Lattice QCD calculation of \(\pi \pi \) scattering length

DOI10.1088/0253-6102/57/1/13zbMATH Open1247.81573arXiv1110.3918OpenAlexW3123058998MaRDI QIDQ2913528

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Publication date: 26 September 2012

Published in: (Search for Journal in Brave)

Abstract: We study s-wave pion-pion (

p i p i

) scattering length in lattice QCD for pion masses ranging from 330 MeV to 466 MeV. In the "Asqtad" improved staggered fermion formulation, we calculate the

p i p i

four-point functions for isospin I=0 and 2 channels, and use chiral perturbation theory at next-to-leading order to extrapolate our simulation results. Extrapolating to the physical pion mass gives the scattering lengths as

m_{p} i a_{0}^{I = 2} = - 0.0416 (2)

and

m_{p} i a_{0}^{I = 0} = 0.186 (2)

for isospin I=2 and 0 channels, respectively. Our lattice simulation for

p i p i

scattering length in the I=0 channel is an exploratory study, where we include the disconnected contribution, and our preliminary result is near to its experimental value. These simulations are performed with MILC 2+1 flavor gauge configurations at lattice spacing

a a p p r o x 0.15

fm.

Full work available at URL: https://arxiv.org/abs/1110.3918

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