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New tests for high energy factorization in Drell-Yan lepton pair production
Nikolay P. Zotov
SINP MSU, Moscow, Russia

in collaboration with S.P. Baranov, A.V. Lipatov

N.P. Zotov

QFTHEP 2013, St. Petersburg, Russia, June 24, 2013


Content


Introduction Theoretical framework - off-shell amplidudes - unintegrated (TMD) parton densities





Numerical results Conclusions



N.P. Zotov

QFTHEP 2013, St. Petersburg, Russia, June 24, 2013


Collinear & kt-factorization in QCD



DGLAP evolution resummation of the terms ~ ln Q 2 strong ordering in Q no kt of incoming partons on-shell hard matrix elements collinear QCD factorization



2



BFKL or CCFM evolution resummation of the terms ~ ln 1 / x no ordering in kt non-zero kt of incoming partons unintegrated (TMD) parton densities off-shell hard matrix elements kt-factorization

N.P. Zotov

QFTHEP 2013, St. Petersburg, Russia, June 24, 2013


Drell-Yan lepton pair production at high energies


Major source of background to a number of SM processes and processes beyond the SM (Higgs, W'/Z' etc) Previously, we have used the quark-antiquark annihilation and QCD Compton subprocesses
A.V. Lipatov, M.A. Malyshev, N.P. Zotov, JHEP 12, 117 (2011)



Contributions from last diagrams are taken into account by quark-antiquark annihilation On-shell hard matrix elements and KMR uPDFs have been applied An additional K-factor was included:

A.Kulesza. W.J. Stirling, NPB 555, 279 (1999)

But we need CCFM-evolved partons for MC generator CASCADE which widely used by the CMS collaboration N.P. Zotov QFTHEP 2013, St. Petersburg, Russia, June 24, 2013


off-shell amplitude for q*q* Z/* ll


Effective quark-to-photon vertex for reggeized quarks
L.N. Lipatov, M.I. Vyazovsky, NPB 597, 399 (2001) A.V. Bogdan, V.S. Fadin, NPB 740, 36 (2006)

P1 P2 ( k 1 , k 2 )= - k 1 -k2 P1k 2 P2k





1

where k 1 , k 2 , P1 and P2 are the initial quarks and protons 4-momenta


Ward identity is satisfied: ( k 1 , k 2 ) ( k 1 +k 2) = 0 Effective reggeized quark-to-Z boson vertex is constructed in a similar way:



Z ( k 1 , k 2 )= ( k 1 , k 2 ) ( gV - g A )
where gV and g A are usual vector and axial quark to Z boson coupling constants





5

N.P. Zotov

QFTHEP 2013, St. Petersburg, Russia, June 24, 2013


off-shell amplitude for q*q* Z/* ll


Simple small-x approximation to calculate partonic amplitudes involving initial off-shell quarks has been proposed
S.P. Baranov, A.V. Lipatov, N.P. Zotov, PRD 81, 094034 (2010)

In this prescription, the initial off-shell quark is considered as the internal line in the «extended» diagram. At small x, in the zero mass limit this results in the special form of off-shell quark spin density matrix:



u ( k ) ( k )= xP u

where k and P are the off-shell quark and beam 4-momenta.


In this way, gauge invariance is achieved in the small-x limit, where high-energy factorization is valid

N.P. Zotov

QFTHEP 2013, St. Petersburg, Russia, June 24, 2013


TMD parton densities in a proton


CCFM-evolved gluon distributions are available: H. Jung, arXiv: hep-ph/0411287 Valence quark densities have been proposed:
M. Deak, K. Kutak, H. Jung, Progress in High Energy Physics 2, 168 (2008)





Sea quark densities can be calculated from gluon ones if we restrict to the case where gluon-to-quark splitting occurs in the last evolution step:

where TMD gluon-to-quark splitting function is given by

with = q -- zk, and k and q are the the gluon and quark transverse momenta
S. Catani, F. Hautmann, NPB 427, 475 (1994) F. Hautmann, H. Jung, M. Hentschinski, NPB 865, 54 (2012)

N.P. Zotov

QFTHEP 2013, St. Petersburg, Russia, June 24, 2013


Effective vertex vs. small-x approximation
CCFM-evolved partons no theta-function applied effective vertex small-x approximation

N.P. Zotov

QFTHEP 2013, St. Petersburg, Russia, June 24, 2013


Our numerical predictions vs. Tevatron & LHC data
CCFM without theta-function CCFM with theta-function

N.P. Zotov

QFTHEP 2013, St. Petersburg, Russia, June 24, 2013


Angular distributions in Drell-Yan pair production
KMR fit unc.
d 1+ cos2 d cos 1 + A 0 ( 1- 3cos2 ) 2 + A 4 cos d 1+3 cos +2 cos 2 d A2 3 3= A 3 2= 16 4

Lam-Tung relation: A0 = A collinear QCD prediction: flat behaviour of A3

2

Phys. Rev. D 53, 011201 (2001)

N.P. Zotov

QFTHEP 2013, St. Petersburg, Russia, June 24, 2013


Conclusions


We considered an important processes of Drell-Yan lepton pair production in the framework of kt-factorization QCD approach Our consideration was based on the gauge-invariant amplitude of quark annihilation subprocess (involving Z-boson exchange) and CCFM-evolved TMD PDFs in a proton We introduced TMD sea quarks and investigate the dependence of our predictions on the gluon-to-quark splitting function We have obtained a reasonable agreement of our numerical predictions and the Tevatron and LHC data taken by the D0, CDF and CMS collaborations Furher investigations of Drell-Yan process at the LHC are in progress









N.P. Zotov

QFTHEP 2013, St. Petersburg, Russia, June 24, 2013