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Two-loop analysis of the pion-mass dependence of the $\rho$ meson

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arxiv 2009.04479 v2 pith:UZFZQAIZ submitted 2020-09-09 hep-ph hep-latnucl-th

Malwin Niehus , Martin Hoferichter , Bastian Kubis , Jacobo Ruiz de Elvira This is my paper · ORCID
classification hep-phhep-latnucl-th
keywords dependencepion-masslatticetwo-loopamplitudeschiralfitsresults
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Analyzing the pion-mass dependence of $\pi\pi$ 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 $\rho$ 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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Cited by 5 Pith papers

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