AI 中文总结
研究有限温度 QCD 中介子磁化率紫外发散结构，分析其加性和乘性重整化，推导对称比，表明其重整化群不变且与方案无关，推导 $Z$ 因子链并对比威尔逊费米子发散结构。
AI 中文摘要
我们分析了具有精确手征对称性的有限温度 QCD 中晶格表述下介子磁化率的紫外发散结构。裸磁化率分为加性发散和乘性重整化 $Z_\Gamma^{2}$。加性发散与温度无关，通过温度减法去除，包括来自恒等算符的主导幂次发散 $\alpha_\Gamma/(2a^2)$ 以及与质量相关的对数项 $\propto m^2\ln(1/(am))$。精确手征对称性禁止磁化率所有与质量相关的幂次发散。乘性因子 $Z_\Gamma^{2}$ 对晶格间距有对数依赖，由算符反常维度控制。我们表明，由对称伙伴的温度减法磁化率构建的对称比 $\kappa_{AB} = (\chi_A^{\rm reg} - \chi_B^{\rm reg})/ (\chi_A^{\rm reg} + \chi_B^{\rm reg})$ 是精确的重整化群不变且与方案无关的。加性发散通过减法去除，乘性因子通过 $Z_A = Z_B$ 等式抵消。该等式在质量无关方案中对任意味数和任意夸克质量都成立，不受自发对称破缺或 $U(1)_A$ 反常影响。我们推导了所有介子通道的完整 $Z$ 因子链，并将发散结构与威尔逊费米子的进行对比，威尔逊费米子中显式手征对称性破缺会导致手征奇数幂次发散混合并破坏构建所依赖的 $Z_A = Z_B$ 等式。
英文摘要
We analyze the ultraviolet divergence structure of meson susceptibilities in finite-temperature QCD, for lattice formulations with exact chiral symmetry. The bare susceptibility separates into additive divergences and a multiplicative renormalization $Z_Γ^{2}$. The additive divergences are temperature-independent, and are removed by the temperature subtraction. They consist of the leading power divergence $α_Γ/(2a^2)$ from the identity operator, together with a mass-dependent logarithmic term $\propto m^2\ln(1/(am))$. Exact chiral symmetry forbids all mass-dependent \emph{power} divergences of the susceptibility. The multiplicative factor $Z_Γ^{2}$ has a logarithmic dependence on the lattice spacing, controlled by the operator anomalous dimension. We show that the symmetry ratio $κ_{AB} = (χ_A^{\rm reg} - χ_B^{\rm reg})/ (χ_A^{\rm reg} + χ_B^{\rm reg})$, built from temperature-subtracted susceptibilities of symmetry partners, is exactly renormalization-group invariant and scheme-independent. The additive divergence is removed by the subtraction, and the multiplicative factor cancels through the equality $Z_A = Z_B$. This equality holds for any number of flavors and any quark masses in a mass-independent scheme, unaffected by spontaneous symmetry breaking or the $U(1)_A$ anomaly. We derive the complete $Z$-factor chains for all meson channels and contrast the divergence structure with that of Wilson fermions, for which the explicit chiral-symmetry breaking induces a chiral-odd power-divergent mixing and spoils the equality $Z_A = Z_B$ on which the construction relies.
CommentsLaTeX, 22 pages, v2:revised and expanded
