Phase transition to color-flavor-locked matter and condensation of Goldstone bosons in neutron star matter

Deconfinement phase transition and condensation of Goldstone bosons in neutron star matter are investigated in a chiral hadronic model (also referred as to the FST model) for the hadronic phase (HP) and in the color-flavor-locked (CFL) quark model for the deconfined quark phase. It is shown that the hadronic-CFL mixed phase (MP) exists in the center of neutron stars with a small bag constant, while the CFL quark matter cannot appear in neutron stars when a large bag constant is taken. Color superconductivity softens the equation of state (EOS) and decreases the maximum mass of neutron stars compared with the unpaired quark matter. The K⁰ condensation in the CFL phase has no remarkable contribution to the EOS and properties of neutron star matter. The EOS and the properties of neutron star matter are sensitive to the bag constant B, the strange quark mass m_s and the color superconducting gap Δ. Increasing B and m_s or decreasing Δ can stiffen the EOS which results in the larger maximum masses of neutron stars.     

Isospin breaking in nuclear physics: The Nolen-Schiffer effect

Using the QCD sum rules we calculate the neutron-proton mass difference at zero density as a function of the difference in bare quark massm _d—m _u. We confirm results of Hatsuda, Høgaasen and Prakash that the largest term results from the difference in up and down quark condensates, the explicitC(m _d—m _u) entering with the opposite sign. The quark condensates are then extended to finite density to estimate the Nolen-Schiffer effect. The neutron-proton mass difference is extremely density dependent, going to zero at roughly nuclear matter density.The Ioffe formula for the nucleon mass is interpreted as a derivation, within the QCD sum rule approach, of the Nambu-Jona-Lasinio formula. This clarifies theN _c counting and furthermore provides an alternative interpretation of the Borel mass.     

Stars of strange matter?

We investigate suggestions that quark matter with strangeness per baryon of order unity may be stable. We model this matter at nuclear matter densities as a gas of close packed Λ-particles. From the known mass of the Λ-particle we obtain an estimate of the energy and chemical potential of strange matter at nuclear densities. These are sufficiently high to preclude any phase transition from neutron matter to strange matter in the region near nucleon matter density. Including effects from gluon exchange phenomenologically, we investigate higher densities, consistently making approximations which underestimate the density of transition. In this way we find a transition density ρ_tr≳7ρ₀, where ρ₀ is nuclear matter density is not far from the maximum density in the center of the most massive neutron stars that can be constructed. Since we have underestimated ρ_tr and still find it to be ∼7ρ₀, we do not believe that the transition from neutron to quark matter is likely in neutron stars. Moreover, measured masses of observed neutron stars are ≅1.4 M_⊙, where M_⊙ is the solar mass. For such masses, the central (maximum) density is ρ_c<5ρ₀. Transition to quark matter is certainly excluded for these densities.     

Cooling of a compact star with LOFF matter core

Specific heat and neutrino emissivity due to direct URCA processes for quark matter in the color superconductive Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of Quantum-Chromodynamics have been evaluated. The cooling rate of simplified models of compact stars with a LOFF matter core is estimated. The text was submitted by the author in English.     

Effects of mesonic correlations in the QCD phase transition

The finite-temperature phase transition of strongly interacting matter is studied within a nonlocal chiral quark model of the NJL type coupled to a Polyakov loop. In contrast to previous investigations which were restricted to the mean-field approximation, mesonic correlations are included by evaluating the quark-antiquark ring sum. For physical pion masses, we find that the pions dominate the pressure below the phase transition, whereas above T _c the pressure is well described by the mean-field-approximation result. For large pion masses, as realized in lattice simulations, the meson effects are suppressed. The text was submitted by the authors in English.     

Mass and mixing angle predictions from infra-red fixed points

It is argued that low energy parameters, such as masses and mixing angles, may be related by the infra-red fixed points of the underlying field theory. For the Kobayashi-Maskawa 6 quark model the infra-red fixed points predicts the top quark mass m_t = 135 GeV and the Higgs mass m_H = 72 GeV. The implications for the mixing angles and phase are discussed and we also show that grand unification predictions should not be significantly affected.     

The ferromagnetic phase of quark matter in the framework of one gluon exchange and thermodynamics with the density-temperature-dependent particle mass model

In the current work we examine the possibility of ferromagnetism phase of quark matter by using the one gluon exchange interaction and the thermodynamics with the density-temperature-dependent particle masses as well as the normal thermodynamics (with constant masses). We calculate the free energy per particle of the polarized and unpolarized states to discuss the difference between these two phases at various densities and temperatures. In our calculations we assume that the QCD coupling, α_c, is constant (the simple model) or varies with the temperature and the density (the asymptotic freedom); but we keep α_c less than one, because we intend to use the perturbation method to calculate the exchange energy. We also assume that the up and down quarks are massless and do not interact. Only the strange quarks interact with each other via the one gluon exchange interaction. The free and internal energies as well as the effective masses and the pressure are calculated at different densities and temperatures. The results are discussed and a comparison is made with those of Tatsumi. Finally it is shown that the present models do not predict any transition for the strange quark matter to its ferromagnetic phase.     

The Flavor Physics in Unified Gauge Theory from an S3 × P Discrete Symmetry

We investigate the phenomenological implication of the discrete symmetry S₃ × P on flavor physics in SO(10) unified theory. We construct a minimal renormalizable model which reproduce all the masses and mixing angle of both quarks and leptons. As usually the SO(10) symmetry gives up to relations between the down sector and the charged lepton masses. The underlining discrete symmetry gives a contribution (from the charged lepton sector) to the PMNS mixing matrix which is bimaximal. This gives a strong correlation between the down quark and charged lepton masses, and the lepton mixing angles. We obtain that the small entries V _ub, V _cb, V _td, and V _ts in the CKM matrix are related to the small value of the ratio δ m² _solΔ m² _atm: they come from both the S₃×P structure of our model and the small ratio of the other quark masses with respect to m _t. Wonderfully, with our model, we fit 17 experimental data %with only 13 free relevant combinations of vevs.     

Quark matter formation in dense stellar objects

It is expected that at very large densities and/or temperatures a quark-hadron phase transition takes place. Lattice QCD calculations at zero baryon density indicate that the transition occurs at T _c ∼ 150–170 MeV. The transition is likely to be second order or a cross over phenomenon. Although not much is known about the density at which the phase transition takes place at small temperatures, it is expected to occur around the nuclear densities of few times nuclear matter density. Also, there is a strong reason to believe that the quark matter formed after the phase transition is in colour superconducting phase. The matter densities in the interior of neutron stars being larger than the nuclear matter density, the neutron star cores may possibly consist of quark matter which may be formed during the collapse of supernova. Starting with the assumption that the quark matter, when formed consists of predominantly u and d quarks, we consider the evolution of s quarks by weak interactions in the present work. The reaction rates and time required to reach the chemical equilibrium are computed here. Our calculations show that the chemical equilibrium is reached in about 10⁻⁷ seconds. Further more during the equilibration process enormous amont of energy is released and copious numbers of neutrinos are produced. Implications of these on the evolution of supernovae will be discussed.     

Superfluidity in dense nuclear matter

We discuss the onset of superfluidity in neutron stars, where the model of nuclear matter is realized in a high-density and asymmetry state. In particular, we present the study of the effects of microscopic three-body forces on the proton pairing in the ¹ S ₀ channel and neutron pairing in ³ PF ₁ channel for β-stable neutron star matter. It is found that the main effects of three-body forces are to shrink the domain of existence of the ¹ S ₀ below the threshold of the direct URCA process and to stretch the density range of the ³ PF ₁ pairing in a broad domain so to cover most part of the neutron-star core. The text was submitted by the authors in English.     

Core collapse supernovae in the QCD phase diagram

We compare two classes of hybrid equations of state with a hadron-to-quark matter phase transition in their application to core collapse supernova simulations. The first one uses the quark bag model and describes the transition to three-flavor quark matter at low critical densities. The second one employs a Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model with parameters describing a phase transition to two-flavor quark matter at higher critical densities. These models possess a distinctly different temperature dependence of their transition densities which turns out to be crucial for the possible appearance of quark matter in supernova cores. During the early post-bounce accretion phase quark matter is found only if the phase transition takes place at sufficiently low densities as in the study based on the bag model. The increase critical density with increasing temperature, as obtained for our PNJL parametrization, prevents the formation of quark matter. The further evolution of the core collapse supernova as obtained applying the quark bag model leads to a structural reconfiguration of the central protoneutron star where, in addition to a massive pure quark matter core, a strong hydrodynamic shock wave forms and a second neutrino burst is released during the shock propagation across the neutrinospheres. We discuss the severe constraints in the freedom of choice of quark matter models and their parametrization due to the recently observed 2M _?? pulsar and their implications for further studies of core collapse supernovae in the QCD phase diagram.     

Bulk viscosity of strange quark matter in density dependent quark mass model

We have studied the bulk viscosity of strange quark matter in the density dependent quark mass model (DDQM) and compared results with calculations done earlier in the MIT bag model where u, d masses were neglected and first order interactions were taken into account. We find that at low temperatures and high relative perturbations, the bulk viscosity is higher by 2 to 3 orders of magnitude while at low perturbations the enhancement is by 1–2 order of magnitude as compared to earlier results. Also the damping time is 2–3 orders of magnitude lower implying that the star reaches stability much earlier than in MIT bag model calculations.     

Quark mass and the masses of Goldstone bosons

Based on the Dyson-Schwinger Equations (DSEs) of QCD in the “rainbow” approximation, the fully dressed quark propagator S _f (p) is investigated, and then an algebraic parametrization form of the propagator is obtained as a solution of the equations. The dressed quark amplitudes A _f and B _f which built up the fully dressed quark propagator, and the dynamical running masses M _f , which is defined by A _f and B _f for light quarks u, d and s, are calculated, respectively. Using the predicted current masses m _f , quark local vacuum condensates, and our predicted value of pion decay constant, the masses of Goldstone bosons K, π and η and their in-medium values are also evaluated. Our predictions fit to data and to many other different calculations quite well. The numerical results show that the mass of quark is dependent of its momentum p ². The fully dressed quark amplitudes A _f and B _f have correct behaviors and can be used for many purposes in our future researches on non-perturbative QCD.      

Calculation of the pseudoscalar masses from a QCD effective potential

We calculate the effective two-loop potential of QCD with massive quarks in the CJT composite operator formalism. To perform the wave-function renormalization of composite operators we are lead to a condition which corresponds to the Adler-Dashen requirement in the limit of vanishing quark masses. The condition also assures absence of spontaneous breaking of parity. Pseudoscalar masses are calculated from the second derivatives of the effective potential, and a fit is obtained for quark masses m_u = 3.6 MeV, m_d = 7 MeV, m_s = 152 MeV. We also comment on consistuent quark masses and on the effect of heavy quarks.     

Relations between SU(2)- and SU(3)-LECs in chiral perturbation theory

Chiral perturbation theory in the two-flavour sector allows one to analyse Green functions in QCD in the limit where the strange quark mass is considered to be large in comparison to the external momenta and to the light quark masses m _u and m _d . In this framework, the low-energy constants of SU(2) _R × SU(2) _L depend on the value of the heavy quark masses. For the coupling constants which occur at order p ² and p ⁴ in the chiral expansion, we worked out in [1] the dependence on the strange quark mass at two-loop accuracy, and provided in [2] analogous relations for some of the couplings c _i which are relevant at order p ₆. This talk comments on the methods used, and illustrates implications of the results obtained.     

Quark model predictions on the masses of heavier vector mesons

We use the quark model considerations of Federman, Rubinstein and Talmi and the relation (m _ψ/m _ϕ)≃(m _ϒ/m _ψ)≃(m _ϒ/m _ϒ) to compute the masses of beautiful and tasty vector mesons.     

Heavy hybrid stars from multi-quark interactions

We explore the possibility of obtaining heavy hybrid stars within the framework of the two flavor Nambu-Jona-Lasinio model that includes 8-quark interactions in the scalar and in the vector channel. The main impact of the 8-quark scalar channel is to reduce the onset of quark matter, while the 8-quark vector channel acts to stiffen the equation of state at high densities. Within the parameter space where the 4-quark vector channel is small, and the 8-quark vector channel sizeable, stable stars with masses of 2 M _⊙ and above are found to hold quark matter in their cores.

     

Radiative transmission of lepton flavor hierarchies

We discuss a one loop model for neutrino masses which leads to a seesaw-like formula with the difference that the charged lepton masses replace the unknown Dirac mass matrix present in the usual seesaw case. This is a considerable reduction of parameters in the neutrino sector and predicts a strong hierarchical pattern in the right handed neutrino mass matrix that is easily derived from a U(1)_H family symmetry. The model is based on the left–right gauge group with an additional Z₄ discrete symmetry which gives vanishing neutrino Dirac masses and finite Majorana masses arising at the one loop level. Furthermore, it is one of the few models that naturally allow for large (but not necessarily maximal) mixing angles in the lepton sector. A generalization of the model to the quark sector requires three iso-spin singlet vector-like down type quarks, as in E₆. The model predicts an inert doublet type scalar dark matter.     

Empirical lepton-quark mass formula: Four dimensional state space for fermion structure?

It is observed that a simple mass formula of the formm =¯mQ ²(exp) is wholly consistent with experimental measurements and quark model estimates for all 12 fundamental fermions. Here¯m = 433.3 MeV is an input (mean fermion mass) constant,Q is the charge number of the lepton or quark, and is a real root of a quartic equation that brings in a principal quantum numbern (= 0, 1, 2, 3). The charged lepton masses are given accurately to within 0.3 of 1%, all neutrino masses are zero, and the top mass is predicted by the formula to be close tom _t = 163.6 GeV.     

Spectrum of strange mesons

An energy eigenstates equation for mesons is derived and the energy levels of strange mesons are calculated and compared with those observed. For equal quark masses (m _u =m _d ) the mass formula reduces to the mass formula describing nonflavored mesons withI=1.