Now that the Higgs boson has been observed by the ATLAS and CMS experiments at the LHC, the next important step would be to measure accurately its properties to establish the details of the electroweak symmetry breaking mechanism. Among the measurements which need to be performed, the determination of the Higgs self-coupling in processes where the Higgs boson is produced in pairs is of utmost importance. In this paper, we discuss the various processes which allow for the measurement of the trilinear Higgs coupling: double Higgs production in gluon fusion, vector boson fusion, double Higgs-strahlung and associated production with a top quark pair. We first evaluate the production cross sections for these processes at the LHC with center-of-mass energies ranging from the present √ s = 8 TeV to √ s = 100 TeV, and discuss their sensitivity to the trilinear Higgs coupling. We include the various higher order QCD radiative corrections, at next-to-leading order for gluon and vector boson fusion and at next-to-next-to-leading order for associated double Higgs production with a gauge boson. The theoretical uncertainties on these cross sections are estimated. Finally, we discuss the various channels which could allow for the detection of the double Higgs production signal at the LHC and estimate their potential to probe the trilinear Higgs coupling.

The Next-to-Minimal Supersymmetric Extension of the Standard Model (NMSSM) with a Higgs sector containing five neutral and two charged Higgs bosons allows for a rich phenomenology. In addition, the plethora of parameters provides many sources of CP violation. In contrast to the Minimal Supersymmetric Extension, CP violation in the Higgs sector is already possible at tree-level. For a reliable understanding and interpretation of the experimental results of the Higgs boson search, and for a proper distinction of Higgs sectors provided by the Standard Model or possible extensions, the Higgs boson masses have to be known as precisely as possible including higher-order corrections. In this paper we calculate the one-loop corrections to the neutral Higgs boson masses in the complex NMSSM in a Feynman diagrammatic approach adopting a mixed renormalization scheme based on on-shell and DR conditions. We study various scenarios where we allow for tree-level CP-violating phases in the Higgs sector and where we also study radiatively induced CP violation due to a non-vanishing phase of the trilinear coupling A t in the stop sector. The effects on the Higgs boson phenomenology are found to be significant. We furthermore estimate the theoretical error due to unknown higherorder corrections by both varying the renormalization scheme of the top and bottom quark masses and by adopting different renormalization scales. The residual theoretical error can be estimated to about 10%.

a b s t r a c tWe present the program package NMSSMCALC for the calculation of the loop-corrected NMSSM Higgs boson masses and decay widths in the CP-conserving and CP-violating NMSSM. The full one-loop corrections to the Higgs boson masses are evaluated in a mixed renormalisation scheme of on-shell and DR conditions. The Higgs decay widths include the dominant higher order QCD corrections, and the decays into bottom quarks, strange quarks and τ leptons are supplemented by higher order SUSY corrections through effective couplings. All relevant off-shell decays into two massive gauge bosons, gauge and Higgs boson and Higgs pair final states as well as into heavy quark pairs are computed. The input and output files feature the SUSY Les Houches Accord so that the program can easily be linked with existing computer tools. Program summary Program title: NMSSMCALC Catalogue identifier: AEUE_v1_0Program summary URL: Nature of problem: Computation of the NMSSM Higgs mass spectrum including higher order corrections in a mixed renormalisation scheme of on-shell and DRbar conditions, and numerical calculation of the decay widths and branching ratios, both in the CP-conserving and in the CP-violating NMSSM. The decay widths include the dominant higher order QCD corrections and, for the neutral Higgs boson decays into a bottom quark pair, the higher order SUSY-QCD and the approximate SUSY-electroweak (elw) corrections up to one-loop ✩ This paper and its associated computer program are available via the Computer Physics Communication homepage on ScienceDirect 3373 accuracy. The decays into a strange quark pair include the dominant resummed SUSY-QCD corrections and the one into a τ pair the dominant resummed SUSY-elw corrections. Analogously for the charged Higgs boson the higher order SUSY corrections have been implemented for the decays into fermion pairs. In the real NMSSM, the decays into stop and sbottom pairs, respectively, contain the SUSY-QCD corrections. All relevant off-shell decays into massive gauge bosons, into gauge and Higgs bosons, into Higgs pairs and into heavy quark pairs have been taken into account. The input and output files feature the SUSY Les Houches Accord (SLHA). Solution method:The necessary input values are set in the two input files inp.dat (in the SLHA format) and bhdecay.in. The file inp.dat, where the choice between the real and the complex NMSSM can be made, is read in by CalcMasses.F, which calculates the one-loop corrected NMSSM Higgs mass spectrum. CalcMasses.F writes out all necessary parameters, masses and mixing angles in an SLHA format file slha.in, which is read in by bhdecay.f (by bhdecay c.f in the complex case). This Fortran routine then computes the decay widths and branching ratios and writes them out in an SLHA format file slha decay.out. Furthermore it writes out all parameters and mixing angles. Restrictions:At present the NMSSM Higgs spectrum is calculated at one-loop accuracy, the Higgs self-couplings at leading order, and no renormalisation group running of the input paramete...

The measurement of the trilinear and quartic Higgs self-couplings is necessary for the reconstruction of the Higgs potential. This way the Higgs mechanism as the origin of electroweak symmetry breaking can be tested. The couplings are accessible in multi-Higgs production processes at the LHC. In this paper we investigate the prospects of measuring the trilinear Higgs coupling in composite Higgs models. In these models, the Higgs boson emerges as a pseudoGoldstone boson of a strongly interacting sector, and the Higgs potential is generated by loops of the Standard Model (SM) gauge bosons and fermions. The Higgs self-couplings are modified compared to the SM and controlled by the compositeness parameter ξ in addition to the Higgs boson mass. We construct areas of sensitivity to the trilinear Higgs coupling in the relevant parameter space for various final states.

The Higgs low-energy theorem gives a simple and elegant way to estimate the couplings of the Higgs boson to massless gluons and photons induced by loops of heavy particles. We extend this theorem to take into account possible nonlinear Higgs interactions as well as new states resulting from a strong dynamics at the origin of the breaking of the electroweak symmetry. We show that, while it approximates with an accuracy of order a few percents single Higgs production, it receives corrections of order 50% for double Higgs production. A full one-loop computation of the gg → hh cross section is explicitly performed in MCHM5, the minimal composite Higgs model based on the SO(5)/SO(4) coset with the Standard Model fermions embedded into the fundamental representation of SO(5). In particular we take into account the contributions of all fermionic resonances, which give sizeable (negative) corrections to the result obtained considering only the Higgs nonlinearities. Constraints from electroweak precision and flavor data on the top partners are analyzed in detail, as well as direct searches at the LHC for these new fermions called to play a crucial role in the electroweak symmetry breaking dynamics.

We classify weak-scale extensions of the Standard Model which automatically preserve its accidental and approximate symmetry structure at the renormalizable level and which are hence invisible to low-energy indirect probes. By requiring the consistency of the effective field theory up to scales of Λ eff ≈ 10 15 GeV and after applying cosmological constraints, we arrive at a finite set of possibilities that we analyze in detail. One of the most striking signatures of this framework is the presence of new charged and/or colored states which can be efficiently produced in high-energy particle colliders and which are stable on the scale of detectors.

We present our calculation of the two-loop corrections of O(α 2 t ) to the neutral Higgs boson masses of the CP-violating Next-to-Minimal Supersymmetric extension of the Standard Model (NMSSM). The calculation is performed in the Feynman diagrammatic approach in the gaugeless limit at vanishing external momentum. We apply a mixed DR-on-shell (OS) renormalization scheme for the NMSSM input parameters. Furthermore, we exploit a DR as well as an OS renormalization in the top/stop sector. The corrections are implemented in the Fortran code NMSSMCALC for the calculation of the Higgs spectrum both in the CP-conserving and CP-violating NMSSM. The code also provides the Higgs boson decays including the state-of-the-art higher-order corrections. The corrections computed in this work improve the already available corrections in NMSSMCALC which are the full one-loop corrections without any approximation and the two-loop O(α t α s ) corrections in the gaugeless limit and at vanishing external momentum. Depending on the chosen parameter point, we find that the O(α t α s + α 2 t ) corrections add about 4-7% to the one-loop mass of the SM-like Higgs boson for DR renormalization in the top/stop sector and they reduce the mass by about 6-9% if OS renormalization is applied. For an estimate of the theoretical uncertainty we vary the renormalization scale and change the renormalization scheme and show that care has to be taken in the corresponding interpretation. *

New Physics that becomes relevant at some high scale Λ beyond the experimental reach, can be described in the effective theory approach by adding higher-dimensional operators to the Standard Model (SM) Lagrangian. In Higgs pair production through gluon fusion, which gives access to the trilinear Higgs self-coupling, this leads not only to modifications of the SM couplings but also induces novel couplings not present in the SM. For a proper prediction of the cross section, higher order QCD corrections that are important for this process, have to be taken into account. The various higher-dimensional contributions are affected differently by the QCD corrections. In this paper, we provide the nextto-leading order (NLO) QCD corrections to Higgs pair production including dimension-6 operators in the limit of large top quark masses. Depending on the dimension-6 coefficients entering the Lagrangian, the new operators affect the relative NLO QCD corrections by several per cent, while modifying the cross section by up to an order of magnitude.