On a possible estimation of the constituent-quark parameters from Jefferson Lab experiments on the pion form factor

Abstract

The charge form factor of the pion is calculated for momentum transfer range of Jefferson Lab experiments. The approach is based on the instant form of the relativistic Hamiltonian dynamics. It is shown that the form-factor dependence on the choice of the model for quark wave function in pion is weak, while the dependence on the constituent-quark mass is rather significant. It is possible to estimate the mass of constituent quark and the sum of anomalous magnetic moments of u-andd-quarks from the JLab experiments.PACS numbers: 12.39, 12.60.R, 13.40.G At present time the constituent quark model (CQM) is widely and successfully used for the description of hadron properties at low and intermediate energies [1][2][3][4][5][6][7][8][9][10][11][12][13]. The reasons for this are well known: first, CQM uses the physically adequate degrees of freedom; second, CQM describes nonperturbative effects. These facts give a possibility to use CQM for the investigation of the so called "soft" structure of hadrons, e.g. in exclusive processes, in contrast to QCD (see, e.g. [14]).The main feature of CQM versus QCD is the extraction of finite number of the most important degrees of freedom needed to describe the hadron. All dynamical effects of QCD are incorporated in CQM through the effective (constituent) quark mass and internal quark structure in terms of quark form factors. So, in the framework of CQM constituent quarks have all the material properties of free particles and interact with each other through the confinement potential. This means that constituent quark is characterized by an effective mass, a mean-square-radius (MSR) and an anomalous magnetic moment. Let us remark that the concept of extended constituent quarks also appears in some quantum field theory models, for example, in Nambu-Jona-Lasinio model with spontaneous chiral symmetry breaking [15]. In this context one can imagine that CQM is initiated by QCD. However, it is very important to remind ourselves that CQM is not a direct consequence of QCD, but a very * Electronic address: krutov@info.ssu.samara.ru † Electronic address: troitsky@theory.npi.msu.su successful phenomenological model [16]. For the description of electroweak properties it is necessary to take into account the relativistic effects, especially large in systems of light quarks. We will use the relativistic Hamiltonian dynamics (RHD) [17], which is one of approaches to describe relativistic properties of CQM.In the present paper we discuss the dependence of electromagnetic pion form factor on the internal quark structure. The interest to this problem is due particularly to a possible interpretation of current experiments in Jefferson Lab on the measurement of pion form factor [18] in the range of momentum transfer 0.5(GeV /c) 2 < Q 2 < 5(GeV /c) 2 . Using one of relativistic forms of CQM we obtain that pion form factor in this region of Q 2 depends strongly on the constituent quark mass, while the dependence on model quark interaction in pion is weak. This fact gives hope that it could be possi...

Electroweak properties ofρ-meson in the instant form of relativistic quantum mechanics

“…Relation between the strong-interaction hadronic radius r 2 st and the charge radius r 2 ch for light hadrons. Result for ρ-meson is obtained in our work with wave function (14) at n = 3. Table 1.…”

“…Parameters in our calculation are fixed from description of electroweak properties of pion [14]. Let us note that our RQM describes well the experimental data for the pion form factor including the recent points [22].…”

“…In this work the model parameters are fixed from the calculations of electroweak properties of pion [14] and from description of the lepton decay constant of ρ-meson [15]. So, our calculations of the magnetic moment and the charge radius are performed without fitting parameters and give the good agreement with experimental data.…”

“…All experimental points obtained in JLab up to now agree very well with our prediction of 1998. So, by analogy with pion calculations from [14] we use the following set of parameters: M=0.22 GeV for the constituent quark mass; the quark anomalous magnetic moments enter our expressions through the sum (κ u + κd) and we take κ u + κd = 0.0268 in natural units; for the quark MSR we use the relation r 2 q 0.3/M 2 . The parameters of the wave functions b in (13), (14) were fixed from the requirements of the description of experimental values of ρ-meson lepton decay constants 152 ± 8 MeV [1].…”

“…Table 1. The ρ-meson electromagnetic moments and lepton decay constant obtained with the different model wave functions (13) - (14). r 2 ρ C , r 2 ρ M , are charge and magnetic MSR, respectively, in fm 2 ; μ ρ is relativistic magnetic moment (8) in e/2M ρ ; Q ρ is quadrupole moment (9) in fm 2 .…”