Chiral symmetry and the string description of excited hadrons

Abstract

A large symmetry group is perhaps experimentally observed in excited hadrons which includes the chiral group $U(2{)}_{L}\ifmmode\times\else\texttimes\fi{}U(2{)}_{R}$ as a subgroup. To possess this large symmetry a dynamical model for excited hadrons, presumably a string model, should explain formation of chiral multiplets and, at the same time, predict coinciding slopes of the angular and radial Regge trajectories. This is possible only if both the dynamics of the string and the chirality of the quarks at the ends of the string are considered together. We construct a model-independent unitary transformation from the relativistic chiral basis to the ${^{2S+1}L_{J}}$ basis, commonly used in hadronic phenomenology as well as in the string models, and demonstrate that a hadron belonging to the given chiral representation is a fixed superposition of the basis vectors with different $L$'s. Thus the description of highly excited hadron in terms of a fixed $L$ is not compatible with chiral symmetry and has to be disregarded in favor of the description in terms of the total hadron spin $J$. Therefore, dynamics of the string must deliver the principal quantum number $\ensuremath{\sim}n+J$, in order chiral multiplets with different spins to become degenerate, as required by the large symmetry group.