Correlation functions at small quark masses with overlap fermions

We report on recent work on the determination of low-energy constants describing Delta{S}=1 weak transitions, in order to investigate the origins of the Delta{I}=1/2 rule. We focus on numerical techniques designed to enhance the statistical signal in three-point correlation functions computed with overlap fermions near the chiral limit.Comment: Talk presented at Lattice2004(weak), Fermilab, 21-26 June 2004, 3 pages, 2 figure

Finite-size scaling for the left-current correlator with non-degenerate quark masses

We study the volume dependence of the left-current correlator with non-degenerate quark masses to next-to-leading order in the chiral expansion. We consider three possible regimes: all quark masses are in the $\epsilon$-regime, all are in the $p$-regime and a mixed-regime where the lighest quark masses satisfy $m_v \Sigma V \leq 1$ while the heavier $m_s \Sigma V \gg 1$. These results can be used to match lattice QCD and the Chiral Effective Theory in a large but finite box in which the Compton wavelength of the lightest pions is of the order of the box size. We consider both the full and partially-quenched results.Comment: 27 pages, 4 figure

Charge-Exchange and multi-scattering effects in (e,e'n) knockout

Final-state interactions in (e,e'n) knockout reactions in the quasi-free region are studied by considering the multistep direct scattering of the ejectile nucleon. Primary and multiple particle emission are included within the same model and are found to become important with increasing excitation energy. Charge-exchange effects taken into account through the two-step (e,e'p)(p,n) and three-step (e,e'p)(p,N)(N,n) processes are also found to increase with energy. A comparison with the results obtained with an isospin-dependent optical potential at small excitation energies is presented.Comment: 12 pages, 4 Postscript figures. A new section on multiple particle emission added together with 2 new figures including primary and multiple emission cross section

Non-perturbative renormalisation of left-left four-fermion operators with Neuberger fermions

We outline a general strategy for the non-perturbative renormalisation of composite operators in discretisations based on Neuberger fermions, via a matching to results obtained with Wilson-type fermions. As an application, we consider the renormalisation of the four-quark operators entering the Delta S=1 and Delta S=2 effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays.Comment: 14 pages, 3 figure

Optical Potentials Derived from Nucleon-Nucleon Chiral Potentials at N4LO

Background: Elastic scattering is probably the main event in the interactions of nucleons with nuclei. Even if this process has been extensively studied in the last years, a consistent description, i.e., starting from microscopic two- and many-body forces connected by the same symmetries and principles, is still under development. Purpose: In a previous paper we derived a theoretical optical potential from NN chiral potentials at fourth order (N3LO). In the present work we use NN chiral potentials at fifth order (N4LO), with the purpose to check the convergence and to assess the theoretical errors associated with the truncation of the chiral expansion in the construction of an optical potential. Methods: The optical potential is derived as the first-order term within the spectator expansion of the nonrelativistic multiple scattering theory and adopting the impulse approximation and the optimum factorization approximation. Results: The pp and np Wolfenstein amplitudes and the cross section, analyzing power, and spin rotation of elastic proton scattering from 16O, 12C, and 40Ca nuclei are presented at an incident proton energy of 200 MeV. The results obtained with different versions of chiral potentials at N4LO are compared. Conclusions: Our results indicate that convergence has been reached at N4LO. The agreement with the experimental data is comparable with the agreement obtained in our previous work. We confirm that building an optical potential within chiral perturbation theory is a promising approach for describing elastic proton-nucleus scattering.Comment: Physical Review C, in prin

Proton recoil polarization in exclusive (e,e'pp) reactions

The general formalism of nucleon recoil polarization in the (${\vec e},e'{\vec N}N$) reaction is given. Numerical predictions are presented for the components of the outgoing proton polarization and of the polarization transfer coefficient in the specific case of the exclusive $^{16}$O(${\vec e},e'{\vec p}p$)$^{14}$C knockout reaction leading to discrete states in the residual nucleus. Reaction calculations are performed in a direct knockout framework where final-state interactions and one-body and two-body currents are included. The two-nucleon overlap integrals are obtained from a calculation of the two-proton spectral function of $^{16}$O where long-range and short-range correlations are consistently included. The comparison of results obtained in different kinematics confirms that resolution of different final states in the $^{16}$O(${\vec e},e'{\vec p}p$)$^{14}$C reaction may act as a filter to disentangle and separately investigate the reaction processes due to short-range correlations and two-body currents and indicates that measurements of the components of the outgoing proton polarization may offer good opportunities to study short-range correlations.Comment: 12 pages, 6 figure

On the renormalized scalar density in quenched QCD

We present a non-perturbative determination of the renormalization factor Z_S of the scalar density in quenched QCD with overlap fermions. Results are obtained at four values of the lattice spacing. By combining Z_S with results for the low-energy constant Sigma we are able to compute the renormalization group invariant scalar condensate in the continuum limit with a total accuracy of 7%, excluding dynamical quark effects. Our result translates to Sigma_msbar(2 GeV)=(285+/-9 MeV)^3 if the scale is set by the kaon decay constant. We have also performed scaling studies of the pseudoscalar decay constant and the vector mass. Our results indicate that quantities computed using overlap quarks exhibit excellent scaling behaviour, with small residual lattice artifacts.Comment: 15 pages, 7 figure

A nucleon in a tiny box

We use Chiral Perturbation Theory to compute the nucleon mass-shift due to finite volume and temperature effects. Our results are valid up to next-to-leading order in the "\eps-regime" (mL ~ m\beta << 1) as well as in the "p-regime" (mL ~ m\beta >> 1). Based on the two leading orders, we discuss the convergence of the expansion as a function of the lattice size and quark masses. This result can be used to extrapolate lattice results obtained from lattice sizes smaller than the pion cloud, avoiding the numerical simulation of physics under theoretical control. An extraction of the low-energy coefficient c_3 of the chiral Lagrangean from lattice simulations at small volumes and a ``magic'' ratio \beta=1.22262 L might be possible.Comment: 7 figures, numerical examples and discussion changed. Minor misprints corrected. Version accepted by Phys Rev

Spectral density of the Dirac operator in two-flavour QCD

We compute the spectral density of the (Hermitean) Dirac operator in Quantum Chromodynamics with two light degenerate quarks near the origin. We use CLS/ALPHA lattices generated with two flavours of O(a)-improved Wilson fermions corresponding to pseudoscalar meson masses down to 190 MeV, and with spacings in the range 0.05-0.08 fm. Thanks to the coverage of parameter space, we can extrapolate our data to the chiral and continuum limits with confidence. The results show that the spectral density at the origin is non-zero because the low modes of the Dirac operator do condense as expected in the Banks-Casher mechanism. Within errors, the spectral density turns out to be a constant function up to eigenvalues of approximately 80 MeV. Its value agrees with the one extracted from the Gell-Mann-Oakes-Renner relation