The Distributions And Correlations Of Constituent Quarks In Jets From Quark Recombiantion

In high-energy heavy-ion collisions,the study for production of final state particle is a considerably important subject.People propose many mechanisms in different ways to describe the processes of the final state Particle production,such as string fragmentation model and parton fragmentation model.But both have certain limitations. The string fragmentation model can only describe the processes of particle production at low p_T and the fragmentation model can only describe the processes of particle production at high p_T.Further more,they are troubled in describing data for final state particle at intermediate p_T.They fail to explain some phenomena at RHIC energy.In recent years,the quark recombination model has also been formulated to describe the processes of particle production.It works well by far.There are mainly three kinds of quark recombination models,all of which have two features in common:(â…°) they can be applied at any p_T;(â…±) they can solve all the problems successfully mentioned above.The model that we adopted is derived from jet fragmentation functions' field theoretical formulation and the constituent quark model of hadron structure.Within the constituent quark model,the authors defined constituent quark distributions in a jet as overlapping matrices of the parton field operators and the constituent quark states, similar to the ones for the parton fragmentation functions in vacuum.Extending the formalism to the field theory at finite temperature,they also derived the effective single-hadron fragmentation functions from the recombination of constituent quarks. The single-hadron fragmentation function can be casted as a convolution of the diquark (triquark) distribution functions and the recombination probabilities which are determined by the hadrons' wavefunctions.In this way,the hard parton fragmentation is regarded as a two-stage process:firstly,the initial hard parton evolves into a shower of constituent quarks;secondly,those constituent quarks will combine with each other to form the final state hadrons.One can derive the Dokshitzer-Gribov -Lipatov-Altarelli-Parisi(DGLAP) evolution equations for constituent quark distribution functions.In this case,once they are determined at a given energy scale,their values at any other energy scale can be calculated from the DGLAP evolution equations.In this model,one can also extend the formula to the case of jet fragmentation in a thermal medium,then take into account parton energy loss and detailed balance effect for jet fragmentation inside a thermal medium.Thus,the modified fragmentation function in a thermal medium can be obtained.In this case, many abnormally physical phenomena could be explained successfully and some new physical phenomena at higher energy could be predicted.In principle,once the constituent quarks distribution functions in a jet in vacuum are given,their distribution functions in a thermal medium could be obtained.But, the distribution functions of constituent quark are not calculable in pQCD.If the partons suffer no energy loss,the distribution functions in a jet,which should be independent of the process for the hard parton production,only depend on the energy of the collision system.Then with these distributions at hand,one can get lots of information of the final particles in different collision systems,such as distributions of the final particles.In this paper,we attempt to obtain the distributions of constituent quarks in jets.As is known to all,PYTHIA is an event generator for a large number of physics processes.In this paper,we simulate the fragmentation process of hard partons in the vacuum,then get the constituent quarks distribution functions.Since the generator could describe the physical process well.including the spectrums and correlations of the final particles,we are convinced that the generator takes the QCD effect into account properly for the physical processes,especially for the pQCD effect.We expect that the constituent quark distributions obtained from PYTHIA are close to the real ones.