If the recently discovered Higgs boson's couplings deviate from the Standard Model expectation, we may anticipate new resonant physics in the weak boson fusion channels resulting from high scale unitarity sum rules of longitudinal gauge boson scattering. Motivated by excesses in analyses of multi-leptons+missing energy+jets final states during run 1, we perform a phenomenological investigation of these channels at the LHC bounded by current Higgs coupling constraints. Such an approach constrains the prospects to observe such new physics at the LHC as a function of very few and generic parameters and allows the investigation of the strong requirement of probability conservation in the electroweak sector to high energies. Our analysis is directly relevant for the 2 TeV excess reported recently by the CMS and ATLAS collaborations.
Perturbative probability conservation provides a strong constraint on the presence of new interactions of the Higgs boson. In this work we consider CP violating Higgs interactions in conjunction with unitarity constraints in the gauge-Higgs and fermion-Higgs sectors. Injecting signal strength measurements of the recently discovered Higgs boson allows us to make concrete and correlated predictions of how CP-violation in the Higgs sector can be directly constrained through collider searches for either characteristic new states or tell-tale enhancements in multi-Higgs processes.
We fit the next-to-leading order unitarity conditions to the Two-Higgs-Doublet model with a softly broken $\mathbb{Z}_2$ symmetry. In doing so, we alleviate the existing uncertainty on how to treat higher order corrections to quartic couplings of its Higgs potential. A simplified approach to implementing the next-to-leading order unitarity conditions is presented. These new bounds are then combined with all other relevant constraints, including the complete set of LHC Run I data. The upper $95\%$ bounds we find are $4.2$ on the absolute values of the quartic couplings, and $235$ GeV ($100$ GeV…
In the conventional metric formulation of gravity, the Higgs Inflation model violates unitarity in the electroweak vacuum in Higgs scattering at the energy scale $Λ\sim M_{Pl}/ξ$, where $ξ\sim 10^4$ is the non-minimal coupling of the Higgs to the Ricci scalar. In the Palatini formulation it is commonly believed that $Λ\sim M_{Pl}/\sqrtξ$, where $ξ\sim 10^{9}$. Here we reconsider unitarity violation in the electroweak vacuum in the Palatini formulation. We argue that there is no unitarity violation in Higgs scattering in the Palatini non-minimally coupled Standard Model in the electroweak vacuu…
The Abelian Higgs model forms an essential part of the electroweak standard model: it is the sector containing only Z and Higgs bosons. We present a diagram-based proof of the tree-level unitarity of this model inside the unitary gauge, where only physical degrees of freedom occur. We derive combinatorial recursion relations for off-shell amplitudes in the massless approximation, which allows us to prove the cancellation of the first two orders in energy of unitarity-violating high-energy behaviour for any tree-level amplitude in this model. We describe a deformation of the amplitudes by exten…
We derive the scale of unitarity violation from the geometry of Effective Field Theory (EFT) extensions of the Standard Model Higgs sector. The high-energy behavior of amplitudes with more than four scalar legs depends on derivatives of geometric invariants with respect to the physical Higgs field $h$, such that higher-point amplitudes begin to reconstruct the scalar manifold away from our vacuum. In theories whose low-energy limit can be described by the Higgs EFT (HEFT) but not the Standard Model EFT (SMEFT), non-analyticities in the vicinity of our vacuum limit the radius of convergence of …
We study the observability of new interactions which modify Higgs-pair production via vector-boson fusion processes at the LHC and at future proton-proton colliders. In an effective-Lagrangian approach, we explore in particular the effect of the operator $h^2 W_{μν}^a W^{a,μν}$, which describes the interaction of the Higgs boson with transverse vector-boson polarization modes. By tagging highly boosted Higgs bosons in the final state, we determine projected bounds for the coefficient of this operator at the LHC and at a future 27 TeV or 100 TeV collider. Taking into account unitarity constrain…
The strong nature of Composite Higgs models manifests at high energies through the growing behavior of the scattering amplitudes of longitudinally polarized weak bosons that leads to the formation of composite resonances as well as non-resonant strong effects. In this work the unitarity of these scattering amplitudes is used as a tool to assess the profile of the composite spectrum of the theory, including non-resonant enhancements, vector resonances and the CP-even scalar excitation. These three signatures are then studied in realistic scattering processes at hadron colliders, aiming to estim…
It has long been known that perturbative calculations in scalar multi-particle production could break down since fast growing amplitudes appear. A recent calculation in the regime $ λn \gg 1$, where $ n $ is the multiplicity and $ λ$ is the self-coupling, gives an amplitude which grows exponentially with the energy, resulting in a divergent propagator and leading to the violation of perturbative unitarity. In this paper the transition rate is calculated from the solution of the self-consistent Schwinger-Dyson equation in spectral representation. We get an amplitude growing quadratically with t…
Naïve dimensional analysis seems to suggest possible unitarity violations in the framework of the Higgs and new Higgs inflationary scenarios. These violations seem to happen around the value in which the potential energy, per given Higgs boson's vacuum expectation value, crosses the perturbative cut-off scale calculated around the electroweak vacuum. Conversely to these expectations, in this paper we show that, by using an exact analysis of the background dependent cut-off scale, and by including the contribution of the phase-space volume in the perturbative scattering amplitudes, no violation…
We investigate the general two Higgs doublet model imposing both the unitarity conditions and the bounded-from-below conditions. Both types of conditions restrict the ranges of the parameters of the scalar potential. We study the model in the Higgs basis, i.e. in the basis for the scalar doublets where only one doublet has vacuum expectation value. We use the experimental bounds on the oblique parameter T, to produce scalar particles with masses and cubic and quartic couplings of the Higgs in agreement with the phenomenology. The numerical calculations show that the cubic coupling may be up to…
We compute all of the one-loop corrections that are enhanced, $O(λ_i λ_j / 16 π^2)$, in the limit $s \gg |λ_i | v^2 \gg M_{W}^2$, $s \gg m_{12}^2$ to all the $2 \to 2$ longitudinal vector boson and Higgs boson scattering amplitudes in the $CP$-conserving two-Higgs doublet model with a softly broken $\mathbb{Z}_2$ symmetry. In the two simplified scenarios we study, the typical bound we find is $|λ_i(s)| \lessapprox 4$.
In this Snowmass white paper, we describe how unitarity bounds can convert sensitivities for Higgs couplings at future colliders into sensitivities to the scale of new physics. This gives a model-independent consequence of improving these sensitivities and illustrate the impact they would have on constraining new physics. Drawing upon past successful applications of unitarity as a guide for future colliders (e.g. the Higgs mass bound and discovering it at the LHC), we hope this data will be useful in the planning for next generation colliders.
We study multi-Higgs final states in vector boson fusion (VBF) processes at the LHC and at future proton-proton colliders, focusing on the prospects for measurements at 27 TeV and at 100 TeV. We use an effective Lagrangian which includes higher-dimensional operators in the mass eigenstates which are relevant to VBF processes and relate this to specific parameterizations and models for new physics in the Higgs sector. We derive theoretical constraints on the parameter space from the unitarity of $2\to n$ scattering amplitudes and apply the results to $V V \to hh$ and $h h h$ processes, where $V…
If the scalar sector of the Standard Model is non-minimal, one might expect multiple generations of the hypercharge-1/2 scalar doublet analogous to the generational structure of the fermions. In this work, we examine the structure of a Higgs sector consisting of N Higgs doublets (where N \geq 2). It is particularly convenient to work in the so-called charged Higgs basis, in which the neutral Higgs vacuum expectation value resides entirely in the first Higgs doublet, and the charged components of remaining N-1 Higgs doublets are mass-eigenstate fields. We elucidate the interactions of the gauge…
