Operator analysis ofl=1baryon masses in largeNcQCD

Abstract

We consider in detail the mass operator analysis for the nonstrange lϭ1 excited baryons in large N c QCD. We present a straightforward procedure for constructing the large N c baryon wave functions, and provide complete analytic expressions for the matrix elements of all the independent isosinglet mass operators. We discuss the relationship between the old-fashioned operator analyses based on nonrelativistic SU͑6͒ symmetry and the modern large N c approach, which has a firmer theoretical foundation. We then suggest a possible dynamical interpretation for the subset of operators preferred strongly by the data. ͓S0556-2821͑99͒07809-1͔

Excited baryons in large QCD

“…They are defined in Refs. [ 13] and [ 16]. We recall that for the symmetric (SYM) [N c ] and the mixed (MS) [N c − 1, 1] representations of the permutation group S Nc , the non-vanishing coefficients c ρ,η are given by…”

“…For nonstrange baryons, Table I of Ref. [ 13] gives a list of 18 linearly independent operators. If the core is excited the number of operators appearing in the mass formula is much larger.…”

“…Table 2 Matrix elements of N. We apply the 1/N c counting rules presented in Refs. [ 13] and [ 16] and use their conclusions in selecting the most dominant operators in the practical analysis. For nonstrange baryons, Table I of Ref.…”

“…For excited baryons this symmetry is broken. However, based on the observation that excited states can be approximately classified as SU(2N f ) multiplets, considerable efforts have previously been made to analyze the excited states belonging to the [70, 1 − ] multiplet (N = 1 band) in the large N c limit [ 10,11,12,13,14,15,16,17,18,19,20], with obvious success.…”

“…coupled to a ground state core [ 10,11,12,13,14,15,16,17,18,19,20]. The second term will be treated here as an excited quark coupled to an excited core 5 .…”