The role of form factors in hadron resonances

Abstract

A phenomenological structure is proposed for the couplings of hadron resonances to the 56 baryons and 36 mesons with a view to exploring the possibilities of detailed dynamical applications of resonance data to several other areas of particle physics where these have relevance. The group structure used for hadron (H, H_L) classifications is that of SU(6) × O(3), while the basic framework for a unified description of the H̅PH_L and H̅VH_L interactions is provided by broken SU(3)×SU(3), or partial symmetry, in conjunction with the language (not dynamics) of the quark model. The coupling structures are expressed in terms of generalized Rarita-Schwinger fields and a Lorentz-invariant form factor (f_L) for whose construction a general set of criteria is proposed at the phenomenological level. One explicit construction of the form x^L, satisfying the requirements of crossing symmetry and consistent with Regge universality of the reduced coupling constant (g_L) together with a common form of parametrization for B̅B_LM and MM_LM couplings, is obtained. The coupling structures not only account satisfactorily for several "difficult" branching ratios in baryon decays but also give (i) the observed "transverse" angular distribution in B → ωπ decay and (ii) a ratio (h₁/h₀) ≈ 0.57 of the helicity amplitudes for A₁ → ϱ π in rather good agreement with experiment. A PCAC relation between the A₁ϱπ and ϱππ coupling constants which is derivable in a simple way within this framework is found to be in very good agreement with the value of the meson (L = 1) supermultiplet coupling constant g̅₁ determined from the tensor meson decays. The mathematics of an explicit application of the model, viz., u-channel π^- - p scattering through the exchange of Δ-resonances in the spirit of the Van Hove model, is worked out in some detail to bring out the practical applicability of the model, especially in the intermediate energy region. Several other applications, viz., ranging from photo- and electroproduction of resonances to their effects on electromagnetic mass differences in hadrons, are discussed with special reference to the role of the form factor.