Fermion-scalar interactions with domain wall fermions

Domain wall fermions are defined on a lattice with an extra direction the size of which controls the chiral properties of the theory. When gauge fields are coupled to domain wall fermions the extra direction is treated as an internal flavor space. Here it is found that this is not the case for scalar fields. Instead, the interaction takes place only along the link that connects the boundaries of the extra direction. This reveals a richness in the way different spin particles are coupled to domain wall fermions. As an application, 4-Fermi models are studied using large N techniques and the results are supported by numerical simulations with N=2. It is found that the chiral properties of domain wall fermions in these models are good across a large range of couplings and that a phase with parity-flavor broken symmetry can develop for negative bare masses if the number of sites along the extra direction is finite.Comment: LaTeX, 17 pages, 8 eps figures; comment regarding the width of Aoki phase added in sec. 3; references adde

A numerical reinvestigation of the Aoki phase with N_f=2 Wilson fermions at zero temperature

We report on a numerical reinvestigation of the Aoki phase in lattice QCD with two flavors of Wilson fermions where the parity-flavor symmetry is spontaneously broken. For this purpose an explicitly symmetry-breaking source term $h\bar{\psi} i \gamma_{5} \tau^{3}\psi$ was added to the fermion action. The order parameter $$ was computed with the Hybrid Monte Carlo algorithm at several values of $(\beta,\kappa,h)$ on lattices of sizes $4^4$ to $12^4$ and extrapolated to $h=0$. The existence of a parity-flavor breaking phase can be confirmed at $\beta=4.0$ and 4.3, while we do not find parity-flavor breaking at $\beta=4.6$ and 5.0.Comment: 8 pages, 5 figures, Revised version as to be published in Phys.Rev.

Chirally improving Wilson fermions - I. O(a) improvement

We show that it is possible to improve the chiral behaviour and the approach to the continuum limit of correlation functions in lattice QCD with Wilson fermions by taking arithmetic averages of correlators computed in theories regularized with Wilson terms of opposite sign. Improved hadronic masses and matrix elements can be obtained by similarly averaging the corresponding physical quantities separately computed within the two regularizations. To deal with the problems related to the spectrum of the Wilson--Dirac operator, which are particularly worrisome when Wilson and mass terms are such as to give contributions of opposite sign to the real part of the eigenvalues, we propose to use twisted-mass lattice QCD for the actual computation of the quantities taking part to the averages. The choice $\pm \pi/2$ for the twisting angle is particularly interesting, as O($a$) improved estimates of physical quantities can be obtained even without averaging data from lattice formulations with opposite Wilson terms. In all cases little or no extra computing power is necessary, compared to simulations with standard Wilson fermions or twisted-mass lattice QCD.Comment: 71 pages, Latex, Keywords: Lattice, Improvement, Chirality. Version v2: mistake corrected in transformation properties under \omega -> -\omega, sect. 5.3.1 (see also sect. 6.1). Minor corrections in App. D and argument clarified in App. F. Version v3: minor modifications in sect. 2 (pag. 8-10: on the odd r-parity of M_crit(r)), in sect. 3.1.3 and 5.4.1 (few sentences about cutoff effects at small quark mass) and in sect. 3.2 (details of discussion below eq. 3.17); updated/added some reference