Perturbative renormalization of the first two moments of non-singlet quark distributions with overlap fermions

Using the overlap-Dirac operator proposed by Neuberger, we have computed in lattice QCD the one-loop renormalization factors of ten operators which measure the lowest two moments of unpolarized and polarized non-singlet quark distributions. These factors are necessary to extract physical numbers from Monte Carlo simulations made with overlap fermions. An exact chiral symmetry is maintained in all our results, and the renormalization constants of corresponding unpolarized and polarized operators which differ by a $\gamma_5$ matrix have the same value. We have considered two lattice representations for each continuum operator. The computations have been carried out using the symbolic language FORM, in a general covariant gauge. In some simple cases they have also been checked by hand.Comment: 23 pages, 1 Postscript figure, uses elsevier style. Small corrections made in eqs. (6), (7), (13), (15), (17), (19), (20), (21) and (A.8), with no influence on the result

Magnetic moment of the Roper resonance

The magnetic moment of the Roper resonance is calculated in the framework of a low-energy effective field theory of the strong interactions. A systematic power-counting procedure is implemented by applying the complex-mass scheme.Comment: 13 pages, 4 figure

The Nielsen Identities of the SM and the definition of mass

In a generic gauge theory the gauge parameter dependence of individual Green functions is controlled by the Nielsen identities, which originate from an enlarged BRST symmetry. We give a practical introduction to the Nielsen identities of the Standard Model (SM) and to their renormalization and illustrate the power of this elegant formalism in the case of the problem of the definition of mass.We prove to all orders in perturbation theory the gauge-independence of the complex pole of the propagator for all physical fields of the SM, in the most general case with mixing and CP violation. At the amplitude level, the formalism provides an intuitive and general understanding of the gauge recombinations which makes it particularly useful at higher orders. We also include in an appendix the explicit expressions for the fermionic two-point functions in a generic R_\xi gauge.Comment: 28 pages, LaTeX2e, 4 Postscript Figures, final version to appear on PRD, extensive revision

The Specific Heat of a Ferromagnetic Film.

We analyze the specific heat for the $O(N)$ vector model on a $d$-dimensional film geometry of thickness $L$ using ``environmentally friendly'' renormalization. We consider periodic, Dirichlet and antiperiodic boundary conditions, deriving expressions for the specific heat and an effective specific heat exponent, \alpha\ef. In the case of $d=3$, for $N=1$, by matching to the exact exponent of the two dimensional Ising model we capture the crossover for \xi_L\ra\infty between power law behaviour in the limit {L\over\xi_L}\ra\infty and logarithmic behaviour in the limit {L\over\xi_L}\ra0 for fixed $L$, where $\xi_L$ is the correlation length in the transverse dimensions.Comment: 21 pages of Plain TeX. Postscript figures available upon request from [email protected]

Quenched Approximation Artifacts: A study in 2-dimensional QED

The spectral properties of the Wilson-Dirac operator in 2-dimensional QED responsible for the appearance of exceptional configurations in quenched simulations are studied in detail. The mass singularity structure of the quenched functional integral is shown to be extremely compicated, with multiple branch points and cuts. The connection of lattice topological charge and exactly real eigenmodes is explored using cooling techniques. The lattice volume and spacing dependence of these modes is studied, as is the effect of clover improvement of the action. A recently proposed modified quenched approximation is applied to the study of meson correlators, and the results compared with both naive quenched and full dynamical calculations of the same quantity.Comment: 34 pages (Latex) plus 9 embedded figures; title change

The Gross-Neveu model at finite temperature at next to leading order in the 1/N expansion

We present new results on the Gross-Neveu model at finite temperature and at next-to-leading order in the 1/N expansion. In particular, a new expression is obtained for the effective potential which is explicitly invariant under renormalization group transformations. The model is used as a playground to investigate various features of field theory at finite temperature. For example we verify that, as expected from general arguments, the cancellation of ultraviolet divergences takes place at finite temperature without the need for introducing counterterms beyond those of zero-temperature. As well known, the discrete chiral symmetry of the 1+1 dimensional model is spontaneously broken at zero temperature and restored, in leading order, at some temperature T_c; we find that the 1/N approximation breaks down for temperatures below T_c: As the temperature increases, the fluctuations become eventually too large to be treated as corrections, and a Landau pole invalidates the calculation of the effective potential in the vicinity of its minimum. Beyond T_c, the 1/N expansion becomes again regular: it predicts that in leading order the system behaves as a free gas of massless fermions and that, at the next-to-leading order, it remains weakly interacting. In the limit of large temperature, the pressure coincides with that given by perturbation theory with a coupling constant defined at a scale of the order of the temperature, as expected from asymptotic freedom.Comment: 77 pages, 19 figures (some of them bitmaped, for original figures contact authors

Weakly-bound Hadronic Molecule near a 3-body Threshold

The X(3872) seems to be a loosely-bound hadronic molecule whose constituents are two charm mesons. A novel feature of this molecule is that the mass difference of the constituents is close to the mass of a lighter meson that can be exchanged between them, namely the pion. We analyze this feature in a simple model with spin-0 mesons only. Various observables are calculated to next-to-leading order in the interaction strength of the exchanged meson. Renormalization requires summing a geometric series of next-to-leading order corrections. The dependence of observables on the ultraviolet cutoff can be removed by renormalizations of the mass of the heaviest meson, the coupling constant for the contact interaction between the heavy mesons, and short-distance coefficients in the operator product expansion. The next-to-leading order correction has an unphysical infrared divergence at the threshold of the two heavier mesons that can be eliminated by a further resummation that takes into account the nonzero width of the heaviest meson.Comment: 37 pages, 13 figures, submitted to Phys.Rev.