The Role of the Roper in QCD

S.R. Beane and U. van Kolck (University of Arizona)

Understanding of the pattern of baryon masses and couplings from QCD remains an open challenge for theorists. We argue that chiral symmetry has a tremendous amount of predictive power in the resonance region. In particular, we have shown that existing data suggest a simple scenario in which the nucleon, and the Delta and Roper resonances act as chiral partners in a reducible representation of the full QCD chiral symmetry group [48]. The main point to take from our paper is that even at low energies where chiral symmetry is spontaneously broken, there is a sense in which the baryon spectrum falls into reducible representations of the chiral algebra. This has nothing to do with parity doubling near a chiral symmetry restoring phase transition. We have found that existing data suggest that the nucleon and the $\Delta$ and Roper resonances form a reducible sum of $(0, \textstyle{1\over 2} )$ and $(\textstyle{1\over 2} ,1)$ representations of the chiral group, with maximal mixing. From the perspective of the naive constituent quark model this is equivalent to placing these states in a reducible ${\bf 4}\oplus{\bf 20}$ representation of spin-flavor $SU(4)$. Our results suggest that other baryons also fall into finite-dimensional chiral representations that in principle can be mapped out at JLab and other experimental facilities. It should be noted however that as one moves higher in the excited spectrum the assumption of pole dominance will become increasingly more unreliable due to the broadening of the baryon states. We stress that it is somewhat peculiar that the chiral multiplet involving the nucleon involves only a few states and that the representations enter with approximately equal weight [49]. We find no QCD-based argument which would explain this simple multiplet structure. This is a worthy puzzle whose resolution -we believe- will lead to deep insight into the manner in which the hadron spectrum arises from QCD.