Exploring A New Su(4) Symmetry of Meson Interpolators

In recent lattice calculations it has been discovered that mesons upon truncation of the quasizero modes of the Dirac operator obey a symmetry larger than the SU(2)(L) x SU(2)(R) x U(1)(Lambda) symmetry of the QCD Lagrangian. This symmetry has been suggested to be SU(4) superset of SU(2)(L) x SU(2)(R) x U(1)(Lambda) that mixes not only the u- and d-quarks of a given chirality, but also the left- and right-handed components. Here it is demonstrated that bilinear (q) over barq interpolating fields of a given spin J >= 1 transform into each other according to irreducible representations of SU(4) or, in general, SU (2N(F)). This fact together with the coincidence of the correlation functions establishes SU(4) as a symmetry of the J >= 1 mesons upon quasizero mode reduction. It is shown that this symmetry is a symmetry of the confining instantaneous charge-charge interaction in QCD. Different subgroups of SU(4) as well as the SU(4) algebra are explored.