu^2)$ from MSTW'2008 set\cite{30}.

We note that perturbation theory becomes nonapplicable when the wavelength of the emitted photon
(in the emitting quark rest frame) becomes larger that the typical hadronic scale
${\cal O}$(1~GeV$^{-1}$).
Then the nonperturbative effects of hadronization or fragmentation must be taken
into account. Accordingly, the calculated cross section can be split into two pieses
\begin{equation}
  \sigma = \sigma_{\rm dir}(\mu^2) + \sigma_{\rm fragm}(\mu^2),
\end{equation}

\noindent
with $\sigma_{\rm dir}(\mu^2)$ representing the perturbative contribution and
$\sigma_{\rm fragm}(\mu^2)$ the fragmentation contribution.
In the fragmentation processes photons are produced through
the fragmentation of a parton (produced in a hard subprocess)
into a single photon carrying a large fraction $z$ of parent parton
momentum. These processes are described in terms of quark-to-photon $D_{q\to \gamma}(z,\mu^2)$ and
gluon-to-photon $D_{g\to \gamma}(z,\mu^2)$ fragmentation functions\cite{31}.
In our calculations for quark-gluon scattering~(2) we choose the fragmentation scale $\mu^2$ to be the
invariant mass of the quark + photon subsystem, and restrict $\sigma_{\rm dir}(\mu^2)$
to $\mu \ge M \simeq 1$~GeV. Under this condition, the contribution $\sigma_{\rm dir}(\mu^2)$
is free from divergences (so the mass of the light quark $m$ can be safely sent to zero)
and we checked that the sensitivity of
our results to the choice of $M$ is reasonably soft. As far as
the fragmentation contribution $\sigma_{\rm fragm}(\mu^2)$ is concerned, its size is dramatically reduced by the photon
isolation cuts implemented in the experimental analysis\cite{1,2,3,4,5}.
The isolation condition required that the hadronic transverse energy
$E_T^{\rm had}$, deposited inside a cone with aperture $R$ centered around
the photon direction in the pseudo-rapidity $\eta$ and azimuthal angle $\phi$ plane,
is smaller than some value $E_T^{\rm max}$. In the recent measurements\cite{1,2,3,4,5}
performed at the Tevatron and LHC, these parameters were taken $R \sim 0.4$ and
$E_T^{\rm max} \sim 1 - 2$~ GeV.
According to the estimates\cite{3}, the contribution
from $\sigma_{\rm fragm}(\mu^2)$ amounts to about 10 --- 15\% of
the visible cross section and therefore is neglected in our consideration.

The multidimensional integrations in~(26) --- (28) have been performed
by the means of Monte Carlo technique, using the routine \textsc{vegas}\cite{32}.
The full C$++$ code is available from the author on request.

\section{Numerical results} \indent

We now are in a position to present our numerical results. First we describe our
theoretical input and the kinematic conditions. After we fixed the unintegrated
gluon distributions, the cross sections (26) --- (28) depend on
the renormalization and factorization scales $\mu_R$ and $\mu_F$.
Numerically, we set them to be equal to $\mu_R^2 = \mu_F^2 = (\xi M_{\gamma \gamma})^2$.
In order to estimate the scale
uncertainties of our calculations
we vary the parameter $\xi$ between 1/2 and 2 about the default value $\xi = 1$.
Since the expression for the off-shell quark spin density matrix has been derived
in the massless approximation, numerically we neglect the quark masses.
We use the LO formula for the strong
coupling constant $\alpha_s(\mu^2)$ with $n_f = 4$
active quark flavors at $\Lambda_{\rm QCD} = 200$~MeV, so that $\alpha_s(M_Z^2) = 0.1232$.

Experimental data for prompt photon pair production in $p\bar p$ collisions at the Tevatron come
from both the CDF\cite{1,2} and D$\emptyset$\cite{3} collaborations. Several differential
cross section have been determined: as a function of the diphoton
invariant mass $M_{\gamma \gamma}$, the transverse momentum and rapidity of photon pair
$p_T^{\gamma \gamma}$ and $y_{\gamma \gamma}$, the azimuthal angle difference between the
produced photons $\Delta \phi_{\gamma \gamma}$ and the cosine of
the polar scattering angle $\theta^*$ of leading photon in the Collins-Soper frame.
Recent D$\emptyset$ data\cite{3} refer to the kinematic region defined by
$|\eta^{\gamma 1}| < 0.9$, $|\eta^{\gamma 2}| < 0.9$, $p_T^{\gamma 1} > 21$~GeV and
$p_T^{\gamma 2} > 20$~GeV with the total energy $\sqrt s = 1960$~GeV, and an additional
cut $M_{\gamma \gamma} > p_T^{\gamma \gamma}$ was applied.
The measurements of double differential cross sections
$d\sigma/dM_{\gamma \gamma} dp_T^{\gamma \gamma}$, $d\sigma/dM_{\gamma \gamma} d\Delta \phi_{\gamma \gamma}$ and
$d\sigma/dM_{\gamma \gamma} d|\cos \theta^*|$ for three subdivisions of
$M_{\gamma \gamma}$ range (namely $30 < M_{\gamma \gamma} < 50$~GeV,
$50 < M_{\gamma \gamma} < 80$~GeV and $80 < M_{\gamma \gamma} < 350$~GeV)
have been presented also.
The CDF data\cite{2} refer to the kinematic region defined
by $|y^{\gamma 1}| < 1$, $|y^{\gamma 2}| < 1$, $p_T^{\gamma 1} > 17$~GeV and
$p_T^{\gamma 2} > 15$~GeV. In this analysis, the diphoton
cross section as a function of variable $z = p_T^{\gamma 2}/p_T^{\gamma 1}$ ,
the ratio of sub-leading to leading photon transverse momentum ($0 < z < 1$),
has been measured additionally. Also two specific kinematic cases have been examined separately:
differential cross sections for $M_{\gamma \gamma} > p_T^{\gamma \gamma}$ and
$M_{\gamma \gamma} < p_T^{\gamma \gamma}$. Previous CDF data\cite{1}
refer to the kinematic region defined by $|\eta^{\gamma 1}| < 0.9$, $|\eta^{\gamma 2}| < 0.9$,
$p_T^{\gamma 1} > 14$~GeV, $p_T^{\gamma 2} > 13$~GeV and $\sqrt s = 1960$~GeV.

First experimental data for prompt diphoton production in $pp$ collisions at the LHC
come from the CMS\cite{4} and ATLAS\cite{5} collaborations.
The CMS data\cite{4} have been obtaned in the kinematic region defined by
$|\eta^{\gamma 1}| < 2.5$, $|\eta^{\gamma 2}| < 2.5$ (except pseudo-rapidity
region $1.44 < \eta < 1.57$ for both photons), $p_T^{\gamma 1} > 23$~GeV and
$p_T^{\gamma 2} > 20$~GeV with the total energy $\sqrt s = 7$~TeV. The measurements
for more tight central region with $|\eta^{\gamma 1}| < 1.44$ and $|\eta^{\gamma 2}| < 1.44$
have been presented additionally. The ATLAS data\cite{5} refers to the kinematic region
defined by $|\eta^{\gamma 1}| < 2.37$, $|\eta^{\gamma 2}| < 2.37$ (with the exclusion
of the region $1.37 < \eta < 1.52$ for both photons), $p_T^{\gamma 1} > 16$~GeV and
$p_T^{\gamma 2} > 16$~GeV with the with the same total energy.

\begin{table}
\begin{center}
\begin{tabular}{|l|c|}
\hline
   & \\
  Source & $\sigma(p\bar p \to \gamma \gamma + X)$ [pb] \\
   & \\
\hline
   & \\
   $k_T$-factorization (KMR) & $8.87^{+1.36}_{-0.98}$ (scales)\\
   & \\
   NLO pQCD\cite{12} (\textsc{diphox}) & $10.58\pm 0.55$\\
   & \\
   NNLL pQCD\cite{13} (\textsc{resbos}) & $11.31\pm 2.45$\\
   & \\
   CDF data\cite{2} & $12.47 \pm 0.21$ (stat.) $ \pm 3.74$ (syst.)\\
   & \\
\hline
\end{tabular}
\end{center}
\caption{The total cross section of diphoton production in $p\bar p$ collisions
calculated in the kinematical region defined by $|y^{\gamma 1}| < 1$,
$|y^{\gamma 2}| < 1$, $p_T^{\gamma 1} > 17$~GeV and
$p_T^{\gamma 2} > 15$~GeV at $\sqrt s = 1960$~GeV.}
\end{table}

The results of our calculations are shown in Figs.~1 --- 10 in
comparison with the Tevatron data\cite{1,2,3} and in Figs.~11 --- 15
in comparison with the LHC data\cite{4,5}.
The solid histograms are obtained by fixing both the
factorization and renormalization scales at the default value,
whereas the upper and lower dashed histograms correspond to the scale variation as it
was described above (in left panels). Also, in Figs.~1 --- 6 we plot for comparison
the NNLL pQCD predictions\cite{13} (as given by \textsc{resbos} program)
listed in\cite{1,3}. The relative contributions to the diphoton cross sections
from quark-antiquark annihilation, quark-gluon scattering and gluon-gluon fusion subprocesses
are shown separately by the dash-dotted, dotted and dashed histograms, respectively,
in right panels.

We note that different kinematic variables under consideration probe different aspects
of the diphoton production mechanism. For instance,
the $M_{\gamma \gamma}$ spectrum is particularly sensitive
to potential contributions from physics beyond the SM.
The $\cos \theta^*$ distribution probes the
angular momentum of the final state, which should
be different for QCD-mediated production as compared,
for example, to the decay of a scalar Higgs boson $H \to \gamma \gamma$ (see \cite{13}).

We find that the $k_T$-factorization approach reasonably well describe a full
set of experimental data taken at the Tevatron and LHC. Moreover, the
shape and absolute normalization of measured cross sections are adequately reproduced
within the theoretical and experimental uncertainties.
At the Tevatron, there is some discrepancy between recent CDF data\cite{2} and our predictions at very high
diphoton invariant masses (see Fig.~7). Note, however, that the small-$x$
approximation used in our consideration is broken at high $M_{\gamma \gamma}$
and the more accurate
treatment of, in particular, off-shell quark spin density matrix is needed.
This point, of course, is of importance but it is out of our present consideration.
From another side, we would like to point out that $k_T$-factorization approach provides a better
description of all kinematic variables
(in comparison with the NLO/NNLL pQCD calculations\cite{12,13})
at low $M_{\gamma \gamma}$ values,
where expected effects connected with the small-$x$ physics
becomes important. In the collinear QCD factorization,
observed large discrepancy between data and NLO/NNLL pQCD predictions\cite{12,13} at low $M_{\gamma \gamma}$
attributes to a fragmentation contributions and
higher-order QCD corrections to the gluon-gluon fusion subprocess\cite{1,2,3,4,5}.
However, the main part of these corrections are already effectively taken into
account in our calculations. It is a radiative
QCD corrections described by the ladder-type diagrams
which are naturally included into the $k_T$-factorization
formalism at LO level\footnote{See review\cite{18} for more details.}.
At the LHC, our predictions agree well with the CMS data\cite{4} in a whole
kinematical range and slightly overestimate
the ATLAS data\cite{5} at low values of $\Delta \phi_{\gamma \gamma}$ and
high values of $p_T^{\gamma \gamma}$. This point, probably, can indicate
the inconsistecy of the CMS and ATLAS data and, of course, needs in a further
theoretical and experimental investigations.
Note also that the NLO pQCD predictions\cite{12} underestimate the measured $\cos \theta^*$
distributions at both the Tevatron and LHC energies\cite{2,3,4,5}. This underestimation
is more significant for the central rapidity range ($|\eta| < 1.44$) at the LHC.
Our predictions agree well with the data\cite{2,3,4,5}. It
could be important for experimental detection of Higgs boson signal
and further investigations of Higgs properties.

\begin{table}
\begin{center}
\begin{tabular}{|l|c|}
\hline
   & \\
  Source & $\sigma(p\bar p \to \gamma \gamma + X)$ [pb]\\
   & \\
\hline
   & \\
   $k_T$-factorization (KMR) & $29.9^{+7.4}_{-6.1}$ (scales)\\
   & \\
   NLO pQCD\cite{12} (\textsc{diphox}) & $27.3$ $^{+3.0}_{-2.3}$ (scales) $\pm 1.1$ (PDFs) \\
   & \\
   CMS data\cite{2} & $31.0 \pm 1.8$ (stat.) $^{+2.0}_{-2.1}$ (syst.) $\pm 1.2$ (lumi.)\\
   & \\
\hline
\end{tabular}
\end{center}
\caption{The total cross section of diphoton production in $pp$ collisions
calculated in the kinematical region defined by $|\eta^{\gamma 1}| < 1.44$,
$|\eta^{\gamma 2}| < 1.44$, $p_T^{\gamma 1} > 23$~GeV and
$p_T^{\gamma 2} > 20$~GeV at $\sqrt s = 7$~TeV.}
\end{table}

As it was expected, the main important properties of the $k_T$-factorization approach
clearly manifest themselves in the calculated $p_T^{\gamma \gamma}$, $z$
and $\Delta \phi_{\gamma \gamma}$ distributions.
In the naive LO pQCD approximation, photons produced in $2\to 2$ subprocesses
are back-to-back in the transverse plane and
are balanced in $p_T$ due to momentum conservation. Therefore, these three ditsributions
must be simply a delta functions: $d\sigma/dp_T^{\gamma \gamma} \sim \delta(p_T^{\gamma \gamma})$,
$d\sigma/dz \sim \delta(z - 1)$ and
$d\sigma/d\Delta \phi_{\gamma \gamma} \sim \delta(\Delta \phi_{\gamma \gamma} - \pi)$.
When higher-order QCD processes are considered,
the presence of additional quarks and/or gluons in
the final state allows these distributions to be more spread.
In the $k_T$-factorization approach, taking into account the
non-vanishing initial parton transverse momentum leads to the violation of back-to-back
kinematics even at LO approximation.
So, despite the fact that one from contributed subprocesses
is the $2 \to 3$ subprocess
(that makes the difference between the $k_T$-factorization predictions and ones
from the collinear approximation of QCD not well pronounced),
obtained perfect description of measured $\Delta \phi_{\gamma \gamma}$
distributions\cite{1,2,3,4,5} is notable. Specially we point out a reasonable
description of the Tevatron and LHC data at low
$\Delta \phi_{\gamma \gamma}$ values where the significant underestimation
of the data by the NLO/NNLL pQCD calculations\cite{12,13} was observed (see also Figs.~2, 4 and 6).
The important role of such angular correlations
for understanding an interaction dynamics is well known\cite{18}.
In particular, as it was demonstrated in\cite{33}, these correlations strongly
depend on the unintegrated parton densities involved in the calculations
and can be used as a test to
distinguish the different approaches of non-collinear parton
evolution\footnote{We note, however, that at moment the
KMR prescription is only one provide us with
the unintegrated quark densities $f_q(x,{\mathbf k}_T^2,\mu^2)$
which can be used in a wide region of $x$ and ${\mathbf{k}_T^2}$ in
phenomenological studies. Thus, the problem of estimation of theoretical
uncertainties connected with unintegrated parton densities is still open.}.
We would like to note also that the scale uncertainties of our
calculations are quite small at $\Delta \phi_{\gamma \gamma} \sim 0$
and increases when $\Delta \phi_{\gamma \gamma} \to \pi$.
Similar to $\Delta \phi_{\gamma \gamma}$ distributions,
the calculated $p_T^{\gamma \gamma}$ distributions also directly
connected with the unintegrated quark and gluon distributions
due to transverse momentum conservation. Perfect overall agreement
of our calculations and the data on the $\Delta \phi_{\gamma \gamma}$ and
$p_T^{\gamma \gamma}$ shows that the KMR prescription for evaluation
of unintegrated parton densities reproduces well
the transverse momenta of initial quarks and gluons
in a probed kinematical region.

\begin{table}
\begin{center}
\begin{tabular}{|l|c|}
\hline
   & \\
  Source & $\sigma(p\bar p \to \gamma \gamma + X)$ [pb]\\
   & \\
\hline
   & \\
   $k_T$-factorization (KMR) & $59.2^{+14.4}_{-12.1}$ (scales)\\
   & \\
   NLO pQCD\cite{12} (\textsc{diphox}) & $52.7$ $^{+5.8}_{-4.2}$ (scales) $\pm 2.0$ (PDFs) \\
   & \\
   CMS data\cite{2} & $62.4 \pm 3.6$ (stat.) $^{+5.3}_{-5.8}$ (syst.) $\pm 2.5$ (lumi.)\\
   & \\
\hline
\end{tabular}
\end{center}
\caption{The total cross section of diphoton production in $pp$ collisions
calculated in the kinematical region defined by $|\eta^{\gamma 1}| < 2.5$,
$|\eta^{\gamma 2}| < 2.5$ (except pseudo-rapidity
region $1.44 < \eta < 1.57$ for both photons), $p_T^{\gamma 1} > 23$~GeV and
$p_T^{\gamma 2} > 20$~GeV at $\sqrt s = 7$~TeV.}
\end{table}

Special interest for the $k_T$-factorization phenomenology
is connected also with the events with low invariant mass and high
transverse momentum of produced photon pair. The CDF collaboration has studied
this kinematical region using a special condition $M_{\gamma \gamma} < p_T^{\gamma \gamma}$
in their experimental analysis\cite{2}. Within the mentioned above cuts on the
transverse momenta of the produced photons,
such measurements provide us with an
additional test for unintegrated quark and gluon distributions $f_a(x,{\mathbf k}_T^2,\mu^2)$
at moderate and high ${\mathbf k}_T^2$ values. The
events with back-to-back kinematics are strongly suppressed in this case (see Fig.~10).
In contrast with the
NLO/NNLL pQCD calculations\cite{12,13}, the $k_T$-factorization predictions
agree well with the CDF data.
An opposite condition (namely, $M_{\gamma \gamma} > p_T^{\gamma \gamma}$)
corresponds to the selection of events with kinematics similar to the decay
of a heavy particle with low transverse momentum into a photon pair,
such as, for example, $H \to \gamma \gamma$.
Such events are better described\cite{2} by the NLO pQCD calculations\cite{12} than ones
with low invariant mass and high transverse momentum. Our
predictions agree within the uncertainties with the data\cite{2}, but
overall agreement is a bit worse.

Concerning a relative contributions to the calculated diphoton production cross sections,
we find that quark-antiquark subprocess dominates at both the Tevatron and LHC
energies in the probed kinematical regions\footnote{We strongly disagree with the
estimations\cite{34} of relative contributions from the gluon-gluon fusion and quark-antiquark annihilation
subprocesses performed for the Tevatron energy.}. The contribution from
quark-gluon scattering is similar to gluon-gluon fusion one at
low diphoton invariant masses and overshoot gluon-gluon fusion contribution
at high $M_{\gamma \gamma}$ values.
As it was expected\cite{4,5}, the role of both these subprocesses increases significantly at the LHC energies.
We note also that the contribution
from $q\bar q \to \gamma \gamma g$ subprocess,
which is order of ${\cal O}(\alpha_s \alpha^2)$, is already taken into account
in our calculations. To be precise, this contribution
is effectively included to the quark-antiquark annihilation one
due to the initial state gluon radiation (see also\cite{18}).
Of course, it is in a clear contrast with the collinear QCD factorization where these contributions
should be calculated separately.

The predicted total cross sections for the Tevatron
conditions are listed in Table~1 and for LHC conditions are listed in Tables 2 and 3,
respectively. Our results are slightly below the Tevatron data and NLO/NNLL pQCD
predictions\cite{12,13} but agree with them within the theoretical and experimental uncertainties.
However, at the LHC energy, our predictions overshoot the NLO pQCD ones\cite{12}
and are more close to the data. It could be connected with the small-$x$ effects
which becomes more important for the LHC conditions.

In conclusion, we would like to stress a number of important achievements demonstrated by
the $k_T$-factorization QCD approach. As a general feature, the $k_T$-factorization
predictions are found to be
perfectly compatible with the available data, in particular, on the
production of prompt photons, Drell-Yan lepton pairs, heavy quarks as well as various
quarkonium states at modern colliders\cite{20,21,22,23,24,25,33,35,36}.
The $k_T$-factorization approach succeeds in describing the polarization
phenomena observed in $ep$ and $pp$ interactions (see, for example,\cite{35,36}
and references therein). The latter is essentially related to the initial gluon
off-shellness, which dominates the gluon polarization properties and has a considerable impact
on the kinematics.
So, we believe that the $k_T$-factorization formalism
holds a possible key to understanding the production dynamics at high energies.

\section{Conclusions}

We have investigated the isolated prompt photon pair production in $p\bar p$ and $pp$
collisions at the Tevatron and LHC energies within the framework of the $k_T$-factorization QCD approach.
Our consideration is based on the quark-antiquark annihilation, quark-gluon scattering
and gluon-gluon fusion subprocesses, where the non-zero transverse momenta of incoming
partons are taken into account.
The unintegrated parton densities in a proton are determined using the
Kimber-Martin-Ryskin prescription.
We obtained a reasonable well agreement between our predictions and recent data
taken by the D$\emptyset$, CDF, CMS and ATLAS collaborations.
The achieved description of the data in several kinematical regions (in particular,
at low azimuthal angle distance between produced photons)
is better as compared to the one obtained in the framework of collinear QCD factorization (with NLO or
even NNLL accuracy).
Also, we describe reasonably well the Tevatron and LHC data on the $\cos \theta^*$ distributions
of the diphoton production.
Such quantities (underestimated by the NLO pQCD calculations) probe the
angular momentum of the final state and different
for QCD-mediated production as compared to the decay of a scalar Higgs boson.
It could be important for experimental detection of Higgs
and further theoretical and experimental investigations in this field.
We find that the scale uncertainties of our
calculations are quite small at $\Delta \phi_{\gamma \gamma} \sim 0$,
although they are exceed, of course, the uncertainties of
NLO/NNLL pQCD calculations in general. Moreover,
the problem of estimation of our theoretical
uncertainties (connected in part with the non-collinear parton evolution scheme)
is still open and further theoretical attempts (in order to investigate the unintegrated
quark distributions more detail) are necessary to reduce this uncertainty.
It is important for further studies of small-$x$ physics at hadron colliders,
and, in particular, for searches of effects of new physics beyond the SM at the LHC.

\section{Acknowledgments} \indent
The author would like to thank N.P.~Zotov,
S.P.~Baranov and H.~Jung for their encouraging interest
and helpful discussions. Author is
also grateful to DESY Directorate for the support in the
framework of Moscow --- DESY project on Monte-Carlo
implementation for HERA --- LHC.
This research was supported in part by the
FASI of Russian Federation (grant NS-3920.2012.2),
RFBR grants 11-02-01454-a and 12-02-31030,
grant of president of Russian Federation (MK-3977.2011.2) and the
grant of Ministry of education and sciences of Russia (agreement 8412).

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