We study constraints on new physics from Higgs production at the LHC in the context of an effective field theory (EFT), focusing on Higgs searches in H V (V = W, Z) associated production which are particularly sensitive to the high-energy behavior of certain dimension-six operators. We show that analyses of these searches are generally dominated by a kinematic region where the generic EFT expansion breaks down, and we establish under which conditions they can nevertheless be meaningful. For example, constraints from these searches on the Wilson coefficients of operators whose effects grow with energy can be established in scenarios where a particular combination of fermions and the Higgs are composite and strongly coupled: then, bounds from Higgs physics at high energy are complementary to LEP1 and competitive with LEP2.

We interpret reported hints of a Standard Model Higgs boson at ∼ 125 GeV in terms of high-scale supersymmetry breaking with a shift symmetry in the Higgs sector. More specifically, the Higgs mass range suggested by recent LHC data extrapolates, within the (non-supersymmetric) Standard Model, to a vanishing quartic Higgs coupling at a UV scale between 10 6 and 10 18 GeV. Such a small value of λ can be understood in terms of models with high-scale SUSY breaking if the Kähler potential possesses a shift symmetry, i.e., if it depends on H u and H d only in the combination (H u + H d ). This symmetry is known to arise rather naturally in certain heterotic compactifications. We suggest that such a structure of the Higgs Kähler potential is common in a wider class of string constructions, including intersecting D7-and D6-brane models and their extensions to F-theory or M-theory. The latest LHC data may thus be interpreted as hinting to a particular class of compactifications which possess this shift symmetry.

The Higgs quartic coupling λ has now been indirectly measured at the electroweak scale. Assuming no new low-scale physics, its running is known and, together with gauge and Yukawa couplings, it is a crucial new piece of information constraining UV completions of the Standard Model. In particular, supersymmetry broken at an intermediate or high energy scale with tan β = 1 (i.e. λ = 0) is consistent with present data and has an independent theoretical appeal. We analyze the possible string-theoretic motivations for tan β = 1 (including both the shift-symmetry and the more economical variant of a Z 2 symmetry) in a Higgs sector realized on either 6-or 7-branes. We identify specific geometries where λ 0 may arise naturally and specify the geometrical problems which need to be solved to determine its precise value in the generic case. We then analyze the radiative corrections to λ. Finally we show that, in contrast to naive expectations, λ < 0 at the SUSY breaking scale is also possible. Specifically, string theory may produce an MSSM plus chiral singlet at a very high scale, which immediately breaks to a non-SUSY Standard Model with λ < 0. This classically unstable theory then becomes metastable through running towards the IR. arXiv:1304.2767v4 [hep-th] 8 Oct 2013the Higgs sector appeared several years ago in [23] as well as very recently in [24]. A shift-symmetric Higgs has also been discussed in the context of inflation in [25]. An alternative origin of λ(m S ) = 0 was suggested in [26]. 4 Note that there is an unconventional alternative if one is willing to accept λ < 0 at the matching scale and possible metastability of the SM vacuum. This possibility is discussed in section 4.2.

The first search for a heavy charged vector boson in the final state with a tau lepton and a neutrino is reported, using 19.7 fb −1 of LHC data at √ s = 8 TeV. A signal would appear as an excess of events with high transverse mass, where the standard model background is low. No excess is observed. Limits are set on a model in which the W decays preferentially to fermions of the third generation. These results substantially extend previous constraints on this model. Masses below 2.0 to 2.7 TeV are excluded, depending on the model parameters. In addition, the existence of a W boson with universal fermion couplings is excluded at 95% confidence level, for W masses below 2.7 TeV. For further reinterpretation a model-independent limit on potential signals for various transverse mass thresholds is also presented.