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arXiv · hep-lat/0409063

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

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 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.

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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. 2004-09-14. I=2 Pion Scattering Length from Two-Pion Wave Function. https://arxiv.org/abs/hep-lat/0409063

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