Scaling law for the electromagnetic form factors of the proton

The violation of the scaling law for the electric and magnetic form factors of the proton is examined within the cloudy bag model. We find that the suppression of the ratio of the electric and magnetic form factors is natural in the relativistic bag model. The pion cloud plays a moderate role in moving the ratio towards unity at low momentum transfer. The scaling violation increases as the momentum transfer increases because of the rapid drop of the pionic contribution. Our result is in reasonable agreement with the recent data from TJNAF. (Some figures in this article are in colour only in the electronic version; see www.iop.org) The description of the electromagnetic structure of the nucleon requires two independent form factors. The usual Sachs form factors fully characterize the charge and current distributions inside the nucleon. Electromagnetic probes interact not only with the valence quarks confined inside a quark core by nonlinear, gluon dynamics but also with the pion field required by chiral symmetry. A full understanding of the electromagnetic structure of the nucleon is of fundamental importance. Historically, experimental determination of the electric (GEp) and magnetic (GMp) form factors of the proton was mainly based on the Rosenbluth separation [1] of the unpolarized differential cross section data. The results of various analyses from early experiments are summarized in a simple scaling law, GEp(Q ) = GMp(Q)/μp = GD(Q), (1) for momentum transfers, Q, up to several GeV. Here μp is the proton’s magnetic moment and GD(Q) refers to the standard dipole form. However, from the Rosenbluth formula one sees that at large momentum transfer, the electric contribution to the cross section is kinematically suppressed relative to the magnetic contribution. ThusGEp cannot be determined as accurately as GMp from such an analysis, especially at large Q2. In the literature, the ratios, μpGEp(Q )/GMp(Q 2), obtained from different experiments are not consistent with each other, within the quoted errors. With the advance of polarization technologies and the operation of high-duty electron machines, it is now possible to drastically reduce the systematic uncertainties in this ratio by direct measurement. That is, one can simultaneously measure the two components of the recoil proton polarization, PT and PL, using a longitudinally polarized electron beam [2]. As the transverse component behaves as PT ∼ GEpGMp, and the longitudinal component as PL ∼ GMp, the ratio, μpGEp/GMp, can be determined directly from PT /PL. 0954-3899/00/060075+06$30.00 © 2000 IOP Publishing Ltd L75 L76 Letter to the Editor Precise data for the nucleon electromagnetic form factors set a strong constraint for various quark models of the nucleon. It helps us to develop an understanding of the composite nature of the nucleon as well as its long range chiral structure. The rapid fall-off ofGE relative toGM was indicated in the quark bag model [3], constituent quark models [4], dispersion analysis [5], and soliton models [6]. In our previous work, we studied the nucleon electromagnetic form factors in an improved cloudy bag model (CBM) [7], where the centre-of-mass motion correction and relativistic effects were treated explicitly. As a result, the region of validity of the calculation of the electric and magnetic form factors in the model was extended to larger momentum transfer than had previously been possible. Here we focus on the ratio, μpGEp(Q)/GMp(Q), and examine the mechanism for the violation of the scaling law, equation (1). Let us start with the MIT bag model [8]. Under the static-cavity approximation, the bag surface is spherical and all valence quarks are in the lowest eigenmode. The electric and magnetic form factors for the proton can be written as