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11institutetext:  Department of Physics, University of Oslo, N-0316 Oslo,
Norway22institutetext:  School of Physics and Astronomy, Monash University,
Melbourne, VIC 3800, Australia33institutetext:  Theoretical Particle Physics
and Cosmology (TPPC), Department of Physics, King’s College London, Strand,
London, WC2R 2LS, UK44institutetext:  SUPA, School of Physics and Astronomy,
University of Glasgow, Glasgow, G12 8QQ, UK55institutetext:  Department of
Physics and Astronomy, University College London, Gower St., London, WC1E 6BT,
UK66institutetext:  School of Mathematics and Physics, The University of
Queensland, St. Lucia, Brisbane, QLD 4072, Australia77institutetext:
Department of Physics, Simon Fraser University, Burnaby BC, V5A 1S6,
Canada88institutetext:  Department of Physics, School of Mathematics and
Physics, Xi’an Jiaotong-Liverpool University, 111 Ren’ai Road, Suzhou Dushu
Lake, Science and Education Innovation District, Suzhou Industrial Park,
Suzhou 215123, P.R. China99institutetext:  Institute for Theoretical Particle
Physics (TTP), Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe,
Germany1010institutetext:  Univ Lyon, Univ Lyon 1, CNRS/IN2P3, Institut de
Physique des 2 Infinis de Lyon, UMR 5822, 69622 Villeurbanne,
France1111institutetext:  Theoretical Physics Department, CERN, CH-1211 Geneva
23, Switzerland1212institutetext:  Physics and Astronomy Department,
University of California, Los Angeles, CA 90095, USA1313institutetext:
Physikalisches Institut der Rheinischen Friedrich-Wilhelms-Universität Bonn,
53115 Bonn, Germany1414institutetext:  Quantum Brilliance Pty Ltd, The
Australian National University, Daley Road, Acton ACT 2601,
Australia1515institutetext:  Institute for Theoretical Particle Physics and
Cosmology (TTK), RWTH Aachen University, D-52056 Aachen,
Germany1616institutetext:  ARC Centre of Excellence for Dark Matter Particle
Physics & CSSM, Department of Physics, University of Adelaide, Adelaide, SA
50051717institutetext:  School of Physics, Zhengzhou University, Zhengzhou
450000, China1818institutetext:  Telenor Research, N-1360 Fornebu,
Norway1919institutetext:  CAS Key Laboratory of Theoretical Physics, Institute
of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China

<EMAIL_ADDRESS><EMAIL_ADDRESS>
# Collider constraints on electroweakinos in the presence of a light gravitino

The GAMBIT Collaboration: Viktor Ananyevoslo  Csaba Balázsmonash
Ankit Beniwalkings  Lasse Lorentz Brasethoslo  Andy Buckleyglasgow
Jonathan Butterworthucl  Christopher Changuq  Matthias Danningersfu
Andrew Fowliexjtlu  Tomás E. GonzalokitTTP,a  Anders Kvellestadoslo,b
Farvah Mahmoudilyon,cern  Gregory D. Martinezucla  Markus T. Primbonn
Tomasz Procterglasgow  Are Raklevoslo  Pat Scottqb  Patrick Stöckeraachen
Jeriek Van den Abeeleoslo,telenor  Martin Whiteadelaide  Yang
Zhangzhengzhou,casbejing

(Received: date / Accepted: date)

###### Abstract

Using the GAMBIT global fitting framework, we constrain the MSSM with an eV-
scale gravitino as the lightest supersymmetric particle, and the six
electroweakinos (neutralinos and charginos) as the only other light new
states. We combine 15 ATLAS and 12 CMS searches at 13 TeV, along with a large
collection of ATLAS and CMS measurements of Standard Model signatures. This
model, which we refer to as the $\tilde{G}$-EWMSSM, exhibits quite varied
collider phenomenology due to its many permitted electroweakino production
processes and decay modes. Characteristic $\tilde{G}$-EWMSSM signal events
have two or more Standard Model bosons and missing energy due to the escaping
gravitinos. While much of the $\tilde{G}$-EWMSSM parameter space is excluded,
we find several viable parameter regions that predict phenomenologically rich
scenarios with multiple neutralinos and charginos within the kinematic reach
of the LHC during Run 3, or the High Luminosity LHC. In particular, we
identify scenarios with Higgsino-dominated electroweakinos as light as 140 GeV
that are consistent with our combined set of collider searches and
measurements. The full set of $\tilde{G}$-EWMSSM parameter samples and GAMBIT
input files generated for this work is available via Zenodo.

††journal: Eur. Phys. J. C

###### Contents

  1. 1 Introduction
  2. 2 Model
  3. 3 Collider likelihoods
    1. 3.1 LHC searches
    2. 3.2 LHC measurements of SM signatures
    3. 3.3 Cross-section limits from LEP searches
  4. 4 Global fit setup
    1. 4.1 Software framework and event generation
    2. 4.2 Scanning strategy
  5. 5 Results
    1. 5.1 Best-fit scenarios
    2. 5.2 Non-excluded scenarios
    3. 5.3 Impact of different searches
    4. 5.4 Impact of measurements
    5. 5.5 Scenarios with a chargino NLSP
  6. 6 Conclusions
  7. A Profile likelihood maps for the input parameters
  8. B LHC searches
  9. C Code extensions
    1. C.1 GAMBIT models with a light gravitino
    2. C.2 Additions to DecayBit
    3. C.3 Additions to ColliderBit
    4. C.4 New backend interfaces: Rivet and Contur
    5. C.5 Adaptations to Rivet and Contur

##  1 Introduction

Although supersymmetry (SUSY) was not invented to address shortcomings of the
Standard Model (SM) of particle physics or cosmology, it addresses them in
various aspects. Inflation, dark matter, the cosmic matter-antimatter
asymmetry, neutrino masses, patterns of fermion families, gauge and Yukawa
couplings, naturalness, and more, can all be accommodated if supersymmetry is
a symmetry of nature that is broken near the TeV scale; see for example Refs.
Nilles:1983ge ; Haber:1984rc ; Martin:1997ns ; Chung:2003fi ; Feng:2013pwa
for reviews. Consequently, a major goal of the Large Hadron Collider (LHC) is
to search for superpartners. So far, the LHC experiments have found no
concrete evidence for SUSY and the impact of the null results in simple SUSY
scenarios has been well explored (see e.g. the global fits in Refs. Ruiz06 ;
arXiv:1111.6098 ; Fowlie:2012im ; Fittino12 ; Fittinocoverage ;
MastercodeCMSSM ; MasterCodemSUGRA ; Bagnaschi:2017tru ; Costa:2017gup ; CMSSM
; MSSM ). For example, in our previous work EWMSSM , we investigated the
collider constraints on the electroweakino sector of the Minimal
Supersymmetric Standard Model (MSSM). Gravitinos, however, are an interesting
and often ignored possibility in SUSY collider phenomenology.

The gravitino is the spin-3/2 superpartner of the spin-2 graviton. Its
existence is a necessary consequence of supergravity nath1975generalized ;
deser1976consistent ; freedman1976properties ; arnowitt1975superfield , a
local supersymmetry that implies gravity Akulov:1975ax ; Wess:1977fn ;
Zumino:1979et ; Stelle:1978ye ; Stelle:1978yr ; Ferrara:1976ni . The gravitino
acquires mass through the super-Higgs mechanism and the mass is set solely by
the scale of supersymmetry breaking; $m_{3/2}\sim\langle F\rangle/M_{P}$ for
$F$-term supersymmetry breaking Deser:1977uq ; Cremmer:1978iv ; Cremmer:1978hn
where $M_{P}$ is the Planck mass. In gravity-mediated supersymmetry breaking
Chamseddine:1982jx ; Barbieri:1982eh ; Ibanez:1982ee ; Hall:1983iz ;
Ellis:1982wr ; AlvarezGaume:1983gj ; Brignole:1997wnc , the soft-breaking
masses are of order $m_{\text{soft}}\sim\langle F\rangle/M_{P}\sim m_{3/2}$,
so that the gravitino can lie anywhere in the supersymmetric mass spectrum. In
gauge-mediated supersymmetry breaking (GMSB) Dine:1981za ; Dimopoulos:1981au ;
Alvarez-Gaume:1981abe ; Nappi:1982hm ; Dine:1993yw ; Dine:1994vc ; Dine:1995ag
; Kolda:1997wt , on the other hand, the soft-breaking masses are of order
$m_{\text{soft}}\sim\langle F\rangle/M_{\text{mess}}$, where $M_{\text{mess}}$
is the scale of the messengers mediating SUSY breaking. Consequently, the
gravitino mass is Planck-scale suppressed by $M_{\text{mess}}/M_{P}$ relative
to the masses of the other superpartners. Thus, in GMSB the gravitino is
expected to be the lightest supersymmetric particle (LSP).

Motivated by GMSB, in this work we consider the electroweakino sector and an
approximately massless gravitino LSP, with the other superpartners decoupled.
The next-to-lightest supersymmetric particle (NLSP) must then be a neutralino
or a chargino, though the latter is unusual in the MSSM parameter space
Kribs:2008hq ; Bomark:2013nya . The electroweakinos,
$\tilde{\chi}^{0}_{1,2,3,4}$ and $\tilde{\chi}^{\pm}_{1,2}$, may decay to a
gravitino and an SM particle. Naively, one might expect this to proceed slowly
through gravitational interactions. However, as the gravitino acquires
goldstino interactions through the super-Higgs mechanism fayet1977mixing ;
Fayet:1979qi , the decay may be prompt when $m_{3/2}\lesssim
1\,\text{k$\text{e}\mspace{-0.8mu}\text{V}$}$ Ambrosanio:1996jn . The
neutralino decays $\tilde{\chi}^{0}\to\\{h,H,A,Z\\}\,\tilde{G}$ and the
chargino decays $\tilde{\chi}^{\pm}\to\\{H^{\pm},W^{\pm}\\}\,\tilde{G}$ could
be kinematically allowed depending on the mass spectrum, whereas the
neutralino decays $\tilde{\chi}^{0}\to\gamma\,\tilde{G}$ are guaranteed to be
allowed and dominate for the lightest neutralino, $\tilde{\chi}^{0}_{1}$,
across much of parameter space Dimopoulos:1996vz . We thus assume that the
electroweakinos may decay promptly through any kinematically open channel to
an SM particle and a gravitino.

Direct LHC production of gravitino pairs, or associated production of a
gravitino and another superpartner, can only reach detectable rates if
$m_{3/2}\lll 1\,\text{e}\mspace{-0.8mu}\text{V}$ Maltoni:2015twa ;
Brignole:1998me . For scenarios with electroweakinos within LHC reach and an
eV scale gravitino, which is the focus of our study, the dominant gravitino
production mode is through the prompt decay of the NLSP. This gives rise to
distinctive collider signatures, such as two gravitinos that carry away
missing energy and two energetic photons. Whilst the NLSP always decays
promptly to a gravitino, an eV scale gravitino implies that the heavier
electroweakinos decay predominantly to lighter ones Ambrosanio:1996jn , unless
the mass degeneracy between the electroweakinos is severe (see below).
Production of heavier electroweakinos will therefore typically result in
multi-step decay chains that terminate with the decay of the NLSP to the
gravitino.

The phenomenological impacts of electron-positron collider Fayet:1986zc ;
Dicus:1990dy ; Stump:1996wd ; Dimopoulos:1996vz ; Brignole:1997sk ;
Lopez:1996ey ; Ellis:1996aa ; Ambrosanio:1997rv , Tevatron Dicus:1989gg ;
Dimopoulos:1996va ; Ambrosanio:1996jn ; Brignole:1998me ; Matchev:1999ft ;
Baer:1999tx ; Dimopoulos:1996vz ; Dimopoulos:1996fj ; SUSYWorkingGroup:2000ooo
; Meade:2009qv  and LHC Kim:2017pvm ; Kim:2019vcp ; Dutta:2017jpe ; Lu:2017oee
; Gu:2020ozv ; Arbey:2015vlo ; Maltoni:2015twa ; Asano:2011ri ;
Roszkowski:2004jd ; Cahill-Rowley:2012ydr  searches on these scenarios have
been previously studied. Reference Kim:2017pvm , for example, establishes
limits on the electroweakino sector using light gravitino pair-production via
electroweakino decay in the context of GMSB in the MSSM. This study shows that
while LHC searches specifically designed for such scenarios are important,
other LHC searches and measurements provide useful complementary constraints.
Using the GAMBIT software gambit ; gambit_addendum , we here go beyond
previous works by performing the first global fit of electroweakinos in the
presence of a light gravitino. We include up-to-date results from LHC Run 2,
described in Sec. 3.1, and for the first time in a global fit we check that
our models are allowed by a suite of measurements of SM-like final states
using Contur Butterworth:2016sqg ; Buckley:2021neu ; see Sec. 3.2 for further
details. Lastly, we include constraints from the Large Electron-Positron
collider (LEP); see Sec. 3.3. We do not include Tevatron searches as these
constraints are in general superseded by LHC results, and performing event
simulations for Tevatron searches in addition to LHC searches would greatly
increase the computational expense of our study.

Whilst a gravitino LSP could play the role of dark matter (DM), and there are
strong constraints that we do not consider Asaka:2000zh ; Feng:2004mt ;
Ellis:2003dn ; Steffen:2006hw , each of these requires some additional
assumptions. It was originally thought that to avoid over-closing the Universe
it must be that $m_{3/2}\lesssim 1\,\text{k$\text{e}\mspace{-0.8mu}\text{V}$}$
Pagels:1981ke . Although this constraint is weakened when one considers
inflation Khlopov:1984pf ; Ellis:1984eq , non-thermal production of gravitinos
and the NLSP decays to gravitinos are both constrained by the measured
abundance of DM. There are, furthermore, constraints from cosmic structure
Viel:2005qj  and big-bang nucleosynthesis Moroi:1993mb ; Jedamzik:2009uy ,
however, the latter does not apply to our scenario where the NLSP decays
promptly. We choose not to include constraints from the dark matter properties
of the gravitino in this work, in order to explore electroweakinos more
generally without making any limiting assumptions about cosmology.

A recent motivation for studying the possibility of light electroweakinos in
this scenario is the surprising result from the CDF measurement of the $W$
boson mass CDF:2022hxs , which gives a value considerably above both the SM
prediction and above existing experimental results. See Ref. Workman:2022ynf
for a review of the SM value and a summary of the experimental status. Light
electroweakinos, in particular light winos and Higgsinos, are known to result
in significant positive corrections to the $W$ mass Heinemeyer:2006px ;
Bagnaschi:2022qhb ; Yang:2022gvz . However, given the current uncertainty
about the interpretation of the new result and its compatibility with other
recent measurements, e.g. Ref. LHCb:2021bjt , we will not use this as a
constraint on our model.

##  2 Model

The model under consideration in this study is a variant of the MSSM where all
supersymmetric states except the electroweakinos and a quasi-massless
gravitino are decoupled. This model, henceforth $\tilde{G}$-EWMSSM, differs
from the model in our previous study EWMSSM  by the addition of the light
gravitino. As discussed in the introduction, a very light gravitino can be
motivated in certain supersymmetry breaking scenarios, e.g. gauge mediation.

The general neutralino can be any linear combination of the neutral gauginos
($\tilde{B}$, $\tilde{W}^{0}$), and the neutral Higgsinos
($\tilde{H}^{0}_{u}$, $\tilde{H}^{0}_{d}$),

$\displaystyle\tilde{\chi}_{i}^{0}=N_{i1}\tilde{B}+N_{i2}\tilde{W}^{0}+N_{i3}\tilde{H}_{d}^{0}+N_{i4}\tilde{H}_{u}^{0},$
(1)

where $N_{ij}$ are the mass eigenvectors indicating the weight of each field
component in the gauge basis,
$(\psi^{0})^{T}=(\tilde{B},\tilde{W}^{0},\tilde{H}^{0}_{d},\tilde{H}^{0}_{u})$.
The corresponding bilinear terms in the Lagrangian density are

$\mathcal{L}_{\text{$\tilde{\chi}^{0}$-mass}}=-\frac{1}{2}(\psi^{0})^{T}M_{N}\psi^{0}+\text{c.c.}$
(2)

where the neutralino mass matrix, $M_{N}$, is given by

$\displaystyle M_{N}$
$\displaystyle=\left(\begin{matrix}M_{1}&0&-\tfrac{1}{2}g^{\prime}vc_{\beta}&\tfrac{1}{2}g^{\prime}vs_{\beta}\\\
0&M_{2}&\tfrac{1}{2}gvc_{\beta}&-\tfrac{1}{2}gvs_{\beta}\\\
-\tfrac{1}{2}g^{\prime}vc_{\beta}&\tfrac{1}{2}gvc_{\beta}&0&-\mu\\\
\tfrac{1}{2}g^{\prime}vs_{\beta}&-\tfrac{1}{2}gvs_{\beta}&-\mu&0\end{matrix}\right),$
(3)

and $M_{1}$, $M_{2}$ and $\mu$ are the gaugino and Higgsino soft-breaking
bilinear couplings, respectively, which are free parameters in our model.
Further, we have $s_{\beta}=\sin\beta$ and $c_{\beta}=\cos\beta$, $g$ and
$g^{\prime}$ are the $SU(2)_{L}$ and $U(1)_{Y}$ gauge couplings, and $v$ is
the electroweak VEV. Amongst these, only the ratio $\tan\beta=v_{u}/v_{d}$ is
not fixed by data and remains an additional free parameter in our model.

The general chargino eigenstates correspond to the charged Higgsinos
($\tilde{H}^{+}_{u}$, $\tilde{H}^{-}_{d}$), and gauginos ($\tilde{W}^{+}$,
$\tilde{W}^{-}$). The corresponding bilinear terms in the Lagrangian density
are

$\mathcal{L}_{\text{$\tilde{\chi}^{\pm}$-mass}}=-\frac{1}{2}(\psi^{\pm})^{T}M_{C}\psi^{\pm}+\text{c.c.}$
(4)

where the chargino mass matrix, $M_{C}$, is given by

$\displaystyle M_{C}$ $\displaystyle=\left(\begin{matrix}0&X^{T}\\\
X&0\end{matrix}\right),\quad\text{with}\quad
X=\left(\begin{matrix}M_{2}&\tfrac{1}{\sqrt{2}}gvs_{\beta}\\\
\tfrac{1}{\sqrt{2}}gvc_{\beta}&\mu\end{matrix}\right).$

Figure 1: Branching ratios for the lightest neutralino as a function of $\mu$,
with $M_{1}=900$ GeV, $M_{2}=400$ GeV, and $\tan\beta=1$ (top) or
$\tan\beta=10$ (bottom). The wino and Higgsino NLSP regions are shown in red
and green, respectively. The pink line (dash dot) shows the combined branching
ratio for decays to all states other than on-shell $(Z,h,\gamma)+\tilde{G}$.
The thin, grey bar marks a parameter region where
$m_{\tilde{\chi}_{1}^{\pm}}<m_{\tilde{\chi}_{1}^{0}}$.

The gravitino mass $m_{3/2}$ depends on the dynamics of the supersymmetry
breaking, but for the purpose of our study we fix it to $m_{3/2}=1$ eV,
similar to what is commonly assumed in ATLAS and CMS searches, see for example
Ref. CMS:2019oou . In terms of the collider phenomenology, this makes the
gravitino effectively massless and ensures prompt decays of the NLSP. We do
not set the mass to exactly zero since the limit $m_{3/2}\to 0$ corresponds to
no supersymmetry breaking. The exact choice for the small gravitino mass has
very little impact on the results as long as $m_{3/2}\neq 0$. The one small
exception is for a wino-like chargino around the $W$ mass or lower, where the
gravitino mass may dictate whether the chargino decays directly to the
gravitino or via the neutralino NLSP. However, scenarios with such light
charginos are in any case heavily constrained, independent of this decay.

Since we do not consider direct production of gravitinos, where the cross
section would be low and the signature difficult to disentangle from
backgrounds, the LHC phenomenology of this model is dominated by the
production and decay of the light electroweakinos. The hierarchy of $M_{1}$,
$M_{2}$ and $\mu$, and to some extent the value of $\tan\beta$, determines
their gaugino and Higgsino components, production cross sections and branching
ratios.

A chargino NLSP will decay promptly to the gravitino and a (possibly off-
shell) $W$ boson. However, having a chargino NLSP is only possible in narrow
regions of parameter space; see Fig. 1 for an example. Throughout most of
parameter space the lightest neutralino is the NLSP. In general, a neutralino
NLSP has three possible decay modes:
$\tilde{\chi}_{1}^{0}\rightarrow\\{\gamma,Z,h\\}\,\tilde{G}$. In the limit,
$m_{3/2}\ll m_{\\{\tilde{\chi},Z,h\\}}$, the decay widths take the form
Feng:2004mt ; Covi:2009bk :

$\displaystyle\Gamma(\tilde{\chi}_{1}^{0}\rightarrow\gamma\tilde{G})$
$\displaystyle=|N_{11}c_{W}+N_{12}s_{W}|^{2}\,\mathcal{R}\,,$ (5)
$\displaystyle\begin{split}\Gamma(\tilde{\chi}_{1}^{0}\rightarrow
Z\tilde{G})&=\left(|-N_{11}s_{W}+N_{12}c_{W}|^{2}\right.\\\ &\hskip
7.11317pt\left.+|-N_{13}c_{\beta}+N_{14}s_{\beta}|^{2}/2\right)\\\ &\hskip
28.45274pt\times\mathcal{C}(m_{Z},m_{\tilde{\chi}_{1}^{0}})\,\mathcal{R},\end{split}$
(6) $\displaystyle\begin{split}\Gamma(\tilde{\chi}_{1}^{0}\rightarrow
h\tilde{G})&=\frac{1}{2}|-N_{13}s_{\alpha}+N_{14}c_{\alpha}|^{2}\\\ &\hskip
28.45274pt\times\mathcal{C}(m_{h},m_{\tilde{\chi}_{1}^{0}})\,\mathcal{R}\,.\end{split}$
(7)

Here $s_{W}$, $c_{W}$, $s_{\alpha}$ and $c_{\alpha}$ are the sines and cosines
of the Weinberg angle $\theta_{W}$ and the mixing angle $\alpha$ between the
$CP$-even neutral Higgs states, and

$\displaystyle\mathcal{R}$ $\displaystyle=\frac{1}{48\pi
M_{P}^{2}}\frac{m_{\tilde{\chi}_{1}^{0}}^{5}}{m_{3/2}^{2}}\,,\hskip
14.22636pt\mathcal{C}(m_{i},m_{\tilde{\chi}_{1}^{0}})$
$\displaystyle=\Bigg{(}1-\frac{m_{i}^{2}}{m_{\tilde{\chi}_{1}^{0}}^{2}}\Bigg{)}^{4}\,.$

In Fig. 1 we show representative branching ratios for the lightest neutralino,
using the full expression for the widths from Refs. Feng:2004mt ; Covi:2009bk
; Hasenkamp:2009zz , including also decay modes through off-shell bosons in
the total width. The plots use values of $\mu$ picked to illustrate the
generic behaviour in the different wino NLSP (red) and Higgsino NLSP (green)
regions (see below for further discussion), and two different values of
$\tan\beta$, which cover the impact of $\tan\beta$ on decays to $Z$ and $h$.
The bino NLSP region (low $M_{1}$ values) is much simpler and not illustrated
since here dominantly $\tilde{\chi}_{1}^{0}\to\gamma\tilde{G}$, with some
small branching ratio to $Z\tilde{G}$. We see that the dominant decay mode of
the lightest neutralino depends strongly on the relative ordering of the
masses $M_{1}$, $M_{2}$, and $\mu$, and the size of $\tan\beta$.

To make our presentation more systematic, we now discuss the properties of
these three major phenomenological regions in terms of the ordering of the
gaugino, $M_{1}$ and $M_{2}$, and Higgsino, $\mu$, masses.

Wino NLSP: With $|M_{2}|<|M_{1}|,|\mu|$, the two lightest electroweakinos,
$\tilde{\chi}_{1}^{\pm}$ and $\tilde{\chi}_{1}^{0}$, are a charged and neutral
wino with relatively large LHC production cross sections. The lightest
neutralino decays as $\tilde{\chi}_{1}^{0}\to\\{Z,\gamma\\}\,\tilde{G}$, see
for example the wino NLSP region (red) of Fig. 1 with $\mu>M_{2}$. For the
lightest chargino, when $m_{\tilde{\chi}_{1}^{\pm}}\gg m_{W}$ the small mass
difference between the wino-like chargino and neutralino leads to decays
directly to the gravitino and an on-shell $W$, $\tilde{\chi}_{1}^{\pm}\to
W^{\pm}\tilde{G}$. For smaller chargino masses we have instead decays to two
fermions (via an off-shell $W$), together with the gravitino or lightest
neutralino $\tilde{\chi}_{1}^{0}$.

Higgsino NLSP: If instead $|\mu|<|M_{1}|,|M_{2}|$, the three lightest
electroweakinos, $\tilde{\chi}_{1}^{0}$, $\tilde{\chi}_{2}^{0}$ and
$\tilde{\chi}_{1}^{\pm}$, are dominantly Higgsino and have somewhat smaller
production cross sections compared to the wino scenario. Pure Higgsinos do not
decay to photons at tree level, so in this case the decays
$\tilde{\chi}_{1}^{0}\to\\{Z,h\\}\,\tilde{G}$ are typically dominant, unless
the NLSP mass is so small that the available phase space becomes limiting, or
even that these decays go off-shell. In this case decays to photons become
important again, especially at low masses, along with three-body final states
with two opposite-sign SM fermions at intermediate masses. The relationship
between the branching ratios to Higgs and $Z$ final states is determined by
the sign of $\mu$ and the value of $\tan\beta$. In particular we note that
taking $\mu<0$ and $\tan\beta\rightarrow 1$ suppresses the $Z\tilde{G}$
channel, due to cancellation between the $N_{13}$ and $N_{14}$ terms in Eq.
(6). This interplay of decays is again illustrated in Fig. 1 in the Higgsino
NLSP region (green) with $|\mu|<M_{2}$. The heavier neutralino and the
chargino typically decay to the lightest neutralino and SM fermions in three-
body decays, instead of the gravitino, due to the generically larger mass
differences between the lightest electroweakinos in the Higgsino scenario
Bomark:2013nya .

Bino NLSP: For $|M_{1}|<|M_{2}|,|\mu|$, the NLSP is a mostly bino
$\tilde{\chi}_{1}^{0}$ and the direct pair production cross section at the LHC
is small. Most of the production is then likely to be from decays of the
heavier, wino- or Higgsino-dominated electroweakinos, depending on the
hierarchy of $M_{2}$ and $\mu$. The bino NLSP decays dominantly as
$\tilde{\chi}_{1}^{0}\to\gamma\tilde{G}$.

The overall pattern that can be deduced from the above discussion is that the
model predicts events with a pair of bosons picked from $\\{h,Z,W,\gamma\\}$,
along with missing energy from the escaping gravitinos, possibly with one or
both bosons being off-shell if the mass of the NLSP is below 125 GeV.
Additional bosons may also be produced from the decays of heavier
electroweakinos into the NLSP. In addition to the classic signature of di-
photons plus missing energy, we see that this model features events with final
state SM fermions from the decays of the massive bosons, meaning that many LHC
searches are relevant for the model.

Apart from the addition of the light gravitino LSP, our implementation of the
$\tilde{G}$-EWMSSM model in GAMBIT is identical to our implementation of the
EWMSSM model described in detail in Ref. EWMSSM . In particular, the Higgs
mass, which in this study only matters for event kinematics, is set by hand to
$125.09\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$.

##  3 Collider likelihoods

The total likelihood function explored in our global fit consists of
likelihoods for LHC searches for new particles, LHC measurements of SM
signatures, and LEP cross-section limits for electroweakino production. We
describe each of these likelihoods below.

###  3.1 LHC searches

The likelihood contribution from LHC searches is based on passing simulated
signal events through our emulations of the 13 TeV ATLAS and CMS searches in
Refs. ATLAS:2021yqv ; ATLAS:2020syg ; ATLAS:2017drc ; ATLAS:2017eoo ;
ATLAS:2021hza ; ATLAS:2020aci ; ATLAS:2019lff ; ATLAS:2017avc ; ATLAS:2018tti
; ATLAS:2021moa ; ATLAS:2021yyr ; ATLAS:2019fag ; ATLAS:2021ijy ;
ATLAS:2018nud ; ATLAS:2018vzq ; CMS:2019zmd ; CMS:2017kyj ; CMS:2017gbz ;
CMS:2017jrd ; CMS:2018kag ; CMS:2020bfa ; CMS:2018xqw ; CMS:2020cpy ;
CMS:2021cox-fix ; CMS:2017brl ; CMS:2019vzo ; CMS:2018fon . Reproducing a
collider search to sufficient accuracy can be challenging, e.g. due to limited
available information about technical details of the analysis, or due to
limitations in the tool-chain used for fast event simulation. In some cases we
can therefore only incorporate a subset of the signal regions defined by the
search. In Appendix B we provide a short description of each search, and point
out which signal regions our signal simulation includes.

For all the included LHC searches we have the background uncertainty for each
signal region, but in many cases there is no public information on how these
uncertainties are correlated. We then take a conservative approach and, for
each search, construct a likelihood function that only uses the signal region
$i$ with the best expected sensitivity for the given $\tilde{G}$-EWMSSM
parameter point. Our likelihood function for each of these searches is then
constructed from a simple product of a Poisson and a Gaussian factor,

$\displaystyle\begin{split}\mathcal{L}_{\text{search}}^{\text{1SR}}(s_{i},\gamma_{i})=&\left[\frac{(s_{i}+b_{i}+\gamma_{i})^{n_{i}}\,e^{-(s_{i}+b_{i}+\gamma_{i})}}{n_{i}!}\right]\\\
&\times\frac{1}{\sqrt{2\pi}\sigma_{i}}e^{-\frac{\gamma_{i}^{2}}{2\sigma_{i}^{2}}}\,,\end{split}$
(8)

where $s_{i}$, $b_{i}$ and $n_{i}$ are, respectively, the expected signal
yield, expected background yield and observed yield for the given signal
region $i$. The Gaussian factor with the nuisance parameter $\gamma_{i}$ is
introduced to account for the uncertainty in the total predicted yield, and we
therefore set the width $\sigma_{i}$ by adding in quadrature the uncertainties
of $s_{i}$ and $b_{i}$. For our parameter scans we need a likelihood function
that only depends on the predicted signal yield. Thus, for each sampled
$\tilde{G}$-EWMSSM parameter point we profile
$\mathcal{L}_{\text{search}}^{\text{1SR}}(s_{i},\gamma_{i})$ over the nuisance
parameter $\gamma_{i}$:

$\displaystyle\mathcal{L}_{\text{search}}^{\text{1SR}}(s_{i})\equiv\mathcal{L}_{\text{search}}^{\text{1SR}}(s_{i},\hat{\hat{\gamma_{i}}}),$
(9)

where $\hat{\hat{\gamma_{i}}}$ is the $\gamma_{i}$ value that maximises
$\mathcal{L}_{\text{search}}^{\text{1SR}}(s_{i},\gamma_{i})$ for a given
$s_{i}$.

CMS have for a number of their searches published covariance matrices for the
background uncertainties, following the simplified likelihood approach
Collaboration:2242860 ; Buckley:2018vdr . For these searches we can generalise
Eq. (8) to a likelihood that utilises the information in all signal regions. A
search with $n_{\text{SR}}$ signal regions is then described by the likelihood
function

$\displaystyle\begin{split}\mathcal{L}_{\text{search}}(\bm{s},\bm{\gamma})=&\prod_{i=1}^{n_{\text{SR}}}\left[\frac{(s_{i}+b_{i}+\gamma_{i})^{n_{i}}\,e^{-(s_{i}+b_{i}+\gamma_{i})}}{n_{i}!}\right]\\\
&\hphantom{\int}\times\frac{1}{\sqrt{\det
2\pi\Sigma}}e^{-\frac{1}{2}\bm{\gamma}^{T}\bm{\Sigma^{-1}}\bm{\gamma}}\,.\end{split}$
(10)

Here $\bm{\Sigma}$ is the $n_{\text{SR}}\times n_{\text{SR}}$ covariance
matrix for the nuisance parameters $\gamma_{i}$. We construct $\bm{\Sigma}$ by
taking the covariance matrix provided by CMS and adding in quadrature our
signal yield uncertainties along the diagonal. To obtain a likelihood that
only depends on the set of signal yields $\bm{s}$ we, for each
$\tilde{G}$-EWMSSM point, profile
$\mathcal{L}_{\text{search}}(\bm{s},\bm{\gamma})$ over the set of
$n_{\text{SR}}$ nuisance parameters,

$\displaystyle\mathcal{L}_{\text{search}}(\bm{s})\equiv\mathcal{L}_{\text{search}}(\bm{s},\hat{\hat{\bm{\gamma}}}).$
(11)

We also note that for the searches in Refs. ATLAS:2020syg ; ATLAS:2019lff ;
ATLAS:2021moa ; ATLAS:2021yyr ; ATLAS:2019fag  ATLAS have published the
information required to fully utilise all signal regions, through the full
likelihood framework ATLAS:2019oik . We will make use of these likelihoods in
future GAMBIT studies.

The LHC experiments often present results for multiple categories of final
states in a single publication, e.g. the CMS multilepton search for charginos
and neutralinos in Ref. CMS:2021cox-fix , which presents results for searches
in 2-lepton, 3-lepton and 4-lepton final states. In these cases we follow the
same approach as in EWMSSM  and treat the results for the different final
states as approximately independent searches, meaning that for each final
state category we include a separate likelihood contribution of the form given
in Eqs. (9) or (11).111A new method for identifying non-overlapping
combinations of signal regions from large collections of LHC searches was
recently presented in Ref. Araz:2022vtr . We plan to implement this method in
GAMBIT and use it in future studies.

Similar to the approach in Refs. EWMSSM ; DMEFT ; Chang:2022jgo , we normalise
the likelihood function for each LHC search with the corresponding background-
only ($\bm{s}=\bm{0}$) likelihood. The log-likelihood contribution from each
search therefore takes the form of a log-likelihood difference

$\displaystyle\Delta\ln\mathcal{L}_{\text{search}}(\bm{s})=\ln\mathcal{L}_{\text{search}}(\bm{s})-\ln\mathcal{L}_{\text{search}}(\bm{s}=\bm{0}).$
(12)

Treating the searches as independent, what we consider as the combined log-
likelihood from all the LHC searches is

$\displaystyle\Delta\ln\mathcal{L}_{\text{searches}}(\bm{s})=\sum_{j}\Delta\ln\mathcal{L}_{j}(\bm{s}),$
(13)

where $\Delta\ln\mathcal{L}_{j}$ is the log-likelihood contribution from
search $j$. A positive value for the
$\Delta\ln\mathcal{L}_{\text{searches}}(\bm{s})$ indicates that the combined
set of $\tilde{G}$-EWMSSM signal predictions $\bm{s}(\bm{\theta})$ for
parameter point $\bm{\theta}$ gives an overall better agreement with current
LHC search results than the background-only assumption does. This happens when
the predicted $\tilde{G}$-EWMSSM signals can help accommodate data excesses in
some searches, without conflicting strongly with the results of the other
searches.

We will present the result of our global fit as profile likelihood maps in
different $\tilde{G}$-EWMSSM mass planes. For each plane we show the $1\sigma$
(68.3%) and $2\sigma$ (95.4%) confidence regions, derived using the likelihood
ratio $\mathcal{L}(\bm{\theta})/\mathcal{L}(\bm{\theta}_{\text{best-fit}})$,
where $\bm{\theta}_{\text{best-fit}}$ is the highest-likelihood
$\tilde{G}$-EWMSSM parameter point. Therefore, if the best-fit point can
explain some excesses in the search data
($\Delta\ln\mathcal{L}_{\text{searches}}(\bm{s})>0$), the $\tilde{G}$-EWMSSM
parameter regions outside the $2\sigma$ contour should not be considered
“excluded” in the same sense as for an exclusion limit from an LHC search.
Rather, these parameter regions simply provide a significantly worse fit to
the combined data compared to that of the best-fit point. It is then
interesting to also ask a different question: What $\tilde{G}$-EWMSSM
parameter regions are excluded by the combination of LHC searches, when judged
relative to the background-only expectation? A simple way to estimate this is
to replace $\Delta\ln\mathcal{L}_{\text{searches}}(\bm{s})$ in Eq. (13) with

$\displaystyle\begin{split}\Delta&\ln\mathcal{L}_{\text{searches}}^{\text{cap}}(\bm{s})\\\
&=\min\left[\Delta\ln\mathcal{L}_{\text{searches}}(\bm{s}),\Delta\ln\mathcal{L}_{\text{searches}}(\bm{s}=\bm{0})\right]\\\
&=\min\left[\Delta\ln\mathcal{L}_{\text{searches}}(\bm{s}),0\right].\end{split}$
(14)

This log-likelihood penalises $\tilde{G}$-EWMSSM parameter points that give a
joint prediction in worse agreement with data than the background-only
prediction, while all other points are assigned the same log-likelihood of 0.
We note that the maximum value
$\Delta\ln\mathcal{L}_{\text{searches}}^{\text{cap}}(\bm{s})=0$ can be
obtained in two different ways: The first case is when none of the included
searches are sensitive to the given $\tilde{G}$-EWMSSM parameter point, i.e.
the limit $\bm{s}\rightarrow\bm{0}$. This is typically what happens for high-
mass scenarios, due to small production cross-sections. The second case is
when a $\tilde{G}$-EWMSSM scenario fits the results from some LHC searches
sufficiently better than the SM does, enough to offset any likelihood penalty
from tensions with other LHC analyses. In Sec. 5 we will present results both
for the “full likelihood” ($\mathcal{L}_{\text{searches}}$) case and the
“capped likelihood” ($\mathcal{L}_{\text{searches}}^{\text{cap}}$) case. This
is the same approach as was taken in Refs. EWMSSM ; DMEFT ; Chang:2022jgo .

###  3.2 LHC measurements of SM signatures

The complexity of the phenomenology of the model means that the possibility
that it may produce events which could contribute to well-measured SM-like
final states must also be taken into account. This is the scenario for which
Contur Butterworth:2016sqg ; Buckley:2021neu  is designed. Via Rivet
Bierlich:2019rhm , Contur has access to an extensive library of measurements
from the LHC experiments, mostly corrected for detector effects and thus not
requiring explicit detector simulation. Simulated events are passed through
Rivet and projected into the fiducial phase space of the measured cross
sections. In the release of GAMBIT accompanying this paper, we have interfaced
Contur and Rivet to the GAMBIT ColliderBit module.

As binned unfolding of detector effects requires statistically stable bin
populations, a $\chi^{2}$ test has proven indistinguishable from Poisson log-
likelihood differences for measurement interpretations. The $\chi^{2}$ is
evaluated and used as the log-likelihood difference between the “signal-
injection” hypothesis and the SM null hypothesis, in this application assuming
the data to be equal to the SM:

$\displaystyle\begin{split}\ln\mathcal{L}_{\text{meas}}(\bm{s})&=-\chi^{2}(\bm{s})/2\\\
&\equiv-\sum_{i\,\in\,\text{active
bins}}\left[\frac{y_{i}^{\text{s+b}}(\bm{s})-y_{i}^{\text{obs}}}{(\Delta
y_{i})}\right]^{2}\Big{/}2\,,\end{split}$ (15)

with the log-likelihood difference then evaluated as
$\Delta\ln\mathcal{L}_{\text{meas}}(\bm{s})=\ln\mathcal{L}_{\text{meas}}(\bm{s})-\ln\mathcal{L}_{\text{meas}}(\bm{s}=0)$.
The set of active bins is conservatively selected to avoid acceptance
overlaps, as described in Sec. 4.1, and $y_{i}$ and $\Delta{y_{i}}$ are the
bin values and uncertainties respectively. The experimental uncertainties are
taken into account in the $\chi^{2}$ construction, but are treated as
uncorrelated in the version of Contur (2.3.0) used here.

The set of 13 TeV analyses used by Contur in this analysis are those described
in Refs. CMS:2016oae ; ATLAS:2017xqp ; CMS:2018htd ; ATLAS:2016zkp ;
ATLAS:2017txd ; ATLAS:2018sos ; ATLAS:2019hau ; ATLAS:2021kog ; ATLAS:2016zba
; CMS:2018dxg ; ATLAS:2019rqw ; CMS:2021hnp ; ATLAS:2017cez ; CMS:2018vzn ;
ATLAS:2018orx ; ATLAS:2019ebv ; CMS:2018mdf ; ATLAS:2019kwg ; ATLAS:2017sag ;
CMS:2019raw ; ATLAS:2019zci ; ATLAS:2018acq ; ATLAS:2020juj ; ATLAS:2020nzk ;
ATLAS:2017zda ; ATLAS:2019qet ; ATLAS:2019cbr ; CMS:2018tdx ; ATLAS:2021jgw ;
CMS:2021lxi ; ATLAS:2019hxz ; ATLAS:2019rob ; ATLAS:2018fwl ; CMS:2018mdl ;
LHCb:2018usb ; ATLAS:2020ccu ; ATLAS:2021mbt ; ATLAS:2020vup ; CMS:2016jip ;
CMS:2019fak ; ATLAS:2017bcd ; CMS:2020mxy ; CMS:2019jjp ; CMS:2019eih ;
ATLAS:2017ble ; ATLAS:2020bbn ; ATLAS:2019gey ; ATLAS:2018nci . These cover
final states with (multiple) jets, isolated photons and leptons, as well as
missing energy. When discussing our results in Sec. 5 we will highlight the
analyses with the greatest impact.

###  3.3 Cross-section limits from LEP searches

In addition to the above LHC searches and measurements that are implemented at
the event level, we include LEP searches and measurements that were published
as upper limits on particular electroweakino production cross-sections. See
ColliderBit ; EWMSSM  for general details of our treatment of LEP searches.
First, there are searches for electroweakinos that we applied in EWMSSM  that
we re-interpret as searches for gravitinos. Specifically, we consider searches
for pair production of charginos that each decay into SM particles and a
stable neutralino, $\tilde{\chi}^{\pm}\to\text{SM}+\chi$. In our gravitino
model, the chargino may decay into SM particles and a gravitino,
$\tilde{\chi}^{\pm}\to\text{SM}+\tilde{G}$. This leads to an identical
signature as both the gravitino and a stable neutralino only contribute to
missing energy.

Second, we include a multi-photon and missing energy search by L3 at
$\sqrt{s}=207\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ L3:2003yon . In our
model, neutralinos can be pair produced at LEP and can each decay to a photon
and a gravitino, giving a signature of missing energy and two photons. The
number of observed events in the search was less than expected from SM
backgrounds, leading to strong constraints on the
$e^{+}e^{-}\to\tilde{\chi}^{0}_{1}\tilde{\chi}^{0}_{1}\to\tilde{G}\tilde{G}\gamma\gamma$
cross section as a function of the gravitino and neutralino masses for masses
less than about $\sqrt{s}/2$. We apply the $95\%$ limits shown in Fig. 6c of
L3:2003yon  following the treatment described in ColliderBit . The impact of
this constraint on our $\tilde{G}$-EWMSSM model is limited, however, as our
assumption of decoupled selectrons typically leads to a very small
$e^{+}e^{-}\to\tilde{\chi}^{0}_{1}\tilde{\chi}^{0}_{1}$ production cross-
section.

##  4 Global fit setup

###  4.1 Software framework and event generation

We perform our study of the $\tilde{G}$-EWMSSM with the GAMBIT 2.4 global fit
framework gambit ; GUM , utilising the SpecBit, DecayBit, ColliderBit and
ScannerBit modules SDPBit ; ColliderBit ; ScannerBit . To compute the chargino
and neutralino mass spectrum at one-loop level, SpecBit employs a FlexibleSUSY
Athron:2014yba ; Athron:2017fvs  spectrum generator which uses SARAH
Staub:2008uz ; Staub:2010jh  and routines from SOFTSUSY Allanach:2001kg ;
Allanach:2013kza . A more detailed discussion of this spectrum computation is
given in EWMSSM .

For this study we have extended DecayBit with the capability to compute decay
widths for a neutralino or chargino decaying to final states with a gravitino.
The implementation is based on analytical expressions given in Refs.
Feng:2004mt ; Covi:2009bk ; Hasenkamp:2009zz . To compute neutralino and
chargino decays into final states with a lighter neutralino or chargino,
DecayBit uses SUSY-HIT 1.5 Djouadi:2006bz , which includes the packages SDECAY
Muhlleitner:2003vg  and HDECAY Djouadi:1997yw .

We simulate LHC events with electroweakino production at
$\sqrt{s}=13\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$ using ColliderBit’s
parallelised interface to Pythia 8 Sjostrand:2006za ; Sjostrand:2014zea  and
native fast detector simulator BuckFast ColliderBit .222To avoid the
additional computational cost of simulating light electroweakino production
through decays of SM bosons, we do not consider parameter points with
electroweakino masses below $62.5\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$.
Due to the cost of computing higher-order production cross-sections, we use
the cross-sections computed by Pythia 8 at leading-order plus leading-
logarithmic (LO+LL) accuracy. As we will see in Sec. 5, the lowest-mass
scenarios not disfavoured by current results are scenarios where the lightest
electroweakinos are Higgsinos with masses around
$200\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$. For such scenarios the
production cross-sections at next-to-leading order with next-to-leading-
logarithmic corrections (NLO+NLL) can be up to 30% higher compared the LO+LL
cross-sections Fiaschi:2018hgm , so this choice is somewhat conservative.

For each parameter point included in our final scan results we generate 16
million LHC events to evaluate the impact of the LHC searches. The main reason
that such a high number of events is needed is that for many of the searches
we do not have the information needed to allow a proper statistical
combination of all the signal regions in the search. As discussed in Sec. 3.1,
for these searches the conservative approach is, for each sampled parameter
point, to identify the signal region with the best expected sensitivity, and
only use this signal region when computing the likelihood contribution from
the given search. Many searches will for large parts of the $\tilde{G}$-EWMSSM
parameter space have several signal regions with low and near identical
expected sensitivities. Thus, the signal region choice, and through it the
likelihood value, becomes highly sensitive to Monte Carlo noise.333The
computational cost of overcoming this problem, also discussed in Refs. EWMSSM
; Cranmer:2021urp , is currently a major limiting factor for the proper
utilisation of LHC results through full MC simulations in BSM global fits. The
severity of the problem is reduced with every new LHC search that is published
with enough information to enable a statistical combination of the different
signal regions, e.g. through the simplified likelihood Collaboration:2242860 ;
Buckley:2018vdr  or full likelihood ATLAS:2019oik  approaches.

As a post-processing step, we generate a further $100\,000$ events at each
sampled parameter point, which are then passed to first Rivet and then Contur
using the new ColliderBit interface. This enables evaluation of whether the
parameter point in question would have led to significant but unnoticed
collective deviations from the SM expectation in existing measurements. Since
LHC measurements have much higher acceptances than LHC searches, we here need
fewer simulated events to ensure sufficiently small Monte Carlo uncertainties
and a stable identification of the most sensitive measurements. Contur tests
the full set of measurements for each parameter point, evaluating the expected
likelihood ratio for each measurement. As is usual with Contur, to account for
statistical correlations between measurements and avoid double-counting of BSM
effects, these measurements are divided into non-overlapping “analysis pools”
based upon the run period, experiment and final state. Only the most sensitive
measurement from each pool is used, and the set of pool-likelihoods is then
combined to provide an overall Contur likelihood, which in ColliderBit is then
combined with the likelihoods for the LHC searches and the LEP cross-section
limits. The likelihood provided by Contur in this post-processing step had a
significant impact on the final results, which will be discussed in detail in
Section 5.4.

###  4.2 Scanning strategy

With the gravitino mass fixed at $1\,\text{e}\mspace{-0.8mu}\text{V}$, the
collider phenomenology of our model is determined by the mass parameters
$M_{1}$, $M_{2}$ and $\mu$, and the dimensionless $\tan\beta$ parameter. We
restrict our attention to scenarios where the electroweakino masses are all
$\lesssim 1\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$. This is due to the
substantial computational cost of accurately mapping out the profile
likelihood function across wide, many-dimensional parameter regions where the
likelihood function is mostly flat — especially when MC event simulation is
performed for each scan point. The high detectability of final states with
photons and missing energy ensures that current LHC searches can exclude
specific scenarios of electroweakino production where the masses of the
produced electroweakinos are close to or beyond
$1\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$. These are typically scenarios
with production of a dominantly wino chargino-neutralino pair and a large
$\mathrm{BR}(\tilde{\chi}_{1}^{0}\rightarrow\gamma\tilde{G})$ CMS:2017brl ;
ATLAS:2018nud . But as we will see, within the general electroweakino
parameter space explored here, there are still large, unconstrained parameter
regions with all electroweakinos $\lesssim
1\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$.

Parameter | Range/value | Sampling priors
---|---|---
$M_{1}(Q)$ | $[-1,1]\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$ | hybrid, flat
$M_{2}(Q)$ | $[0,1]\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$ | hybrid, flat
$\mu(Q)$ | $[-1,1]\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$ | hybrid, flat
$\tan\beta(m_{Z})$ | $[1,70]$ | log, flat
$m_{3/2}$ | $1\,\text{e}\mspace{-0.8mu}\text{V}$ | fixed
$Q$ | $3\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$ | fixed
$\alpha_{s}^{\overline{\text{MS}}}(m_{Z})$ | $0.1181$ | fixed
Top quark pole mass | $171.06\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ | fixed
Higgs mass | $125.09\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ | fixed
Table 1:  Ranges and scanning priors for the input parameters. The “hybrid”
prior refers to a prior that is flat on
$|x|<10\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$, and logarithmic
elsewhere.

In Tab. 1 we summarise our choices for the scan input parameters. The MSSM
parametrisation we use is implemented in the GAMBIT MSSM model hierarchy as
MSSM11atQ_mA_mG (Appendix C), which has 11 free parameters. For the six
parameters not listed in Tab. 1 we use the following fixed values: the
trilinear couplings $A_{d_{3}}=A_{e_{3}}=A_{u_{3}}=0$; the gluino mass
parameter $M_{3}=5\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$; the pseudo-
scalar Higgs mass $m_{A}=5\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$; and
the squared soft sfermion mass parameters
$m_{l}^{2}=m_{q}^{2}=(3\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$})^{2}$. The
parameters are defined at an input scale
$Q=3\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$. The specific values for
these fixed parameters are not important, as they simply ensure that all
superpartners except the gravitino and the electroweakinos are decoupled from
the collider phenomenology.

In order to obtain accurate profile likelihood maps we must ensure that the
parameter space is explored in sufficient detail. We therefore combine the
parameter samples from multiple scans using different combinations of the
priors (metrics) listed in Tab. 1 to scan the parameters. The “hybrid” prior
in Tab. 1 combines a logarithmic prior for
$|x|>10\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ with a flat prior for
$|x|<10\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ ($x=M_{1},M_{2},\mu$). As
the physics is invariant under a global sign change for $M_{1}$, $M_{2}$ and
$\mu$, we follow the common approach in the literature of restricting $M_{2}$
to positive values. All scans are performed with the differential evolution
sampler Diver 1.0.4 ScannerBit , interfaced via ScannerBit. We run Diver in
the jDE mode (self-adaptive rand/1/bin evolution), which is based on Ref.
Brest06 . The final combined data set consists of around $3.1\times 10^{5}$
parameter samples.

##  5 Results

###  5.1 Best-fit scenarios

In Fig. 2 we show our fit result in terms of the profile likelihood function
across the $(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ and
$(m_{\tilde{\chi}_{1}^{\pm}},m_{\tilde{\chi}_{1}^{0}})$ planes. We will
present most of our results in one or both of these planes as they are well
suited for mapping out the key phenomenological aspects of the high-likelihood
scenarios. For reference, in Appendix A we provide profile likelihood maps in
terms of the input parameters.

We find that the $\tilde{G}$-EWMSSM scenarios in best agreement with current
LHC searches and measurements are scenarios where the lightest electroweakinos
are dominantly Higgsino, i.e. scenarios with $|\mu|<|M_{1}|,M_{2}$,
corresponding to the Higgsino NLSP region (green) in Fig. 1. As the $\mu$
parameter largely controls the mass of three Higgsino states, these scenarios
have near-degenerate masses for $\tilde{\chi}_{1}^{0}$, $\tilde{\chi}_{2}^{0}$
and $\tilde{\chi}_{1}^{\pm}$, explaining why the best-fit region falls along
the diagonals of the $(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ and
$(m_{\tilde{\chi}_{1}^{\pm}},m_{\tilde{\chi}_{1}^{0}})$ planes.

For the best-fit point, marked by a white star in Fig. 2, the three Higgsinos
have masses $m_{\tilde{\chi}_{1}^{0}}=169.9$ GeV,
$m_{\tilde{\chi}_{2}^{0}}=178.9$ GeV and $m_{\tilde{\chi}_{1}^{\pm}}=177.2$
GeV. This point further has a pair of wino-dominated $\tilde{\chi}_{3}^{0}$
and $\tilde{\chi}_{2}^{\pm}$ at $m_{\tilde{\chi}_{3}^{0}}=740.8$ GeV and
$m_{\tilde{\chi}_{2}^{\pm}}=741.3$ GeV, and a dominantly bino
$\tilde{\chi}_{4}^{0}$ at $m_{\tilde{\chi}_{4}^{0}}=788.1$ GeV. The scenarios
allowed at $2\sigma$ confidence level (CL) relative to the best-fit point, all
predict such a trio of near-degenerate Higgsinos with masses no less than
about $140$ GeV and no greater than about $500$ GeV.

Figure 2: Profile likelihood in the
$(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ plane (left) and in the
$(m_{\tilde{\chi}_{1}^{\pm}},m_{\tilde{\chi}_{1}^{0}})$ plane (right). The
contour lines show the $1\sigma$ and $2\sigma$ confidence regions. The best-
fit point is marked by the white star.

The scenarios within the $2\sigma$ region in Fig. 2 are largely scenarios with
negative $\mu$ parameter, $|\mu|<M_{2},|M_{1}|$, and $\tan\beta\lesssim 5$,
with the highest-likelihood solutions favouring $\tan\beta$ values close to 1.
For such scenarios, the dominant and subdominant decay modes for the lightest
neutralino are the $\tilde{\chi}_{1}^{0}\to h\tilde{G}$ and
$\tilde{\chi}_{1}^{0}\to Z\tilde{G}$ channels, respectively — see e.g. the
region around $\mu\sim-300\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ in the
branching ratio plots in Fig. 1. Low branching ratios for decays to
$\gamma\tilde{G}$ final states ensure that the scenarios in the $2\sigma$
region escape the otherwise highly constraining photons +
$E_{T}^{\textrm{miss}}$ searches. Many of these scenarios also have sizeable
branching ratios for $\tilde{\chi}_{2}^{0}$ to decay directly to a $\tilde{G}$
final state, typically through the $\tilde{\chi}_{2}^{0}\to Z\tilde{G}$ decay
mode, rather than decaying exclusively through $\tilde{\chi}_{2}^{0}\to
Z^{*}\tilde{\chi}_{1}^{0}$, as often assumed in LHC searches for Higgsino
production. Similarly, many scenarios in the higher-mass part of the $2\sigma$
region ($m_{\tilde{\chi}_{1}^{\pm}}\gtrsim
300\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$) have large branching ratios
for direct decays of $\tilde{\chi}_{1}^{\pm}$ to the gravitino, through
$\tilde{\chi}_{1}^{\pm}\to W^{\pm}\tilde{G}$.

By tuning the branching ratios $\text{BR}(\tilde{\chi}_{1,2}^{0}\to
h\tilde{G})$ versus $\text{BR}(\tilde{\chi}_{1,2}^{0}\to Z\tilde{G})$, and
$\text{BR}(\tilde{\chi}_{1}^{\pm}\to W^{\pm}\tilde{G})$ versus
$\text{BR}(\tilde{\chi}_{1}^{\pm}\to ff^{\prime}\tilde{\chi}_{1}^{0})$,444Here
$f$ and $f^{\prime}$ are SM fermions. the model can partly fit small excesses
in the ATLAS and CMS leptons + $E_{T}^{\textrm{miss}}$ searches and the ATLAS
$b$-jets + $E_{T}^{\textrm{miss}}$ search. (The preference for a small signal
contribution in $b$-jet final states in part explains the preference for
$\tan\beta\sim 1$, since this increases the branching ratio for
$\tilde{\chi}_{1}^{0}\rightarrow h\tilde{G}$, see Sec. 2.) In combination,
this produces a weak preference for the lower-mass end of the diagonal in Fig.
2, at masses around $170\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$.555At the
best-fit point, the three dominant contributions to the likelihood come from
i) a signal region requiring $\geq 3$ $b$-jets, no leptons,
$m_{\text{eff}}>860\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ and
$E_{T}^{\text{miss}}\in(150,200)\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$
ATLAS:2018tti ; ii) a signal region requiring 3 leptons, no opposite-sign,
same-flavour lepton pairs and
$E_{T}^{\text{miss}}>50\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$
ATLAS:2021yyr ; and iii) a signal region requiring $\geq 5$ leptons
CMS:2021cox-fix . Due to the many different final state combinations of
leptons and $b$-jets that can arise in the decays of 2–4 on-shell and off-
shell $h$, $Z$ and $W^{\pm}$ bosons, the best-fit parameter point
simultaneously predicts small signal contributions in all of these three
signal regions.

We found a preference for low-mass electroweakino scenarios also in our EWMSSM
fit in EWMSSM . The EWMSSM parameter regions favoured in that study allow for
electroweakino decay chains that produce multiple on-shell $Z$, $h$ and $W$
bosons, and terminate in a bino-dominated $\tilde{\chi}_{1}^{0}$ that provides
the missing energy signal. The favoured low-mass scenarios in the
$\tilde{G}$-EWMSSM predict a similar collider phenomenology, but now with the
gravitino rather than a bino-like neutralino terminating the decay chains.
However, in the present study the preference for these low-mass scenarios is
weaker, as the previously-observed data excesses are less pronounced in the
now larger ATLAS and CMS data sets.

###  5.2 Non-excluded scenarios

Figure 3: Capped profile likelihood in the
$(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ plane (left) and in the
$(m_{\tilde{\chi}_{1}^{\pm}},m_{\tilde{\chi}_{1}^{0}})$ plane (right). The
white contour lines show the $1\sigma$ and $2\sigma$ confidence regions.

Assuming that these small data excesses are just background fluctuations
rather than a true BSM signal, it is interesting to consider what
electroweakino mass combinations the current combined data clearly exclude in
the $\tilde{G}$-EWMSSM. We investigate this in Fig. 3 by showing profile
likelihood plots where we use the capped likelihood,
$\mathcal{L}_{\text{searches}}^{\text{cap}}$ (Eq. 14), as described in Sec.
3.1.

Figure 4: The Higgsino (left), wino (middle) and bino (right) fraction of the
$\tilde{\chi}_{1}^{0}$, plotted across the profile-likelihood surface for the
$(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ plane.

To understand the structures visible in Fig. 3, we first consider Fig. 4,
where we show the Higgsino, wino and bino components of the lightest
neutralino for the highest-likelihood point in each bin across the
$(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ plane. This allows us to
identify which of the three NLSP scenarios discussed in Sec. 2 are preferred
in different parts of the mass plane. We see clearly that the preferred
scenarios along the diagonal are scenarios with a mostly Higgsino NLSP (left
panel), as discussed above. Moving away from the diagonal, towards higher
$m_{\tilde{\chi}_{2}^{0}}$, the best-fitting scenarios are wino NLSP scenarios
(middle panel). We note that around
$m_{\tilde{\chi}_{1}^{0}},m_{\tilde{\chi}_{2}^{0}}\sim 400$ GeV, the current
collider data prefers a fairly even wino/Higgsino admixture for the
$\tilde{\chi}_{1}^{0}$. Finally, at even higher
$\tilde{\chi}_{2}^{0}$–$\tilde{\chi}_{1}^{0}$ mass splittings, the best
possible fits are obtained for bino NLSP scenarios (right panel).666For
$m_{\tilde{\chi}_{2}^{0}}\approx m_{\tilde{\chi}_{1}^{0}}\approx 1$ TeV in
Fig. 4, all neutralino components contribute significantly to the composition
of $\tilde{\chi}_{1}^{0}$. This is largely a consequence of our scan settings:
Since we restrict our study to the parameter space that has all electroweakino
masses below $1\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$, having the
lightest neutralino mass close to
$1\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$ will correspond to parameter
points with $|M_{1}|\sim M_{2}\sim|\mu|\sim
1\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$.

We will in the following use the term profile-likelihood surface to refer to
the set of parameter samples that appear in figures like Fig. 4, where for
each bin in the given plane we visualise some property of the highest-
likelihood parameter sample belonging to that bin. For the interpretation of
these figures it is important to remember that apparent discontinuities, such
as the boundaries between the yellow and black regions in Fig. 4, typically
result from the projection done by the profile likelihood procedure: two
neighbouring bins in a mass plane can have their respective highest-likelihood
points coming from very different parts of the four-dimensional
$\tilde{G}$-EWMSSM parameter space. So for instance the black region in the
right-hand panel of Fig. 4 does not imply that there are no parameter samples
that predict the given $\tilde{\chi}_{1}^{0}$ and $\tilde{\chi}_{2}^{0}$
masses and a bino-dominated $\tilde{\chi}_{1}^{0}$, only that there for these
mass predictions exist other parameter points that give a better fit to data
and for which the $\tilde{\chi}_{1}^{0}$ is dominantly wino or Higgsino.

We can now go back and reconsider Fig. 3. Along the diagonals of the two mass
planes, we see the allowed scenarios with Higgsino-dominated
$\tilde{\chi}_{1}^{0}$, $\tilde{\chi}_{2}^{0}$ and $\tilde{\chi}_{1}^{\pm}$.
This region extends all the way up towards the edge of our scan range,
corresponding to masses around $1\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$.
In addition, there are three other non-excluded scenarios visible.

First, in the $(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ plane, we
find an allowed horizontal region at around $m_{\tilde{\chi}_{1}^{0}}\approx
450\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$, with wino-dominated and mass
degenerate $\tilde{\chi}_{1}^{0}$ and $\tilde{\chi}_{1}^{\pm}$. Second, in the
region of $m_{\tilde{\chi}_{1}^{0}}\lesssim
450\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ and
$m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{\pm}}\gtrsim
800\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$, we see solutions with a
lonely, light, bino-dominated $\tilde{\chi}_{1}^{0}$. Lastly, in the
$(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ plane around
$m_{\tilde{\chi}_{1}^{0}}>700\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ and
away from the diagonal, we see a region of solutions allowed at $2\sigma$,
where again the $\tilde{\chi}_{1}^{0}$ and $\tilde{\chi}_{1}^{\pm}$ are mostly
wino, though with non-negligible Higgsino components.

Before we explore these findings further, let us briefly compare them with the
capped-likelihood results from our analysis of the EWMSSM EWMSSM . In EWMSSM
we found that essentially no combinations of $\tilde{\chi}_{1}^{\pm}$ and
$\tilde{\chi}_{1}^{0}$ masses could be conclusively ruled out by the
combination of LHC search results at the time of that study. The conclusion is
markedly different in the present $\tilde{G}$-EWMSSM study, where only four
distinct scenarios for electroweakinos below
$1\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$ remain viable. There are
several factors contributing to this result: (1) the overall stronger
constraining power due to the now larger LHC data sets; (2) the diminishing of
the data excesses that in EWMSSM  helped improve the fit for low-mass
solutions in the EWMSSM; (3) the additional constraining power in the present
study, coming from our inclusion of LHC measurements in addition to direct BSM
searches; and (4) the distinctive $\tilde{G}$-EWMSSM collider signatures, in
particular the photon signatures, that result in strong constraints on large
parts of the $\tilde{G}$-EWMSSM parameter space.

###  5.3 Impact of different searches

Figure 5:  The total log-likelihood plotted across the profile-likelihood
surface in the $(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ plane
(left) and in the $(m_{\tilde{\chi}_{1}^{\pm}},m_{\tilde{\chi}_{1}^{0}})$
plane (right).

Figure 6:  Log-likelihood contribution from various groups of LHC searches
across the profile-likelihood surface for the
$(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ plane.

Figure 7: Total LHC production cross-section for electroweakinos, and selected
branching ratios for the decays of $\tilde{\chi}_{1}^{0}$ and
$\tilde{\chi}_{1}^{\pm}$, plotted across the profile-likelihood surface for
the $(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ plane.

To understand our results in greater detail, we will in the following discuss
the contributions from the LHC searches and measurements that most strongly
influence the fit result. To aid this discussion we consider Figs. 5, 6 and 7:
In Fig. 5 we show the total log-likelihood difference
$\ln\mathcal{L}(\bm{s})-\ln\mathcal{L}(\bm{s}=\bm{0})$. The various solutions
in Figs. 2 and 3 are visible as regions of greater likelihood. In Fig. 6 we
consider the profile likelihood surface for the
$(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ plane and break the
total log-likelihood down into contributions from photon searches, lepton
searches, other searches and measurements of SM-like final states. Finally, in
the six panels of Fig. 7 we show the total electroweakino LHC production
cross-section and a selection of relevant branching ratios across the
$(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ profile likelihood
surface.

The top-left panel of Fig. 6 shows that for the scenarios with a bino NLSP
(see Fig. 4, right), the most constraining LHC analyses are the photons +
$E_{T}^{\textrm{miss}}$ searches. This can be understood from the fact that
for these scenarios the dominant $\tilde{\chi}_{1}^{0}$ decay mode is
$\tilde{\chi}_{1}^{0}\rightarrow\gamma\tilde{G}$ (Fig. 7, top right), while
the heavier wino- or Higgsino-dominated electroweakinos, which here dominate
the production cross-section, decay via the $\tilde{\chi}_{1}^{0}$ rather than
directly to a $\tilde{G}$ final state (Fig. 7, bottom right). Towards larger
masses for the heavier electroweakinos the production cross-section diminishes
(Fig. 7, top left) enough to leave an allowed region at
$m_{\tilde{\chi}_{1}^{0}}\lesssim
450\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ and
$m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{\pm}}\gtrsim
800\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$.

In the middle sector of the
$(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ plane, where the
highest-likelihood scenarios are wino NLSP scenarios (see Fig. 4, middle), the
most important contributions to the profile likelihood surface come from the
leptons + $E_{T}^{\textrm{miss}}$ searches (Fig. 6, top right), and searches
for jets + $E_{T}^{\textrm{miss}}$ final states, with or without leptons (Fig.
6, bottom left). This is largely explained by the fact that the dominant decay
modes of the now wino-dominated and near mass-degenerate
$\tilde{\chi}_{1}^{0}$ and $\tilde{\chi}_{1}^{\pm}$ are
$\tilde{\chi}_{1}^{0}\rightarrow Z\tilde{G}$ and
$\tilde{\chi}_{1}^{\pm}\rightarrow W^{\pm}\tilde{G}$, respectively (Fig. 7,
middle right and bottom left). Thus,
$\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{0}$ production will for these
scenarios typically give rise to the same collider signatures as the commonly
studied SUSY scenarios where wino-dominated
$\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{0}$ are produced and decay to final
states with a stable, light $\tilde{\chi}_{1}^{0}$ through
$\tilde{\chi}_{2}^{0}\rightarrow Z\tilde{\chi}_{1}^{0}$ and
$\tilde{\chi}_{1}^{\pm}\rightarrow W^{\pm}\tilde{\chi}_{1}^{0}$. However,
while $\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{0}$ is the most important
production mode for these $\tilde{G}$-EWMSSM scenarios, relevant signal
contributions can also arise from production of some of the heavier, Higgsino-
dominated electroweakinos. Towards low $m_{\tilde{\chi}_{1}^{0}}$
($m_{\tilde{\chi}_{1}^{0}}\lesssim
200\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$), phase space suppression of
the $\tilde{\chi}_{1}^{0}\rightarrow Z\tilde{G}$ decay makes
$\tilde{\chi}_{1}^{0}\rightarrow\gamma\tilde{G}$ the dominant decay mode for
$\tilde{\chi}_{1}^{0}$ (Fig. 7, top right). Here the photons +
$E_{T}^{\textrm{miss}}$ searches contribute strongly to the total log-
likelihood, as does the measurements of SM signatures, to be discussed in more
detail below (Fig. 6, top left and bottom right). At around
$m_{\tilde{\chi}_{1}^{0}}\sim 450\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$,
the reduction in the production cross-section with increasing mass (Fig. 7,
top left), combined with a balancing of the
$\tilde{\chi}_{1}^{0}\rightarrow\gamma\tilde{G}$ and
$\tilde{\chi}_{1}^{0}\rightarrow Z\tilde{G}$ branching ratios (Fig. 7, top
right and middle right) means that the combined constraining power of the
searches is sufficiently weakened so that a horizontal band in the mass plane
avoids exclusion at the $2\sigma$ level. This is also partly due to the model
fitting some weak excesses in leptons + $E_{T}^{\textrm{miss}}$ and photons +
$E_{T}^{\textrm{miss}}$ searches (light blue bands in Fig. 6, top left and top
right). However, towards even higher $m_{\tilde{\chi}_{1}^{0}}$, the ATLAS
search for $E_{T}^{\textrm{miss}}$ \+ boosted bosons ATLAS:2021yqv  gains
sensitivity (Fig. 6, bottom left) and the total likelihood therefore drops
below the $2\sigma$ threshold for $m_{\tilde{\chi}_{1}^{0}}$ between $\sim
500\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ and $\sim
700\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$.

As discussed above, the overall highest-likelihood scenarios are Higgsino NLSP
scenarios, close to the diagonals of the
$(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ and
$(m_{\tilde{\chi}_{1}^{\pm}},m_{\tilde{\chi}_{1}^{0}})$ planes. Here the model
obtains positive contributions to $\Delta\ln\mathcal{L}_{\text{searches}}$
from small excesses in leptons + $E_{T}^{\textrm{miss}}$ searches and the
ATLAS $b$-jets + $E_{T}^{\textrm{miss}}$ search (Fig. 6, top right and bottom
left). Some examples of the balancing of different branching ratios that these
scenarios exhibit, discussed in Sec. 5.1, can be seen in the middle left,
middle right and bottom left panels of Fig. 7.

###  5.4 Impact of measurements

The present study is the first to include LHC measurements of SM signatures in
a many-parameter BSM global fit. It is therefore interesting to explore what
impact these likelihood contributions have on our results. The log-likelihood
contribution $\Delta\ln\mathcal{L}_{\text{meas}}$ on the
$(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ profile-likelihood
surface is shown in the bottom-right panel of Fig. 6. The contribution is
significant in the regions with wino- or Higgsino-dominated
$\tilde{\chi}_{1}^{0}$ with $m_{\tilde{\chi}_{1}^{0}}\lesssim
200\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$, where
$\mathrm{BR}(\tilde{\chi}_{1}^{0}\rightarrow\gamma\tilde{G})$ is large. In
particular, the SM signature measurements contribute to excluding low-mass
scenarios where the constraints from leptons + $E_{T}^{\textrm{miss}}$
searches would otherwise have been largely balanced by positive log-likelihood
contributions from the photons + $E_{T}^{\textrm{miss}}$ searches (Fig. 6, top
panels, $m_{\tilde{\chi}_{1}^{0}}\lesssim
100\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$).

The $(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ profile likelihood
surface discussed above is by definition made up of the overall least
constrained parameter sample within each
$(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ bin. To get a more
complete picture of the constraining power of the SM signature measurements,
it is interesting to also look at $\Delta\ln\mathcal{L}_{\text{meas}}$ across
the surface of parameter samples that are most strongly constrained by this
log-likelihood contribution. This is shown in the top-left panel of Fig. 8.
For the $\tilde{G}$-EWMSSM scenarios where the SM signature measurements have
their largest sensitivity, they rule out scenarios that have both
$m_{\tilde{\chi}_{2}^{0}}$ and $m_{\tilde{\chi}_{1}^{0}}$ below $\sim
500\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$, and scenarios towards higher
$m_{\tilde{\chi}_{2}^{0}}$ when $m_{\tilde{\chi}_{1}^{0}}\lesssim
150\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$. The three other panels in
Fig. 8 show the individual log-likelihood contributions from the pools of
measurements that contribute most strongly to the combined
$\Delta\ln\mathcal{L}_{\text{meas}}$ in the upper-left panel: ATLAS
measurements of the $pp\rightarrow ZZ\rightarrow 4l$ cross-section (top right)
ATLAS:2021kog ; ATLAS:2019qet ; ATLAS:2017bcd ; ATLAS measurements of final
states with two different flavour leptons and missing energy, with or without
jets (bottom left) ATLAS:2021jgw ; ATLAS:2019rob ; ATLAS:2019ebv ;
ATLAS:2019hau , where the dominant contribution is coming from the
$pp\rightarrow W^{+}W^{-}$ cross-section measurements in ATLAS:2021jgw ;
ATLAS:2019rob ; and an ATLAS measurement of the $pp\rightarrow Z(\rightarrow
l^{+}l^{-})\gamma+X$ production cross-section ATLAS:2019gey  (bottom right).

Figure 8:  Log-likelihood contributions from different pools of LHC
measurements, plotted across the
$(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ plane for the scan
points where the combined constraint from the LHC measurements is at its
strongest.

Figure 9: The Higgsino (left), wino (middle) and bino (right) fraction of the
$\tilde{\chi}_{1}^{0}$, plotted across the
$(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ plane for the scan
points where the combined constraint from the LHC measurements is the largest.

In Fig. 9 we show the $\tilde{\chi}_{1}^{0}$ composition for the parameter
samples contributing to Fig. 8. From Figs. 8 and 9 we see that the $ZZ$ cross-
section measurements most strongly constrain low-mass scenarios where the
$\tilde{\chi}_{1}^{0}$ is dominantly Higgsino or a wino-Higgsino mixture.
These $\tilde{G}$-EWMSSM scenarios combine a large total electroweakino
production cross-section,777A balanced wino-Higgsino mixture for a low-mass
$\tilde{\chi}_{1}^{0}$ implies that $M_{2}$ for these points typically is
within $\sim 100\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ of $|\mu|$. This
means that at least four of the five heavier electroweakino states will have
masses not too much larger than $m_{\tilde{\chi}_{1}^{0}}$. with significant
branching ratios for some of the decays $\tilde{\chi}_{i}^{0}\rightarrow
Z\tilde{G}$ and/or $\tilde{\chi}_{i}^{0}\rightarrow Z\tilde{\chi}_{j}^{0}$.
The measurements of $W^{+}W^{-}$ production cross-sections exclude low-mass
scenarios with wino-dominated $\tilde{\chi}_{1}^{0}$. Here the strongest
$W^{+}W^{-}$ signal contribution comes from the production of pairs of light,
wino-dominated $\tilde{\chi}_{1}^{\pm}$, which decay as
$\tilde{\chi}_{1}^{\pm}\rightarrow W^{\pm}\tilde{G}$. Finally, the
$Z(\rightarrow l^{+}l^{-})\gamma+X$ cross-section measurement constrains
scenarios with bino-dominated $\tilde{\chi}_{1}^{0}$. These scenarios
typically have a large
$\mathrm{BR}(\tilde{\chi}_{1}^{0}\rightarrow\gamma\tilde{G})$ and a non-
negligible $\mathrm{BR}(\tilde{\chi}_{1}^{0}\rightarrow Z\tilde{G})$, such
that production of any pair of electroweakinos that decay to
$\tilde{\chi}_{1}^{0}$’s can result in signal contributions to the measured
cross-section.

Figure 10: The log-likelihood impact from including
$8\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$ LHC measurements of SM
signatures, shown for the highest-likelihood scan points in the mass region
around the best-fit point (left) and a higher-mass region (right).

Since the best-fit region predicts light Higgsinos, at masses around
$170\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$, the LHC searches and
measurements performed at
$\sqrt{s}=8\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$ can also be relevant.
A full investigation of the impact of
$8\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$ results is beyond the scope of
this study, as it would effectively double the computational cost of our
parameter scans. However, to gauge the possible impact, we generate $100\,000$
events at $8\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$ for each of our 100
highest-likelihood parameter points. We pass the events through Rivet and
Contur to compute a log-likelihood contribution from the collection of
$\sqrt{s}=8\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$ measurements in Rivet.
The result of this is illustrated in Fig. 10, where we show the change in the
total log-likelihood for each point when the contribution from
$8\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$ measurements is added. In the
left-hand panel we show the points close to the best-fit point at
$m_{\tilde{\chi}_{1}^{0}}\sim 170\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$.
Of our 100 highest-likelihood points, some also belong to the higher-mass
region, at $m_{\tilde{\chi}_{1}^{0}}\gtrsim
280\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$, shown in the right-hand
panel. For the best-fit points in the low-mass region, including the
$8\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$ measurements reduces the total
log-likelihood by around $0.2$ units. As expected, there is a smaller impact
on points in the higher-mass region.

###  5.5 Scenarios with a chargino NLSP

In contrast with the EWMSSM, the $\tilde{G}$-EWMSSM admits the possibility of
a chargino as the lightest electroweakino. Such a scenario was highlighted in
Fig. 1 where the gray band signals a sudden drop in branching ratio due to
$m_{\tilde{\chi}_{1}^{\pm}}<m_{\tilde{\chi}_{1}^{0}}$. While rare for MSSM-
like electroweakino mass matrices, and featuring small mass differences, our
scan identified still-viable parameter regions with
$m_{\tilde{\chi}_{1}^{\pm}}<m_{\tilde{\chi}_{1}^{0}}$, shown in Fig. 11.

We find that in these cases, the points with the highest likelihoods have
Higgsino-like electroweakinos, with only small splittings for the
$\tilde{\chi}_{1}^{\pm}$, $\tilde{\chi}_{1}^{0}$ and $\tilde{\chi}_{2}^{0}$,
with masses preferred to be in the region of
$400$–$500\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$. Here, the decay mode
for $\tilde{\chi}_{1}^{\pm}$ is always $\tilde{\chi}_{1}^{\pm}\rightarrow
W\tilde{G}$. Hence, the detectable signal for
$\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\pm}$ pair production is two on-shell
$W$ bosons and some missing energy from the gravitinos. For the
$\tilde{\chi}_{1}^{0}$, the dominant decay modes are
$\tilde{\chi}_{1}^{0}\rightarrow Z\tilde{G}$ and
$\tilde{\chi}_{1}^{0}\rightarrow h\tilde{G}$ due to the dominant Higgsino
component. The detectable signal for
$\tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{\pm}$ production would then be on-shell
$WZ$ or $Wh$ plus missing energy from the gravitinos. Finally,
$\tilde{\chi}_{2}^{0}$ decays to soft SM fermions and the
$\tilde{\chi}_{1}^{0}$ or $\tilde{\chi}_{1}^{\pm}$. Thus, the production of
$\tilde{\chi}_{1}^{0}\tilde{\chi}_{2}^{0}$ and
$\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{0}$ will in effect enhance the cross
sections for $\tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{\pm}$ and
$\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\pm}$ production.

Figure 11:  The total log-likelihood plotted across the profile-likelihood
surface for the subset of points with
$m_{\tilde{\chi}_{1}^{\pm}}<m_{\tilde{\chi}_{1}^{0}}$, shown in the
$(m_{\tilde{\chi}_{2}^{0}},m_{\tilde{\chi}_{1}^{0}})$ plane (left) and in the
$(m_{\tilde{\chi}_{1}^{\pm}},m_{\tilde{\chi}_{1}^{0}})$ plane (right).

##  6 Conclusions

In this study we have investigated the current viability of the
$\tilde{G}$-EWMSSM, the simplest realisation of a light supersymmetric
electroweak sector together with a nearly massless gravitino LSP. We have
confronted the $\tilde{G}$-EWMSSM with a comprehensive selection of the
relevant Run 2 searches at the LHC, relevant past searches at LEP, and, we
have, for the first time in a global fit, used a broad set of SM measurements
at the LHC to constrain the model by building a new interface between GAMBIT
and Contur.

Our best-fit region for the model is where $|\mu|<|M_{1}|,M_{2}$, and is
characterised phenomenologically by a trio of relatively light degenerate
Higgsinos in the mass range of
$140$–$500\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$, with a best fit point
around $170\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$. Due to the collective
effect of small excesses over multiple ATLAS and CMS searches we find closed
$2\sigma$ contours in the parameter space, but we emphasise that this is a
model-specific best-fit region and does not constitute a measure of goodness-
of-fit.

Our main result is that the bulk of the $\tilde{G}$-EWMSSM parameter space
with electroweakino masses below
$1\,\text{T$\text{e}\mspace{-0.8mu}\text{V}$}$ is excluded by collider
searches and measurements. The four exceptions, classified according to the
nature of the lightest electroweakinos, are:

  * i)

degenerate Higgsinos from $140\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ and
up,

  * ii)

a region of degenerate winos around
$400$–$500\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ allowed at the
$2\sigma$ level,

  * iii)

degenerate winos above $700\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$, and

  * iv)

a ‘lonely’ bino from $62\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ and up,
decoupled from heavier Higgsinos and winos lying above
$800\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$.

For Run 3 of the LHC the degenerate Higgsino region, i), will be challenging
to test fully. Drawing from the lessons learnt in this study, the measurement
of SM multi-lepton signatures will continue to be important to exclude
parameter space at the low-mass end of the region. Potential improvements to
searches sensitive to the important $\tilde{\chi}_{1}^{0}\to h\tilde{G}$ decay
(see Fig. 7, middle left), will also improve the reach. However, fully
excluding this still very viable region will need future $e^{+}e^{-}$ or muon
colliders operating at high enough centre-of-mass energies.

On the other hand, the surviving wino band, ii), with masses around
$450\,\text{G$\text{e}\mspace{-0.8mu}\text{V}$}$ seems to be fully excludable
with the slightly higher Run 3 centre-of-mass energy and more data, in
particular since its survival is already marginal. For the same reason it
should also be possible to push the remaining wino region, iii), to somewhat
higher masses with higher cross sections and more data.

For the lonely bino region, iv), the search for pair production of light binos
decaying to photons is also hampered by low production cross sections.
However, we expect some impact here with increasing statistics in Run 3 and
beyond to the High-Luminosity LHC, in particular on the parts of parameter
space where there is bino production through the decay of heavier
electroweakinos, which could realistically be pushed out beyond 1 TeV.

We emphasise the still open interesting possibility of a reverse mass
hierarchy of charginos and neutralinos, with
$m_{\tilde{\chi}_{1}^{\pm}}<m_{\tilde{\chi}_{1}^{0}}$, with distinct signal
predictions for LHC Run 3 searches. Although the base production cross section
is not so high given their Higgsino nature, the preferred region of this
scenario should be within reach of Run 3 statistics and the slightly higher
centre-of-mass energy, when considering all final states $WW$, $WZ$ and $Wh$.

We make all our generated parameter samples available from Zenodo for further
study Zenodo_gravitino .

###### Acknowledgements.

We thank our colleagues in the GAMBIT Community for helpful discussions and
comments. For computing resources, we thank PRACE for awarding us access to
Marconi at CINECA and Joliot-Curie at CEA. Computing resources were also
provided by Sigma2, the National Infrastructure for HPC in Norway, under
project NN9284K. AF was supported by the National Natural Science Foundation
of China (NNSFC) Research Fund for International Excellent Young Scientists
grant 1950410509. ABu and JB were supported by the UK Science and Technology
Facilities Council (STFC) Consolidated Grant programme awards ST/S000887/1 and
ST/S000666/1 respectively, ABe by STFC grant ST/T00679X/1, and TP by the STFC
Doctoral Training Programme. The work of CB was supported by the Australian
Research Council Discovery Project grant DP210101636. AK and AR were supported
by the Research Council of Norway FRIPRO grant 323985. TEG was funded by the
Deutsche Forschungsgemeinschaft (DFG) through the Emmy Noether Grant No. KA
4662/1-1. The work of VA was supported by the European Union Framework
Programme for Research and Innovation Horizon 2020 (2014–2021) under the Marie
Sklodowska-Curie Grant Agreement No. 765710. YZ was supported by the NNSFC
under grant No. 12105248 and 12047503 (Peng-Huan-Wu Theoretical Physics
Innovation Center). MJW is supported by the ARC Centre of Excellence for Dark
Matter Particle Physics (CE200100008). We made use of pippi v2.2 pippi  for
this work.

##  Appendix A Profile likelihood maps for the input parameters

Figure 12: Profile likelihood maps for the $(M_{1},\mu)$, $(M_{2},\mu)$ and
$(\tan\beta,\mu)$ parameter planes, using the full likelihood (top row) or the
capped likelihood (bottom row). The white contour lines show the $1\sigma$ and
$2\sigma$ confidence regions, and the white star in the top-row panels mark
the point of highest likelihood. The region with $M_{2}<0$ (grey) in the
middle panels is included only to ensure equal aspect ratio for all three mass
parameters.

In Fig. 12 we show profile likelihood results for three different planes of
the $\tilde{G}$-EWMSSM parameters. The panels in the top row show likelihood
maps using the full likelihood, i.e. corresponding to the results in Fig. 2.
In the bottom row we show results for the same parameter planes using the
capped likelihood (see Sec. 3.1), corresponding to the results in Fig. 3. As
discussed in Sec. 5.1, the highest-likelihood solutions are found for
$|\mu|<|M_{1}|,M_{2}$, $\mu<0$ and $\tan\beta$ close to 1. When $|\mu|$ is
larger than $|M_{1}|$ or $M_{2}$, the likelihood is only very weakly dependent
on $|\mu|$ and $\tan\beta$. This explains the patchiness of the capped profile
likelihood in the bottom-right panel, since the set of high-likelihood scan
samples (which pick out the required $M_{1}$ or $M_{2}$ values) is spread out
across large regions in the $(\tan\beta,\mu)$ plane.

##  Appendix B LHC searches

Below we give a short description of each 13 TeV LHC search we include in our
study, and point out which signal regions our simulation includes. A list of
all the searches, along with the corresponding labels used in ColliderBit, is
given in Table 2.

Search label | Luminosity | Source
---|---|---
ATLAS_2BoostedBosons | 139 $\text{fb}^{-1}$ | ATLAS hadronic chargino/neutralino search ATLAS:2021yqv
ATLAS_0lep | 139 $\text{fb}^{-1}$ | ATLAS 0-lepton search ATLAS:2020syg
ATLAS_0lep_stop | 36 $\text{fb}^{-1}$ | ATLAS 0-lepton stop search ATLAS:2017drc
ATLAS_1lep_stop | 36 $\text{fb}^{-1}$ | ATLAS 1-lepton stop search ATLAS:2017eoo
ATLAS_2lep_stop | 139 $\text{fb}^{-1}$ | ATLAS 2-lepton stop search ATLAS:2021hza
ATLAS_2OSlep_Z | 139 $\text{fb}^{-1}$ | ATLAS stop search with Z/H final states ATLAS:2020aci
ATLAS_2OSlep_chargino | 139 $\text{fb}^{-1}$ | ATLAS 2-lepton chargino search ATLAS:2019lff
ATLAS_2b | 36 $\text{fb}^{-1}$ | ATLAS 2-$b$-jet stop/sbottom search ATLAS:2017avc
ATLAS_3b | 24 $\text{fb}^{-1}$ | ATLAS 3-$b$-jet Higgsino search ATLAS:2018tti
ATLAS_3lep | 139 $\text{fb}^{-1}$ | ATLAS 3-lepton chargino/neutralino search ATLAS:2021moa
ATLAS_4lep | 139 $\text{fb}^{-1}$ | ATLAS 4-lepton search ATLAS:2021yyr
ATLAS_MultiLep_strong | 139 $\text{fb}^{-1}$ | ATLAS leptons + jets search ATLAS:2019fag
ATLAS_PhotonGGM_1photon | 139 $\text{fb}^{-1}$ | ATLAS 1-photon GGM search ATLAS:2021ijy
ATLAS_PhotonGGM_2photon | 36 $\text{fb}^{-1}$ | ATLAS 2-photon GGM search ATLAS:2018nud
ATLAS_Z_photon | 80 $\text{fb}^{-1}$ | ATLAS Z + photon search ATLAS:2018vzq
CMS_0lep | 137 $\text{fb}^{-1}$ | CMS 0-lepton search CMS:2019zmd
CMS_1lep_bb | 36 $\text{fb}^{-1}$ | CMS 1-lepton + $b$-jets chargino/neutralino search CMS:2017kyj
CMS_1lep_stop | 36 $\text{fb}^{-1}$ | CMS 1-lepton stop search CMS:2017gbz
CMS_2lep_stop | 36 $\text{fb}^{-1}$ | CMS 2-lepton stop search CMS:2017jrd
CMS_2lep_soft | 36 $\text{fb}^{-1}$ | CMS 2 soft lepton search CMS:2018kag
CMS_2OSlep | 137 $\text{fb}^{-1}$ | CMS 2-lepton search CMS:2020bfa
CMS_2OSlep_chargino_stop | 36 $\text{fb}^{-1}$ | CMS 2-lepton chargino/stop search CMS:2018xqw
CMS_2SSlep_stop | 137 $\text{fb}^{-1}$ | CMS 2 same-sign lepton stop search CMS:2020cpy
CMS_MultiLep | 137 $\text{fb}^{-1}$ | CMS multilepton chargino/neutralino search CMS:2021cox-fix
CMS_photon | 36 $\text{fb}^{-1}$ | CMS 1-photon GMSB search CMS:2017brl
CMS_2photon | 36 $\text{fb}^{-1}$ | CMS 2-photon GMSB search CMS:2019vzo
CMS_1photon_1lepton | 36 $\text{fb}^{-1}$ | CMS 1-photon + 1-lepton GMSB search CMS:2018fon
Table 2: The different ATLAS and CMS searches we simulate for our LHC
likelihood, with associated short-hand labels.

The ATLAS search for electroweak production of charginos and neutralinos in
final states with two boosted, hadronically-decaying bosons and missing
transverse momentum ATLAS:2021yqv : This search (ATLAS_2BoostedBosons) targets
the pair production of electroweakinos, where each of them is assumed to decay
into the LSP and an on-shell $W$, $Z$ or SM Higgs boson. The mass difference
between the produced electroweakinos and the LSP is assumed to be at least 400
GeV. The analysis is optimised on three different scenarios: 1) a baseline
MSSM scenario where the produced electroweakinos and the LSPs can be either
binos, winos or Higgsinos, 2) a general gauge mediation-inspired scenario in
which the LSP is a gravitino and the heavier particles are Higgsinos and 3) a
scenario with an axino LSP, where the heavier particles are assumed to be
Higgsinos. Various simplified models are considered in each case. The analysis
is performed in two fully-hadronic final states: the $qqqq$ final state
arising from $W$/$Z$ bosons each decaying to light-flavour quarks/antiquarks,
and the $bbqq$ final state which arises from a $Z$ or Higgs boson decaying to
$b\bar{b}$ and a $W$ or $Z$ boson decaying to light-flavour quarks/antiquarks.
The analysis uses events with at least two large-$R$ jets, and counts the
$b$-multiplicity of each of these jets using a $b$-tagged track jet procedure.
Boosted boson tagging algorithms are then defined to identify various SM boson
decays in the two leading large-$R$ jets: $W_{qq}(Z_{qq})$-tagging targets
$W(Z)\rightarrow qq$, whilst $Z_{bb}(h_{bb})$-tagging targets $Z(h)\rightarrow
bb$. $V_{qq}$-tagging is used to denote the logical OR of $W_{qq}$\- and
$Z_{qq}$-tagging. Signal regions are then defined using the multiciplities of
the different boson tags $n(W_{qq})$, $n(Z_{qq})$, $n(V_{qq})$, $n(Z_{bb})$
and $n(h_{bb})$. Additional background rejection is provided by selections
such as a veto on $b$-jets that do not originate from the boosted boson
candidates, lower bounds on the effective mass $m_{\text{eff}}$ (defined as
the scalar sum of the $p_{T}$ of the two leading large-$R$ jets and
$E_{\text{T}}^{\text{miss}}$), lower bounds on $E_{\text{T}}^{\text{miss}}$,
cuts on an event shape variable, and a lower bound on the stransverse mass
$m_{\text{T2}}$ constructed from the two leading large-$R$ jets. Our
implementation of this search includes the signal regions 4Q-WW, 4Q-WZ, 4Q-ZZ
and 4Q-VV. Due to difficulties with reproducing the $b$-tagging for small
radius track jets we do not include the signal regions that rely on this.

The ATLAS search for gluino and squark production in final states with jets
and missing transverse momentum ATLAS:2020syg : This is the flagship ATLAS
supersymmetry search for squarks and gluinos (ATLAS_0lep), targeting events
with multiple jets and significant missing transverse momentum. Although it is
optimised on models of squark and gluino production, similar final states can
be produced by electroweakino production with subsequent cascade decay
processes that produce hadronically-decaying gauge bosons. We implement the
optimised single-bin signal regions that are designed to present the ATLAS
results in a model-independent way (2j-1600, 2j-2200, 2j-2800, 4j-1000,
4j-2200, 4j-3400, 5j-1600, 6j-1000, 6j-2200 and 6j-3400). The signal region
selections include requirements on the multiplicity and transverse momenta of
the jets in each event, the angular separation between the jets and the
missing transverse momentum vector, the aplanarity,
$E_{\text{T}}^{\text{miss}}/\sqrt{H_{\text{T}}}$ and $m_{\text{eff}}$.

The ATLAS search for top squarks in the jets plus missing transverse momentum
final state ATLAS:2017drc : This search (ATLAS_0lep_stop) seeks to uncover
evidence of stop production in final states with four or more jets plus
missing transverse momentum. Five sets of signal region are defined in the
analysis, targeting different stop simplified models, with a range of
different included sparticles and sparticle mass differences. The six SRA and
SRB regions employ top-mass reconstruction to increase sensitivity to models
in which the stop produces a top quark, which makes them less relevant for the
scenario considered in this paper. The five SRC regions use recursive jigsaw
variables to target regions with a small $\tilde{t}_{1}-\tilde{\chi}^{0}_{1}$
mass difference, the details of which are highly-dependent on the treatment of
initial state radiation in the Monte Carlo generator used to model LHC events.
We do not include these SRC regions due to known deficiencies of the Pythia
initial state radiation model in this region. The two SRD regions are
optimised for direct top squark production where both top squarks decay via
$\tilde{t}\rightarrow b\tilde{\chi}^{\pm}_{1}$. At least five jets are
required, two of which must be $b$-tagged, and further requirements are placed
on the jet transverse momenta and the scalar sum of the transverse momenta of
the two jets with the highest $b$-tag weights. Finally, the SRE signal region
is designed for models with highly boosted top quarks. Requirements on the jet
mass of reclustered fat jets are used, alongside requirements on the main
discriminating variables $H_{T}$, $E_{T}^{\text{miss}}$ and
$E_{T}^{\text{miss}}/\sqrt{H_{T}}$.

The ATLAS search for top squarks in final states with one lepton, jets plus
missing transverse momentum ATLAS:2017eoo : This search (ATLAS_1lep_stop) is
optimised on simplified models of stop production with decays that produce one
lepton (through a real or off-shell leptonically-decaying $W$ boson), and also
on a dark matter model with a spin-0 mediator produced in association with two
top quarks. All signal region are required to have exactly one signal lepton,
and 2, 3 or 4 jets. Five regions labelled tN are optimised for the decay
pattern $\tilde{t}\rightarrow t\tilde{\chi}^{0}_{1}$, using selections on
variables such as the $am_{\text{T2}}$ variable, the transverse mass $m_{T}$
formed from the lepton and missing transverse momentum, the
$H^{\text{miss}}_{\text{T,sig}}$888$H^{\text{miss}}_{\text{T,sig}}$ is defined
as
$H^{\text{miss}}_{\text{T,sig}}=\frac{|\vec{H}_{\text{T}}^{\text{miss}}|-M}{\sigma_{|\vec{H}_{\text{T}}^{\text{miss}}|}}$,
where $\vec{H}_{\text{T}}^{\text{miss}}$ is the negative vectorial sum of the
momenta of the signal jets and the lepton, $M=100$ GeV is an offset parameter,
and the denominator is computed from the per-event jet energy uncertainties.
and the mass of a reconstructed hadronic top quark. Note that we do not
include three signal regions that use a boosted decision tree in the
definition of the signal region, since this is very difficult to reproduce
outside of the ATLAS collaboration. Two additional signal regions, bWN and
bffN, are dedicated to the three-body ($\tilde{t}\rightarrow
bW\tilde{\chi}^{\pm}_{1}$) and four-body ($\tilde{t}\rightarrow
bff^{\prime}\tilde{\chi}^{\pm}_{1}$) decay searches. Six signal regions target
various $\tilde{t}\rightarrow b\tilde{\chi}^{\pm}_{1}$ scenarios: three are
optimised on a simplified model that assumes
$m_{\tilde{\chi}^{\pm}_{1}}=2m_{\tilde{\chi}^{0}_{1}}$ (labels bC2x_diag,
bC2x_med, bCbv), and three are designed to search for the case of a Higgsino
LSP, in which the $\tilde{\chi}^{\pm}_{1}$, $\tilde{\chi}^{0}_{2}$ and
$\tilde{\chi}^{0}_{1}$ are close in mass (labels bCsoft_diag, bCsoft_med,
bCsoft_high). In the latter case, the signature is characterised by low-
momentum leptons or jets from highly off-shell $W$ or $Z$ bosons, and the
analysis benefits from a dedicated soft lepton reconstruction. Finally, three
extra signal regions (DM_low_loose, DM_low, DM_high) are optimised on the dark
matter mediator model, with the analysis using similar variables to the
regions targeting the decay $\tilde{t}\rightarrow t\tilde{\chi}^{0}_{1}$.

The ATLAS search for top squarks in final states with two opposite-charge
leptons and missing transverse momentum ATLAS:2021hza : This search
(ATLAS_2lep_stop) is optimised on similar models of direct stop production to
the 0 lepton and 1 lepton searches. Events are required to have exactly two
light leptons (electrons or muons) of opposite charge, with an invariant mass
outside of the $Z$ boson mass window in the case of same flavour leptons. A
series of discriminating variables are constructed from the missing transverse
momentum and $p_{T}$ values of the leading leptons and jets, with other useful
variables including a variant of $m_{\text{T2}}$ and the super-razor variables
first defined in Ref. Buckley:2013kua . Various signal regions are optimised
for 2-body, 3-body and 4-body stop decays. For the case of 2-body decays, the
ATLAS analysis also defines a set of seven inclusive signal regions (labelled
SR2bInc) intended to provide less model-specific sensitivity. Our
implementation of the search uses this set of inclusive signal regions.

The ATLAS search for top squarks in events with a Higgs or $Z$ boson
ATLAS:2020aci : This search (ATLAS_2OSlep_Z) is optimised on various
simplified models of top squark production in which a top squark decays to
produce a Higgs or $Z$ boson. Top squark decays involving $Z$ bosons are
targeted using a 3-lepton selection, with at least one same-flavour-opposite-
sign pair (SFOS) whose invariant mass is consistent with $Z$ boson mass.
Further selections are placed on the transverse momenta of the three leading
leptons, the jet multiplicity, the $b$-jet multiplicity, the transverse
momenta of the leading jet and $b$-jet, the missing transverse energy, a
variant of $m_{\text{T2}}$ and the transverse momentum of the SFOS pair.
Events containing Higgs bosons are targeted using a 1-lepton event selection,
with further selections placed on the jet and $b$-jet multiplicity, the
transverse mass formed from the lepton and the missing transverse momentum,
and the missing transverse energy significance. In addition, a Higgs tagger
built from a neural network is used to identify Higgs boson candidates, and
events must contain at least one of them. Due to the difficulty of reproducing
this Higgs tagging with sufficient accuracy, our implementation of this search
covers only the 3-lepton final states (labels SRZ1A, SRZ1B, SRZ2A, SRZ2B).

The ATLAS search for charginos and sleptons in final states with two leptons
and missing transverse momentum ATLAS:2019lff : This search
(ATLAS_2OSlep_chargino) is optimised on simplified models of slepton and
chargino production, targeting chargino pair production with decays to
lightest neutralinos and $W$ bosons, chargino cascade decays through sleptons
to lightest neutralinos, and the direct production of slepton pairs. Events
are required to have exactly two opposite-charge light leptons with an
invariant mass greater than 100 GeV. Selected events must also have no
$b$-tagged jets, and large values of $E_{T}^{\text{miss}}$ and
$E_{T}^{\text{miss}}$ significance. Further discrimination comes from the use
of the $m_{\text{T2}}$ variable. Four sets of signal regions are defined
(labels SR-SF-0J, SR-SF-1J, SR-DF-0J, SR-DF-1J) based on whether the leptons
have the same or a different flavour, and whether the events have 0 or 1
non-$b$-tagged jets. From this, the ATLAS analysis defines a total of 16
inclusive signal regions, intended for more model-independent sensitivity, and
a set of 36 signal regions with fine-grained binning in $m_{\text{T2}}$, to
maximise sensitivity to the simplified model studied by ATLAS. In our study we
use the inclusive signal regions.

The ATLAS search for bottom and top squarks in final states with two
$b$-tagged jets and missing transverse momentum ATLAS:2017avc : This search
(ATLAS_2b) is optimised on various simplified models of stop and sbottom
production, targeting final states with 2 $b$-tagged jets, large missing
transverse momentum and either zero leptons or one lepton. A long list of
discriminating variables is used, including the minimum $\Delta\Phi$ between
any of the leading jets and the missing transverse momentum vector,
$H_{\text{T}}$ (defined as the scalar sum of the $p_{T}$ values of a subset of
the jets in the event), $m_{\text{eff}}$, ratios of the missing transverse
energy with $m_{\text{eff}}$ and $\sqrt{H_{\text{T}}}$, the contranverse mass,
$am_{\text{T2}}$ and others. Three zero lepton signal regions and three one
lepton signal regions are defined. Due to challenges in reproducing the cuts
based on $am_{\text{T2}}$ our study only uses the zero lepton signal regions
(labels 0L_SRA350, 0L_SRA450, 0L_SRA550, 0L_SRB, 0L_SRC).

The ATLAS search for Higgsinos in final states with at least three $b$-tagged
jets ATLAS:2018tti : This search (ATLAS_3b) targets Higgsino production and
decay in gauge-mediated supersymmetry scenarios, in which each Higgsino is
assumed to decay to a Higgs boson and a gravitino. Two complementary analyses,
targeting high- and low-mass signals, are performed. For the high-mass
analysis, events with at least three $b$-tagged jets are selected, and jet
pairs are assigned to two Higgs candidates. For the low-mass analysis, events
with four $b$-jets are analysed by grouping the jets into Higgs candidates.
Selections are placed on a number of kinematic variables including
$m_{\text{eff}}$, $E_{\text{T}}^{\text{miss}}$, the mass of the Higgs boson
candidates, angular variables and the minimum transverse mass formed with the
missing transverse momentum vector and any of the leading four jets. Due to
some overlaps between the signal regions for the low-mass and high-mass
analyses, our analysis only uses the low-mass signal regions. From this
analysis we have implemented all the 46 signal regions optimised for
exclusion.

The ATLAS search for chargino-neutralino pair production in final states with
three leptons and missing transverse momentum ATLAS:2021moa : This search
(ATLAS_3lep) is optimised on two scenarios of electroweakino production. In
the first, a $\tilde{\chi}_{1}^{\pm}$ and $\tilde{\chi}_{2}^{0}$ are produced
(both wino-dominated), with subsequent decay to a bino-dominated
$\tilde{\chi}_{1}^{0}$. In the second, the $\tilde{\chi}_{1}^{\pm}$,
$\tilde{\chi}_{2}^{0}$ and $\tilde{\chi}_{1}^{0}$ are pure Higgsino states,
and are therefore typically more mass degenerate (although an arbitrary mass
hierarchy is assigned in order to define a parameter plane in which to
optimise the analysis). The analysis has three dedicated selections to cover
different mass regimes and assumptions, including an on-shell $WZ$ selection,
an off-shell $WZ$ selection and a $Wh$ selection. All consider final states
with exactly three leptons, possible ISR jets and
$E_{\text{T}}^{\text{miss}}$. Events with at least one SFOS pair are divided
into three bins of the SFOS pair invariant mass, $m_{ll}$, covering the
regions below, on and above the $Z$ mass. Each $m_{ll}$ bin is further divided
into $E_{\text{T}}^{miss}$ and $m_{\text{T}}$ bins, where the transverse mass
$m_{T}$ is defined using the lepton that is not in the SFOS pair (and which
can therefore be assumed to arise from a $W$ boson decay). Events are further
separated by their jet multiplicity, and by two different variants of
$H_{\text{T}}$, defined as the scalar sum of the transverse momenta of jets or
leptons depending on the definition. Signal regions for events with a
different-flavour-opposite-sign (DFOS) lepton pair are defined separately,
using selections on the jet multiplicity, $E_{\text{T}}^{\text{miss}}$
significance, transverse momentum for the third-leading lepton, and the
$\Delta R$ between the DFOS leptons and the same-flavour-same-sign lepton that
is nearest in $\phi$. Our implementation includes 39 of the 41 signal regions
targeting on-shell $WZ$ or $Wh$ production, leaving out the two regions SR-Wh-
DFOS-1 and SR-Wh-DFOS-2 for which some cuts rely on object resolution
variables that are not available in our fast event simulation framework.

The ATLAS search for gluino, electroweakino or slepton production in final
states with four or more leptons ATLAS:2021yyr : This search (ATLAS_4lep) is
optimised on different R-parity violating and R-parity conserving SUSY
scenarios that can produce lepton-rich final states. The simplified model used
for the R-parity conserving scenarios is a model with Higgsino production and
a gravitino LSP, thus highly relevant for our study. Events are required to
have four or more leptons (electrons, muons or hadronically-decaying taus).
The signal regions for four-lepton events are classified by whether the events
have four light leptons and zero taus, three light leptons and one tau, or two
light leptons and two taus. Further selections are placed on the number of
$b$-tagged jets, the presence or absence of a $Z$ boson, $E_{T}^{\text{miss}}$
and $m_{\text{eff}}$. A further signal region is also defined, requiring at
least five light leptons, subject to no kinematic requirements. Our
implementation includes all the zero-tau signal regions, i.e. the five-lepton
region (label SR5L) and the seven regions with four light leptons (the regions
with the SR0 label). In particular, this includes the the two signal regions
SR0-ZZ-loose-bveto and SR0-ZZ-tight-bveto designed to target the Higgsino plus
gravitino scenario.

The ATLAS search for squarks and gluinos in final states with same-sign
leptons and jets ATLAS:2019fag : This search (ATLAS_MultiLep_strong) is
optimised on simplified models of gluino and squark production, covering the
case of both R-parity conversation and R-parity violation. Events are required
to have two same-sign leptons and may contain additional leptons. In the case
of the R-parity conserving search, large missing transverse momentum is
required. Five signal regions are defined using the number of leptons and
their relative electric charges, the number of jets and the number of
$b$-tagged jets. Key kinematic variables used include the effective mass
$m_{\text{eff}}$, $E_{T}^{\text{miss}}$ and its ratio to $m_{\text{eff}}$ and
the invariant mass of same-sign electron pairs (which reduces contamination
from $Z\rightarrow e^{+}e^{-}$ decays where the charge of one electron is
mismeasured). We include all five signal regions in our analysis.

The ATLAS search for gauge-mediated supersymmetry in final states with
photons, jets and missing transverse momentum ATLAS:2021ijy : This search
(ATLAS_PhotonGGM_1photon) is optimised on a simplified model in which pair-
produced gluinos decay to neutralinos, which in turn decay to a gravitino, at
least one photon and jets. Three signal regions are defined which target the
cases of large, medium and small mass differences between the gluino and
neutralino, and all of them veto leptons in the selected events. Further
selections are placed on the transverse momentum of the leading photon, the
jet multiplicity, the angular separations of the jet and photon momenta with
the missing transverse energy vector, $E_{\text{T}}^{\text{miss}}$,
$H_{\text{T}}$ and a variable called $R_{\text{T}}^{4}$, defined as the ratio
of the scalar sum of the $p_{\text{T}}$ for the four leading jets, and the
scalar sum of the $p_{\text{T}}$ for all signal jets in the event. Our
implementation includes all three signal regions.

The ATLAS search for photonic signatures from gauge-mediated supersymmetry
models ATLAS:2018nud : This search (ATLAS_PhotonGGM_2photon) is optimised on
models of both strong and electroweak sparticle production, and targets final
states with either a single photon and multiple jets, or two photons, plus
significant missing transverse momentum in both cases. Discriminating
variables include $m_{\text{eff}}$, $E_{\text{T}}^{\text{miss}}$, a variant of
$H_{\text{T}}$, the angular separation between photons and the missing
transverse momentum vector and $R_{\text{T}}^{4}$ (the scalar sum of the
transverse momenta of the four leading jets divided by the scalar sum of the
transverse momenta of all jets in the event). Our implementation contains all
signal regions from the paper, but in our analysis we only use the two-photon
signal regions (labels SRaa_SL, SRaa_SH, SRaa_WL, SRaa_WH), since the one-
photon signal regions largely overlap with (and are superseded by) the signal
regions in ATLAS_PhotonGGM_1photon above.

The ATLAS search for exotic decays of the Higgs boson to at least one photon
and missing transverse momentum ATLAS:2018vzq : This search (ATLAS_Z_photon)
targets exotic decays of the Higgs boson to, for example, a gravitino and a
lightest neutralino, with the neutralino subsequently decaying to a gravitino
and a photon, This generates a final state with a single photon plus missing
transverse energy, and one can reduce SM backgrounds by looking for events
with a Higgs boson produced in association with a $Z$ boson. One can also
generate final states with two photons if the Higgs boson decays to a pair of
neutralinos that subsequently decay. Events are selected in the analysis if
they have at least one photon, moderate $E_{\text{T}}^{\text{miss}}$ and two
opposite-sign electrons or muons with an invariant mass within 10 GeV of the
$Z$ boson mass (and no additional leptons). A $\gamma
E_{\text{T}}^{\text{miss}}$ system is defined by performing the vector sum of
the photon momentum or momenta and the missing momentum vector in the
transverse plane. The search relies on two discriminating variables that
quantify the angular separation of the two-lepton and $\gamma
E_{\text{T}}^{\text{miss}}$ systems and the $p_{T}$ asymmetry of the two
systems, and the analysis has only one signal region.

The CMS search for gluino and squark production in final states with multiple
jets and missing transverse momentum CMS:2019zmd : This is the flagship CMS
search for gluino and squark production (CMS_0lep), and is the CMS equivalent
of the ATLAS search presented in Ref. ATLAS:2020syg . Search regions are
defined in a four-dimensional space of variables given by the total number of
jets, the number of $b$-tagged jets, the scalar sum of the jet $p_{\text{T}}$
values ($H_{\text{T}}$), and the magnitude of the vector $p_{\text{T}}$ sum of
the jets ($H_{\text{T}^{\text{miss}}}$). In total, there are 174 exclusive
signal region bins. For our analysis, we implement 12 aggregate search bins
which are presented in an appendix of the paper, and which are constructed
from the original search bins after taking correlations into account.

The CMS search for chargino and neutralino production in the WH final state
CMS:2017kyj : This search (CMS_1lep_bb) is optimised on simplified models of
chargino and neutralino production, with subsequent decays to a lightest
neutralino and either a $W$ or Higgs boson. Events are required to have an
electron or muon, two $b$-tagged jets with an invariant mass close to the
Higgs boson mass and significant missing transverse momentum. Discriminating
variables include the transverse mass of the lepton-neutrino system, the
contranverse mass, and the $E_{\text{T}}^{\text{miss}}$. The paper defines two
signal regions, distinguished by the selection on
$E_{\text{T}}^{\text{miss}}$. In our analysis we use both signal regions, and
account for the correlated background uncertainties using the correlation
coefficient provided by the CMS collaboration.

The CMS search for stop production in final states with one lepton CMS:2017gbz
: This search (CMS_1lep_stop) is optimised on simplified models of stop
production, and targets events with a single isolated electron or muon, jets
and large missing transverse momentum. Two sets of signal regions are defined;
one for a large range of $\tilde{t}_{1}-\tilde{\chi}_{1}^{0}$ mass splittings,
and one for compressed spectra. For the first set of 27 signal regions, events
are selected based on the number of jets, the $E_{\text{T}}^{\text{miss}}$,
the invariant mass of the lepton and the closest $b$-tagged jet and a special
“topness” variable. For the second set of 4 signal regions, at least five jets
are required, and with the highest $p_{\text{T}}$ jet must not be $b$-tagged
since it is expected to arise from initial state radiation. Further selections
are placed on the angular separations of the missing transverse momentum and
the lepton/jets, plus the $p_{\text{T}}$ of the lepton. Our analysis makes use
of a smaller set of six aggregated signal regions that are provided in an
appendix of the paper.

The CMS search for stop production and dark matter in final states with two
opposite-charge leptons CMS:2017jrd : This search (CMS_2lep_stop) is optimised
on models of stop production, and on dark matter models with a scalar or
pseudo-scalar mediator in which the mediator is produced in association with a
pair of top quarks. Events are selected if they have exactly two leptons with
opposite charge and, in the case of a same-flavour lepton pair, the invariant
mass of the lepton pair must not be close to the $Z$ mass. Events must also
have at least two jets, at least one $b$-tagged jet and a moderate amount of
missing transverse momentum. Signal regions are defined in bins of three
variables: two variants of $m_{\text{T2}}$, and $E_{\text{T}}^{\text{miss}}$,
giving 13 signal regions, which are further split into 26 regions by
separating events with same-flavour and different-flavour lepton pair. Our
analysis includes all 26 signal regions, plus makes use of the covariance
matrix provided by the CMS collaboration to account for the correlated
background uncertainties.

The CMS search for charginos and neutralinos in final states with two low-
momentum opposite-charge leptons CMS:2018kag : This search (CMS_2lep_soft) is
optimised on simplified models of chargino and neutralino production where the
mass difference between the mass-degenerate $\tilde{\chi}_{2}^{0}$ and
$\tilde{\chi}_{1}^{\pm}$ and the $\tilde{\chi}_{1}^{0}$ is small, such that
decays proceed via off-shell $W$ and $Z$ bosons. A separate series of signal
regions targets stop production. Selected events in both cases must contain
two opposite-charge leptons (of either the same or different flavour) with a
low transverse momentum, moderate $E_{\text{T}}^{\text{miss}}$ and at least
one jet. No $b$-tagged jets must be present and further selections are applied
to variables such as the invariant mass and transverse momentum of the
dilepton pair, $E_{\text{T}}^{\text{miss}}/H_{\text{T}}$, $H_{\text{T}}$ and
the transverse masses form from the leptons and the missing transverse
momentum. For the electroweakino search, signal regions are defined in bins of
$E_{\text{T}}^{\text{miss}}$ and the dilepton invariant mass. For the stop
search, signal regions are defined in bins of $E_{\text{T}}^{\text{miss}}$ and
the transverse momentum of the leptons. We implement all of the signal regions
in our analysis, and treat the correlated background uncertainties using the
covariance matrices provided by CMS.

The CMS search for supersymmetry in final states with two opposite-sign same-
flavour leptons and missing transverse energy CMS:2020bfa : This search
(CMS_2OSlep) is optimised on various simplified models of gluino, squark,
slepton and electroweakino production, and targets three potential signatures:
1) an excess of events with a lepton pair, whose invariant mass is consistent
with the $Z$ boson mass, 2) a kinematic edge in the invariant mass
distribution of the lepton pair and 3) non-resonant production of two leptons.
A set of strong production signal regions is defined using selections on the
jet and $b$-jet multiplicities, $H_{\text{T}}$, a variant of $m_{\text{T2}}$
and $E_{\text{T}}^{\text{miss}}$, with the signal regions binned in the latter
of these variables. On-$Z$ electroweak production signal regions are defined
using selections on the jet and $b$-jet multiplicities, the dijet invariant
mass (sometimes defined using the $b$-jets), two different variants of
$m_{\text{T2}}$ and $E_{\text{T}}^{\text{miss}}$. In addition, a set of
boosted signal regions is defined by requiring that there is a large radius
jet with $p_{T}>200$ GeV, consistent with a hadronically-decaying gauge boson.
For the dilepton edge search, a first approach is based on a fit to the
dilepton invariant mass using events that pass selections on $m_{\text{T2}}$
and $E_{\text{T}}^{\text{miss}}$. A second approach uses counts in various
bins of $E_{\text{T}}^{\text{miss}}$, after applying other selections on
$m_{\text{T2}}$ and the jet and $b$-jet multiplicities. An additional
requirement is placed on a novel variable that characterises how
“$t\bar{t}$-like” the events are. Finally, a set of slepton search regions are
defined using selections on the jet and $b$-jet multiplicities,
$m_{\text{T2}}$, $E_{\text{T}}^{\text{miss}}$ and the ratio of the transverse
momenta of the sub-leading lepton with the leading jet. Our implementation
includes all signal regions except the edge fit regions, due to difficulty of
implementing these outside of the CMS collaboration. We use the covariance
matrices provided by CMS to account for correlated background uncertainties.

The CMS search for charginos and stops in final states with two opposite-
charge leptons CMS:2018xqw : This search (CMS_2OSlep_chargino_stop) is
optimised on various simplified models of chargino and stop production and
decay. Events are selected if they contain two opposite-charge electrons or
muons, plus missing transverse momentum. For events with a same-flavour lepton
pair, the invariant mass of the dilepton pair must not be close to the $Z$
mass. For the chargino search, signal regions are defined in bins of the
$E_{\text{T}}^{\text{miss}}$, number of $b$-tagged jets, number of jets, same-
flavour or different-flavour status of the leptons and $m_{\text{T2}}$. For
the stop search, an extra requirement is added on the number of “ISR jets”,
defined as jets with $p_{\text{T}}>$150 GeV and no $b$-tag. We implement all
of the chargino and stop regions, and make use of the covariance matrices
provided by the CMS collaboration.

The CMS search for beyond-Standard Model physics in final states with jets and
two same-sign or at least three charged leptons CMS:2020cpy : This search
(CMS_2SSlep_stop) is optimised on various simplified models of gluino
production and decay, including both R-parity conserving and violating
processes. Six exclusive categories of events are defined using preliminary
selections on the lepton multiplicity and charge, plus
$E_{\text{T}}^{\text{miss}}$. For events with two leptons, the leptons must
have the same sign. For events with at least three charged leptons, separate
categories are defined for the cases where there either is or is not an
opposite-sign same-flavour pair with an invariant mass consistent with the $Z$
boson mass. The main search is performed using a very large number of binned
regions, and we instead implement the set of 17 inclusive signal regions
(labels ISR1–ISR17) that are designed for easier interpretation of the
results. These are defined in bins of the minimum transverse mass formed from
either of the leptons and the missing transverse momentum,
$E_{\text{T}}^{\text{miss}}$, the jet and $b$-tagged jet multiplicities and
$H_{\text{T}}$.

The CMS search for electroweak production of charginos and neutralinos in
final states with three or four leptons, up to two hadronically-decaying
$\tau$ leptons or two same-sign light leptons CMS:2021cox-fix : This search
(CMS_MultiLep) is optimised on a broad range of simplified models of chargino
and neutralino production, including
$\tilde{\chi_{2}}^{0}\tilde{\chi_{1}}^{\pm}$ production with decays to
lightest neutralinos via intermediate sleptons or with Higgs, $W$ or $Z$
bosons, and $\tilde{\chi_{1}}^{0}\tilde{\chi_{1}}^{0}$ production with decays
to gravitinos and $Z$ or Higgs bosons. A number of event categories are
defined in the analysis, based on the lepton multiplicity, whether there is a
same-sign lepton pair or same-flavour-opposite-sign lepton pair, and the
hadronically-decaying $\tau$ lepton multiplicity. The analysis is performed
using a large number of binned signal regions for each category. The key
variables used are various variants of $m_{\text{T2}}$, the transverse
momentum of the dilepton system in 2 lepton events,
$E_{\text{T}}^{\text{miss}}$, the dilepton invariant mass of same-flavour-
opposite-sign lepton pairs, the transverse mass formed from the trilepton
system, dilepton system or a single lepton and the missing transverse energy
vector, $H_{\text{T}}$, the $\Delta R$ separation between leptons, and the
invariant mass formed from a light lepton and a hadronically-decaying $\tau$
lepton. Our analysis includes the signal regions labelled SS01–SS20 (two same-
sign leptons), A01–A64 (three leptons, one SFOS pair), B01–B03 (three leptons,
no SFOS pair), G01–G05 (four leptons, two SFOS pairs) and H01–H03 (four
leptons, one or zero SFOS pairs).

The CMS search for gauge-mediated supersymmetry in events with at least one
photon and missing transverse momentum CMS:2017brl : This search (CMS_photon)
is optimised on various simplified models of gauge-mediated supersymmetry
breaking, in which neutralinos and charginos decay to produce gravitinos and
photons, as well as $Z$, $W$ and Higgs bosons. Events are required to contain
at least one high-energy photon plus large missing transverse momentum. The
signal regions feature common selections on the transverse mass formed from
the missing transverse momentum and the photon, and the
$E_{\text{T}}^{\text{miss}}$. After these selections, four signal regions are
defined as bins in $S_{\text{T}}^{\gamma}$, the scalar sum of
$E_{\text{T}}^{\text{miss}}$ and the $p_{\text{T}}$ of all photons in the
event. We implement all four signal regions in our analysis.

The CMS search for gauge-mediated supersymmetry in events with two photons and
missing transverse momentum CMS:2019vzo : This search (CMS_2photon) is
optimised on simplified models of squark and gluino production, with cascade
decays terminating in lightest neutralinos that always decay to a photon and a
gravitino. Events are required to have two photons and large missing
transverse momentum, and to satisfy various selections on their
electromagnetic activity. Six signal regions are defined by selecting
different ranges of $E_{\text{T}}^{\text{miss}}$, and all of these are
implemented in our analysis.

The CMS search for gauge-mediated supersymmetry in events with a photon, an
electron or muon and large missing transverse momentum CMS:2018fon : This
search (CMS_1photon_1lepton) is optimised on simplified models of gauge-
mediated supersymmetry breaking that include gluino and quark production, plus
direct production of neutralinos and charginos. Events are required to have at
least one photon and at least one electron or muon. In the case of more than
one light lepton, the lepton with the highest transverse momentum is used in
the analysis. Selections are placed on the transverse mass formed from the
lepton plus missing transverse momentum, and the $E_{\text{T}}^{\text{miss}}$,
and multiple signal regions are defined in bins of
$E_{\text{T}}^{\text{miss}}$, the transverse momentum of the photon and
$H_{\text{T}}$ (defined as the scalar sum of the jet $p_{\text{T}}$ values in
the event). The CMS search defines 18 signal regions per lepton channel (i.e.
electron or muon), and we implement all regions in our analysis.

##  Appendix C Code extensions

In this Appendix we describe the extensions to the GAMBIT framework introduced
for this study, and how to use them. See Refs. gambit ; GUM  for a general
introduction to the GAMBIT framework and Ref. ColliderBit  for an introduction
to the ColliderBit module.

###  C.1 GAMBIT models with a light gravitino

The first modification is the addition of a new family of models MSSMXatY_mG,
mirroring the existing family of MSSM models MSSMXatY in GAMBIT, supplemented
with a new parameter mG which codifies the mass of a light gravitino. As in
the existing MSSMXatY models, X refers to the number of parameters and Y to
the scale at which the parameters are defined (which itself could be a
parameter in MSSMXatQ models) (e.g. MSSM30atMGUT has 30 parameters defined at
the GUT scale). Models with alternate parametrisation are labelled with
increasing alphabetical letters after the number of parameters (e.g.
MSSM10batQ) or in the specific case of reparametrisation with $m_{A}$ and
$\mu$ instead of $m_{H_{u}}$ and $m_{H_{d}}$, models are labelled with the
suffix _mA (e.g. MSSM30atMGUT_mA. The specific model used in the study is the
MSSM11atQ_mA_mG, defined as

MSSM11atQ_mA_mG:

M1, M2, mu, TanBeta, Ad_3, Ae_3, Au_3, M3, Qin, mA, mG, ml2, mq2

An MSSM parametrisation with 11 parameters plus a gravitino mass mG, of which
we vary only four in this study: TanBeta, M1, M2 and mu. We fix the other
parameters to mG = 1 eV, Ad_3 = Ae_3 = Au_3 = 0, M3 = mA = 5 TeV and ml2 = mq2
= (3 TeV)2, to decouple all superpartners other than the electroweakinos and
the gravtino from the low energy phenomenology. The input parameters are
defined at a scale Qin = 3 TeV. We choose to use a model parametrised with mA
and mu instead of mHu2 and mHd2, as $\mu$ controls the Higgsino masses.

###  C.2 Additions to DecayBit

Table 3: Capabilities and module functions added to DecayBit for this study.
The

Capability Function (type) Dependencies [type] /
Backend reqs [type (args)] neutralino_i_decay_rates_gravitino
neutralino_i_decays_gravitino (DecayTable::Entry) MSSM_spectrum [Spectrum]
Z_decay_rates [DecayTable::Entry] chargino_j_decay_rates_gravitino
chargino_j_decays_gravitino (DecayTable::Entry) MSSM_spectrum [Spectrum]
W_plus_decay_rates [DecayTable::Entry] neutralino_i_decay_rates
neutralino_i_decays_all (DecayTable::Entry) neutralino_i_decay_rates_gravitino
[DecayTable::Entry]
neutralino_i_decay_rates_SH [DecayTable::Entry] chargino_j_decay_rates
chargino_j_decays_all (DecayTable::Entry) chargino_j_decay_rates_gravitino