Mass Degeneracy of Squarks and Sleptons in Supergravity

Abstract

Mass degeneracy of squarks and sleptons is discussed in the framework of Einstein supergravity. It is shown that under plausible assumptions, the mass degeneracy naturally occurs even in the supergravity with non-minimal couplings, which is phenomenologically required for suppression of flavor·changing neutral currents. 1. Supersymmetry (SUSY) provides an intriguing solution to the gauge hierar­ chy problem where the cancellation of all quadratic divergences takes place between boson and fermion loops.l) It is, however, well known that the presence of superpart­ ners of quarks and leptons (squarks and sleptons) causes significant effects in the low-energy physics. Examples include the proton decay due to dimension five opera­ tors2) and the flavor-changing neutral currents (FCNCs) induced by one-loop diagrams including squarks and sleptons. 3 ) Observed suppression of the KG_KG mixing and f.1 -> er decay strongly implies that the masses of squarks and sleptons in different flavors (more precisely in the first and the second generations) with the same SU(3) X SU(Z).x U(l) quantum numbers should be highly degenerate. (For their masses m ~1 TeV, the mass differences 8m 2 are constrained as 8m2/m2s10-2-10-3.3» In the minimal N =1 supergravity where a flat Kahler metric is postulated, all soft SUSY breaking masses of the scalar bosons are the same as a gravitino mass m3/2 (for a review of supergravity, see Ref. 4». But there is no apparent reason why nature chooses the minimal coupling in the Kahler potential. Indeed, as we will see below, when fields which are singlet under SU(3) X SUeZ) X U(l) gauge symmetry non­ minimally couple to squarks and sleptons, the soft SUSY breaking masses of the squarks and sleptons have additional terms and are not automatically degenerate. In order to confirm that the non-minimal coupling is not a peculiar one, let us consider string theory.5) In a superstring theory (or more precisely a heterotic string theory) compactified into four dimensions,6) there exist moduli fields whose vacuum expectation values (VEVs) specify the shape (the complex structure) and the size (the Kahler class) of the six-dimensional compact space. They are gauge singlets and non-minimally couple to the non-singlet fields (squarks and sleptons) in the Kahler potential, as we will illustrate in an orbifold model. 7 ) Thus the string theory appears