FURTHER ALL-LOOP RESULTS IN SOFTLY-BROKEN SUPERSYMMETRIC GAUGE-THEORIES

It is proven that the recently found, renormalization-group invariant sum rule for the soft scalar masses in softly-broken N=l supersymmetri c gauge-Yukawa unified theories can be extended to all orders in pertu rbation theory. Ln the case of finite unified theories, the sum rule e nsures the all-loop finiteness in the soft supersymmetry breaking sect or. As a byproduct the exact beta function for the soft scalar masses in the Novikov-Shifman-Vainstein-Zakharov (NSVZ) scheme for softly-bro ken supersymmetric QCD is obtained. It is also found that the singular ity appearing in the sum rule in the NSVZ scheme exactly coincides wit h that which has been previously found in a certain class of superstri ng models in which the massive string states are organized into N=4 su permultiplets. (C) 1998 Elsevier Science B.V. All rights reserved.