Universal features of JIMWLK and BK evolution at small x

By K. Rummukainen, H. Weigert. 2003

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Abstract In this paper we present the results of numerical studies of the JIMWLK and BK equations with a particular emphasis on the universal scaling properties and phase space structure involved. The results are valid for near zero impact parameter in DIS. We demonstrate IR safety due to the occurrence of a rapidity-dependent saturation scale Q s ( τ ). Within the set of initial conditions chosen, both JIMWLK and BK equations show remarkable agreement. We point out the crucial importance of running coupling corrections to obtain consistency in the UV for both equations. Explicit studies of this have been performed with BK. Despite the scale breaking induced by the running coupling we find that evolution drives correlators towards an asymptotic form with near scaling properties. We discuss asymptotic features of the evolution, such as the τ - and A -dependence of Q s away from the initial condition.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d1098bf47eb73a70ec0504559a8f9af0e57bb05e

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Citations in the corpus

Nonlinear QCD meets data: A global analysis of lepton-proton scattering with running coupling Balitsky-Kovchegov evolution (2009, methodology): “This is in part due to the relative simplicity of the BK equation with respect to JIMWLK, whose solution demands the use of rather complicated numerical methods [35].”
Parton distributions and lattice-QCD calculations: Toward 3D structure (2020, methodology): “The former can be solved using standard methods for integro-differential equations, while the latter, being a functional equation, can be solved by means of lattice-QCD methods, after reformulation as an Langevin equation (Rummukainen and Weigert, 2004).”
When does the gluon reggeize? (2013, methodology): “In this regime the Balitsky-JIMWLK evolution can be solved numerically through Monte-Carlo simulations [16–18].”
Triumvirate of running couplings in small-x evolution (2006, background): “In the past there have been several good guesses of the scale of the running coupling in the JIMWLK and BK kernels in the literature [33, 35].”
Small-x physics beyond the Kovchegov equation☆ (2004, background): “-r, ∗This work is supported in part by the US Department of Energy. aarb@phys.columbia.edu (A.H.Mueller) bshoshi@phys.columbia.edu”