Lattice QCD Simulations in External Background Fields
Massimo D'Elia
备注：
31 pages, 10 figures, minor changes and references added. To appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Yee
We discuss recent results and future prospects regarding the investigation, by lattice simulations, of the non-perturbative properties of QCD and of its phase diagram in presence of magnetic or chromomagnetic background fields. After a brief introduction to the formulation of lattice QCD in presence of external fields, we focus on studies regarding the effects of external fields on chiral symmetry breaking, on its restoration at finite temperature and on deconfinement. We conclude with a few comments regarding the effects of electromagnetic background fields on gluodynamics.
N$_f$ = 1 QCD in External Magnetic Fields: Staggered Fermions
本文研究了格点上外加磁场的N $_f$ = 1量子色动力学。背景场是通过所谓的薛定谔泛函引入的。我们采用标准交错费米子与恒定裸质量$am = 0.025$和磁场恒定磁通量高达$a^2 e H \simeq 2.3562$。我们发现解禁闭温度和手征对称性恢复温度与外加磁场的强度无关。我们的方法使我们能够容易地研究外部磁场对QCD热力学的影响。我们确定了外加磁场对强相互作用物质的自由能、压强和状态方程的影响。
This is an introductory review of lattice QCD with external fields. The study of external magnetic fields is one of the greatest achievements in modern lattice QCD. Large-scale simulations and detailed analyses have revealed intriguing properties of QCD in the magnetic fields. The study of external electric fields is more challenging because of a technical difficulty. We overview the successes and challenges of the lattice simulations with the electromagnetic fields. We also introduce a newly developing field, the lattice simulation of rotating QCD matters.
We study QCD at finite temperature in the presence of imaginary electric fields. In particular, we determine the electric susceptibility, the leading coefficient in the expansion of the QCD pressure in the imaginary field. Unlike for magnetic fields, at nonzero temperature this coefficient requires a non-trivial separation of genuine electric field-related effects and spurious effects related to the chemical potential, which becomes an unphysical gauge parameter in this setting. Our results are based on lattice simulations with stout improved dynamical staggered quarks at physical quark masses…
In this proceeding we present our first results of the study of the QCD Equation of State at non-zero baryon density and in external magnetic field. We focused on the first three non-vanishing expansion coefficients of pressure in chemical potential and their dependence on magnetic field. The study is carried out within lattice simulations with $N_f=2+1$ dynamical quarks with physical quark masses. To overcome the sign problem, the simulations are carried out at imaginary baryon chemical potential. Our results suggest that external magnetic field considerably enhances the expansion coefficient…
Thermal Field Theory in the Presence of a Background Magnetic Field and its Application to QCD
Saha Institute of Nuclear Physics, HBNI（萨哈核物理研究所，HBNI）；Department of Physics, Indian Institute of Technology Bombay（孟买印度理工学院物理系）；West University of Timişoara（蒂米什瓦拉西部大学）；Institute of Theoretical Physics, University of Wrocław（弗罗茨瓦夫大学理论物理研究所）；Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität（约翰·沃尔夫冈·歌德大学理论物理研究所）；Center for Astrophysics and Cosmology, University of Nova Gorica（新戈里察大学天体物理学与宇宙学中心）；Department of Physics, Aliah University（阿利亚大学物理系）
Freezing of QCD coupling affects the short distance static potential
Bali G.S.观察到的晶格短程静电势（nf=0）与标准微扰势之间的一个显著矛盾，在背景微扰理论的框架下研究了该问题。使用的背景耦合，其中包含唯一的背景参数-质量mB，固定的精细结构拟合在bottomonium，晶格数据很好地解释没有引进外来的短程线性势与大的“弦张力”约。1 GeV的平方。在0.05 fm < r<0.15 fm的范围内，背景耦合与标准扰动耦合有显著差异，而在更大的距离，r > 0.3 fm，背景耦合快速接近冻结值。讨论了有关短距离和长距离强耦合特性的一些问题，并提出了解决办法。
We discuss the phase diagram of QCD in the presence of a strong background magnetic field, providing numerical evidence, based on lattice simulations of QCD with $2+1$ flavours and physical quark masses, that the QCD crossover turns into a first order phase transition for large enough magnetic field, with a critical endpoint located between $eB=4$ GeV$^2$ (where we found an analytic crossover at a pseudo-critical temperature $T_c=(98\pm3)$ MeV) and $eB=9$ GeV$^2$ (where the measured critical temperature is $T_c=(63\pm5)$ MeV).
We provide numerical evidence that the thermal QCD crossover turns into a first order transition in the presence of large enough magnetic background fields. The critical endpoint is found to be located between $eB = 4$ GeV$^2$ (where the pseudocritical temperature is $T_c = (98 \pm 3)$ MeV) and $eB = 9$ GeV$^2$ (where the critical temperature is $T_c = (63 \pm 5)$ MeV). Results are based on the analysis of quark condensates and number susceptibilities, determined by lattice simulations of $N_f = 2+1$ QCD at the physical point, discretized with three different lattice spacings, $a = 0.114, 0.08…
