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arXiv 2002.11696hep-ph
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非零手征不平衡的手征微扰理论

Chiral perturbation theory for nonzero chiral imbalance

Domènec Espriu, Angel Gómez Nicola, Andrea Vioque-Rodríguez

摘要:

我们构建了最一般的低能量有效拉格朗日量,包括局部宇称违反项参数化的轴向化学势或手性不平衡$μ_5$,高达${\cal O}(p^4)$顺序的手征展开两个轻的味道。为此,我们在手征微扰理论框架内工作,其中仅包括伪NGB场,遵循外部源方法。$\cal{O}(p^2)$拉格朗日量仅由常数项修改,而$\cal{O}(p^4)$拉格朗日量包括与$μ_5^2$成比例的新项和新的低能常数(LEC),它们被重整化并与特定的可观测量相关。特别是,我们分析了修正的π色散关系和观察到的真空能量密度,即轻夸克凝聚,手征和拓扑的兼容性和手征电荷密度,提供数值确定的新LEC时,可能的。特别地,我们探索了手性恢复温度$T_c$与$μ_5$的依赖性。增加的$T_c(μ_5)$与我们对基于ChPT的表达的点阵数据的拟合一致。虽然晶格的不确定性仍然很大,并转化为新的LEC确定,这些观测值的一致的物理描述出现从我们目前的工作,提供了一个理论上强大的模型独立的框架,进一步研究的物理系统,宇称破缺效应可能是相关的,如重离子碰撞。

英文摘要:

We construct the most general low-energy effective lagrangian including local parity violating terms parametrized by an axial chemical potential or chiral imbalance $μ_5$, up to ${\cal O}(p^4)$ order in the chiral expansion for two light flavours. For that purpose, we work within the Chiral Perturbation Theory framework where only pseudo-NGB fields are included, following the external source method. The $\cal{O}(p^2)$ lagrangian is only modified by constant terms, while the $\cal{O}(p^4)$ one includes new terms proportional to $μ_5^2$ and new low-energy constants (LEC), which are renormalized and related to particular observables. In particular, we analyze the corrections to the pion dispersion relation and observables related to the vacuum energy density, namely the light quark condensate, the chiral and topological susceptibilities and the chiral charge density, providing numerical determinations of the new LEC when possible. In particular, we explore the dependence of the chiral restoration temperature $T_c$ with $μ_5$. An increasing $T_c(μ_5)$ is consistent with our fits to lattice data of the ChPT-based expressions. Although lattice uncertainties are still large and translate into the new LEC determination, a consistent physical description of those observables emerges from our present work, providing a theoretically robust model-independent framework for further study of physical systems where parity-breaking effects may be relevant, such as heavy-ion collisions.

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