A recent signal of 750 GeV diphotons at the LHC can be explained within the framework of supersymmetric unification by the introduction of vector quarks and leptons with Yukawa couplings to a singlet S that describes the 750 GeV resonance. We study the most general set of theories that allow successful gauge coupling unification, and find that these Yukawa couplings are severely constrained by renormalization group behavior: they are independent of ultraviolet physics and flow to values at the TeV scale that we calculate precisely. As a consequence the vector quarks and leptons must be light; typically in the region of 375 GeV to 700 GeV, and in certain cases up to 1 TeV. The 750 GeV resonance may have a width less than the experimental resolution; alternatively, with the mass splitting between scalar and pseudoscalar components of S arising from oneloop diagrams involving vector fermions, we compute an apparent width of 10s of GeV. We take the resonance to be the scalar component of a gauge singlet chiral multiplet S. Production and decay of S is accomplished by coupling to TeV-scale multiplets Φ i andΦ i , so that the effective theory below M G is described by
Keywords: Supersymmetry PhenomenologyTo preserve precision supersymmetric gauge coupling unification, we study theories where Φ i andΦ i form complete multiplets of SU (5). We study the complete set of such theories: the "(5 + 5) N 5 " theory containing N 5 = 1, 2, 3 or 4 copies of (D,L) + (D, L), the "10 + 10" theory containing (Q, U, E) + (Q,Ū ,Ē), and the "15 + 15" theory that contains a full generation of vector quarks and leptons. In the (5 + 5) 4 and 15 + 15 theories, the standard model gauge couplings near M G are in the strong coupling regime, so they correspond to the scenario of strong "unification" [17,18], rather than precision perturbative unification, which applies to the other theories. The parameters µ S and µ i are assumed to be of order the TeV scale, with an origin that may be similar to that of the supersymmetric Higgs mass parameter. Any S 3 coupling in the superpotential is assumed to be sufficiently small not to affect our analysis. The effective theory of eq. (1) possesses a parity on the vector matter, so that the lightest Φ i is stable. We therefore add Yukawa interactions between these vector quarks and leptons and the standard model quarks and leptons via the MSSM Higgs doublets; this can be done without violating R-parity if Φ i andΦ i are R-parity odd. We take these couplings to be sufficiently small that they do not affect the production and decay of the 750 GeV resonance, and do not violate bounds on flavor-changing processes. This allows the vector quarks and leptons to have prompt decays to known quarks and leptons with the emission of W, Z or h, the 125 GeV Higgs boson. (An alternative possibility will be discussed at the end of the paper.)Soft supersymmetry breaking masses for the scalar components of S, Φ i ,Φ i are present, as well as A and B type soft trilinears and bilinears. For simplicity, these paramet...