arXiv subjects

Tuomas V. I. Tenkanen

Publications and source records attributed to Tuomas V. I. Tenkanen.

At least 19 recordsLinked to original sources

arXiv2026

Higher-dimensional operators at finite-temperature affect gravitational-wave predictions

We investigate the effect of higher-dimensional marginal operators on the thermodynamics of cosmological phase transitions. Using the Abelian Higgs model as a representative for radiatively-generated one-step transitions, we systematically match these operators, which arise at higher orders in the underlying high-temperature expansion of thermal effective field theory, and use field redefinitions to construct a complete, minimal, and gauge-invariant operator basis. The Abelian Higgs model shares the essential infrared structure of more realistic gauge-Higgs theories at high temperatures, allowing us to test the validity of dimensional reduction in a simplified setting. We argue that for strong transitions, temporal gauge modes, which enhance the transition strength, should be treated on equal footing with spatial ones. Marginal operators are found to weaken the transition and introduce significant uncertainties for strong transitions. For transitions strong enough to produce gravitational waves detectable by LISA, our findings suggest that the high-temperature expansion may break down entirely. This would limit the applicability of effective theory techniques, including their use in non-perturbative lattice studies.

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arXiv2026

Non-perturbative determination of the sphaleron rate for first-order phase transitions

In many extensions of the Standard Model electroweak phase transitions at high temperatures can be described in a minimal dimensionally reduced effective theory with SU(2) gauge field and fundamental Higgs scalar. In this effective theory, all thermodynamic information is governed by two dimensionless ratios $x \equiv λ_3/g^2_3$ and $y\equiv m^2_3/g^4_3$, where $λ_3$, $m^2_3$ and $g_3$ are the effective thermal scalar self-interaction coupling, the thermal mass and the effective gauge-coupling, respectively. By using non-perturbative lattice simulations to determine the rate of sphaleron transitions in the entire $(x,y)$-plane corresponding to the Higgs phase, and by applying previous lattice results for the bubble nucleation, we find a condition $x(T_c) \lesssim 0.025$ to guarantee preservation of the baryon asymmetry, which translates to $v/T_c \equiv \sqrt{2 Δ\langle ϕ^\dagger ϕ\rangle}/T_c \gtrsim 1.33$ for the (gauge-invariant) discontinuity in Higgs condensate. This indicates that viability of the electroweak baryogenesis requires the phase transition to be slightly stronger than previously anticipated. Finally, we present a general template for analysing such viability in a wide class of beyond the Standard Model theories, in which new fields are heavy enough to be integrated out at high temperature.

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arXiv2025

Finite-temperature bubble nucleation with shifting scale hierarchies

Focusing on supercooled phase transitions in models with classical scale symmetry, we formulate a state-of-the art framework for computing the bubble-nucleation rate, accounting for the presence of various energy scales. In particular, we examine the limitations of derivative expansions in constructing a thermal effective field theory for bubble nucleation. We show that for gauge field fluctuations, derivative expansions diverge after the leading two orders due to the strong variation in gauge field masses between the high- and low-temperature phases. By directly computing these contributions using the fluctuation determinant, we capture these effects while also accounting for large explicit logarithms at two loops, utilising the exact renormalisation group structure of the EFT. Finally, we demonstrate how this approach significantly improves nucleation rate calculations compared to leading-order results, providing a more robust framework for predicting gravitational-wave signals from supercooled phase transitions in models such as the SU(2)cSM.

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arXiv2025

Cosmological phase transitions without high-temperature expansions

We introduce a new framework for perturbatively computing equilibrium thermodynamic properties of cosmological phase transitions to high loop orders, using the full four-dimensional resummed thermal effective potential and avoiding the limitations of standard high-temperature approximations. By systematically disentangling the physics of hard and soft momentum scales, our approach unifies their treatment within a single expression, enabling consistent handling of both vacuum and thermal divergences across all mass regimes. This core innovation enables the efficient numerical evaluation of massive multiloop thermal sum-integrals, achieved through a finite-temperature generalization of Loop-Tree Duality -- an advanced algorithmic technique originally developed to render vacuum Feynman integrals numerically tractable via Monte Carlo methods. As a proof of principle, we apply the framework to a scalar-Yukawa model, presenting a complete two-loop calculation and a novel three-loop extension -- the first fully massive three-loop sum-integral computation without relying on high-temperature expansions. Our approach opens the door to precise perturbative predictions of the phase structure in a broad class of beyond-the-Standard-Model scenarios, including those featuring strong first-order phase transitions relevant for gravitational-wave signals, where conventional high-temperature approximations break down.

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arXiv2025

An Effective Sphaleron Awakens

Using thermal effective field theory, we present a self-consistent perturbative formulation of the Higgs phase sphaleron rate after a radiatively-induced first-order phase transition. This gauge-invariant formulation is based on dimensionally reduced effective field theory (3D EFT) at high temperatures and paves a way for including higher order corrections within the 3D EFT perturbation theory without double counting. Concretely, we compute the Higgs phase sphaleron rate in a semi-classical approximation within the two-loop resummed 3D EFT. We find compact results for the sphaleron rate and the baryon washout factor as well as criteria for the baryon number preservation by providing a clear connection to the results obtained using a similar 3D EFT description for the bubble nucleation. We demonstrate these calculations for the real triplet-extended Standard Model, and conclude that when all two-loop thermal effects for the matching are accounted, no sufficiently strong one-step electroweak phase transitions exist within the parameter space regime that can be mapped onto the 3D EFT we have considered.

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arXiv2024

Refining Gravitational Wave and Collider Physics Dialogue via Singlet Scalar Extension

Employing effective field theory techniques, we advance computations of thermal parameters that enter predictions for the gravitational wave spectra from first-order electroweak phase transitions. Working with the real-singlet-extended Standard Model, we utilize recent lattice simulations to confirm the existence of first-order phase transitions across the free parameter space. For the first time, we account for several important two-loop corrections in the high-temperature expansion for determining thermal parameters, including the bubble wall velocity in the local thermal equilibrium approximation. We find that the requirement of completing bubble nucleation imposes stringent bounds on the new scalar boson mass. Moreover, the prospects for detection by LISA require first-order phase transitions in a two-step phase transition, which display strong sensitivity to the portal coupling between the Higgs and the singlet. Interestingly, signals from di-Higgs boson production at the HL-LHC probe parameter regions that significantly overlap with the LISA-sensitive region, indicating the possibility of accounting for both signals if detected. Conversely, depending on the mixing angle, a null result for di-Higgs production at the HL-LHC could potentially rule out the model as an explanation for gravitational wave observations.

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arXiv2024

Investigating two-loop effects for first-order electroweak phase transitions

We study first-order electroweak phase transitions in the real-singlet extended Standard Model, for which non-zero mixing between the Higgs and the singlet can efficiently strengthen the transitions. We perform large-scale parameter space scans of the model using two-loop effective potential at next-to-next-to leading order in the high-temperature expansion, greatly improving description of phase transition thermodynamics over existing one-loop studies. We find that 1) two-loop corrections to the effective potential lead to narrower regions of strong first-order transitions and significantly smaller critical temperatures, 2) transitions involving a discontinuity in the singlet expectation value are significantly stronger at two-loop order, 3) high-temperature expansion is accurate for a wide range of parameter space that allows strong transitions, although it is less reliable for the very strongest transitions. These findings suggest revisiting past studies that connect the possibility of a first-order electroweak phase transition with future collider phenomenology.

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arXiv2024

Cosmological phase transitions at three loops: the final verdict on perturbation theory

We complete the perturbative program for equilibrium thermodynamics of cosmological first-order phase transitions by determining the finite-temperature effective potential of gauge-Higgs theories at next-to-next-to-next-to-next-to-leading order (N$^4$LO). The computation of the three-loop effective potential required to reach this order is extended to generic models in dimensionally reduced effective theories in a companion article. Our N$^4$LO result is the last perturbative order before confinement renders electroweak gauge-Higgs theories non-perturbative at four loops. By contrasting our analysis with non-perturbative lattice results, we find a remarkable agreement. As a direct application for predictions of gravitational waves produced by a first-order transition, our computation provides the final fully perturbative results for the phase transition strength and speed of sound.

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arXiv2024

Addressing the Gravitational Wave - Collider Inverse Problem

We provide a roadmap for analyzing the interplay between hypothetical future collider observations and the detection of a gravitational wave signal produced by a strong first order electroweak phase transition in beyond the Standard Model (BSM) theories. A cornerstone of this roadmap is a combination of a dimensionally reduced, three-dimensional effective field theory and results of both perturbation theory and non-perturbative lattice simulations. For the first time we apply these state-of-the-art methods to a comprehensive parameter space scan of a BSM theory. Concretely, we study an extension with the real scalar triplet, which admits a possible two-step electroweak symmetry-breaking thermal history. We find that (1) a first order transition during the second step could generate a signal accessible to LISA generation detectors and (2) the gravitational wave signal displays a strong sensitivity to the portal coupling between the new scalar and the Higgs boson, and (3) the ability for future experiments to detect the produced gravitational waves depends decisively on the wall velocity of the bubbles produced during the phase transition. We illustrate how a combination of direct and indirect measurements of the new scalar properties, in combination with the presence or absence of a gravitational wave detection, could test the model and identify the values of the model parameters.

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arXiv2024

Gravitational waves from supercooled phase transitions: dimensional transmutation meets dimensional reduction

Models with radiative symmetry breaking typically feature strongly supercooled first-order phase transitions, which result in an observable stochastic gravitational wave background. In this work, we analyse the role of higher order thermal corrections for these transitions, applying high-temperature dimensional reduction to a theory with dimensional transmutation. In particular, we study to what extent high-temperature effective field theories (3D EFT) can be used. We find that despite significant supercooling down from the critical temperature, the high-temperature expansion for the bubble nucleation rate can be applied using the 3D EFT framework, and we point out challenges in the EFT description. We compare our findings to previous studies, and find that the next-to-leading order corrections obtained in this work have a significant effect on the predictions for GW observables, motivating a further exploration of higher order thermal effects.

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arXiv2024

Singlet-assisted electroweak phase transition at two loops

We investigate the electroweak phase transition in the real-singlet extension of the Standard Model at two-loop level, building upon existing one-loop studies. We calculate the effective potential in the high-temperature approximation and detail the required resummations at two-loop order. In typical strong-transition scenarios, we find deviations of order $20\% - 50\%$ from one-loop results in transition strength and critical temperature for both one- and two-step phase transitions. For extremely strong transitions, the discrepancy with one-loop predictions is even larger, presumably due to sizable scalar couplings in the tree-level potential. Along the way, we obtain a dimensionally-reduced effective theory applicable for non-perturbative lattice studies of the model.

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arXiv2023

Perturbative effective field theory expansions for cosmological phase transitions

Guided by previous non-perturbative lattice simulations of a two-step electroweak phase transition, we reformulate the perturbative analysis of equilibrium thermodynamics for generic cosmological phase transitions in terms of effective field theory (EFT) expansions. Based on thermal scale hierarchies, we argue that the scale of many interesting phase transitions is in-between the soft and ultrasoft energy scales, which have been the focus of studies utilising high-temperature dimensional reduction. The corresponding EFT expansions provide a handle to control the perturbative expansion, and allow us to avoid spurious infrared divergences, imaginary parts, gauge dependence and renormalisation scale dependence that have plagued previous studies. As a direct application, we present a novel approach to two-step electroweak phase transitions, by constructing separate effective descriptions for two consecutive transitions. Our approach provides simple expressions for effective potentials separately in different phases, a numerically inexpensive method to determine thermodynamics, and significantly improves agreement with the non-perturbative lattice simulations.

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arXiv2022

Strong electroweak phase transition in $t$-channel simplified dark matter models

Beyond the Standard Model physics is required to explain both dark matter and the baryon asymmetry of the universe, the latter possibly generated during a strong first-order electroweak phase transition. While many proposed models tackle these problems independently, it is interesting to inquire whether the same model can explain both. In this context, we link state-of-the-art perturbative assessments of the phase transition thermodynamics with the extraction of the dark matter energy density. These techniques are applied to a next-to-minimal dark matter model containing an inert Majorana fermion that is coupled to Standard Model leptons via a scalar mediator, where the mediator interacts directly with the Higgs boson. For dark matter masses 180 GeV $ < M_χ<$ 300 GeV, we discern regions of the model parameter space that reproduce the observed dark matter energy density and allow for a first-order phase transition, while evading the most stringent collider constraints.

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arXiv2022

Computing the gauge-invariant bubble nucleation rate in finite temperature effective field theory

A gauge-invariant framework for computing bubble nucleation rates at finite temperature in the presence of radiative barriers was presented and advocated for model-building and phenomenological studies in an accompanying article arXiv:2112.05472. Here, we detail this computation using the Abelian Higgs Model as an illustrative example. Subsequently, we recast this approach in the dimensionally-reduced high-temperature effective field theory for nucleation. This allows for including several higher order thermal resummations and furthermore delineate clearly the approach's limits of validity. This approach provides for robust perturbative treatments of bubble nucleation during possible first-order cosmic phase transitions, with implications for electroweak baryogenesis and production of a stochastic gravitational wave background. Furthermore, it yields a sound comparison between results of perturbative and non-perturbative computations.

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arXiv2022

Speed of sound in cosmological phase transitions and effect on gravitational waves

The energy budget for gravitational waves of a cosmological first order phase transitions depends on the speed of sound in the thermal plasma in both phases around the bubble wall. Working in the real-singlet augmented Standard Model, which admits a strong two-step electroweak phase transition, we compute higher order corrections to the pressure and sound speed. We compare our result to lower-order approximations to the sound speed and the energy budget and investigate the impact on the gravitational wave signal. We find that deviations in the speed of sound from $c_s^2 = 1/3$ are enhanced up to $\mathcal O(5\%)$ in our higher-order computation. This results in a suppression in the energy budget of up to $\mathcal O (50\%)$ compared to approximations assuming $c_s^2 = 1/3$. The effect is most significant for hybrid and detonation solutions. We generalise our discussion to the case of multiple inert scalars and the case of a reduced number of fermion families in order to mimic hypothetical dark sector phase transitions. In this sector with modified field content, the sound speed can receive significant suppression, with potential order-of-magnitude impact on the gravitational wave amplitude.

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arXiv2022

DRalgo: a package for effective field theory approach for thermal phase transitions

DRalgo is an algorithmic implementation that constructs an effective, dimensionally reduced, high-temperature field theory for generic models. The corresponding Mathematica package automatically performs the matching to next-to-leading order. This includes two-loop thermal corrections to scalar and Debye masses as well as one-loop thermal corrections to couplings. DRalgo also allows for integrating out additional heavy scalars. Along the way, the package provides leading-order beta functions for general gauge-charges and fermion-families; both in the fundamental and in the effective theory. Finally, the package computes the finite-temperature effective potential within the effective theory. The article explains the theory of the underlying algorithm while introducing the software on a pedagogical level.

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arXiv2022

Combining thermal resummation and gauge invariance for electroweak phase transition

For computing thermodynamics of the electroweak phase transition, we discuss a minimal approach that reconciles both gauge invariance and thermal resummation. Such a minimal setup consists of a two-loop dimensional reduction to three-dimensional effective theory, a one-loop computation of the effective potential and its expansion around the leading-order minima within the effective theory. This approach is tractable and provides formulae for resummation that are arguably no more complicated than those that appear in standard techniques ubiquitous in the literature. In particular, we implement renormalisation group improvement related to the hard thermal scale. Despite its generic nature, we present this approach for the complex singlet extension of the Standard Model which has interesting prospects for high energy collider phenomenology and dark matter predictions. The presented expressions can be used in future studies of phase transition thermodynamics and gravitational wave production.

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arXiv2021

Nucleation at finite temperature: a gauge-invariant, perturbative framework

We present a gauge-invariant framework for bubble nucleation in theories with radiative symmetry breaking at high temperature. As a procedure, this perturbative framework establishes a practical, gauge-invariant computation of the leading order nucleation rate, based on a consistent power counting in the high-temperature expansion. In model building and particle phenomenology, this framework has applications such as the computation of the bubble nucleation temperature and the rate for electroweak baryogenesis and gravitational wave signals from cosmic phase transitions.

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