Global Polarization In Relativistic Heavy-ion Collisions

Quantum chromodynamics(QCD)is a fundamental theory for strong interactions.At low energy,quarks and gluons are always bound in hadrons due to color confine-ment.Through relativistic heavy-ion collisions,nuclear matter can undergo deconfine-ment phase transition to form a plasma of free quarks and gluons,meanwhile the chiral symmetry is restored.The properties of quark matter play a significant role for understanding the na-ture of strong interactions and the evolution of the early universe.Currently,there are two main high energy heavy-ion colliders that are running in the world:the Rela-tivistic Heavy Ion Collider(RHIC)at the Brookhaven National Laboratory(BNL)and the Large Hadron Collider(LHC)at the European Organization for Nuclear Rsearch(CERN).In off-central heavy-ion collisions,strong magnetic fields and huge angular mo-menta can be generated.Then the angular momentum can be transferred into the local fluid vorticity.These extreme magnetic and vorticity fields can induce various anoma-lous transport phenomena,such as Chiral Magnetic Effect(CME)and Chiral Vortical Effect(CVE).The CME refers to charged current induced by the the magnetic field due to unequal number of left-and right-handed fermions.Kharzeev,Mclerran and Warringa suggested that in the deconfined QCD matter,the metastable domains with non-zero topological charge will induce charge separation along the direction of the magnetic field.In condensed matter system such as Dirac or Weyl semi-metals,CME has been observed.There have been a lot of attempts to search for the signal of CME in heavy-ion collision experiments.However,it is challenging to extract the CME signal from the backgrounds.How to accurately calculate the magnetic field is one of the most difficult problems.Theoretically the magnetic field magnitude at the initial moment of relativistic heavy-ion collisions at the top RHIC energy can reach 1018 Gauss and it is even stronger at LHC energies.With the use of the Lienard-Wiechert potential or by solving the Maxwell equation,one can calculate the magnetic field in the early time of the heavy-ion collisions when the QGP has not been formed.However,the calculation of magnetic field becomes complicated after the formation of QGP.Since the QGP is a good con-ductor,the conductivity of QGP can affect the evolution of the magnetic field.At the same time,the existence of the chiral magnetic effect will also influence the evolution of the magnetic field.In this work,we use the Green's function method to calculate the time evolution and space distribution of the magnetic field in presence of electrical conductivity and chiral magnetic conductivity.With the MC Glauber model,we calcu-late the time evolution and space distribution of magnetic field in heavy-ion collisions.The main results are:(1)the existence of the electrical conductivity will slow down the decay of the magnetic field since the QGP is a good conductor;(2)the chiral magnetic conductivity gives rise to a non-zero radial magnetic field,resulting in an asymmetric spatial distribution of the magnetic field.Our work provides a theoretical basis for the study of the magnetic field related anomalous transport phenomena.The essence of chiral anomalous transport phenomena is that chiral fermions get polarized in an external magnetic or vorticity field which makes the right-and left-handed fermions move parallel or anti-parallel to the direction of the magnetic or vor-ticity field.The polarization of the quark will be eventually converted to that of hadrons in the final states.The properties of the magnetic field and vorticity field can be probed by the global hadron polarization in relativistic heavy-ion collisions,which are key gra-dients of chiral magnetic and vortical effects.Liang and Wang first proposed the global polarization in off-central heavy-ion collisions that the initial angular momentum can be transferred to the local fluid vorticity through the spin-orbit or spin-vorticity coupling effect.Experimentally,the global polarization effect can be measured by the weak decay of A to a proton and a pion.The proton in the decay prefers to fly along the spin direction of the ? hyperon.The polarization of the A hyperon can be measured by the angular distribution of the proton.The global polarization effects has been observed at low collisional energies.In this thesis,we show how to use the statistical physics to derive the spin vector of fermions in the non-relativistic and relativistic case.Then we use A Multi-Phase Transport(AMPT)model to calculate the velocity,vorticity field and the global polarization of A hyperons in heavy-ion collisions.The numerical results are in good agreement with the experimental data.Furthermore,we explain why the global A polarization depends on collisional energies,which is important for understanding the structure of the fluid vorticity in the hot and dense matter.