Документ взят из кэша поисковой машины. Адрес оригинального документа : http://qfthep.sinp.msu.ru/talks2013/malyshev_photoproduction.pdf Дата изменения: Wed Jul 3 15:47:30 2013 Дата индексирования: Thu Feb 27 20:31:53 2014 Кодировка:

Prompt photon photoproduction at HERA in the kT-factorization approach
M.A. Malyshev in collaboration with A.V. Lipatov N.P. Zotov
M.V. Lomonosov Moscow State University D.V. Skobeltsyn Institute of Nuclear Physics


Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Outline
1. Motivation 2. kT-factorization approach - unintegrated parton distributions - off-shell matrix elements 3. Parameters 4. Numerical results 5. Conclusion

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Motivation
The prompt photon production in ep collisions at HERA is a direct probe of the hard subrocess dynamics, since produced photons are largely insensitive to the effect of finalstate hadronization. In the present work we have studied the prompt photon photoproduction in the kT-factorization approach, which was successfully used before to describe other various high energy processes. In particular, it was used to describe the prompt photon production at HERA [A.V. Lipatov, N.P. Zotov, Phys.Rev. D 72, 054002 (2005); D 81, 094027 (2007)]. Recently new experimental data on prompt photon photoproduction have been presented by the ZEUS collaboration. Here we present the theoretical description of these and also previously published HERA data with taking into account additional contributions which are important for a better understanding of the evolution dynamics of the process.
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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Motivation

Graphs from the presentation by A. Iudin at DIS'13

The results obtained with with O(2) matrix elements [Lipatov, Zotov, 2005, 2007] tend to underestimate the new ZEUS data. In the NLO collinear approximation results also the box contributions were taken into account. This demands a reconsidering with the including higher order matrix elements in the kT-factorization calculation.

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

kT-factorization approach
1. Matrix elements which depend on the transverse momenta of incoming gluons. 2. Unintegrated parton distributions

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Considered subprocesses
We extend our consideration to the O(2S) and O(2S2) subprocesses:

1. q qg 2. g* qq 3. g g

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Consequence for +jet
In the case of photon and associated jet production the considering of the O(2S) and O(2S2) subprocesses allows us to take into account the kinematics of the accompanied jet more accurately as compared with the previous consideration. Additional mot based on the description of heavy (b or predictions. ivation of off-shell 2 the Tevatr c) quark our on jet study is that similar consideration, 3 subprocesses, results to a better data on the associated photon and as compared to the NLO pQCD

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Cross section

where ET, y, are the transverse energy, rapidity and azimuthal angle of the produced photon, and 1, azimuthal angles and the rapidities of the matrix elements are convoluted with depending on the transverse momenta) were taken in the KMR form.

2, y1 and y2 are the outcoming partons. The the unintegrated (i.e. parton densities, which
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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Unintegrated parton distributions

KMR approach(Kimber, Martin, Ryskin) [M.A. Kimber, A.D. Martin, M.G. Ryskin, Phys. Rev. D 63, 114027 (2001); G. Watt, A.D. Martin, M.G. Ryskin, Eur. Phys. J. C 31, 73 (2003)]. Weakening of the strong ordering:

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Unintegrated parton distributions
In the KMR approach the distribution functions start to depend on the transverse momenta of the partons, and fa(x,kT2)=const, if kT2<02~1 GeV2, otherwise they take the form:

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Parameters


Theoretical uncertainties are connected with the choice of the factorization and renormalization scales. We took R = F = = ET . We varied the scale parameter between 1/2 and 2 about the default value = 1. We neglected the quark masses. For completeness, we use LO formula for the strong coupling constant s(2) with nf = 4 active quark flavors at QCD = 200 MeV. We used the standard isolation experimental cuts: EThadEmax (had - )2 + (had - )2 R2. The isolation not only reduces the background but also significantly reduces the so called fragmentation components, connected with collinear photon radiation (10%). Both H1 and ZEUS collaborations take R=1 and Emax = 0.1 ET.
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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Numerical results -- inclusive , H1-2009
1. Differential cross section of the inclusive prompt photon photoproduction production ep X at HERA as a function of the prompt photon transverse energy ET and pseudo-rapidity . Left: the solid line -- the predictions; the dashed line -- the uncertainties; dotted line -- the predictions based on method of [Lipatov, Zotov, 2005, 2007]. Right: different contributions to the total cross-section (solid line): q qg (dash-dotted), g* qq (dashed), box (dotted). The experimental data are of H1 (2009).

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Numerical results -- inclusive , ZEUS-2013
2. Differential cross section of the inclusive prompt photon photoproduction production ep X at HERA as a function of the prompt photon transverse energy ET and pseudo-rapidity . Left: the solid line -- the predictions; the dashed line -- the uncertainties; dotted line -- the predictions based on method of [Lipatov, Zotov, 2005, 2007]. Right: different contributions to the total cross-section (solid line): q qg (dash-dotted), g* qq (dashed), box (dotted). The experimental data are of ZEUS (2013).

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Numerical results -- +jet, H1-2009
3. Differential cross section of the associated with a jet prompt photon photoproduction production ep X at HERA as a function of the prompt photon transverse energy ET and pseudo-rapidity . Left: the solid line -- the predictions; the dashed line -- the uncertainties; dotted line -- the predictions based on method of [Lipatov, Zotov, 2005, 2007]. Rightt: different contributions to the total crosssection (solid line): q qg (dash-dotted), g* qq (dashed), box (dotted). The experimental data are of H1 (2009).

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Numerical results -- +jet, H1-2009
3. Differential cross section of the associated with a jet prompt photon photoproduction production ep X at HERA as a function of the jet transverse energy ETjet and pseudorapidity jet . Left: the solid line -- the predictions; the dashed line -- the uncertainties; dotted line -- the predictions based on method of [Lipatov, Zotov, 2005, 2007]. Right: different contributions to the total cross-section (solid line): q qg (dash-dotted), g* qq (dashed), box (dotted). The experimental data are of H1 (2009).

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Numerical results -- +jet, ZEUS-2013
4. Differential cross section of the associated with a jet prompt photon photoproduction production ep X at HERA as a function of the prompt photon transverse energy ET and pseudo-rapidity . Leftt: the solid line -- the predictions; the dashed line -- the uncertainties; dotted line -- the predictions based on method of [Lipatov, Zotov, 2005, 2007]. Right: different contributions to the total crosssection (solid line): q qg (dash-dotted), g* qq (dashed), box (dotted). The experimental data are of ZEUS (2013).

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Numerical results -- +jet, ZEUS-2013
4. Differential cross section of the associated with a jet prompt photon photoproduction production ep X at HERA as a function of the jet transverse energy ETjet and pseudorapidity jet . Left: the solid line -- the predictions; the dashed line -- the uncertainties; dotted line -- the predictions based on method of [Lipatov, Zotov, 2005, 2007]. Right: different contributions to the total cross-section (solid line): q qg (dash-dotted), g* qq (dashed), box (dotted). The experimental data are of ZEUS (2013).

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

x-variables
Important variables for testing the structure of the colliding proton and photon are the longitudinal momenta fractions of the partons in these particles. The ZEUS collaboration measures cross sections with the dependence from the following variable:

The H1 collaboration introduces the following observables:

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Numerical results - x-variables
5. Differential cross section of the associated with a jet prompt photon photoproduction production ep X at HERA as a function of the longitudinal momentum of a parton from the initial photon xobs and of a parton from the initial proton in the leading order xpLO. Left: the solid line -- the predictions; the dashed line -- the uncertainties; dotted line -- the predictions based on method of [Lipatov, Zotov, 2005, 2007]. Right: different contributions to the total cross-section (solid line): q qg (dash-dotted), g* qq (dashed), box (dotted). The experimental data are of H1 (2009) and ZEUS (2013).

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Conclusion
In the presented talk the process of the the prompt photon photoproduction in the kT-factorization QCD approach at HERA has been studied. The matrix elements for qqg and g*qq have been calculated. Also the 'box' matrix element for gg has been included into the consideration. The transverse momenta of the incoming quarks and gluons have been taken into account. A reasonably good description of the experimental data of the ZEUS and H1 collaborations for the prompt photon photoproduction at HERA has been obtained.

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Back up

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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Divergencies


We do not use the concept of fragmentation functions obviously. In our approach the effect of final state radiation is already included in calculations at the level of partonic subprocess matrix elements (we have a 2 3 rather than 2 2 subprocesses). But as in the traditional approach the calculated cross sections can be split into two pieces: the direct and fragmentation contributions. They depend from fragmentation scale 2. In our calculations is the invariant mass of the produced photon and any final quark and we restrict direct contribution to M = 1GeV in order to eliminate the collinear divergences in the direct cross section. Then the mass of light quark mq can be safely to zero. The numerical effects of M is really small. It is less important than other theoretical uncertainties (connected with choice of renormalization and factorization scales).



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Maxim Malyshev, QFTHEP'13

St.-Petersburg, June, 29, 2013

Off-shell quarks
In the presented work we article [S.P. Baranov, A.V. 81, 094034 (2010)]. Acco quark spin density matrix mas s es ): used a method, described in the Lipatov, N.P. Zotov, Phys. Rev D rding to this method, the off-shell has the form (in the limit of zero


s

s k = x P u k u

s

Here P is the momentum of the incoming proton.

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