Constraining grand unification using first and second generation sfermions

We investigate the spectrum of supersymmetric grand unification models based on the gauge groups $SU(5)$, $SO(10)$ and $E_6$, paying particular attention to the first and second generation. We demonstrate how the measurement of the first or second generation sfermion spectrum may be used to constrain the underlying grand unification structure. The smallness of first and second generation Yukawa interactions allows us to perform an analytic analysis, deriving expressions for the high scale parameters in terms of the low scale sfermion masses. We also describe a sum rule that provides an $SO(10)$ mass prediction, distinct from $SU(5)$, and discuss $E_6$ models, both with and without extra exotic matter at low energies. The derived relations are compared with numerical results including two-loop running and the full Yukawa dependence.

Figure 1

A comparison of the $SU(5)$ analytic sum rules with SOFTSUSY for example scenarios 1, 2, and 3. The lower solid line is the sum rule of Eq. (97) while the upper solid line is that for Eq. (98). The corresponding dashed lines are the results obtained from SOFTSUSY.

Figure 2

A comparison of the $SO(10)$ analytic sum rules with SOFTSUSY for example scenarios 1, 2, and 3. The lower solid line is now the sum rule of Eq. (102), while the middle solid line and the upper solid line are the sum rules given by Eqs. (97, 98), respectively. The corresponding dashed lines are the results obtained from SOFTSUSY.