We employ a geometric framework to compute the leading high-energy behaviour of tree-level scattering amplitudes in theories containing $\textit{N}$ Nambu-Goldstone bosons and a single Higgs-like scalar with an arbitrary potential $\textit{V}$. 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.

United Kingdom

Rodrigo Alonso

India

Susobhan Chattopadhyay

James Ingoldby

The potential of HEFT and the scale of new physics

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.

Christoph Englert

Germany

Wrishik Naskar

Shakeel Rahaman

Assessing (H)EFT theory errors by pitting EoM against field redefinitions

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 $\textit{p}$ = 1 gap, and analyse the magnetic spectrum while connecting its UV and IR realisations.

Despoina Dimakou

Yunji Ha

Valentin Khoze

Charge quantisation, monopoles and emergent symmetry in the Standard Model and its embeddings

<p>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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math>-boson measurements at hadron colliders. Due to the difference in the initial states at the Tevatron and the LHC, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math>-boson decays to a right-handed neutrino would artificially increase the mass measured at the Tevatron while only affecting the difference between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>W</mi><mo>+</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>W</mi><mo>−</mo></msup></math> 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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math> bosons produced with transverse momentum above <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>≈</mo><mn>50</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>.</p>

Michael Spannowsky

Sam Bates

Chris Hays

Chris Pollard

Sensitivity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math>-boson measurements to low-mass right-handed neutrinos

This letter presents a counting problem and its solution in two forms, one derived by the author and one worked out by Young (private correspondence). The problem can be mapped to both (i) ways to lace a $\textit{N}$-holes-per-side shoe with $$\ell $$ shoestrings and (ii) a sum over the indexes of 2$\textit{N}$-tensors made of symmetric 2-tensors. The coefficients that answer this question are then connected to spin $$J=N$$ boson exchange amplitudes and perturbative unitarity constraints, deriving relations with Legendre polynomials and sum rules.

A particle physicist lacing their shoes

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 $\textit{(i)}$ connects the counting formula presented in [1] in the CCWZ formulation with the linear frame and makes this connection explicit in HEFT $\textit{(ii)}$ outlines the differences in perturbation theory in each frame $\textit{(iii)}$ presents a new counting formula with measure in the full SU(3) × SU(2) × U(1) group for HEFT and $\textit{(iv)}$ provides a Mathematica code that produces the number of operators at the user-specified order in HEFT.

Counting and building operators in theories with hidden symmetries and application to HEFT

Functional methods and a derivative expansion are employed for laying out a procedure to compute the effective action to any loop order, for scalar fields parametrising an arbitrary Riemannian manifold, while maintaining explicit field-space covariance. These results are of use in the characterization of effective field theories for electroweak symmetry breaking and extend a geometric perspective in field space beyond one loop.

Mia West

On the effective action for scalars in a general manifold to any loop order

Experimental measurements point at the Standard Model (SM) as the theory of electroweak symmetry breaking, but as we close in on our characterization the question arises of what limits in theory space lead to the SM. The class of theories with this property cannot be ruled out, only constrained to an ever smaller neighborhood of the SM. In contrast, which class of theories does not possess this limit and can therefore potentially be ruled out experimentally? In this work we study both classes and find evidence to support the Standard Model effective field theory being the single road to the Standard Model, theories that fall outside this class keeping a “minimum distance” from the SM characterized by a cutoff of at most <math><mn>4</mn><mi>π</mi><mi>v</mi><mo>/</mo><msub><mi>g</mi><mrow><mi>SM</mi></mrow></msub></math>.

Roads to the Standard Model

We study the prospects for probing the CP structure of hqq interactions using the decays of the lightest baryon Λ q  formed in the quark’s hadronization. The low yields of reconstructible events make it unlikely for tests to be performed with the next generation of colliders. In h → b   <math> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ \overline{b} $$  → Λ b    <math> <mover> <mi>Λ</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\Lambda} $$   b  decays a CP-sensitive distribution could be measured with a high-luminosity e + e  −  collider, while in both h → b   <math> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ \overline{b} $$  → Λ b    <math> <mover> <mi>Λ</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\Lambda} $$   b  and h → c   <math> <mover> <mi>c</mi> <mo>¯</mo> </mover> </math>  $$ \overline{c} $$  → Λ c    <math> <mover> <mi>Λ</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\Lambda} $$   c  decays such a distribution could be measured with a very high luminosity μ + μ  −  collider. However, we find that only the μ + μ  −  collider can produce enough h → b   <math> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ \overline{b} $$  → Λ b    <math> <mover> <mi>Λ</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\Lambda} $$   b  decays to probe a physical CP asymmetry in the hbb vertex.

Cristofero Fraser-Taliente

Prospects for direct CP tests of hqq interactions

We investigate the possibility that the dark matter abundance is sourced by the baryon/lepton asymmetry of the early Universe. It turns out that a Goldstone field of a global classically preserved symmetry in the Standard Model experiences a kick during a period of baryon/lepton number generation. This mechanism can be regarded as dynamical generation of initial conditions for misalignment yet the prediction for relic abundance presents an inverse dependence on the coupling in parallel with freeze-in vs freeze-out. We explore two realizations of this mechanism and show that in conjunction with leptogenesis, it is possible to identify a viable promising region of parameter space for dark matter production with mass 10 MeV–1 GeV and decay constant <math><mi>f</mi></math> in the range of <math><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>10</mn></mrow></msup><mi>–</mi><msup><mrow><mn>10</mn></mrow><mrow><mn>12</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>.