ar X iv : h ep - p h / 95 02 24 4 v 1 7 F eb 1 99 5 E 2 / M 1 Ratio for the γN → ∆ Transition in the Chiral Quark Soliton Model

We calculate the electric quadrupole to magnetic dipole transition ratio E2/M1 for the reaction γN → ∆(1232) in the chiral quark soliton model. The calculated E2/M1 ratio is in a good agreement with the very new experimental data. We obtain non-zero negative value for the electric quadrupole N −∆ transition moment, which suggests an oblate deformed charge structure of the nucleon or/and the delta isobar. Other observables related to this quantity, namely the N −∆ mass splitting, the isovector charge radius, and isovector magnetic moment, are properly reproduced as well. PACS number(s):12.39.Fe,13.40.Hq,14.20.Gk Typeset using REVTEX ∗[email protected] †[email protected] ‡[email protected] 1 The ratio of electric quadrupole to magnetic dipole amplitude (E2/M1) for the reaction γ+N → ∆(1232) is a quantity sensitive to a presence of charge deformations in the baryon structure. The most reliable phenomenological estimate E2/M1 = (−1.5 ± 0.2)% so far comes from detailed analysis [1] of the available photoproduction data, assuming the most general γN∆ gauge coupling and taking into account the unitary condition via Watson theorem. Very recently a very precise π-photoproduction experiment [2] has been performed at MAMI, Mainz, which allows for a direct model-independent estimate of the ratio E2/M1. The preliminary result E2/M1 = (−2.4 ± 0.2)% [2] confirms the negative sign suggested from the analysis [1] and shows a larger E2/M1-asymmetry. This non-zero negative value is a clear indication for the presence of an oblate charge deformation in the nucleon or/and delta and as such it imposes strong constraints for the effective models of baryon structure. Wirzba and Weise have investigated the E2/M1 ratio in a modified Skyrme model which includes stabilizing fourthand sixth-order terms [3]. They obtained values between −5% and −2.5% depending on the coupling parameters of stabilizing terms. However, the other related observables, namely the N −∆ mass difference, charge radii, and the isovector magnetic moment, are not properly described. In the present work we study E2/M1 ratio for the process γ+N → ∆(1232) in the chiral quark soliton model (for review see ref. [4]). We employ the simplest SU(2)-version of the model with up and down quark degenerated in mass, which is based on the semibosonized Nambu Jona-Lasinio lagrangean [5,6]: L = Ψ̄(−iγ∂μ +m0 +MU5)Ψ, (1) with auxiliary meson fields U(~x) = e ·~π(~x)/fπ , (2) constrained on the chiral circle. The model is non-renormalizable and a finite cutoff is needed. The latter is treated as a parameter of the model and together with the current quark mass m0 is fixed in the mesonic sector to reproduce the physical pion mass mπ and the pion decay constant fπ. The last model parameter, the constituent quark mass M , can be related to the empirical value of the quark condensate but actually it still leaves a broad range for M . In the model the baryons appear as a bound state ofNc (number of colors) valence quarks coupled to the polarized Dirac sea. Since the model lacks confinement the proper way to describe the nucleon is to consider [7] a correlation function of two Nc-quark currents with nucleon quantum numbers JJ3, TT3 at large euclidean time-separation: lim T→∞ ΠN (T ) = 〈JN(~x,+T/2)J N(~y,−T/2)〉 = 1 Z Γ {f} JJ3,TT3 Γ {g}∗ JJ3,TT3 ∫