Relation of constituent quark models to QCD: Why several simple models work "so well"

Abstract

We discuss the relationship between exact QCD and constituent quark models (nonrelativistic, bag, or others) to clarify why different models work reasonably in many cases. For this we use the general parametrization method [G. Morpurgo, Phys. Rev. D {bold 40}, 2997 (1989)] now expressed in terms of the standard current quark fields ({ital m}{sub {ital u}} and {ital m}{sub {ital d}} a few MeV; {ital m}{sub {ital s}}{approx_equal}150 MeV, at the usual mass renormalization point {ital q}=1 GeV). The method provides for several quantities the most general exact form of the spin-flavor structure derivable from the QCD Lagrangian. We can thus determine for many important quantities (masses of lowest baryons and mesons, baryon magnetic moments, semileptonic decays, etc.), from a fit to the data, the coefficients of the parametrization, the same ones that a direct QCD calculation, if feasible, would give. It turns out that only a few coefficients are relatively important. Because different models, each with its few free parameters, can produce these terms by some choice of parameters, one can see why models so different as the nonrelativistic or quasichiral models work {open_quote}{open_quote}well.{close_quote}{close_quote} Finally, expressing the coefficients in the general parametrization dimensionally in terms of current quark massesmore » and {Lambda}, we find that the {ital m}{sub {ital s}} expansion of broken SU(3){times}SU(3) is just an expansion in {Delta}{ital m}/({xi}{Lambda}){approx_equal}{ital m}{sub {ital s}}/({xi}{Lambda}){approx_equal}0.3. The {xi}{close_quote}s determined from different data are rather close (from 2.3 to 3.7). The resulting effective light quark masses in constituent models are of order ({xi}{Lambda}). None of the above conclusions depend on whether or not the chiral limit {ital m}{sub {ital u}},{ital m}{sub {ital d}},{ital m}{sub {ital s}}{r_arrow}0 is mathematically sound. {copyright} {ital 1996 The American Physical Society.}« less