arXiv subjects
Publications and source records attributed to B. Hiller.
An implicit four dimensional regularization is applied to calculate the axial-vector-vector anomalous amplitude. The present technique always complies with results of Dimensional Regularization and can be easily applied to processes involving odd numbers of $γ_5$ matrices. This is illustrated explicitely in the example of this letter.
We calculate the width for the omega -> pi pi decay in nuclear medium. Chiral dynamics and low-density approximation are used. At densities around twice the nuclear saturation density we estimate the partial width for the decay of the longitudinal mode to be of the order of a few tens of MeV, and for the transverse mode a few times less.
The problem of the $ρ$ meson resonance solution in the extended NJL model is studied. It has been shown previously that the solution for the $ρ$ meson changes smoothly from a bound state to a "virtual state" when the vector channel attraction becomes too weak to support bound state solutions. We have found that together with these solutions a separate resonance branch appears which is not connected smoothly with the bound state solutions. At small values of constituent quark mass, $m\sim 200$ MeV, it corresponds to the physical vector meson resonance solution in the quark-continuum region. The $a_1$ and $σ$ resonances are also discussed.
We calculate the one-quark-loop amplitude for the low energy $γγ\toππ$ collision in the context of the Nambu and Jona-Lasinio model with scalar and pseudoscalar four quark couplings to all orders in the external momenta. We show that the NJL predictions for the $γγ\toπ^+π^-$ reaction are not far from the Born amplitude, which is close to the data, and is compatible with the chiral perturbation theory estimations. We determine the corrections given by the NJL model in leading order of $1/N_c$ to the chiral loop amplitude for $γγ\toπ^0π^0$. Numerical results for the $γγ\rightarrowππ$ cross sections and for pion polarizabilities are given.
The momentum-space bosonization method of a Nambu and Jona-Lasinio type model with vector and axial-vector mesons is applied to $ππ$ scattering. Unlike the case in earlier published papers, we obtain the $ππ$ scattering amplitude using the linear and nonlinear realizations of chiral symmetry and fully taking into account the momentum dependence of meson vertices. We show the full physical equivalence between these two approaches. The chiral expansion procedure in this model is discussed in detail. Chiral expansions of the quark mass, pion mass and constant $f_π$ are obtained. The low-energy $ππ$ phase shifts are compared to the available data. We also study the scalar form factor of the pion.
We calculate the momentum dependence of three particle vertices $σγγ$, $σργ$ and $σρρ$ in the context of a Nambu Jona Lasinio type model. We show how they influence the processes $γγ\rightarrow σ\rightarrow ππ$, $ρ\rightarrow γσ$ and $γγ\rightarrow ρρ$ and how chiral symmetry shadows the presence of the $σ$.
We investigate strong and radiative meson decays in a generalized Nambu--Jona-Lasinio model. The one loop order calculation provides a satisfactory agreement with the data for the mesonic spectrum and for radiative decays. Higher order effects for strong decays of $ρ$ and $K^*$ are estimated to be large. We also discuss the role of the flavour mixing determinantal interaction.