Momentum projection and relativistic boost of solitons. II. Nucleon and meson properties

Abstract

In a previous paper we presented a method for calculating center-of-mass corrections to hadron properties in soliton models. Here we apply this method to the soliton bag model. We construct quantum bag solutions of quarks interacting with a scalar o field and color gauge fields in the onegluon-exchange approximation. The o part of Hilbert space is described by a coherent or general one-mode state. The Lorentz invariance of the theory requires the construction of momentum eigenstates with energies obeying the Einstein relation. Variation after projection onto zero momentum gives approximate mass eigenstates which are boosted relativistically onto states of nonzero momentum. This avoids the well-known Peierls-Yoccoz problem. Electromagnetic moments are evaluated. We obtain expressions for charge rms radii and nucleon magnetic moments, including recoil corrections. Other observables, which require the use of zero-momentum states are nucleon and meson masses, the axial-vector coupling constant g, (0) , and the pion decay constant f,. We determine the soliton bag parameters by a least-squares fit to the observed nucleon and pion masses, the charge rms radius and the magnetic moment of the proton and g~; the other observables are then "predicted."

The nucleon-nucleon potential in the chromodielectric soliton model: Statics

“…Approximate recoil corrections [30], momentum projection and boost [31] are not incorporated into the present six-quark calculations. For consistency, the potentials we calculate here are therefore normalized with respect to the energy and not the mass of two noninteracting nucleons.…”

“…We note that due to the scalar nature of the medium, the field equations are diagonal in the color indices, which have hence been omitted in Eqs. (28) to (31). From these equations we can furthermore deduce the mutual and self-interaction energies between the quarks which arise due to the OGE through…”

Transverse polarisation of quarks in hadrons

“…In the literature this procedure is known as "variation after projection" (VAP), to be distinguished from the simpler "variation before projection" (VBP), which consists of minimising the unprojected Hamiltonian first and then using the solutions in the Peierls-Yoccoz projection (8.1.2). For a detailed discussion of these techniques see [204,205].…”

Medium modifications of baryon properties in nuclear matter and hypernuclei

“…There are several methods for the removal of the center-of-mass motion in the FL model [27][28][29]. In our previous work [37], we used two approaches for the center-of-mass correction.…”

“…Also, it could be used to investigate the deconfinement phase transition at high densities and/or temperatures based on its dynamical formation of solitons. In past decades, the FL model has been extensively used to study the properties of hadrons in free space [26][27][28][29][30][31][32][33][34]. It has also been applied to study the medium modifications of the nucleon [4,35] and dense-matter properties [6,36].…”