A simple construction of fermion measure term in U(1) chiral lattice gauge theories with exact gauge invariance

In the gauge invariant formulation of U(1) chiral lattice gauge theories based on the Ginsparg-Wilson relation, the gauge field dependence of the fermion measure is determined through the so-called measure term. We derive a closed formula of the measure term on the finite volume lattice. The Wilson line degrees of freedom (torons) of the link field are treated separately to take care of the global integrability. The local counter term is explicitly constructed with the local current associated with the cohomologically trivial part of the gauge anomaly in a finite volume. The resulted formula is very close to the known expression of the measure term in the infinite volume with a single parameter integration, and would be useful in practical implementations.Comment: 25 pages, uses JHEP3.cls, the version to appear in JHE

Towards Weyl fermions on the lattice without artefacts

In spite of the breakthrough in non-perturbative chiral gauge theories during the last decade, the present formulation has stubborn artefacts. Independently of the fermion representation one is confronted with unwanted CP violation and infinitely many undetermined weight factors. Renormalization group identifies the culprit. We demonstrate the procedure on Weyl fermions in a real representation

Non-perturbatively Renormalized Light-Quark Masses with the Alpha Action

We have computed the light quark masses using the O(a^2) improved Alpha action, in the quenched approximation. The renormalized masses have been obtained non-perturbatively. By eliminating the systematic error coming from the truncation of the perturbative series, our procedure removes the discrepancies, observed in previous calculations, between the results obtained using the vector and the axial-vector Ward identities. It also gives values of the quark masses larger than those obtained by computing the renormalization constants using (boosted) perturbation theory. Our main results, in the RI (MOM) scheme and at a renormalization scale \mu=2 GeV, are m^{RI}_s= 138(15) MeV and m^{RI}_l= 5.6(5) MeV, where m^{RI}_s is the mass of the strange quark and m^{RI}_l=(m^{RI}_u+m^{RI}_d)/2 the average mass of the up-down quarks. From these results, which have been obtained non-perturbatively, by using continuum perturbation theory we derive the \bar{MS} masses, at the same scale, and the renormalization group invariant (m^{RGI}) masses. We find m^{NLO \bar{MS}}_s= 121(13)$ MeV and m^{NLO\bar{MS}}_l= 4.9(4) MeV at the next-to-leading order; m^{N^2LO \bar{MS}}_s= 111(12) MeV, m^{N^2LO \bar{MS}}_l= 4.5(4) MeV, m_s^{RGI}= 177(19) MeV and m^{RGI}_l= 7.2(6) MeV at the next-to-next-to-leading order.Comment: 13 pages, 1 figur

Coulomb Energy, Vortices, and Confinement

We estimate the Coulomb energy of static quarks from a Monte Carlo calculation of the correlator of timelike link variables in Coulomb gauge. We find, in agreement with Cucchieri and Zwanziger, that this energy grows linearly with distance at large quark separations. The corresponding string tension, however, is several times greater than the accepted asymptotic string tension, indicating that a state containing only static sources, with no constituent gluons, is not the lowest energy flux tube state. The Coulomb energy is also measured on thermalized lattices with center vortices removed by the de Forcrand-D'Elia procedure. We find that when vortices are removed, the Coulomb string tension vanishes.Comment: 8 pages, 4 EPS figures, RevTeX4; reference adde

Non-perturbative renormalisation and improvement of the local vector current for quenched and unquenched Wilson fermions

By considering the local vector current between nucleon states and imposing charge conservation, we determine its renormalisation constant and quark mass improvement coefficient for Symanzik $O(a)$ improved Wilson fermions. The computation is first performed for quenched fermions (and for completeness also with unimproved fermions) and compared against known results. The two-flavour unquenched case is then considered.Comment: 15 pages, 5 figures, Latex, Final versio

A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance

We present a gauge-invariant and non-perturbative construction of the Glashow-Weinberg-Salam model on the lattice, based on the lattice Dirac operator satisfying the Ginsparg-Wilson relation. Our construction covers all SU(2) topological sectors with vanishing U(1) magnetic flux and would be usable for a description of the baryon number non-conservation. In infinite volume, it provides a gauge-invariant regularization of the electroweak theory to all orders of perturbation theory. First we formulate the reconstruction theorem which asserts that if there exists a set of local currents satisfying cetain properties, it is possible to reconstruct the fermion measure which depends smoothly on the gauge fields and fulfills the fundamental requirements such as locality, gauge-invariance and lattice symmetries. Then we give a closed formula of the local currents required for the reconstruction theorem.Comment: 32 pages, uses JHEP3.cls, the version to appear in JHE

The Landau Pole at Finite Temperature

We study the Landau pole in the lambda phi^4 field theory at non-zero and large temperatures. We show that the position of the thermal Landau pole Lambda_L(T) is shifted to higher energies with respect to the zero temperature Landau pole Lambda_L(0). We find for high temperatures T > Lambda_L(0), Lambda_L(T) simeq pi^2 T / log (T / Lambda_L(0)). Therefore, the range of applicability in energy of the lambda phi^4 field theory increases with the temperature.Comment: LaTex, 6 pages, 2 .ps figures. Improved version. To appear in Phys. Rev. D, Rapid Communication

Short distance behaviour of the effective string

We study the Polyakov loop correlator in the (2+1) dimensional Z_2 gauge model. An algorithm that we have presented recently, allows us to reach high precision results for a large range of distances and temperatures, giving us the opportunity to test predictions of the effective Nambu-Goto string model. Here we focus on the regime of low temperatures and small distances. In contrast to the high temperature, large distance regime, we find that our numerical results are not well described by the two loop-prediction of the Nambu-Goto model. In addition we compare our data with those for the SU(2) and SU(3) gauge models in (2+1) dimensions obtained by other authors. We generalize the result of L\"uscher and Weisz for a boundary term in the interquark potential to the finite temperature case.Comment: 38 pages, 7 figures, version accepted for publication in JHE

Inequalities for low-energy symmetric nuclear matter

Using effective field theory we prove inequalities for the correlations of two-nucleon operators in low-energy symmetric nuclear matter. For physical values of operator coefficients in the effective Lagrangian, the S = 1, I = 0 channel correlations must have the lowest energy and longest correlation length in the two-nucleon sector. This result is valid at nonzero density and temperature.Comment: 9 page

I=2I=2 pion scattering amplitude with Wilson fermions

We present an exploratory calculation of the $I=2$ $\pi-\pi$ scattering amplitude at threshold using Wilson fermions in the quenched approximation, including all the required contractions. We find good agreement with the predictions of chiral perturbation theory even for pions of mass 560-700 MeV. Within the 10\% errors, we do not see the onset of the bad chiral behavior expected for Wilson fermions. We also derive rigorous inequalities that apply to 2-particle correlators and as a consequence show that the interaction in the antisymmetric state of two pions has to be attractive.Comment: This PS file includes 4 tables and figures 1-8 on 25 pages. Los Alamos Preprint Number LAUR-92-364