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Pierre Fayet

Publications and source records attributed to Pierre Fayet.

At least 19 recordsLinked to original sources
arXiv2026

Technical Proposal for the Atom Interferometer CERN Experiment (AICE) Facility

We present the technical proposal for the Atom Interferometer CERN Experiment (AICE), a $\mathcal{O}(100)$ m vertical atom interferometer to be installed against the wall of the PX46 access shaft to the LHC. AICE is conceived as a versatile and flexible long-baseline atom-interferometry facility whose primary scientific goal is probing for bosonic ultralight dark matter (ULDM) in a mass range inaccessible to other experiments, with a secondary goal of pioneering the exploration of gravitational waves (GWs) with frequencies in the range ${\sim}$0.03-3 Hz as a pathfinder for future longer-baseline detectors. The initial configuration employs ultracold $^{87}$Sr atoms in a single-photon 698-nm interferometer with three shaft-based atom sources in a multi-source gradiometer geometry, supported by one surface reference source for laser stabilisation and diagnostics, to target scalar ULDM. Operation with $^{88}$Sr will give sensitivity to axion-like particles (ALPs), vector ULDM with $B-L$ couplings and violation of the principle of equivalence, while a $^{171}$Yb upgrade will improve the sensitivity to $B-L$ couplings and equivalence violations. Probing the Einstein equivalence principle (EP) and measuring $\alpha$ will proceed in parallel with the ULDM searches. A conceptual feasibility study and a detailed technical implementation study have established that PX46 is a uniquely mature and implementation-ready site, with no technical showstoppers. Completing site preparation works during LS3 would enable the subsequent installation and operation of AICE without impacting HL-LHC operations. The detector design builds on the VLBAI and MAGIS experiments and the AION-10 Technical Design Report, scaling the strontium gradiometer architecture to the $\sim$100 m baseline. AICE is endorsed by the TVLBAI Proto-Collaboration, comprising 57 institutions in 22 countries.

hep-ex↗
arXiv2026

Hyperbolic form factors for Yukawa interactions, and applications to the Earth

We define the hyperbolic form factor of a density distribution as its bilateral Laplace transform, related by duality or analytic continuation to its form factor. For a sphere it is given by $\Phi(x = kR) =\langle \cosh \vec k.\vec r\rangle=\langle\sinh kr /kr\rangle $, expanded as $\sum \frac{x^{2n}}{(2n+1)!} \frac{\langle r^{2n}\rangle}{R^{2n}} $, and similarly for the form factor $ \langle \sin kr/kr\rangle$. It is also obtained from the bilateral Laplace transform of $2\pi r\,\rho(|r|)$, and enters in the determination of the outside Yukawa potential induced by a new charge for a mediator of mass $m=k=1/\lambda$. $\Phi(x)$ may be expressed as $\frac{3}{x^3}\,(x \cosh x - \sinh x)\ \bar\rho(x)/\rho_0$, where $\bar\rho(x)$ is an effective density decreasing, for $d\rho/dr<0$, from the average $\rho_0$ at small $x$, down to $\rho(R)$. An inversion formula allows one to recover $\rho(r)$ from an analytic continuation of $\Phi(x)$, as $\rho(r) =\rho_0\,(2R/3\pi r)\int\Phi(ix) \sin (x\frac{r}{R})\,x\,dx$. $\Phi(x)$ for the Earth is essential to determine limits on a new force, as tested by MICROSCOPE, depending on the density distribution within the Earth. Quite remarkably, much simplified density profiles, such as $\rho = \rho_0\ 2R/3r $ or $\rho = \rho_0\, (\frac54-\frac{r}{R}+ \frac{R}{3r})$, provide analytic expressions of $\Phi(x)$ and $\bar\rho(x)$ giving almost the same values as in a 5-shell model. $\,\Phi(x)=(\sinh\frac{x}{2}/\frac{x}{2})^2$ is valid to within $\simeq 1\,\%$ up to $x=4$. $\,\Phi(x)= [7x^2\cosh x-24\cosh x+9x\sinh x -4x^2+24]/(4x^4)$ is valid to within 1 % for $\lambda > $ 100 km (or $m< 2\times 10^{-12}$ eV/$c^2$). For $m=10^{-12}$ eV/$c^2$ the coupling limits are increased by 34 as compared to a massless mediator, to $|g_{B-L}|< 3.6 \times 10^{-24} $ and $|g_B|<2.6\times 10^{-23}$ for a spin-1 mediator, with slightly different limits in the spin-0 case.

hep-ph↗
arXiv2025

The Yukawa potential of a non-homogeneous sphere, with new limits on an ultralight boson

Extremely weak long-range forces may lead to apparent violations of the Equivalence Principle. The final MICROSCOPE result, leading at 95 % c.l. to $|\delta| < 4.5 \times 10^{-15}$ or $6.5 \times 10^{-15}$ for a positive or negative E\"otv\"os parameter $\delta$, requires taking into account the spin of the mediator, and the sign of $\Delta (Q/A_r)_{\rm{Ti-Pt}}$ ($Q$ denoting the new charge involved). A coupling to $B-L$ or $B$ should verify $|g_{B-L}|<1.1 \times 10^{-25}$ or $|g_{B}| < 8 \times 10^{-25}$, for a spin-1 mediator of mass $m < 10^{-14}$ eV$/c^2$, with slightly different limits of $1.3 \times 10^{-25}$ or $\,6.6 \times 10^{-25}$ in the spin-0 case. The limits increase with $m$, in a way which depends on the density distribution within the Earth. This involves an hyperbolic form factor, expressed through a bilateral Laplace transform as $\Phi(x=mR)= \langle\,\sinh mr/mr \,\rangle$, related by analytic continuation to the Earth form factor $\Phi(ix)= \langle \,\sin mr/mr \,\rangle $. It may be expressed as $\Phi(x) = \frac{3}{x^2}\, (\cosh x - \frac{\sinh x}{x}) \times\, \bar\rho(x)/\rho_0\,$, where $\bar\rho(x)$ is an effective density, decreasing from the average $\rho_0$ at $m=0$ down to the density at the periphery. We give general integral or multishell expressions of $\Phi(x)$, evaluating it, and $\bar\rho(x)$, in a simplified 5-shell model. $\Phi(x)$ may be expanded as $\, \sum \frac{x^{2n}}{(2n+1)!} \frac{\langle \,r^{2n}\,\rangle}{R^{2n}} \simeq 1 + .0827\ x^2 + .00271 \ x^4 + 4.78 \times 10^{-5}\,x^6 + 5.26\times 10^{-7}\, x^8 +\ ... \ $, absolutely convergent for all $x$ and potentially useful up to $x\approx 5$. The coupling limits increase at large $x$ like $mR \ e^{mz/2}/\sqrt{1+mr}$ ($z=r-R$ being the satellite altitude), getting multiplied by $\simeq 1.9,\ 34$, or $1.2\times 10^9$, for $m = 10^{-13},\ 10^{-12}$ or $10^{-11}$ eV$/c^2$, respectively.

hep-ph↗
arXiv2025

Long-Baseline Atom Interferometry

Long-baseline atom interferometry is a promising technique for probing various aspects of fundamental physics, astrophysics and cosmology, including searches for ultralight dark matter (ULDM) and for gravitational waves (GWs) in the frequency range around 1~Hz that is not covered by present and planned detectors using laser interferometry. The MAGIS detector is under construction at Fermilab, as is the MIGA detector in France. The PX46 access shaft to the LHC has been identified as a very suitable site for an atom interferometer of height $\sim 100$m, sites at the Boulby mine in the UK and the Canfranc Laboratory are also under investigation, and possible sites for km-class detectors have been suggested. The Terrestrial Very-Long-Baseline Atom Interferometry (TVLBAI) Proto-Collaboration proposes a coordinated programme of interferometers of increasing baselines.

hep-ex↗
arXiv2024

Terrestrial Very-Long-Baseline Atom Interferometry: Summary of the Second Workshop

This summary of the second Terrestrial Very-Long-Baseline Atom Interferometry (TVLBAI) Workshop provides a comprehensive overview of our meeting held in London in April 2024, building on the initial discussions during the inaugural workshop held at CERN in March 2023. Like the summary of the first workshop, this document records a critical milestone for the international atom interferometry community. It documents our concerted efforts to evaluate progress, address emerging challenges, and refine strategic directions for future large-scale atom interferometry projects. Our commitment to collaboration is manifested by the integration of diverse expertise and the coordination of international resources, all aimed at advancing the frontiers of atom interferometry physics and technology, as set out in a Memorandum of Understanding signed by over 50 institutions.

hep-ex↗
arXiv2024

Searching for a new light gauge boson with axial couplings in muon beam dump experiments

We present a formalism for new $U(1)$ interactions involving weak hypercharge, baryon, and lepton numbers, and a possible axial symmetry generator $F_A$ in the presence of a second Brout-Englert-Higgs doublet. The resulting $U$ boson, after mixing with the $Z$, interpolates between a generalised dark photon, a dark $Z$, and an axially coupled gauge boson. We especially focus on the axial couplings originating from $F_A$ or from mixing with the $Z$, determined by the scalar sector via parameters like $\tan\beta$ and the v.e.v. of an extra dark singlet. We explore the distinctive features of axially coupled interactions, especially in the ultrarelativistic limit, where the $U$ boson behaves much as an axion-like particle, with enhanced interactions to quarks and leptons. This enhancement is particularly relevant for future muon beam dump experiments, since the muon mass considerably increases the effective coupling, proportional to $2m_\mu/m_U$, compared to analogous experiments with electrons. We also analyse the shape of the expected beam dump exclusion or discovery regions, influenced by $U$ boson interactions and the experiment geometry. Different situations are considered, limited in particular by cases for which the $U$ decays before reaching the detector, or has too small couplings to produce detectable events. We also compare to vectorially coupled bosons and axion-like pseudoscalars, highlighting the importance of understanding the parameter space for future experiment design and optimisation.

hep-ph↗
arXiv2023

Terrestrial Very-Long-Baseline Atom Interferometry: Workshop Summary

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions.

hep-ex↗
arXiv2022

Result of the MICROSCOPE Weak Equivalence Principle test

The space mission MICROSCOPE dedicated to the test of the Equivalence Principle (EP) operated from April 25, 2016 until the deactivation of the satellite on October 16, 2018. In this analysis we compare the free-fall accelerations ($a_{\rm A}$ and $a_{\rm B}$) of two test masses in terms of the E\"otv\"os parameter $\eta({\rm{A, B}}) = 2 \frac{a_{\rm A}- a_{\rm B}}{a_{\rm A}+ a_{\rm B}}$. No EP violation has been detected for two test masses, made from platinum and titanium alloys, in a sequence of 19 segments lasting from 13 to 198 hours down to the limit of the statistical error which is smaller than $10^{-14}$ for $ \eta({\rm{Ti, Pt}})$. Accumulating data from all segments leads to $\eta({\rm{Ti, Pt}}) =[-1.5\pm{}2.3{\rm (stat)}\pm{}1.5{\rm (syst)}] \times{}10^{-15}$ showing no EP violation at the level of $2.7\times{}10^{-15}$ if we combine stochastic and systematic errors quadratically. This represents an improvement of almost two orders of magnitude with respect to the previous best such test performed by the E\"ot-Wash group. The reliability of this limit has been verified by comparing the free falls of two test masses of the same composition (platinum) leading to a null E\"otv\"os parameter with a statistical uncertainty of $1.1\times{}10^{-15}$.

gr-qc↗
arXiv2022

MICROSCOPE mission: final results of the test of the Equivalence Principle

The MICROSCOPE mission was designed to test the Weak Equivalence Principle (WEP), stating the equality between the inertial and the gravitational masses, with a precision of $10^{-15}$ in terms of the E\"otv\"os ratio $\eta$. Its experimental test consisted of comparing the accelerations undergone by two collocated test masses of different compositions as they orbited the Earth, by measuring the electrostatic forces required to keep them in equilibrium. This was done with ultra-sensitive differential electrostatic accelerometers onboard a drag-free satellite. The mission lasted two and a half years, cumulating five-months-worth of science free-fall data, two thirds with a pair of test masses of different compositions -- Titanium and Platinum alloys -- and the last third with a reference pair of test masses of the same composition -- Platinum. We summarize the data analysis, with an emphasis on the characterization of the systematic uncertainties due to thermal instabilities and on the correction of short-lived events which could mimic a WEP violation signal. We found no violation of the WEP, with the E\"otv\"os parameter of the Titanium and Platinum pair constrained to $\eta({\rm Ti, Pt})~=~ [-1.5 \pm 2.3~{\rm (stat)} \pm 1.5~{\rm (syst)}]~\times 10^{-15}$ at $1\sigma$ in statistical errors.

gr-qc↗
arXiv2020

The $U$ boson, interpolating between a generalized dark photon or dark $Z$, an axial boson and an axionlike particle

A light boson $U$ from an extra $U(1)$ interpolates between a generalized dark photon coupled to $Q,\ B$ and $L_i$ (or $B-L$), plus possibly dark matter, a dark $Z$ coupled to the $Z$ current, and one axially coupled to quarks and leptons. We identify the corresponding $U(1)_F$ symmetries, with $F= \gamma_Y Y+\gamma_B B+\gamma_{L_i}L_i+\gamma_A F_A+\gamma_{F'}F'\!+\gamma_d F_d$, $F_d$ acting in a dark sector and $F'$ on possible semi-inert BEH doublets uncoupled to quarks and leptons. The $U$ current is obtained from the $U(1)_F $ and $Z$ currents, with a mixing determined by the spin-0 BEH fields. The charge $Q_U$ of chiral quarks and leptons is a combination of $Q,\ B,\ L_i$ and $T_{3L}$ with the axial $F_A$. It involves in general isovector and isoscalar axial terms, in the presence of two BEH doublets. A longitudinal $U$ with axial couplings has enhanced interactions, and behaves much as an axionlike particle. Its axial couplings $g_A$, usually restricted to $< 2\times 10^{-7} m_U$(MeV), lead to effective pseudoscalar ones $g_P= g_A\times 2m_{q,l}\,/m_U=2^{1/4}\, G_F^{1/2}\, m_{q,l} \ A_\pm $. $\,A_\pm$ is proportional to an invisibility parameter $r=\cos\theta_A$ induced by a singlet v.e.v., possibly large and allowing the $U$ to be very weakly interacting. This allows for a very small gauge coupling, expressed with two doublets and a singlet as $g"\!/4\simeq 2\times 10^{-6} m_U$(MeV) $ r/\sin 2\beta$. We discuss phenomenological implications for meson decays, neutrino interactions, atomic-physics parity violation, naturally suppressed $\pi^0\to\gamma U$ decays, etc.. The $U$ boson fits within the grand-unification framework, in symbiosis with a $SU(4)_{\rm es }$ electrostrong symmetry broken at the GUT scale, with $Q_U$ depending on $Q,\ B-L,\ F_A$ and $T_{3A}$ through three parameters $\gamma_Y,\ \gamma_A$ and $\eta$.

hep-ph↗
arXiv2019

Space test of the Equivalence Principle: first results of the MICROSCOPE mission

The Weak Equivalence Principle (WEP), stating that two bodies of different compositions and/or mass fall at the same rate in a gravitational field (universality of free fall), is at the very foundation of General Relativity. The MICROSCOPE mission aims to test its validity to a precision of $10^{-15}$, two orders of magnitude better than current on-ground tests, by using two masses of different compositions (titanium and platinum alloys) on a quasi-circular trajectory around the Earth. This is realised by measuring the accelerations inferred from the forces required to maintain the two masses exactly in the same orbit. Any significant difference between the measured accelerations, occurring at a defined frequency, would correspond to the detection of a violation of the WEP, or to the discovery of a tiny new type of force added to gravity. MICROSCOPE's first results show no hint for such a difference, expressed in terms of Eötvös parameter $δ(Ti,Pt)=[-1\pm{}9{\rm (stat)}\pm{}9{\rm (syst)}] \times{}10^{-15}$ (both 1$σ$ uncertainties) for a titanium and platinum pair of materials. This result was obtained on a session with 120 orbital revolutions representing 7\% of the current available data acquired during the whole mission. The quadratic combination of 1$σ$ uncertainties leads to a current limit on $δ$ of about $1.3\times{}10^{-14}$.

gr-qc↗
arXiv2019

The local dark sector. Probing gravitation's low-acceleration frontier and dark matter in the Solar System neighborhood

We speculate on the development and availability of new innovative propulsion techniques in the 2040s, that will allow us to fly a spacecraft outside the Solar System (at 150 AU and more) in a reasonable amount of time, in order to directly probe our (gravitational) Solar System neighborhood and answer pressing questions regarding the dark sector (dark energy and dark matter). We identify two closely related main science goals, as well as secondary objectives that could be fulfilled by a mission dedicated to probing the local dark sector: (i) begin the exploration of gravitation's low-acceleration regime with a man-made spacecraft and (ii) improve our knowledge of the local dark matter and baryon densities. Those questions can be answered by directly measuring the gravitational potential with an atomic clock on-board a spacecraft on an outbound Solar System orbit, and by comparing the spacecraft's trajectory with that predicted by General Relativity through the combination of ranging data and the in-situ measurement (and correction) of non-gravitational accelerations with an on-board accelerometer. Despite a wealth of new experiments getting online in the near future, that will bring new knowledge about the dark sector, it is very unlikely that those science questions will be closed in the next two decades. More importantly, it is likely that it will be even more urgent than currently to answer them. Tracking a spacecraft carrying a clock and an accelerometer as it leaves the Solar System may well be the easiest and fastest way to directly probe our dark environment.

astro-ph.IM↗
arXiv2019

A New Dual System For The Fundamental Units, including and going beyond the newly revised SI

We propose a new system for the fundamental units, which includes and goes beyond the present redefinition of the SI, by choosing also $c=\hbar=1$. By fixing $c=c_\circ $m/s = 1, $\hbar=\hbar_\circ $ Js = 1 and $\underline{μ_\circ}=μ_\circ $N/A$^2$ = 1, it allows us to define the metre, the joule, and the ampere as equal to (1/299 792 458) s, $(1/\hbar_\circ = .948 ... \times \ 10^{34})\ {\rm s}^{-1}$ and $\sqrt{μ_\circ \rm N}= \sqrt{μ_\circ c_\circ / \hbar_\circ}\ {\rm s}^{-1}= 1.890...\times 10^{18}\ {\rm s}^{-1}$. It presents at the same time the advantages and elegance of a system with $\hbar = c = \underline{μ_\circ} = \underline{ε_\circ } = k = N_A = 1\,$, where the vacuum magnetic permeability, electric permittivity, and impedance are all equal to 1. All units are rescaled from the natural ones and proportional to the s, s$^{-1}$, s$^{-2}$, ... or just 1, as for the coulomb, ohm and weber, now dimensionless. The coulomb is equal to $\sqrt{μ_\circ c_\circ / \hbar_\circ}= 1.890... \times 10^{18}$, and the elementary charge to $e=1.602...\times 10^{-19} {\rm C} = \sqrt{4πα}=.3028... $ . The ohm is equal to $1/μ_\circ c_\circ$ so that the impedance of the vacuum is $Z_\circ = 376.730... Ω=1$. The volt is $ 1/ \sqrt{μ_\circ c_\circ \hbar_\circ}\ {\rm s}^{-1} = 5.017... \times\ 10^{15}\ {\rm s}^{-1}$, and the tesla $c_\circ $V/m = $ \sqrt{{c_\circ^3}/{μ_\circ\hbar_\circ}}\ {\rm s}^{-2} = 4.509... \times 10^{32}\ {\rm s}^{-2}$. The weber is $ 1/ \sqrt{μ_\circ c_\circ \hbar_\circ} = 5.017... \times\ 10^{15}$. $\ K_J =483\,597. \ $... GHz/V $= e/π= $ .09639..., and $R_K = 25\,812.\ ...\ Ω=1/2α\simeq 68.518$. One can also fix $e$ = 1.602 176 634 $\times 10^{-19}$ C, at the price of adjusting the coulomb and all electrical units with $μ_\circ=4π\times 10^{-7}η^2$ where $η^2, \propto α$, is very close to 1.

physics.gen-ph↗
arXiv2019

Completing the International System of units with $c=\hbar=μ_\circ=ε_\circ=k_B=N_A=1$

A drawback of the new SI is that by fixing the value of the elementary charge $e$, the vacuum magnetic permeability $μ_\circ$ and impedance $Z_\circ=μ_\circ c$ are no longer fixed, but get written proportionately to $α$. All electrical units get dependent on $α$ (and might even, conceivably, vary with time). This may be cured by embedding the SI in a new framework in which the "fundamental constants of nature" are fixed and equal to 1, i.e. $c=\hbar=μ_\circ=ε_\circ=Z_\circ= k_B=N_A=1$. The metre, joule, and kilogram get identified as 1 m = (1/$c_\circ$) s = (1/299 792 458) s, 1 J = $(1/\hbar_\circ)$ s$^{-1}= (2π/6.626\;070\;15) \times 10^{34}\ \rm s^{-1}$ and 1 kg = $(c_\circ^2/\hbar_\circ)\ \rm s^{-1}= 0.852 ... \times\ 10^{51}\ s^{-1}$. Fixing $μ_\circ= μ_{\circ\circ}$ N/A$^2=1 $ provides 1 A = $\sqrt{μ_{\circ\circ} \rm N} =\!\sqrt{μ_{\circ\circ} c_\circ/\hbar_\circ}\ \rm s^{-1}$ and 1 C = $\sqrt{μ_{\circ\circ} c_\circ/\hbar_\circ} = 1.890 ...\times\ 10^{18} $, with $e = 1.602 ... \times\ 10^{-19}\ \rm C$ also equal to $ \sqrt{4πα} = 0.3028 ... $. All SI units can be defined in terms of the second, with the coulomb, ohm and weber dimensionless, and the mole identified as the very large Avogadro number.

physics.gen-ph↗
arXiv2019

MICROSCOPE limits on the strength of a new force, with comparisons to gravity and electromagnetism

Extremely weak new forces could lead to apparent violations of the Equivalence Principle. The MICROSCOPE experiment implies that the relative strength of a new long-range force, compared with gravity, is constrained to $|\barα_g|<3.2\ 10^{-11},2.3\ 10^{-13},2.2\ 10^{-13},6.7\ 10^{-13}$ and $1.5\ 10^{-12}$ at $2σ$, for a coupling to $B,\ L,\ B-L,\ B+L$ or $3B+L$; or, for a coupling to isospin, $|α_g|<8.4\ 10^{-12}$. This is a gain in sensitivity $\simeq 3$ for a coupling to $B$, to $\approx$ 15 in the other cases, including $B-L$ as suggested by grand unification. This requires paying attention to the definition of $\barα_g$. A force coupled to $L$ (or $B-L$) would act effectively on protons (or neutrons) only, its relative intensity being reduced from $α_g$ to about $\barα_g=α_g/4$ for an average nucleon. It is thus convenient to view such forces as acting on $\bar Q =B,\ 2L,\ 2(B-L),2(B+L)/3$ or $2(3B+L)/7$, leading to $\barα_g=α_g\times(1,1/4,1/4,9/4$ or $49/4$). The sensitivity for a coupling to $L$ or $B-L$ is better than for $B$ by two orders of magnitude (as $Δ(2L/A_r)\simeq 144\ Δ(B/A_r)$ for Ti-Pt); and about 3 or 7 times better than for $B+L$ or $3B+L$. A coupling to $(ε_BB+ε_{Q_{el}}Q_{el})e$ should verify $|ε_B|<5\ 10^{-24}$; similarly $|ε_L|$ or $|ε_{B-L}|<.9\ 10^{-24}$, $|ε_{B+L}|<.5\ 10^{-24},|ε_{3B+L}|<.32\ 10^{-24}$ and $|ε_{B-2L}|<2.6\ 10^{-24}$, implying a new interaction weaker than electromagnetism by more than $10^{46}$ to $10^{48}$. The resulting hierarchy between couplings, typically by $>10^{24}$, may be related within supersymmetry with a large hierarchy in energy scales by $>10^{12}$. This points to a $\sqrtξ\approx 10^{16}$ GeV scale, associated with a huge vacuum energy density that may be responsible for the inflation of the early Universe.

hep-ph↗
arXiv2018

MICROSCOPE limits for new long-range forces and implications for unified theories

Many theories beyond the Standard Model involve an extra U(1) gauge group. The resulting gauge boson U, in general mixed with the Z and the photon, may be massless or very light, and very weakly coupled. It may be viewed as a generalized dark photon interacting with matter through a linear combination (ε_Q Q + ε_B B+ε_L L) e, involving B-L in a grand-unified theory, presumably through B-L-.61 Q, inducing effectively a very small repulsive force between neutrons. This new force, if long-ranged, may manifest through apparent violations of the Equivalence Principle. They are approximately proportional to ε_B+ε_L/2, times a combination involving mostly ε_L. New forces coupled to B-L or L should lead to nearly opposite values of the Eötvös parameter δ, and to almost the same limits for ε_{B-L} or ε_L, as long as no indication for δ\neq 0 is found. We derive new limits from the first results of the MICROSCOPE experiment testing the Equivalence Principle in space. A long-range force coupled to (ε_Q Q + ε_{B-L} (B-L)) e or (ε_Q Q + ε_L L) e should verify |ε_{B-L}| or |ε_L| < .8 10^{-24}, and a force coupled to (ε_Q Q + ε_B B) e, |ε_B| < 5 10^{-24}. We also discuss, within supersymmetric theories, how such extremely small gauge couplings g", typically \simle 10^{-24}, may be related to a correspondingly large ξ"D" term associated with a huge initial vacuum energy density, \propto 1/g"^2. The corresponding hierarchy between energy scales, by a factor \propto 1/\sqrt g" \simge 10^{12}, involves a very large scale ~ 10^{16} GeV, that may be associated with inflation, or supersymmetry breaking with a very heavy gravitino, leading to possible values of δ within the experimentally accessible range.

hep-ph↗
arXiv2017

The MICROSCOPE mission: first results of a space test of the Equivalence Principle

According to the Weak Equivalence Principle, all bodies should fall at the same rate in a gravitational field. The MICROSCOPE satellite, launched in April 2016, aims to test its validity at the $10^{-15}$ precision level, by measuring the force required to maintain two test masses (of titanium and platinum alloys) exactly in the same orbit. A non-vanishing result would correspond to a violation of the Equivalence Principle, or to the discovery of a new long-range force. Analysis of the first data gives $δ\rm{(Ti,Pt)}= [-1 \pm 9 (\mathrm{stat}) \pm 9 (\mathrm{syst})] \times 10^{-15}$ (1$σ$ statistical uncertainty) for the titanium-platinum Eötvös parameter characterizing the relative difference in their free-fall accelerations.

astro-ph.IM↗