Eur. Phys. J. C (2020) 80:531 https://doi.org/10.1140/epjc/s10052-020-8076-6
Special Article - Tools for Experiment and Theory
Reinterpreting the results of the LHC with MadAnalysis 5:uncertainties and higher-luminosity estimates
Jack Y. Araz1,a , Mariana Frank1,b , Benjamin Fuks2,3,c
1 Concordia University, 7141 Sherbrooke St. West, Montréal, QC H4B 1R6, Canada2 Laboratoire de Physique Théorique et Hautes Energies (LPTHE), UMR 7589, Sorbonne Université et CNRS, 4 place Jussieu,
75252 Paris Cedex 05, France3 Institut Universitaire de France, 103 boulevard Saint-Michel, 75005 Paris, France
Abstract The MadAnalysis 5 framework can be usedto assess the potential of various LHC analyses for unravel-ing any specific new physics signal. We present an extensionof the LHC reinterpretation capabilities of the programmeallowing for the inclusion of theoretical and systematicaluncertainties on the signal in the reinterpretation procedure.We have implemented extra methods dedicated to the extrap-olation of the impact of a given analysis to higher lumi-nosities, including various options for the treatment of theerrors. As an application, we study three classes of newphysics models. We first focus on a simplified model inwhich the Standard Model is supplemented by a gluino anda neutralino. We show that uncertainties could in particulardegrade the bounds by several hundreds of GeV when consid-ering 3000/fb of future LHC data. We next investigate anothersupersymmetry-inspired simplified model, in which the Stan-dard Model is extended by a first generation squark speciesand a neutralino. We reach similar conclusions. Finally, westudy a class of s-channel dark matter setups and comparethe expectation for two types of scenarios differing in thedetails of the implementation of the mediation between thedark and Standard Model sectors.
1 Introduction
The discovery of the Higgs boson has accomplished one ofthe long awaited objectives of the LHC physics programmeand confirmed our understanding of the fundamental laws ofnature. However, the concrete realisation of the electroweaksymmetry breaking mechanism remains unexplained and
no evidence for physics beyond the Standard Model (SM),whose existence is motivated by the SM theoretical incon-sistencies and limitations, has emerged from data. There aretwo classes of possible explanations as to why the associatednew particles and/or interactions have escaped detection sofar. The first one is that the new states are too heavy and/orthe new interactions too feeble to be observed with presentcollider reaches. Alternatively, new particles may be hidingjust around the corner, but lie in a specific configuration (likebeing organised in a compressed spectrum) that renders theirdiscovery challenging. The possible observation of any newphenomena therefore is the foremost goal of the future LHCruns, including in particular the LHC Run 3, to be startedin two years, and the high-luminosity operations planned tobegin in half a decade.
In order to investigate whether new physics could bepresent in existing data, several groups have developed andmaintained public software dedicated to the reinterpretationof the results at the LHC [1–5]. In practice, these tools relyon predictions detailing how the different signal regions ofgiven LHC analyses are populated to derive the potential ofthese searches for its observation. However, signal uncer-tainties are in general ignored by users in this procedure,although they could sometimes lead to incorrect interpreta-tions [6]. With the limits on the masses of any hypotheticalparticle being pushed to higher and higher scales, the theo-retical uncertainties related with the new physics signals canmoreover sometimes be quite severe, in particular if the asso-ciated scale and Bjorken-x value lead to probing the partondensities in a regime in which they are poorly constrained [7].
On the other hand, it would be valuable to get estimatesof the capabilities of the future runs of the LHC with respectto a given signal, possibly on the basis of the interpretationof the results of existing analyses of current data. Predictionsin which the signal and the background are naively scaled
up could hence be useful to obtain an initial guidance on thereach of future collider setups within new physics parameterspaces.
In this paper, we address the above mentioned issuesby presenting an extension of the recasting capabilities ofthe MadAnalysis 5 platform [3,8] so that signal theoret-ical and systematics uncertainties could be included in therecasting procedure. Moreover, we show how the reinterpre-tation results, with uncertainties included, could be correctlyextrapolated to different luminosities to get insight on thesensitivity of the future LHC data on given signals.
As an illustration of these new features within concretecases, we consider several classes of widely used simplifiedmodels. We first extract bounds on various model param-eters from recent LHC results. Next, we study how thoseconstraints are expected to evolve with the upcoming high-luminosity run of the LHC through a naive rescaling of thesignal and background predictions. In practice, we make useof the recasting capabilities of MadAnalysis 5 and pay aspecial attention to the theoretical uncertainties.
We begin with a simplified model inspired by the MinimalSupersymmetric Standard Model (MSSM) in which the SMis complemented by a gluino and a neutralino, all other super-partners being assumed heavy and decoupled [9,10]. Such aparticle spectrum leads to a signature comprised of jets andmissing transverse energy originating from the gluino decaysinto an invisible neutralino and quarks. We reinterpret theresults of corresponding ATLAS searches for the signal in36 fb−1 [11] and 139 fb−1 [12] of LHC data. We investigatethe impact of the theory errors on the derived bounds at thenominal luminosity of the search, and extrapolate the find-ings to estimate the outcome of similar searches analysing300 and 3000 fb−1 of LHC data. Secondly, we make use ofthese recent LHC searches to perform an equivalent exer-cise in the context of a simplified model in which the SMis extended by a single species of first generation squarksand a neutralino [9,10]. Such a spectrum also leads to a newphysics signature made of jets and missing transverse energy,although the squark colour triplet nature yields a signal fea-turing a smaller jet multiplicity. As the considered ATLASstudy includes a large set of signal regions each dedicatedto a different jet multiplicity, it is sensitive to this simplifiedmodel that has moreover not been covered the result inter-pretations performed in the experimental publication.
As a last example, we study the phenomenology of a sim-plified dark matter model in which a Dirac fermion darkmatter candidate couples to the SM via interactions with ans-channel spin-1 mediator [13,14]. This model is known to bereachable via standard LHC monojet and multijet plus miss-ing transverse energy searches for dark matter. We extractup-to-date bounds on the model by reinterpreting the resultsof the ATLAS search of Ref. [12] that analyses the full Run 2ATLAS dataset. This search includes signal regions dedi-
cated to both the monojet and the multijet plus missing energysignatures, so that it consists in an excellent probe for darkmatter models. We focus on two specific configurations ofour generic simplified models in which the mediator coupleswith the same strength to the dark and SM sectors. In thefirst case, we consider mediator couplings of a vector nature,whilst in the second case, we focus on axial-vector mediatorcouplings. We investigate how the bounds evolve with theluminosity for various dark matter and mediator masses andthe nature of the new physics couplings.
The rest of this paper is organised as follows. We discussthe details of the recasting capabilities of MadAnalysis 5
in Sect. 2, focusing not only on the new features that havebeen implemented in the context of this work, but also onhow the code should be used for LHC recasting. We thenapply it to extracting gluino and neutralino mass limits inSect. 3 for various luminosities of LHC data. We analyse thesquark/neutralino simplified model in Sect. 4 and performour dark matter analysis in Sect. 5. We summarise our workand conclude in Sect. 6.
2 LHC recasting withMadAnalysis 5
The MadAnalysis 5 package [15,16] is a framework ded-icated to new physics phenomenology. Whilst the first aimof the programme was to facilitate the design and the imple-mentation of analyses targeting a given collider signal ofphysics beyond the Standard Model, and how to unravel itfrom the background, more recently it has been extended byLHC reinterpretation capabilities [3,8]. This feature allowsthe user to derive the sensitivity of the LHC to any collidersignal obtained by matching hard-scattering matrix elementswith parton showers, based on the ensemble of analyses thathave implemented in the MadAnalysis 5 Public Analysisdatabase (PAD) [3].1 For each of these analyses, the codesimulates the experimental strategies (which includes boththe simulation of the detector response and the selection)to predict the number of signal events that should populatethe analysis signal regions. It then compares the results withboth data and the SM expectation, so that conclusive state-ments could be drawn. As in all recasting codes relying on thesame method [2,4,5], the uncertainty on the signal is ignoredalthough it could be relevant [7].
With the release of MadAnalysis 5 version v1.8, theuser has now the possibility to deal with various classes ofsignal uncertainties and to extrapolate any reinterpretationresult to higher luminosities. This section documents all thesenew functionalities. Section 2.1 briefly summarises how toinstall MadAnalysis 5, get the code running and down-
1 See the webpage https://madanalysis.irmp.ucl.ac.be/wiki/PublicAnalysisDatabase.
load a local copy of its public analysis database. Section 2.2details how the code can be used to reinterpret the results ofa specific LHC analysis. A more extensive and longer ver-sion of this information onMadAnalysis 5 installation andrunning procedures can be found in Ref. [8]. Section 2.3 isdedicated to the new methods that have been developed inthe context of this work, and which are available from Mad-
Analysis 5 version v1.8 onwards. We also introduce in thissection several new optional features that can be used for thedesign of the analysis .info files. One such file accompa-nies each analysis of the database and contains informationon the observation and the SM expectation of the differentanalysis signal regions. In Sect. 2.4, we describe the corre-sponding modifications of the output format relevant for arecasting run of MadAnalysis 5.
2.1 Prerequisites and installation
MadAnalysis 5 is compatible with most recent Unix-based operating systems, and requires the GNU G++ orCLang compiler, a Python 2.7 installation (or more recent,but not a Python 3 one) and GMake. In order for the recast-ing functionalities to be enabled, the user must ensure that theSciPy library is present, as it allows for limit computations,and that the Delphes 3 package [17] is locally availablewithin the MadAnalysis 5 installation. The latter, whichrequires the Root framework [18] and the FastJet pro-gramme [19], is internally called by MadAnalysis 5 todeal with the simulation of the response of the LHC detec-tors and to reconstruct the events. Moreover, reading com-pressed event files can only be performed if the Zlib libraryis available.
The latest version ofMadAnalysis 5 can be downloadedfrom LaunchPad,2 where it is provided as a tarball namedma5_v < xxx > .tgz, that contains all MadAnalysis 5
source files (< xxx > standing for the version number).After unpacking the tarball, the code can be started by issuingin a shell
./bin/ma5 -R
where the -R options enforces the reco mode of Mad-
Analysis 5, that is relevant for LHC recasting. The pro-gramme begins with checking the presence of all mandatorypackages and determining which of the optional packages areavailable. The MadAnalysis 5 command-line interface isthen initialised and the user is prompted to type in commands.
In the case where any of the Zlib or Delphes 3 pack-age would not be found by MadAnalysis 5, they can beinstalled locally by typing, directly in the MadAnalysis 5
interpreter,
2 See the webpage https://launchpad.net/madanalysis5.
install zlibinstall delphes
Whilst Root can in principle be installed similarly, we rec-ommend the user to handle this manually, following theinstructions available on the Root website.3 Furthermore,all existing and validated recast LHC analyses in the Mad-
Analysis 5 framework can be locally downloaded by typingin,
install PADinstall PADForMA5tune
The second command triggers the installation of olderimplemented analyses, that requires a (now disfavoured)MA5tune version of Delphes 3. The latter can be installedby typing, in the MadAnalysis 5 shell,
install delphesForMA5tune
2.2 Recasting LHC analyses with MadAnalysis 5
In this section, we rely on a generic example in which a useraims to estimate the sensitivity of a specific LHC analysis toa given signal with MadAnalysis 5. The analysis consistsof one of the analyses available from the PAD and the signalis described by simulated events collected into a file that wecall events.hepmc.gz. Such an event file includes thesimulation of the considered hard-scattering process matchedwith parton showers, as well as the hadronisation of the final-state partons present in each of the showered events.
As mentioned above, MadAnalysis 5 has to be startedin the reco mode,
./bin/ma5 -R
In a first step, the recasting mode of the programme hasto be enabled and the event file, physically located at<path-to-events.hepmc.gz> on the user system,has to be imported. This is achieved by issuing the commands
set main.recast = onimport <path-to-events.hepmc.gz> \
as <label>
The second command defines a dataset identified by the label<label> that here solely includes the imported sample.Several event files can be imported and collected either undera unique dataset (by using the same <label> for each callto the import command) or split into different datasets (byemploying different labels). When studying the signal underconsideration, MadAnalysis 5 will run over all defineddatasets and imported event files.
In addition, the user can activate the storage of the Root
file(s) generated by Delphes 3 by issuing the command,
where < status > can take the True or False value,and directly provide a predefined recasting card (availableon the system at < path − to − a − card >), through
set main.recast.card_path = \<path-to-a-card>
In the case where no card is provided, MadAnalysis 5
creates a consistent new card with one entry for each of theavailable analyses. Such an entry is of the form
<tag> <type> <switch> <detector> # <comment>
The <tag> label corresponds to the filename of the C++code associated with the considered analysis (located inthe Build/SampleAnalyzer/User/Analyzer sub-directory of the PAD installation in tools/PAD), the<type> label indicates whether the PADForMA5tune(v1.1) or PAD (v1.2) recasting infrastructure should beused and the <switch> tag (to be set to on or off)drives whether the analysis has to be recast. The name ofthe Delphes 3 card to use (see the Input/Cards subdi-rectory of the PAD installation) is passed as <detector>,and <comment> consists of an optional comment (usuallybriefly describing the analysis).
The run is finally started by typing in the interpreter,
submit
Firstly, MadAnalysis 5 simulates the detector impact onthe input events, for each of the necessary Delphes 3 cardsaccording to the analyses that have been switched on in therecasting card. Next, the code derives how the different sig-nal regions are populated by the signal events and finallycomputes, by means of the CLs prescription [20], the cor-responding exclusion limits, signal region by signal region.This is achieved by a comparison of the results with the infor-mation on the SM background and data available from thedifferent info files shipped with the PAD.
The output information is collected into a folder namedANALYSIS_X, whereX stands for the next available positiveinteger (in terms of non-existing directories). On top of basicdetails about the run itself, this folder contains the recast-ing results that are located in the ANALYSIS_X/Outputfolder. The latter includes the CLs_output_summary.dat file that concisely summarises all the results of therun. A more extensive version of these results can be foundin the set of subfolders named after the labels of the importeddatasets. The CLs_output_summary.dat file containsone line for each signal region of each reinterpreted analysis,and this for each of the datasets under consideration. Each ofthese lines follows the format
<set> <tag> <SR> <exp> <obs> || <eff> <stat>
where the <set> and <tag> elements respectively con-sist in the names of the dataset and analysis relevant for theconsidered line of the output file. The <SR> entry relates toone of the analysis signal regions, the exact name being theone defined in the analysis C++ source code. The <exp>and <obs> quantities are the expected and observed cross-section values for which the signal modelled by the eventsstored within the dataset <set> is excluded by the signalregion <SR> of the analysis <tag> at the 95% confidencelevel. In the former case, the code makes use of the SM expec-tation to predict the number of events populating the signalregion <SR>, whilst in the latter case, data is used. Finally,the <eff> and <stat> entries respectively refer to the cor-responding selection efficiency and the associated statisticalerror.
The user has the option to specify the cross section corre-sponding to the investigated signal by issuing, in the Mad-
Analysis 5 interpreter,
set <label>.xsection = <value>
prior to the call to the submit command. Following thissyntax, <label> stands for one of the labels of the consid-ered datasets and <value> for the associated cross-sectionvalue, in pb. In this case, the confidence level at which theanalysed signal is excluded is included in the output summaryfile (before the double vertical line).
The Output folder additionally contains a specific sub-folder for each of the defined datasets. Such a directorycontains a file named CLs_output.dat that includes thesame information as in the CLs_output_summary.datfile, following the same syntax, but restricted to a specificdataset. A second file encoded into the SAF format [15]and named <label>.saf (<label> being the datasetname) contains general information on the dataset organisedaccording to an XML-like structure. The latter relies on threeclasses of elements, namely <SampleGlobalInfo>,<FileInfo> and <SampleDetailedInfo>. The firstof these contains global information on the dataset, such asits cross section (xsec), the associated error (xsec_err),the number of events (nev) or the sum of the positive andnegative event weights (sum_w and sum_w-). The corre-sponding entry in the output file would read
where the numerical values have been omitted for clar-ity. The <FileInfo> element sequentially provides thepaths to the different event files included in the dataset,while detailed information on each file is provided withinthe <SampleDetailedInfo> XML root element, in a
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similar manner as for the sample global information (withone line for each file).
Furthermore, the dataset output directory includes aRecoEvents folder dedicated to the storage of Delphes 3
output files (one file for each considered detector param-eterisation), provided that the corresponding option hasbeen turned on (see above), as well as one folder foreach of the recast analyses. Each of these folders containsone SAF file listing all signal regions implemented in theassociated analysis, as well as two subfolders Cutflowsand Histograms. The former includes one SAF filefor each signal region, and the latter a single file namedhistos.saf.
A cutflow is organised through XML-like elements,<InitialCounter> and<Counter> being used for theinitial number of events and the results of each selection cutrespectively. As depicted by the example below, in which allnumbers have been omitted for clarity,
<Counter>"my_cut_name" # 1st cut.... .... # nentries.... .... # sum of weights.... .... # sum of weightsˆ2</Counter>
any of such elements includes a cut name as defined in theanalysis C++ file (first line), the number of events passingthe cut (second line), the weighted number of events passingthe cut (third line) and the sum of the squared weights ofall events passing the cut (last line). Moreover, the first (sec-ond) column refers to the positively-weighted (negatively-weighted) events only.
Histograms are all collected into the file histos.saf,that is also organised according to an XML-like structurerelying on several <Histo> elements. Each of these corre-sponds to one of the histograms implemented in the analy-sis. A <Histo> element includes the definition of the his-togram (provided within the <Description> element),general statistics (as part of the <Statistics> element)and the histogram data itself (within the <Data> element).The description of a histogram schematically reads
<Description>"name"# nbins xmin xmax
.. ... ...# Defined regions
... # Region nr. 1
... # Region nr. 2</Description>
and is self-explanatory, all numbers having been replaced bydots. This moreover shows that a given histogram can be asso-ciated with several signal regions, provided they are indis-
tinguishable at the moment the histogram is filled. Statisticsare typically given as
<Statistics>... ... # nevents... ... # sum of event-weights over events... ... # nentries... ... # sum of event-weights over entries... ... # sum weightsˆ2... ... # sum value*weight... ... # sum valueˆ2*weight
</Statistics>
which include information about the number of entries,the weighted number of entries, the variance, etc. Moreover,the contributions of the positively-weighted and negatively-weighted events are again split and provided within the firstand second column respectively. The values of each bin arefinally available from the <Data> element,
<Data>... ... # underflow... ... # bin 1 / 15
.
.
.... ... # bin 15 / 15... ... # overflow
</Data>
where all bin values are omitted and the two columns respec-tively refer to events with positive (first column) and negative(second column) weights. The underflow and overflow binsare also included.
To close this section, we detail below how limits on agiven signal are derived by MadAnalysis 5, using the CLs
prescription. The output file generated by the code containsthree numbers associated with those limits, the expected andobserved cross sections excluded at the 95% confidence level,σ
exp95 and σ obs
95 , as well as the confidence level at which theinput signal is excluded. Those numbers are extracted onthe basis of the information available from the .info file,shipped with each recast analysis and that contains, for eachsignal region, the number of expected SM events nb, the asso-ciated error Δnb and the observed number of events popu-lating the signal region nobs. As said above, starting fromthe input event file, MadAnalysis 5 simulates the responseof the LHC detector, applies the analysis selection, and esti-mates how the different signal regions are populated. In thisway, for each signal region, the number of signal events nsis known.
This enables the computation of the background-only andsignal-plus-background probabilities pb and pb+s and to fur-ther derive the related CLs exclusion. In practice, the codeconsiders a number of toy experiments (the default being
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100000 that can be changed by issuing, in the MadAnaly-
sis 5 interpreter and before the call to the submit method,
set main.recast.CLs_numofexps = \<value>
where <value> stands for the desired number of toy exper-iments. For each toy experiment, the expected number ofbackground events Nb is randomly chosen assuming that itsdistribution is Gaussian, with a mean nb and a width Δnb.The corresponding probability density thus reads
f (Nb|nb,Δnb) =exp
{− (Nb−nb)2
2Δn2b
}
Δnb√
2π. (1)
Imposing Nb ≥ 0, the actual number of background eventsNb is randomly generated from the Poisson distribution
f (Nb|Nb) = N Nbb e−Nb
Nb!. (2)
Accounting for the observation of nobs events, pb is definedas the percentile of score associated with Nb ≤ nobs, whichconsists in the probability for the background to fluctuate aslow as nobs.
The signal-plus-background probability pb+s is computedsimilarly, assuming that the actual number of signal-plus-background events Nb + Ns follows a Poisson distribution ofparameter ns+Nb (after imposing this time that Nb+ns > 0).The resulting CLs exclusion is then derived as
CLs = max(
0, 1 − pb+s
pb
). (3)
and σ obs95 is calculated as above in a case where the number of
signal events ns is kept free. From the (derived) knowledgeof the analysis selection efficiencies, MadAnalysis 5 canextract the upper allowed cross section value for which thesignal is not excluded, i.e. σ obs
95 . The expected cross sectionexcluded at the 95% confidence level, σ
exp95 , is obtained by
replacing nobs by nb in the above calculations.
2.3 Including signal uncertainties and extrapolation tohigher luminosities
In the procedure described in the previous section, any erroron the signal is ignored, both concerning the usual theoryuncertainties (scale variations, parton densities) and the sys-tematics, mostly stemming from more experimental aspects.In particular, with the constantly growing mass bounds onhypothetical new particles, the scale entering the relevanthard-scattering processes is larger and larger, so that theo-retical errors could start to impact the derived limits in animportant and non-negligible manner.
Starting from version v1.8 onwards, MadAnalysis 5
offers the user a way to account for both the theoretical and
systematical errors on the signal when a limit calculation isperformed. The scale and parton density (PDF) uncertaintiescan be entered, within the MadAnalysis 5 interpreter, sim-ilarly to the cross section associated with a given dataset (seeSect. 2.2),
set <label>.xsection = <xsec_val>set <label>.scale_variation = <scale>set <label>.pdf_variation = <pdf>
where <label> stands for the label defining the sig-nal dataset. In this case, the signal cross section σs isprovided through the xsection attribute of the dataset,as described in the previous section, while the scale andparton density uncertainties Δσscales and ΔσPDF are giventhrough the scale_variation and pdf_variationattributes. The errors are symmetric with respect to the cen-tral value σs , and their value (given by<scale> and<pdf>in the above example) must be inputted as the absolute val-ues of the relative errors on the cross section (i.e. as positivefloating-point numbers). Asymmetric errors can also be pro-vided, the upper and lower uncertainties being independentlyfixed by issuing, in the MadAnalysis 5 interpreter,
Each error is again provided as a positive floating-pointnumber and refers to the relative error on the cross section, inabsolute value. On top of the computation of the confidencelevel at which the signal is excluded, MadAnalysis 5 addi-tionally calculates the CLs variation band associated with thescale uncertainties, as well as with the total theory uncertain-ties where both the scale and PDF contributions to the totalerror are added linearly. Such a behaviour can however bemodified by issuing, in the interpreter
set main.recast.THerror_combination = \<value>
where <value> can be set either to quadratic (the the-ory errors are added quadratically) or linear (default,the theory errors are added linearly). The CLs band is thenderived by allowing the signal cross section to vary withinits error band, deriving the associated spread on pb+s.
The user can also specify one or more values for the levelof systematics on the signal. This is achieved by issuing, inthe command line interface,
set main.recast.add.systematics = \<syst>
This command can be reissued as many times as needed,MadAnalysis 5 taking care of the limit calculation foreach entered value independently. The level of systematics
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(<syst>) has to be given either as a floating-point numberlying in the [0, 1] range, or as a pair of floating-point num-bers lying in the same interval. In the former case, the error issymmetric with respect to the central value σs , whilst in thelatter case, it is asymmetric with the first value being associ-ated with the upper error and the second one with the lowererror.
In addition, we have also extended the code so that naiveextrapolations for a different luminosity Lnew could be per-formed. This is achieved by typing, in the interpreter,
set main.recast.add.extrapolated_luminosity \=<lumi>
Once again, the user has the possibility to reissue the com-mand several times, so that the extrapolation will be per-formed for each luminosity <lumi> independently (wherethe value has to be provided in fb−1). Those extrapolationsassume that the signal and background selection efficien-cies of a given region in a specific analysis are identical tothose corresponding to the reference luminosity L0 initiallyconsidered. In this framework, the extrapolated number ofbackground events nnew
b is related to nb (the number of back-ground events expected for the reference luminosity L0) as
nnewb = nb
Lnew
L0, (4)
that we assume equal to the extrapolated number of observedevents,
nnewobs = nnew
b . (5)
On the other hand, the associated uncertainties, Δnnewb , are
derived from the relation
Δnnewb = Δb,syst
Lnew
L0⊕ Δb,stat
√Lnew
L0, (6)
where the statistics and systematics components are added inquadrature. The systematics are extrapolated linearly, whilstthe statistical uncertainties assume that the event counts fol-low a Poisson distribution. Such an extrapolation of the back-ground error requires an access to the details of the back-ground uncertainties. This is however not achievable withinthe XML info file format dedicated to the transfer of thebackground and data information to MadAnalysis 5 [3].We therefore introduce two new XML elements to thisformat, namely deltanb_stat and deltanb_syst.These offer the user the option to implement his/her infofileby either providing a unique combined value for the uncer-tainties (via the standard deltanb XML element) or bysplitting them into their statistical and systematical com-ponents (via a joint use of the new deltanb_stat anddeltanb_syst XML elements). In this way, a region ele-ment could be either implemented according to the old syn-
tax, as in the schematic example below (with all numbersomitted),
Whilst the usage of the new syntax is encouraged, this newpossibility for embedding the error information stronglydepends on how the background uncertainties are providedin the experimental analysis notes. For this reason, as well asfor backward-compatibility, MadAnalysis 5 supports bothchoices. If only a global error is provided, the user can freelychoose how to scale the error (linearly or in a Poisson way),by typing in the interpreter,
set main.recast.error_extrapolation = \<value>
where <value> has to be set either to linear or to sqrt.The user has also the choice to use a single floating-pointnumber for the <value> parameter. In this case, the relativeerror on the number of background events at the new lumi-nosity, Δnnew
b /nnewb , is taken equal to this number. Finally,
the user can provide a comma-separated pair of floating-pointnumbers κ1 and κ2, as in
set main.recast.error_extrapolation = \<k1>,<k2>
The background error is here defined by[Δnnew
b
nnewb
]2
= κ21 + κ2
2
nb, (7)
where the two values provided by the user respectively con-trol the systematical component of the uncertainties (<k1>,κ1) and the statistical one (<k2>, κ2). Finally, all extrapola-tions are based on expectations and not on observations, sothat nobs will be effectively replaced by the correspondingSM expectation nb.
2.4 Output format
MadAnalysis 5 propagates the information on the impactof the uncertainties all through the output file, which
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is then written in a format slightly extending the onepresented in Sect. 2.2. Starting with the summary fileCLs_output_summary.dat, each line (correspondingto a given signal region of a given analysis) is now followedby information schematically written as
Scale var. band [..., ...]TH error band [..., ...]+<lvl_up>%, -<lvl_dn>% syst [..., ...]
The uncertainties on the exclusion stemming from scalevariations are given in the first line, which is trivially omittedif the corresponding information on the signal cross sectionis not provided by the user. In the second line, MadAnaly-
sis 5 adds either quadratically or linearly (according to thechoice of the user) all theory errors, such a line being writtenonly if at least one source of theory uncertainties is providedby the user. Finally, if the user inputted one or more optionsfor the level of systematics, MadAnalysis 5 computes theband resulting from the combination of all errors and writesit into the output file (one line for each choice of level of sys-tematics). In the above snippet, the user fixed an asymmetriclevel of systematics (for the sake of the example) indicatedby the <lvl_up> and <lvl_dn> tags.
In cases where the band would have a vanishing size, theuncertainty information is not written to the output file. Thiscould be due either to negligibly small uncertainties, to thefact that for the considered region, the signal is excludedregardless the level of systematics (at the 100% confidencelevel), or to the region not targeting the signal at all (thecorresponding selection efficiency being close to zero).
The CLs_output.dat dataset-specific files presentin the output subdirectory associated with each importeddataset all contain similar modifications. In case of extrap-olations to different luminosities, copies of this file namedCLs_output_lumi_<lumi>.dat are provided for eachdesired luminosity <lumi>.
3 Gluino and neutralino mass limits
To illustrate the usage of the new functionalities of Mad-
Analysis 5 introduced in the previous section, we per-form several calculations in the context of a simplified modelinspired by the MSSM. In this framework, all superpartnersare heavy and decoupled, with the exception of the gluinog and the lightest neutralino χ0
1 , taken to be bino-like. Anygiven benchmark is thus defined by two parameters, namelythe gluino and the neutralino masses mg and mχ0
1. Such a
new physics setup can typically manifest itself at the LHCthrough a signature made of a large hadronic activity andmissing transverse energy. As shown by the schematic Feyn-man diagram of Fig. 1, such a signature originates from theproduction of a pair of gluinos, each of them promptly decay-
g
g
χ01
χ01
j
j
j
j
P
P
Fig. 1 Generic Feynman diagram associated with the production anddecay of a pair of gluinos in the considered MSSM-inspired gluinosimplified model. The figure has been produced with the help of theJaxoDraw package [21]
ing into two jets and a neutralino (via virtual squark contri-butions).
We study the sensitivity of the LHC and its higher-luminosity upgrades to this signal by analysing state-of-the-art Monte Carlo simulations achieved by means ofthe MG5_aMC framework (version 2.6.6) [22], using theMSSM-NLO model implementation developed in Ref. [7].Hard-scattering matrix elements are generated at the next-to-leading-order (NLO) accuracy in QCD and convoluted withthe NLO set of NNPDF 3.0 parton densities [23], as pro-vided by the LHAPDF interface [24]. The gluino leading-order (LO) decays are handled with the MadSpin [25] andMadWidth [26] packages. The resulting NLO matrix ele-ments are then matched with Pythia parton showers andhadronisation (version 8.240) [27], following the MC@NLOmethod [28]. Our predictions include theoretical uncertain-ties stemming from the independent variations of the renor-malisation and factorisation scales by a factor of two up anddown relatively to the central scale, taken as half the sum ofthe transverse masses of the final-state particles, as well asfrom the parton densities extracted following the recommen-dations of Ref. [29].
In the upper panel of Fig. 2, we present the total LO(red) and NLO (blue) gluino pair-production cross sectionfor gluino masses ranging from 1 to 3 TeV, the error barsbeing associated with the quadratic sum of the scale andPDF uncertainties. The cross section central value is foundto vary within the 100–0.001 fb range when the gluino massvaries from 1 to 3 TeV, so that at least tens of gluino eventscould be expected even for a very heavy gluino benchmark ata high-luminosity upgrade of the LHC. We compare our pre-dictions with the total rates traditionally employed by theATLAS and CMS collaborations to extract gluino limits,as documented by the LHC Supersymmetry Cross SectionWorking Group [30]. Hence we include, in the first panel ofFig. 2, total gluino-pair production cross sections matchingapproximate fixed-order results at next-to-next-to-leading
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Fig. 2 Total LO (red), NLO (blue) and NNLOapprox+NNLL (green)cross sections (upper panel) and K -factors (three lower panels, wherethe results are normalised to the LO central value) for gluino pair-production, at a centre-of-mass energy of
√s = 13 TeV. In the upper
panel, the error bands correspond to the quadratic sum of the scale andPDF uncertainties, whilst in the second and third panels, respectively,they refer to the scale uncertainties on the LO and NLO predictions.The last panel focuses on the PDF errors
order and threshold-resummed predictions at the next-to-next-to-leading logarithmic accuracy (NNLOapprox + NNLL,in green). Following the PDF4LHC recommendations, thosemore accurate NNLOapprox+NNLL predictions are obtainedby convoluting the partonic cross section with a combinationof NLO CTEQ6.6M [31] and MSTW2008 [32] densities.This choice, together with the impact of the higher-order cor-rections, leads to NNLOapprox+NNLL results greater than ourNLO predictions by a factor of about 2. While in the follow-ing we use NLO-accurate total rates (as the latter exist for anynew physics model through a joint use of FeynRules [33],NLOCT [34] and MG5_aMC), we evaluate the impact ofhigher-order corrections whenever the relevant calculationsexist, i.e. in this section and Sect. 4.
With the second and third panels of the figure, we empha-sise the significant reduction of the scale uncertainties at NLOby depicting the LO and NLO scale uncertainty bands respec-tively, the KLO and KNLO quantities, presented in the twosubfigures, these being the LO and NLO cross sections nor-malised to the LO central value. Such better control in thetheoretical predictions is one of the main motivations for rely-ing on NLO simulations instead of on LO ones. In the lowerpanel of Fig. 2, we focus on the PDF uncertainties associatedwith the total rates and present the KPDF quantity where the
Fig. 3 Constraints on the gluino-neutralino simplified model underconsideration, represented as 95% confidence level exclusion con-tours in the (mg,mχ0
1) plane. We compare the exclusion obtained with
the ATLAS-SUSY-2016-07 reimplementation in the MadAnalysis 5
framework [36] when normalising the signal to NLO (blue) and toNNLOapprox+NNLL (red) with the official ATLAS results, extractedusing the Meff signal regions only [11] (solid green). Moreover, weinclude the uncertainty band on the MadAnalysis 5 results as origi-nating from scale uncertainties (dotted) and from the quadratic combi-nation of the scale and PDF uncertainties (dashed). The colour schemerepresents the cross section value excluded at the 95% confidence levelfor each mass configuration
NLO result (with its PDF error band) is again shown rela-tively to the LO central result. We omit the correspondingLO curve, as it is similar to the NLO one, the same PDF setbeing used both at LO and NLO in order to avoid having todeal with the poor-quality LO NNPDF 3.0 fit [23]. Whilst theuncertainties are under good control over most of the probedmass range, the poor PDF constraints in the large Bjorken-xregime lead to predictions plagued by sizeable uncertaintiesfor gluino heavier than about 2.6–2.7 TeV. Finally, our resultsshow that the NLO K -factor KNLO is of about 1.6–1.7, a typ-ical value for a strong supersymmetric production process,and features a significant gluino mass dependence. The lat-ter originates from the quark–antiquark contributions to thecross section that become relatively larger with respect to thegluon fusion ones with increasing Bjorken-x values [35].
We then predict, for several (mg,mχ01) configurations,
how the signal events would populate the different signalregions of the ATLAS-SUSY-2016-07 search for supersym-metry [11]. In practice, we use the corresponding recastanalysis as implemented in the MadAnalysis 5 publicdatabase [36], together with the appropriate Delphes 3 con-figuration for the simulation of the detector response. In thisanalysis, the ATLAS collaboration investigates the potentialof a signature featuring multiple jets and missing transverseenergy through two approaches. The first one relies on theso-called effective mass Meff(N ), a variable defined as the
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scalar sum of the transverse momenta of the N leading jetsand the missing transverse energy. The second one is based onthe recursive jigsaw reconstruction technique [37]. Whilst allMeff -based signal regions have been implemented in Mad-
Analysis 5, the recursive jigsaw reconstruction ones havebeen ignored due to the lack of information allowing for theirproper recasting. They are thus ignored in the following studyas well.
Our results are presented in Fig. 3 in the form of exclu-sion contours in the (mg,mχ0
1) mass plane, to which we
supplement the values of the signal cross section that areexcluded at the 95% confidence level through a colour code.The exclusion contours and excluded cross sections at the95% confidence level are extracted by means of Gaussianprocess regression with a conservative amount of data asimplemented in the Excursion package [38].
We compare our predictions (the solid blue line), obtainedwith the setup described above, with the official ATLAS lim-its (the green line) as originating from the Meff -based signalregion yielding the best expectation. ATLAS simulations arebased on calculations at the LO accuracy in which samples ofevents describing final states featuring up to two extra jets aremerged [39]. Moreover, the ATLAS results are normalised toNLO cross sections matched with threshold resummation atthe next-to-leading logarithmic accuracy (NLO+NLL) [30].The ATLAS setup therefore differs from ours both at the levelof the differential distributions, as we model the propertiesof the second radiation jet solely at the level of the partonshowers, and at the level of the total rates that are evaluatedat the NLO matched with parton showers (NLO+PS) accu-racy. This consequently results in MadAnalysis 5 limitsslightly weaker than the ATLAS ones by about 10%, espe-cially in the light neutralino mass regime.
With the goal of assessing the importance of the signalnormalisation, we extract bounds on the model by makinguse of NNLOapprox+NNLL rates (red contour) instead ofNLO ones (blue contour), NNLOapprox+NNLL predictionsbeing the most precise estimates for gluino-pair productionto date. While still different from what has been used in theATLAS study, NLO-NLL and NNLOapprox+ NNLL predic-tions are known to be consistent with each other when theoryerror bands are accounted for. This has been documented, inthe case of a gluino simplified model in which all squarksare decoupled, by the LHC Supersymmetry Cross SectionWorking Group.4 We observe a better agreement with theATLAS results, showing the important role played by thenew physics signal normalisation in the limit setting proce-dure. Large differences of about 5% on the mass limits arenevertheless still noticeable, showing that not only the nor-malisation but also the shape of the distributions are impor-
4 See the webpage https://twiki.cern.ch/LHCPhysics/SUSYCrossSections13TeVgluglu.
tant ingredients. The ATLAS-SUSY-2016-07 analysis indeedrelies on the Meff(N ) variable that is particularly sensitive tothe modelling of the second jet, as N ≥ 2 for all the analysissignal regions. In our setup in which NLO matrix elementsare matched with parton shower, the second jet properties aredescribed at the leading-logarithmic accuracy, the presenceof this jet in the event final state solely originating from partonshowering. This contrasts with ATLAS simulations in whichLO matrix-element corrections are included as well, theirfinal merged Monte Carlo signal samples including the con-tributions of LO matrix elements for gluino pair-productionin association with two jets. This should motivate the usageof merged NLO samples matched with parton showers, sothat predictions for observables sensitive to the sub-leadingjet activity could be precisely achieved both for the shapesand the rates. The investigation of the actual impact of suchan NLO multipartonic matrix element merging however goesbeyond the scope of this work.
We also estimate in Fig. 3, the impact of the scale andPDF errors on the exclusion contours. For bothMadAnaly-
sis 5 predictions in which NLO (blue contour) and more pre-cise NNLOapprox+NNLL (red contour) are used for the signalnormalisation, we describe the effect of the scale uncertain-ties through dotted contours and the one of the combinedscale and parton density uncertainties through dashed con-tour. It turns out that the uncertainties on the signal impactsthe gluino mass limits by about 50 GeV in both cases, theeffect being mostly dominated by scale variations. The reachof the considered ATLAS-SUSY-2016-07 analysis concernsgluino masses smaller than about 1.8 TeV. This correspondsto a mass range where the uncertainty on the predictions isdominated by the scale variations, as shown in Fig. 2. Thelatter indeed shows that the PDF errors (lower panel of thefigure) are at the level of a few percents for mg < 1.8 TeV,the parton density fits being under a very good control forthe corresponding Bjorken-x values.
In order to estimate the reach of this ATLAS supersym-metry search in the context of the future runs of the LHC, wemake use of the framework detailed in Sect. 2.3 to extrapolatethe results to 300 fb−1 and 3000 fb−1. As the ATLAS note ofRef. [11] does not include detailed and separate informationon the systematical and statistical components of the uncer-tainties associated with the SM expectation in each signalregion, we consider the two implemented options for theirextrapolation to higher luminosities. More conservative, alinear extrapolation assumes that the error on the SM back-ground is mostly dominated by its systematical componentand scales proportionally to the luminosity (see the first termin Eq. (6)). More aggressive, an extrapolation in which theerror scales proportionally to the square root of the luminosity(second term of Eq. (6)) considers that the background uncer-tainties are mainly of a statistical origin. The second optionhence naively leads to a more important gain in sensitivity
Fig. 4 Expected constraints on the gluino-neutralino simplified modelunder consideration, represented as 95% confidence level exclusioncontours in the (mg,mχ0
1) plane. We present the exclusions derived
by extrapolating with MadAnalysis 5 the expectation of the ATLAS-SUSY-2016-07 analysis for 36 fb−1 of LHC collisions to 300 fb−1
(upper) and 3000 fb−1 (lower). In the left panel, we extrapolate the
uncertainties on the background linearly (i.e. the errors are assumed tobe dominated by the systematics) while in the right panel, we extrap-olate them proportionally to the square root of the luminosity (i.e. theerrors are assumed to be dominated by statistics). The colour schemerepresents the cross section value excluded at the 95% confidence levelfor each mass configuration
for higher luminosities, by definition. For all our predictions,we normalise the signal rates to NLO.
The results are presented in Fig. 4, first, by scaling thebackground uncertainties linearly to the luminosity (leftpanel, assuming that the background errors are dominated bythe systematics), and second, by scaling them proportionallyto the square root of the luminosity (right panel, assumingthat the background errors are dominated by the statisticaluncertainties). In all cases, we moreover assess the impactof the theory errors, the scale and PDF uncertainties beingcombined quadratically.
For an extrapolation to 300 fb−1 (upper subfigures), thegluino mass limits are pushed to 2.1–2.2 TeV for a light bino-like neutralino with mχ0
1� 500 GeV. The 36 fb−1 exclusion
is then found to be improved by about 15–20% (or 300–400 GeV). For such a mass range, the error on the theoreti-
cal predictions is still dominated by the scale variations (seeFig. 2) and only mildly impacts the exclusion, the effectsreaching a level of about 5%. Such a small effect on a masslimit is related to the behaviour of the cross section with theincreasing gluino mass, that is only reduced by a factor ofa few. Comparing the left and right upper figures, one canassess the impact of the different treatment for the extrapola-tion of the background uncertainties. In the parameter spaceregion under discussion, the impact is mild, reaching roughlya level of about 5% on the gluino mass limit. Such a smalleffect originates from the small resulting difference on thebackground error, that is 3 times smaller in the more aggres-sive case. Correspondingly, this allows us to gain a factor ofa 3 in cross section, or equivalently a few hundreds of GeVin terms of a mass reach.
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For more compressed scenarios in which the neutralinois heavier (mχ0
1� 800 GeV) and the gluino lighter (mg ∈
[1, 1.7] TeV), the treatment of the background extrapolationhas a quite severe impact on the bounds on the neutralinomass. A more conservative linear extrapolation of the back-ground error does not yield any significant change compar-atively to the 36 fb−1 case, neutralinos lighter than about800 GeV being excluded. However, treating more aggres-sively the background uncertainties as being purely statisti-cal, leads to an important increase in the bounds, neutralinomasses ranging up to about 1 TeV becoming reachable. Inthose configurations, the spectra are more compressed andtherefore more complicated to probe than for split configura-tions, consequently to the fact that the signal regions are lesspopulated by the supersymmetry signals. A more preciselyknown background (with a relatively smaller uncertainty)is therefore crucial for being able to draw conclusive state-ments. As found in our results, any improvement, as little itis, can have a large impact.
In the lower subfigures, we present the results of an extrap-olation to 3000 fb−1. All above-described effects are empha-sised to a larger extent. The differences in the treatment ofthe background uncertainties corresponding to knowing thebackground more accurately indeed now involve a factor of10 in precision. A more interesting aspect concerns the the-oretical predictions themselves that turn out to be knownless and less precisely consequently to large parton densityuncertainties. The limits indeed enter a regime in which largeBjorken-x are probed, which corresponds to PDF uncertain-ties contributing significantly to the total theory error. A bet-ter knowledge of the parton densities at large x and largescale is thus mandatory to keep our capacity to probe newphysics in this regime.
We have verified that the obtained bounds were compati-ble with the naive extrapolations performed by theColliderReach
5 platform that extracts naive limits of a given collidersetup with respect to the reach of a second collider setup,rescaling the results of the later by ratio of partonic luminosi-ties. For instance, an 1.8 TeV gluino excluded with 36 fb−1
of LHC collisions would correspond to a 2.4–2.7 TeV exclu-sion at 300 fb−1. This is in fair agreement with our findings,after accounting for the fact that Collider Reach uses theNNPDF 2.3 set of parton densities [40], a set of parton distri-bution functions whose fit only includes 2010 and 2011 LHCdata, so that important differences are expected, particularlyfor large x-values.
Whilst our extrapolations rely on the reinterpretation ofan ATLAS analysis of 36 fb−1 of LHC collisions, they arequite robust despite the small luminosity under consideration.Multijet plus missing transverse energy studies targeting amonojet-like topology (i.e. with a hard selection on the lead-
5 See the webpage http://collider-reach.web.cern.ch.
ing jet) are indeed limited by systematics [41], so that onlymild improvements could be expected with a higher luminos-ity. This is what has been found in the results of Fig. 4, thebounds being improved by at most 20% in mass when goingfrom 300 to 3000 fb−1. This subsequently also implies thatthe expected sensitivity should be rather independent of theinitially-analysed luminosity. We further demonstrate thoseconsiderations in Fig. 5.
In the left panel of the figure, we extrapolate the results ofthe ATLAS-SUSY-2016-07 analysis to the full Run 2 lumi-nosity of 139 fb−1, the theory errors being combined quadrat-ically. In our extrapolation procedure, we have consideredboth that the background uncertainties are dominated by thesystematics (linear scaling) and by the statistics (scaling pro-portional to the square root of the luminosity). The two set ofresults have been merged and presented as the unique enve-lope of the exclusion bands derived from the two extrapola-tion procedures. They could hence be seen as a conservativetheory estimate for the LHC sensitivity at 139 fb−1, whenestimated from official 36 fb−1 results.
The ATLAS-SUSY-2016-07 analysis has been updatedlast summer as the ATLAS-CONF-2019-040 analysis [12],so that the most recent and stringent ATLAS limits on the con-sidered gluino simplified model now encompass the analysisof the full LHC Run 2 dataset. On the other hand, the updatedanalysis has been recently added to the PAD [42], so that itcan be used within theMadAnalysis 5 framework for rein-terpretation studies. The corresponding 95% confidence levelcontour is shown on the left panel of Fig. 5 (solid blue line),together with the uncertainty band stemming from combin-ing the scale and PDF uncertainties in quadrature. In addition,we also present predictions for the bounds as obtained froman extrapolations of early Run 2 results focusing on 36 fb−1
of LHC data. After accounting for the error bands, the twosets of constraints are found in good agreement, as expected.
On the right panel of Fig. 5, we consider the twoATLAS multijet plus missing transverse energy analysesthat have been above-mentioned, namely the early LHCRun 2 ATLAS-SUSY-2016-07 analysis (36 fb−1, red) andthe full Run 2 ATLAS-CONF-2019-040 analysis (139 fb−1,blue). We reinterpret their results with MadAnalysis 5,and extrapolate the predictions that have been obtained forthe nominal luminosities of the two analyses to 3000 fb−1.The contours shown on the figure are obtained as before,i.e. by considering independent scalings of the backgroundassuming that it is either dominated by the systematical or bythe statistical uncertainties. The envelopes of the two exclu-sion bands (including the theory errors) are then reported inthe figure. The two solid areas presented on the figure arefound to largely overlap and be consistent with each other.
In Fig. 6, we make use of the MadAnalysis 5 infras-tructure to estimate, for various benchmark points, the lumi-nosity L95 that is required to exclude the scenario at the 95%
Fig. 5 Expected constraints on the gluino-neutralino simplified modelunder consideration, represented as 95% confidence level exclusioncontours in the (mg,mχ0
1) plane for 139 fb−1 (left) and 3000 fb−1 (right)
of proton-proton collisions at a centre-of-mass energy of 13 TeV. Wecompare predictions obtained by recasting the results of the ATLAS-CONF-2019-140 analysis (blue lines), which we then extrapolate to
3000 fb−1 (filled blue area), with those obtained by extrapolating theexpectation of the ATLAS-SUSY-2016-07 analysis of 36 fb−1 of LHCdata to 139 fb−1 and 3000 fb−1 (solid red areas). The parameter spaceregions spanned by the various contours correspond to including boththe PDF and scale uncertainties. The extrapolations are moreover per-formed conservatively (see the text)
Fig. 6 Luminosity necessary to exclude, at the 95% confidence level, agiven gluino-neutralino new physics setup with the ATLAS-SUSY-16-07 analysis. We fix the neutralino mass to mχ0
1= 50 GeV, assume that
the uncertainties on the background are dominated by their statisticalcomponent, and include systematical uncertainties on the signal of 0%(solid line), 10% (dotted line) and 20% (dashed line)
confidence level. We still consider the ATLAS-SUS-2016-07 analysis, fix the neutralino mass to 50 GeV and let thegluino mass vary. We compute L95 for two choices of sys-tematics on the signal (combined in both cases with the the-
ory errors quadratically), namely 10% (dotted line) and 20%(dashed line), and compare the predictions with the centralvalue where the signal is perfectly known (solid line). Inthose calculations, we scale the error on the background pro-portionally to the square root of the luminosity, as if it wasmainly dominated by its statistical component. Our analy-sis first shows that light gluinos with masses smaller thanabout 1.5 TeV can be excluded with a luminosity L95 of afew fb−1, as confirmed by the early Run 2 ATLAS search ofRef. [43] that consists of the 3.2 fb−1 version of the ATLAS-SUSY-2016-07 analysis. The steep fall of the cross sectionwith an increasing gluino mass moreover implies that thehigh-luminosity LHC reach of the analysis under consider-ation will be limited to gluinos of about 2.5 TeV, a boundthat could be reduced by about 10% if the systematics onthe signal are of about 10–20%. This order of magnitude hasbeen found to agree with older ATLAS estimates [12].
4 Squark and neutralino mass limits
In this section, we consider a second class of simplified mod-els inspired by the MSSM that is widely studied in the contextof the LHC searches for new physics. As in Sect. 3, all super-partners, except for two under investigation, are decoupled.This time, these are taken to be a squark and the lightestneutralino. In practice, we hence supplement the SM fieldcontent by one species of first generation squark q and the
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q*
q
χ01
χ01
j
j
P
P
Fig. 7 Generic Feynman diagram associated with the production anddecay of a pair of squarks in the considered MSSM-inspired squarksimplified model. The figure has been produced with the help of theJaxoDraw package [21]
lightest neutralino χ01 , assumed to be bino-like. In this config-
uration, squarks can be pair-produced through standard QCDinteractions, and then each decays into the lightest neutralinoand an up quark, as illustrated by the generic Feynman dia-gram of Fig. 7. Such a parton-level final state comprised oftwo quarks and two invisible neutralinos therefore manifestsitself, after parton showering and hadronisation, as a multijetplus missing transverse energy topology.
The ATLAS analyses considered in Sect. 3, targeting mul-tijet plus missing energy signs of new physics, are thereforeappropriate to put constraints on the model under considera-tion. Those analyses indeed include not only signal regionsdedicated to probe final state featuring a large jet multiplicity(that are thus ideal to target the previously considered gluinosimplified model), but also include signal regions targetingsignals exhibiting a smaller jet multiplicity (that are thusexcellent probes for the present squark simplified model). Inthe following, we only make use of the most recent search,ATLAS-CONF-2019-140 [12].
Making use of the same simulation setup as in Sect. 3, westudy the LHC sensitivity to this model after the full Run 2and present the expectation of its high-luminosity operationrun. Our results are derived from simulations at the NLO+PSaccuracy, so that our signal samples are normalised at theNLO accuracy. The rates that we employ in the followingare depicted in the upper panel of Fig. 8, where we showtotal NLO-accurate squark-pair production cross sections asreturned by MG5_aMC when using the MSSM implemen-tation developed in Ref. [7] and the NLO set of NNPDF 3.0parton densities [23] (blue). Predictions are given for squarkmasses ranging from 250 GeV to 2 TeV and include theoryerrors that we estimate by adding scale and PDF uncertain-ties in quadrature. Those uncertainties are further describedmore precisely in the middle and lower panels of the fig-ure, where they are given after normalising the results to thecentral NLO cross section value for each mass point.
Fig. 8 Total NLO (blue) and approximate NNLO+NNLL (red) crosssection (upper panel) for squark pair production in proton-proton col-lisions at a centre-of-mass energy of 13 TeV. The error bars representthe quadratic sum of the scale and PDF uncertainties. In the middle andlower panels of the figure, we report the NLO scale and PDF uncertain-ties respectively, after normalising the results to the central NLO crosssection value
We obtain cross sections that vary from 10 pb for mq ∼250 GeV to 0.01 fb for 2 TeV squarks. They are two ordersof magnitude lower than in the gluino case for a specificmass value, as expected from the fact that squarks are scalarsand are colour triplets and not octets. Scale uncertainties arefound to be independent of the squark mass for the consideredmq range, and are of about 15% (middle panel of the figure).In contrast, the PDF errors strongly depend on the squarkmass mq (lower panel of the figure), as they are correlatedwith the associated Bjorken-x regime. They are of a fewpercents and thus subleading for small mq values, and growfor increasing squark masses, eventually reaching 20% formq = 2 TeV. For larger and larger x-values (and thus largerand largermq ), the quark-antiquark contributions to the crosssection play a bigger and bigger role. Simultaneously, theimpact of the Bjorken-x regime in which the PDF sets aremore poorly constrained by data gets more important.
As in Sect. 3, we compare our predictions to the crosssection values usually employed by the LHC collabora-tions (red curve), as reported by the LHC SupersymmetryCross Section Working Group [30]. The latter are howeveronly provided for a simplified model in which all squarksexcept the two stop squarks are mass-degenerate. We there-fore normalise the NNLOapprox+NNLL results by an extrafactor of 1/10, which should be a fair enough approxima-
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Fig. 9 Expected constraints on the squark-neutralino simplified modelunder consideration, represented as 95% confidence level exclusioncontours in the (mq ,mχ0
1) plane for 139 fb−1 (red) and 3000 fb−1 (blue)
of proton–proton collisions at a centre-of-mass energy of 13 TeV. Wederive those bounds with the ATLAS-CONF-2019-140 implementation
inMadAnalysis 5 and extrapolate the uncertainties on the backgroundas if they are systematically-dominated (left, scaling proportional to theluminosity ) or statistically-dominated (right, scaling proportional tothe square root of the luminosity)
tion for small squark masses. Nevertheless, as both NLO andNNLOapprox+NNLL predictions are consistent, we consider(exact) NLO rates in the following.
In Fig. 9, we reinterpret the results of the ATLAS-CONF-2019-040 analysis with MadAnalysis 5 and present theexpected exclusion contours both at the nominal luminosityof 139 fb−1, after extrapolating the findings to 3000 fb−1,using for each point the region yielding the best expectedsensitivity. Neutralino masses below about 300 GeV are cur-rently (i.e. for a luminosity of 139 fb−1) excluded, for squarkmasses ranging up to about 900 GeV. This may seem tocontrast by a factor of about 2 with the current bounds onthis class of simplified model set by the ATLAS collabora-tion [12]. This is however not surprising as the collaborationonly interprets its results for a simplified model in whichthe superpartner spectrum exhibits 10 mass-degenerate left-handed and right-handed squarks (i.e. all squarks except thetwo stop squarks are degenerate). The corresponding signalcross sections are therefore about 10 times larger, so thatmuch stronger limits could be extracted. In comparison withfinal Run 2 CMS results [44,45] for which result interpre-tations both for eight mass-degenerate squarks and a singlesquark species are provided, we obtain more conservativebounds that are roughly 20% weaker in terms of excludedmasses. When accounting for the uncertainty bands, our pre-dictions agree with the experimental findings, as the uncer-tainty bands overlap.
Extrapolating the results to a luminosity of 3000 fb−1,i.e. expected luminosity of the high-luminosity phase of theLHC, we obtain expected bounds which are improved quitea bit. The magnitude of the improvement is found strongly
related to how the background uncertainties will be con-trolled, as visible by comparing the curves correspondingto 3000 fb−1 (blue) in the two panels of the figure. Assum-ing that the background is dominated by the systematics orthe statistics change the results by more than 40%.
5 Sensitivity to simplified s-channel dark matter models
In this section, we investigate the sensitivity of the LHC to asimplified dark matter (DM) model. We assume that DM isdescribed by a massive Dirac fermionic particle X that com-municates with the Standard Model through the exchange ofa spin-1 mediator Y . Motivated by models with an extendedgauge group, we consider that the mediator couples onlyeither to a pair of DM particles, or to a pair of SM fermions.Such a configuration is typical from the so-called s-channeldark matter models [13,14]. In this class of scenarios, DMcan only be pair-produced at colliders, from the scattering ofa pair of SM quarks and through the s-channel exchange ofthe mediator.
The corresponding Lagrangian can generically be writtenas
L = LSM + Lkin + Xγμ
[gVX + gA
Xγ5]X Yμ
+∑q
{qγμ
[gVq + gA
q γ5]q}Yμ (8)
where LSM refers to the SM Lagrangian and Lkin containsgauge-invariant kinetic and mass terms for all new fields. Thenext term includes the vector and axial-vector interactions of
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P
P
X
X
j
j
Fig. 10 Generic Feynman diagram associated with the production ofa pair of dark matter particles X in association with two hard jets. Thefigure has been produced with the help of the JaxoDraw package [21]
the mediator with DM, their strength being denoted by gVXand gA
X respectively, and the last term focus on the mediatorinteractions with the SM quarks. The latter are assumed uni-versal and flavour-independent, their strength being gVq andgAq in the vector and axial-vector case respectively, regardless
of the quark flavour.In our analysis, we focus on two further simplified sce-
narios originating from that model. In a first case (that welabel S1), the mediator couplings are taken as of a vectorialnature, whilst in the second case (that we label S2), they aretaken as of an axial-vectorial nature. In other words, the twoscenarios are defined as
S1 : gAq = gA
X = 0 ; S2 : gVq = gVX = 0. (9)
In order to study the sensitivity of the LHC to these twoclasses of scenarios, we make use of the publicly available6
implementation of the model in theFeynRules package [33]introduced in Ref. [13], as well as of the corresponding publicUFO [46] library. As in the previous sections, hard scatter-ing events are generated at the NLO accuracy in QCD withMG5_aMC [22] and then matched with parton showeringand hadronisation as performed by Pythia [27]. In our sim-ulations, the matrix elements are convoluted with the NLOset of NNPDF 3.0 parton densities [23]. We derive the LHCsensitivity to the model by considering the associated produc-tion of a pair of dark matter particles with jets, a signaturetargeted by the ATLAS-CONF-2019-040 analysis [12] intro-duced in the previous sections. This ATLAS study searchesfor new phenomena in a luminosity of 139 fb−1 of LHC dataat a centre-of-mass energy of 13 TeV, investigating eventsfeaturing at least two hard jets and a potential subleading jetactivity.
As the analysis selection requires at least two very hardjets, we consider as a hard-scattering process the productionof a pair of DM particles with two hard jets, as sketched in
6 See the webpage http://feynrules.irmp.ucl.ac.be/wiki/DMsimp.
Fig. 10. Moreover, we impose two conservative (with respectto the ATLAS analysis) generator-level selections. We con-strain the transverse momentum of the hardest of the jets tosatisfy pT > 150 GeV, and the parton-level missing trans-verse energy (i.e. the transverse energy of the vector sumof the transverse momenta of the two DM particles) to ful-fil /ET > 150 GeV. Moreover, the reference renormalisationand factorisation scales are set to the mass of the mediatormY , and we estimate the associated uncertainties as usual, byindependently varying the two scales by a factor of 2 up anddown around the central scale choice.
We begin with considering a series of scenarios featur-ing light dark matter, i.e. with a dark matter mass mX fixedto 100 GeV. The mediator mass is kept free to vary in the[0.3, 2] TeV range. In Table 1, we present the sensitivityof the ATLAS-CONF-2019-040 analysis to those scenar-ios, both at the nominal luminosity of 139 fb−1 and forthe high-luminosity LHC run (with 3000 fb−1). For eachspectrum configuration, we show NLO signal cross sections(second and fifth columns for the S1 and S2 benchmarksrespectively), as obtained following the simulation setupdescribed above and for couplings obeying to Eq. (9). More-over, those predictions are obtained after fixing the remainingnon-vanishing free parameters to the reference values
S1 : gVq = 0.25 , gVX = 1;S2 : gA
q = 0.25 , gAX = 1, (10)
which consist in one of the benchmarks studied by the LHCdark matter working group [14].
We first assess the LHC sensitivity to each point for thetwo considered luminosities in terms of the signal cross sec-tion that is reachable at the LHC σ95 (third and sixth columnsof table 1 for the S1 and S2 benchmarks respectively) by rein-terpreting, withMadAnalysis 5, the results of the ATLAS-CONF-2019-040 analysis. Second, we translate the crosssection limits that we have obtained into a bound on a uni-versal new physics coupling strength g95 that is defined forscenarios in which
gq = gX . (11)
Moreover, we provide the g95 limits together with the theoryuncertainty stemming from scale and PDF variations (fourthand seventh column of the table). The most stringent boundson the model originate from a single signal region of the anal-ysis in which, the effective mass Meff is imposed to be largerthan 2.2 TeV. Such a cut is applied together with looser cutson the jet properties, as compared with other signal regionsfeaturing smaller effective masses.
For fixed vector couplings (S1 scenarios), the NLO crosssection σNLO decreases when the mediator mass increasesand spans a range extending from about 450 fb for heavymediators with a mass of about 2 TeV, to more than 10 pb
Table 1 Expected constraints on various light dark matter s-channelscenarios. The dark matter mass is fixed tomX = 100 GeV and the cou-plings satisfy Eq. (9). Reference NLO cross sections (second and fifthcolumns) are provided for a case where the remaining free couplingsare set as in Eq. (10), and can be compared with the 95% confidencelevel limits expected from the reinterpretation of the ATLAS-CONF-
2019-040 analysis of (third and sixth columns). Our results are presentboth at the nominal luminosity of 139 fb−1 and after being extrapolatedto 3000 fb−1 assuming systematics-dominated uncertainties (in paren-theses). Those bounds are also translated into a bound on the couplingsfor a gq = gX configuration (fourth and seventh columns)
mY [TeV] Vector couplings (S1) Axial-vector couplings (S2)
for mediators lighter than 500 GeV. Those values and thissteeply-falling behaviour are mainly driven by the heavymass of the mediator as compared with the small dark mattermass. Larger cross sections are indeed obtained for smallermediator masses as we lie closer to the resonant regime inwhich mY ∼ 2mX . The cross section that is expected to beexcluded at the 95% confidence level also falls down withmY , although the slope is much flatter. Moreover, σ95 <
σNLO. Consequently, all scenarios defined by the couplingassumptions of Eqs. (9) and (10) are excluded, already withthe present full Run 2 luminosity.
Relaxing the coupling definitions of Eq. (10) and replacingit by the universal coupling constraint of Eq. (11), it turns outthat couplings of 0.4–0.7 are excluded over the entire massrange, the best limits being obtained for scenarios featur-ing sub-TeV mediators and a spectrum such that one lies farenough from the resonant regime. In the latter case, the anal-ysis is less sensitive as a consequence of the associated softerfinal state objects populating the signal events. The overallweak dependence of the excluded coupling on the mediatormass stems from various interplaying effects. First, the crosssection has a quartic dependence on the couplings, so that asmall coupling change leads to a large modification of thecross section. Second, there is a strong interplay between themediator mass and the dark matter mass (i.e. if ones lies forenough from the resonant regime) and the kinematical con-
figuration probed by the analysis cuts, especially for lightmediators.
In the heavy-mediator regime, considering S2 scenariosfeaturing axial-vector mediator couplings leads to very sim-ilar results. In this limit, the relevant matrix elements areinsensitive to the mediator nature. On the contrary, when oneapproaches the resonant regime, significant changes arise:The cross section turns out to be suppressed relatively tothe vector S1 scenario. This originates from the impact ofthe threshold regime that plays a larger and larger role forsmaller and smaller masses. At threshold, the pair of darkmatter particles is organised into a 3P1 state, and not into a3S1 configuration as in the S1 scenario. Consequently, signalcross sections are relatively suppressed. The small increasein cross section for low mY values in the S2 case hence stemsfrom those threshold effects that are more and more tamedwhen one gets further from threshold, as well as from thecut on the leading jet of 150 GeV. As in the S1 scenario, theentire mass range is excluded by the ATLAS-CONF-2019-040 analysis, which translates in the exclusion of couplings inthe 0.4–0.7 ballpark for the considered mediator mass range.
Finally, those bounds are expected to only be sightlyimproved, by about 4–9%, after including 3000 fb−1 of datafor both scenarios. This is related to the systematical dom-inance of the uncertainties on the background, as we havechosen to scale it under that assumption, so that more lumi-
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Table 2 Same as Table 1, but for a scenario in which mX is free and mY has been set to 1.5 TeV
nosity will not bring much compared with the Run 2 results.Moreover, we observe that the results are plagued by quitemodest theoretical uncertainties at the g95 level (by virtueof the quartic dependence of the matrix element of the cou-pling).
In Table 2, we consider a new class of scenarios. This time,the mediator mass mY is fixed to 1.5 TeV and we vary thedark matter mass mX from 200 to 900 GeV.
We first consider scenarios with couplings satisfyingEqs. (9) and (10). We evaluate fiducial NLO cross sectionsfor the different considered mass spectra (second and fifthcolumns of the table for the S1 and S2 cases respectively),after imposing the previously-mentioned cuts on the trans-verse momentum of the leading jet pT ( j1) > 150 GeVand on the parton-level missing transverse energy /ET >
150 GeV. For both the S1 and S2 scenarios, the NLO predic-tions are found to decrease with the dark matter mass, payingthe price of a phase-space suppression. The falling behaviouris found steeper once the dark matter mass is greater than halfthe mediator mass, as it has to be produced off-shell (i.e. formY > 2mX ). Moreover, for given masses and couplings, S1cross sections (i.e. in the case of mediator vector couplings)are larger. This originates from the p-wave suppression ofDM production through an axial-vector mediator (i.e. in theS2 scenario), as already mentioned earlier in this section.
We then evaluate the cross section value σ95 that isexcluded at the 95% confidence level (third and sixth columnsof the table) by reinterpreting the results of the ATLAS-CONF-2019-040 analysis. We observe that small dark mattermasses are excluded already with the full Run 2 dataset, crosssections as small as 100 fb being excluded regardless of theDM mass. Moving on with a scenario in which the couplingssatisfy Eqs. (9) and (11), we translate the bounds that wehave obtained into bounds on a universal coupling. The lat-ter is found to be of at most in the 0.5–0.7 range once onelies in a configuration below threshold (2mX < mY ), andis mostly unconstrained for larger DM mass values. As forthe previous class of scenarios in which the DM mass was
fixed and the mediator mass was varying, 3000 fb−1 will notimprove the limits much, as the analysis being dominated bythe systematics. We indeed expect an improvement on thebounds of at most 3–4%.
6 Conclusion
In this paper we showcased new features of the MadAnal-
ysis 5 package that improve the recasting functionalities ofthe programme. These features focus on two aspects.
First, we have designed a way to include the uncertaintieson the signal when the code is used to reinterpret given LHCresults in different theoretical contexts. Theory errors on thetotal signal production cross section induced by scale andPDF variations can be propagated through the reinterpreta-tion procedure. This results in an uncertainty band attachedto the confidence level at which a given signal is excluded.In addition, the user has the option to provide informationon the systematic uncertainties on the signal. With the exis-tence of new physics masses being pushed to higher andhigher scales, keeping track of error information on the signalbecomes mandatory, especially for what concerns the theo-retical uncertainties, which can be significant for beyond theStandard Model physics signals involving heavy particles.
Second, we have implemented a new option allowing theuser to extrapolate the constraining power of any specificanalysis to a different luminosity, assuming a naive scalingof the signal and background selection efficiencies. Severaloptions are available for the treatment of the backgrounduncertainties, depending on the information provided by theexperimental collaborations for the analyses under consider-ation. If information on the statistical and systematical com-ponents of the uncertainties is available separately, signalregion by signal region, MadAnalysis 5 can use it to scalethem up accordingly, i.e. proportionally to the square root ofthe luminosity and linearly to the luminosity for the statisti-cal and systematical uncertainties respectively. In contrast, if
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such a detailed information is absent, the user is offered thechoice to treat the total error as being dominated either bystatistics or by systematics, or in his/her preferred fashion.
We have illustrated the usage of these new MadAnaly-
sis 5 features in the framework of three simplified modelsfor new physics.
First, we consider a signal that originates from the pro-duction of a pair of gluinos that each decay into two jets andmissing transverse momentum. As an example, we make pre-dictions in the context of a simplified model inspired by theMSSM, in which only the gluino and the lightest neutralinoare light enough to be reachable at the LHC. We have inves-tigated the potential of two ATLAS searches for supersym-metry in 36 fb−1 and 139 fb−1 of LHC data. Those searchesboth rely on the effective mass variable and on the pres-ence of a large amount of missing transverse energy, andinclude a large variety of signal regions featuring differentjet multiplicity and hadronic activity. We have reproducedto a good approximation the ATLAS results at the nominalluminosity of the analysis and compared our extrapolationsat higher luminosities with those obtained either through themore naive approach of theCollider Reach platform, or topublicly available ATLAS estimates for the high-luminosityruns of the LHC. Fair agreement has been found. We havemoreover studied the differences in the expected sensitivitythat arise when one considers, as a starting point, an analysisof 36 or 139 fb−1 of Run 2 LHC data. Our predictions arefound fairly compatible, once theory errors are accounted for.
Second, we have focused on another MSSM-inspired sim-plified model in which the SM field content is supplementedby one species of first generation squark and one neutralino,all other supersymmetric states being decoupled. The spec-trum configuration is therefore such that the squark is heavierthan the neutralino and thus always decay into a light quarkand a neutralino. This gives rise to a multijet plus missingtransverse energy signatures stemming from squark pair pro-duction and decay. However, in contrast with the gluino case,a smaller signal jet multiplicity is expected. We have consid-ered the same ATLAS supersymmetry search in 139 fb−1 ofLHC data as above-mentioned, as it includes signal regionswith a smaller jet multiplicity so that some sensitivity to theconsidered simplified model is expected. We have reinter-preted the results of the search and derived up-to-date con-straints on the model. We have then extrapolated our findingsto the high-luminosity LHC case.
Finally, we have considered an s-channel dark matter sim-plified model in which one extends the Standard Model bya single dark matter candidate and one mediator that con-nects the dark sector (made of the dark matter state) to theSM sector. We have considered a fermionic dark matter stateand a spin-1 mediator that couples to a pair of SM quarksand a pair of dark matter particles. Typical dark matter sig-nals hence arise from the production of a pair of dark matter
particles (through an s-channel mediator exchange) in asso-ciation with a hard visible object. The most common caseinvolves the production of a jet with a pair of invisible darkmatter particles, the signal being dubbed monojet in this case.As the above ATLAS search is sensitive to such a signature(by virtue of the properties of its low jet multiplicity signalregions), we reinterpret its results to constrain the simpli-fied model under consideration. We focus on and comparetwo cases where the mediator couplings are of a vector andaxial-vector nature respectively. We then extract the currentlimits on the model, and additionally project them at a higher-luminosity to get estimates for the LHC sensitivity to the twostudied s-channel dark matter setups.
In all the models investigated , our results emphasise theimportance of embedding the uncertainties on the signal. Inone considered example, this could degrade the expectedbounds by about 10–20%, especially as a consequence ofthe large theory errors originating from the poor PDF fit con-straints at large Bjorken-x . Such a regime is indeed relevantfor new physics configurations still allowed by current dataand that involve the production of massive particles lying inthe multi-TeV mass range.
Acknowledgements JYA acknowledges the hospitality of the LPTHE(Sorbonne Université) and IPPP (Durham University) where parts ofthis work were completed. MF acknowledges the NSERC for partialfinancial support under Grant number SAP105354. BF has been sup-ported by the LABEX ILP (ANR-11-IDEX-0004-02, ANR-10-LABX-63).
Data Availability Statement This manuscript has no associated dataor the data will not be deposited. [Authors comment: This is a theorywork, so that there is no data.].
Open Access This article is licensed under a Creative Commons Attri-bution 4.0 International License, which permits use, sharing, adaptation,distribution and reproduction in any medium or format, as long as yougive appropriate credit to the original author(s) and the source, pro-vide a link to the Creative Commons licence, and indicate if changeswere made. The images or other third party material in this articleare included in the article’s Creative Commons licence, unless indi-cated otherwise in a credit line to the material. If material is notincluded in the article’s Creative Commons licence and your intendeduse is not permitted by statutory regulation or exceeds the permit-ted use, you will need to obtain permission directly from the copy-right holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.Funded by SCOAP3.
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