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The hMSSM is a special parameterization of the minimal supersymmetric extension of the Standard Model (MSSM) in which the mass of the lightest Higgs boson is automatically set to the LHC measured value, $M_h\!\!=\!\! 125$ GeV, by adjusting the supersymmetric particle spectrum such that it provides the required amount of radiative corrections to the Higgs boson masses. The latter spectrum was in general assumed to be very heavy, as indicated by the present exclusion limits of the LHC, not to affect the phenomenology of the Higgs sector. In this work, we investigate the impact on the hMSSM by a light gaugino and higgsino sector, that is allowed by the present LHC data. In particular, we discuss the radiative corrections due to charginos and neutralinos to the Higgs boson masses and couplings and show that an hMSSM can still be realized in this context. We first describe how this scenario is implemented in the package SuSpect that generates the MSSM Higgs and supersymmetric spectra. We then analyze the possible impact of Higgs boson decays into these new states, as well as the reverse cascade channels with Higgs bosons in the final states, for the constraints on the MSSM Higgs sector at the LHC. We further explore the cosmological constraints on the hMSSM with a light gaugino--higgsino spectrum. We analyze the relic abundance of the lightest neutralino as a candidate of the dark matter in the Universe and the constraints on its mass and couplings by the present and future astroparticle physics experiments.

We continue our study of strongly-coupled, approximately scale-invariant gauge theories with a large number of flavours, which provide a suitable ultraviolet completion of the composite-Higgs scenario. We identify the requisite operators to realise partial compositeness of the Standard-Model fermions. In order to compute the spectrum of composite fermionic states, we extend the bottom-up holographic models, which we previously introduced to capture the main features of the non-perturbative dynamics in the Veneziano limit, by adding fermion fields in the bulk. We identify regions in parameter space where some fermionic bound states become light, depending in particular on the number of flavours, the operator scaling dimensions, and the bulk Yukawa couplings. We also observe a dense spectrum of states, when multi-scale dynamics is induced by a large backreaction of bulk scalars on the geometry. Adapting the formalism of the holographic Wilsonian renormalisation group, we study the linear coupling between the composite and elementary fermions, as a function of energy scale. We find that, in some circumstances, the associated operators are dangerously irrelevant: the renormalisation-group flow gives rise to a large linear coupling in the infrared, even when it is irrelevant from the point of view of the ultraviolet fixed point. We finally compute the partially composite spectrum, correlate it with the analysis of the flow, and assess the potential phenomenological implications, e.g. for the top-quark partners.

In the Minimal Supersymmetric Standard Model (MSSM) the mass of the lightest neutral Higgs boson is determined by the supersymmetric parameters. In the $m_h$MSSM the precisely measured Higgs boson replaces the trilinear coupling $A_t$ as input parameter. Expressions are derived to extract $A_t$ in a semi-analytical form as a function of the light Higgs boson (pole) mass. An algorithm is developed and implemented at two--loop precision, generalizable to higher orders, to perform this inversion consistently. The result of the algorithm, implemented in the SuSpect spectrum calculator, is illustrated on a parameter set compatible with LHC measurements.

The cold and dense QCD equation of state (EoS) at high baryon chemical potential $\mu_B$ involves at order $\alpha^2_S$ an all-loop summation of the soft mode $m_E\sim \alpha_S^{1/2} \mu_B$ contributions. Recently, the complete soft contributions at order $\alpha^3_S$ were calculated, using the hard thermal loop (HTL) formalism. By identifying {\em massive} renormalization group (RG) properties within HTL, we resum to all orders $\alpha_S^p, p\ge 3$ the leading and next-to-leading logarithmic soft contributions. We obtain compact analytical expressions, that show visible deviations from the state-of-the art results, and noticeably reduced residual scale dependence. Our results should help to reduce uncertainties in extending the EoS in the intermediate $\mu_B$ regime, relevant in particular for the phenomenology of neutron stars.

We investigate the renormalization group optimized perturbation theory (RGOPT) at the next-to-next-to-leading order (NNLO) for the thermal scalar field theory. From comparing three thus available successive RGOPT orders, we illustrate the efficient resummation and very good apparent convergence properties of the method. In particular, the remnant renormalization scale dependence of thermodynamical quantities is drastically improved as compared to both standard perturbative expansions and other related resummation methods, such as the screened perturbation theory. Our present results thus constitute a useful first NNLO illustration in view of NNLO applications of this approach to the more involved thermal QCD.