ABSTRACT
We show that the matrix element of a local operator between hadronic states can be used to unambiguously define the associated spatial density. As an explicit example, we consider the charge density of a spinless particle and clarify its relationship to the electric form factor. Our results lead to an unconventional interpretation of the spatial densities of local operators and their moments.
ABSTRACT
We consider an extension of the one-nucleon sector of baryon chiral perturbation theory beyond the low-energy region. The applicability of this approach for higher energies is restricted to small scattering angles, i.e. the kinematical region, where the quark structure of hadrons cannot be resolved. The main idea is to re-arrange the low-energy effective Lagrangian according to a new power counting and to exploit the freedom of the choice of the renormalization condition for loop diagrams. We generalize the extended on-mass-shell scheme for the one-nucleon sector of baryon chiral perturbation theory by choosing a sliding scale, that is, we expand the physical amplitudes around kinematical points beyond the threshold. This requires the introduction of complex-valued renormalized coupling constants, which can be either extracted from experimental data, or calculated using the renormalization group evolution of coupling constants fixed in threshold region.
ABSTRACT
It is shown that both the universal coupling of the rho meson and the Kawarabayashi-Suzuki-Riadzuddin-Fayyazuddin expression for the magnitude of its coupling constant follow from the requirement that chiral perturbation theory of pions, nucleons, and rho mesons is a consistent effective field theory. The prerequisite of the derivation is that all ultraviolet divergences can be absorbed in the redefinition of fields and the available parameters of the most general effective Lagrangian.