{"arxiv_id":"hep-lat/0409063","title":"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 L\\\"uscher'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 $m_\\pi^2 = 0.273-0.736 {\\rm GeV}^2$. 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.","primary_cat":"hep-lat","cross_cats":[],"submitted_at":"2004-09-14T09:14:32+00:00","latest_version":1,"source":"arxiv","source_label":"arXiv","source_url":null,"has_pdf":true,"has_source":false,"verdict":null,"confidence":null,"one_line_summary":null,"novelty_score":null,"correctness_risk":null,"formal_verification":null,"upvotes":0,"downvotes":0,"pith_score":0.0,"inbound_count":2,"_links":{"html":"https://pith.science/paper/hep-lat/0409063","verdict":"/api/v1/verdicts/hep-lat/0409063"}}