SU(4) × SU(4) as an approximate symmetry of hadrons

The (4, 4*) + (4*, 4) model of broken SU(4) ×{} SU(4) as an approximate symmetry of hadrons is investigated. Spectral-function sum rules for scalar and pseudoscalar densities are derived in this model. Sum rules based on octet-type breaking of SU(3) at q²=0 and q²=∞ are also obtained. It is shown that the q²=0 sum rule rules out SU(2) ×{} SU(2) as a good symmetry of the Hamiltonian, when the vacuum is approximately SU(3)-invariant, in the present model. Thus the problem of understanding SU(2) ×{} SU(2) and SU(3) as approximate symmetries of the Hamiltonian persists as in the case of the popular (3, 3*) + (3*, 3) model of broken SU(3) ×{} SU(3). It is shown that the q²=∞ sum rule is consistent with the idea that SU(2) ×{} SU(2) is a good symmetry of the Hamiltonian. A mass formula for charmed pseudoscalar mesons is also derived.