Early Universe Explanations of the Higgs Boson Mass – EUHiggs

In previous work we identified a common feature of models of cosmological selection of the weak

scale. They all possess a special operator called ’trigger’ which is sensitive to the Higgs boson vacuum expectation value. In some sense this is quite obvious: if you want to explain (or select some value for) the Higgs mass, you need something sensitive to it. However it is not trivial at all to find local quantities sensitive to the Higgs mass squared. In the Standard Model (SM) only one example exists: the asymmetric contraction of two gluon field strengths: Tr[GG~]. Even allowing us infinite freedom in the choice of particle content and couplings while going beyond the SM, only two examples exist: a new Higgs doublet H1 with the trigger operator H1H2 and new vector-like fermions with Yukawa couplings to the Higgs charged under a confining gauge group. The equivalent of Tr[GG~] for the new group can serve as a trigger.

The project consists in two steps:

1. Work out the experimental phenomenology of existing trigger operators

2. Make sure that the list of trigger operators is complete

Once we identify all operators and their experimental signatures we can test the idea of cosmological selection of the Higgs mass, since selecting it cosmologically (without traditional anthropic arguments or a measure problem) requires the existence of such operators.

We have already completed the second step of the project in the paper

"Weak Scale Triggers in the SMEFT"

Authors: P.G. Catinari, R.T. D'Agnolo and P. Sesma

arXiv:2512.11026

which was recently accepted for publication in the Journal of High Energy Physics (JHEP). In this work we have shown that Tr[WW~] where W is the field strength of the Standard Model weak interactions cannot be used as a trigger and that the same is true for any other gauge-invariant Standard Model operator of dimension less or equal to 8. This effectively excludes the existence of new triggers beyond those listed in the previous Section and circumscribes our remaining tasks to working out in more detail the signatures of H1H2 and Tr[FF~].

Several other papers that my group and I have completed since the beginning of ANR funding are relevant to the projects' objectives. In

"A cosmological solution to the doublet-triplet splitting problem"

C. Csaki, R.T. D'Agnolo, E. Kuflik and P. Sesma,

JHEP \textbf{02}, 048 (2025) doi:10.1007/JHEP02(2025)048

We have shown that the same mechanism that can select the observed value of the Higgs mass can also solve the strong-CP problem and the doublet-triplet splitting problem of Grand Unified Theories. This makes the results of this project relevant for two more long-standing problems in particle physics. In

"A multiverse outside of the swampland,''

R.T. D'Agnolo, P. Mangini, G. Rigo and L.T. Wang,

Phys. Rev. D \textbf{110}, no.5, 055007 (2024), doi:10.1103/PhysRevD.110.055007

we have proven that the existence of the Multiverse (a key ingrendient for many of the selection mechanisms relevant to this work) is consistent with all conjectured low-energy consequences of quantum gravity. In

"Landscapes at Colliders,''

R.T. D'Agnolo, M. Ettengruber and L.T. Wang,

[arXiv:2512.18001 [hep-ph]].

we have worked out the signatures of simple quantum field theory models of the Multiverse. In

A Prototype Hybrid Mode Cavity for Heterodyne Axion Detection

Z. Li, K. Zhou, M. Oriunno, A. Berlin, S. Calatroni, R.T. D'Agnolo, S.A.R. Ellis, P. Schuster, S.G. Tantawi and N. Toro,

[arXiv:2507.07173 [physics.ins-det]].

We have realized an experimental prototype for the detection of axions and axion-like particles, relevant to the Tr[GG~] trigger operator.

The project is on track, with its most difficult part (excluding the existence of new trigger operators) already completed. We are left with the more conceptually straightforward task of working out in detail the experimental implications of existing trigger operators. In practice we are going to focus on the three operators listed above (H1H2, Tr[FF~] and Tr[GG~].

1. H1H2 Operator

The best opportunity to detect the trigger operator H1H2, is to study the new weak doublet H1. Its masses and couplings are very constrained by the requirements that H1H2 be a trigger, making it observable at the Large Hadrdon Collider now operating at CERN. I made the first theory calculations in previous work and now a preliminary analysis is ongoing within the CMS experimental collaboration at CERN. During the remaining part of the project we will sharpen these predictions, compute cross sections for the CMS collaboration and develop new analyses strategies.

2. Tr[FF~] Operator

In the case of Tr[FF~], new fermions close in mass to the Higgs are predicted. We will conduct thorough study, going in depth on the properties of the confining gauge group under which these new fermions are charged, using lattice results from QCD and known properties of approximately conformal confining groups.

3. Tr[GG~] Operator

(pseudo)scalars coupled to GG have axion-like experimental signatures and I have already made precise predictions for their masses and couplings in the context of specific models in previous work and proposed experiments to detect them. In the rest of the project we are going to unify theoretical predictions into a general framework and continue to develop our experimental prototypes for direct detection.

For decades we have tried to explain the value of the Higgs boson mass in terms of symmetry. We have expected new symmetries and the new particles realizing them, to appear, first at LEP, then at the Tevatron and finally at the LHC. After more than 40 years we have not observed them and the origin of the scale of weak interactions remains mysterious. In this proposal I argue for a complete change of perspective on the problem. The origin of the weak scale can be found at early times in the history of the Universe, but it leaves non-trivial traces in the laboratory today. I discuss how the value of the Higgs boson mass can be tied to the evolution of the Universe, developing a program to fully explore the experimental consequences of this possibility. The impact of such a change of perspective is far reaching: it changes sharply our understanding of the origin of the weak scale. It offers a completely new motivation for current and future cosmological experiments. The impact is profound also on the high energy physics experimental program since this class of ideas points to a number of new experiments and signatures, ranging from probes of long-range forces to new signatures at the LHC and at future colliders.