Pi-K Scattering in Full QCD with Domain-Wall Valence Quarks

TL;DR

This study computes pi-K scattering lengths using fully-dynamical lattice QCD with domain-wall valence quarks, analyzing data at multiple pion masses and extrapolating to physical values with chiral perturbation theory.

Contribution

It provides the first fully-dynamical lattice QCD calculation of pi-K scattering lengths with domain-wall valence quarks and chiral extrapolation to physical pion masses.

Findings

Calculated scattering lengths for I=3/2 and I=1/2 channels.

Results agree with experimental and theoretical expectations.

Quantified statistical and systematic uncertainties.

Abstract

We calculate the pi+ K+ scattering length in fully-dynamical lattice QCD with domain-wall valence quarks on MILC lattices with rooted staggered sea-quarks at a lattice spacing of b=0.125 fm, lattice spatial size of L =2.5 fm and at pion masses of m_pi=290, 350, 490 and 600 MeV. The lattice data, analyzed at next-to-leading order in chiral perturbation theory, allows an extraction of the full pi K scattering amplitude at threshold. Extrapolating to the physical point gives m_pi a_3/2 = -0.0574 (+- 0.0016)(+0.0024 -0.0058) and m_pi a_1/2 = 0.1725 (+- 0.0017)(+0.0023 -0.0156) for the I=3/2 and I=1/2 scattering lengths, respectively, where the first error is statistical and the second error is an estimate of the systematic due to truncation of the chiral expansion.