The search for new sources of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation is a cornerstone of the beyond the Standard Model (BSM) phenomenology program at the LHC and beyond. We provide a comprehensive analysis of such searches at a range of future facilities with the aim of informing the currently unfolding future collider roadmap. Focusing on new sources of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation specifically in the gauge-Higgs sector, we demonstrate the outstanding potential held by future electron-positron and proton-proton colliders to reveal and identify BSM physics with direct relevance for the observed matter-antimatter asymmetry. In particular, the future colliders will provide an order of magnitude improvement in sensitivity to anomalous <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating interactions induced by dimension-six effective field theory operators when compared to the high-luminosity LHC program.

United Kingdom

Arun Atwal

Jessica Burridge

António Jacques Costa

Christoph Englert

Sinead Farrington

Jay Nesbitt

Germany

Leonor Santos Pereira Trigo

Andrew Pilkington

Aidan Robson

Júlia Cardoso Silva

Sarah Williams

Yuyang Zhang

Future collider perspectives on Higgs sector <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation

We explore the phenomenological consequences of non-minimal hidden sector interactions on observable correlations in the Higgs sector, mediated through the ℤ -symmetric Higgs portal. Particular attention is given to non-standard momentum dependencies of the hidden sector scalar, which arise naturally in an effective field theory (EFT) framework, e.g. in Composite Scalar Dark Matter theories. We discuss the implications of such hidden sector interactions for the thermal history of the universe. We show that aspects of such non-standard momentum dependencies can be probed at future lepton colliders such as a FCC-ee, potentially also through radiative corrections. This gives rise to precision probes for regions where direct detection constraints and relic abundance can be accounted for as predicted in, e.g., Composite Scalar Dark Matter theories.

 Anisha

Switzerland

Lisa Biermann

Margarete Mühlleitner

Phenomenology of a kinetic Higgs portal

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.

Rodrigo Alonso

Wrishik Naskar

Shakeel Rahaman

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

The Standard Model effective field theory (SMEFT) provides a robust framework for probing deviations in the couplings of Standard Model particles from their theoretical predictions. This framework relies on an expansion in higher-dimensional operators, often truncated at dimension-six. In this work, we compute the effective dimension-eight operators generated by integrating out heavy scalar fields at one-loop order in the Green’s basis within two extended scalar sector models: the two Higgs doublet model and the complex triplet scalar model. In this work, we consider loops that consist of heavy field propagators only. We also investigate the impact of heavy scalar fields on the fermion sector, deriving the fermionic effective operators up to dimension-eight for these models, and detail how contributions can be mapped onto nonredundant bases. To assess the importance of higher-order contributions in the SMEFT expansion, we analyze dimension-eight effects for electroweak precision observables at the next frontier of precision lepton machines such as GigaZ.

India

Nilabhra Adhikary

Tisa Biswas

Joydeep Chakrabortty

Michael Spannowsky

Electroweak scalar effects beyond dimension-six in SMEFT

Interference effects in effective field theory (EFT) analyses can significantly distort sensitivity expectations, leaving subtle yet distinct signatures in the reconstruction of final states crucial for limit setting around Standard Model predictions. Using the specific example of four-fermion operators in top-quark pair production at the Large Hadron Collider (LHC), we provide a detailed quantitative assessment of these resonance distortions. We explore how continuum four-fermion interactions affect the resonance shapes, creating potential tensions between the high-statistics resonance regions and rare, high momentum-transfer continuum excesses. Our findings indicate that, although four-fermion interactions do modify the on-shell region comparably to continuum enhancements, current experimental strategies at the high-luminosity LHC are unlikely to capture these subtle interference-induced distortions. Nonetheless, such effects could become critical for precision analyses at future lepton colliders, such as the FCC-ee. Our work underscores the importance of resonance-shape measurements as complementary probes in global EFT approaches, guiding robust and self-consistent experimental strategies in ongoing and future high-energy physics programs.

Felix Egle

Distorting the top resonance with effective interactions

We investigate the potential of future electron-positron colliders, such as FCC-ee and CEPC, to probe 2-Higgs-doublet models (2HDMs) that facilitate a strong first-order electroweak phase transition (SFOEWPT), a necessary condition for electroweak baryogenesis. Focusing on a 2HDM in the CP-conserving limit, we identify parameter regions consistent with an SFOEWPT and evaluate their compatibility with projected precision electroweak and Higgs measurements, as well as searches for exotic Higgs bosons. We show that radiative corrections to $\textit{e}$ $\textit{e}$ → $\textit{hZ}$ production introduce deviations in the cross section that are resolvable with the anticipated sub-percent precision at lepton colliders even when experimental outcomes of the LHC and $\textit{Z}$ pole measurements are in agreement with the SM. This underscores the opportunities of a precision lepton collider to explore BSM quantum corrections to the Higgs sector more broadly.

Francisco Arco

Stefano Noi

$\textit{Z}$ and Higgs factory implications of two Higgs doublets with first-order phase transitions

TeV-scale <math altimg='si16.svg'><msup><mi>Z</mi><mo>&#8242;</mo></msup></math> bosons with family-dependent couplings can explain some anomalies inferred from <math altimg='si37.svg'><mrow><mi>B</mi><mo linebreak='goodbreak'>&#8722;</mo></mrow></math>meson measurements of processes involving the <math altimg='si38.svg'><mrow><mi>b</mi><mo>&#8594;</mo><mi>s</mi><msup><mi>&#8467;</mi><mo>+</mo></msup><msup><mi>&#8467;</mi><mo>&#8722;</mo></msup></mrow></math> transition. A <math altimg='si16.svg'><msup><mi>Z</mi><mo>&#8242;</mo></msup></math> originating from kinetically-mixed spontaneously broken <math altimg='si39.svg'><mrow><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><msub><mi>B</mi><mn>3</mn></msub><mo>&#8722;</mo><msub><mi>L</mi><mn>2</mn></msub></mrow></msub></mrow></math> gauge symmetry has been shown to greatly ameliorate global fits [1] in a &#8216;flavour-preferred&#8217; region of parameter space. We provide an exploration of this region at the high luminosity (HL-)LHC with particular attention to which signals could be verified across different discovery modes. Even if the HL-LHC does not discover the <math altimg='si16.svg'><msup><mi>Z</mi><mo>&#8242;</mo></msup></math> boson in a resonant di-lepton channel, a FCC-ee <math altimg='si11.svg'><mi>Z</mi></math>-pole run would detect oblique corrections to the electroweak precision observables (EWPOs). Changes due to <math altimg='si16.svg'><msup><mi>Z</mi><mo>&#8242;</mo></msup></math>-induced non-oblique corrections are unlikely to be detected, to within experimental precision. In any case, the extended discovery potential offered by a 100 TeV <math altimg='si40.svg'><mrow><mi>p</mi><mi>p</mi><mo linebreak='goodbreak'>&#8722;</mo></mrow></math>collider would afford sensitivity to the entire flavour-preferred region and enable a fine-grained and forensic analysis of the model.

Ben Allanach

A <math altimg='si37.svg'><mrow><mi>B</mi><mo linebreak='goodbreak'>&#8722;</mo></mrow></math>anomaly motivated <math altimg='si16.svg'><msup><mi>Z</mi><mo>&#8242;</mo></msup></math> boson at the energy and precision frontiers

The evaluation of effective potentials is critical for a range of phenomenological applications, including inflation, vacuum stability, and phase transitions. A drawback arises from the gauge dependence of the effective potential. Furthermore, in theories with spontaneous symmetry breaking, the effective potential exhibits infrared (IR) divergences in the limit of vanishing Goldstone masses. By considering the multiplicative anomaly that arises due to nonfactorization of elliptic operators in the Fermi gauge when computing the effective potential at one-loop order, we demonstrate that its gauge independence and IR behavior are improved to the corresponding findings of Landau gauge calculations simultaneously. The latter are straightforwardly and transparently reproduced using an approach that employs the heat kernel technique, thereby providing a shortcut to reflect anomaly-related cancellations from the outset. Our findings generalize to the treatment of the effective potential at finite temperature. In particular, the heat kernel extends gauge independence to any value of the expansion in mass over temperature.

Debanjan Balui

Debmalya Dey

Subhendra Mohanty

Gauge choices, infrared pitfalls, and thermal effects in effective potentials

We present a momentum-dependent reweighting strategy to extend current LHC di-Higgs analyses within the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi></math> framework and Standard Model effective field theory into the bosonic sector of the Higgs effective field theory (HEFT). Unlike Standard Model effective field theory, where symmetry constraints tightly correlated multi-Higgs processes, HEFT allows for a broader range of momentum-dependent deviations that can substantially impact di-Higgs kinematics and offer a powerful probe of nonlinear Higgs dynamics. We generalize the interpretation of existing experimental analyses by integrating HEFT operators up to chiral dimension 4 into differential Monte Carlo reweighting. We quantify the sensitivity to representative HEFT operators using multidimensional likelihoods for Run 3 and project the reach at the high-luminosity LHC. Particular emphasis is placed on how different exclusive final states, such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover><mi>γ</mi><mi>γ</mi></math>, respond to momentum enhancements and how their complementary event selections drive exclusion limits. We further explore how rare final states, especially four-top production, can provide orthogonal constraints on HEFT-induced modifications, thereby enhancing global sensitivity to new physics effects in the Higgs sector.

Sweden

Tom Ingebretsen Carlson

Jörgen Sjölin

Harnessing Higgs boson kinematics for HEFT constraints

We investigate the impact of momentum-dependent particle widths and propagators on gauge and Higgs bosons and the top quark within the Standard Model (SM) and its effective field theory (SMEFT) extensions near thresholds. By incorporating self-energy corrections via Dyson resummation, we quantify deviations from the fixed-width approximation and assess their implications for collider observables. While effects on the Higgs boson are negligible and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math> boson shows percent-level deviations in reconstructed transverse mass distributions, the top quark exhibits significant sensitivity near its mass threshold. Future lepton colliders, e.g., electron-positron machines or muon colliders, can offer sensitivity to these effects, enabling constraints on SMEFT Wilson coefficients. We perform a representative case study for the precision frontier available with a staged future muon collider. Our results highlight that momentum dependencies can provide additional sensitivity at precision-era experiments, enhancing the potential for discovering new physics there.

Impact of new physics on momentum-dependent particle widths and propagators