Perturbative Renormalization of Wilson line operators

We present results for the renormalization of gauge invariant nonlocal fermion operators which contain a Wilson line, to one loop level in lattice perturbation theory. Our calculations have been performed for Wilson/clover fermions and a wide class of Symanzik improved gluon actions. The extended nature of such `long-link' operators results in a nontrivial renormalization, including contributions which diverge linearly as well as logarithmically with the lattice spacing, along with additional finite factors. We present nonperturbative prescriptions to extract the linearly divergent contributions.Comment: 8 pages, 2 figures. Talk presented at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spai

Gauge theories with overlap fermions in an arbitrary representation: Evaluation of the 3-loop beta-function

This work presents the calculation of the relation between the bare coupling constant g_0 and the MSbar-renormalized coupling g_MS, g_0 = Z_g(g_0,a\mu) g_MS, to 2 loops in perturbation theory, with fermions in an arbitrary representation of the gauge group SU(N). Our calculation is performed using overlap fermions and Wilson gluons, and the background field technique has been chosen for convenience. The corresponding results in the fundamental representation appear in our longer publication [arXiv:0709.4368]. The 3-loop coefficient of the bare beta-function, b_2^L, is extracted using the 2-loop expression for Z_g, and it is presented as a function of the overlap parameter rho, the number of fermion flavors (N_f) and the number of colors (N). We also provide the expression for the ratio Lambda_L/Lambda_MS, in an arbitrary representation. A plot of Lambda_L/Lambda_MS is given in the adjoint representation.Comment: 15 pages, 5 figure

Dense matter equation of state for neutron star mergers

In simulations of binary neutron star mergers, the dense matter equation of state (EOS) is required over wide ranges of density and temperature as well as under conditions in which neutrinos are trapped, and the effects of magnetic fields and rotation prevail. Here we assess the status of dense matter theory and point out the successes and limitations of approaches currently in use. A comparative study of the excluded volume (EV) and virial approaches for the $np\alpha$ system using the equation of state of Akmal, Pandharipande and Ravenhall for interacting nucleons is presented in the sub-nuclear density regime. Owing to the excluded volume of the $\alpha$-particles, their mass fraction vanishes in the EV approach below the baryon density 0.1 fm$^{-3}$, whereas it continues to rise due to the predominantly attractive interactions in the virial approach. The EV approach of Lattimer et al. is extended here to include clusters of light nuclei such as d, $^3$H and $^3$He in addition to $\alpha$-particles. Results of the relevant state variables from this development are presented and enable comparisons with related but slightly different approaches in the literature. We also comment on some of the sweet and sour aspects of the supra-nuclear EOS. The extent to which the neutron star gravitational and baryon masses vary due to thermal effects, neutrino trapping, magnetic fields and rotation are summarized from earlier studies in which the effects from each of these sources were considered separately. Increases of about $20\% (\gtrsim 50\%)$ occur for rigid (differential) rotation with comparable increases occurring in the presence of magnetic fields only for fields in excess of $10^{18}$ Gauss. Comparatively smaller changes occur due to thermal effects and neutrino trapping. Some future studies to gain further insight into the outcome of dynamical simulations are suggested.Comment: Revised manuscript with one additional figure and previous Fig. 4 replaced, 19 additional references and new tex

Degenerate limit thermodynamics beyond leading order for models of dense matter

Analytical formulas for next-to-leading order temperature corrections to the thermal state variables of interacting nucleons in bulk matter are derived in the degenerate limit. The formalism developed is applicable to a wide class of non-relativistic and relativistic models of hot and dense matter currently used in nuclear physics and astrophysics (supernovae, proto-neutron stars and neutron star mergers) as well as in condensed matter physics. We consider the general case of arbitrary dimensionality of momentum space and an arbitrary degree of relativity (for relativistic mean-field theoretical models). For non-relativistic zero-range interactions, knowledge of the Landau effective mass suffices to compute next-to-leading order effects, but in the case of finite-range interactions, momentum derivatives of the Landau effective mass function up to second order are required. Numerical computations are performed to compare results from our analytical formulas with the exact results for zero- and finite-range potential and relativistic mean-field theoretical models. In all cases, inclusion of next-to-leading order temperature effects substantially extends the ranges of partial degeneracy for which the analytical treatment remains valid.Comment: 28 pages, 8 figure

Improved Perturbation Theory for Improved Lattice Actions

We study a systematic improvement of perturbation theory for gauge fields on the lattice; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed for the Wilson gluon action, is extended here to encompass all possible gluon actions made of closed Wilson loops; any fermion action can be employed as well. The effect of resummation is to replace various parameters in the action (coupling constant, Symanzik coefficients, clover coefficient) by ``dressed'' values; the latter are solutions to certain coupled integral equations, which are easy to solve numerically. Some positive features of this method are: a) It is gauge invariant, b) it can be systematically applied to improve (to all orders) results obtained at any given order in perturbation theory, c) it does indeed absorb in the dressed parameters the bulk of tadpole contributions. Two different applications are presented: The additive renormalization of fermion masses, and the multiplicative renormalization Z_V (Z_A) of the vector (axial) current. In many cases where non-perturbative estimates of renormalization functions are also available for comparison, the agreement with improved perturbative results is significantly better as compared to results from bare perturbation theory.Comment: 17 pages, 3 tables, 6 figure