0.92 0.94 0.96 0.98 1 10 2 10 3 m [GeV] n s λ =1 λ =0.5 λ =0.3 λ =0.1 $_{λ}$=0.02 m u ˜,d ˜ =690 GeV m u ˜,d ˜ =1.9 TeV m u ˜,d ˜ =1.92 TeV FIG. 9: Contours of λ for δ$_{H}$ = 1 . 91 × 10 − 5 in the n$_{s}$ - m$_{φ}$ plane. The blue band on the left is due to the stau-neutralino coannihilation region for tan β = 10 and the blue band on the right (which continues beyond the plotting range) denotes the focus point region [714]. above terms in Eq. (314) are invariant under the SM. Once the SM is embedded within a GUT at the scale M$_{G}$ , where gauge couplings are unified, the gauge group will be enlarged. Then the question arises whether such terms in Eq. (314) are invariant under the GUT gauge group or not. Note that a GUT singlet is also a singlet under the SM, however, the vice versa is not correct. • SU (5): We briefly recollect representations of matter fields in this case: L and d belong to ¯ 5 , while e and u belong to 10 of SU (5) group. Thus under SU (5) the superpotential terms in Eq. (314) read [714] ¯ 5 × ¯ 5 × 10 × ¯ 5 × ¯ 5 × 10 M 3 P . (330) This product clearly includes a SU (5) singlet. Therefore in the case of SU (5), we expect that M$_{P}$ suppressed terms as in Eq. (310) appear with λ ∼ O (1). If we were to obtain the ( LLe ) 2 term by integrating out the heavy fields of the SU (5) GUT, 150