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Register a new userSymmetries and Ambiguities in the linear sigma model with light quarks
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Authors
E. W. Dias
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We investigate the role of undetermined finite contributions generated by radiative corrections in a $SU(2)times SU(2)$ linear sigma model with quarks. Although some of such terms can be absorbed in the renormalization procedure, one such contribution is left in the expression for the pion decay constant. This arbitrariness is eliminated by chiral symmetry.
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We compute the critical temperature for the chiral transition in the background of a magnetic field in the linear sigma model, including the quark contribution and the thermo-magnetic effects induced on the coupling constants at one loop level. We show that the critical temperature decreases as a function of the field strength. The effect of fermions on the critical temperature is small and the main effect on this observable comes from the charged pions. The findings support the idea that the anticatalysis phenomenon receives a contribution due only to quiral symmetry effects independent of the deconfinement transition.
We compute the magnetic field-induced modifications to the boson self-coupling and the boson-fermion coupling, in the static limit, using an effective model of QCD, the linear sigma model with quarks. The former is computed for arbitrary field strengths as well as using the strong field approximation. The latter is obtained in the strong field limit. The arbitrary field result for the boson self-coupling depends on the ultraviolet renormalization scale and this dependence cannot be removed by a simple vacuum subtraction. Using the strong field result as a guide, we find the appropriate choice for this scale and discuss the physical implications. The boson-fermion coupling depends on the Schwingers phase and we show how this phase can be treated consistently in such a way that the magnetic field induced vertex modification is both gauge invariant and can be written with an explicit factor corresponding to energy-momentum conservation for the external particles. Both couplings show a modest decrease with the field strength.
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.
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.
A very specific two-Higgs-doublet extension of the Glashow-Salam-Weinberg model for one generation of quarks is advocated for, in which the two doublets are parity transformed of each other and both isomorphic to the Higgs doublet of the Standard Model. The chiral group U(2)_L X U(2)_R gets broken down to U(1) X U(1)_{em}. In there, the first diagonal U(1) is directly connected to parity through the U(1)_LX U(1)_R algebra. Both chiral and weak symmetry breaking can be accounted for, together with their relevant degrees of freedom. The two Higgs doublets are demonstrated to be in one-to-one correspondence with bilinear quark operators.
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