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Phase diagram of neutron star quark matter in nonlocal chiral models

Phase diagram of neutron star quark matter in nonlocal chiral models. A. Gabriela Grunfeld Tandar Lab. – Buenos Aires ARGENTINA. In collaboration with D. Gomez Dumm N. N. Scoccola D. Blaschke. PLAN OF THE TALK. Motivation Non-local chiral quark models Numerical results Conclusions.

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Phase diagram of neutron star quark matter in nonlocal chiral models

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  1. Phase diagram of neutron star quark matterin nonlocal chiral models A. Gabriela Grunfeld Tandar Lab. – Buenos Aires ARGENTINA In collaboration with D. Gomez Dumm N. N. Scoccola D. Blaschke PLAN OF THE TALK • Motivation • Non-local chiral quark models • Numerical results • Conclusions

  2. Motivation The understanding of the behavior of strongly interacting matter at finite temperature and/or density is a subject of fundamental interest • Cosmology (early Universe) • Physics of RHIC • Physics of neutron stars Applications in:

  3. Problem: the study of strong interactions at finite temperature and/or density is a nontrivial task; rigorous theoretical approaches are not available yet • Development of effective models for interacting quark matter • that obey the symmetry requirements of the QCD Lagrangian • Inclusion of simplified quark interactions in a systematic way NJL model : the most simple and widely used model of this type The extension to NJL-like theories including nonlocal quark interactions represents a step towards a more realistic modeling of QCD. Several advantages over the NJL model: consistent description of loops and anomalies, some description of confinement, etc. Successful description of meson properties at T =  = 0 Bowler, Birse, NPA(95); Plant, Birse, NPA(98); Scarpettini, DGD, Scoccola, PRD(04)

  4. Formalism Euclidean action at T, m = 0 – Case of two active flavors mc(current quark mass), G and H parameters of the model We consider two alternative ways of introducing nonlocality : Model I (Instanton Liquid Model inspired) Model II (One Gluon Exchange interaction inspired) Here,r(x) and g(x) are nonlocal form factors, and

  5. The partition function for the model at T, m= 0 is given by We proceed by bosonizing the model, thus we introduce s and D bosonic fields and integrate out the quark fields Mean field approximation (MFA) : the bosonic fields are written as and fluctuations are dropped :

  6. The corresponding potential WMFA(T,mfc)for finite temperature T and chemical potential is obtained by replacing Matsubara frequencies ωn=(2n+1) p T The thermodynamical potential per unit volume reads then Here S-1 (inverse of the propagator) is a 48 x 48 matrix in Dirac, flavor, color and Nambu-Gorkov spaces ( 4 x 2 x 3 x 2 )

  7. The determinant can be analytically calculated : where Here we have defined with f = u,d , c = r,g,b and Due to the nonlocality, and are here momentum-dependent quantities

  8. In quark matter, the chemical potential matrix can be expressed in terms of the quark chemical potentialm(m = mB/3), the quark electric charge chemical potential mQ and the color chemical potential m8required to impose color neutrality The mean fields and can be obtained from the coupled gap equations : Q acts on flavor space, T8 over color space. The chemical potentials mfc are given by

  9. NEUTRON STARS (quark matter + electrons) Electric and colorcharge neutrality where + Beta equilibrium : (no neutrino trapping assumed)

  10. Numerical results For the nonlocal regulators we choose a smooth Gaussian form: Model parameters mc, G and L fixed so as to reproduce the empirical values of the pion mass and the pion decay constant at T= = 0, and leading to a condensate In this way, one obtains: Model I →GL2 = 15.41 mc = 5.1 MeV L = 971 MeV Model II → GL2 = 18.78 mc = 5.1 MeV L = 827 MeV There is no strong phenomenological constraint on the parameter H. Hence we consider here values of H/Gin the range from 0.5 to 1.0

  11. Typical behavior of MF quantities as functions of m for some representative values of T ( caseH/G = 0.75 ) Model I Model II

  12. Phase diagrams for different values of the ratio H/G Model I Model II

  13. Summary We have studied some chiral quark models with effective nonlocalcovariant separable quark-quark and quark-antiquark interactions at finite T andm. We find that: • Different quark matter phases can occur at low T and intermediate m: normal quark matter (NQM), superconducting quark matter (2SC) and mixed phase (NQM-2SC) states. • In the region of interest for applications to compact stars (medium mand low T), for the standard value H/G = 0.75 models I and II predict the presence of a mixed 2SC-NQM phase. The latter turns into a pure 2SC phase for larger H/G ratios. • Model I (ILM inspired) shows stronger SC effects. However, it leads to a relatively low value of TC (m = 0) in comparison with lattice expectations. Model II leads to a larger quark mass gap, and a larger value of TC(about 140 MeV), though SC region is smaller. • The critical T for the second order 2SC-NQM phase transitions rises with m for Model I while it is approximately m-independent for Model II. This can be understood from the different mdependences associated with the diquark gaps in both models. To be done: – Extension to larger m (strangeness, color-flavor locked phase) – Inclusion of vector-vector channels, hadronic matter effects, … – Implications on compact star sizes & radii – …

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