<p>We study the effects of the oscillating axion field present in our environment on the Casimir pressure between two metallic plates. We take into account the finite conductivity of the boundary plates and model the interactions between matter and photons in the Schwinger-Keldysh formalism. This allows us to take into account dissipation in the quantum field description of this open quantum system and retrieve the Lifschitz results for the Casimir interaction between two metallic plates. We then compute the leading correction to the Lifschitz theory in inverse powers of the axion suppression scale and show that the Casimir pressure receives oscillating corrections depending on the product of the axion mass and the distance between the plates. This contribution is repulsive at large distance compared to the axion Compton wavelength as a consequence of the breaking of parity invariance by the axion dark matter background.</p>

France

Philippe Brax

Pierre Brun

Casimir pressure with dissipation and quantum corrections from axion dark matter

Scalar field theories with a shift symmetry come equipped with the K-mouflage (or kinetic screening) mechanism that suppresses the scalar interaction between massive objects below a certain distance, the screening radius. In this work, we study the linear response of the scalar field distribution around a screened (point-like) object subject to a long range external scalar field perturbation for the Dirac-Born-Infeld theory. We find that, for regular boundary conditions at the position of the particle, some multipoles have vanishing response for a lacunar series of the multipole order ℓ for any dimension. Some multipoles also exhibit a logarithmic running when the number of spatial dimensions is even. We construct a ladder operator structure, with its associated ladder symmetries, formed by two sets of ladders that are related to the properties of the linear response and the existence of conserved charges. Our results exhibit a remarkable resemblance with the Love numbers properties of black holes in General Relativity, although some intriguing differences subsist.

Spain

Jose Jiménez

Dario Bettoni

Resilience of DBI screened objects and their ladder symmetries

We study the effects of an oscillating axion field on the pressure between two metallic plates. We consider the situation where a magnetic field parallel to the plates is present and show that the electric field induced by the coupling of the axion to photons leads to resonances. When the boundary plates are perfect conductors, the resonances are infinitely thin whilst they are broadened when the conductivity of the boundary plates is taken into account. The resonances take place at the tower of distances close to <math><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><mfrac><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mi>π</mi></mrow><mrow><mi>m</mi></mrow></mfrac></mrow></math>, where <math><mi>m</mi></math> is the axion mass and have a finite width and height depending on the conductivity. The resulting resonant pressure on the plate depends on the induced polarization at the surface of the plates. We investigate the reach of future Casimir experiments in terms of the axion mass and the conductivity of the boundary plates. We find that for large enough conductivities, the axion-induced pressure could be larger than the quantum Casimir effect between the plates.

Classical Casimir pressure in the presence of axion dark matter

We describe a simple technique for generating solutions to the classical field equations for an arbitrary nonlinear sigma-model minimally coupled to gravity. The technique promotes an arbitrary solution to the coupled Einstein/Klein-Gordon field equations for a single scalar field σ to a solution of the nonlinear sigma-model for N scalar fields minimally coupled to gravity. This mapping between solutions does not require there to be any target-space isometries and exists for every choice of geodesic computed using the target-space metric. In some special situations — such as when the solution depends only on a single coordinate (e.g. for homogeneous time-dependent or static spherically symmetric configurations) — the general solution to the sigma-model equations can be obtained in this way. We illustrate the technique by applying it to generate Euclidean wormhole solutions for multi-field sigma models coupled to gravity starting from the simplest Giddings-Strominger wormhole, clarifying why in the wormhole case Minkowski-signature target-space geometries can arise. We reproduce in this way the well-known axio-dilaton string wormhole and we illustrate the power of the technique by generating simple perturbations to it, like those due to string or α′ corrections.

Ireland

Canada

C. Burgess

United Kingdom

F. Quevedo

Lifting Klein-Gordon/Einstein solutions to general nonlinear sigma-models: the wormhole example

We analyze the dynamics of a light scalar field responsible for the <math><mi>μ</mi></math> term of the Higgs potential and coupled to matter via the Higgs-portal mechanism. We find that this dilaton model is stable under radiative corrections induced by the standard model particle masses. When the background value of the scalar field is stabilized at the minimum of the scalar potential, the scalar field fluctuations only couple quadratically to the massive fields of the standard model preventing the scalar direct decay into standard model particles. Cosmologically and prior to the electroweak symmetry breaking, the scalar field rolls down along its effective potential before eventually oscillating and settling down at the electroweak minimum. These oscillations can be at the origin of dark matter due to the initial misalignment of the scalar field compared to the electroweak minimum, and we find that, when the mass of the scalar field is less than the electron volt scale and acts as a condensate behaving like dark matter on large scales, the scalar particles cannot thermalize with the standard model thermal bath. As matter couples in a composition-dependent manner to the oscillating scalar, this could lead to a violation of the equivalence principle aboard satellites such as the MICROSCOPE experiment and the next generation of tests of the equivalence principle. Local gravitational tests are evaded thanks to the weakness of the quadratic coupling in the dark matter halo, and we find that, around other sources, these dilaton models could be subject to a screening akin to the symmetron mechanism.

CERN

Clare Burrage

Jose A. R. Cembranos

Patrick Valageas

Invisible dilaton

We compute bounds on screened scalar field theories from hydrogenlike systems. New light scalar fields generically have a direct coupling to matter. Such a coupling is strongly constrained by myriad experimental measurements. However, certain theories possess a screening mechanism that allows the effects of this coupling to weaken dynamically, and to evade many such bounds. We compute the perturbations to the energy levels of hydrogenlike systems due to screened scalar fields. We then use this result in two ways. First, we compute bounds from hydrogen spectroscopy, finding significantly weaker bounds than have been reported before as screening effects were overlooked. Second, we show that muonium is an intrinsically much more sensitive probe of screened scalar fields. For chameleon models, muonium experiments probe a large part of the parameter space that is as yet unexplored by low-energy physics and has so far only been tested by high-energy particle physics experiments.

Anne-Christine Davis

United States

Benjamin Elder

Screened scalar fields in hydrogen and muonium

We consider a family of non-linear theories of electromagnetism that interpolate between Born-Infeld at small distances and the recently introduced ModMax at large distances. These models are duality invariant and feature a K-mouflage screening in the Born-Infeld regime. We focus on computing the static perturbations around a point-like screened charge in terms of two decoupled scalar potentials describing the polar and the axial sectors respectively. Duality invariance imposes that the propagation speed of the odd perturbations goes to zero as fast as the effective screened charge of the object, potentially leading to strong coupling and an obstruction to the viability of the EFT below the screened radius. We then consider the linear response to external fields and compute the electric polarisability and the magnetic susceptibility. Imposing regularity of the perturbations at the position of the particle, we find that the polarisability for the odd multipoles vanishes whilst for the magnetisation Born-Infeld emerges as the only theory with vanishing susceptibility for even multipoles. The perturbation equations factorise in terms of ladder operators connecting different multipoles. There are two such ladder structures for the even sector: one that acts as an automorphism between the first four multipoles and another one that connects multipoles separated by four units. When requiring a similar ladder structure for the odd sector, Born-Infeld arises again as the unique theory. We use this ladder structure to relate the vanishing of the polarisability and the susceptibility to the values of conserved charges. Finally the perturbation equations correspond to a supersymmetric quantum mechanical system such that the polar sector can be described in terms of Schrödinger’s equations with four generalised hyperbolic Pösch-Teller potentials whose eigenfunctions are in correspondence with the multipoles.

Polarisability and magnetisation of electrically K-mouflaged objects: the Born-Infeld ModMax case study

We consider the environment-dependent dilaton in the laboratory and the solar system and derive approximate analytical solutions to the field theory equations of motion in the presence of a one or two mirror system or a sphere. The solutions obtained herein can be applied to qBOUNCE experiments, neutron interferometry and for the calculation of the dilaton field induced “Casimir force” in the Cannex experiment as well as for Lunar Laser Ranging. They are typical of the Damour–Polyakov screening mechanism whereby deviations from General Relativity are suppressed by a vanishingly small direct coupling of the dilaton to matter in dense environments. We specifically focus on dilaton models which are compatible with the late time acceleration of the expansion of the Universe, i.e. the cosmological dilaton. We show how future laboratory experiments will essentially test a region of parameter space with  $$A_2\simeq \lambda ^2$$  <math> <mrow> <msub> <mi>A</mi> <mn>2</mn> </msub> <mo>≃</mo> <msup> <mi>λ</mi> <mn>2</mn> </msup> </mrow> </math>   where  $$A_2$$  <math> <msub> <mi>A</mi> <mn>2</mn> </msub> </math>   is the quadratic coupling strength of the dilaton to matter and  $$\lambda $$  <math> <mi>λ</mi> </math>   is the steepness of the exponential runaway potential. Current constraints favour the large  $$A_2$$  <math> <msub> <mi>A</mi> <mn>2</mn> </msub> </math>   regime implying that the environment-dependent dilaton satisfies two of the swampland conjectures, i.e. the distance conjecture whereby the field excursion should not exceed the Planck scale and the de Sitter conjecture specifying that the running dilaton potential should be steep enough with a large  $$\lambda $$  <math> <mi>λ</mi> </math>  .

Austria

Hauke Fischer

Christian Käding

Mario Pitschmann

The environment dependent dilaton in the laboratory and the solar system

We show how light scalar fields could account for the discrepancy between the theoretical and observed values of the anomalous magnetic moment of the (anti)muon. When coupled to both matter and photons, light scalar fields induce a change of the anomalous magnetic moment of charged particles. This arises from two concurrent effects. Classically, light scalars induce a change of the cyclotron frequency, complementing the electromagnetic effects coming from the magnetic and electric fields used experimentally. Light scalars also contribute to the anomalous magnetic moment quantum mechanically at the one-loop level. For unscreened scalar fields coupling with a Yukawa interaction to matter, these contributions are negligible after applying the Cassini bound on deviations from Newtonian gravity. On the other hand, screened scalars such as chameleons or symmetrons can couple strongly to matter in the laboratory and decouple in the Solar System. This allows us to probe branches of their parameter spaces where the recently measured anomalous magnetic moment of the (anti)muon can be accounted for in the chameleon and symmetron cases. We consider the compatibility of these models with other cosmological and particle physics observables. We find that prototype chameleon and symmetron models considered here are in tension with the bounds on the branching ratio of kaons into pions and invisible matter.

<math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo>)</mo><mi>μ</mi></msub></math> and screened modified gravity

The increasing observational pressure on the standard cosmological model motivates analyses going beyond the paradigm of the collisionless cold dark matter (DM). Since the only clear evidence for the existence of DM is based on gravitational interactions, it seems particularly fitting to study them in this sector where extensions to the standard model can be naturally introduced. A promising avenue can be obtained using modifications of the space-time metric coupled to DM and induced by the presence of a new ultralight scalar field <math><mi>ϕ</mi></math>. The <math><mi>ϕ</mi></math> field can contribute to the DM density and can couple all the matter species universally, including additional heavy DM particles. We present a simple two-component DM model employing derivative conformal interactions between the two DM species. This can simultaneously (1) guarantee the necessary symmetries to stabilize the dark species, (2) predict a subdominant thermal relic density of the heavy DM component, and (3) alleviate small-scale structure tensions of the cold DM scenario due to the possible cointeractions in the dark sector. The scenario is highly predictive with future observational prospects ranging from the Large Hadron Collider to gravitational-wave searches and can be generalized to more rich and realistic dark sector models.