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Prompt photon production at HERA in the kt-factorization approach
S.P. Baranov, A.V. Lipatov, N.P. Zotov
1
2 2

1 -- Lebedev Physical Institute, Moscow, Russia 2 -- SINP MSU, Moscow, Russia

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Content


Motivation Phenomenology of kt-factorization Some calculation details Numerical results - photoproduction regime - DIS









Summary

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Motivation I


Prompt photons are directly coupled to the interacted quarks At HERA, they can be produced via direct and resolved photon events They directly probe the proton and photon PDFs They not affected by the subsequent fragmentation and hadronization







A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Motivation II


The NLO QCD predictions are typically 30 -- 40% below the photoproduction data
A. Zembrzuski, M. Krawczyk, PRD 64, 114017 (2001) M. Fontannaz, J.Ph. Guillet, G. Heinrich, EPJ C 21, 303 (2001)



At DIS, there is substantial underestimation of the data at low Q 2
A. Gehrmann-De Rider, G. Kramer, H. Spiesberger, PRL 96, 132006 (2006)

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Motivation III


The visible disagreement in NLO calculations can be reduced by the introducing «by hands» of some intrinsic partonic transverse momentum kt ~ 2 GeV. However, such large kt should have a significant QCD component The non-zero partonic kt is naturally occurs in the kt-factorization approach of QCD, where it is controlled by the non-collinear (BFKL-like) of evolution equations First applications of the kt-factorization approach to the prompt photon photo-production have been made
A.V. Lipatov, N.P. Zotov, PRD 72, 054002 (2005)





A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Motivation IV

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


kt-factorization approach II


The large logarithms ~1/x are summed up via BFKL or CCFM equations Matrix elements of partonic subprocesses should be off-shell Partonic PDFs should be unintegrated (i.e. kt-dependent) Any observable can be calculated by the convolution of off-shell matrix elements with the unintegrated PDFs in both x and kt See more details in
Small-x Collaboration, EPJ C 48, 53 (2006); EPJ C 35, 67 (2004); EPJ C 25, 77 (2002)







A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


kt-factorization approach I
DGLAP BFKL

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Calculations I
Photoproduction

DIS

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Calculations II
In off-shell matrix elements:


Polarization tensor for off-shell qluons:



k k e e = T2 kT


T



To calculate the spin density matrix for off-shell quarks, we extend the original diagram and consider the off-shell quark line as internal line in the extended diagram.
In the small-x approximation: u u = x p (neglecting also the quark masses)
p



A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Calculations III


KMR unintegrated PDFs
M.A. Kimber, A.D. Martin, M.G. Ryskin, PRD 63, 114027 (2001)
2 f q x , k 2 , 2 ~T q k 2 , 2 [ Pqq вq x , k T P qg в g x , k 2 ] T T T
2 f g x , k 2 , 2 ~ T g k T , 2 [ P g q в q x , k 2 P g в g x , k 2 ] T T T



CCFM unintegrated PDFs gluon density has been fitted on DIS data H. Jung, arXiv:hep-ph/0411287 valence quark density has been proposed
M. Deak, H. Jung, K. Kutak, DIS'08

sea quark density is approximated by the last gluon splitting, i.e.
f
s q 2 x , k 2 , 2 ~ P qg в f g x , k T , 2 T

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Calculations IV
Numerical parameters:


Massless approximation for all quark flavours Isolation criterion (also removes the fragmentation photons)





N f =4,

QCD

= 200 MeV
2 2 T



Hard scale = E

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Numerical results: incl. photoproduction
Soild histograms -- KMR uPDFs Dashed (dash-dotted) -- CCFM set A0 (B0) Missing sea quarks component in CCFM

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Numerical results: incl. photoproduction
Soild histograms -- KMR uPDFs Dashed (dash-dotted) -- CCFM set A0 (B0) Missing sea quarks component in CCFM

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Numerical results: excl. photoproduction
Soild histograms -- KMR uPDFs Dashed (dash-dotted) -- CCFM set A0 (B0)

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Numerical results: excl. photoproduction
p T = E T si n Sensitive to the high-order contributions


Soild histograms -- KMR Dashed (dash-dotted) -- CCFM

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Numerical results: DIS
Soild histograms -- KMR uPDFs Upper and lower dashed histograms -- scale variations in KMR

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Numerical results: DIS
Soild histograms -- KMR uPDFs Upper and lower dashed histograms -- scale variations in KMR

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Numerical results: DIS
Soild histograms -- KMR uPDFs Upper and lower dashed histograms -- scale variations in KMR

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Numerical results: DIS
Different description of the H1 and ZEUS data in the exclusive production case

A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010


Summary


We presented the numerical calculations for the prompt photon production at HERA (both photo-production and DIS) We find a good agreement with the HERA data The transverse momentum of initial partons is important for description of the HERA data The higher-order QCD contributions are effectively simulated in the kt-factorization approach at LO level The contribution from the quarks are important and should be included into the non-collinear evolution cascade









A.V. Lipatov

QFTHEP 2010, Golitsyno, Russia, September 10, 2010