While the constrained minimal supersymmetric standard model (CMSSM) with universal gaugino masses, m1/2, scalar masses, m0, and A-terms, A0, defined at some high energy scale (usually taken to be the GUT scale) is motivated by general features of supergravity models, it does not carry all of the constraints imposed by minimal supergravity (mSUGRA). In particular, the CMSSM does not impose a relation between the trilinear and bilinear soft supersymmetry breaking terms, B0=A0-m0, nor does it impose the relation between the soft scalar masses and the gravitino mass, m0=m3/2. As a consequence, tanβ is computed given values of the other CMSSM input parameters. By considering a Giudice-Masiero (GM) extension to mSUGRA, one can introduce new parameters to the Kähler potential which are associated with the Higgs sector and recover many of the standard CMSSM predictions. However, depending on the value of A0, one may have a gravitino or a neutralino dark matter candidate. We also consider the consequences of imposing the universality conditions above the GUT scale. This GM extension provides a natural UV completion for the CMSSM.
Bibliographical noteFunding Information:
The work of E.D. was supported in part by the ERC Advanced Investigator Grant no. 226371 “Mass Hierarchy and Particle Physics at the TeV Scale” (MassTeV), by the contract PITN-GA-2009-237920. The work of E.D. and Y.M. was supported in part by the French ANR TAPDMS ANR-09-JCJC-0146. The work of A.M. and K.A.O. is supported in part by DOE grant DE-FG02-94ER-40823 at the University of Minnesota.