Rodrigo Alonso

A bstract: We employ a geometric framework to compute the leading high-energy behaviour of tree-level scattering amplitudes in theories containing N Nambu-Goldstone bosons and a single Higgs-like scalar with an arbitrary potential V . Using these methods, we obtain closed-form expressions for the leading contribution to the full infinite set of tree amplitudes involving any number of Goldstone and Higgs-like external states. These results are then used to derive total cross sections, decay rates, and perturbative unitarity bounds. We then apply our general formalism to the Standard Model scalar sector using the equivalence theorem, working in the regime of small field-space curvature, and use it to characterise the relation between Higgs Effective Field Theory (HEFT) and the Standard Model Effective Field Theory (SMEFT). We analyse three representative classes of models. Two reproduce previously known behaviours, while the third, based on a dilaton effective theory, exhibits a noteworthy feature within the HEFT framework: a smooth decoupling limit that connects HEFT directly to the Standard Model without passing through a SMEFT regime, providing a possible backdoor to the Standard Model.

A bstract: Truncations of effective field theory expansions are technically necessary but inherently intertwined with the redundancies of general field redefinitions. This can be viewed as a juxtaposition of power-counting and theoretical uncertainties, which seek to estimate neglected higher-dimensional interactions through approaches based on community consensus. One can then understand the invariance of physics under field redefinitions as a data-informed validation of different power-counting schemes, or as a means of assigning theoretical errors in comparison with algebraic, equation of motion-based replacements. Such an approach generalises widely accepted procedures for estimating theoretical uncertainties within the SM to non-renormalisable interactions. We perform a case study for a representative example in Higgs Effective Field theory, focusing on universal Higgs properties tensioned against process-dependent sensitivity expectations.

A bstract: This work studies the connection of the global properties of the SM gauge group to 1-form discrete symmetries, the possible non-Abelian embeddings of the SM group, and electric and magnetic charge quantisation. Building on previous work, we introduce indexes to characterise the group choices, connect the concept of compositeness degree to emergent electric 1-form symmetry, introduce a new model to fill in the p = 1 gap, and analyse the magnetic spectrum while connecting its UV and IR realisations.

A low-mass right-handed neutrino could interact with electroweak bosons via mixing, a mediator particle, or loop corrections. Using an effective field theory, we determine constraints on these interactions from W -boson measurements at hadron colliders. Due to the difference in the initial states at the Tevatron and the LHC, W -boson decays to a right-handed neutrino would artificially increase the mass measured at the Tevatron while only affecting the difference between W + and W − mass measurements at the LHC. Measurements from CDF and the LHC are used to infer the corresponding parameter values, which are found to be inconsistent between the two. The LHC experiments can improve sensitivity to these interactions by measuring the cosine of the helicity angle using W bosons produced with transverse momentum above ≈ 50 GeV .

Identifying a full basis of operators to a given order is key to the generality of Effective Field Theory (EFT) and is by now a problem of known solution in terms of the Hilbert series. The present work is concerned with hidden symmetry in general and Higgs EFT in particular and (i) connects the counting formula presented in [1] in the CCWZ formulation with the linear frame and makes this connection explicit in HEFT (ii) outlines the differences in perturbation theory in each frame (iii) presents a new counting formula with measure in the full SU(3) × SU(2) × U(1) group for HEFT and (iv) provides a Mathematica code that produces the number of operators at the user-specified order in HEFT.

As experiment charts new territory at the electroweak scale, the enterprise to characterise all possible theories becomes all the more necessary. In the absence of new particles, this ambitious enterprise is attainable and has led to the Higgs Effective Field Theory (HEFT) as the most general characterising framework, containing the Standard Model Effective Field Theory (SMEFT) as a subspace. The characterisation of this theory space led to the dichotomy SMEFT vs. HEFT SMEFT as the two possible realisations of symmetry breaking. The criterion to distinguish these two possibilities is non-local in field space, and phenomena which explore field space beyond the neighbourhood of the vacuum manifold are in a singular position to tell them apart. Cosmology allows for such phenomena, and this work focuses on HEFT SMEFT, the less explored of the two options, to find that first order phase transitions with detectable gravitational wave remnants, domain wall formation and vacuum decay in the far, far distant future can take place and single out HEFT SMEFT. Results in cosmology are put against LHC constraints, and the potential of future ground- and space-based experiments to cover parameter space is discussed.