Non-decoupling SUSY in LFV Higgs decays: a window to new physics at the LHC

The recent discovery of a SM-like Higgs boson at the LHC, with a mass around 125-126 GeV, together with the absence of results in the direct searches for supersymmetry, is pushing the SUSY scale ($m_\text{SUSY}$) into the multi-TeV range. This discouraging situation from a low-energy SUSY point of view has its counterpart in indirect SUSY observables which present a non-decoupling behavior with $m_\text{SUSY}$. This is the case of the one-loop lepton flavor violating Higgs decay rates induced by SUSY, which are shown here to remain constant as $m_\text{SUSY}$ grows, for large $m_\text{SUSY} >$ 2 TeV values and for all classes of intergenerational mixing in the slepton sector, $LL$, $LR$, $RL$ and $RR$. In this work we focus on the LFV decays of the three neutral MSSM Higgs bosons $h$, $H$, $A \to \tau \mu$, considering the four types of slepton mixing ($\delta_{23}^{LL}$, $\delta_{23}^{LR}$, $\delta_{23}^{RL}$, $\delta_{23}^{RR}$), and show that all the three channels could be measurable at the LHC, being $h \to \tau \mu$ the most promising one, with up to about hundred of events expected with the current LHC center-of-mass energy and luminosity. The most promising predictions for the future LHC stage are also included.