Stable and unstable classical solutions in an effective gauge theory for low energy mesons

Abstract

-19807 (Rev.) We study the stability of two related classical solutions in an effective gauge theory, which correctly describes the properties of ~ and p mesons at low energies.· The first solution (sphaleron), which excites only the p field, with baryon number B = 0 and energy E = 1.5 GeV, is unstable. The second (Skyrmion), which excites both the~ and p fields, with B = 1 and E z 1.0 GeV, is perhaps stable locally. We show how to make this Skyrmion absolutely stable without raising its energy too much, both of which are desirable for identification with the nucleon. 'we comment on the potential of heavy ion collision experiments to study configuration space. The Skyrmion solution may also have some relevance for the electroweak interactions (now ·• E ~ 10 TeV).

Interaction energy in infinite nuclear matter in the hybrid soliton model

“…The reason, as was recognized already by several authors [12,13,22] is that above certain values of TJ or 'Y I e 2 no solution, i.e no minimum in the energy surface, exists for the chiral angle with the boundary conditions 3.20. The fourth order terms with the signs used here destabilize the soliton solution as can be seen from the expression for the soliton mass, eq.…”

“…In addition, we introduced a stabilizing sixth order term in the meson field, .Cs, which is supposed to model the influence of the vector-meson [14,15]. Without this term, the soliton solution would be instable [22]. For the fourth order term we could choose between the newly proposed £ 3 [12] and the old Skyrme term £4 [4,13,14].…”

Stability of weak Skyrmions

“…Clearly, in the Skyrme Lagrangian (up to order four in derivatives), there exists a stable weak skyrmion because c 4 turns out to be positive and the series stops at this order. However for L tot , the small distance behavior (large momentum) is dominated by the remaining terms of the series which are generated by the third term in (13). There is absolute stability if there exist a global minimum for M tot (R) and if it occurs at a non vanishing skyrmion size R.…”

“…Since the gauge terms of the HGS Lagrangian is insufficient to guarantee stability, it is also customary to add some sort of stabilizing Skyrme-like term to L tot , preferably a "gauge invariant" Skyrme term of the form [8,13]:…”