Spin Polarization Effect And High Dimensional Numerical Integration In High Energy Heavy Ion Collisions

We study the local spin polarization effects in high-energy heavy-ion collisions using relativistic hydrodynamics.With the state-of-art parallel computing technology,we also study the algorithm for solving high-dimensional integration numerically in high-energy physics such as in collision integrals of Boltzmann equations.STAR collaboration has measured the local spin polarization effects in high-energy heavy ion collisions,which do not agree with predictions of previous theoretical mod-els.The sign of the longitudinal spin polarization in the beam direction calculated in relativistic hydrodynamics model with the thermal vorticity is different from the STAR data.In the direction of the global orbital angular momentum of two colliding nuclei,the spin polarization calculated in relativistic hydrodynamic model with thermal vortic-ity shows an opposite azimuthal angle dependence to the STAR preliminary data.How to understand the STAR observation is an important topic in high-energy heavy-ion collisions.We construct the general spin chemical potential ??v from the temperature field and velocity field in the fluid system and give the expression of spin polarization vec-tor with the constructed ??v· We choose four kinds of vorticities with clear physical meaning,namely,the kinematic vorticity,the relativitic extension of the nonrelativistic vorticity,the temperature vorticity and the thermal vorticity.Then we use the(3+1)-dimensional hydrodynamics model CLVisc on GPU to simulate the collisions of Au+Au at 200 GeV and Pb+Pb at 2760 GeV.The calculation results show that only the temper-ature vorticity can describe the longitudinal polarization data of the STAR experiment.The other three kinds of vorticities give the opposite sign to the STAR data.For the polarization in the direction of the global orbital angular momentum,the calculated re-sults with all four kinds of vorticities give the same sign and magnitude as the STAR data.However,when considering the azimuthal angle dependence of the polarization in the direction of the global orbital angular momentum,only the result from tempera-ture vorticity shows the same trend as the STAR preliminary data,i.e.,the polarization is stronger in the reaction plane and weaker off the reaction plane.The temperature vorticity can explain the current observations of the local spin polarization in the STAR experiment,but why the temperature vorticity works needs further investigation.The second topic of this thesis is the numerical solution of high-dimensional inte-grals encountered in the transport theory for the spin polarization.Due to the dimen-sionality curse problem,the size of the integral parameter space increases exponentially with the increase of the integral dimensions,which leads to an exponentially growing time required to calculate the integral.How to tackle the problem is a challenge.We propose a numerical algorithm called ZMCintegral for high-dimensional integrals with GPU parallel computing power.Its core algorithm is based on the stratified sampling and heuristic tree search strategy.With the help of Python,TensorFlow,Numba,Ray and other tools,we have implemented three versions of ZMCintegral.For integrand functions with dramatic oscillation and singularity,we conduct performance tests on ZMCintegral in single-node and multi-node environments.The results of the tests show that after setting a reasonable search depth and threshold ratio,ZMCintegral can give high-precision numerical results within a reasonable time.The Numba-Ray version of ZMCintegral can be automatically run on large-scale GPU computing clusters.On the other hand,for integrand functions which contain additional parameters,it takes more computing resources to carry out the integration when considering parameter combinations.Making use of the characteristics of GPU parallel computing,we propose an algorithm called ZMCintegral-v5 for this problem.It uses one thread of GPU to calculate one set of parameters for the integraion and then quickly give the final result in reasonable time.The strategy of ZMCintegral and ZMCintegral-v5 can be further extended to the GPU parallelization of current computing programs in high-energy physics.With the help of TensorFlow,Numba,Ray and other tools,researchers can implement high per-formance computing programs with very little work.