Boosting Asymmetric charged DM via Thermalization_2

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Prepared for submission to JHEP

Boosting Asymmetric Charged DM via

Thermalization

Michael Geller and Zamir Heller-Algazi

School of Physics and Astronomy, Tel-Aviv University,

Tel-Aviv 69978, Israel

E-mail: mic.geller@gmail.com,zamir.heller@gmail.com

Abstract: We consider a dark sector scenario with two dark matter species with opposite

dark U(1) charges and an asymmetric population comprising some fraction of the dark

matter abundance. A new mechanism for boosting dark matter is introduced, arising

from the large mass hierarchy between the two particles. In the galaxy, the two species

thermalize eﬃciently through dark Rutherford scattering greatly boosting the lighter dark

matter particle, far above the virial and escape velocities in the galaxy, while the dark charge

prevents it from escaping. We study the consequences of this scenario for direct-detection

experiments, assuming a kinetic mixing between the dark photon and the photon. If the

charged dark sector makes up 5% of the total DM mass in our galaxy and the mass ratio is

between 103–104, we ﬁnd that current and future experiments may probe the boosted light

dark matter for masses down to 100 keV, in a hitherto unexplored parameter range.

Keywords: Dark Matter, Boosted Dark Matter

ArXiv ePrint: 2210.03126

arXiv:2210.03126v2 [hep-ph] 30 Apr 2023

Contents

1 Introduction 1

2 The Setup 3

3 Galactic MCP Distribution 4

4 Thermodynamic Considerations 7

4.1 `−XThermalization 8

4.2 Thermal Conduction 9

4.3 Cooling 11

5 Direct-detection Prospects 13

5.1 Bound Electron-Relativistic MCP Kinematics 14

5.2 Oﬀ-shell Matrix Element Approximation 14

5.3 Scattering Rate Formulae with Relativistic MCP 15

6 Detector Reach and Predictions 18

7 Conclusions 21

A Analytic Results for the MCP Galactic Distribution 21

A.1 Isothermal MCP Halo 21

A.2 Adiabatic MCP Halo 22

A.3 Mixed MCP Halo 23

B Thermalization and Conduction Times of the MCP Halo 24

C Gravothermal Collapse 25

1 Introduction

Astrophysical and cosmological observations of galaxy rotation curves [1], colliding galaxy

clusters [2] and the Cosmic Microwave Background (CMB) [3] all indicate that a signiﬁcant

portion of matter in the Universe is not made of baryonic matter, the particles of the

Standard Model (SM). Thus far, the missing Dark Matter (DM) has only been observed

indirectly by its gravitational inﬂuence on baryons, indicating that its non-gravitational

interactions with the SM are, at most, very weak. Its underlying nature remains mostly

unknown; we do not know its mass, whether it’s made up of a single or of several diﬀerent

DM species, or how it interacts with itself or with baryonic matter.

– 1 –

Results from various measurements and simulations point towards several noteworthy

astrophysical properties of DM: it forms a halo around our galaxy whose proﬁle is usually

parameterized as NFW [4,5] (other parameterizations are Burkert [4,6,7] and Einasto [8–

10]) with a local density of ρDM '0.3 GeV/cm3[11] at the Earth’s galactic location.

The DM velocity distribution is usually taken as a Maxwellian distribution, truncated by

the galactic escape velocity vesc ∼10−3c[12], which produces an approximately constant

velocity rotation curve as seen in observations.

In the last few decades the leading DM candidate has been the Weakly Interacting Mas-

sive Particle (WIMP), a single weak-scale particle weakly-coupled to the SM. For O(TeV)

scale masses and couplings of the same order as the weak force, the correct relic abun-

dance is reproduced in what has been colloquially referred to as the “WIMP miracle”.

Such particles are predicted by several well-motivated theories beyond the Standard Model

(BSM), most notably in supersymmetry (see for example [13] for a review on WIMPs

and the minimal supersymmetric Standard Model). On the experimental front — state

of the art DM direct-detection experiments are taking data, with the main eﬀort focused

on searching for the nuclear recoil from a rare scattering of DM against some target ma-

terial. The current nuclear-recoil direct-detection experiments are XENON1T [14,15],

PICO [16], CRESST [17], DarkSide-50 [18], CDMSlite [19], PandaX-4T [20] and LZ [21],

and more are planned for the near future, most notably XENONnT [22], SuperCDMS [23]

and DAMIC-M [24]. This detection method is sensitive to heavier DM, in the WIMP range,

while other experiments and analyses are based on electron recoil sensitive to lighter DM

masses: XENON10 [25], SENSEI [26], DAMIC [27], DarkSide-50 [28], CDMSHVeV [29] and

EDELWEISS [30]. For even lighter masses, a detection strategy utilizing the wave nature

of DM [31] is employed in CAST [32], ADMX [33,34], CASPEr [35], MADMAX [36],

IAXO [37] and ABRACADABRA [38].

The immense experimental eﬀort of searching for WIMPs has resulted in no discovery,

and a signiﬁcant fraction of the WIMP parameter space has already been excluded. At

this stage, it is therefore important to consider broader ideas for DM beyond the standard

paradigms. One such idea is the boosted DM scenario proposed in [39], wherein the DM is

boosted to velocities signiﬁcantly higher than its virial velocity ∼10−3c. In [39] a second

subdominant and lighter component of DM is introduced. The massive species annihilate to

the lighter species, transferring their rest-mass energy into kinetic energy, and as a result the

lighter species are produced at high velocities. The higher momentum of the lighter species

allows them to pass the detection threshold in direct-detection, enabling these experiments

to probe mass ranges typically outside their reach. Other mechanisms of boosting DM were

studied in [40–46].

In this work we consider a new type of boosted dark matter, based on thermalization

instead of the annihilation in [39]. Here, the dark sector will have a dark U(1)Dgauge group

and two fermions of opposite charges, a heavy Xand a light `. We assume an asymmetry

in the dark sector, so that the fermion anti-particles are not present while the total charge

is still zero because the fermion particles have opposite charge (similarly to the electron and

the proton in the SM). The two components couple through dark-electric interactions and

can therefore thermalize so that by the equipartition theorem, the light `will be boosted

– 2 –

to have similar kinetic energy as the heavy X. If the mass hierarchy of the light and heavy

particles is large enough, the light DM may reach speeds far above the escape velocity while

the dark-electric interaction with the heavy component will keep it bound to our galaxy.

The cosmological history and possible signatures of a similar setting was analyzed in [47,48]

within the context of the Mirror Twin Higgs model [49].

Our dark sector interacts with the SM through a small kinetic mixing of the dark and

SM photons. The kinetic mixing naturally induces an electric milli-charge on the DM [50]

while its dark EM charges are ∼ O(1) (see [51–58] for examples of other studies of milli-

charged DM). As in [39] the lighter but faster DM can pass the energy detection threshold

of terrestrial experiments, and we will see that future SENSEI runs will eﬀectively probe

milli-charge values of boosted `at a range of 100 keV–10 MeV unconstrained by any current

data.

2 The Setup

For our boosted dark matter model we introduce a dark sector with a U(1)Dgauge group

kinetically mixed with the SM U(1)EM. The dark photon γDis assumed to be massless,

and the dark sector is comprised of two Dirac fermions, denoted Xand `, with opposite

dark charges ±1. They are singlets under all other gauge groups. The Lagrangian is

L⊃−1

4Fµν Fµν −1

4F0

µν F0µν −

2Fµν F0

µν

+¯

Xi/

∂−gD/

A0−mXX+¯

`i/

∂+gD/

A0−m``,

(2.1)

where A(0)

µis the SM (dark) photon, F(0)

µν its ﬁeld strength, and mithe mass of fermion

i(i=X, `).gDis the dark elementary charge and is the mixing of the dark and SM

photons. Assuming small , we can change the basis of the Lagrangian up to O()to

decouple the dark and SM photons, which induces an electric charge on the dark fermions:

L⊃−1

4Fµν Fµν −1

4F0

µν F0µν

+¯

Xi/

∂−gD/

A0−eQ /

A−mXX+¯

`i/

∂+gD/

A0+eQ /

A−m``,

(2.2)

with Q≡p2αD/αQED the eﬀective EM charge of the DM and αD=g2

D/4πthe U(1)D

ﬁne-structure constant. With a small , therefore, Xand `obtain milli-charges. We set αD

to αQED from here on out for simplicity so Q=||.

We will further assume both milli-charged particles (MCPs) have an asymmetric abun-

dance where Xand `remain, while ¯

Xand ¯

`were annihilated. This asymmetry is similar to

the SM baryon asymmetry, and can be produced with any of the many proposed baryogen-

esis mechanisms (see e.g. [59] for a review). We will assume that the MCPs are thermalized

via the dark-electric interactions, and that Xis heavy while `is light and that their mass

ratio is mX/m`1. When this mass ratio is large enough, the temperature of the Xand

`particles in the halo will be larger than the binding energy of (X`)bound states, and

hence the dark bound states which were formed during “dark” recombination are re-ionized.

– 3 –

The binding energy of hydrogen-like atoms is BX` =m`α2

D/2while the temperature is

TX=mXv2

X/2, where vX∼10−3is roughly the virial velocity in the Milky Way, so requir-

ing that TX&BX` results in mX/m`&102. In this work we will consider larger mass ratios

mX/m`= 103,104such that the dark plasma can be assumed to be completely ionized.

While there are strong constraints on the magnitude of DM self-interactions [53,54,

60,61], the constraints disappear if the self-interacting component is less than 10% of

the DM mass [47,55]. We will assume for the rest of the paper that the MCP plasma

makes up 5% of the DM by mass. Our model also implicitly contains a standard cold dark

matter (CDM) candidate χ, neutral under U(1)D, that accounts for most of the DM in the

galaxy. We remain agnostic about its exact nature and the early universe dynamics which

produce the abundances of the CDM and the charged dark sector. It should also be noted

that, while there are claims that MCPs are evacuated from the galactic disk by supernova

shock waves and prevented from returning to it by magnetic ﬁelds [62,63], this is not the

case for our model since any energy gained by shocks is quickly turned into heat via their

self-interactions [64,65].

The constraints and new signatures arising from the cosmological history in a similar

scenario were analyzed in [47], where the equivalent Xand `are the mirror proton and the

mirror electron of the Mirror Twin Higgs model [49], and the U(1)Dis mirror electromag-

netism. A viable cosmological history can be accommodated, with the main constraints

stemming from the dark U(1)Dcontribution to Neﬀ. Additionally, new signatures arise due

to the dark acoustic oscillations, which arise similarly to regular baryon acoustic oscillations.

The oscillatory evolution of the density perturbation modiﬁes the matter power spectrum

on large scales, with the main eﬀect of suppressing structure formation. A comprehensive

study of the cosmological signatures of this model was performed in [66].

Another interesting phenomena to consider is plasma instability, which can occur in

much of the parameter space of MCPs and U(1)Dmediators, including the massless dark

photon with strong self-interactions in our model [54,67,68]. However, although the plasma

almost certainly exhibits instability, its observational eﬀects are poorly understood due to

the highly nonlinear nature of instabilities. Simulations of dark plasma instabilities have

been performed previously [69] in the context of galaxy cluster collisions, and may oﬀer a

viable explanation for some features of the DM distribution of some observations. Dark

plasma instabilities oﬀer an intriguing avenue of exploration for dark photon models, with

potentially huge constraining power in much of the parameter space, but would require

detailed numerical studies and simulations to make concrete statements about said models.

We ignore these complexities here, and therefore we will refrain from deriving robust bounds

on our scenario in this work.

We summarize the dark sector particle content in table 1.

3 Galactic MCP Distribution

In order to study the potential for detection of the boosted MCPs on Earth, we ﬁrst analyze

their distribution in our galaxy. The charged dark sector has a subdominant mass fraction

with little eﬀect on the dominant neutral CDM distribution, for which we take a standard

– 4 –

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PreparedforsubmissiontoJHEPBoostingAsymmetricChargedDMviaThermalizationMichaelGellerandZamirHeller-AlgaziSchoolofPhysicsandAstronomy,Tel-AvivUniversity,Tel-Aviv69978,IsraelE-mail:mic.geller@gmail.com,zamir.heller@gmail.comAbstract:Weconsideradarksectorscenariowithtwodarkmatterspecieswithoppositedark...

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