A Study On QCD Matter:From Field Theory To Machine Learning

As one of the four fundamental forces in our universe,strong interaction describes the interactions between hadrons and its constituents quarks and gluons therein.The basic theory of strong interaction is quantum chromodynamics(QCD),which is a SU(3)Non-Abelian gauge field theory and exhibits the feature of asymptotic freedom.Thus in high energy domain one can tackle the scattering problems perturbatively by expansion in terms of Feynman diagrams.While in the low energy domain,the strong coupling constant increases such that perturbation theory breaks down,QCD features the non-trivial vacuum structure and hence dynamical chiral symmetry breaking(DCSB)and color confinement phenomena emerge.In order to tackle these issues,a variety of non-perturbative methods including lattice QCD,Dyson-Schwinger Equations(DSEs),Nambu-Jona-Lasinio model(NJL)and other effective field theories are developed.In the aspect of experiments,hot and dense strongly-interacting matter is created in relativistic heavy ion collisions.A new state of matter-strongly coupled quark gluon plasma(sQGP)is believed to form in a short time,which can be well described by relativistic hydrodynamics.In this QCD medium,quarks and gluons are deconfined from hadrons and have longer free path,meanwhile chiral symmetry is partially re-stored.As the medium expands,the density and temperature decrease such that the fluid re-hadronizes and finally final-state particles will be collected by plenty of parti-cle detectors.Obviously this process involves pretty complicated dynamics such that it's rather knotty to understand the thorough evolution of QCD matter from spectra of final-state particles.Physicists have proposed variety of experimental probes,including the elliptic flow,production of dileptons,suppression of heavy quarkonium,enhanced production of strange hadrons,jet quenching phenomena.Several cold and hot QCD issues will be emphatically addressed from different perspectives in this thesis.First of all,we focus on jet quenching phenomenon,which is thought to be the hard probe to the transport property of QGP.How to extract the transport parameter of the medium is an issue of great interest in the community.The first part of this thesis revisit the calculation of multiple parton scattering of a heavy quark in nuclei within the framework of recently improved high-twist factorization formalism,in which gauge invariance is ensured by a delicate setup of the initial partons' transverse momenta.We derive a new result for medium modified heavy quark fragmentation functions in deeply inelastic scattering.It is consistent with the previous calculation of light quark energy loss in the massless limit,but leads to a new correction term in the heavy quark case,which vanishes in the soft gluon radiation limit.We show numerically the significance of the new correction term in the calculation of heavy quark energy loss as compared to previous studies and with soft gluon radiation approximation.Moreover,how to locate the critical-end point in the QCD phase diagram and in-vestigate the critical behavior when the medium evolves near this critical point attract both theorists and experimentalists.In the second part of this thesis,chiral symmetry breaking and its restoration are revisited in the mean field approximation of 2-flavor and(2+1)flavor Nambu-Jona-Lasinio model,respectively.A first-order phase tran-sition exists at low temperature,but is smeared out at high temperature.We strictly derive several sets of coupled equations for the chiral susceptibility,the quark number susceptibility,etc.at finite temperature and quark chemical potential.Then we discuss the rationality of using susceptibilities as the criteria to determine the crossover region as well as the critical point.Based on our results,it is found that to define a critical band instead of an exclusive line in this region might be a more suitable choice.The critical exponents of these susceptibilities in the vicinity of the QCD critical end point(CEP)are presented.It is found that these various susceptibilities share almost the same critical behavior near the CEP.The comparisons between the critical exponents for the order parameters and the theoretical predictions are also included.The last part of this thesis attempts to adopt deep learning technique to identify the QCD transition from the simulated final-state particle spectrum.By employing state-of-the-art deep convolutional neural network(CNN)techniques and supervised learning,we use final-state pion spectra to identify the order of the QCD transition in the hybrid model simulations of heavy-ion collisions.The hybrid model(iEBE-VISHNU)cou-ples a(2+1)-D relativistic viscous hydrodynamic simulation,with different equations of state(EoS)of the medium,to a hadronic cascade "afterburner"(UrQMD model).Different scenarios are compared.When using only event-by-event(fluctuating)spec-tra ?(pT,?),the prediction accuracy of the CNN is poor,while cascade-averaged spec-tra ?c(pT,?)and centrality-bin-averaged spectra ?b(pPT,?)lead to sufficiently smooth spectra to reveal hidden correlations from the EoS which can be effectively classified by the neural network.A well-trained neural network can thus serve as an effective"EoS-meter" to distinguish the nature of the QCD transition.A systematic study of the robustness of the result with respect to variations of various simulation inputs,such as the collision energy,fluctuating initial conditions,equilibration times,the shear vis-cosity to entropy ratio as well as the hadronization and freeze-out switching criteria,is performed.The EoS-meter relates directly the final-state observables from the hybrid model simulations of heavy-ion collisions with the bulk properties of the QCD matter created in the intermediate state.