This work proposes a direct link between the hierarchy problem and Weakly Interacting Massive Particles (WIMPs): we suggest that the small mass of the Higgs boson arises from being dynamically driven to the scale of the WIMP. Such a special electroweak vacuum is singled out by lying close to the critical boundary of a phase transition, as recently explored in a new class of cosmological solutions to the hierarchy problem. They generically predict the Higgs potential to be destabilised just above the weak scale. Intriguingly, the requirement for new physics to achieve this coincides with two independently well-motivated expectations: a split spectrum of light fermions and heavy bosons, as anticipated from naturalness, and the so-called “WIMP miracle”. A WIMP with mass around the weak scale not only happens to have the correct thermal relic abundance to be the dark matter (DM), it can also give rise to the necessary critical boundary at the TeV scale through its Yukawa couplings to the Higgs. We use a higgsino-like singlet-doublet model to illustrate our Higgs-DM criticality scenario and show that if this WIMP DM mass is observed to be greater than ~ 1$\textit{.}$2 TeV then it necessarily implies a strong bound on the Higgs mass and an upper bound on the scale of heavy new physics that restores vacuum stability. It can be thoroughly probed in direct detection experiments, astrophysical signals and future collider searches, further motivating a comprehensive exploration of the remaining heavy WIMP parameter space.

United Kingdom

Maximilian Detering

United States

Spain

Thomas Steingasser

Tevong You

A new connection between WIMP dark matter and the hierarchy problem

We develop a contour integral formalism for computing the K-theoretic equivariant 3-vertex. Within the Jeffrey-Kirwan (JK) residue framework, we show that, by an appropriate choice of the reference vector, both the equivariant Donaldson-Thomas (DT) and Pandharipande-Thomas (PT) 3-vertices can be extracted from the same integrand. We analyze three distinct limits of the PT 3-vertex, recovering the unrefined topological vertex, the refined topological vertex, and the Macdonald refined topological vertex. Higher-rank extensions of PT counting and the DT/PT correspondence are also explored. From a quantum algebraic perspective, we construct an operator version of the equivariant PT 3-vertex and term it the Pandharipande-Thomas $\textit{qq}$-character. We then discuss its connection with the quantum toroidal $${\mathfrak{g}\mathfrak{l}}_{1}$$ .

France

Taro Kimura

Japan

Go Noshita

Gauge origami and quiver W-algebras. Part IV. Pandharipande-Thomas $\textit{qq}$-characters

We present a new solution to the Higgs hierarchy problem based on dynamical vacuum selection in a landscape scanning the Higgs mass. In patches where the Higgs mass parameter takes a natural value, the Higgs potential only admits a minimum with a large and negative energy density. This causes a cosmological crunch, removing such patches from the landscape. Conversely, in patches where the Higgs mass parameter is smaller than a critical value, the Higgs potential admits a metastable minimum with the standard cosmological history. This critical value is determined by the instability scale, where the quartic coupling turns negative due to its running. The ability of this mechanism to explain the observed Higgs mass hinges on new physics at the TeV scale, such as vector-like fermions. We study two simple realizations of this scenario in a heavy neutral lepton model and in the singlet-doublet model, the latter mimicking a Higgsino-bino system. We show that the relevant parts of their parameter spaces can be probed by proposed future colliders, such as the FCC-ee or a muon collider.

Sean Benevedes

Ameen Ismail

Gauge hierarchy and metastability from Higgs-driven crunching

<p>We revisit the path integral description of quantum tunneling and its generalization to excited states. For clarity, we focus on the simple toy model of a point particle in a double-well potential, for which we perform all steps explicitly. Instead of performing the familiar Wick rotation from physical to imaginary time—which is inconsistent with the requisite boundary conditions when treating tunneling from excited states—we regularize the path integral by adding an infinitesimal complex contribution to the Hamiltonian, while keeping time strictly real. We find that this gives rise to a complex stationary-phase solution, in agreement with recent insights from Picard-Lefshetz theory. We then show that there exists a class of analytic solutions for the corresponding equations of motion, which can be made to match the appropriate boundary conditions in the physically relevant limits of a vanishing regulator and an infinite physical time. We provide a detailed discussion of this nontrivial limit. We find that, for systems without an explicit time-dependence, our approach reproduces the picture of an instantonlike solution defined on a finite Euclidean-time interval. Lastly, we discuss the generalization of our approach to broader classes of systems, for which it serves as a reliable framework for high-precision calculations.</p>

David I. Kaiser

Toward quantum tunneling from excited states: Recovering imaginary-time instantons from a real-time analysis

We further develop the BPS/CFT correspondence between quiver W-algebras/ -characters and partition functions of gauge origami. We introduce -characters associated with multi-dimensional partitions with nontrivial boundary conditions which we call Donaldson-Thomas (DT) -characters. They are operator versions of the equivariant DT vertices of toric Calabi-Yau three and four-folds. Moreover, we revisit the construction of the D8 -characters with no boundary conditions and give a quantum algebraic derivation of the sign rules of the magnificent four partition function. We also show that under the proper sign rules, the D6 and D8 -characters with no boundary conditions all commute with each other and discuss its physical interpretation.

Gauge origami and quiver W-algebras. Part III. Donaldson-Thomas

We analyze the angular momentum balance for a particle undergoing Thomas precession. The relationships among relativistic torque, the center of mass, and the center of inertia for a spinning particle are clarified. We show that spin precession is accompanied by orbital angular momentum precession, and present examples of the resulting out-of-plane motion.

Canada

Andrzej Czarnecki

Andrei Zelnikov

Thomas precession, relativistic torque, and non-planar orbits

We derive the finite-temperature quantum-tunneling rate from first principles. The tunneling rate depends on both temperature and time. We demonstrate that the relevant instantons should, therefore, be defined on a Keldysh-Schwinger contour, and we discuss how the familiar Euclidean time result arises from the limit of large physical times. We identify distinct behavior in the high- and low-temperature limits, incorporating effects from background fields. We construct a consistent perturbative scheme that incorporates large finite-temperature effects.

Morgane König

Finite-temperature instantons from first principles

Thomas-Whitehead (TW) gravity is a recently formulated projectively invariant extension of Einstein-Hilbert gravity. Projective geometry was used long ago by Thomas et al. to succinctly package equivalent paths encoded by the geodesic equation. Projective invariance in gravity has further origins in string theory through a geometric action constructed from the method of coadjoint orbits using the Virasoro algebra. A projectively invariant connection arises from this construction, a part of which is known as the diffeomorphism field. TW gravity exploits projective Gauss-Bonnet terms in the action functional to endow the diffeomorphism field with dynamics, while allowing the theory to collapse to general relativity in the limit that the diffeomorphism field vanishes and the connection becomes Levi-Civita. In the original formulation of TW gravity, the diffeomorphism field is projectively invariant but not tensorial and the connection is projectively invariant but not affine. In this paper we reformulate TW gravity in terms of projectively invariant tensor fields and a projectively invariant covariant derivative, derive field equations respecting these symmetries, and show that the field equations obtained are classically equivalent across formulations. This provides a “Rosetta Stone” between this newly constructed covariant and projective invariant formulation of TW gravity and the original formulation that was manifestly projective invariant, but not covariant.

Tyler Grover

Kory Stiffler

Patrick Vecera

Covariant and manifestly projective invariant formulation of Thomas-Whitehead gravity

The so-called metastability bound asserts that an unnaturally small Higgs mass is a necessary condition for electroweak vacuum metastability, offering a new approach toward solving the hierarchy problem. So far, this result relies on the assumption of a negative Higgs mass parameter, or equivalently, on electroweak spontaneous symmetry breaking. We derive a new, corresponding bound for the case of a positive mass parameter. When the new bound is significantly more restrictive than or comparable to its established counterpart, it may offer an explanation for the sign of the Higgs mass parameter, and thus, spontaneous symmetry breaking itself. New physics at scales <math><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mi>–</mi><mn>10</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math> can lower these bounds as far as the TeV scale. As an illustration, we consider vacuum stability in the presence of additional TeV-scale fermions with Yukawa couplings to the Higgs, as well as a dimension-six term parametrizing new physics in the UV. This scenario requires new physics that couples strongly to the Higgs, and can potentially be probed at future colliders. Finally, to allow for comparison with concrete mechanisms predicting metastability, we provide the mass-dependent lifetime of the electroweak vacuum for this model.

Sokratis Trifinopoulos

Spontaneous symmetry breaking, gauge hierarchy, and electroweak vacuum metastability

Both parameters in the Higgs field’s potential, its mass and quartic coupling, appear fine-tuned to near-critical values, which gives rise to the hierarchy problem and the metastability of the electroweak vacuum. Whereas such behavior appears puzzling in the context of particle physics, it is a common feature of dynamical systems, which has led to the suggestion that the parameters of the Higgs potential could be set through some dynamical process. In this article, we discuss how this notion could be extended to physics beyond the Standard Model (SM). We first review in which sense the SM Higgs parameters can be understood as near-critical and show that this notion can be extrapolated in a unique way for a generic class of SM extensions. Our main result is a prediction for the parameters of such models in terms of their corresponding Standard Model effective field theory Wilson coefficients and corresponding matching scale. For generic models, our result suggests that the scale of new (bosonic) physics lies close to the instability scale. We explore the potentially observable consequences of this connection, and illustrate aspects of our analysis with a concrete example. Lastly, we discuss implications of our results for several mechanisms of dynamical vacuum selection associated with various beyond-the-Standard-Model constructions.