Bare current-quark masses, inelastic reactions and light-cone algebra

Abstract

Relations connecting the effective bare current-quark masses with asymptotic meson-nucleon and lepton-nucleon scattering are derived by making use of the extended light-cone algebra which includes commutators of pseudoscalar densities. The commutators are relevant to meson-nucleon scattering amplitudes since the pseudoscalar densities act as fields of the (composite) mesons. Assuming pomeron-exchanged Regge behaviour, sufficient analyticity in the meson mass-squared variable is established to obtain finite-mass dispersion and superconvergence relations. Making additionally certain other reasonable assumptions, we are then able to show how these relations yield testable connections among the asymptotic πN and KN total cross sections, the structure functions of the deep inelastic lepton-nucleon scattering (for the scaling variable, ξ→0) and the bare current-quark masses μ_{p, n, λ} that appear essentially as parametrising the breaking of the chiral SU(3)⊗SU(3) symmetry. One interesting consequence of our results is at the Llewellyn-Smith inequality on the said structure functions should be experimentally satisfied as a near equality for ξ→0, if chiral SU(2)⊗SU(2) turns out to be a rather good symmetry of nature. Moreover, taking the specific symmetry breaking model of Gell-Mann Oakes and Renner, we find that μ_{p, n}≈35 MeV and μ_λ≈800 MeV.