Electroproduction of the Roper resonance and the constituent quark model

A parameter-free evaluation of the N −P11(1440) electromagnetic transition form factors is performed within a light-front constituent quark model, using for the first time the eigenfunctions of a mass operator which generates a large amount of configuration mixing in baryon wave functions. A one-body electromagnetic current, which includes the phenomenological constituent quark form factors already determined from an analysis of pion and nucleon experimental data, is adopted. For Q2 up to few (GeV/c)2, at variance with the enhancement found in the elastic channel, the effect of configuration mixing results in a significant suppression of the calculated helicity amplitudes with respect to both relativistic and non-relativistic calculations, based on a simple gaussian-like ansatz for the baryon wave functions. PACS numbers: 13.60.Rj, 13.40.Gp, 12.39.Ki, 12.39.Pn The investigation of the electromagnetic (e.m.) excitations of nucleon resonances can shed light on their structure in terms of quarks and gluons. In this respect, the Roper resonance, P11(1440), plays a particular role. As is known, within the constituent quark (CQ) picture (see, e.g., [1, 2]) this resonance is commonly assigned to a radial excitation of the nucleon, whereas it has been argued [3, 4, 5] that the P11(1440) resonance might be a hybrid state, containing an explicit excited glue-field configuration (i.e., a qG state). Within the q assignment the spin-flavour part of the Roper-resonance wave function is commonly considered to be identical to that of the nucleon, whereas the qG state is directly orthogonal to the nucleon in the spin-flavour space. Then, it is expected [4] that such different spin structures of the Roper resonance could lead to different behaviours of its e.m. helicity amplitudes as a function of the four-momentum transfer, so that future experiments planned at TJNAF [6] might provide signatures for hybrid baryons. However, the predictions of Ref. [4] have been obtained within a non-relativistic framework and using simple gaussian-like wave functions. Within the CQ model, the relevance of the relativistic effects on the helicity amplitudes of the Roper resonance has been illustrated by Weber [7] and by Capstick and Keister [2], where (we stress) gaussian-like wave functions were still adopted. The purpose of this letter is to compute the e.m. N − P11(1440) transition form factors in a CQ model, which incorporates the following features: i) a proper treatment of relativistic effects; ii) the use of the eigenfunctions of a baryon mass operator having a much closer connection to the mass spectrum with respect to a gaussian-like ansatz; iii) the use of a one-body approximation for the e.m. current able to reproduce the experimental data on the nucleon form factors. To this end, the relativistic CQ model, developed in [8, 9, 10], is extended to the P11(1440) resonance. The model describes the hadrons as systems of CQ’s, the other degrees of freedom being frozen, and the relativistic effects are properly taken care of by formulating the model on the light-front (LF ). Inside baryons the CQ’s are assumed to interact via the q− q potential of Capstick and Isgur (CI) [11]. A relevant feature of this interaction is the presence of an effective one-gluon-exchange (OGE) term, which produces a huge amount of high-momentum components and SU(6) breaking terms in the baryon wave functions (see [9, 10]); in what follows we will refer to these effects as the configuration mixing. It will be shown that the wave function of the Roper resonance, obtained with the CI interaction, contains a sizable mixed-symmetry S -wave component (∼ 9%), whose spin-flavour structure is orthogonal to the dominant symmetric S-wave component of the nucleon wave function. Thus, because of the configuration mixing, the CQ structure of the P11(1440) resonance can hardly be considered as a simple (first) radial excitation of the nucleon. Finally, an effective one-body e.m. current, including Dirac and Pauli form factors for the CQ’s, is adopted. The CQ form factors have been determined in [9] using as constraints the pion and nucleon experimental data. In [10] our parameter-free prediction for the magnetic form factor of the N −∆(1232) transition has been checked against available data. In this letter, our parameter-free results for the N − P11(1440) helicity amplitudes, using the same CQ form factors of Refs. [9, 10], will be presented, showing that the effect of the configuration mixing is opposite in the transition to the Roper resonance and in the elastic channel, so that a significant suppression of the calculated helicity amplitudes with