Nucleon form factors in a relativistic quark model

Abstract

We demonstrate that a relativistic constituent-quark model can give nucleon form factors in agreement with data for both low and high momentum transfer. The relativistic features of the model and the specific form of the wave function are essential for the result.12.35. Ht, 13.40.Fn Typeset Using REVTEX * Work supported in part by the Department of Energy, contract DE-AC03-76SF00515. It is therefore important to have a model that is valid for all values of Q 2 .The hadronic matrix element of the radiative transition of the nucleon N → N ′ γ is represented in terms of the form factors aswith momentum transfer Q = p ′ − p, nucleon mass M N , and quark current J µ =qγ µ q.The Sachs form factor for the magnetic transition is given by G M = F 1 + F 2 . The matrix elements can be calculated within a relativistic constituent quark model on the light cone [4,5,6]. This approach has been extended to asymmetric wave functions [7], which provide an excellent and consistent picture of electroweak transitions of the baryon octet. In this report we focus on the high energy behavior of the wave function.Usually harmonic-oscillator-type wave functions are used [4,5,6] with α being the confinement scale of the bound state and N being the normalization. The operator M is the free mass operator of the noninteracting three-body system, and it is a function of the internal momentum variables q i of the quarks and the quark mass m:2 With this special form of the wave function the form factors fall off exponentially for high Q 2 . This is why the form factors calculated with Eq. (2) are only valid up to 4-6 GeV 2 , an energy scale well below the perturbative region [3].The orbital wave function we use iswith a scale α and normalization factor N different from Eq. (2). The two parameters of the model, the confinement scale α and the quark mass m, have to be determined by comparison with experimental data. We find a quark mass m = 263 MeV and a scale α = 607 MeV by fitting the magnetic moment of the proton µ(p) and the neutron µ(n). In addition, these parameters give also excellent results for the magnetic moments and the semileptonic decays of the baryon octet [7].For reference, we calculate the form factors with Eq. (2) using parameters α = 560 MeV and m = 267 MeV as well. The results are shown in Figs. 1-3. Note that the low energy behavior of both wave functions is almost identical, while only the wave function in Eq. (4) fits the data. It is therefore significant to choose an appropriate Ansatz for the orbital wave function. The relativistic features of the model are also important. In the nonrelativistic limit, α/m → 0, the form factor G M for the proton is (for small Q 2 )which is too small for any reasonable value of α and m (compare Figs. 1 and 2). This limit shows that the relativistic treatment of the problem increases the form factors significantly, even for low values of the momentum transfer. The same effect has also been found for the pion [8]. While the asymptotic falloff for the wave function in Eq. (4) is still larg...

Electroweak structure of the nucleon, meson cloud, and light-cone wave functions

“…As in Ref. [51] and quite generally in the light-front formalism (see, e.g., Refs. [37, 60, 63, 64, 65]), it is always difficult to reproduce all the three quantities simultaneously, so that some compromise has to be accepted.…”

Baryons as relativistic three-quark bound states

“…Nucleon form factors have been calculated in light-front constituent-quark models [517][518][519][520][521][522], also including dressed quark form factors which effectively add higher Fock components to the wave functions [523][524][525][526]. Light-front quark model calculations are also available for nucleon resonances [21,527,528].…”

Electromagnetic form factors of the nucleon in chiral perturbation theory

“…Clearly, a quantitative description of these four form factors is a stringent test for any theory or model of the strong interactions (see, e.g., Refs. [22,23,24,25,26,27,28,29,30]). In chiral perturbation theory, these form factors have been calculated within the early relativistic approach [4], HBχPT [6,31], the small-scale expansion [32], and within the relativistic infrared regularization approach [33].…”