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

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.

20 pages, 5 figures; version published in PRL: Appendix E.1 and Bayesian information criterion added; Mathematica notebook with two-loop expressions included as supplementary material

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Cited by in corpus (25)

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• Elastic nucleon-pion scattering at $m_{\pi }=200\mathrm{MeV}$ from lattice QCD
• The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations
• Nucleon resonance parameters from Roy-Steiner equations
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• Chiral extrapolation of hadronic vacuum polarization
• What can we learn about light-meson interactions at electron-positron colliders?
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• Dispersion relation for hadronic light-by-light scattering: $\eta$ and ${\eta }^{\prime }$ poles
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• Precision evaluation of the $\eta$- and ${\eta }^{\prime }$-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Global parametrizations of $\pi \pi$ scattering with dispersive constraints: Beyond the S0 wave
• From pole parameters to line shapes and branching ratios
• Scrutinizing $\pi \pi$ scattering in light of recent lattice phase shifts
• Physical-mass calculation of $\rho (770)$ and $K^{\ast }(892)$ resonance parameters via $\pi \pi$ and $K\pi$ scattering amplitudes from lattice QCD
• Analytical dispersive parameterization for elastic scattering of spinless particles
• On the pole trajectory of the subthreshold negative parity nucleon with varying pion masses
• Advanced parametrisations for hadronic form factors
• Subthreshold parameters of $\pi \pi$ scattering revisited
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$
• Dispersive Analysis of $D$- and $B$-Meson Form Factors with Chiral and Heavy-Quark Constraints