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Register a new userI=2 pion scattering length with the parametrized fixed point action
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Authors
K. J. Juge
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We report on the pion-pion scattering length in the I=2 channel using the parametrized fixed point action. Pion masses of 320 MeV were reached in this quenched calculation of the scattering length.
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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 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.
We have constructed a new fermion action which is an approximation to the (chirally symmetric) Fixed-Point action, containing the full Clifford algebra with couplings inside a hypercube and paths built from renormalization group inspired fat links. We present an exploratory study of the light hadron spectrum and the energy-momentum dispersion relation.
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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