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Register a new userThe Linear Sigma Model and the formation of a charged pion condensate in the presence of an external magnetic field
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We discuss the charged pion condensation phenomenon in the linear sigma model, in the presence of an external uniform magnetic field. The critical temperature is obtained as a function of the external magnetic field, assuming the transition is of second order, by considering a dilute gas at low temperature. As a result we found magnetic anti-catalysis in the Bose-Einstein condensation for lower values of the external magnetic field, and catalysis for higher values of the external magnetic field. This behavior confirms previous results with a single charged scalar field.
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We use the linear sigma model with quarks to find the magnetic field-induced modifications to the neutral pion mass at one-loop level. The magnetic field effects are introduced by using charged particle propagators in the presence of a magnetic background in the strong field regime. We show that when accounting for the effects of the magnetic field on the model couplings, the vacuum sigma field and the neutral pion self-energy, the neutral pion mass decreases monotonically as a function of the field strength. We find an excellent qualitative and quantitative agreement with recent lattice QCD calculations, reproducing the monotonically decreasing trend with the field strength as well as the decrease when lattice data approaches the physical vacuum pion mass from larger values.
We calculate the neutral pion mass in the presence of an external magnetic field of arbitrary strength in the framework of the linear sigma model coupled to quarks at zero temperature. We find nonmonotonic behavior of the pion mass as a function of magnetic field. We are also able to reproduce existing results for the weak-field approximation.
In this work, the self energies of $pi^0$ and $pi^{pm}$ up to one loop order have been calculated in the limit of weak external magnetic field. The effective masses are explicitly dependent on the magnetic field which are modified significantly for the pseudoscalar coupling due to weak field approximation of the external field. On the other hand, for the pseudovector coupling, there is a modest increment in the effective masses of the pions. These theoretical developments are relevant for the study of the phenomenological aspect of mesons in the context of neutron stars as well as heavy ion collisions.
The classical relationship between the Tutte polynomial of graph theory and the Potts model of statistical mechanics has resulted in valuable interactions between the disciplines. Unfortunately, it does not include the external magnetic fields that appear in most Potts model applications. Here we define the V-polynomial, which lifts the classical relationship between the Tutte polynomial and the zero field Potts model to encompass external magnetic fields. The V-polynomial generalizes Nobel and Welshs W-polynomial, which extends the Tutte polynomial by incorporating vertex weights and adapting contraction to accommodate them. We prove that the variable field Potts model partition function (with its many specializations) is an evaluation of the V-polynomial, and hence a polynomial with deletion-contraction reduction and Fortuin-Kasteleyn type representation. This unifies an important segment of Potts model theory and brings previously successful combinatorial machinery, including complexity results, to bear on a wider range of statistical mechanics models.
We extend the standard second order effective chiral Lagrangian of pions and nucleons by considering the coupling to an external gravitational field. As an application we calculate one-loop corrections to the one-nucleon matrix element of the energy-momentum tensor to fourth order in chiral counting, and next-to-leading order tree-level amplitude of the pion-production in an external gravitational field. We discuss the relation of the obtained results to experimentally measurable observables. Our expressions for the chiral corrections to the nucleon gravitational form factors differ from those in the literature. That might require to revisit the chiral extrapolation of the lattice data on the nucleon gravitational form factors obtained in the past.
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