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arXiv · hep-lat/0503025

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

PACS Collaboration·S. Aoki·M. Fukugita·K-I. Ishikawa·N. Ishizuka·Y. Iwasaki·K. Kanaya·T. Kaneko·Y. Kuramashi·M. Okawa·A. Ukawa·T. Yamazaki·T. Yoshié
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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 $1/a=1.207(12) {\rm GeV}$ 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 $m_π^2 = 0.273-0.736 {\rm GeV}^2$. We obtain the scattering length with a smaller statistical error from the wave function than from the two-pion time correlator.

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PACS Collaboration, S. Aoki, M. Fukugita, K-I. Ishikawa, N. Ishizuka, Y. Iwasaki, K. Kanaya, T. Kaneko, Y. Kuramashi, M. Okawa, A. Ukawa, T. Yamazaki, T. Yoshié. 2005-05-14. I=2 Pion Scattering Length from Two-Pion Wave Functions. https://doi.org/10.1103/physrevd.71.094504

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