Finite-volume two-pion energies and scattering in the quenched approximation

We investigate how L\"uscher's relation between the finite-volume energy of two pions at rest and pion scattering lengths has to be modified in quenched QCD. We find that this relation changes drastically, and in particular, that ``enhanced finite-volume corrections" of order L^0=1 and L^{-2} occur at one loop (L is the linear size of the box), due to the special properties of the \eta' in the quenched approximation. We define quenched pion scattering lengths, and show that they are linearly divergent in the chiral limit. We estimate the size of these various effects in some numerical examples, and find that they can be substantial

On Lattice Computations of K+ --> pi+ pi0 Decay at m_K =2m_pi

We use one-loop chiral perturbation theory to compare potential lattice computations of the K+ --> pi+ pi0 decay amplitude at m_K=2m_pi with the experimental value. We find that the combined one-loop effect due to this unphysical pion to kaon mass ratio and typical finite volume effects is still of order minus 20-30%, and appears to dominate the effects from quenching.Comment: 4 pages, revte

Domain-wall fermions with U(1)U(1) dynamical gauge fields

We have carried out a numerical simulation of a domain-wall model in $(2+1)$-dimensions, in the presence of a dynamical gauge field only in an extra dimension, corresponding to the weak coupling limit of a ( 2-dimensional ) physical gauge coupling. Using a quenched approximation we have investigated this model at $\beta_{s} ( = 1 / g^{2}_{s} ) =$ 0.5 ( ``symmetric'' phase), 1.0, and 5.0 (``broken'' phase), where $g_s$ is the gauge coupling constant of the extra dimension. We have found that there exists a critical value of a domain-wall mass $m_{0}^{c}$ which separates a region with a fermionic zero mode on the domain-wall from the one without it, in both symmetric and broken phases. This result suggests that the domain-wall method may work for the construction of lattice chiral gauge theories.Comment: 27 pages (11 figures), latex (epsf style-file needed