Abstract. Recent LHC searches have provided strong evidence for the Higgs, a boson whose gauge quantum numbers coincide with those of a SM fermion, the neutrino. This raises the question of whether Higgs and neutrino can be related by supersymmetry. I will show explicitly the implications of models where the Higgs is the sneutrino: from a theoretical point of view an R-symmetry, acting as lepton number, is necessary; on the experimental side, squarks exhibit novel decays into quarks and leptons, allowing to differentiate these scenarios from the ordinary MSSM.
MotivationOn the 4th of July 2012, CERN announced the discovery of a new particle [1]. Its couplings, it has often been said, resemble those of the SM Higgs boson. Indeed, the fact that its couplings to the W ± (to the Z) electroweak gauge bosons is within 30% of 2m -8], tells us that this scalar must be part of a doublet of S U(2) L , with hypercharge 1/2 and that its vacuum expectation value (vev) is responsible for the W ± , Z masses. It strikes that the quantum numbers of these scalars are the same as the ones of the known leptons. So, the first question one is brought to ask is whether there can be an underlying symmetry connectingIt is well known that the only such a symmetry, capable of relating bosons with fermions, is supersymmetry (SUSY). This observation brings a glimpse of hope in a moment in which all the supersymmetric particles, predicted in the minimal supersymmetric models (MSSM), are being pushed to higher and higher scales by the stringent LHC limits. Indeed, if the relation Eq. (1) were really due to a symmetry, then the implications would be fantastic: the first supersymmetric particle, has already been discovered! In this note I explore this possibility further, to outline the low-energy behaviour of SUSY models that explain Eq. (1). This note is based mainly on Ref.
One, Two or No Higgs doublet?In the SM, the Higgs doublet H couples to down-type quarks through the Yukawa structureQ L Hd R (and similarly for leptons). Up-type quarks, couple to the same a e-mail: francesco.riva@epfl.chHiggs. However, due to their different charge, they get masses throughQSupersymmetric theories need more structure than just a SUSY version of the SM model. First of all, a SUSY version of the SM with only one Higgs doublet is inconsistent, as a single higgsino induces non-vanishing anomalies that break the SM gauge group; an even number of Higgs-doublets is necessary. Furthermore, the couplings of Eq. (2) involving H † are incompatible with unbroken SUSY. So, theories in which the Higgs is the partner of a lepton doublet are consistent from the point of view of anomalies (since there are no higgsinos), and they can successfully account for down-type quark masses throughbut they need large supersymmetry breaking contributions in order to account for up-type masses. Traditionally, this was considered unsatisfactory, as can be read in many books about early supersymmetric model-building " An obvious possibility is to identify the Higgs S U(2) doublet as th...