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

Jorinde Vis

Tristan Pree

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

Pions of a dark sector gauge group can be strongly interacting massive particle (SIMP) dark matter, produced by the freeze-out of 3 → 2 interactions, with naturally large self-interactions. We study if adding a dark photon to the set-up can do it all: i) maintain thermalization with the visible sector, ii) resonantly enhance the 3 → 2 interactions, thus allowing for a perturbative pion description, and iii) provide a velocity dependent self-interaction that can affect small scale structure formation. For N  f  = 3 this minimal setup is marginally excluded, as the required kinetic mixing is too small to maintain thermal equilibrium with the SM. Adding an extra dark quark opens up parameter space, and — perhaps somewhat surprisingly — we find that all bounds can be satisfied for dark pion masses m  π  ∼ 250 − 600 MeV. Dropping the small scale structure requirement iii), a viable setup is reproduced for dark charges of α  d  = 0.01 − 1 and a dark pion mass m  π  ≥ 30 MeV. Late time annihilations are non-negligible making the SIMP dark pion a bit WIMPy.

Pieter Braat

SIMPly add a dark photon

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

In the vev insertion approximation (VIA) the spacetime dependent part of the mass matrix is treated as a perturbation. We calculate the source terms for baryogenesis expanding both the self-energy and propagator to first order in mass insertions, which gives the same results as the usual approach of calculating the self-energy at second order and using zeroth order propagators. This procedure shows explicitly the equivalence between including the mass in the free or in the interaction Lagrangian. The VIA source then originates from the same term in the kinetic equation as the semi-classical source, but at leading order in the derivative expansion (the expansion in diamond operators). On top, another type of derivative expansion is done, which we estimate to be valid for a bubble width larger than the inverse thermal width. This cuts off the divergence in the VIA source in the limit that the thermal width vanishes.

A different perspective on the vev insertion approximation for electroweak baryogenesis

To obtain a first order phase transition requires large new physics corrections to the Standard Model (SM) Higgs potential. This implies that the scale of new physics is relatively low, raising the question whether an effective field theory (EFT) description can be used to analyse the phase transition in a (nearly) model-independent way. We show analytically and numerically that first order phase transitions in perturbative extensions of the SM cannot be described by the SM-EFT. The exception are Higgs-singlet extension with tree-level matching; but even in this case the SM-EFT can only capture part of the full parameter space, and if truncated at dim-6 operators, the description is at most qualitative. We also comment on the applicability of EFT techniques to dark sector phase transitions.

Cosmological phase transitions: is effective field theory just a toy?

Most of the inflationary models that are in agreement with the Planck data rely on the presence of non-renormalizable operators. If the connection to low energy particle physics is made, the renormalization group (RG) introduces a sensitivity to ultraviolet (UV) physics that can be crucial in determining the inflationary predictions. We analyse this effect for the Standard Model (SM) augmented with non-minimal derivative couplings to gravity. Our set-up reduces to the SM for small values of the Higgs field, and allows for inflation in the opposite large field regime. The one-loop beta functions in the inflationary region are calculated using a covariant approach that properly accounts for the non-trivial structure of the field space manifold. We run the SM parameters from the electroweak to the inflationary scale, matching the couplings of the different effective field theories at the boundary between the two regimes, where we also include threshold corrections that parametrize effects from UV physics. We then compute the spectral index and tensor-to-scalar ratio and find that RG flow corrections can be determinant: a scenario that is ruled out at tree level can be resurrected and vice versa.

Jacopo Fumagalli

Melvin Bout

Matching and running sensitivity in non-renormalizable inflationary models

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

We investigate the role of leptons in electroweak baryogenesis by studying a relatively simple framework inspired by effective field theory that satisfies all Sakharov conditions. In particular, we study the effectiveness of CP-violating source terms induced by dimension-six Yukawa interactions for quarks and charged leptons. Despite the relatively small Yukawa coupling, CP-violating source terms involving taus are quite effective and can account for the observed matter-antimatter asymmetry. We obtain analytical and numerical expressions for the total baryon asymmetry, the former providing important insight into what makes lepton CP violation relatively effective compared to quark CP violation. Leptons also play an important role if the CP-violating source involves top quarks. While the tau Yukawa coupling in the Standard Model is small, it significantly enhances the baryon asymmetry by transferring the chiral asymmetry in quarks, which is washed out by strong sphalerons, to a chiral asymmetry in leptons. We conclude that leptons should not be ignored even if CP violation is limited to the quark sector. The role of leptons can be further increased in scenarios of new physics with additional chiral-symmetry-breaking interactions between quarks and leptons, as can happen in models with additional Higgs bosons or leptoquarks. Finally, we study CP-violating dimension-six Yukawa interactions for lighter quarks and leptons but conclude that these lead to too small baryon asymmetries.

Jordy Vries

The role of leptons in electroweak baryogenesis

In new Higgs inflation the Higgs kinetic terms are non-minimally coupled to the Einstein tensor, allowing the Higgs field to play the role of the inflaton. The new interaction is non-renormalizable, and the model only describes physics below some cutoff scale. Even if the unknown UV physics does not affect the tree level inflaton potential significantly, it may still enter at loop level and modify the running of the Standard Model (SM) parameters. This is analogous to what happens in the original model for Higgs inflation. A key difference, though, is that in new Higgs inflation the inflationary predictions are sensitive to this running. Thus the boundary conditions at the EW scale as well as the unknown UV completion may leave a signature on the inflationary parameters. However, this dependence can be evaded if the kinetic terms of the SM fermions and gauge fields are non-minimally coupled to gravity as well. Our approach to determine the model’s UV dependence and the connection between low and high scale physics can be used in any particle physics model of inflation.

Switzerland

Sander Mooij

Unitarity and predictiveness in new Higgs inflation

We investigate electroweak baryogenesis within the framework of the Standard Model Effective Field Theory. The Standard Model Lagrangian is supplemented by dimension-six operators that facilitate a strong first-order electroweak phase transition and provide sufficient CP violation. Two explicit scenarios are studied that are related via the classical equations of motion and are therefore identical at leading order in the effective field theory expansion. We demonstrate that formally higher-order dimension-eight corrections lead to large modifications of the matter-antimatter asymmetry. The effective field theory expansion breaks down in the modified Higgs sector due to the requirement of a first-order phase transition. We investigate the source of the breakdown in detail and show how it is transferred to the CP-violating sector. We briefly discuss possible modifications of the effective field theory framework.