Matching next-to-leading order predictions to parton showers in supersymmetric QCD

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Matching next-to-leading order predictions to parton

showers in supersymmetric QCD

Céline Degrande, Benjamin Fuks, Valentin Hirschi, J. Proudom, Hua-Sheng

Shao

To cite this version:

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Matching

next-to-leading

order

predictions

to

parton

showers

in

supersymmetric

QCD

Céline Degrande

a

,

Benjamin Fuks

b

,

c

,

∗

,

Valentin Hirschi

d

,

Josselin Proudom

e

,

Hua-Sheng Shao

f

a_{InstituteforParticlePhysicsPhenomenology,DepartmentofPhysics, DurhamUniversity,DurhamDH13LE,UnitedKingdom} b_{SorbonneUniversités,UPMCUniv. Paris06,UMR7589,LPTHE,F-75005Paris,France}

c_{CNRS,UMR7589,LPTHE,F-75005Paris,France}

d_{SLAC,NationalAcceleratorLaboratory,2575SandHillRoad,MenloPark,CA94025-7090,USA}

e_{LaboratoiredePhysiqueSubatomiqueetdeCosmologie,UniversitéGrenoble-Alpes,CNRS/IN2P3,53AvenuedesMartyrs,F-38026GrenobleCedex,France} f_{CERN,PH-TH,CH-1211Geneva23,Switzerland}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received12October2015

Receivedinrevisedform13January2016 Accepted31January2016

Availableonline3February2016 Editor:G.F.Giudice

Wepresentafullyautomatedframeworkbasedonthe FeynRules and MadGraph5_aMC@NLO programs thatallowsforaccuratesimulationsofsupersymmetricQCDprocessesattheLHC.Startingdirectlyfroma modelLagrangianthatfeaturessquarkandgluinointeractions,eventgenerationisachievedatthe next-to-leadingorderinQCD,matchingshort-distanceeventstopartonshowersandincludingthesubsequent decayoftheproducedsupersymmetricparticles.Asanapplication,westudytheimpactofhigher-order correctionsingluinopair-productioninasimplifiedbenchmarkscenarioinspiredbycurrentgluinoLHC searches.

©2016TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

The LHC has been designed with the aim of exploring the electroweaksymmetry breaking mechanismandto possiblyshed light on phenomena beyond the Standard Model.During its first run,both the ATLASandCMSCollaborations haveextensively in-vestigated manydifferent channelsin orderto get hintsfor new physics.However,nostrikingsignal hasbeenfoundsothat limits havebeensetonpopularmodels,suchastheMinimal Supersym-metricStandardModel (MSSM)[1,2],oron simplifiedmodels for newphysics [3,4].Allthesesearcheswillnevertheless bepursued during the next LHC runs, benefiting from larger statistics and higher center-of-mass energy. In this work, we focus on MSSM-inspiredsimplifiednewphysicsscenariosinwhichgluinopairscan becopiouslyproducedattheLHC.Asinmanyrelatedexperimental searches[5–8],weconsiderthecasewherebothproducedgluinos decayintoapairofjetsandaninvisible neutralino,andthen re-visitthephenomenologyofsuchmodels.

Experimental gluino analyses are currently based on Monte Carlosimulations of the signalswhere leading-order (LO) matrix

*

Correspondingauthorat:LPTHE- CNRS- UPMC,Box126,T13-14fourthfloor, 4placeJussieu,75252ParisCedex05,France.

E-mailaddress:fuks@lpthe.jussieu.fr(B. Fuks).

elements of different partonic multiplicities are matched to par-ton showers and merged. The predictions are then normalized to resummed total rates combined with the next-to-leading or-der(NLO)result[9–13].Moresophisticateddifferentialtheoretical predictions are howeveralways helpful forsettingmore accurate exclusion limits,possibly refining thesearch strategies,and mea-suring the model free parameters in caseof a discovery [14]. In this context, it has been recently demonstrated that the Mad-Graph5_aMC@NLO framework[15]canprovideageneralplatform for computing(differential) observableswithin manybeyond the StandardModeltheories[16].Thisapproachreliesinparticularon the useof the FeynRules [17] and NLOCT [18] packagesfor (au-tomatically) generatinga UFO library[19] containing thevertices andtheneededcountertermsforNLOcomputations.

Withinthis framework, we matchforthe firsttime NLO QCD matrix-element-based predictions to parton showers for gluino pair-production. Virtualcontributions are evaluated following the Ossola–Papadopoulos–Pittau (OPP) formalism as implemented in MadLoop _{[20–22] and combined with real emission} contribu-tions by means of the FKS subtraction method as embedded in MadFKS [23,24]; these two modules being fully incorporated in MadGraph5_aMC@NLO. The matching to parton showers is then achievedbyemployingtheMC@NLOmethod[25].Afteraccounting

http://dx.doi.org/10.1016/j.physletb.2016.01.067

for(LO)gluinodecays,we studytheimpactofboththeNLO con-tributionsandthepartonshowersinthecontextofLHCphysics. 2. Theoreticalframework

Our study of gluino pair-production and decay is based on an MSSM-inspired simplified model. We complement the Stan-dardModelwiththreegenerationsofnon-mixingleft-handedand right-handedsquarkfieldsq

˜

L,R ofmassmq_˜L,R andwithaMajorana fermionic gluino field

˜

g of mass m_g˜. The dynamics of the new fieldsisdescribedbythefollowingLagrangian,

L

SQCD

=

Dμq

˜

†LDμq

˜

L

+

Dμq

˜

† RDμq

˜

R

+

i 2

¯˜

gD

/

˜

g

−

m2_q˜ Lq

˜

† Lq

˜

L

−

m 2 ˜ qRq

˜

† Rq

˜

R

−

1 2mg˜

¯˜

g

˜

g

+

√

2gs



− ˜

q†_LT

¯˜

g PLq



+



q P

¯

Lg

˜



Tq

˜

R

+

h.c.



−

gs2 2



˜

q†_RTq

˜

R

− ˜

q†_LTq

˜

L



˜

q†_RTq

˜

R

− ˜

q†_LTq

˜

L



,

thatcontainsallinteractionsallowedbyQCDgaugeinvarianceand supersymmetry, as well as squark and gluino kinetic and mass terms.In ournotation, T stands forthefundamental representa-tionmatricesofSU

(

3

)

, PL ( PR)fortheleft-handed(right-handed)

chiralityprojector and gs is the strong couplingconstant. Flavor

andcolorindicesareleftunderstoodforbrevity.

Inaddition,weenable the(possibly three-body)decaysofthe coloredsuperpartnersbyincluding(s)quarkcouplingstoa gauge-singletMajoranafermion

χ

ofmass mχ thatisidentified witha bino,

L

decay

=

i 2

χ

¯

/

∂

χ

−

1 2mχ

χ χ

¯

+

√

2g



− ˜

q†_LYq



¯

χ

PLq



+



q P

¯

L

χ



Yqq

˜

R

+

h.c.



.

InthisLagrangian, Yq denotesthe hypercharge quantumnumber

ofthe(s)quarksandgthehyperchargecoupling.

At the NLO in QCD, gluino pair-production receives contribu-tionsfromrealemissiondiagramsaswellasfromtheinterferences oftree-leveldiagramswithvirtualone-loop diagramsthat exhibit ultraviolet divergences. These must be absorbed through a suit-ablerenormalizationoftheparametersandofthefieldsappearing in

L

SQCD. To this aim,we replace all (non-)fermionic bare fields



(



) andbareparameters y by thecorrespondingrenormalized quantities,



→



1

+

1 2

δ

Z



, 

→



1

+

1 2

δ

Z L PL

+

1 2

δ

Z R PR



,

y

→

y

+ δ

y

,

wherethe renormalizationconstants

δ

Z and

δ

y aretruncated at thefirstorderinthestrongcoupling

α

s.

The wave-function renormalization constants of the massless quarks(

δ

ZqL,R),ofthetopquark(

δ

ZtL,R),ofthegluon(

δ

Zg)andthe

topmassrenormalizationconstant(

δ

mt)aregiven,whenadopting

theon-shellrenormalizationscheme,by

δ

Zg

= −

g2 s 24

π

2



−

1 3

+

B0

(

0

,

m 2 t

,

m2t

)

+

2m2tB0

(

0

,

mt2

,

m2t

)

−

nc 3

+

ncB0

(

0

,

m 2 ˜ g

,

m2g˜

)

+

2ncm2˜gB0

(

0

,

m2˜g

,

m2g˜

)

+

˜ q



₁ 6

+

1 4B0

(

0

,

m 2 ˜ q

,

m 2 ˜ q

)

−

m 2 ˜ qB0

(

0

,

m2q˜

,

m 2 ˜ q

)



,

δ

Z_qL,R

=

g 2 sCF 8

π

2 B1

(

0

;

m 2 ˜ g

,

m2q˜L,R

),

δ

Z_tL,R

=

g 2 sCF 16

π

2



1

+

2B1

(

m2t

;

m2g˜

,

m 2 ˜ tL,R

)

+

2B1

(

m2t

;

m2t

,

0

)

+

8m2tB0

(

mt2

;

m2t

,

0

)

+

4m2_tB₁

(

m2_t

;

m2_t

,

0

)

+

2m2_t

i=L,R B₁

(

m2_t

;

m2_g˜

,

m2_˜t i

)

,

δ

mt

= −

g2 sCFmt 16

π

2



−

1

+

4B0

(

mt2

;

m2t

,

0

)

+

2B1

(

m2t

;

mt2

,

0

)

+

i=L,R B1

(

m2t

;

m2g˜

,

m 2 ˜ ti

)

,

where the B0,1 (and A0, for further references) functions and

their derivatives stand for the standard two-point (one-point) Passarino–Veltmanloop-integrals[26].Moreover,nc

=

3 andCF

=

(

n2

c

−

1

)/(

2nc

)

denoterespectively the number ofcolors and the

quadratic Casimirinvariant associated withthefundamental rep-resentation of SU

(

3

)

. The gluino wave-function and mass renor-malizationconstants

δ

ZL,R_˜g and

δ

mg_˜ aregivenby

δ

Zg_˜

=

g2_s 16

π

2



nc

+

2ncB1

(

m2_˜g

;

m2g˜

,

0

)

+

8ncm2_˜gB₀

(

m2_g˜

;

m2_˜g

,

0

)

+

4ncm2_˜gB₁

(

m2_g˜

;

m2_g˜

,

0

)

+

˜ q=˜qL,q˜R



B1

(

m2_˜g

;

mq2

,

mq2_˜

)

+

2mg2˜B1

(

m2_˜g

;

m2q

,

m2q_˜

)



,

δ

m_g˜

=

g 2 smg˜ 16

π

2



nc

−

4ncB0

(

m2_˜g

;

m2_g˜

,

0

)

−

2ncB1

(

m_g2_˜

;

m2_g˜

,

0

)

−

˜ q=˜qL,q˜R B1

(

m2g_˜

;

m2q

,

m2q_˜

)

,

while the squarkwave-function(

δ

Zq_˜) andmass (

δ

m_q2_˜)

renormal-izationconstantsread,

δ

Z_q˜

=

g 2 sCF 8

π

2



−

B0

(

m2_q˜

;

m2_˜g

,

m2q

)

+

B0

(

m2_q˜

;

m2_q˜

,

0

)

+ (

m2_˜g

−

m2_q˜

+

m_q2

)

B₀

(

m2_q˜

;

m2_g˜

,

m2_q

)

+

2m2_q˜B₀

(

m2_q˜

;

m2_q˜

,

0

)

,

δ

m2_q˜

=

g 2 sCF 8

π

2



A0

(

m2_q˜

)

−

A0

(

m2_g˜

)

−

2m2_q˜B0

(

m_q2_˜

;

m2_q˜

,

0

)

+ (

m2_q˜

−

m2_g˜

−

m2_q

)

B0

(

m_q2_˜

;

m2_˜g

,

m2q

)

−

A0

(

m2q

)

,

with

(

−)

L

≡

1 and

(

−)

R

≡ −

1, andwith mq

=

0 fortop squarks

only.Asaresultofthestructureofthegluino–squark–quark inter-actions, squark mixing effects proportional to the corresponding quark masses are generated at the one-loop level and must be accountedforinthe renormalizationprocedure.Inoursimplified setup,weconsidernf

=

5 flavorsofmasslessquarkssothatthese

effectsare onlyrelevantforthe sectorofthe topsquarks. Inthis case,matrixrenormalizationisinorder,

˜

tL

˜

tR



→

˜

tL

˜

tR



+

1 2

δ

Z_˜t L

δ

Z˜t,LR

δ

Z_˜t,RL

δ

Z_˜t R



˜

tL

˜

tR



,

bystopcouplingstotheHiggssectorthatgenerateanoff-diagonal masscounterterm,

δ

L

off

= −δ

m2_˜t,LR

(˜

tL†

˜

tR

+ ˜

t†R

˜

tL

) .

These Higgs couplings beingabsent in our simplified model, we therefore introduce

δL

off explicitly. The off-diagonal stop

wave-function (

δ

Z_˜t,LR

= δ

Z_t,˜RL) andmass(

δ

m2_˜

t,LR) renormalization

con-stantsarethenfoundtobe

δ

Z_t,˜LR

=

g 2 sCFm˜gmt 4

π

2

₍

_m2 ˜ tR

−

m 2 ˜ tL

)

i=L,R

(

−)

iB0

(

m2_˜t i

;

m 2 t

,

m2_˜g

),

δ

m2_˜ t,LR

=

g2 sCFm˜gmt 8

π

2

i=L,R B0

(

m2_˜t i

;

m 2 t

,

m2_˜g

),

where

δ

Z_t,˜LR hasbeen symmetrized. In thisway, it incorporates therenormalization ofthestop mixingangle(taken vanishingin ourmodel)whichdoesnotneedtobeexplicitlyintroduced[27].

Inordertoensurethattherunningof

α

ssolelyoriginatesfrom

gluonsand nf active flavors of light quarks, we renormalizethe

strongcouplingby subtractingatzero-momentumtransfer,inthe gluonself-energy,allmassiveparticlecontributions.Thisgives

δ

α

s

α

s

=

α

s 2

π

¯



_n f 3

−

11nc 6

+

α

s 6

π



1

¯

−

log m_t2

μ

2 R

+

α

snc 6

π



1

¯

−

log m2_˜g

μ

2 R

+

α

s 24

π

˜ q



1

¯

−

log m2_q˜

μ

2 R

.

The ultraviolet-divergent parts of

δ

α

s

/

α

s are written in terms of

thequantity 1 _¯

=

1

−

γ

E

+

log 4πwhere

γ

EistheEuler–Mascheroni

constantand

isconnectedtothenumberofspace–time dimen-sions D

=

4

−

2 .

Finally, the artificial breaking of supersymmetry by the mis-matchofthetwogluinoandthe(D

−

2)transversegluondegrees offreedom mustbe compensated by finitecounterterms. Impos-ingthatthedefinitionofthestrongcouplinggs isidenticaltothe

StandardModel one,only quark–squark–gluinoverticesand four-scalarinteractionshavetobeshifted[28],

L

SCT

=

√

2gs

α

s 3

π



− ˜

q†_LTa

¯˜

gaPLq



+



q P

¯

Lg

˜

a



Taq

˜

R

+

h.c.



+

g2s 2

α

s 4

π



˜

q†_R

{

Ta

,

Tb

}˜

qR

+ ˜

q†_L

{

Ta

,

Tb

}˜

qL



×



q

˜

†_R

{

Ta

,

Tb

}˜

qR

+ ˜

q†_L

{

Ta

,

Tb

}˜

qL



−

g2s 2

α

s 4

π



˜

q†_RTaq

˜

R

− ˜

q†LTaq

˜

L



˜

q†_RTaq

˜

R

− ˜

q†LTaq

˜

L



,

wherewehaveintroducedadjointcolorindicesforclarity.

Inourphenomenologicalstudy,loop-calculationsareperformed numericallyinfourdimensionsbymeansofthe MadLoop package andthereforerequirethe extractionofrationalparts that are re-latedtothe

-piecesoftheloop-integraldenominators(R1,which

are automatically reconstructed within the OPP reduction proce-dure) and numerators (R2). For any renormalizable theory, the

number of R2 terms is finite and they can be seen as

counter-termsderivedfromthebareLagrangian[29].Inthecontextofthe

L

SQCD Lagrangian,all necessary R2 counterterms canbe found in

Ref.[30].

Thesetupdescribedabovehasbeenimplementedinthe Feyn-Rules package and we have made use of the NLOCT program to automatically calculate all the ultraviolet and R2

countert-ermsof the model. The specificity of the renormalization ofthe

Table 1

LOand NLOQCD inclusivecrosssectionsfor gluinopair-productionat theLHC, runningatacenter-of-massenergyof√s=13 TeV.Theresultsareshowntogether withtheassociatedscaleandPDFrelativeuncertainties.

mg˜[GeV] σLO[pb] σNLO[pb] 200 2104+₋3021..3%9%+ 14.0% −14.0% 3183+ 10.8% −11.6%+ 1.8% −1.8% 500 15.46+₋3424..7%1%+ 19.5% −19.5% 24.90+ 12.5% −13.4%+ 3.7% −3.7% 750 1.206+₋3524..9%6%+ 23.5% −23.5% 2.009+ 13.5% −14.1%+ 5.5% −5.5% 1000 1.608·10−1+36.3% −24.8%+ 26.4% −26.4% 2.743·10−1+ 14.4% −14.8%+ 7.3% −7.3% 1500 6.264·10−3+36.2% −24.7%+ 29.4% −29.4% 1.056·10− 2+16.1% −15.8%+ 11.3% −11.3% 2000 4.217·10−4+35.6% −24.5%+ 29.8% −29.8% 6.327·10− 4+17.7% −16.6%+ 17.8% −17.8% stop sector has been implemented via a new option of NLOCT,

SupersymmetryScheme->"OS"

, that allows to treat all scalar fieldsthatmixattheloop-levelasdescribedabove.Wehave vali-datedtheoutputagainst ouranalyticalcalculations, andthese re-sultsrepresentthefirstvalidationof NLOCT inthecontextof com-putations involving massive Majoranacolored particles. We have finally generated a UFOversion of themodel that canbe loaded into MadGraph5_aMC@NLO and which we have made publicly available on

http://feynrules.irmp.ucl.ac.be/wiki/

NLOModels

.Wehavefurthervalidatedthemodel,togetherwith the numerical treatment of the loop-diagrams by MadLoop, by comparing MadGraph5_aMC@NLO predictionstothoseofthecode Prospino [31],usingafullydegeneratemassspectrumduetothe limitationsofthelatter.

3. LHCphenomenology

InTable 1,wecompute gluinopair-productiontotalcross sec-tions for proton–proton collisions at a center-of-mass energy of

√

s

=

13 TeV andfordifferent gluinomasses. Squarks are decou-pled(m_˜tL

=

16 TeV,m_˜tR

=

17 TeV andmq_˜L

=

mq˜R

=

15 TeV)sothat any resonant squark contribution appearing in the real-emission topologiesisoff-shellandthereforesuppressed.Thelatter produc-tion modescan be seenasthe associatedproduction ofa gluino andasquarkthat subsequentlydecaysintoagluinoandaquark. IncludingthesecontributionsaspartsoftheNLOQCDcorrections forgluinopair-productionwouldhenceresultinadouble-counting when considering together all superpartner production processes inclusively. Moreover, these resonant channels require a special treatment in the fully-automated MadGraph5_aMC@NLO frame-work, that isleft to future work [32]. Our choice forthe squark spectrumcorrespondstotheonemadebyATLASandCMS Collab-orationsintheirrespectivegluinosearches[5–8].

Ourresults areevaluated both attheLOandNLO accuracyin QCD and presented together with scale and parton distribution (PDF) uncertainties. Forthe central values, we set the renormal-ization andfactorizationscales to half thesum ofthe transverse massofallfinalstate particlesandusetheNNPDF 3.0setof par-tondistributions[33]accessedviatheLHAPDF 6library[34].Scale uncertainties arederivedby varyingbothscales independentlyby factors1

_/

2,1 and2,andthePDFuncertaintieshavebeenextracted from the crosssection values spanned by all NNPDF distribution replicasfollowing theNNPDF recommendations [35].We observe a significant enhancement of the crosssection of about50% due togenuineNLOcontributions,aswellasasizablereductionofthe uncertainties. In particular, theapparent drastic reduction of the PDF uncertainties isrelatedto thepoor qualityofthe LONNPDF fitwhencomparedtotheNLOfit[33].

analyticallycalculatedthosedecaymatrixelementsandintegrated them over the phase space, after checking our results with the MadSpin _{[36] and MadWidth [37] programs. These latter two} programs havebeenused inthecomputation ofthe NLO predic-tions matched to parton showers. Due to the three-body nature ofthe gluino decays,spin correlationsare here omittedas Mad-Spincanonlyhandlethemfortwo-bodydecays.Wetheninterface the partonic events obtained in this way to a parton showering andhadronization descriptionas providedby the Pythia 8 pack-age [38], and use the anti-kT jet reconstruction algorithm [39]

witharadiusparametersetto0.4,asimplementedin FastJet[40], toreconstructallfinalstate parton-levelandhadron-leveljetsfor fixed-order and parton-shower-matched calculations respectively. Finally,the phenomenological analysisofthe generated eventsis performedwith MadAnalysis 5[41].

Key differential distributions particularly sensitive to both NLO and shower effects are presented in Fig. 1. We show the transverse-momentum (pT) spectra of the first five leading jets

(firstfivesubfigures)fortwobenchmarkscenariosfeaturingeither alight (mg_˜

=

1 TeV)oraheavy(m˜g

=

2 TeV) gluino,aswell asa

ratherlight bino(mχ

=

50 GeV). Wecomparefixed-order predic-tions (dashed) to results matched to partonshowers (solid) and consider bothLO (blue)and NLO (red) accuracyin QCD. We ob-serve that most of the differential K -factors (i.e., the bin-by-bin ratios of the NLO result to the LO one) both with and without parton-showermatchingstronglydependonthejet pT inthe

con-sidered pT range.TheNLO effectsthereforenotonlyincreasethe

overall normalization of the distributions, but also distort their shapes.The K -factorisindeedgreateratlow pT thanathighpT,

sothatthetraditionalprocedureofusingLOpredictionsscaledby inclusive K -factors cannot be used foran accurate gluino signal description.

Fig. 1alsounderlinestheeffectsofmatchingLOandNLO ma-trixelementstopartonshowers.Sincemostparton-leveljets orig-inatefromthe decayofvery massivegluinos, thefixed-order pT

distributions peakatlarge pT values.In addition,thelow-pT

re-gionofthesespectraisdepleted,withtheexception ofthefourth andfifthjet pT spectrawhereradiationeffectsarenon-negligible.

As a result of the matching to parton showers, the fixed-order NLOdistributions aredistortedandsoftened.Whilethechangeis milder in the large-pT tails whose shapes are controlled by the

hardmatrixelement,thelow-pT regionsaremostlysensitiveto

ef-fectsduetomultipleemissionsandhencebecomepopulated.The partonshower emissionsfromhard partonsare indeedoftennot reclusteredbackwiththejetthey areissued from,hence distort-ingthejetpT spectra.Forthisreason,resummationeffectsbecome

significantbelowthepeakofthevarious pT distributions.This

ef-fect is also illustrated on the last subfigure of Fig. 1, where we showthepT spectrumofthegluinopairinthesmallpT range.We

haveverifiedthat thematched resultsagreewiththefixed-order onesforverylargepT valuesoftheorderofthegluinomass.

4. Conclusions

WehaveperformedthefirstcalculationofNLO supersymmet-ric QCD corrections to gluino pair-production matched to parton showersand havestudied the impact ofboth the NLO contribu-tionsandofthepartonshowers. Wehaveshownthat observable effectscouldbeinducedonquantitiestypicallyusedtoobtain ex-clusion limitsand that more accurate calculationsare crucial for extractingmodelparametersincaseofadiscovery.

Ourcalculationhasbeenperformedfullyautomaticallyandwe haveappliedittothecaseofasimplifiedmodelsimilartooneof thoseusedby theATLAS andCMSCollaborationsfortheir respec-tivegluinosearches.Inaddition,wehavepubliclyreleasedtheUFO

modelassociatedwithourcomputation,thatissufficientlygeneral to bereadilyusedtoexplore thephenomenologyassociatedwith anysupersymmetricQCDprocess.

Finally, our results also show that all technical obstacles for automating thematching of fixed-ordercalculations forinclusive supersymmetric particleproductionatthe NLO inQCD toparton showershavebeencleared,uptotheambiguityissueofthe dou-blecountingarisinginrealemissionresonantcontributions[32]. Acknowledgements

We are grateful to R. Frederix, S. Frixione, F. Maltoni and O. Mattelaerforenlighteningdiscussions.Thisworkhasbeen sup-ported in part by the ERC grant 291377 LHCtheory:Theoretical

predictionsandanalysesofLHCphysics:advancingtheprecision

fron-tier, theResearch ExecutiveAgencyofthe European Unionunder

GrantAgreementPITN-GA-2012-315877(MCNet)andthe Theory-LHC-France initiative of the CNRS (INP/IN2P3). C.D. isa Durham InternationalJuniorResearchFellow,V.H. issupported bytheSNF grantPBELP2146525andJ.P. byaPhDgrantoftheInvestissements

d’avenir, LabexENIGMASS.

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