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

Abstract

We present a report on a calculation of scattering length for I=2 $S$-wave two-pion system from two-pion wave function. Calculations are made with an RG-improved action for gluons and improved Wilson action for quarks at $a^{-1}=1.207(12)\mathrm{GeV}$ on $16^3\times 80$, $20^3\times 80$ and $24^3\times 80$ lattices. We investigate the validity of necessary condition for application of Lüscher's formula through the wave function. We find that the condition is satisfied for lattice volumes $L\ge 3.92\mathrm{fm}$ for the quark mass range $m_{\ddot{I}}{€}^2=0.273-0.736{\mathrm{GeV}}^2$. We also find that the scattering length can be extracted with a smaller statistical error from the wave function than with a time correlation function used in previous studies.

3 pages, 4 figures, Talk presented at Lattice2004(spectrum), Fermilab, June 21-26, 2004