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

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

Generalized seniority for the shell model with realistic interactions

The generalized seniority scheme has long been proposed as a means of dramatically reducing the dimensionality of nuclear shell model calculations, when strong pairing correlations are present. However, systematic benchmark calculations, comparing results obtained in a model space truncated according to generalized seniority with those obtained in the full shell model space, are required to assess the viability of this scheme. Here, a detailed comparison is carried out, for semimagic nuclei taken in a full major shell and with realistic interactions. The even-mass and odd-mass Ca isotopes are treated in the generalized seniority scheme, for generalized seniority v<=3. Results for level energies, orbital occupations, and electromagnetic observables are compared with those obtained in the full shell model space.Comment: 13 pages, 8 figures; published in Phys. Rev.

Perturbatively improving renormalization constants

Renormalization factors relate the observables obtained on the lattice to their measured counterparts in the continuum in a suitable renormalization scheme. They have to be computed very precisely which requires a careful treatment of lattice artifacts. In this work we present a method to suppress these artifacts by subtracting one-loop contributions proportional to the square of the lattice spacing calculated in lattice perturbation theory.Comment: 7 pages, 2 figures, LATTICE 201

Renormalization of local quark-bilinear operators for Nf=3 flavors of SLiNC fermions

The renormalization factors of local quark-bilinear operators are computed non-perturbatively for $N_f=3$ flavors of SLiNC fermions, with emphasis on the various procedures for the chiral and continuum extrapolations. The simulations are performed at a lattice spacing $a=0.074$ fm, and for five values of the pion mass in the range of 290-465 MeV, allowing a safe and stable chiral extrapolation. Emphasis is given in the subtraction of the well-known pion pole which affects the renormalization factor of the pseudoscalar current. We also compute the inverse propagator and the Green's functions of the local bilinears to one loop in perturbation theory. We investigate lattice artifacts by computing them perturbatively to second order as well as to all orders in the lattice spacing. The renormalization conditions are defined in the RI$'$-MOM scheme, for both the perturbative and non-perturbative results. The renormalization factors, obtained at different values of the renormalization scale, are translated to the ${\bar{\rm MS}}$ scheme and are evolved perturbatively to 2 GeV. Any residual dependence on the initial renormalization scale is eliminated by an extrapolation to the continuum limit. We also study the various sources of systematic errors. Particular care is taken in correcting the non-perturbative estimates by subtracting lattice artifacts computed to one loop perturbation theory using the same action. We test two different methods, by subtracting either the ${\cal O}(g^2\,a^2)$ contributions, or the complete (all orders in $a$) one-loop lattice artifacts.Comment: 33 pages, 27 figures, 6 table