The Instantaneous Approximation to the Transition Matrix Elements between Two Bound States

Abstract

Under the framework of the Bethe-Salpeter (B.S.) wave functions and the Mandelstam formalism as well, to make ``instantaneous approximation'' to a transition matrix element (a current operator sandwiched between two bound-states of double heavy quarks) is described. By taking the typical concerned decays as examples, such as $B_c$ meson decaying to $J/\psi +(\bar{l}\nu )$, the advantages of the approach and its limitations are illustrated. Finally, potential applications to various processes for possible double heavy flavoured systems, such as those of $(Q^{\prime }\bar{Q})$ and $(Q^{\prime }Q)$ ($m_Q,m_{Q^{\prime }}\gg {\Lambda }_{QCD}$), are discussed.

Comments: 27 pages, 3 figures ( not included ), AS-ITP-93-80