Pseudospin Symmetry in Nuclei, Spin Symmetry in Hadrons

Ginocchio argued that chiral symmetry breaking in QCD is responsible for the relativistic pseudospin symmetry in the Dirac equation, explaining the observed approximate pseudospin symmetry in sizable nuclei. On a much smaller scale, it is known that spin-orbit splittings in hadrons are small. Specifically, new experimental data from CLEO indicate small splittings in D-mesons. For heavy-light mesons we identify a cousin of pseudospin symmetry that suppresses these splittings in the Dirac equation, known as spin symmetry. We suggest an experimental test of the implications of spin symmetry for wave functions in electron-positron annihilation. We investigate how QCD can give rise to two different dynamical symmetries on nuclear and hadronic scales. Recently, Isgur [1] has re-emphasized the experimental fact that spin-orbit splittings in meson and baryon systems, which might be expected to originate from one-gluon-exchange (OGE) effects between quarks, are absent from the observed spectrum. He conjectures that this is due to a fairly precise, but accidental, cancellation between OGE and Thomas precession effects, each of which has “splittings of hundreds of MeV)’ [1]. Taking the point of view that precise cancellations reflect symmetries rather than accidents, we have examined what dynamical requirements would lead to such a result. Below, we first elucidate the experimental evidence for small spin-orbit splittings. ,Then we identify the symmetry that suppresses these splittings. We show how this symmetry leads to a proposed experimental test in electron-positron annihilation. The existence of pseudospin symmetry in nuclei is also indicated. Finally, we investigate how QCD can give rise to two different dynamical symmetries on nuclear and hadronic scales. We study systems made from one light quark and one heavy antiquark. Because the light quark is expected to move relativistically, and the heavy quark can be treated as stationary, we examine the relativistic Dirac Equation. The equation includes the possibility of the OGE and Thomas precession effects mentioned before. 1) E-mail: [email protected], tgoldman@anLgov, gino&5.lanl.gov RECEIVED