WallGo is an open-source software designed to compute the bubble wall velocity in first-order cosmological phase transitions. Additionally, it evaluates the energy budget available for generating gravitational waves. The main part of WallGo, built in Python, determines the wall velocity by solving the scalar-field(s) equation of motion, the Boltzmann equations and energy-momentum conservation for the fluid velocity and temperature. WallGo also includes two auxiliary modules: WallGoMatrix, which computes matrix elements for out-of-equilibrium particles, and WallGoCollision, which performs higher-dimensional integrals for Boltzmann collision terms. Users can implement custom models by defining an effective potential and specifying a list of out-of-equilibrium particles and their interactions.

Sweden

Andreas Ekstedt

United Kingdom

Oliver Gould

Finland

Joonas Hirvonen

Canada

Benoit Laurent

Lauri Niemi

Switzerland

Philipp Schicho

Jorinde Vis

How fast does the WallGo? A package for computing wall velocities in first-order phase transitions

Determining the bubble wall velocity in first-order phase transitions is a challenging task, requiring the solution of (coupled) equations of motion for the scalar field and Boltzmann equations for the particles in the plasma. The collision terms appearing in the Boltzmann equation present a prominent source of uncertainty as they are often known only at leading log accuracy. In this paper, we derive upper and lower bounds on the wall velocity, corresponding to the local thermal equilibrium and ballistic limits. These bounds are completely independent of the collision terms.

Wen-Yuan Ai

Bounds on the bubble wall velocity

The production of three Higgs bosons at hadron colliders can be enhanced by a double-resonant effect in the ℤ2-symmetric two-real-singlet extension of the Standard Model, making it potentially observable in future LHC runs. The production rate is maximized for large scalar couplings, which prompts us to carefully reconsider the perturbativity constraints on the theory. This leads us to construct a new set of 140 benchmark points that have a triple Higgs boson production cross-section at least 100 times larger than the SM value.

Netherlands

Osama Karkout

United States

Andreas Papaefstathiou

Marieke Postma

France

Germany

Gilberto Tetlalmatzi-Xolocotzi

Tristan Pree

Triple Higgs boson production and electroweak phase transition in the two-real-singlet model

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.

Poland

Maciej Kierkla

Bogumiła Świeżewska

China

Tuomas Tenkanen

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

We reassess nonstandard triple gauge couplings in the light of the recent <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo>)</mo><mi>μ</mi></msub></math> measurement at FNAL, the new lattice theory result of <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo>)</mo><mi>μ</mi></msub></math>, and the updated measurements of several <math><mi>B</mi></math>-decay modes. In the framework of SMEFT, three bosonic dimension-6 operators are invoked to parametrize physics beyond the Standard Model, and their contributions to such low-energy observables are computed. Constraints on the corresponding Wilson coefficients are then derived from fits to the current experimental bounds on the observables and compared with the most stringent ones available from the 13 TeV LHC data in the <math><msup><mi>W</mi><mo>+</mo></msup><msup><mi>W</mi><mo>−</mo></msup></math> and <math><msup><mi>W</mi><mo>±</mo></msup><mi>Z</mi></math> production channels.

India

Debajyoti Choudhury

Kuldeep Deka

Suvam Maharana

Lalit Kumar Saini

Anomalous gauge couplings vis-à-vis <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo>)</mo><mi>μ</mi></msub></math> and flavor observables

We re-derive the vev-insertion approximation (VIA) source in electroweak baryogenesis. In contrast to the original derivation, we rely solely on 1-particle-irreducible self-energy diagrams. We solve the Green’s function equations both perturbatively and resummed over all vev-insertions. The VIA source corresponds to the leading order contribution in the gradient expansion of the Kadanoff-Baym (KB) equations. We find that it vanishes both for bosons and fermions, both in the perturbative and in the resummed approach. The non-existence of the source is a result of a cancellation between different terms in the KB equations, and persists after resumming the masses.

Japan

Graham White

Resummation and cancellation of the VIA source in electroweak baryogenesis

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   <math> <msubsup> <mi>c</mi> <mi>s</mi> <mn>2</mn> </msubsup> </math>  $$ {c}_s^2 $$  = 1/3 are enhanced up to   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (5%) in our higher-order computation. This results in a suppression in the energy budget of up to   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (50%) compared to approximations assuming   <math> <msubsup> <mi>c</mi> <mi>s</mi> <mn>2</mn> </msubsup> </math>  $$ {c}_s^2 $$  = 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.

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

We derive one- and two-loop renormalization group equations (RGEs) of Higgs-R 2 inflation. This model has a non-minimal coupling between the Higgs and the Ricci scalar and a Ricci scalar squared term on top of the standard model. The RGEs derived in this paper are valid as long as the energy scale of interest (in the Einstein frame) is below the Planck scale. We also discuss implications to the inflationary predictions and the electroweak vacuum metastability.

Yohei Ema

Kyohei Mukaida

Renormalization group equations of Higgs-R 2 inflation

We point out that a model with scalar fields with a large nonminimal coupling to the Ricci scalar, such as Higgs inflation, can be regarded as a nonlinear sigma model (NLSM). With the inclusion of not only the scalar fields but also the conformal mode of the metric, our definition of the target space of the NLSM is invariant under the frame transformation. We show that the σ-meson that linearizes this NLSM to be a linear sigma model (LSM) corresponds to the scalaron, the degree of freedom associated to the R 2 term in the Jordan frame. We demonstrate that quantum corrections inevitably induce this σ-meson in the large-N limit, thus providing a frame independent picture for the emergence of the scalaron. The resultant LSM only involves renormalizable interactions and hence its perturbative unitarity holds up to the Planck scale unless it hits a Landau pole, which is in agreement with the renormalizability of quadratic gravity.

Higgs inflation as nonlinear sigma model and scalaron as its σ-meson

In electroweak baryogenesis the baryon asymmetry of the universe is created during the electroweak phase transition. The quantum transport equations governing the dynamics of the plasma particles can be derived in the vev-insertion approximation, which treats the vev-dependent part of the particle masses as a perturbation. We calculate the next-to-leading order (NLO) contribution to the CP-violating source term and CP-conserving relaxation rate, corresponding to Feynman diagrams for the self-energies with four mass insertions. We consider both a pair of Weyl fermions and a pair of complex scalars, that scatter off the bubble wall. We find: (i) The NLO correction becomes large for   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (1) couplings. If only the Standard Model (SM) Higgs obtains a vev during the phase transition, this implies the vev-insertion approximation breaks down for top quarks. (ii) The resonant enhancement of the source term and relaxation rate, that exists at leading order in the limit of degenerate thermal masses for the fermions/scalars, persists at NLO.

Source terms for electroweak baryogenesis in the vev-insertion approximation beyond leading order