Determination of crossing-symmetric π π scattering amplitudes and the quark mass evolution of the σ constrained by lattice QCD

Rodas, Arkaitz; Dudek, Jozef J.; Edwards, Robert G.

doi:10.1103/PhysRevD.109.034513

Title: Determination of crossing-symmetric $π π$ scattering amplitudes and the quark mass evolution of the $σ$ constrained by lattice QCD

Journal Article · 19 February 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.109.034513 · OSTI ID:2309774

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Lattice QCD spectra can be used to constrain partial-wave scattering amplitudes that, while satisfying unitarity, do not have to respect crossing symmetry and analyticity. This becomes a particular problem when extrapolated far from real energies, e.g. in the case of broad resonances like the $σ$ , leading to large systematic uncertainties in the pole position. In this manuscript, we will show how dispersion relations can implement the additional constraints, using as input lattice-determined $π π$ partial-wave scattering amplitudes with isospin–0,1,2. We will show that only certain combinations of amplitude parametrizations satisfy all constraints, and that when we restrict to these, the $σ$ pole position is determined with minimal systematic uncertainty. The evolution of the now well-constrained $σ$ pole with varying light quark mass is presented, showing how it transitions from a bound-state to a broad resonance. Published by the American Physical Society 2024

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Research Organization:: Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC02-05CH11231; AC05-00OR22725; AC05-06OR23177; SC0018416

OSTI ID:: 2309774

Report Number(s):: DOE/OR/23177-5982; JLAB-THY-23-3791; 034513

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 3 Vol. 109; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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