BFKL pomeron in the next-to-leading approximation

Abstract

We find one-loop correction to the integral kernel of the BFKL equation for the total cross section of the high energy scattering in QCD and calculate the next-to-leading contribution to anomalous dimensions of twist-2 operators near j = 1.The BFKL equation is very important for the theory of the Regge processes at high energies √ s in the perturbative QCD [1]. In particular, it can be used together with the DGLAP evolution equation [2] for the description of structure functions for the deep inelastic ep scattering at small values of the Bjorken variable x = −q 2 /(2pq), where p and q are the momenta of the proton and the virtul photon correspondingly. But up to recent years the integral kernel for the BFKL equation was known only in the leading logarithmic approximation (LLA), which did not allow one to find its region of applicapability, including the scale in transverse momenta fixing the argument of the QCD coupling constant α(ck 2 ⊥ ) and the longitudinal scale √ s 0 for the minimal initial energy. In this paper we calculate the QCD radiative corrections to this kernel.In LLA the gluon is reggeized and the Pomeron is a compound state of two reggeized gluons. One can neglect multi-gluon components of the Pomeron wave function also in the next-to-leading logarithmic approximation (NLLA) and express the total cross-section σ(s) for the high energy scattering of colourless particles A, B in terms of their impact factors Φ i ( − → q i ) and the t-channel partial wave G ω ( − → q , − → q ′ ) for the reggeized gluon scattering at t = 0:Here − → q and − → q ′ are transverse momenta of gluons with the virtualities − − → q 2 ≡ −q 2 and − − → q ′ 2 ≡ −q ′2 correspondingly, s = 2p A p B is the squared invariant mass of the colliding particles with momenta p A and p B . Note, that the dependence of the Regge factor from 1

Elliptic flow from minijet production in heavy ion collisions

“…This behavior seems to contradict recent results reported by PHENIX [23,53] where the two-particle correlation function C(∆φ = φ 1 − φ 2 ) has maxima at both ∆φ = π (back-to-back) and ∆φ = 0. Relaxing the y 1 ≫ y 2 (or y 1 ≪ y 2 ) condition would greatly complicate the particle production calculations [43] though would give predictions for elliptic flow in a much more realistic kinematics. The appropriate calculations were performed for production of a pair of particles with y 1 ∼ y 2 by Leonidov and Ostrovsky in [44].…”

Dimensional regularisation and factorisation schemes in the BFKL equation at subleading level

“…However, due to the different form ofᾱ s (t), the Jacobians induced by Eq. (3.8) are different: 11) and this explains the different ε-dependence of the exponents at fixed value ofᾱ s (t):…”

“…The structure and the explicit expression of such a kernel with dimensional regularisation were given in several papers for the gluon [7] and the quark [8,9] parts, and summarised in Refs. [10][11][12]. It has the form…”

Forward jet production at the Large Hadron Collider

“…On one hand, once convoluted with the small-x gluon Green's function according to the method [25,30], these matrix elements control the summation of high-energy logarithmic corrections, contributing both to the next-to-leading-order BFKL kernel [31] and to the jet impact factors [32,33]. On the other hand, they can be used in a shower Monte Carlo implementing parton-branching kernels at unintegrated level (see e.g.…”