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arXiv 2009.04479hep-phhep-latnucl-th
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$ρ$介子介子质量依赖性的双圈分析

Two-loop analysis of the pion-mass dependence of the $ρ$ meson

Malwin Niehus, Martin Hoferichter, Bastian Kubis, Jacobo Ruiz de Elvira

摘要:

分析π介子质量依赖的$ππ$散射相移超出低能区需要从手征微扰理论的振幅的么正化。在双味理论中,通过反振幅方法(IAM)的幺正化可以从色散关系中得到证明,因此有望为格点量子色动力学计算结果的π介子质量依赖性提供可靠的预言。在这项工作中,我们提供了紧凑的解析表达式的双回路分波振幅的$J=0,1,2$所需的IAM在次领先的顺序。为了分析最近的格点量子色动力学结果的$P$波的π介子质量的依赖性,我们开发了一个适合的策略,第一次允许我们执行稳定的双回路IAM适合和评估手征收敛的IAM方法。虽然后续订单的比较表明,击穿规模不低于$ρ$质量,详细了解系统的不确定性的格点量子色动力学数据是至关重要的,以获得可接受的拟合,特别是在较大的π介子质量。

英文摘要:

Analyzing the pion-mass dependence of $ππ$ scattering phase shifts beyond the low-energy region requires the unitarization of the amplitudes from chiral perturbation theory. In the two-flavor theory, unitarization via the inverse-amplitude method (IAM) can be justified from dispersion relations, which is therefore expected to provide reliable predictions for the pion-mass dependence of results from lattice QCD calculations. In this work, we provide compact analytic expression for the two-loop partial-wave amplitudes for $J=0,1,2$ required for the IAM at subleading order. To analyze the pion-mass dependence of recent lattice QCD results for the $P$-wave, we develop a fit strategy that for the first time allows us to perform stable two-loop IAM fits and assess the chiral convergence of the IAM approach. While the comparison of subsequent orders suggests a breakdown scale not much below the $ρ$ mass, a detailed understanding of the systematic uncertainties of lattice QCD data is critical to obtain acceptable fits, especially at larger pion masses.

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