HERA data and collinearly-improved BK dynamics

Abstract

Within the framework of the dipole factorisation, we use a recent collinearly-improved version of the Balitsky-Kovchegov equation to fit the HERA data for inclusive deep inelastic scattering at small Bjorken x. The equation includes an all-order resummation of double and single transverse logarithms and running coupling corrections. Compared to similar equations previously proposed in the literature, this work makes a direct use of Bjorken x as the rapidity scale for the evolution variable. We obtain excellent fits for reasonable values for the four fit parameters. We find that the fit quality improves when including resummation effects and a physically-motivated initial condition. In particular, the resummation of the DGLAP-like single transverse logarithms has a sizeable impact and allows one to extend the fit up to relatively large photon virtuality Q 2 .

QCD thermalization: Ab initio approaches and interdisciplinary connections

“…While as we have discussed there are good analytical approximations, a full analytical solution of the BK equation does not exist. Numerical simulations have, however, been known for some time for the LLx BK equation [169], the LLx+running coupling BK equation [170,171], and even more recently the full NLLx equation implementing collinear resummation [172,173]. In particular, it was shown in [173] that this NLLx framework provides very good agreement with the HERA data.…”

Diffractive deeply inelastic scattering in future electron-ion colliders

“…The studies performed in Refs. [69][70][71], which disregarded the dependence on the impact parameter, demonstrated that it is possible to obtain a good description of the inclusive HERA data by taking into account these corrections to the kernel. However, in order to describe in detail exclusive processes, it is fundamental to take into account also the impactparameter dependence of the dipole-target scattering amplitude.…”

Sub-femtometer scale color charge fluctuations in a proton made of three quarks and a gluon

“…The initial condition for Im S, which we derive here, depends not only on the impact parameter and the dipole vectors but also on their relative angle, and on the light-cone momentum fraction x in the target. In fact, the BK equation in its standard formulation evolves the wave function of the dipole projectile, and the evolution "time" is then related to the minus component of the momentum of the gluon in the proton target [47][48][49]. Ducloué et al have reformulated [48] BK evolution at NLO in terms of the target rapidity (or Bjorken-x).…”

“…In fact, the BK equation in its standard formulation evolves the wave function of the dipole projectile, and the evolution "time" is then related to the minus component of the momentum of the gluon in the proton target [47][48][49]. Ducloué et al have reformulated [48] BK evolution at NLO in terms of the target rapidity (or Bjorken-x). They obtained an evolution equation which is non-local in rapidity and which depends explicitly on the gluon's plus momentum fraction x = k + g /P + .…”