Precision measurements of the Higgs boson properties at the LHC provide relevant constraints on possible weak-scale extensions of the Standard Model (SM). In the context of the Minimal Supersymmetric Standard Model (MSSM) these constraints seem to su
ggest that all the additional, non-SM-like Higgs bosons should be heavy, with masses larger than about 400 GeV. This article shows that such results do not hold when the theory approaches the conditions for alignment independent of decoupling, where the lightest CP-even Higgs boson has SM-like tree-level couplings to fermions and gauge bosons, independently of the non-standard Higgs boson masses. The combination of current bounds from direct Higgs boson searches at the LHC, along with the alignment conditions, have a significant impact on the allowed MSSM parameter space yielding light additional Higgs bosons. In particular, after ensuring the correct mass for the lightest CP-even Higgs boson, we find that precision measurements and direct searches are complementary, and may soon be able to probe the region of non-SM-like Higgs boson with masses below the top quark pair mass threshold of 350 GeV and low to moderate values of $tanbeta$.
In models with an extended Higgs sector there exists an alignment limit, in which the lightest CP-even Higgs boson mimics the Standard Model Higgs. The alignment limit is commonly associated with the decoupling limit, where all non-standard scalars a
re significantly heavier than the $Z$ boson. However, alignment can occur irrespective of the mass scale of the rest of the Higgs sector. In this work we discuss the general conditions that lead to alignment without decoupling, therefore allowing for the existence of additional non-standard Higgs bosons at the weak scale. The values of $tanbeta$ for which this happens are derived in terms of the effective Higgs quartic couplings in general two-Higgs-doublet models as well as in supersymmetric theories, including the MSSM and the NMSSM. Moreover, we study the information encoded in the variations of the SM Higgs-fermion couplings to explore regions in the $m_A - tanbeta$ parameter space.
Current Higgs data at the Large Hadron Collider is compatible with a SM signal at the 2$sigma$ level, but the central value of the signal strength in the diphoton channel is enhanced with respect to the SM expectation. If the enhancement resides in t
he diphoton partial decay width, the data could be accommodated in the Minimally Supersymmetric Standard Model (MSSM) with highly mixed light staus. We revisit the issue of vacuum instability induced by large mixing in the stau sector, including effects of a radiatively-corrected tau Yukawa coupling. Further, we emphasize the importance of taking into account the $tanbeta$ dependence in the stability bound. While the metastability of the Universe constrains the possible enhancement in the Higgs to diphoton decay width in the light stau scenario, an increase of the order of 50% can be achieved in the region of large $tanbeta$. Larger enhancements may be obtained, but would require values of $tanbeta$ associated with non-perturbative values of the tau Yukawa coupling at scales below the GUT scale, thereby implying the presence of new physics beyond the MSSM.
