I=2 pion scattering length from twopion wave functions
Abstract
We calculate the twopion wave function in the ground state of the I=2 Swave system and find the interaction range between two pions, which allows us to examine the validity of the necessary condition for the finitevolume 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) GeV on 16^{3}×80, 20^{3}×80, and 24^{3}×80 lattices. We conclude that the necessary condition is satisfied within the statistical errors for the lattice sizes L≥24 (3.92 fm) when the quark mass is in the range that corresponds to m^{2}_{π}=0.273 0.736 GeV^{2}. We obtain the scattering length with a smaller statistical error from the wave function than from the twopion time correlator.
 Publication:

Physical Review D
 Pub Date:
 May 2005
 DOI:
 10.1103/PhysRevD.71.094504
 arXiv:
 arXiv:heplat/0503025
 Bibcode:
 2005PhRvD..71i4504A
 Keywords:

 12.38.Gc;
 11.15.Ha;
 Lattice QCD calculations;
 Lattice gauge theory;
 High Energy Physics  Lattice
 EPrint:
 LaTeX2e, 34 pages, 11 eps figures, uses revtex4 and graphicx