$(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ and screened modified gravity

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$(g - 2)_{μ}$ and screened modified gravity

Philippe Brax, Anne-Christine Davis, and Benjamin Elder

Phys. Rev. D 106, 044040 – Published 18 August 2022

Abstract

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.

Received 23 November 2021
Accepted 14 July 2022

DOI:https://doi.org/10.1103/PhysRevD.106.044040

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Alternative gravity theories Laboratory studies of gravity

Muons

Magnetic moment

Gravitation, Cosmology & AstrophysicsParticles & Fields

Authors & Affiliations

Philippe Brax¹, Anne-Christine Davis², and Benjamin Elder ³

¹Institut de Physique Théorique, Université Paris-Saclay, CEA, CNRS, F-91191 Gif-sur-Yvette Cedex, France
²DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
³Department of Physics and Astronomy, University of Hawai’i, 2505 Correa Road, Honolulu, Hawai’i 96822, USA

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Vol. 106, Iss. 4 — 15 August 2022

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Figure 1
Scalar field (dashed line) contributions at one-loop order to the magnetic moment of the muon. These contributions involve either only the matter coupling (a) or both the matter and photon couplings (b), (c). Reproduced from [59].
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Figure 2
Definition of the coordinate system on the storage ring, matching the conventions of [72].
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Figure 3
(a) The values of $M$ , $Λ$ for the $n = 1$ chameleon that produce the discrepancy between experimental and theoretical values of the muon magnetic moment are plotted with a black line. The zero skin depth approximation fails in the upper right corner, while the perfect vacuum approximation fails in the lower left half. The areas where the classical and quantum components of Eq. (81) each dominate are indicated. Only the classical component relies on the perfect vacuum approximation. The hydrogen bounds have been reinterpreted from [52] to include the screening of the hydrogen nucleus [75]. The region where $M \approx 10^{- 16} M_{Pl}$ , $Λ ≲ meV$ remains viable. The curve stops at $Λ \approx 10^{- 7} eV$ due to the large chameleon mass inside the storage ring.
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Figure 4
Symmetron parameters that eliminate the tension between experimental and theoretical values of $a_{μ}$ , for $μ = R_{vac}^{- 1} = 4 μ eV$ . The calculation of the classical effect is only valid in the unshaded middle region. The black curve is a sum of the classical and quantum contributions to the anomalous magnetic moment, although the classical component is the dominant one in this regime, while the quantum component dominates for $M ≲ 10^{- 2} GeV$ . This plot is for illustrative purposes only, as at this mass the bouncing neutron experiment [51] rules out the symmetron parameter space shown here.
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Figure 5
Symmetron parameters, with the mass at the dark energy scale $μ = 2.4 meV = Λ_{DE}$ , that could explain the muon $g - 2$ anomaly. We see that all viable parameter combinations at this mass, indicated by the black line, are excluded by cold neutrons [51].
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Figure 6
Symmetron parameters that could resolve the muon $g - 2$ anomaly, at 4 different representative mass scales $μ$ : (a) $10 eV$ , (b) $1 keV$ , (c) $1 MeV$ , and (d) $1 GeV$ . The combinations of parameters $μ$ , $M$ , $λ$ that do this are indicated by the black line. Perturbation theory breaks down for $λ ≳ 1 / 6$ , so models in that regime are not viable. Likewise, the EFT is not valid for very small values of $λ$ . Parameter combinations with $μ ≲ 1 eV$ are ruled out by bouncing neutrons [51] and hydrogen. Those with masses larger than $\sim 10 GeV$ do not have any region where the calculation may be trusted and where the resulting correction to $δ a_{μ}$ is the right size to explain the anomaly. Only the most limiting constraints on symmetron parameter space are plotted, corresponding to Eqs. (93) and (95), as well as new bounds deriving from precision hydrogen spectra [75].
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Physical Review D

covering particles, fields, gravitation, and cosmology

$(g - 2)_{μ}$ and screened modified gravity

Philippe Brax, Anne-Christine Davis, and Benjamin Elder

Phys. Rev. D 106, 044040 – Published 18 August 2022

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Physical Review D

covering particles, fields, gravitation, and cosmology

(g−2)μ and screened modified gravity

Philippe Brax, Anne-Christine Davis, and Benjamin Elder

Phys. Rev. D 106, 044040 – Published 18 August 2022

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$(g - 2)_{μ}$ and screened modified gravity