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
Abstract
Abstract We present the first direct $$N_f=2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>f</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> lattice QCD computation of two- and three- $$\pi ^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:math> 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 $$M_\pi a_0 = -0.0481(86)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>π</mml:mi> </mml:msub> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mn>0.0481</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>86</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> 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.