Soliton bag model

Dynamical properties and flux tubes of the Friedberg-Lee model

“…However, unlike the bag model there is a finite surface interface between the perturbative and nonperturbative regions in this model. As shown by Wilets and collaborators [2,3] static properties of hadrons can be well described in terms of this model. The problem we address here is related to non-static, dynamic properties of the model.…”

“…Therefore we have to construct the model carefully in order to ensure this. As we shall see in the next section this imposes severe constraints on the functional form of K( a), which have not been taken into account in previous approaches [1,2,3].…”

“…(11) can also be obtained by minimizing t after eliminating E via (13). As a measure for the radius of the flux tube we define (16) In order to make a calculation we have to specify the functional forms of U and "'· As in previous references [1,2,3] we use a quartic polynomial for U: (17) For c > 0 and 0 < aM < av 12 this potential has a minimum at 0 and av and a maximum at aM. The ratio aM I av determines the shape of the potential, whereas c and av simply rescale it 2 • Most previous approaches made the ansatz that K( a) is a polynomial of the form 11-(a I av )n lm [1 ,2,3].…”

“…However, coupling a linearly to the quarks neither gives rise to absolute quark confinement, as the mass of a quark in the nonperturbative vacuum is still finite, nor does it explain why the quarks have to be coupled to colour singlets. Confinement is achieved by coupling the gluon field to the a-field via a dielectric constant ~~:(a) [1,2]. The functional form of K is chosen so that it is 1 for a = 0 and approaches zero for a ----+ av, as shown in fig.…”

“…The field tensor F;v is given by (2) with the structure constants !abc of SU(3). The field a is supposed to describe a condensate, being zero for the perturbative vacuum and taking on some value av in the QCD ground state, which we shall also refer to as the nonperturbative vacuum.…”