On the Analytic Structure of the Quark Self-Energy in Nambu-Jona- Lasinio Models

The self-energy of quarks is investigated for various models which are inspired by the Nambu--Jona-Lasinio (NJL) model. Including, beyond the Hartree-Fock approximation, terms up to second-order in the quark interaction, the real and imaginary parts of scalar and vector components of the self-energy are discussed. The second-order contributions depend on the energy and momentum of the quark under consideration. This leads to solutions of the Dirac equation which are significantly different from those of a free quark or a quark with constant effective mass, as obtained in the Hartree-Fock approximation.Comment: 15 pages LaTeX, 6 figures can be obtained from author

Two tricritical lines from a Ginzburg-Landau expansion: application to the LOFF phase

We study the behavior of the two plane waves configuration in the LOFF phase close to T=0. The study is performed by using a Landau-Ginzburg expansion up to the eighth order in the gap. The general study of the corresponding grand potential shows, under the assumption that the eighth term in the expansion is strictly positive, the existence of two tricritical lines. This allows to understand the existence of a second tricritical point for two antipodal plane waves in the LOFF phase and justifies why the transition becomes second order at zero temperature. The general analysis done in this paper can be applied to other cases.Comment: LaTex file, 15 pages, 6 figure

Dependence of interface conductivity on relevant physical parameters in polarized Fermi mixtures

We consider a mass-asymmetric polarized Fermi system in the presence of Hartree-Fock (HF) potentials. We concentrate on the BCS regime with various interaction strengths and numerically obtain the allowed values of the chemical and HF potentials, as well as the mass ratio. The functional dependence of the heat conductivity of the N-SF interface on relevant physical parameters, namely the temperature, the mass ratio, and the interaction strength, is obtained. In particular, we show that the interface conductivity starts to drop with decreasing temperature at the temperature, $T_{\text{m}}$, where the mean kinetic energy of the particles is just sufficient to overcome the SF gap. We obtain $T_{\text{m}}$ as a function of the mass ratio and the interaction strength. The variation of the heat conductivity, at fixed temperature, with the HF potentials and the imbalance chemical potential is also obtained. Finally, because the range of relevant temperatures increases for larger values of the mass ratio, we consider the $^6\text{Li}$-$^{40}\text{K}$ mixture separately by taking the temperature dependence of the pair potential into account.Comment: To appear in Physica C (2012

Coarse graining Nuclear Interactions

We consider a coarse graining of NN interactions in coordinate space very much in the spirit of the well known Vlowk approach. To this end we sample the interaction at about the minimal de Broglie wavelength probed by NN scattering below pion production threshold. This amounts to provide a simple delta-shell potential plus the standard OPE potential above 2 fm. The possible simplifications in the Nuclear many body problem are discussed.Comment: Presented by RNP at the Erice School on Nuclear Physics 2011: From Quarks and Gluons to Hadrons and Nuclei, Erice, Sicily (Italy), 16-24 September 2011, 7 pages, 6 figure

Minimal Cooling of Neutron Stars: A New Paradigm

A new classification of neutron star cooling scenarios, involving either ``minimal'' cooling or ``enhanced'' cooling is proposed. The minimal cooling scenario replaces and extends the so-called standard cooling scenario to include neutrino emission from the Cooper pair breaking and formation process. This emission dominates that due to the modified Urca process for temperatures close to the critical temperature for superfluid pairing. Minimal cooling is distinguished from enhanced cooling by the absence of neutrino emission from any direct Urca process, due either to nucleons or to exotica. Within the minimal cooling scenario, theoretical cooling models can be considered to be a four parameter family involving the equation of state of dense matter, superfluid properties of dense matter, the composition of the neutron star envelope, and the mass of the neutron star. Consequences of minimal cooling are explored through extensive variations of these parameters. Results are compared with the inferred properties of thermally-emitting neutron stars in order to ascertain if enhanced cooling occurs in any of them. All stars for which thermal emissions have been clearly detected are at least marginally consistent with the lack of enhanced cooling. The two pulsars PSR 0833-45 (Vela) and PSR 1706-44 would require enhanced cooling in case their ages and/or temperatures are on the lower side of their estimated values whereas the four stars PSR 0656+14, PSR 1055-52, Geminga, and RX J0720.4-3125 may require some source of internal heating in case their age and/or luminosity are on the upper side of their estimated values. The new upper limits on the thermal luminosity of PSR J0205+6449 and RX J0007.0+7302 are indicative of the occurrence of some enhanced neutrino emission beyond the minimal scenario.Comment: Version to appear in ApJ Supplements. Minor modifications in text and discussion of updated data with new figure

Chiral dynamics and the growth of the nucleon's gluonic transverse size at small x

We study the distribution of gluons in transverse space in the nucleon at moderately small x (~10^{-2}). At large transverse distances (impact parameters) the gluon density is generated by the 'pion cloud' of the nucleon, and can be calculated in terms of the gluon density in the pion. We investigate the large-distance behavior in two different approaches to chiral dynamics: i) phenomenological soft-pion exchange, ii) the large-N_c picture of the nucleon as a classical soliton of the pion field, which corresponds to degenerate N and Delta states. The large-distance contributions from the 'pion cloud' cause a \~20% increase in the overall transverse size of the nucleon if x drops significantly below M_pi/M_N. This is in qualitative agreement with the observed increase of the slope of the t-dependence of the J/psi photoproduction cross section at HERA compared to fixed-target energies. We argue that the glue in the pion cloud could be probed directly in hard electroproduction processes accompanied by 'pion knockout', gamma^* + N -> gamma (or rho, J/psi) + pi + N', where the transverse momentum of the emitted pion is large while that of the outgoing nucleon is restricted to values of order M_pi.Comment: 20 pages, revtex4, 10 eps figure

Inhomogeneous Superconductivity in Condensed Matter and QCD

Inhomogeneous superconductivity arises when the species participating in the pairing phenomenon have different Fermi surfaces with a large enough separation. In these conditions it could be more favorable for each of the pairing fermions to stay close to its Fermi surface and, differently from the usual BCS state, for the Cooper pair to have a non zero total momentum. For this reason in this state the gap varies in space, the ground state is inhomogeneous and a crystalline structure might be formed. This situation was considered for the first time by Fulde, Ferrell, Larkin and Ovchinnikov, and the corresponding state is called LOFF. The spontaneous breaking of the space symmetries in the vacuum state is a characteristic feature of this phase and is associated to the presence of long wave-length excitations of zero mass. The situation described here is of interest both in solid state and in elementary particle physics, in particular in Quantum Chromo-Dynamics at high density and small temperature. In this review we present the theoretical approach to the LOFF state and its phenomenological applications using the language of the effective field theories.Comment: RevTex, 83 pages, 26 figures. Submitted to Review of Modern Physic

Pairing in nuclear systems: from neutron stars to finite nuclei

We discuss several pairing-related phenomena in nuclear systems, ranging from superfluidity in neutron stars to the gradual breaking of pairs in finite nuclei. We focus on the links between many-body pairing as it evolves from the underlying nucleon-nucleon interaction and the eventual experimental and theoretical manifestations of superfluidity in infinite nuclear matter and of pairing in finite nuclei. We analyse the nature of pair correlations in nuclei and their potential impact on nuclear structure experiments. We also describe recent experimental evidence that points to a relation between pairing and phase transitions (or transformations) in finite nuclear systems. Finally, we discuss recent investigations of ground-state properties of random two-body interactions where pairing plays little role although the interactions yield interesting nuclear properties such as 0+ ground states in even-even nuclei.Comment: 74 pages, 33 figs, uses revtex4. Submitted to Reviews of Modern Physic

Global Study of Nuclear Structure Functions

We present the results of a phenomenological study of unpolarized nuclear structure functions for a wide kinematical region of x and Q^2. As a basis of our phenomenology we develop a model which takes into account a number of different nuclear effects including nuclear shadowing, Fermi motion and binding, nuclear pion excess and off-shell correction to bound nucleon structure functions. Within this approach we perform a statistical analysis of available data on the ratio of the nuclear structure functions F_2 for different nuclei in the range from the deuteron to the lead. We express the off-shell effect and the effective scattering amplitude describing nuclear shadowing in terms of few parameters which are common to all nuclei and have a clear physical interpretation. The parameters are then extracted from statistical analysis of data. As a result, we obtain an excellent overall agreement between our calculations and data in the entire kinematical region of x and Q^2. We discuss a number of applications of our model which include the calculation of the deuteron structure functions, nuclear valence and sea quark distributions and nuclear structure functions for neutrino charged-current scattering.Comment: 67 pages, 18 figures (v3: updated text and references, a new section with discussion about relation between off-shell effect and modification of the nucleon size in nuclei, accepted for publication in Nucl. Phys. A

Realistic Model of the Nucleon Spectral Function in Few- and Many- Nucleon Systems

By analysing the high momentum features of the nucleon momentum distribution in light and complex nuclei, it is argued that the basic two-nucleon configurations generating the structure of the nucleon Spectral Function at high values of the nucleon momentum and removal energy, can be properly described by a factorised ansatz for the nuclear wave function, which leads to a nucleon Spectral Function in the form of a convolution integral involving the momentum distributions describing the relative and center-of-mass motion of a correlated nucleon-nucleon pair embedded in the medium. The Spectral Functions of $^3He$ and infinite nuclear matter resulting from the convolution formula and from many-body calculations are compared, and a very good agreement in a wide range of values of nucleon momentum and removal energy is found. Applications of the model to the analysis of inclusive and exclusive processes are presented, illustrating those features of the cross section which are sensitive to that part of the Spectral Function which is governed by short-range and tensor nucleon-nucleon correlations.Comment: 40 pages Latex , 16 ps figures available from the above e-mail address or from [email protected]