Scattering of two and three physical pions at maximal isospin from lattice QCD

Matthias Fischer; Bartosz Kostrzewa; Liuming Liu; Fernando Romero-López; Martin Ueding; Carsten Urbach

doi:10.1140/epjc/s10052-021-09206-5

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2021) 81: 436
https://doi.org/10.1140/epjc/s10052-021-09206-5

Regular Article - Theoretical Physics

Extended Twisted Mass Collaboration

Matthias Fischer¹^,2, Bartosz Kostrzewa³, Liuming Liu⁴^,5, Fernando Romero-López⁶^d, Martin Ueding¹^,2 and Carsten Urbach¹^,2

¹ Helmholtz-Institut für Strahlen- und Kernphysik, University of Bonn, 53115, Bonn, Germany
² Bethe Center for Theoretical Physics, University of Bonn, 53115, Bonn, Germany
³ High Performance Computing and Analytics Lab, University of Bonn, 53115, Bonn, Germany
⁴ Institute of Modern Physics, Chinese Academy of Sciences, 730000, Lanzhou, China
⁵ University of Chinese Academy of Sciences, 100049, Beijing, China
⁶ Instituto de Física Corpuscular, Universitat de València and CSIC, 46980, Paterna, Spain

^d fernando.romero@uv.es

Received: 18 March 2021
Accepted: 2 May 2021
Published online: 20 May 2021

Abstract

We present the first direct $N_{f} = 2$ $$N_f=2$$ lattice QCD computation of two- and three- $π^{+}$ $\pi ^+$ scattering quantities that includes an ensemble at the physical point. We study the quark mass dependence of the two-pion phase shift, and the three-particle interaction parameters. We also compare to phenomenology and chiral perturbation theory (ChPT). In the two-particle sector, we observe good agreement to the phenomenological fits in s- and d-wave, and obtain $M_{π} a_{0} = - 0.0481 (86)$ $M_\pi a_0 = -0.0481(86)$ at the physical point from a direct computation. In the three-particle sector, we observe reasonable agreement at threshold to the leading order chiral expansion, i.e. a mildly attractive three-particle contact term. In contrast, we observe that the energy-dependent part of the three-particle quasilocal scattering quantity is not well described by leading order ChPT.

© The Author(s) 2021

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