# Updated LHC bounds on MUED after Run 2

Marvin M. Flores  Jong Soo Kim  Krzysztof Rolbiecki  Roberto Ruiz de Austri
Bazan  National Institute of Physics, University of the Philippines, Diliman,
Quezon City, Philippines  National Institute for Theoretical Physics and
School of Physics, University of the Witwatersrand, Johannesburg, South Africa
Faculty of Physics, University of Warsaw, Warsaw, Poland  Instituto de Física
Corpuscular, IFIC-UV/CSIC, 46980 Paterna, Valencia, Spain

###### Abstract

We present updated LHC limits on the minimal universal extra dimensions (MUED)
model from the Run 2 searches. We scan the parameter space against a number of
searches implemented in the public code CheckMATE and derive up-to-date limits
on the MUED parameter space from 13 TeV searches. The strongest constraints
come from a search dedicated to squarks and gluinos with one isolated lepton,
jets and missing transverse energy. In the procedure we take into account
initial state radiation and stress its importance in the MUED searches, which
is not always appreciated.

##  1 Introduction

Over the years, the LHC collaborations have put emphasis on probing various
incarnations of low energy supersymmetry (SUSY) such as the minimal
supergravity (mSUGRA) [1], gauge-mediated SUSY [2], anomaly-mediated SUSY [3,
4], phenomenological Minimal Supersymmetric Standard Model (pMSSM) [5], and
the electroweak-MSSM [6], usually represented by simplified models. After
extensively collecting data for almost a decade, however, no convincing signal
of supersymmetric models has been seen. This naturally led to a growing
interest in various alternative beyond-the-Standard-Model (BSM) scenarios.
Among these are the Universal Extra Dimensions (UED) [7, 8, 9, 10, 11, 12, 13]
which represent a simple extension of the Standard Model (SM) that include a
dark matter candidate and are also testable at the LHC. Here we focus on the
minimal version, Minimal UED (MUED) [14]. The phenomenology of MUED model
bears some similarities to SUSY in that each particle of the SM has a heavier
Kaluza-Klein (KK) partner with the same gauge quantum numbers and couplings.
However, in contrast to SUSY, KK-particles have the same spin as their SM
counterparts. The lightest particle in the KK spectrum is assumed stable and
can be a dark matter candidate.

Consequently, the usual collider signatures of the MUED are similar to the
SUSY missing energy signatures with additional jets and leptons. The most
important differences are the degenerate spectrum of a typical MUED model and
several times higher cross-section, for the same overall mass scale. The
definitive differentiation between these models requires a detailed analysis
of angular and invariant mass distributions of the final state products [15,
16, 17, 18, 19, 20]. Thus, SUSY searches should provide a high discovery and
exclusion potential for the MUED model. Since ATLAS and CMS have performed
many searches targeting SUSY, these can be recast to provide bounds on the
MUED model as was done in [21, 22, 23, 24]. In addition, non-SUSY-like
searches can provide bounds as well, for example the CMS search for a di-
lepton resonance at $\sqrt{s}=8$ TeV with 20.6 fb-1 which can be used to set
limits on the second KK-photon [25].

A huge advantage of MUED is its predictivity and simplicity since it only
depends on two parameters, the compactification radius of the extra dimension
$R$, and a cutoff scale $\Lambda$ at which it is replaced by a high-energy
theory. The inverse compactification radius $R^{-1}$ sets the mass scale of
the first KK excitations while $\Lambda\cdot R$ controls the allowed KK modes
present in the spectrum below the cutoff. Existing bounds prior to this paper
exclude models with $R^{-1}$ values of up to 1500 GeV [22, 24].

As already mentioned, MUED spectra tend to have smaller mass splittings than
supersymmetric spectra which results in softer final state products and thus
decreased missing transverse energy. As a result, exclusion limits rely on
initial state radiation (ISR) which provides transverse boost to the hard
scattering system, especially for low values of $\Lambda\cdot R$. As pointed
out in Refs. [26, 27] this may result in significant QCD uncertainties when
setting limits. Therefore, in this Letter we also explore how different
settings in Monte-Carlo (MC) event generator Pythia 8 [28], affect constraints
and their uncertainties when setting limits on the MUED parameter space. We
note that this question was not considered in the earlier studies [22, 23]. We
do not compare different MC event generators (e.g. Herwig [29] or Sherpa [30])
since after the matching procedure, the differences between the different
parton shower event generators should be marginal [31]. We rather focus on the
change of the parton shower scale uncertainty in Pythia as discussed in [32,
33]. Additionally, we take advantage of several ATLAS studies using full
luminosity collected in Run 2.

This paper is arranged as follows: Section 2 gives a brief overview of the
MUED model. Section 3 then explains the technical details of ISR in MC
simulation and the matching procedure. Section 4 provides details of the
numerical simulations and analysis as well as a discussion of our bounds in
the $R^{-1}$–$\Lambda\cdot R$ plane.

##  2 MUED Overview

We focus on the LHC phenomenology of the first KK level excitation. In that
case, each chiral SM fermion ($Q_{i}$, $u_{i}$, $d_{i}$, $L_{i}$, $e_{i}$)
(where $i$ is the SM generation index) has one Dirac-fermion partner
($Q_{i}^{(1)}$, $u_{i}^{(1)}$, $d_{i}^{(1)}$, $L_{i}^{(1)}$, $e_{i}^{(1)}$),
each SM gauge boson $g_{\mu}$, $W_{\mu}$, $B_{\mu}$ has a massive boson
partner $g_{\mu}^{(1)}$, $W_{\mu}^{(1)}$, $B_{\mu}^{(1)}$, and the Higgs
partner sector contains a scalar, a pseudo-scalar and a charged partner
($h^{(1)}$, $A_{0}^{(1)}$, $H_{\pm}^{(1)})$. The couplings between new states
are equal to the SM couplings of their partners. The masses of the KK modes
are at the tree level given by [34, 35]

$\displaystyle m_{n}=\sqrt{(n/R)^{2}+m_{\mathrm{SM}}^{2}}~{}~{}~{}n\geq
1~{}~{}\mbox{(for bosons)},$ (1) $\displaystyle
m_{n}=~{}n/R+m_{\mathrm{SM}}~{}~{}~{}n\geq 1~{}~{}\mbox{(for fermions)},$ (2)

where $n$ is the KK level, $R$ is the compactification radius and
$m_{\mathrm{SM}}$ the mass of SM state. Since the KK modes at $n=1$ are the
lightest, they can be abundantly produced at the LHC and will be our main
focus. Equations (1) and (2) suggests a very compressed mass spectrum.
However, at the loop level, the near-mass-degeneracy is partially lifted with
splittings growing with $\Lambda\cdot R$, making the KK-gluon the heaviest
state and the KK-partner of the $U(1)_{B}$ gauge boson the lightest state at
each KK level.

We restrict ourselves to the strong production of the colored KK-modes, i.e.
KK-gluons and KK-quarks,

$pp\rightarrow
g^{(1)}g^{(1)},~{}pp\rightarrow\mathcal{Q}_{i}^{(1)}\mathcal{Q}_{j}^{(1)},~{}pp\rightarrow
g^{(1)}\mathcal{Q}_{j}^{(1)},$ (3)

where $\mathcal{Q}^{(1)}=Q^{(1)},q^{(1)}$ and $Q^{(1)}$ denote the SU(2)
doublet quark partners (or their anti-particles) and $q^{(1)}=u^{(1)},d^{(1)}$
are the SU(2) singlet quark partners (or their anti-particles). The production
of other states is suppressed by the electroweak couplings.111Although this is
not the case if we consider the second KK level [25].

The typical decay patterns of the KK-states, shown diagrammatically in Fig. 1,
proceed as follows. The KK-gluon is the heaviest particle and decays into KK-
doublet and singlet quarks with about equal branching ratio. The KK-quark
decay modes depend mainly on its SU(2) charge. The SU(2) singlet KK-quark
directly decays to the KK-photon which is stable and the lightest KK particle
(LKP). The SU(2) doublet KK-quarks mainly decay into the KK-gauge-bosons
$W_{\pm}^{(1)}$ and $Z^{(1)}$. The KK-$W$ and $Z$ bosons are lighter than the
KK-quarks and so decay mostly into leptonic KK-states which in turn decay
further to the LKP and a lepton. Hence, events usually have a relatively large
lepton multiplicity, multiple jets, and missing transverse momentum
($\not{E}_{T}$) in the final states, although all decay products can be
relatively soft due to the compressed spectrum. Explicit mass spectra are
shown in Table 1 for various benchmark points with $\Lambda\cdot R=5$ together
with cross sections at $\sqrt{s}=13$ TeV.

Figure 1: A typical decay chain of the KK particles following their dominant branching ratios. Table 1: The total production cross sections, $\sqrt{s}=13$ TeV, and mass spectra for various $R^{-1}$ with $\Lambda\cdot R=5$. |  | Mass [GeV]
---|---|---
$R^{-1}$ [GeV] | Total $\sigma$ [fb] | $g^{(1)}$ | $Q^{(1)}$ | $q^{(1)}$ |  $W^{(1)}$/$Z^{(1)}$ | $L^{(1)}$ | $\gamma^{(1)}$
1700 | 76.858 | 1970.48 | 1878.22 | 1854.21 | 1755.49 | 1727.33 | 1698.55
1800 | 45.614 | 2086.39 | 1988.7 | 1963.28 | 1858.54 | 1828.94 | 1798.40
1900 | 27.209 | 2202.3 | 2099.19 | 2072.35 | 1961.60 | 1930.54 | 1898.26
2000 | 16.335 | 2318.22 | 2209.67 | 2181.14 | 2064.68 | 2032.15 | 1998.11

##  3 ISR and the matching procedure

For models with compressed mass spectra, a large recoil is necessary to
produce a signature with relatively low SM background. The recoil provides
large missing transverse momentum (if there are heavy particles escaping
detection) and gives additional transverse boost to leptons if present. The
recoil is provided by the initial state radiation from incoming partons. At
the MC level, the ISR can be produced in the hard matrix elements or in parton
shower. However, modeling ISR using a parton shower approach results in large
uncertainties which are mainly due to a choice of a starting scale for parton
shower evolution. This is known to have a large effect in squark and gluino
production, where the uncertainty can be illustrated by varying between the
”wimpy” and ”power” shower settings, which respectively refers to the
SpaceShower:pTmaxMatch = 1 and SpaceShower:pTmaxMatch = 2 settings in Pythia 8
[26, 36, 37].

In Pythia 8 for the “default” shower setting (which is SpaceShower:pTmaxMatch
= 0) $pT_{max}$ is chosen to be the factorization scale for internal processes
and the scale value for Les Houches input if the final state of the hard
process (not counting subsequent resonance decays) contains at least one quark
(excluding top), gluon or photon. If this is not the case, the emissions are
allowed to go all the way up to the kinematical limit. This is because in the
former set of processes the ISR emission of yet another quark, gluon or photon
could lead to double-counting, while no such danger exists in the latter case.
The “wimpy” setting, on the other hand, always uses the factorization scale
for an internal process and the scale value for Les Houches input, i.e. the
lower value. This avoids double-counting, but may leave out some emissions
that ought to have been simulated. Finally, the “power” setting always allows
emissions up to the kinematical limit which will simulate all possible event
topologies, but may lead to double-counting [28].

Since MUED has a compressed spectrum, especially in the low $\Lambda\cdot R$
region of its parameter space as discussed in Section 2 and suggested by Eqs.
(1) and (2), we must rely on the ISR and therefore expect the variation in
model limits when using different shower settings. This can be seen in Fig. 2
where the production of KK-gluon was simulated using the Pythia 8 setup found
in the Appendix C of Ref. [24] for the benchmark point $R^{-1}=1700$ GeV and
$\Lambda\cdot R=5$ with 10,000 events at $\sqrt{s}=13$ TeV and analysed using
Rivet [38].

Leading Jet

Figure 2: A comparison of the leading jet $p_{T}$ distribution between the
“wimpy” and “power” settings for the production of KK gluons using Pythia 8
for the benchmark point $R^{-1}=1700$ GeV and $\Lambda\cdot R=5$ with 10,000
events at 13 TeV normalised to an integrated luminosity of 150 fb-1.

Therefore, if our search strategy relies on the presence of ISR, we cannot
solely use parton shower simulation for determination of limits. The
simulation of additional emissions at the hard matrix element level matched to
the parton shower is the method that reduces the uncertainty due to ISR
modelling.

##  4 Numerical Analysis

The samples, either with or without matching, of QCD production of KK-
particles, as outlined in Section 2, are generated using MadGraph 5 with the
UFO [39] implementation of MUED [40, 41, 42, 43] and the parton distribution
function (PDF) set NN23LO1 [44, 45]. For the matched samples we use MLM
matching [46] implemented in Pythia 8 and matrix element with up to one extra
parton. Following the guidelines from MadGraph for MLM matching, we checked
that varying xqcut and qcut neither change the matched cross sections nor any
jet distributions. Moreover, we checked that the matched cross section is
consistent with the unmatched cross section. The matching scale was also
varied in the range between $(m_{1}+m_{2})/12$ and $(m_{1}+m_{2})/3$, where
$m_{1}$ and $m_{2}$ are the masses of the final state KK-particles and the
resulting total cross section was stable regardless of the parton shower
setting. In the following we present the results for a matching scale equal to
$(m_{1}+m_{2})/8$. With these settings, we scanned the parameter space
$R^{-1}$–$\Lambda\cdot R$ producing 50,000 events at each grid point.

The events where then fed into CheckMATE [47, 48, 49] for detector simulation
and checked for exclusion against 29 ATLAS and CMS searches (the full list is
given in the Appendix), corresponding to version 2.0.30. Each analysis
typically contains a large number of signal regions which target different
mass hierarchies and final state multiplicities. For a given search, the best
signal region for each point in the parameter space is defined by CheckMATE as
the one with the largest expected exclusion potential. This criterion is then
repeated to select the best search which is defined as the search whose best
signal region provides the strongest exclusion. This means that the best
observed limit is not always used but it ensures that the result is less
sensitive to downward fluctuations in the data that are bound to be present
when scanning over many searches and many signal regions. Once the best search
is found for a given point in the parameter space, the signal yield in our
model is then compared to the observed limit at 95% confidence level (CL),

$r=\frac{S-1.64\cdot\Delta S}{S^{95}_{\mbox{obs}}},$ (4)

where $S$ denotes the number of signal events, $\Delta S$ is the 1-$\sigma$
uncertainty on $S$ combining the statistical MC uncertainty and the 8%
systematic cross section uncertainty222This approximately amounts to a size of
the uncertainty for the next-to-leading order corrections to the cross section
[50]. and $S^{95}_{\mbox{obs}}$ is the observed 95% CL exclusion limit. The
quantity $S-1.64\cdot\Delta S$ corresponds to the 95% CL lower bound on our
prediction for the number of signal events, which ensures that the limits we
set are conservative. The $r$ value is only calculated for the expected best
signal region. CheckMATE does not, by default, combine signal regions nor
analyses in order to optimize exclusion since the correlations between
different searches and signal regions are not known in most cases. We consider
a model point as excluded if $r>1$.

The searches which turn out to be the most sensitive to the MUED model are:
atlas_conf_2019_040 (2-6 jets and $\not{E}_{T}$, $\mathcal{L}=139$ fb-1) [51],
atlas_2101_01629 (1 lepton, jets and $\not{E}_{T}$, $\mathcal{L}=139$ fb-1)
[52], and cms_sus_16_039 (2 same-sign leptons or at least 3 leptons plus
$\not{E}_{T}$, $\mathcal{L}=35.9$ fb-1) [53]. These analyses are also
summarized in Table 2.

Table 2: Relevant $\sqrt{s}=13$ TeV analyses used in our study. The middle column denotes the target final state while the last column shows the total integrated luminosity. Analysis | Final State |  $\mathcal{L}$ [fb-1]
---|---|---
atlas_2101_01629 [52] | 1$l$ \+ jets + $\not{E}_{T}$ | 139
atlas_conf_2019_040 [51] | jets + $\not{E}_{T}$ | 139
cms_sus_16_039 [53] | leptons + $\not{E}_{T}$ | 35.9

We start our numerical analysis by comparing an exclusion limit in the
$R^{-1}$–$\Lambda\cdot R$ plane obtained for different showering settings in
both matched and unmatched samples as discussed in Section 3. Figure 3 shows
limit comparison of shower-only and matched samples using the “wimpy” and
“power” mode for the signal region 4J_lx_bveto_1600 from the ATLAS search
atlas_2101_01629 [52]. As can be seen the limit derived from the matched
samples is stronger regardless of the shower setting. A band between power and
wimpy setting can be understood as an uncertainty in the exclusion limit due
to showering. As expected from the discussion in Section 3 it becomes more
pronounced towards lower values of of $\Lambda\cdot R$ which correspond to
more compressed mass spectra. For the unmatched case, the uncertainty band
widens significantly in the low $\Lambda\cdot R$.

Figure 3: Limit comparison of shower-only and matched samples using the
“wimpy” and “power” mode for the signal region 4J_lx_bveto_1600 from the ATLAS
search atlas_2101_01629 [52]. The difference is noticeable for the unmatched
case at lower values of $\Lambda\cdot R$ which corresponds to a compressed
mass spectrum.

Figure 4 compares limits from the searches listed in Table 2, which have the
highest sensitivity to the MUED signal. We see that the strongest limit comes
from the atlas_2101_01629 search for any value of $\Lambda\cdot R$. Figure 5
shows the three best signal regions that provide the strongest exclusion for
this particular search. For $\Lambda\cdot R<10$, the most sensitive signal
region (SR) is 2J squark discovery SR (CheckMATE label 2J_disc_squark) which
requires at least two jets and a low-$p_{T}$ lepton: $p_{T}>7(6)$ GeV for
electron (muon) and $p_{T}<20$ or $25$ GeV, depending on a number of jets. The
requirements placed on missing transverse momentum and effective mass,
$E_{\mathrm{T}}^{\mathrm{miss}}>400$ GeV, $m_{\mathrm{eff}}>1200$ GeV, enhance
the sensitivity by selecting signal events with boosted final-state particles
recoiling against energetic ISR jets. It is therefore well-suited for probing
parameter space with low mass splitting, as it is the case for $\Lambda\cdot
R<10$. As we go up in $\Lambda\cdot R$, the sensitivity then shifts to the 4J
low-x SR (CheckMATE label 4J_lx_bveto_1600) which corresponds to a higher jet
multiplicity (with no $b$-jets) of 4 to 5, and effective mass
$m_{\mathrm{eff}}>1600$ GeV, which is expected in the larger mass splitting
region of higher $\Lambda\cdot R$.

Figure 4: Exclusion plot for the searches listed in Table 2 obtained with the
MLM matching and the default shower setting, as discussed in Section 4. The
excluded region is to the left of the lines. Figure 5: The most sensitive
signal regions comprising the atlas_2101_01629 search. The corresponding
labels are the ones used by CheckMATE, see text for details. The excluded
region is to the left of the lines.

It is also illuminating to look at the next two most sensitive searches just
to understand the shape of exclusion lines. For the search cms_sus_16_039, the
most sensitive signal regions is SR_A14 (SR_A09) where events are required to
have three electrons or muons that form at least one opposite-sign same-flavor
pair and with $E_{\mathrm{T}}^{\mathrm{miss}}$ $\geq$ 250 GeV (200 GeV).
Notably, the multi-lepton search using $35.9$ fb-1 of data reaches similar
sensitivity to the multi-jet search atlas_conf_2019_040 using $139$ fb-1. In
case of the latter search, the most sensitive signal region is SR_4j_1000
which requires at least 4 jets, the leading jet $p_{T}>200$ GeV,
$m_{\mathrm{eff}}>1000$ GeV and
$E_{\mathrm{T}}^{\mathrm{miss}}/\sqrt{H_{\mathrm{T}}}>16$.333We note these
limits are different from those obtained in Ref. [54].

As already suggested, the leptonic searches can be expected to have an
improved sensitivity to MUED due to the relatively large expected number of
leptons in the final state compared to SUSY. Indeed, our study finds the
1-lepton search, atlas_2101_01629, having the best sensitivity in the full
data set but the CMS multilepton search, cms_sus_16_039 using $\mathcal{L}=36\
\mathrm{fb}^{-1}$, was also very promising and it is likely that a similar
study using the full data set will be at least as sensitive as the ATLAS
search. We note that in Ref. [21] it was found that same-sign/3-lepton search
[55] was the most constraining for moderate to large values of $\Lambda\cdot
R$. In our study, however, the ATLAS same-sign leptons study,
atlas_1909_08457, was lagging behind in sensitivity. Similarly, at low
$\Lambda\cdot R$ Ref. [21] points to a search based on 2 soft leptons [56].
Again, it turns out that the full luminosity search for soft-leptons final
states, atlas_1911_12606 [57], is not as strong as the 1-lepton search
atlas_2101_01629.

Finally, in Fig. 6 we summarize our findings. It shows the exclusion line of
the MUED model obtained with the matched samples and different shower
settings. The exclusion in $1/R$ shows little variation at large $\Lambda\cdot
R$, stabilizing around 1860 GeV. Note that most NLO calculations are missing
in the literature except for KK gluons[50]. The correction is modest, up to
14%. Uncertainty due to cross section was estimated in Ref. [50] to be
${}^{+5\%}_{-8\%}$ at the NLO and ${}^{+15\%}_{-17\%}$ and was accounted for
in CheckMATE.

In the LHC-allowed region above $R^{-1}\sim 1700$ GeV the dark matter relic
density is too high [58]. Thus, the LHC constraints together with the dark
matter relic density bound essentially rule out MUED, at least for the
standard cosmology.

Figure 6: The combined exclusion in the minimal UED model obtained with the
matched samples and different shower settings discussed in the text. Note that
the exclusion is entirely due to the atlas_2101_01629 search. The excluded
region is to the left of the line.

##  5 Conclusion

We showed that in updating the limits for the MUED model, using parton showers
alone yields large uncertainty at lower $\Lambda\cdot R$, i.e. for compressed
mass spectra. This clearly demonstrates the case for employing an appropriate
matching procedure. We then updated existing limits using the current LHC
searches concluding that the strongest limit comes from the atlas_2101_01629
search, which targets the final states with one lepton, jets and missing
transverse energy.

## Appendix A: List of CheckMATE Analyses

Table 3 shows the list of 13 TeV ATLAS and CMS analyses implemented into
CheckMATE as of completing this study.

Table 3: A list of $\sqrt{s}=13$ TeV analyses implemented in the CheckMATE version used throughout this work. The last column shows the total integrated luminosity. Analysis |  $\mathcal{L}$ [fb-1]
---|---
atlas_1604_01306 [59] | 3.2
atlas_1605_09318 [60] | 3.2
atlas_1609_01599  [61] | 3.2
atlas_1704_03848 [62] | 36.1
atlas_1706_03731 [63] | 36.1
atlas_1708_07875 [64] | 36.1
atlas_1709_04183 [65] | 36.1
atlas_1712_02332 [66] | 36.1
atlas_1712_08119 [67] | 36.1
atlas_1802_03158 [68] | 36.1
atlas_1803_02762 [69] | 36.1
atlas_1908_08215 [70] | 139
atlas_1909_08457 [71] | 139
atlas_1911_12606 [57] | 139
atlas_2101_01629 [52] | 139
atlas_conf_2015_082 [72] | 3.2
atlas_conf_2016_013 [73] | 3.2
atlas_conf_2016_050 [74] | 13.2
atlas_conf_2016_054 [75] | 14.8
atlas_conf_2016_066 [76] | 13.3
atlas_conf_2016_076 [77] | 13.3
atlas_conf_2016_096 [78] | 13.3
atlas_conf_2017_060 [79] | 36.1
atlas_conf_2019_020 [80] | 139
atlas_conf_2019_040 [51] | 139
cms_pas_sus_15_011 [81] | 2.2
cms_sus_16_025 [82] | 12.9
cms_sus_16_039 [53] | 35.9
cms_sus_16_048 [83] | 35.9

## Acknowledgements

MF is funded by the UP System Enhanced Creative Work and Research Grant
(ECWRG-2020-2-8R). KR is supported by the National Science Centre, Poland
under grants: 2016/23/G/ST2/04301, 2015/18/M/ST2/00518, 2018/31/B/ST2/02283,
2019/35/B/ST2/02008. R. RdA acknowledges partial funding/support from the
Elusives ITN (Marie Skłodowska-Curie grant agreement No 674896) and the “SOM
Sabor y origen de la Materia” (FPA 2017-85985-P).

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