Asteroids for ultralight dark-photon dark-matter detection Michael A. Fedderke orcidand Anubhav Mathur orcidy The William H. Miller III Department of Physics and Astronomy

2025-05-02 0 0 809.89KB 8 页 10玖币

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Asteroids for ultralight dark-photon dark-matter detection

Michael A. Fedderke ∗and Anubhav Mathur †

The William H. Miller III Department of Physics and Astronomy,

The Johns Hopkins University, Baltimore, MD 21218, USA

(Dated: February 7, 2023)

Gravitational-wave (GW) detectors that monitor ﬂuctuations in the separation between inertial

test masses (TMs) are sensitive to new forces acting on those TMs. Ultralight dark-photon dark

matter (DPDM) coupled to U(1)Bor U(1)B−Lcharges supplies one such force that oscillates with

a frequency set by the DPDM mass. GW detectors operating in diﬀerent frequency bands are thus

sensitive to diﬀerent DPDM mass ranges. A recent GW detection proposal based on monitoring

the separation of certain asteroids in the inner Solar System would have sensitivity to µHz frequen-

cies [Fedderke et al., Phys. Rev. D 105, 103018 (2022)]. In this paper, we show how that proposal

would also enable access to new parameter space for DPDM coupled to B[respectively, B−L]

charges in the mass range 5 [9] ×10−21 eV .mdm .2×10−19 eV, with peak sensitivities about a

factor of 500 [50] beyond current best limits on εB[εB−L] at mdm ∼2×10−19 eV. Sensitivity could

be extended up to mdm ∼2×10−18 eV only if noise issues associated with asteroid rotational motion

could be overcome.

I. INTRODUCTION

Dark matter (DM) constitutes 26% of the energy bud-

get of the Universe [1]. Despite decades of increasingly

sensitive search eﬀorts, its fundamental identity remains

a mystery. Ultralight bosons are one interesting class of

DM candidates. They admit a classical-ﬁeld description

that oscillates in time at a frequency set by the DM mass.

In typical models, they are also very weakly coupled to

the Standard Model (SM). This permits sensitive exper-

imental approaches targeting narrowband time-varying

phenomena to shed light on the nature of the DM.

A compelling new-physics scenario involves gauging

either the U(1)Bor U(1)B−Lglobal symmetry of the

SM, with the new gauge boson—the ‘dark’ or ‘hidden’

photon—coupling weakly to the associated current.1The

static, Weak Equivalence Principle (EP) violating, ﬁfth-

force eﬀects induced by such couplings have been strin-

gently constrained [5–13].2Suﬃciently feebly coupled

dark photons can however additionally serve as an ultra-

light bosonic DM candidate. In this case, the oscillations

of the dark-photon dark-matter (DPDM) ﬁeld exert a

minute oscillatory force on SM matter. In particular,

such a force will cause the test masses (TMs) utilized

in certain classes of gravitational-wave (GW) detectors

to oscillate in a detectable fashion, allowing them to do

double duty as DM detectors;3the theory of this eﬀect

∗mfedderke@jhu.edu

†a.mathur@jhu.edu

1A dark photon can also couple to the SM photon directly via the

‘vector portal’, in which case it is referred to as the kinetically

mixed dark photon; see, e.g., Refs. [2–4].

2Yukawa modiﬁcations to the 1/r2gravitational force law also

supply constraints, but these are typically weaker than the best

direct EP-violation constraints in the DM mass range of interest

in this work; see, e.g., Ref. [7] and references therein.

3Other DM candidates can also be searched for, in diﬀerent ways:

e.g., via the transient acceleration signals induced by supermas-

sive DM states moving past the detector [14–17].

has been thoroughly developed [18–25].4See also, e.g.,

Refs. [26–28] for further discussion of the related case of

scalar DM.

In this paper, we evaluate the DPDM detection

prospects for the future GW detector concept based on

direct ranging between certain inner Solar System as-

teroids that was recently proposed in Ref. [29] and that

would have µHz frequency sensitivity (see also Ref. [30]

for a related noise study, and Refs. [31–35] for other re-

cent work on µHz GW detection).

The rest of this paper is structured as follows: in

Sec. II, we discuss the DPDM signal and relate it to GW

detector sensitivity. We present results, discuss them,

and conclude in Sec. III. In Appendix A, we discuss some

correction factors that are applied to published GW de-

tector sensitivity curves in order to use them in this work.

In Appendix B we discuss how appropriate it is to con-

sider results averaged over DPDM polarization and mo-

mentum orientations.

II. SIGNAL AND SENSITIVITY

Consider gauging the SM U(1)Ssymmetry, where

S∈ {B, B −L}, with that symmetry broken so as to

give rise to a (St¨uckelberg) mass mVfor the associated

U(1)Sgauge boson Vµ:

L=Lsm −1

4Vµν Vµν +1

2m2

VVµVµ−εSeemVµJµ

S,(1)

where Vµν ≡∂µVν−∂νVµ;Jµ

Sis the relevant SM cur-

rent; eem ≡√4παem is the fundamental EM charge unit,

with αem the electromagnetic (EM) ﬁne-structure con-

stant; and εSparametrizes the U(1)Scoupling strength

to the DM, normalized to that of EM for εS= 1. For

mV6= 0, we necessarily have ∂µVµ= 0.

4Note in particular Sec. V.A.4 in the published version of Ref. [19].

arXiv:2210.09324v2 [hep-ph] 4 Feb 2023

The coupling S6= 0 gives rise to a force on a SM

object moving at speed v:

F=εSeemQS−∇V0−∂tV+v×(∇×V),(2)

where QSis the U(1)Scharge of the SM object.

If the Vµgauge boson comprises all of the local, non-

relativistic DM (speed vdm ∼10−3), we write Vµ≡

(V0,V) exp [−iωdmt+ikdm ·x+iα] within a single co-

herence time/length,5with αan arbitrary phase, ωdm ≈

mdmp1 + v2

dm ≈mdm, and |kdm| ≈ mdmvdm. Note that

we have identiﬁed mV≡mdm. Now, ∂µVµ= 0 implies

that |V0| ∼ vdm|V|. Moreover, we have6|∇×V| ∼

mdmvdm|V|and |∇V0| ∼ mdmvdm|V0| ∼ mdmv2

dm|V|.

Additionally, |∂tV| ∼ mdm|V|. Since, by assumption,

T00

V=ρdm, it follows that7|V| ∼ √2ρdm/mdm.

Considering objects gravitationally bound to the Solar

System, we also have |v|.vdm, owing to the motion

of the Solar System relative to the galactic rest frame.

Therefore, the force can be written as

F≈iεSeemQSmdmVe−imdm(t−vdm·x)+iα

+O(v2

dm, vdm|v|)×εSeemQSmdm|V|.(3)

If the relevant SM object has mass M, and we drop the

subleading corrections,8this force causes an oscillatory

acceleration of that object [19,21,24,25]:

a≈2εSp2παemρdm

Me−imdm(t−vdm·x)+iφ ˆ

V,(4)

where

Vgives the polarization state of the DM (

V·ˆ

V∗=

1), and we have absorbed a phase into φ.

Consider now a GW detector that operates by mea-

suring ﬂuctuations in the proper distance between two

or more inertial test masses that deﬁne the endpoints of

one or more detector baselines. The DM-induced accel-

eration Eq. (4) causes the TMs to oscillate, leading to

a modulation of the proper length of the detector base-

line(s) that manifests as an oscillatory strain component.

5The coherence time is Tcoh ∼2π/(mdmv2

dm) and the coherence

length is λcoh ∼2π/(mdmvdm) [i.e., the de Broglie wavelength].

6We clarify that these are order of magnitude estimates for the

largest that the expressions on the lhs can be; additional geo-

metrical factors can suppress these even further.

7Technically this is only true as an average statement over many

coherence times of the DM ﬁeld, as the ﬁeld amplitude executes

O(1) stochastic ﬂuctuations from one coherence time to the next

(see, e.g., Refs. [36–38]); nevertheless, it is a good ﬁgure of merit.

8The vectorial orientation of the force relative to a GW detec-

tor baseline is the relevant quantity to consider for GW detector

eﬀects. Because the subleading corrections can be oriented dif-

ferently than the leading term, it is possible that the leading

term gives no eﬀect, but that the subleading terms do. However,

because the subleading corrections are suppressed by at least

∼v2

dm, this can only occur in highly tuned orientations. Real

GW detector baselines evolve in orientation over time relative

to inertial space, which will always spoil the tuning required for

such cancellation to be maintained; see also Appendix B. The

subleading terms can thus always be dropped.

There are two contributions to this strain: (1) a term

arising from the ﬁnite light-travel time for a null signal

propagating between the TMs, present even if the acceler-

ation had no spatial dependence at all (i.e., vdm = 0) [18–

20,22,24,25], and (2) a term arising from the spatial

gradient of the acceleration [19,21–25].

Averaged over time, DM ﬁeld orientations with respect

to the baseline, and DM momentum directions, and ig-

noring further corrections at O(v2

dm), the mean square of

the strain signal h(t)≡∆t/(2L), where ∆tis the change

to the round-trip light travel time between the TMs, can

be written as [24]:9

hh2i=hh2

1i+hh2

2i; (5)

hh2

1i ≡ 4cgeom

1H2×sin41

2mdmL; (6)

hh2

2i ≡ 1

3cgeom

2H2×(mdmLvdm)2; (7)

H2≡8π

3ε2

Sαem

ρdm

dmL2QS

M2

,(8)

where cgeom

jare O(1) geometrical factors that depend on

the baseline orientation, and Lis the unperturbed base-

line length. The baseline is assumed to be approximately

ﬁxed at least on the ∼2Lround-trip light travel time be-

tween the TMs, but it can vary secularly both in length

and orientation on longer timescales. The expression

for hh2

2iat Eq. (7) is correct in the limit mdmLvdm 1;

this is satisﬁed in all cases that we consider. We dis-

cuss the appropriateness of averaging over DPDM ﬁeld

orientations and momentum directions at length in Ap-

pendix B, as well as a relevant correction we apply when

we ﬁnd this to be incompletely justiﬁed.

Note that hh2

2i/hh2

1i ∝ (mdmLvdm)2cosec41

2mdmL.

Because mdmLvdm 1, the h2signal is only dominant

when either (1) the baseline is much shorter than the

DM Compton wavelength mdmL.vdm (never the case

for interesting mass ranges for the detectors we consider),

or (2) in certain narrow mass ranges where the round-trip

light travel time is such that the h1signal is nearly zero:

|mdmL−2πn| ∼ 2√mdmLvdm for n= 1,2, . . .. The latter

occurs only at frequencies above the peak sensitivity for

every detector we consider.

The geometrical factors for a single-baseline detector

are given by

cgeom

1=cgeom

2=1

2,[single baseline] (9)

9For detectors that are constructed with Fabry-P´erot (FP) cav-

ities in the baseline arms, these expressions are referred to the

input in the sense that the FP transfer function has been omitted.

Published GW characteristic-strain curves for detectors with FP

cavities are similarly referred to the GW input. Since the FP

cavity transfer function is the same for a GW and the DPDM

case that we consider in this work, no correction is required for

this [24]; see also Ref. [39] for further discussion of FP cavities

in GW detectors.

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Asteroidsforultralightdark-photondark-matterdetectionMichaelA.FedderkeandAnubhavMathuryTheWilliamH.MillerIIIDepartmentofPhysicsandAstronomy,TheJohnsHopkinsUniversity,Baltimore,MD21218,USA(Dated:February7,2023)Gravitational-wave(GW)detectorsthatmonitoructuationsintheseparationbetweeninertialtestma...

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Asteroids for ultralight dark-photon dark-matter detection Michael A. Fedderke orcidand Anubhav Mathur orcidy The William H. Miller III Department of Physics and Astronomy

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