O(N)model within theΦ-derivable expansion to orderλ2: On the

Abstract

We discuss various aspects of the O(N )-model in the vacuum and at finite temperature within the Φ-derivable expansion scheme to order λ 2 . In continuation of an earlier work, we look for a physical parametrization in the N = 4 case that allows us to accommodate the lightest mesons. Using zero-momentum curvature masses to approximate the physical masses, we find that, in the parameter range where a relatively large sigma mass is obtained, the scale of the Landau pole is lower compared to that obtained in the two-loop truncation. This jeopardizes the insensitivity of the observables to the ultraviolet regulator and could hinder the predictivity of the model. Both in the N = 1 and N = 4 cases, we also find that, when approaching the chiral limit, the (iterative) solution to the Φ-derivable equations is lost in an interval around the would-be transition temperature. In particular, it is not possible to conclude at this order of truncation on the order of the transition in the chiral limit. Because the same issue could be present in other approaches, we investigate it thoroughly by considering a localized version of the Φ-derivable equations, whose solution displays the same qualitative features, but allows for a more analytical understanding of the problem. In particular, our analysis reveals the existence of unphysical branches of solutions which can coalesce with the physical one at some temperatures, with the effect of opening up a gap in the admissible values for the condensate. Depending on its rate of growth with the temperature, this gap can eventually engulf the physical solution.

New algorithm to study the pseudo-Wigner solution of the quark gap equation in the framework of the ( 2+1 )-flavor NJL model

“…It is noted that the previous studies also throw light on the loss of solutions of the gap equation [35,50]. Similar to the analysis in these papers, the algorithm we employ in this paper also meet this issue when dealing with the evolution from the Wigner solution to the pseudo-Wigner solution, because the derivatives of the effective quark masses M 0 u , M 0 s might diverge for some values of (T, μ) as the current quark mass increases.…”

New algorithm to study the pseudo-Wigner solution of the quark gap equation in the framework of the (2+1)-flavor NJL model

“…It is noted that the previous studies also throw light on the loss of solutions of the gap equation [35,50]. Similar to the analysis in these papers, the algorithm we employ in this paper also meet this issue when dealing with the evolution from the Wigner solution to the pseudo-Wigner solution, because the derivatives of the effective quark masses M ′ u , M ′ s might diverge for some values of (T, µ) as the current quark mass increases.…”

One-loop constituent quark contributions to the vector and axial-vector meson curvature mass

“…In this localized approximation the dressed bosonic inverse propagator appearing in ( 7) is of tree-level type, just that the tree-level mass is replaced by the one-loop curvature mass M 2 (φ) ≡ m2 (φ)+Π(K = 0; φ). Since with a homogeneous scalar background the curvature mass does not depend on the momentum, the renormalization of the integral becomes an easy task, as discussed in [23] (see also (58) in Sec. V).…”

“…The superscripts indicate the absence or the presence of statistical factors in the respective integrands. In a covariant calculation the vacuum part T (0) (m f ) is the integral in (23), while in a noncovariant calculation it is…”