Chiral effective theory of diquarks and the UA(1) anomaly

Abstract

The diquark is a strongly correlated quark pair that plays an important role in hadrons and hadronic matter. In order to treat the diquak as a building block of hadrons, we formulate an effective theory of diquark fields with $SU(3)_R \times SU(3)_L$ chiral symmetry. We concentrate on the scalar ($0^+$) and pseudoscalar ($0^-$) diquarks and construct a linear-sigma-model Lagrangian. It is found that the effective Lagrangian contains a new type of chirally symmetric meson-diquark-diquark coupling that breaks axial $U_A(1)$ symmetry. We discuss consequences of the $U_A(1)$ anomaly term to the diquark masses as well as to the singly heavy baryon spectrum, which is directly related to the diquark spectrum. We find an inverse mass ordering between strange and nonstrange diquarks. The parameters of the effective theory can be determined by the help of lattice QCD calculations of diquarks and also from the mass spectrum of the singly heavy baryons. We determine the strength of the $U_A(1)$ anomaly term, which is found to give a significant portion of the diquark masses.