Sum Rule Constraint on Models Beyond the Standard Model

Abstract: In most versions of beyond the standard model (BSM) physics, the Yukawa couplings of the quarks and charged leptons are not all to the same complex scalar doublet but to different ones. Comparison to the standard model (SM) with only one scalar doublet, using the known mass of the W boson, provides a sum rule constraint on the Yukawa couplings $Y_i,~~ i=t, b, \tau,.....$ of the form $\Sigma_i r_i^2 = 1$ where $r_i = Y_i^{(SM)}/Y_i^{(BSM)}$ and the sum is over distinct scalar doublets. The LHC data on the branching ratios $H \rightarrow \gamma\gamma, ~\bar{b}b, ~\tau^+\tau^-, ~etc.,$ allows detailed comparison to this sum rule constraint and, as accuracy improves, will constrain or exclude many BSM theories.