UPS PARQUE DE USUARIOS EDIFICIO ASCA

Measurements of di-Higgs production test the hypothesis that the Higgs boson couples to new physics with a mass scale m ∼ 100GeV − 1TeV. In the hot conditions of the early universe, these particles would have been in thermal equilibrium with the SM plasma. As the universe expanded and cooled, the presence of this new physics could affect the nature of the electroweak phase tran- sition (EWPT).

Electroweak phase transition and electroweak baryogenesis: The electroweak phase transition is the dynamical process by which the Higgs field acquired its nonzero vacuum expectation value in the early universe. The SM predicts that the phase transition is a smooth, continuous crossover with the Higgs field evolving almost homogeneously from 0 to 246 GeV as the temperature is de- creased through the weak scale. However, the presence of new physics can easily and dramatically change the predicted nature of the phase transition, even leading to a first order phase transition. Unlike the gentle continuous crossover, a first order phase transition is a violent event during which bubbles nucleate, expand, collide, and eventually merge to overtake the whole system. Today, our understanding of Higgs physics is too poor to discriminate between even these two qualitatively different scenarios.

If the cosmological electroweak phase transition was a first order one, it would have profound implications for cosmology. The out-of-equilibrium conditions of a first order phase transition pro- vide the right environment for the generation of cosmological relics. In this way, a first order elec- troweak phase transition could explain why our universe has an excess of matter over antimatter on cosmological scales through the mechanism of electroweak baryogenesis [121,335]. A strong first- order electroweak phase transition can have other interesting cosmological consequences, such as the dilution of pre-existing thermal relics through entropy injection [336] and the generation of a stochastic gravitational wave background (discussed below).

3.6. Connection to Cosmology 85 −4 −2 0 2 4 6 8 10 λ221/v −10 −5 0 5 10 b3 /v m2= 170 GeV, sin θ = 0.05 −4 −2 0 2 4 6 8 10 λ221/v −10 −5 0 5 10 b3 /v m2= 170 GeV, sin θ = 0.2

Figure 3.20: Figure adapted from Ref. [337] showing slices of the real singlet extension of the SM for a singlet-like scalar mass of 170 GeV and two different mixing angles with the Higgs. Blue and purple shaded points feature a strong first-order electroweak phase transition. Regions outside of the red dashed contours feature deviations in the 125 GeV Higgs self-coupling larger than 30%. The green (yellow) shaded regions show the discovery (exclusion) reach for pair production of the new scalar at the 14 TeV HL-LHC in a trilepton final state discussed further in Ref. [337].

tential responsible for strengthening the electroweak phase transition. A typical example of this in the real singlet extension of the SM is illustrated in Fig.3.20(adapted from Ref. [337]), which shows slices of the parameter space consistent with a strong first-order electroweak phase transi- tion (blue and purple points). Outside of the red dashed contours the deviations in the Higgs self coupling are larger than 30%. Precise measurements of the double Higgs production rate can thus provide a powerful probe of the electroweak phase transition in this scenario (see also Ref. [338]). Similar conclusions hold in other extensions of the SM as well [120,123]. For scenarios in which a new scalar heavier than 250 GeV coupled to the Higgs generates a strong first-order EWPT, resonant double Higgs production mediated by the new scalar provides a powerful handle on the nature of electroweak symmetry breaking [193]. The prospects for such a search at the high luminosity LHC are shown in Fig.3.21(adapted from Ref. [209]), again for slices of the singlet model parameter space. Strong first order phase transitions generated by new scalars with masses up to the TeV scale can be probed by resonant di-Higgs production (see also Refs. [190,193,203]). In models with addi- tional scalars, pair production of the other scalar states can provide a complementary probe of the electroweak phase transition [337,339]. The shaded regions of Fig.3.20correspond to the projected HL-LHC sensitivity to pair production of singlet-like scalars in a particular trilepton channel de- tailed in Ref. [337]. The sensitivity shown is likely conservative, and searches for double scalar pair production involving states other than the 125 GeV Higgs can be a promising avenue for probing electroweak symmetry breaking in the early Universe at the LHC and beyond.

Complementarity with gravitational wave observations: The inhomogeneous nature of a first order phase transition provides the requisite quadrupole moment to source gravitational waves [340]. Since gravitational waves are very weakly interacting, they propagate freely until reaching us at Earth today. If we can observe this primordial stochastic gravitational wave background, it could provide direct evidence for a first order electroweak phase transition and thereby indicate the pres- ence of new physics coupled to the Higgs.

1st Order PT w/ interference w/o interference 2σ 5σ 300 400 500 600 700 800 900 0.5 0.6 0.7 0.8 0.9 1.0 mS(GeV) λ111 /λSM tanβ= 1 @ HL-LHC 1st Order PT w/ interference w/o interference 2σ 5σ 300 400 500 600 700 800 900 0.5 0.6 0.7 0.8 0.9 1.0 mS(GeV) λ111 /λSM tanβ=10 @ HL-LHC

Figure 3.21: Sensitivity of resonant di-Higgs production (black and red contours) to regions of the singlet model parameter space with a strong first-order electroweak phase transition (purple). De- tails can be found in Ref. [209] from which this figure was adopted.

ular fashion by the LIGO and VIRGO collaborations [341]. Moreover, efforts are underway to build and launch a gravitational wave interferometer in space. The Laser Interferometer Space Antenna (LISA) [342] collaboration has recently celebrated a successful pathfinder mission and is expected to be launched in the early 2030s. With an interferometer that is no longer tethered to the Earth, the length of its arms can be increased to millions of kilometers, which gives it sensitivity to the ∼ mHz gravitational waves that are expected to arise from a first order electroweak phase transition [343].

It is important to understand how future collider measurements, such as Higgs pair produc- tion, and observations of a stochastic GW background can complement each other in exploring new physics yielding a strong first-order electroweak phase transition. The simplest template where these questions can be studied is an extension of the SM by a singlet scalar discussed above. The complementarity between GW and collider measurements has recently been explored in this model by the authors of Refs. [208] and [207], and we summarize the main results here. The left panel of Fig.3.22displays the GW spectrum obtained at a benchmark point in this model which is compat- ible with electroweak precision measurements and all other phenomenological constraints. The mass of the extra singlet is 455 GeV. The total GW signal is shown in red, while the different contri- butions from sound waves (turbulence) are shown in blue (brown). The color-shaded regions are the experimentally sensitive regions for various GW detectors. The right panel of Fig.3.22shows AT- LAS (solid green lines) [66] and CMS (solid brown lines) [67] limits on resonant di-Higgs production for 36.1 fb−1and 35.9 fb−1 of data, respectively, combining several final states. A simple rescaling of the current limits to 3000 fb−1at the HL-LHC (13 TeV) is performed to obtain the correspond- ing dashed line future projections. For the points on the parameter space giving detectable GWs with a signal-to-noise ratio at LISA larger than 10, the resonant cross sections from gluon fusion at NNLO+NNLL are computed using the results in [19]. It is clear that resonant di-Higgs studies at the HL-LHC and GW signals from LISA can play complementary roles in exploring this model in the future.

3.7. H H and Dark Matter (Missing Energy) 87