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Register a new userI=2 Two-Pion Wave Function and Scattering Phase Shift
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Kiyoshi Sasaki
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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.
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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 $a^{-1}=1.207(12) {rm GeV}$ 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 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 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.
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.
The pi+pi+ s-wave scattering phase-shift is determined below the inelastic threshold using Lattice QCD. Calculations were performed at a pion mass of m_pi~390 MeV with an anisotropic n_f=2+1 clover fermion discretization in four lattice volumes, with spatial extent L~2.0, 2.5, 3.0 and 3.9 fm, and with a lattice spacing of b_s~0.123 fm in the spatial direction and b_t b_s/3.5 in the time direction. The phase-shift is determined from the energy-eigenvalues of pi+pi+ systems with both zero and non-zero total momentum in the lattice volume using Luschers method. Our calculations are precise enough to allow for a determination of the threshold scattering parameters, the scattering length a, the effective range r, and the shape-parameter P, in this channel and to examine the prediction of two-flavor chiral perturbation theory: m_pi^2 a r = 3+O(m_pi^2/Lambda_chi^2). Chiral perturbation theory is used, with the Lattice QCD results as input, to predict the scattering phase-shift (and threshold parameters) at the physical pion mass. Our results are consistent with determinations from the Roy equations and with the existing experimental phase shift data.
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