Some indication for a missing chiral partner eta_4 around 2 GeV

Abstract

The high-lying mesons in the light quark sector previously obtained from the partial wave analysis of the proton-antiproton annihilation in flight at 1.9 - 2.4 GeV region at CERN reveal a very high degree of degeneracy. This degeneracy can be explained as due to an effective restoration of both SU(2)_L * SU(2)_R and U(1)_A symmetries combined with a principal quantum number n + J. In this case there must be chiral partners for the highest spin states in the 2 and 2.3 GeV bands presently missing in the data. Here we reanalyze the Crystal Barrel data and show an indication for existence of the missing $4^{-+}$ state around 2 GeV. This result calls for further experimental search of the missing states both in the proton-antiproton annihilation and in the production reactions.