On the Spectrum of Scalar-Scalar Bound States

A new, exactly solvable, Barbieri-Remiddi like equation for bound states of two scalar constituents interacting with massless vector particles is presented, both for stable and unstable particles. With the help of this equation the bound state spectrum is calculated to O(\alpha^4) for a SU(N) nonabelian gauge theory. The result for the abelian case reproduces the known result from the Foldy-Wouthuysen calculation. It is shown how different graphs as in the fermionic theory contribute to the spectrum to this order. Furthermore the bound state correction to the decay width for a weakly decaying system is calculated. This result is equal to its fermionic counterpart. Thus the theorem on bound state corrections for weakly decaying particles, formulated previously for fermions only, has been extended to the scalar theory.