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JHEP11(2018)042

Published for SISSA by Springer

Received: May 15, 2018

Revised: August 28, 2018

Accepted: October 27, 2018

Published: November 7, 2018

Search for black holes and sphalerons in

high-multiplicity ﬁnal states in proton-proton collisions

√

s = 13 TeV

The CMS collaboration

E-mail: cms-publication-committee-chair@cern.ch

Abstract: A search in energetic, high-multiplicity ﬁnal states for evidence of physics

beyond the standard model, such as black holes, string balls, and electroweak sphalerons,

is presented. The data sample corresponds to an integrated luminosity of 35.9 fb

−1

collected

with the CMS experiment at the LHC in proton-proton collisions at a center-of-mass energy

of 13 TeV in 2016. Standard model backgrounds, dominated by multijet production, are

determined from control regions in data without any reliance on simulation. No evidence for

excesses above the predicted background is observed. Model-independent 95% conﬁdence

level upper limits on the cross section of beyond the standard model signals in these ﬁnal

states are set and further interpreted in terms of limits on semiclassical black hole, string

ball, and sphaleron production. In the context of models with large extra dimensions,

semiclassical black holes with minimum masses as high as 10.1 TeV and string balls with

masses as high as 9.5 TeV are excluded by this search. Results of the ﬁrst dedicated search

for electroweak sphalerons are presented. An upper limit of 0.021 is set at 95% conﬁdence

level on the fraction of all quark-quark interactions above the nominal threshold energy of

9 TeV resulting in the sphaleron transition.

Keywords: Beyond Standard Model, Hadron-Hadron scattering (experiments)

ArXiv ePrint: 1805.06013

We dedicate this paper to the memory of Prof. Stephen William Hawking,

on whose transformative ideas much of this work relies.

Open Access, Copyright CERN,

for the beneﬁt of the CMS Collaboration.

Article funded by SCOAP

https://doi.org/10.1007/JHEP11(2018)042

JHEP11(2018)042

of a large number of energetic objects (jets, leptons, and/or photons) in the ﬁnal state. The

search described in this paper targets these models of beyond-the-SM (BSM) physics by

looking for ﬁnal states of various inclusive multiplicities featuring energetic objects. Fur-

thermore, since such ﬁnal states can be used to test a large variety of models, we provide

model-independent exclusions on hypothetical signal cross sections. Considering concrete

examples of such models, we interpret the results of the search explicitly in models with

microscopic semiclassical black holes (BHs) and string balls (SBs), as well as in models

with electroweak (EW) sphalerons. These examples are discussed in detail in the rest of

this section.

1.1 Microscopic black holes

In our universe, gravity is the weakest of all known forces. Indeed, the Newton constant,

∼10

−38

GeV

−2

, which governs the strength of gravity, is much smaller than the Fermi con-

stant, ∼10

−4

GeV

−2

, which characterizes the strength of EW interactions. Consequently,

the Planck scale M

∼ 10

GeV, i.e., the energy at which gravity is expected to become

strong, is 17 orders of magnitude higher than the EW scale of ∼100 GeV. With the discovery

of the Higgs boson [18–20] with a mass [21, 22] at the EW scale, the large diﬀerence between

the two scales poses what is known as the hierarchy problem [23]. This is because in the SM,

the Higgs boson mass is not protected against quadratically divergent quantum corrections

and — in the absence of ﬁne tuning — is expected to be naturally at the largest energy scale

of the theory: the Planck scale. A number of theoretical models have been proposed that

attempt to solve the hierarchy problem, such as supersymmetry, technicolor [24], and, more

recently, theoretical frameworks based on extra dimensions in space: the Arkani-Hamed,

Dimopoulos, and Dvali (ADD) model [13–15] and the Randall–Sundrum model [16, 17].

In this paper, we look for the manifestation of the ADD model that postulates the

existence of n

≥ 2 “large” (compared to the inverse of the EW energy scale) extra spatial

dimensions, compactiﬁed on a sphere or a torus, in which only gravity can propagate.

This framework allows one to elude the hierarchy problem by explaining the apparent

weakness of gravity in the three-dimensional space via the suppression of the fundamentally

strong gravitational interaction by the large volume of the extra space. As a result, the

fundamental Planck scale, M

, in 3 + n

dimensions is related to the apparent Planck

scale in 3 dimensions via Gauss’s law as: M

∼ M

, where R is the radius of

extra dimensions. Since M

could be as low as a few TeV, i.e., relatively close to the EW

scale, the hierarchy problem would be alleviated.

At high-energy colliders, one of the possible manifestations of the ADD model is the

formation of microscopic BHs [25, 26] with a production cross section proportional to the

squared Schwarzschild radius, given as:

√

πM

8Γ(

)

+ 2

where Γ is the gamma function and M

is the mass of the BH. In the simplest production

scenario, the cross section is given by the area of a disk of radius R

, i.e., σ ≈ πR

[25,

– 2 –

JHEP11(2018)042

26]. In more complicated production scenarios, e.g., a scenario with energy loss during

the formation of the BH horizon, the cross section is modiﬁed from this “black disk”

approximation by a factor of order one [26].

As BH production is a threshold phenomenon, we search for BHs above a certain

minimum mass M

min

≥ M

. In the absence of signal, we will express the results of the

search as limits on M

min

. In the semiclassical case (strictly valid for M

 M

), the BH

quickly evaporates via Hawking radiation [27] into a large number of energetic particles,

such as gluons, quarks, leptons, photons, etc. The relative abundance of various particles

produced in the process of BH evaporation is expected to follow the number of degrees of

freedom per particle in the SM. Thus, about 75% of particles produced are expected to be

quarks and gluons, because they come in three or eight color combinations, respectively. A

signiﬁcant amount of missing transverse momentum may be also produced in the process

of BH evaporation via production of neutrinos, which constitute ∼5% of the products of

a semiclassical BH decay, W and Z boson decays, heavy-ﬂavor quark decays, gravitons, or

noninteracting stable BH remnants.

If the mass of a BH is close to M

, it is expected to exhibit quantum features, which

can modify the characteristics of its decay products. For example, quantum BHs [28–30] are

expected to decay before they thermalize, resulting in low-multiplicity ﬁnal states. Another

model of semiclassical BH precursors is the SB model [31], which predicts the formation of

a long, jagged string excitation, folded into a “ball”. The evaporation of an SB is similar to

that of a semiclassical BH, except that it takes place at a ﬁxed Hagedorn temperature [32],

which depends only on the string scale M

. The formation of an SB occurs once the mass

of the object exceeds M

, where g

is the string coupling. As the mass of the SB grows,

eventually it will transform into a semiclassical BH, once its mass exceeds M

> M

A number of searches for both semiclassical and quantum BHs, as well as for SBs have

been performed at the CERN LHC using the Run 1 (

√

s = 7 and 8 TeV) and Run 2 (

√

s =

13 TeV) data. An extensive review of Run 1 searches can be found in ref. [33]. The most

recent Run 2 searches for semiclassical BHs and SBs were carried out by ATLAS [34, 35]

and CMS [36] using 2015 data. Results of searches for quantum BHs in Run 2 based on

2015 and 2016 data can be found in refs. [37–42]. The most stringent limits on M

min

set by

the Run 2 searches are 9.5 and 9.0 TeV for semiclassical and quantum BHs, respectively,

for M

= 4 TeV [34, 36]. The analogous limits on the minimum SB mass depend on the

choice of the string scale and coupling and are in the 6.6−9 TeV range for the parameter

choices considered in refs. [34, 36].

1.2 Sphalerons

The Lagrangian of the EW sector of the SM has a possible nonperturbative solution, which

includes a vacuum transition known as a “sphaleron”. This class of solutions to gauge ﬁeld

theories was ﬁrst proposed in 1976 by ’t Hooft [43]. The particular sphaleron solution of the

SM was ﬁrst described by Klinkhamer and Manton in 1984 [44]. It is also a critical piece

of EW baryogenesis theory [45], which explains the matter-antimatter asymmetry of the

universe by such processes. The crucial feature of the sphaleron, which allows such claims

to be made, is the violation of baryon (B) and lepton (L) numbers, while preserving B −L.

– 3 –

JHEP11(2018)042

The possibility of sphaleron transitions at hadron colliders and related phenomenology has

been discussed since the late 1980s [46].

Within the framework of perturbative SM physics, there are twelve globally conserved

currents, one for each of the 12 fundamental fermions: J

= ψ

. An anomaly breaks

this conservation, in particular ∂

= [g

/(16π

)]Tr[F

µν

]. This is because the integral

of this term, known as a Chern–Simons (or winding) number N

[47], is nonzero. The

anomaly exists for each fermion doublet. This means that the lepton number changes

by 3N

, since each of three leptons produced has absolute lepton number of 1. The

baryon number will also change by 3N

because each quark has an absolute baryon

number of 1/3 and there are three colors and three generations of quarks produced. This

results in two important relations, which are essential to the phenomenology of sphalerons:

∆(B + L) = 6N

and ∆(B −L) = 0. The anomaly only exists if there is enough energy to

overcome the potential in N

, which is ﬁxed by the values of the EW couplings. Assuming

the state at 125 GeV to be the SM Higgs boson, the precise measurement of its mass [21, 22]

allowed the determination of these couplings, giving an estimate of the energy required for

the sphaleron transitions of E

sph

≈ 9 TeV [44, 48].

While the E

sph

threshold is within the reach of the LHC, it was originally thought that

the sphaleron transition probability would be signiﬁcantly suppressed by a large potential

barrier. However, in a recent work [48] it has been suggested that the periodic nature

of the Chern–Simons potential reduces this suppression at collision energies

√

ˆs < E

sph

removing it completely for

√

ˆs ≥ E

sph

. This argument opens up the possibility of observing

an EW sphaleron transition in proton-proton (pp) collisions at the LHC via processes such

as: u + u → e

t t b c c s d + X. Fundamentally, the N

= +1 (−1) sphaleron tran-

sitions involve 12 (anti)fermions: three (anti)leptons, one from each generation, and nine

(anti)quarks, corresponding to three colors and three generations, with the total electric

charge and weak isospin of zero. Nevertheless, at the LHC, we consider signatures with

14, 12, or 10 particles produced, that arise from a q + q

→ q + q

+ sphaleron process,

where 0, 1, or 2 of the 12 fermions corresponding to the sphaleron transition may “can-

cel” the q or q

inherited from the initial state [49, 50]. Since between zero and three

of the produced particles are neutrinos, and also between zero and three are top quarks,

which further decay, the actual multiplicity of the visible ﬁnal-state particles may vary

between 7 and 20 or more. Some of the ﬁnal-state particles may also be gluons from either

initial- or ﬁnal-state radiation. While the large number of allowed combinations of the

12 (anti)fermions results in over a million unique transitions [51], many of the ﬁnal states

resulting from these transitions would look identical in a typical collider experiment, as no

distinction is made between quarks of the ﬁrst two generations, leading to only a few dozen

phenomenologically unique transitions, determined by the charges and types of leptons and

the third-generation quarks in the ﬁnal state. These transitions would lead to characteristic

collider signatures, which would have many energetic jets and charged leptons, as well as

large missing transverse momentum due to undetected neutrinos.

A phenomenological reinterpretation in terms of limits on the EW sphaleron production

of an ATLAS search for microscopic BHs in the multijet ﬁnal states at

√

s = 13 TeV [34],

comparable to an earlier CMS analysis [36], was recently performed in ref. [49]. In the

present paper, we describe the ﬁrst dedicated experimental search for EW sphaleron tran-

sitions.

– 4 –

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