外磁场中的粲偶素  

Charmonia in an external magnetic field

作　　者：龚闯 郭星雨 Gong Chuang;Guo Xing-Yu(Provincial Key Laboratory of Nuclear Material Science and Technology of Guangdong,Institute of Quantum Matter,South China Normal University,GuangZhou 510006,China;Guangdong-Hong Kong Quantum Matter Joint Laboratory,Southern Nuclear Science Computing Center,South China Normal University,GuangZhou 510006,China)

机构地区：[1]华南师范大学量子物质研究院,广东省核物质科学与技术重点实验室,广州510006 [2]华南师范大学南方核科学计算中心,粤港量子物质联合实验室,广州510006

出　　处：《物理学报》2021年第17期10-16,共7页Acta Physica Sinica

基　　金：广东省基础与应用基础重大项目(批准号:2020B0301030008);国家自然科学基金(批准号:11905066)资助的课题.

摘　　要：在相对论重离子碰撞早期,会产生一个极强的磁场.初始碰撞产生的粲偶素会受到磁场的影响,进而携带磁场的信息.本文利用磁场下的两体薛定谔方程研究磁场对粲偶素的影响.利用角动量展开的方法,数值计算了不同磁场强度下粲夸克偶素的能谱.采取的方案是把三维波函数展开成不同轨道角动量以及自旋态的叠加,实际计算过程中发现,当n≤2,l≤7时能很好地满足精确度.进一步,哈密顿量可以写成H=H_(0)+(qB)^(2)H_(1)+qBP_(PS,⊥)H_(2)形式,其中H_(0),H_(1),H_(2)不依赖于B和P_(PS,⊥),因此只要计算出H_(0),H_(1),H_(2),就能求出任意B和P_(PS,⊥)下的哈密顿量.这样的数值方法在保证计算精度的同时显著减少了计算量.计算结果表明随着磁场和总动量的增加,粲偶素的质量增大,在磁场强度为20m_(x)^(2),总动量为1.8GeV时,质量的增加量为20%.Heavy ion collisions are an important method to study the quantum chromodynamics.In the early stage of relativistic heavy ion collisions,an extremely strong magnetic field is generated.The magnetic field will induce novel phenomena such as the chiral magnetic effect.However,the magnetic field will decrease rapidly,so it is difficult to measure its effect on the system.Charmonium states which are created by the initial scattering will be affected by the magnetic field and carry the information about it.We use the two-body Schrodinger equation with magnetic field to study the influence of the magnetic field on the charmonium state.The magnetic field is introduced via minimal coupling and its effect breaks the conservation of momentum and the conservation of angular momentum as well.The energy of the charmonium state depends not only on the magnetic field,but also on the momentum of the charmonium,thereby leading the final charmonium yield to be anisotropic.For a constant and homogeneous magnetic field,using the method of angular momentum expansion,we numerically calculate the energy spectra of the charm quark bound states with different magnetic field strengths and total momentum.The method is used to expand the three-dimensional wave function on the basis of different orbital angular momentum and spin states whose wave functions are numerically calculated first.In the actual calculation process,it is found that a good accuracy is achieved when taking n≤2,l≤7.Furthermore,the dependence of the Hamiltonian on the magnetic field and total momentum is analytically determined to be H=H_(0)+(qB)^(2)H_(1)+qBP_(PS,⊥)H_(2).Therefore,only the coefficient matrices H_(1)and H_(2)need to be numerically calculated once and the Hamiltonian with arbitrary magnetic field and momentum can be determined.The inverse power method is then used to find the lowest eigenvalue in the angular momentum space.Such a numerical method significantly reduces the amount of calculation and still ensures the accuracy of the calculation as well.

关 键 词：束缚态 自旋 重粒子碰撞 粲夸克 

分 类 号：O572.33[理学—粒子物理与原子核物理]