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Register a new userSpectroscopy and Renormalisation Group Flow of a Lattice Nambu-Jona-Lasinio Model
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We investigate a lattice Nambu--Jona-Lasinio model both by the Monte Carlo method and Schwinger-Dyson equations. A comparison allows the discussion of finite size effects and the extrapolation to infinite volume. We pay special attention to the identification of particles and resonances. This enables us to discuss renormalisation group flows in the neighbourhood of the critical coupling where the chiral symmetry breaking phase transition takes place. In no region of the bare parameter space do we find renormalisability for the model.
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We investigate the neighbourhood of the chiral phase transition in a lattice Nambu--Jona-Lasinio model, using both Monte Carlo methods and lattice Schwinger-Dyson equations.
A novel strategy to handle divergences typical of perturbative calculations is implemented for the Nambu--Jona-Lasinio model and its phenomenological consequences investigated. The central idea of the method is to avoid the critical step involved in the regularization process, namely the explicit evaluation of divergent integrals. This goal is achieved by assuming a regularization distribution in an implicit way and making use, in intermediary steps, only of very general properties of such regularization. The finite parts are separated of the divergent ones and integrated free from effects of the regularization. The divergent parts are organized in terms of standard objects which are independent of the (arbitrary) momenta running in internal lines of loop graphs. Through the analysis of symmetry relations, a set of properties for the divergent objects are identified, which we denominate consistency relations, reducing the number of divergent objects to only a few ones. The calculational strategy eliminates unphysical dependencies of the arbitrary choices for the routing of internal momenta, leading to ambiguity-free, and symmetry-preserving physical amplitudes. We show that the imposition of scale properties for the basic divergent objects leads to a critical condition for the constituent quark mass such that the remaining arbitrariness is removed. The model become predictive in the sense that its phenomenological consequences do not depend on possible choices made in intermediary steps. Numerical results are obtained for physical quantities at the one-loop level for the pion and sigma masses and pion-quark and sigma-quark coupling constants.
The effects of meson fluctuations are studied in a nonlocal generalization of the Nambu-Jona-Lasinio model, by including terms of next-to-leading order (NLO) in 1/N_c. In the model with only scalar and pseudoscalar interactions NLO contributions to the quark condensate are found to be very small. This is a result of cancellation between virtual mesons and Fock terms, which occurs for the parameter sets of most interest. In the quark self-energy, similar cancellations arise in the tadpole diagrams, although not in other NLO pieces which contribute at the sim 25% level. The effects on pion properties are also found to be small. NLO contributions from real $pipi$ intermediate states increase the sigma meson mass by $sim 30%$. In an extended model with vector and axial interactions, there are indications that NLO effects could be larger.
We derive the critical temperature in a nonlocal Nambu-Jona-Lasinio model with the presence of a chiral chemical potential. The model we consider uses a form factor derived from recent studies of the gluon propagator in Yang-Mills theory and has the property to fit in excellent way the form factor arising from the instanton liquid picture for the vacuum of the theory. Nambu-Jona-Lasinio model is derived form quantum chromodynamics providing all the constants of the theory without any need for fits. We show that the critical temperature in this case always exists and increases as the square of the chiral chemical potential. The expression we obtain for the critical temperature depends on the mass gap that naturally arises from Yang-Mills theory at low-energy as also confirmed by lattice computations.
The formalism of Riemannian geometry is applied to study the phase transitions in Nambu -Jona Lasinio (NJL) model. Thermodynamic geometry reliably describes the phase diagram, both in the chiral limit and for finite quark masses. The comparison between the geometrical study of NJL model and of (2+1) Quantum Chromodynamics at high temperature and small baryon density shows a clear connection between chiral symmetry restoration/breaking and deconfinement/confinement regimes.
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