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 $a^{-1}=1.207(12) {\rm GeV}$ 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 $L\ge 3.92 {\rm fm}$ for the quark mass range $m_π^2 = 0.273-0.736 {\rm GeV}^2$. 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