VARIATION OF HADRON STRUCTURE WITH QUARK MASS

Abstract

Summary:  In the region of quark masses ¯ m > 60 MeV or so ( m π greater than typically 400-500 MeV) hadronproperties are smooth, slowly varyingfunctions of somethinglike a constituent quark mass, M  M 0 + cm ¯ (with c 1).  Indeed, M N  3 M ; M ρ ; ω 2 M and magnetic moments behave like 1 = M .  As ¯ m decreases below 60 MeV or so, chiral symmetry leads to rapid, non-analytic variation, with δ M N  m ¯ 3 = 2 ; δ µ H m ¯ 1 andδ ch  ln ¯ m .  Chiral quark models like the cloudy bag provide a natural explanation of thistransition. The scale is basically set by the inverse size of the pion source – theinverse of the bag radius in the bag model.  When the pion Compton wavelength is smaller than the size of the compositesource chiral loops are strongly suppressed. On the other hand, as soon as thepion Compton wavelength is larger than the source one begins to see rapid,non-analytic chiral corrections.These are remarkable results that will have profound consequences for our fur-ther exploration of hadron structure within QCD as well as the analysis of the vastamount of data now being taken concerning unstable resonances. In terms of imme-diate results for the structure of the nucleon, we note that the careful incorporationofthe correct chiral behaviourof QCD into the extrapolationof its properties calculatedon the lattice has produced: