We use recently derived Ward identities and lattice data for the light- and strange-quark condensates to reconstruct the scalar and pseudoscalar susceptibilities (\(\chi _S^\kappa \), \(\chi _P^K\)) in the isospin 1/2 channel. We show that \(\chi _S^\kappa \) develops a maximum above the QCD chiral transition, after which it degenerates with \(\chi _P^K\). We also obtain \(\chi _S^\kappa \) within Unitarized Chiral Perturbation Theory (UChPT) at finite temperature, when it is saturated with the \(K_0^*(700)\) (or \(\kappa \)) meson, the dominant lowest-energy state in the isospin 1/2 scalar channel of \(\pi K\) scattering. Such UChPT result reproduces the expected peak structure, revealing the importance of thermal interactions, and makes it possible to examine the \(\chi _S^\kappa \) dependence on the light- and strange-quark masses. A consistent picture emerges controlled by the \(m_l/m_s\) ratio that allows one studying \(K-\kappa \) degeneration in the chiral, two-flavor and SU(3) limits. These results provide an alternative sign for \(O(4)\times U(1)_A\) restoration that can be explored in lattice simulations and highlight the role of strangeness, which regulated by the strange-quark condensate helps to reconcile the current tension among lattice results regarding \(U(1)_A\) restoration.

我们使用最近导出的轻夸克凝聚体和奇夸克凝聚体的沃德恒等式和晶格数据来重建同位旋中的标量和赝标量磁化率（ \(\chi _S^\kappa \) 、 \(\chi _P^K\) ） 1/2 通道。我们证明\(\chi _S^\kappa \)在 QCD 手性跃迁之上发展出最大值，之后它随着\(\chi _P^K\)退化。我们还在有限温度下，当它饱和于\(K_0^*(700)\) （或 \(\kappa \) ）时，在酉手性微扰理论（UChPT）中获得\(\chi _S^\kappa \ )介子， \(\pi K\)散射同位旋 1/2 标量通道中主要的最低能量态。这样的 UChPT 结果再现了预期的峰结构，揭示了热相互作用的重要性，并使得检查\(\chi _S^\kappa \)对轻夸克质量和奇夸克质量的依赖性成为可能。由\(m_l/m_s\)比率控制的一致图像出现，允许研究手性、二味和SU (3) 极限中的\(K-\kappa \)简并。这些结果为\(O(4)\times U(1)_A\)恢复提供了一个替代符号，可以在晶格模拟中进行探索，并强调奇异性的作用，奇异夸克凝聚态的调节有助于协调当前的关于\(U(1)_A\)恢复的晶格结果之间的张力。