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تسجيل مستخدم جديدI=2 Pion Scattering Length from Two-Pion Wave Functions
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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 Luscher. 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 $Lge 24$ ($3.92 {rm fm}$) 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.
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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 $a^{-1}=1.207(12) {rm GeV}$ o
n $16^3 times 80$, $20^3 times 80$ and $24^3 times 80$ lattices. We investigate the validity of necessary condition for application of Luschers formula through the wave function. We find that the condition is satisfied for lattice volumes $Lge 3.92 {rm fm}$ 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.
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