I=2 Pion Scattering Length from Two-Pion Wave Functions

Abstract

We calculate the two-pion wave function in the ground state of the I=2 $S$-wave system and find the interaction range between two pions, which allows us to examine the validity of the necessary condition for the finite-volume method for the scattering length proposed by Lüscher. We work in the quenched approximation employing a renormalization group improved gauge action for gluons and an improved Wilson action for quarks at $1/a=1.207(12)\mathrm{GeV}$ on $16^3\times 80$, $20^3\times 80$ and $24^3\times 80$ lattices. We conclude that the necessary condition is satisfied within the statistical errors for the lattice sizes $L\ge 24$ ($3.92\mathrm{fm}$) when the quark mass is in the range that corresponds to $m_{\ddot{I}}{€}^2=0.273-0.736{\mathrm{GeV}}^2$. We obtain the scattering length with a smaller statistical error from the wave function than from the two-pion time correlator.

LaTeX2e, 34 pages, 11 eps figures, uses revtex4 and graphicx