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Register a new userI=2 Pion Scattering Length and Phase Shift with Wilson Fermions
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We present preliminary results of scattering length and phase shift for I=2 S-wave $pipi$ system with the Wilson fermions in the quenched approximation. The finite size method presented by Luscher is employed, and calculations are carried out at $beta=5.9$ on a $24^3times 60$ and $32^3times 60$ lattice.
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We present results of phase shift for I=2 $S$-wave $pipi$ system with the Wilson fermions in the quenched approximation. The finite size method proposed by Luscher is employed, and calculations are carried out at $beta=5.9$ ($a^{-1}=1.934(16)$ GeV from $m_rho$) on $24^3 times 60$, $32^3 times 60$, and $48^3 times 60$ lattices.
We present results for I=2 pion scattering length with the Wilson fermions in the quenched approximation. The finite size method presented by Luscher is employed, and calculations are carried out at $beta=5.9$, 6.1, and 6.3. In the continuum limit, we obtain a result in reasonable agreement with the experimental value.
We calculate a two-pion wave function for the I=2 $S$-wave two-pion system with a finite scattering momentum and estimate the interaction range between two pions, which allows us to examine the validity of a necessary condition for the finite size formula presented by Rummukainen and Gottlieb. We work in the quenched approximation employing the plaquette gauge action for gluons and the improved Wilson action for quarks at $1/a=1.63 {rm GeV}$ on $32^3times 120$ lattice. The quark masses are chosen to give $m_pi = 0.420$, 0.488 and $0.587 {rm GeV}$. We find that the energy dependence of the interaction range is small and the necessary condition is satisfied for our range of the quark mass and the scattering momentum, $k le 0.16 {rm GeV}$. We also find that the scattering phase shift can be obtained with a smaller statistical error from the two-pion wave function than from the two-pion time correlator.
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 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.
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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