Hard processes at high energies in the Reggeized-parton approach
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rd Processes at High Energies in the Reggeized-Parton Approach1 A. V. Karpishkov, M. A. Nefedov, V. A. Saleev*, and A. V. Shipilova Samara National Research University, Samara, 443086 Russia *e-mail: [email protected] Abstract⎯Dominant contributions to the cross sections of hard processes at high energies come from the processes with multi-Regge kinematics which reflect the Reggeization of partonic amplitudes as a fundamental property of quantum-field gauge theories. The report briefly describes the Reggeized-parton approach based on the kT factorization at high energies and on the Lipatov’s effective field theory for Reggeized gluons and quarks. DOI: 10.1134/S1063779617050227
1. REGGEIZED-PARTON APPROACH In the collinear parton model (CPM), partonic amplitudes are expanded in the powers of the strongcoupling constant α S (Q 2 ) using the perturbation theory, and higher-order corrections are consistently taken into account. This model adequately describes the processes with a single hard scale in Q such as the lepton deep-inelastic scattering on protons and nuclei and hadronic production of heavy quarks and gauge bosons [1]. When applied to processes with several hard scales in Q , the CPM encounters problems arising from the presence of large logarithmic terms proportional to [α S log(Q1 Q2 )]n in higher orders of the perturbation series. In the Regge limit in which the Q scale of the high-energy is much less than the total collision energy, Q ! S, one has to take into account large logarithmic terms [α S log(1 x)]n where x ∼ Q S . This can be done using the approach of highenergy factorization, i.e., the kT factorization depending on the transverse momenta and virtualities of initial partons [2]. In this approach, the cross section of a hard process in a hard-energy hadron collision factorizes as
d σ( pp → * + X ) =
∑ Φ (x , t ,Q ) 2
i
1 1
i, j
(1)
ˆ ij (*, t1, t 2 ), ⊗ Φ j ( x 2, t 2, Q ) ⊗ d σ 2
where d σ ˆ ij(*, t1, t 2 ) is the hard-scattering coefficient (equal to the cross section of the partonic subprocess ij → * in the leading approximation), and 1 Talk
at the International Session–Conference on the Physics of Fundamental Interactions (JINR Section, Physics Department, Russian Academy of Sciences), Dubna, April 12–15, 2016.
Φ( x1,2, t1,2, Q 2 ) are the unintegrated parton distribution functions (UPDFs). In a specific case, when t1,2 ! Q 2 and parton virtualities in a hard process can be neglected, the calculus may rely on the so-called “transverse-momentum-dependent” scheme in which the large logarithmic corrections proportional to [α S log 2(Q 2 t1,2 )]n and [α S log(Q 2 t1,2 )]n are consistently estimated. This applies, in particular, to the production of massive leptonic pairs with small transverse momenta when Λ QCD ! pT ∼ t1,2 ! Q ! S. However, initial-parton virtualities cannot longer be neglected in the region of large transverse momenta, pT ∼ t1,2 ∼ x1,2 S. In this case, one must use the Reggeized-parton approach (RPA) which is based on the properties of BFKL factorization in the Regge limi
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