Baryon spectrum in largeNcchiral soliton and in quark models

Abstract

In memory of Karen Avetovich Ter-Martirosyan, the Teacher. IntroductionDescription of hadrons structure in terms of their quark constituents is generally accepted, but the alternative description within e.g. topological soliton (Skyrme) model [1,2] and its modifications also is useful and has certain advantages in comparison with traditional approaches. The chiral (topological) soliton approach is based on general principles and few ingredients incorporated in the effective chiral lagrangian, this is the reason for apparent simplifications in comparison, for example, with attempts to solve relativistic many-body problem. To simplify the latter, some additional objects like diquarks and triquarks have been phenomenologically introduced and discussed especially intensively after recent observations of the so called pentaquarks [3,4] 1 . Concept of diquarks "as an organizing principle for hadron spectroscopy" is considered in details in [12], see also [13]. The concepts of diquarks, triquarks or other correlated quark clusters are certainly of useful heuristic value, although their properties have not been deduced rigorously from basic QCD lagrangian. It should be noted that diquarks present in different physical states, baryons or mesons, can have different properties like the effective mass and size, even for same quantum numbers. 2In the present paper we perform explicit calculation of the strangeness contents of exotic and nonexotic baryon states at arbitrary number of colors N c , and discuss connection of the chiral soliton approach (CSA) and simple quark (pentaquark) model for exotic baryon states, 1 A contradictive present situation with experimental observation of possible pentaquark states is discussed, e.g. in [5,6]. Consideration of baryon states in the present paper is relevant independently on particular values of masses, widths and other properties of exotic baryon states measured experimentally. A detailed discussion of theoretical predictions of these states can be found in [7,8,9,10,11] 2 Some analogy with nuclei can be noted: two-, three-, etc. nucleon clusters play an important role in the structure of heavy nuclei, however, it is not possible to evaluate their properties from those of deuteron, helium etc., only. See, e.g. [14] for discussion of the role of femtometer toroidal structures in nuclei.

Pentaquarks in chiral soliton models

“…Detailed calculations of the strangeness contents of all components of exotic multiplets of baryons (pentaquarks) have been performed recently at an arbitrary number of colors N c [112] within the rigid rotator model. The leading terms in the 1/N c expansion for the positive strangeness states coincide with those in the rigid oscillator model, but the next-to-leading order terms differ essentially from those obtained within the RO model in its commonly accepted version, as for the "octet" and "decuplet" of baryons discussed in [108] and in present paper.…”

Positive parity pentaquark towers in largeNcQCD

“…Given the difficulties still faced by first principle QCD calculations, the 1/N c expansion [16] of QCD, where N c is the number of colors, provides a very useful analytical tool (for a recent account see [17]). It is based on the fundamental theory of the strong interactions, and relates the chiral soliton model to the more intuitive quark model picture [18,19,20,21], where the pentaquark correspond to states with quark contentqq 4 . In the large N c limit, QCD has a contracted spin-flavor symmetry SU(2F ) c [22,23] in the baryon sector, also known as K-symmetry, that constrains their mass spectrum and couplings.…”

Selected problems of baryon spectroscopy: Chiral soliton versus quark models

“…can be calculated exactly with the help of wave functions in SU (3) configuration space, for arbitrary number of colors N c [6,7]. Some examples of values of C S at arbitrary number of colors N c are presented in Tables 1 and 2…”

“…A ( p, q), B ( p, q), C ( p, q) depend on particular SU (3) multiplet. For the 'octet', for example [7],…”