Moments of the Neutron Charge Form Factor and theN→ΔQuadrupole Transition

Abstract

Recent data allow a new parametrization of the neutron charge form factor G n E . A parameter-free quark-model relation between G n E and the N →∆ quadrupole form factor G N→∆ C2is used to predict G N→∆ C2 from G n E data. In particular, < r 2 n > is related to N →∆ quadrupole moment QN→∆, while < r 4 n > connects to the N →∆ quadrupole transition radius < r 2 N→∆ >. From the latter we derive an experimental value for the charge radius of the light constituent quarks rγq = 0.8 fm. Finally, the C2/M1 ratio in pion electroproduction is predicted from the elastic neutron form factor data.Intrinsic nucleon structure -The nucleon is a complicated many-particle system composed of valence quarks, which carry the quantum numbers, and nonvalence quark degrees of freedom, which describe the cloud of quark-antiquark (qq) pairs and gluons. The constituent quark model (CQM) with two-body exchange currents describes both these aspects of nucleon structure [1]. One-body currents describe the interaction of the photon with one valence quark at a time. Two-body exchange currents are connected with the exchange particles (gluons, pions) and with qq pairs (see Fig. 1(b-d)). Nucleon properties which are dominated by two-body exchange currents show their common dynamical origin in analytical interrelations.In this paper, a quark model relation between the neutron charge form factor G n E and the quadrupole transition form factor G N →∆ C2is used together with a parametrization of new G n E data to predict G N →∆ C2and the C2/M1 ratio usually measured by pion electroproduction. The spin-isospin dependence of the two-body charge operator ρ [2] , e.g. for the gluon, can be written schematically aswhere q is the three-momentum transfer, e i and σ i the quark charge and spin. Explicit expressions can be found in Ref.[1]. As a result of (i) the dominance of ρ [2] [1,2] and of (ii) the spin-isospin structure in ρ [2] and in the N and ∆ wave functions, a connection between the neutron charge form factor G n E (q 2 ) and the N →∆ quadrupole transition form factor G N →∆ C2(q 2 ) emerges [3] as follows:The derivation is independent of the spatial part of the quark wave functions and holds irrespective of whether gluon or pion exchange or both are employed. One-body contributions to G n E and G N →∆ C2arise only through excited-state admixtures which amount to less than 20% of the empirical values if a quark core radius consistent with the excitation spectrum [2,4] is used. Three-body corrections are estimated to contribute less than 30% of the two-body currents using a QCD parametrization [5] and a large 1/N c approach [6]. These approaches also show the dominance of the two-body exchange currents for both observables.The dominance of nonvalence quark degrees of freedom in G n E and G N →∆ C2is not specific to this quark model. Also chiral approaches, e.g. the Skyrme model [7], the σ-model [8], the Nambu-Jona-Lasinio model [9], and the chiral 1

Improved empirical parametrizations of theγ*N→Δ(1232)andγ*N<

“…In addition, the electric and Coulomb quadrupole moments would both vanish [G E (0) = G C (0) = 0]. Non-zero results for G En , G E (0) and G C (0) are then a consequence of the SU (6) symmetry breaking [32,[51][52][53].…”

“…Recall that the qq cloud is the reason why G En , G E and G C are non vanishing functions of Q 2 . Large values for r 2 C reflect the increment of the size of the constituent quarks due to the qq pair/meson cloud dressing [51,52,56]. In particular the results r 2 C ≈ 2 fm 2 can be interpreted as r 2 C ≃ r 2 π , where r π = 1/m π is the pion Compton wavelength, that characterizes the pion cloud distribution inside the nucleon [51].…”

“…The relation (5.8) was derived for the first time in the context of a constituent quark model with two-body exchange currents [32,52,53]. Since the two-body currents are connected with diagrams involving qq pairs, those contributions can be regarded as the contributions of the cloud of quark-antiquark pairs.…”

“…Combining the low Q 2 expansion of the electric form factor, G En (Q 2 ) = −r 2 n Q 2 /6, where r 2 n is the neutron squared radius, one can show in the context of a constituent quark model with two-body exchange currents, that G E (0), G C (0) ∝ r 2 n [47, 51,52]. It then becomes clear that, the mechanisms responsible for the symmetry breaking, which induce r 2 n = 0, are also the mechanisms responsible for the non-zero quadrupole moments [32,[51][52][53]. The relation (5.8) is still valid when the three-body exchange currents are included for both observables, as can be shown using the expansion in 1/N c [48,54].…”

“…In particular a is determined by the second momentum r 2 n (neutron squared radius) through a = 2M 2 3µn r 2 n . As for d, it is determined by r 2 n and the fourth momentum r 4 n [51,52]. The MAID2007 parametrization for G C is inspired by the Galster form (5.10) [15].…”