arXiv subjects
Publications and source records attributed to Eduardo de Rafael.
The contributions to the muon anomalous magnetic moment from hadronic vacuum polarization and from hadronic light-by-light scattering are reexamined within the frame work of chiral perturbation theory; the $1/N_c$-expansion; and the extended Nambu Jona-Lasinio model of low-energy QCD.
We discuss vector, axial-vector, scalar and pseudoscalar two-point functions at low and intermediate energies. We first review what is known from chiral perturbation theory, as well as from a heat kernel expansion within the context of the extended Nambu-Jona-Lasinio (ENJL) model of ref. \cite{12}. In this work we derive then these two-point functions to all orders in the momenta and to leading order in $1/N_c$. We find an improved high-energy behaviour and a general way of parametrizing them that shows relations between some of the two-point functions, which are also valid in the presence of gluonic interactions. The similarity between the shape of the experimentally known spectral functions and the ones we derive, is greatly improved with respect to those predicted by the usual constituent quark like models. We also obtain the scalar mass $M_S = 2 M_Q$ independent of the regularization scheme. In the end, we calculate fully an example of a nonleptonic matrix element in the ENJL--model, the $π^+-π^0$ electromagnetic mass difference and find good agreement with the measured value.
It is shown that in the constituent quark model of Georgi-Manohar, the dispersion relation that leads to the Adler-Weisberger sum rule for the axial vector coupling $g_A$ requires a subtraction constant. This fact explains the discrepancy between the results of different recent estimates of the $1/N_c$ corrections to Weinberg's large $N_c$ result $g_A=1$, where $N_c$ is the number of QCD colors. We also discuss a possible scenario which shows that $g_A=1$ might not be a necessary consequence of QCD in the large $N_c$ limit.
We present a derivation of the low energy effective action of an extended Nambu Jona-Lasinio (ENJL) model to $O(p^4)$ in the chiral counting. Two alternative scenarios are considered on how the ENJL model could originate as a low energy approximation to QCD. The low energy effective Lagrangian we derive includes the usual pseudoscalar Goldstone modes, as well as the lower scalar, vector and axial-vector degrees of freedom. By taking appropriate limits, we recover most of the effective low-energy models discussed in the literature; in particular the gauged Yang-Mills vector Lagrangian, the Georgi-Manohar constituent quark-meson model, and the QCD effective action approach model. Another property of the ensuing effective Lagrangian is that it incorporates most of the short-distance relations which follow from QCD. (We derive these relations in the presence of all possible gluonic interactions to leading order in the $1/N_c$-expansion.) Finally the numerical predictions are compared to the experimental values of the low energy parameters