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I = 2 π π scattering from fully-dynamical mixed-action lattice QCD

2006; American Physical Society; Volume: 73; Issue: 5 Linguagem: Inglês

10.1103/physrevd.73.054503

1550-7998

Silas R. Beane, Paulo F. Bedaque, Kostas Orginos, Martin J. Savage,

High-Energy Particle Collisions Research

We compute the $I=2$ $\ensuremath{\pi}\ensuremath{\pi}$ scattering length at pion masses of ${m}_{\ensuremath{\pi}}\ensuremath{\sim}294$, 348, and 484 MeV in fully-dynamical lattice QCD using L\"uscher's finite-volume method. The calculation is performed with domain-wall valence-quark propagators on asqtad-improved MILC configurations with staggered sea quarks at a single lattice spacing, $b\ensuremath{\sim}0.125\text{ }\text{ }\mathrm{fm}$. Chiral perturbation theory is used to perform the extrapolation of the scattering length from lattice quark masses down to the physical value, and we find ${m}_{\ensuremath{\pi}}{a}_{2}=\ensuremath{-}0.0426\ifmmode\pm\else\textpm\fi{}0.0006\ifmmode\pm\else\textpm\fi{}0.0003\ifmmode\pm\else\textpm\fi{}0.0018$, in good agreement with experiment. The $I=2$ $\ensuremath{\pi}\ensuremath{\pi}$ scattering phase shift is calculated to be $\ensuremath{\delta}=\ensuremath{-}43\ifmmode\pm\else\textpm\fi{}10\ifmmode\pm\else\textpm\fi{}5\ifmmode^\circ\else\textdegree\fi{}$ at $|\mathbf{p}|\ensuremath{\sim}544\text{ }\text{ }\mathrm{MeV}$ for ${m}_{\ensuremath{\pi}}\ensuremath{\sim}484\text{ }\text{ }\mathrm{MeV}$.