Anomalous Higgs Couplings as a Window to New Physics

TL;DR

This work develops and applies a unified framework to probe Higgs sector anomalies and BSM physics using HEFT (an electroweak chiral Lagrangian with a light Higgs) combined with unitarization techniques. It provides a complete one-loop renormalization within HEFT, explores vector and scalar resonances via the IAM and improved K-matrix methods (including coupled-channel dynamics), and derives nontrivial bounds on Higgs self-interactions from unitarity and causality. The scalar sector, in particular, reveals sensitivity to multiple ${ m O}(p^4)$ couplings and can accommodate a light H(650) resonance only with additional operators beyond the leading terms, while vector resonances are mainly governed by $a_4$ and $a_5$ with notable but smaller roles for $a_3$ and $ ext{Zeta}$. Extending the methodology to gravity as an EFT (with an $R^2$-driven scalaron) uncovers graviton–scalar dynamics and a graviball, illustrating the broad applicability of unitarization beyond the SM. Together, these results offer a principled route to constrain Higgs self-interactions and to anticipate signatures of strong dynamics in current and future collider experiments, as well as to illuminate EFT-based gravity phenomenology at high energies.

Abstract

Throughout this thesis, we investigate how effective field theories, combined with unitarization techniques, can be used to explore physics beyond the Standard Model, with particular emphasis on the dynamical origin of electroweak symmetry breaking. Since effective theories often produce amplitudes that violate unitarity at high energies, restoring unitarity is essential before comparing predictions with data. The first part of the work focuses on longitudinal $WW$ scattering, a process that, despite being subdominant at the LHC, provides a sensitive probe of Higgs dynamics. We perform a full one-loop computation within the HEFT framework, determine the required counterterms in the on-shell scheme, and analyze for the first time how the inclusion of transverse gauge bosons modifies the masses and widths of the dynamical resonances obtained through unitarization in the vector--isovector and scalar--isoscalar channels. This provides the technical foundation for studying HEFT low-energy couplings subject to unitarity and causality. While vector resonances are relatively well characterized through Weinberg sum rules and unitarization, scalar resonances remain more elusive and depend on HEFT parameters that are experimentally difficult to constrain. We show that unitarization, together with causality, imposes nontrivial bounds on Higgs self-interactions. In the scalar channel, the necessity of treating coupled processes becomes a key ingredient, enabling us to extract information about the Higgs sector from elastic $WW \to WW$ scattering without requiring double-Higgs production. Finally, we apply the formalism developed throughout the thesis to unitarize the amplitudes of a quantum theory of gravity treated as an effective field theory, illustrating the broader applicability of these methods.

Figures (36)

• Figure 1: Complete matter content of the SM. The outer circle represents the flavor sector, featuring quarks in the upper half and leptons in the lower half. The middle circle contains the gauge sector with the so-called intermediante vector bosons, and the Higgs particle is placed in the innermost circle. This picture is taken from Ref. SMcircle.
• Figure 2: Potential of a theory with one self-interacting scalar (left) before and (right) after spontaneous symmetry breaing of the vacuum of the theory by flipping the sign of the mass term.
• Figure 3: Figure showing the production cross sections of a Higgs boson at the LHC, computed for the processes gluon-gluon fusion ($pp \to H$), vector boson fusion ($pp \to qqH$), associated productions with a gauge boson ($pp \to VH$), with a pair of quarks $t\bar{t}$ and $b\bar{b}$ ($pp \to bbH/ttH$), and with a single quark $t$ ($pp \to tH$), assuming a Higgs boson mass of $m_H = 125~\mathrm{GeV}$. The labels for each process indicate the precision level of the calculations achieved. This figure is not of our authorship and can be found in Ref. LHCHiggsWG.
• Figure 4: Schematic representation showing the correspondence between some SMEFT and HEFT arbitrary operators. This illustration is taken from Ref. Brivio:2016uid
• Figure 5: Cross section for different helicity combinations of the process (left) $W_{\lambda_1}W_{\lambda_2} \to Z_{\lambda_3}Z_{\lambda_4}$ and (right) $W_{\lambda_1}W_{\lambda_2} \to hh$. In both panels, the solid line represents the cross section in the SM limit, while the dots indicate the cross section with anomalous Higgs couplings, specifically for $a = 0.94$ and $b = 1.05$, the latter contributing only to the $HH$ final state. The modifier of the trilinear coupling, $d_3$, also participating only in $WW\to HH$ is set to its SM value.