We study the formation of primordial black holes (PBHs) and stochastic gravitational waves background (SGWB) produced by the supercooled radion phase transition (PT) in warped extra-dimension models solving the gauge hierarchy problem. We first determine how the SGWB and the produced PBH mass and abundance depend on the warped model’s infrared energy scale $\textit{ρ}$, and the number of holographic colors $\textit{N}$. With this finding, we recast on the plane {$\textit{ρ}$, $\textit{N}$} the current SGWB and PBH constraints, as well as the expected parameter reaches of GW detectors, as LISA and ET, and the gravitational lensing ones, such as NGRST. On the same plane, we also map the collider bounds on massive graviton production, and cosmological bounds on the radion phenomenology. We find that, for $\textit{N}$ ∼ 10 − 50, the considered PT predicts a PBH population mass in the range $\textit{M}$ ∼ (10 − 10 )$\textit{M}$ for $\textit{ρ}$ ∼ (10 − 10 ) TeV. In the range $\textit{ρ}$ ≃ (0.05 − 0.5) GeV, it can explain the recent SGWB hint at nHz frequencies and generate PBH binaries with mass $\textit{M}$ ∼ (0.1 – 1)$\textit{M}$ detectable at LISA and ET. The experimentally allowed mass region where PBHs can account for the whole dark matter abundance, and are produced with a tuning ≲ 10 , corresponds to 10 TeV ≲ $\textit{ρ}$ ≲ 10 TeV. These PBHs can compensate the lack of natural candidates for dark matter in warped extra dimensional models. Such a region represents a great science case where forthcoming and future colliders like HE-LHC and FCC-hh, gravitational-wave observatories and other PBHs probes play a key complementary role.

Poland

Anish Ghoshal

Spain

Eugenio Megías

Norway

Germano Nardini

Mariano Quirós

Complementary probes of warped extra dimension: colliders, gravitational waves and primordial black holes from phase transitions

We investigate the potential of the warped extradimension framework as an explanation for the recently observed stochastic gravitational background at nHz frequencies in pulsar timing arrays (PTA). Our analysis reveals that the PTA data can be effectively accommodated by a first-order phase transition triggered by a radion at the MeV-GeV scale feebly coupled to the Standard Model. Remarkably, this outcome remains robust irrespective of the specific details of the warped extradimension embedding, providing a foundation for future investigations aiming to develop concrete extradimension descriptions of Nature. We also demonstrate that many existing embeddings are not viable, as their radion and graviton phenomenology clash with a MeV–GeV scale radion. As a possible way out, we sketch a promising solution involving multiple branes, wherein the light radion, graviton, and ensuing light resonances remain consistent with collider bounds and gravity tests.

Pulsar timing array stochastic background from light Kaluza-Klein resonances

We systematically study the holographic phase transition of the radion field in a five-dimensional warped model which includes a scalar potential with a powerlike behavior. We consider Kaluza-Klein (KK) resonances with masses <math><msub><mi>m</mi><mrow><mi>KK</mi></mrow></msub></math> at the TeV scale or beyond. The backreaction of the radion field on the gravitational metric is taken into account by using the superpotential formalism. The confinement/deconfinement first order phase transition leads to a gravitational wave stochastic background which mainly depends on the scale <math><msub><mi>m</mi><mrow><mi>KK</mi></mrow></msub></math> and the number of colors, <math><mi>N</mi></math>, in the dual theory. Its power spectrum peaks at a frequency that depends on the amount of tuning required in the electroweak sector. It turns out that the present and forthcoming gravitational wave observatories can probe scenarios where the KK resonances are very heavy. Current aLIGO data already rule out vector boson KK resonances with masses in the interval <math><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>KK</mi></mrow></msub><mo>∼</mo><mo>(</mo><mn>1</mn><mi>–</mi><mn>10</mn><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>5</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math>. Future gravitational experiments will be sensitive to resonances with masses <math><msub><mi>m</mi><mrow><mi>KK</mi></mrow></msub><mo>≲</mo><msup><mn>10</mn><mn>5</mn></msup><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> (LISA), <math><msup><mn>10</mn><mn>8</mn></msup><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> (aLIGO Design) and <math><msup><mn>10</mn><mn>9</mn></msup><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> (ET). Finally, we also find that the big bang nucleosynthesis bound in the frequency spectrum turns into a lower bound for the nucleation temperature as <math><msub><mi>T</mi><mi>n</mi></msub><mo>≳</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup><msqrt><mi>N</mi></msqrt><msub><mi>m</mi><mrow><mi>KK</mi></mrow></msub></math>.

Gravitational imprints from heavy Kaluza-Klein resonances

We study the electroweak phase transition within a 5D warped model including a scalar potential with an exponential behavior, and strong back-reaction over the metric, in the infrared. By means of a novel treatment of the superpotential formalism, we explore parameter regions that were previously inaccessible. We find that for large enough values of the t’Hooft parameter (e.g. N ≃ 25) the holographic phase transition occurs, and it can force the Higgs to undergo a first order electroweak phase transition, suitable for electroweak baryogenesis. The model exhibits gravitational waves and colliders signatures. It typically predicts a stochastic gravitational wave background observable both at the Laser Interferometer Space Antenna and at the Einstein Telescope. Moreover the radion tends to be heavy enough such that it evades current constraints, but may show up in future LHC runs.

Switzerland

Cosmological phase transitions in warped space: gravitational waves and collider signatures

If the electroweak phase transition (EWPT) is of strongly first order due to higher dimensional operators, the scale of new physics generating them is at the TeV scale or below. In this case the effective-field theory (EFT) neglecting operators of dimension higher than six may overlook terms that are relevant for the EWPT analysis. In this article we study the EWPT in the EFT to dimension eight. We estimate the reach of the future gravitational wave observatory LISA for probing the region in which the EWPT is strongly first order and compare it with the capabilities of the Higgs measurements via double-Higgs production at current and future colliders. We also match different UV models to the previously mentioned dimension-eight EFT and demonstrate that, from the top-down point of view, the double-Higgs production is not the best signal to explore these scenarios.

United Kingdom

Mikael Chala

United States

Claudius Krause

Signals of the electroweak phase transition at colliders and gravitational wave observatories

We investigate multi-lepton signals produced by ElectroWeakino (EWino) decays in the MSSM and the TMSSM scenarios with sfermions, gluinos and non Standard Model Higgses at the TeV scale, with dark matter due to electroweak-scale Binos. We recast the present LHC constraints on EWinos for these models and we find that wide MSSM and TMSSM parameter regions prove to be allowed. We forecast the number of events expected in the signal regions of the experimental multi-lepton analyses in the next LHC runs. The correlations among these numbers will help to determine whether future deviations in multi-lepton data are ascribable to the EWinos, as well as the supersymmetric model they originate from.

Belgium

Chiara Arina

Germany

Víctor Martín-Lozano

Confronting SUSY models with LHC data via electroweakino production

We study the general NMSSM with an emphasis on the parameter regions with a very strong first-order electroweak phase transition (EWPT). In the presence of heavy fields coupled to the Higgs sector, the analysis can be problematic due to the existence of sizable radiative corrections. In this paper we propose a subtraction scheme that helps to circumvent this problem. For simplicity we focus on a parameter region that is by construction hidden from the current collider searches. The analysis proves that (at least) in the identified parameter region the EWPT can be very strong and striking gravitational wave signals can be produced. The corresponding gravitational stochastic background can potentially be detected at the planned space-based gravitational wave observatory eLISA, depending on the specific experiment design that will be approved.

Stephan J. Huber

Thomas Konstandin

Ingo Rues

Detectable gravitational waves from very strong phase transitions in the general NMSSM

We consider dark sector particles (DSPs) that obtain sizeable interactions with Standard Model fermions from a new mediator. While these particles can avoid observation in direct detection experiments, they are strongly constrained by LHC measurements. We demonstrate that there is an important complementarity between searches for DSP production and searches for the mediator itself, in particular bounds on (broad) dijet resonances. This observation is crucial not only in the case where the DSP is all of the dark matter but whenever — precisely due to its sizeable interactions with the visible sector — the DSP annihilates away so efficiently that it only forms a dark matter subcomponent. To highlight the different roles of DSP direct detection and LHC monojet and dijet searches, as well as perturbativity constraints, we first analyse the exemplary case of an axial-vector mediator and then generalise our results. We find important implications for the interpretation of LHC dark matter searches in terms of simplified models.

Felix Kahlhoefer

CERN

Matthew McCullough

Kai Schmidt-Hoberg

Constraining dark sectors with monojets and dijets

By means of a relativistic microscopic approach we calculate the expansion velocity of bubbles generated during a first-order electroweak phase transition. In particular, we use the gradient expansion of the Kadanoff-Baym equations to set up the fluid system. This turns out to be equivalent to the one found in the semi-classical approach in the non-relativistic limit. Finally, by including hydrodynamic deflagration effects and solving the Higgs equations of motion in the fluid, we determine velocity and thickness of the bubble walls. Our findings are compared with phenomenological models of wall velocities. As illustrative examples, we apply these results to three theories providing first-order phase transitions with a particle content in the thermal plasma that resembles the Standard Model.

From Boltzmann equations to steady wall velocities

The Triplet extension of the MSSM (TMSSM) alleviates the little hierarchy problem and provides a significant enhancement of the loop-induced diphoton rate of the lightest CP-even Higgs h . In this paper we pursue the analysis of the TMSSM Higgs phenomenology by computing for the first time the h → Z γ decay. Interestingly we find that the rates of loop-induced decays are correlated and their signal strengths can rise up to 40%-60% depending on the channel. We furthermore study the dark matter phenomenology of the TMSSM. The lightest neutralino is a good dark matter candidate in two regions. The first one is related to the Higgs and Z resonances and the LSP is mostly Bino. The second one is achieved for a mass larger than 90 GeV and the LSP behaves as the well-tempered neutralino. An advantage of the triplet contribution is that the well-tempered neutralino can be a Bino-Triplino mixture, relieving the problem of achieving M 2 ~ M 1 in unified scenarios. The dark matter constraints strongly affect the Higgs phenomenology, reducing the potential enhancements of the diphoton and of the Z γ channels by 20% at most. In the near future, dark matter direct searches and collider experiments will probe most of the parameter space where the neutralino is the dark matter candidate.