Two-loop calculations with vertex corrections in the Walecka model

Abstract

Two-loop corrections with scalar and vector form factors are calculated for nuclear matter in the Walecka model. The on-shell form factors are derived from vertex corrections within the framework of the model and are highly damped at large spacelike momenta. The two-loop corrections are evaluated first by using the one-loop parameters and mean fields and then by refitting the total energy/baryon to empirical nuclear matter saturation properties. The modified two-loop corrections are significantly smaller than those computed with bare vertices. Contributions from the anomalous isoscalar form factor of the nucleon are included for the first time. The effects of the implicit density dependence of the form factors, which arise from the shift in the baryon mass, are also considered. Finally, necessary extensions of these calculations are discussed.Typeset using REVT E X where F µν = ∂ µ V ν − ∂ ν V µ and δL contains the counterterms. We observe that the off-shell vertex functions should be used in a fully satisfactory calculation with loops. A full offshell calculation is quite complicated, however, as one needs to know the off-shell behavior of the vertices at all spacelike momenta, as well as the modification of the vertices in the presence of valence nucleons at finite density. Calculations exploring these off-shell vertex functions are in progress [19]. Here, as a first step, we use an on-shell approximation, in which the off-shell vertex functions are replaced by their on-shell forms at zero density. This procedure is analogous to that used in Refs. [15] and [16], where parametrized, on-shell form factors were used at the vertices, except that we use form factors obtained from within our model. Note also that the form factors used in Refs. [15] and [16] were chosen to have

Kaons in dense matter, kaon production in heavy-ion collisions, and kaon condensation in neutron stars

“…[81,82]. Instead of the usual linear and non-linear σ-ω [83] as in Refs. [80][81][82], we base our model on an effective chiral Lagrangian recently developed by Furnstahl, Tang, and Serot [31], which will also be used in our studies of neutron star properties.…”

Matter induced ϱ - ω mixing

“…with E * (| k|) = | k| 2 + M * 2 , M * being the effective mass of the nucleon in nuclear matter [8]. This density dependent shift of the nucleon mass (M → M * ) in nuclear matter is estimated, for the present purpose, by solving the self-consistent equation within the framework of the Walecka Model [8,9].…”

“…involving θ(k F −| k|), arising from Pauli blocking, describes the modifications of the same in the nuclear matter at zero temperature [8], as it deletes the on mass-shell propagation of the nucleon in nuclear matter with momenta below the Fermi momentum. Finite temperature effects may be incorporated by replacing the Heaviside θ-function by the Fermi distribution, but the main features to be exposed in this letter are not modified significantly.…”

“…This density dependent shift of the nucleon mass (M → M * ) in nuclear matter is estimated, for the present purpose, by solving the self-consistent equation within the framework of the Walecka Model [8,9]. The first term in G(k), namely G F (k), is the same as the free propagator of a spin 1 2 fermion, except for the fact that the effective mass of the nucleon in nuclear matter is to be used, while the second part,…”

Shape coexistence around 1644S28: The deformed N = 28 region

“…The basic building blocks in the relativistic mean-field approach [30] are the baryons (protons and neutrons) and the σ−, ω−, and ρ− mesons. The σ-meson is assumed to move in a non-linear potential…”