Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2005-03-18
Phys.Rev.D71:094504,2005
Physics
High Energy Physics
High Energy Physics - Lattice
LaTeX2e, 34 pages, 11 eps figures, uses revtex4 and graphicx
Scientific paper
10.1103/PhysRevD.71.094504
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 L\"uscher. We work in the quenched approximation employing a renormalization group improved gauge action for gluons and an improved Wilson action for quarks at $1/a=1.207(12) {\rm GeV}$ 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 $L\ge 24$ ($3.92 {\rm fm}$) when the quark mass is in the range that corresponds to $m_\pi^2 = 0.273-0.736 {\rm GeV}^2$. We obtain the scattering length with a smaller statistical error from the wave function than from the two-pion time correlator.
Aoki CP-PACS Collaboration : S.
Fukugita Masaaka
Ishikawa Kei-Ichi
Ishizuka Naruhito
Iwasaki Yoshihito
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