Black Hole Evaporation Beyond the Standard Model of Particle Physics Michael J. Baker1and Andrea Thamm1y

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Black Hole Evaporation Beyond the Standard Model of Particle

Physics

Michael J. Baker1, ∗and Andrea Thamm1, †

1ARC Centre of Excellence for Dark Matter Particle Physics,

School of Physics, The University of Melbourne, Victoria 3010, Australia

(Dated: October 7, 2022)

The observation of an evaporating black hole would provide deﬁnitive information

on the elementary particles present in nature. In particular, it could discover or

exclude particles beyond those present in the standard model of particle physics.

We consider a wide range of motivated scenarios beyond the standard model and

identify those which would be best probed in the event of an observation. For those

models we deﬁne representative benchmark parameters and characterise the photon

spectra as a function of time. For the supersymmetric benchmark model, where most

of the new particles produce secondary photons, we provide secondary spectra and

discuss the subtle interplay between faster black hole evaporation and an increased

ﬂux of secondary photons. Finally, we discuss the impact of these models on future

experimental analysis strategies.

1 Introduction

Black holes are now known to exist, and their properties are being studied via gravitational

waves from binary black hole mergers and directly via photons emitted from their accretion

disks. Beyond these solar mass and supermassive black holes, much lighter black holes could

exist in the universe. For example, primordial black holes may have been produced in the

early universe [1–25]. Those with masses around 1015 g would have been continually losing

mass via Hawking radiation and would be reaching their ﬁnal stages of evaporation today

(see, e.g., refs. [26–31] for recent reviews of primordial black holes). There are currently a

range of experiments searching for both the explosive ﬁnal stages of black hole evaporation,

e.g., ref. [32], and indirect signatures from a population of low-mass black holes, e.g., refs. [30,

33–36].

In this work we emphasise that the observation of an exploding black hole would provide

deﬁnitive information on the particles present in nature, and that this in turn could provide

evidence for, or rule out, a wide range of models Beyond the Standard Model (BSM). A

broad range of BSM models have been proposed and are widely studied. These models

usually aim to address a question not answered by the Standard Model (SM), such as the

gauge hierarchy problem, the nature of dark matter, the strong-CP problem, etc. We ﬁrst

survey contemporary BSM models and identify those which are widely studied and would

have a signiﬁcant and calculable impact on the signal seen from a black hole explosion. These

are supersymmetry (for a recent review see, e.g., ref. [37]), Nnaturalness [38], models inspired

by string theory (for a recent review, see, e.g., ref. [39]) and dark sectors (e.g., refs. [40–47]).

∗michael.baker@unimelb.edu.au

†andrea.thamm@unimelb.edu.au

arXiv:2210.02805v1 [hep-ph] 6 Oct 2022

We then deﬁne representative benchmark parameter points for these models and determine

the relevant particle mass spectra and decay properties. This allows us to compute the mass

evolution of the black hole and the primary and secondary photon spectra. We use this

to characterise the range of behaviours seen in this set of BSM models, and brieﬂy discuss

experimental strategies to distinguish between the SM and BSM scenarios.

Conversely, we emphasise that assumptions about the particles present in nature will

impact experimental limits on the rate-density of exploding black holes. While searches

for evaporating black holes typically assume the SM particles, we demonstrate that BSM

models can dramatically alter the expected black hole evolution and the associated photon

signatures. This means that if a BSM model is realised in nature, then the direct and indirect

limits could be drastically altered. Similarly, existing gamma-ray bursts of unknown origin

could potentially be attributed to evaporating black holes. These may currently be missed

in searches that assume only the SM particles. The benchmark models we propose could

therefore be used as a framework for a wider interpretation in future searches.

Previous work on black holes and BSM physics has mainly focused on BSM particle

production in the early universe, e.g., refs. [48–67]. Ref. [68] considers the impact of a

single 5TeV squark on the observation of an evaporating black hole and suggests that a

deviation from the SM could be seen if a black hole explodes within ∼0.015 pc. In ref. [69]

we demonstrated that if the HAWC observatory observed ∼200 photons from an exploding

black hole it could probe dark sector models containing one or more copies of the SM particles

with any mass scale up to 100 TeV.

2 Beyond the Standard Model of Particle Physics

There are a wide variety of motivations for proposing new fundamental degrees of freedom

(dof) beyond those present in the standard model of particle physics. The standard model

was chieﬂy developed and veriﬁed using particle colliders, and this is the environment where

it is most applicable. As such, the SM can not describe gravity, dark matter, dark energy,

neutrino masses, or the matter-antimatter asymmetry. There are also theoretical problems

within the SM. Those which have been most widely studied are the gauge hierarchy problem

(why the Higgs boson has a mass at the weak scale and not at a higher scale) and the

strong-CP problem (which is related to the absence of CP violation in the strong sector).

Furthermore, the SM has many unexplained features (such as three gauge groups, three

generations, etc) and many unrelated parameters, which motivate the search for a deeper

uniﬁed model. There are also experimental results which are in tension with SM predictions,

such as the ﬂavour anomalies in Bphysics and the anomalous magnetic moment of the muon.

To guide our identiﬁcation of the most promising models to probe via black hole evap-

oration, we recap some of the conclusions from refs. [68,69]. Both ref. [68] and ref. [69]

demonstrate potential sensitivity to models of new physics. One of the signiﬁcant diﬀer-

ences between the studies is that while the single squark analysed in ref. [68] produces extra

secondary photons, the models considered in ref. [69] do not. However, even without extra

secondary photons, ‘dark’ degrees of freedom still take energy from the evaporating black

hole and lead to an increased rate of mass loss, which is detectable in the photon signal

originating from purely SM processes. As such, it is not essential to consider only models

that produce extra photons. We also emphasise that Hawking radiation is independent of all

non-gravitational couplings. As such, the increased rate of mass loss induced by new degrees

of freedom depends only on the particle mass and spin, and an observation can probe models

that are essentially decoupled from the SM.

The BSM models that will have the largest impact on the signal from an evaporating black

hole are those with a large number of new degrees of freedom, at a mass scale that is not too

high. For example, ref. [69] shows that the observation of 200 photons from an evaporating

black hole at the HAWC observatory would be able to probe a dark sector containing one

copy of the SM, around 100 new degrees of freedom, at any mass scale below 105GeV. The

observation of 10 photons would be enough to probe ten copies of the SM (around 1000 new

dof) up to a similar mass scale. This provides an initial indication that we should ﬁrst focus

on models with &100 new degrees of freedom.

We will also focus on models that have standard black hole evaporation at black hole

temperatures below ∼107GeV. Models with a fundamental Planck scale below ∼107GeV

would lead to a striking signature where the black hole evaporation suddenly stops when

the fundamental Planck scale is reached. This would be the case in the large Nspecies and

extra-dimensional models discussed below. However, modelling of the ﬁnal burst requires

some assumptions about the eﬀects of quantum gravity. Furthermore, some BSM scenarios,

such as extra-dimensional models, modify black hole dynamics below the fundamental Planck

scale. These scenarios require detailed, model-speciﬁc study which we defer to future work.

Ref. [69] demonstrates that it is unlikely that searches will be sensitive to physics above

∼107GeV, so we will still consider BSM scenarios which modify black hole dynamics above

this scale (such as Nnaturalness).

Astrophysical observations will typically only be sensitive to photons above a certain en-

ergy cutoﬀ. HAWC, for example, only has a signiﬁcant eﬀective area at Eγ&102GeV.

Furthermore, an analysis may only want to select higher energy events for eﬀective back-

ground reduction. This means that while these observations will be able to infer the presence

of new dof with masses below these energies, it will not be sensitive to their precise mass

scales. While this is a reasonable cutoﬀ for HAWC-like experiments, where an exploding

black hole would likely ﬁrst be seen, a lower cutoﬀ may be more appropriate for exploding

black holes seen using other experimental techniques or for attempts to probe BSM models

using an integrated ﬂux of lower energy photons from a more distant population of evapo-

rating black holes. For this reason, we consider new particles to be ‘massless’ if, for a black

hole exploding today, they could have been produced by the black hole shortly after the Big

Bang.

We now survey contemporary models in BSM physics, with an emphasis on those that are

widely studied and/or are expected to have a signiﬁcant impact on the photon signal from a

nearby evaporating black hole:

•Supersymmetry – From the 1980’s to the mid-2010’s supersymmetry was very widely

studied as it could address the gauge hierarchy problem, gauge coupling uniﬁcation and

dark matter, it is a necessary ingredient of string theory, and it was widely expected to

lead to new TeV scale particles (for a recent review, see, e.g., ref. [37]). Although these

particles have not been seen at the LHC or in dark matter direct detection experiments,

supersymmetry is still studied and certain regions of parameter space remain viable.

In contrast to the other models we highlight, most of these new particles will produce

secondary photons.

•Large NSpecies Solution to the Hierarchy Problem [70–73] and Nnaturalness [38]

– These models relax the hierarchy problem since the apparent Planck mass MPl is

related to the scale at which gravity becomes strongly coupled, M∗, by M2

Pl &NM2

∗. In

refs. [70–73] the hierarchy problem can be solved when gravity becomes strongly coupled

at the TeV scale, which can be achieved for N∼1032 copies of the SM. However, this

would mean that black hole evaporation stops at the TeV scale, rather than continuing

above 107GeV, so we do not consider this scenario in this work. Nnaturalness [38]

solves the hierarchy problem while introducing fewer copies, and can retain a Planck

scale above 107GeV. This is the scenario that we will focus on.

•String Inspired Models – String theory is the most promising approach for combining

general relativity and quantum ﬁeld theory, to provide a quantum theory of gravity

(for a recent review, see, e.g., ref. [39]). In string theory, the fundamental particles

of quantum ﬁeld theory are replaced by fundamental one-dimensional strings. While

this class of theories is not yet well understood and a realistic model (in the sense of

containing the SM particles) is yet to be constructed, some properties of the theory are

relatively well understood. One generic prediction is an abundance of particles, called

moduli, which are naively very light and which must obtain a mass through some

mechanism to satisfy cosmological constraints. These moduli may be light enough to

impact the signal from an evaporating black hole, and we study two ‘string inspired’

scenarios containing these moduli ﬁelds.

•Dark Sectors and Hidden Valleys – The presence of dark matter is perhaps the strongest

direct evidence for new particles beyond the SM. The simplest and most widely studied

models introduce just a few new degrees of freedom, and as such have a relatively

small impact on the signal from an evaporating black hole. However, dark matter

could be part of a richer dark sector containing multiple new particles and dark gauge

forces. Hidden valley models [45] similarly introduce a rich sector that only weakly

communicates with the SM. A representative class of dark sector models was studied

in ref. [69] and we include these models here for comparison.

•Extra-Dimensional Models – These models were initially introduced to address the

gauge hierarchy problem and are widely studied alternatives to supersymmetry. In

contrast to the other models we consider, extra-dimensional models alter the space-time

geometry and so fundamentally change the black holes themselves, making the situation

more complicated. The main classes of models are large extra-dimensional models [74–

77] and warped extra-dimensional models [78–81]. Large extra-dimensional models

lower the Planck scale, so these models suggest that black holes could be produced

at colliders [82,83] or in cosmic ray collisions [84–87] (although none have yet been

observed). While this would signiﬁcantly alter the signature, since the black hole would

reach the end-point of its evaporation at a temperature 1018 GeV, it would likely do

so in a way that depends on the details of quantum gravity [64,88–94]. While this may

produce a signature quite obviously diﬀerent from the SM expectation, quantitative

analysis requires detailed study which we leave to future work. While warped extra-

dimensional models maintain a larger Planck scale [80,81,95], no analytical solution

exists for a ﬁve-dimensional asymptotically anti-de Sitter black hole localised on the

brane and therefore the impact of the extra-dimension on the black hole evaporation

is not well understood [94]. As such we also do not consider these models in this work.

There are a host of other motivated models which could potentially be probed through

the observation of an evaporating black hole. However, since they require dedicated study or

will only produce small deviations from the SM signal, we do not propose benchmarks for:

•Composite Higgs Models – These models also address the gauge hierarchy problem

and are widely studied alternatives to supersymmetry and extra-dimensional models.

Although warped extra-dimensional models are in some ways dual to a wide class of

composite Higgs models, this is not true for black hole evaporation. While this could

provide an intriguing way of distinguishing between these models in the event of more

conventional evidence for these theories, conﬁnement in the models makes the situation

very complicated. In the same way that Hawking evaporation near the QCD scale

is beset with diﬃculties which are debated in the literature [96–99], similar problems

would emerge at the new conﬁnement scale. We also do not expect a very large number

of fundamental degrees of freedom in these theories, so we do not expect their impact

to be particularly large.

•Grand Uniﬁed Theories – While GUT theories are strongly motivated and aim to

unify the gauge forces into one structure, they typically have new degrees of freedom

at around 1016 GeV, the expected uniﬁcation scale. Since this scale is so high, these

models will only impact an evaporating black hole in the very last moments of its life

and so will be very hard to probe via black hole explosion.

•Light Dark Matter, Axions, ALPs, Dark Photons – Despite an intensive, dedicated

search for WIMP dark matter, no convincing signal has yet been observed. As such,

the theoretical and experimental communities are broadening their approach. Light

dark matter and axions, as well as axion like particles (ALPs) and dark photons, have

recently received a lot of attention. These particles are typically lighter than ∼1GeV

and are very weakly coupled to the SM particles, which could make them good models

to consider in an exploding black hole search. However, these models typically only

introduce a few degrees of freedom, so many photons would need to be observed to

probe them. In ref. [69], for example, around 105photons would need to be observed

in HAWC to detect the presence of a light Dirac fermion dark matter candidate. Since

the black hole would need to evaporate very close to the Earth for this many photons

to be detected (closer than 10−3pc), we would need to be very lucky to see one.

•Neutrino Masses – While there are a range of models which explain the neutrino masses,

perhaps the simplest explanation of the neutrino masses is the type-I see-saw, which

introduces right-handed neutrinos at a high scale (typically around 1015 GeV). Since

this scale is so high, it is very hard to probe and will only impact an exploding black hole

in the very last instants of its life. While there is interest in lower scale mechanisms,

these typically only introduce a few new particles and the spectrum is very model

dependent.

•Matter-Antimatter Asymmetry – The main classes of models which aim to explain this

asymmetry are electroweak baryogenesis and leptogenesis. While electroweak baryo-

genesis requires a strongly ﬁrst-order electroweak phase transition, which implies new

degrees of freedom around the weak scale, relatively few new degrees of freedom are

typically introduced. Leptogenesis models also introduce relatively few new degrees of

freedom and typically around 1015 GeV to tie in to seesaw explanations of the neutrino

masses.

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BlackHoleEvaporationBeyondtheStandardModelofParticlePhysicsMichaelJ.Baker1,andAndreaThamm1,y1ARCCentreofExcellenceforDarkMatterParticlePhysics,SchoolofPhysics,TheUniversityofMelbourne,Victoria3010,Australia(Dated:October7,2022)Theobservationofanevaporatingblackholewouldprovidedenitiveinformationon...

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