QCD Short-distance constraints and hadronic approximations

Abstract

This paper discusses a general class of ladder resummation inspired hadronic approximations. It is found that this approach naturally reproduces many successes of single meson per channel saturation models (e.g. VMD) and NJL based models. In particular the existence of a constituent quark mass and a gap equation follows naturally. We construct an approximation that satisfies a large set of QCD shortdistance and large N c constraints and reproduces many hadronic observables.We show how there exists in general a problem between QCD short-distance constraints for Green Functions and those for form factors and cross-sections following from the quark-counting rule. This problem while expected for Green functions that do not vanish in purely perturbative QCD also persists for many Green functions that are order parameters.

The vector form factor at the next-to-leading order in 1/N C : chiral couplings L9(μ) and C88(μ) − C90(μ)

“…1 In ref. [20], it has been argued that large discrepancies may occur between the values of the masses and couplings of the full large-N C theory and those from descriptions with a finite number of resonances. Even in this case, it is found that one can obtain safe determinations of the LECs as far as one is able to construct a good interpolator that reproduces the right asymptotic behaviour at low and high energies.…”

ChPT Progress on Non-Leptonic and Radiative Kaon Decays

“…This strategy is both complementary and necessary, see for instance [23,50,52] as unique probes unveiling physics beyond the SM. For recent efforts in that direction using large N c hadronic approaches see [58,62,63] and references therein. Lattice proposals to study radiative kaon decays also appeared [64] while I refer to Chris Sachrajda and Bob Mawhinney's talks at this Conference for non-leptonic kaon decays lattice efforts.…”

A rational approach to resonance saturation in large-NcQCD

“…[16]. In this paper it was observed that it is impossible to satisfy the large momentum fall-off expected in large-N c QCD for the form factors which can be defined through a three-point Green's function, if the sum over resonances in the Green's function is restricted to a finite set.…”