Chiral Symmetry Breaking and Stability of Quark Droplets

Abstract

We discuss the stability of strangelets -quark droplets with strangeness -in the Nambu-Jona-Lasinio model supplemented by a boundary condition for quark confinement. Effects of dynamical chiral symmetry breaking are considered properly inside quark droplets of arbitrary baryon number. We obtain the energy per baryon number of quark droplets with baryon number from one to thousands. It is shown that strangelets are not the ground states as compared with nuclei, though they can be locally stable.

Quark droplets with chiral symmetry in the Nambu–Jona-Lasinio model

“…It is then measured from the vacuum energy of the bulk vacuum in the NJL model. In the previous investigations [22,23], it was shown that the effective bag constant in this procedure agreed with the phenomenological value which is used in the MIT bag model. The effective bag constant is given by…”

“…At R = 0.750 fm, we obtain F/π = −0.327. The appearance of the second local minimum is due to the R dependence of the effective bag constant B ef f [23]. Here, we note that the minimum value of the volume energy B ef f V depends on the smoothness parameter a in the regularization, while the corresponding bag radius does little.…”

“…Here K P refers to the eigenstate in the vacuum part in the bag for q = u, d and s, respectively. The vacuum quark contribution is cut off by a smooth regularization function of a Lorentzian type [23] with a momentum cutoff Λ g(p/Λ) = 1 1 + (p/Λ) a (25) for smearing of the discrete energy levels of the quarks in the bag. The smoothness parameter a in the regularization (25) is fixed to reproduce the nucleon mass E N +∆ = 1.1 GeV.…”

Chiral symmetry breaking and vacuum polarization in a bag

“…In recent studies of strangelets, a model has been presented for a discussion of chiral symmetry breaking inside a quark droplet of finite volume quark matter [5,6,7,8]. There, in addition to quark confinement for a finite volume system, it was allowed that the quarks acquire a finite mass by dynamical chiral symmetry breaking.…”

“…In earlier works, the quark wave function was given by the MIT bag in Refs. [5,6,7]. Later, in order to overcome the chiral symmetry breaking at the bag surface, the chiral bag model was introduced in Ref.…”