Abstract
In this paper we present solutions of evolution equations for inclusive distribution of gluons as produced by jet traversing quark–gluon plasma. We reformulate the original equations in such a form that virtual and unresolved-real emissions as well as unresolved collisions with medium are resummed in a Sudakov-type form factor. The resulting integral equations are then solved most efficiently with use of newly developed Markov Chain Monte Carlo algorithms implemented in a dedicated program called MINCAS. Their results for a gluon energy density are compared with an analytical solution and a differential numerical method. Some results for gluon transverse-momentum distributions are also presented. They exhibit interesting patterns not discussed so far in the literature, in particular a departure from the Gaussian behaviour – which does not happen in approximate analytical solutions.
Highlights
Quantum chromodynamics (QCD) is the well established theory of strong interactions
There are QCD phenomena that still require better understanding. One of such phenomena is jet quenching predicted in [1,2] and already observed in the context of the RHIC physics [3], i.e. stopping of a hadronic jet produced in an early stage of heavy ion collisions and propagating through quark-gluon plasma (QGP) which is formed in a later stage of the collisions
The formal solutions given in Eqs. (19) and (21) can be used to develop Markov Chain Monte Carlo algorithms for numerical evaluation of the distribution functions D(x, τ ) and D(x, k, τ ), given some initial functions D(x0, τ0) and D(x0, k0, τ0), respectively
Summary
Quantum chromodynamics (QCD) is the well established theory of strong interactions. there are QCD phenomena that still require better understanding. In this paper we look closer at the results obtained in [30,31] and focus on an analysis of the generation of transverse momenta via cascades of subsequently emitted jets from an energetic jet traversing QGP. In this approach the plasma is modelled by static centres and the jet interacts with it weakly. 5, we describe a numerical algorithm for solving the integro-differential equation for the jet energy distribution which is based on application of the Runge–Kutta method and discuss its limitations in obtaining high accuracy solutions. In Appendix A we provide some further details on the MCMC algorithms, in particular we describe a combination of the branching Monte Carlo method with the importance sampling
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