P u b l i s h e d f o r SISSA b y S p r i n g e r R e c e iv e d : February 1, 2016
R e v ise d : May 24, 2016
A c c e p te d : May 31, 2016 P u b lis h e d : June 10, 2016
A search for top squarks with R-parity-violating decays to all-hadronic final states with the A T L A S detector in √ s = 8 T e V proton-proton collisions
T h e A T L A S collaboration
E -m a il: a t l a s . p u b l i c a t i o n s @ c e r n .c h
A b s t r a c t : A search for th e pair p ro d u ctio n of to p squarks, each w ith R -parity-violating decays into two S tan d ard M odel quarks, is perform ed using 17.4 fb -1 of √ s = 8T eV p ro to n -p ro to n collision d a ta recorded by th e ATLAS experim ent a t th e LH C . E ach top squark is assum ed to decay to a b- and an s-quark, leading to four quarks in th e final state.
B ackground d iscrim ination is achieved w ith th e use of b-tagging and selections on th e m ass and su b stru c tu re of large-radius jets, providing sensitivity to to p squark masses as low as 100 GeV. No evidence of an excess beyond th e S tan d ard M odel background prediction is observed and to p squarks decaying to bs are excluded for to p squark m asses in th e range 100 < m j < 315 GeV a t 95% confidence level.
K e y w o r d s : H adron-H adron scatterin g (experim ents)
A r X i y e P r i n t : 1601.07453
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Contents
1 I n tr o d u c tio n 1
2 T h e A T L A S d e t e c t o r 3
3 M o n te C a r lo s im u la tio n s a m p le s 4
4 O b je c t d e fin itio n s 6
5 T r ig g e r a n d o fflin e e v e n t s e le c tio n s 7
6 B a c k g r o u n d e s t im a t io n 13
7 S y s t e m a t ic u n c e r ta in t ie s 17
7.1 b-jet-m ultiplicity m iJg shape u n certain ty 17
7.2 B ackground estim atio n m iJg shape u n certain ty 17
7.3 B ackground t t co n trib u tio n system atic u n certain ty 18
7.4 Signal system atic uncertain ties 19
8 R e s u lts 21
9 C o n c lu s io n s 24
T h e A T L A S c o lla b o r a tio n 32
1 In tr o d u c tio n
S upersym m etry (SUSY) is an extension of th e S tan d ard M odel (SM) [1- 7] th a t fu n d a
m entally relates ferm ions and bosons. It is an especially alluring th eo retical possibility given its p o ten tial to solve th e hierarchy problem [8- 11] and to provide a d a rk -m a tte r can d id a te [12, 13].
T his p a p e r presents a search for th e p air productio n of supersym m etric to p squarks (sto p s),1 which th e n each decay to two SM quarks, using 17.4 fb -1 of y fs = 8T eV proton- pro to n (pp) collision d a ta recorded by th e ATLAS experim ent a t th e Large H adron Collider (LHC). T his decay violates th e R -p arity conservation (R P C ) [14] assum ed by m ost searches for stops [15, 16]. In R P C scenarios, SUSY particles are required to be produced in pairs and decay to th e lightest supersym m etric particle (LSP), which is stable. In R -parity-violating
1The superpartners of the left- and right-handed top quarks, t L and t R, mix to form the two mass eigen
states 11 and 12, where t 1 is the lighter one. This analysis focuses on t1, which is referred to hereafter as t
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(R PV ) models, decays to only SM particles are allowed, and generally relax th e strong con
s tra in ts now placed on sta n d a rd R P C SUSY scenarios by th e LHC experim ents. It is th e re fore crucial to expand th e scope of th e SUSY search program m e to include R P V models.
C om m on signatures used for R P V searches include resonant lepto n-p air pro du ction [17], exotic decays of long-lived particles w ith displaced vertices [18- 21], high lepton m ultiplici
ties [22, 23], and high-jet-m ultiplicity final sta te s [24]. Scenarios which have stops of m ass below 1TeV are of p a rticu la r interest as these address th e hierarchy problem [25- 28].
SUSY R P V decays to SM q uarks and leptons are controlled by th re e Yukawa couplings in th e generic supersym m etric su p erp o ten tial [29, 30]. These couplings are represented by X ijk , A j , A j , w here i , j , k € 1 ,2 ,3 are g eneration indices th a t are som etim es o m itted in th e discussion th a t follows. T he first two (A, A') are lepton-num ber-violating couplings, w hereas th e th ird (A'') violates baryon num ber. It is therefore generally necessary th a t eith er of th e couplings to quarks, A' or A'', be vanishingly small to prevent spontaneous pro to n decay [7].
It is com m on to consider non-zero values of each coupling separately. Scenarios in which A'' = 0 are often referred to UDD scenarios because of th e baryon-num ber-violating term th a t A'' controls in th e su p erp o tential. C u rren t indirect experim ental co n strain ts [31] on th e sizes of each of th e UDD couplings A'' from sources o th er th a n pro to n decay are prim arily valid for low squark m ass and for first- and second-generation couplings. Those lim its are driven by double nucleon decay [32] (for A'/12), n eu tro n oscillations [33] (for A// 13), and Z -boson branching ratios [34].
T he b en chm ark m odel considered in this p a p e r is a baryon-num ber-violating R P V scenario in which th e stop is th e LSP. T he search specifically ta rg e ts low-mass stops in th e range 100-400 GeV th a t decay via th e A323 coupling, th u s resulting in stop decays i ^ bs (assum ing a 100% branching ratio) as shown in figure 1. T he m otivation to focus on th e th ird -g en eratio n UDD coupling originates prim arily from th e m inim al flavour violation (M FV) hypothesis [35] and th e p o ten tial for th is decay channel to yield a possible signal of R P V SUSY w ith a viable d a rk -m a tte r c an d id ate [36]. T he M FV hypothesis essentially requires th a t all flavour- and C P -violating interactions are linked to th e known stru c tu re of Yukawa couplings, and has been used to argue for th e im po rtan ce of th e A'' couplings [37].
T he process tt* ^ bsb s represents an im p o rta n t channel in which to search for SUSY in scenarios not yet excluded by LHC d a ta [36- 38]. Some of th e best co n strain ts on this process are from th e A L E PH C ollaboration, which set lower bounds on th e m ass of th e stop a t m j > 80 GeV [39]. T he C D F C ollaboration extended these lim its, excluding 50 < m j <
90 GeV [40]. T he CMS C o llaboration recently released th e results of a search th a t excludes 200 < m j < 385 GeV [41] in th e case w here heavy-flavour jets are present in th e final sta te . In addition, two ATLAS searches have placed co n straints on R P V stops th a t decay to bs w hen th ey are produced in th e decays of light gluinos (mg < 900-1000 GeV) [42, 43].
T he search presented here specifically focuses on direct stop pair p ro d u ctio n and seeks to close th e gap in excluded sto p m ass betw een ~ 100-200 GeV. C on tribu tion s from R P V interactio n s a t p ro d u ctio n — such as would be required for resonant single stop p ro d u ctio n — are neglected in this analysis. T his approach is valid provided th a t th e R P V in teractio n stre n g th is small com pared to th e strong coupling co n stant, which is th e case for A323 < 10- 2 - 1 0 -1 [44] and for th e estim ated size of A323 ~ 10-4 from M FV in th e m odel described in ref. [37].
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Figure 1. Benchmark signal process considered in this analysis. The solid black lines represent Standard Model particles, the dashed red lines represent the stops, and the blue points represent RPV vertices labelled by the relevant coupling for this diagram.
The reduced sensitivity of standard SUSY searches to R PV scenarios is primarily due to the limited effectiveness of the high missing transverse momentum requirements used in the event selection common to many of those searches, motivated by the assumed presence of undetected LSPs. Consequently, the prim ary challenge in searches for R PV SUSY final states is to identify suitable substitutes for background rejection to the canonical large missing transverse momentum signature.
Backgrounds dom inated by m ultijet final states typically overwhelm the signal in the four-jet topology. In order to overcome this challenge, new observables are employed to search for tt* ^ bsbs in the low-mp regime [38]. For mp & 100-300 GeV, the initial stop transverse momentum (py) spectrum extends significantly into the range for which pT ^ mp. This feature is the result of boosts received from initial-state radiation (ISR) as well as originating from the parton distribution functions (PDFs). As the Lorentz boost of each stop becomes large, the stop decay products begin to merge with a radius roughly given by A R & 2mp/pT, and thus can be clustered together within a single large- radius (large-R) je t w ith a mass mjet & m p. By focusing on such cases, the dijet and m ultijet background can be significantly reduced via selections th a t exploit this kinematic relationship and the structure of the resulting stop jet, in a similar way to boosted objects used in previous measurements and searches by ATLAS [45- 49]. In this case, since the stop is directly produced in pairs instead of from the decay of a massive parent particle, the strategy is most effective at low mp where the boosts are the largest.
2 T h e A T L A S d e te c to r
The ATLAS detector [50, 51] provides nearly full solid angle2 coverage around the collision point with an inner tracking system (inner detector, or ID) covering the pseudorapidity
2T h e A T L A S re fe re n c e s y s te m is a C a r te s i a n r i g h t- h a n d e d c o o r d in a te s y s te m , w i t h t h e n o m in a l c o llis io n p o i n t a t t h e o rig in . T h e a n tic lo c k w is e b e a m d i r e c ti o n d e fin e s t h e p o s itiv e z -a x is , w h ile t h e p o s itiv e x - a x is is d e fin e d a s p o i n ti n g fro m t h e c o llis io n p o in t t o t h e c e n tr e o f t h e L H C r in g a n d t h e p o s itiv e y -a x is p o i n ts u p w a r d s . T h e a z im u th a l a n g le d is m e a s u r e d a r o u n d t h e b e a m a x is , a n d t h e p o l a r a n g le 6 is m e a s u r e d w i t h r e s p e c t t o t h e z -a x is . P s e u d o r a p i d it y is d e fin e d a s n = — l n [ ta n ( 6 / 2 ) ] , r a p id i t y is d e fin e d a s y = 0.5 l n [ ( E + p z ) / ( E — p z )], w h e re E is t h e e n e r g y a n d p z is t h e z - c o m p o n e n t o f t h e m o m e n tu m , a n d
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range |n| < 2.5, electrom agnetic (EM ) and hadronic calorim eters covering |n| < 4.9, and a m uon sp ectrom eter covering |n| < 2.7 th a t provides m uon trigger capability up to |n| < 2.4.
T he ID com prises a silicon pixel track er closest to th e beam line, a m icrostrip silicon tracker, and a straw -tu b e tran sitio n -rad ia tio n track er a t radii up to 108 cm. A th in solenoid surrounding th e tracker provides a 2 T axial m agnetic field enabling th e m easurem ent of charged-particle m om enta. T he overall ID acceptance spans th e full azim uthal range in
¢, and th e range |n| < 2.5 for particles originating near th e nom inal LHC in teractio n region [52].
T he EM and hadronic calorim eters are com posed of m ultiple su b detectors spanning
|n| < 4.9. T he EM barrel calorim eter uses a liquid-argon (LAr) active m edium and lead absorbers. In th e region |n| < 1.7, th e hadronic (Tile) calorim eter is con stru cted from steel absorber and scintillator tiles and is separated into barrel (|n| < 1.0) and extended-barrel (0.8 < |n| < 1.7) sections. T he endcap (1.375 < |n| < 3.2) and forw ard (3.1 < |n| <
4.9) regions are in stru m en ted w ith LA r calorim eters for EM as well as hadronic energy m easurem ents.
A three-level trig ger system is used to select events to record for offline analysis. T he different p a rts of th e trigg er system are referred to as th e level-1 trigger, th e level-2 trigger, and th e event filter [53]. T he level-1 trig ger is im plem ented in hardw are and uses a subset of d e te c to r inform ation to reduce th e event ra te to a design value of at m ost 75 kHz. T he level-1 trigger is followed by two softw are-based triggers, th e level-2 trigg er and th e event filter, which to g eth er reduce th e event ra te to a few hundred Hz. T he search presented in th is docum ent uses a trigger th a t requires a high-pT je t and a large sum m ed je t transverse m om entum (H T), as described in section 5.
3 M o n te C arlo sim u la tio n sa m p le s
M onte C arlo (MC) sim ulation is used to stu d y th e signal acceptance and system atic un certainties, to te s t th e background estim atio n m ethods used, and to estim ate th e t t back
ground. In all cases, events are passed th ro u g h th e full GEANT4 [54] d e te c to r sim ulation of ATLAS [55] after th e sim ulation of th e p a rto n shower and had ro n isatio n processes. Follow
ing th e d etecto r sim ulation, identical event reco nstruction and selection c riteria are applied to b o th th e MC sim ulation and to th e d a ta . M ultiple pp collisions in th e sam e and neigh
bouring bunch crossings (pile-up) are sim ulated for all sam ples by overlaying additio nal soft pp collisions which are generated w ith PYTHIA 8.160 [56] using th e ATLAS A2 set of tu n e d p aram eters (tune) in th e MC g enerator [57] and th e M STW 2008LO P D F set [58].
T hese ad d itio n al interactio n s are overlaid onto th e hard sc a tte r and events are rew eighted such th a t th e MC d istrib u tio n of th e average num ber of pp in teractions per bunch crossing m atches th e m easured d istrib u tio n in th e full 8 TeV d a ta sample.
T he signal process is sim ulated using H e rw ig + + 2.6.3a [59] w ith th e U E E E 3 tu n e [60]
for several stop-m ass hypotheses using th e P D F set CTEQ 6L1 [61, 62]. All non-SM p a r
ticles m asses are set to 5 TeV except for th e stop m ass, which is scanned in 25 GeV steps from mp = 100 GeV to mp = 400 GeV.
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F ig u re 2. Cross-section for direct it* pair production at the LHC centre-of-mass energy of a/s = 8 TeV [63-65],
The signal cross-section used (shown in figure 2) is calculated to next-to-leading order in the strong coupling constant, adding the resumm ation of soft gluon emission at next.-to- leading-logarithmic accuracy (NLO+NLL) [63-65], For the range of stop masses consid
ered, the uncertainty on the cross-section is approxim ately 15% [66], MadGraph 5.1.4.8 [67]
is used to study the impact of ISR on the stop p t spectrum . The MadGraph samples have one additional parton in the m atrix element, which improves the modelling of a hard ISR jet.
MadGraph is then interfaced to PYTHIA 6.426 with the AUET2B tune [68] and the CTEQ6L1 P D F set for parton shower and hadronisation. The distribution of pT(ii*) from the nominal H erw ig++ signal sample is then reweighted to m atch th a t of the MadGraph+PYTHIA sample.
Dijet and m ultijet events, as well as top quark pair (ti) production processes, are simulated in order to study the SM contributions and background estim ation techniques.
For optim isation studies, SM dijet and m ultijet events are generated using H erw ig++ 2.6.3a with the CTEQ6L1 P D F set. Top quark pair events are generated with the P0WHEG-BOX- r2129 [69-71] event generator w ith the CT10 NLO PD F set [72], These events are then interfaced to PYTHIA 6.426 with the P2011C tune [73] and the same CTEQ6L1 P D F set as H erw ig++.
The t i production cross-section is calculated at next-to-next-to-leading order (NNLO) in QCD including resumm ation of next-to-next-to-leading logarithmic (NNLL) soft gluon term s with top++2.0 [74-79]. The value of the t i cross-section is atf = 253/}g pb.
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4 O b je c t d e fin itio n s
T he d a ta are required to have satisfied c riteria designed to reject events w ith significant co n tam in atio n from d etecto r noise, non-collision beam backgrounds, cosmic rays, and o th er spurious effects. To reject non-collision beam backgrounds and cosmic rays, events are required to contain a p rim ary vertex consistent w ith th e LHC beam spo t, reconstructed from a t least two tracks w ith tran sv erse m om enta p y ack > 400 MeV. If m ore th a n one vertex satisfies these criteria, th e p rim ary vertex is chosen as th e one w ith th e highest ^ tracks(pT).
T he an ti-kt algorithm [80], w ith a radius p a ra m ete r of R = 0.4, is used for initial jet-finding using version 3 of F a stJe t [81]. T he inputs to th e je t reconstruction are th re e dim ensional topo-clusters [82]. T his m etho d first clusters to g eth er topologically connected calorim eter cells and classifies these clusters as eith er electrom agnetic or hadronic. T he classification uses a local clu ster weighting calibration scheme based on cell-energy density and shower d e p th w ithin th e calorim eter [83]. B ased on this classification, energy correc
tions are applied which are derived from single-pion MC sim ulations. D edicated hadronic corrections are derived to account for th e effects of differences in response to hadrons com pared to electrons, signal losses due to noise-suppression th resho ld effects, and energy lost in n on -in strum en ted regions. T he final je t energy calibratio n is derived from MC sim ulation as a correction relatin g th e calorim eter response to th e je t energy a t g enerato r level. In order to determ ine these corrections, th e sam e je t definition used in th e reconstruction is applied to stable (w ith lifetimes g reater th a n 10 ps) generator-level particles, excluding m uons and neutrinos. A su b tra c tio n procedure is also applied in o rder to m itig ate th e effects of pile- up [84]. Finally, th e R = 0.4 je ts are fu rth e r calib rated w ith additio nal correction factors derived in s i t u from a com bination of y + je t, Z + je t, and d ijet-balance m ethods [83].
All je ts reco nstru cted w ith th e an ti-k t algorithm using a radius p a ra m ete r of R = 0.4 and a m easured p T > 20 GeV are required to satisfy th e quality c riteria discussed in detail in ref. [85]. These q u ality c riteria selections for jets are extended to prevent co n tam inatio n from d e te c to r noise th ro u g h several detector-region-specific requirem ents. Je ts co n tam inated by energy deposits due to noise in th e forw ard hadronic endcap calorim eter are rejected and je ts in th e central region (|n| < 2.0) th a t are at least 95% contained w ithin th e EM calorim eter are required to not exhibit any electronic pulse shape anom alies [86].
Any event w ith a je t th a t fails these requirem ents is removed from th e analysis.
Identification of je ts containing b-hadrons (so-called b-jets) is achieved th ro u g h th e use of a m ultivariate b-tagging algorithm referred to as MV1 [87]. T his algorithm is based on an artificial neural-netw ork algorithm th a t exploits th e im pact param eters of charged-particle tracks, th e p aram eters of recon stru cted secondary vertices, and th e topology of b- and c- had ro n decays inside an an ti-k t R = 0.4 je t. A w orking point corresponding to a 70% b-jet efficiency in sim ulated t t events is used. T he corresponding m is-tag rates, defined as th e fraction of je ts originating from non-b-jets which are tagged by th e b-tagging algorithm in an inclusive je t sam ple, for light jets and c-jets are approxim ately 1% and 20%, respectively.
To account for differences w ith respect to d a ta , data-derived corrections are applied to th e MC sim ulation for th e identification efficiency of b-jets and th e prob ability to m is-identify je ts resulting from light-flavour quarks, charm quarks, and gluons.
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In itial jet-finding is extended using an approach called j e t r e - c lu s te r in g [88]. T his allows th e use of larger-radius je t algorithm s while m ain tainin g th e calibrations and system atic un certainties associated w ith th e in p u t je t definition. Sm all-radius a n ti - k R = 0.4 jets w ith p T > 20 GeV and |n| < 2.4 are used as in p u t w ith ou t m odification to an anti-kt R = 1.5 large-R je t algorithm , to identify th e hadronic stop decays. T he sm all-R jets w ith p T < 50 GeV are required to have a je t vertex fraction (JV F ) of a t least 50%. A fter sum m ing th e p T of charged-particle tracks m atched to a je t, th e J V F is th e fraction due to tracks from th e selected h ard -sc atte rin g in teraction and it provides a m eans by which to suppress je ts from pile-up.
To fu rth e r im prove th e background rejection, a sp littin g procedure is perform ed on each of th e two leading large-R jets. A fter jet-finding, th e co n stitu en ts of these large-R je ts — th e an ti-kt R = 0.4 in p u t o bjects — are processed separately by th e Cam bridge-A achen (C /A ) algorithm [89, 90], as im plem ented in F a stJe t 3. T he C /A algorithm perform s p air
wise recom binations of proto -jets (th e inp uts to th e je t algorithm ) purely based on th eir ang ular separation. Sm aller-angle pairs are recom bined first, th u s th e final recom bined pair typically has th e largest separation. T he C /A final clustering is th e n undone by one step, such th a t th ere are two branches “a” and “b” . T he following s p littin g c riteria are th e n applied to th e branches “a” and “b” of each of th e two leading large-R jets:
• B oth branches carry appreciable p T relative to th e large-R jet:
min[P T (a ),P T (b)] > (4 1 )
Pt ( la r g e - R ) > ° . ( ^
• T he m ass of each branch is small relative to its pT:
m ( a ) , m (b ) ., .
— < 0.3 and — — < 0.3. (4.2)
PT(a) PT(b)
If eith er of th e leading two large-R je ts fails these selections, th e event is discarded. This im plem entation is identical to ref. [38], which is derived from th e diboson-jet tagg er [91].
T his approach differs som ew hat from th a t used in ref. [92] in th a t no requirem ent is placed on th e relative m asses of th e large-R and sm all-R jets.
5 T rigger and offlin e e v en t se le c tio n s
E vents m ust satisfy je t and H T selections applied in th e trigger which require H T = ^ p t >
500 GeV, calculated as th e sum of level-2 trig ger je ts w ithin |n| < 3.2, and a leading je t w ithin |n| < 3.2 w ith p t > 145 GeV. This relatively low -threshold je t trigger cam e online part-w ay th ro u g h th e d a ta -ta k in g period in 2012 and collected 17.4 fb -1 of d a ta . T he corresponding offline selections require events to have a t least one an ti-k t R = 0.4 je t w ith p T > 175 GeV and |n| < 2.4, as well as H T > 650 GeV, w here th e sum is over all anti-k t R = 0.4 jets w ith p T > 20 GeV, |n| < 2.4, and JV F > 0.5 if p T < 50 GeV. T he cum ulative trig ger selection efficiency is g reater th a n 99% for these offline requirem ents. T he offline event preselection fu rth e r requires th a t a t least two large-R jets w ith p T > 200 GeV and
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m ass > 20 GeV be present in each event. These requirem ents select a range of phase space for low sto p masses in which th e tran sverse m om entum of th e stops is often significantly g reater th a n th e ir mass.
T he signal region (SR) is defined to suppress th e large m ultijet background and to en
hance th e fraction of events th a t contain large-R je ts consistent w ith th e p ro d uction of stop pairs, w ith each stop decaying to a light q u ark and a b-quark. Sim ulation studies indicate th a t th ree kinem atic observables are p articu larly useful for background discrim ination:
1. T he m ass asym m etry betw een th e two leading large-R je ts in th e event (w ith masses m 1 and m 2, respectively), defined as
A = |m i - m '21, (5 1 )
m 1 + m 2
differentiates signal from background since th e two sto p su b je t-p a ir resonances are expected to be of equal mass.
2. T he (absolute value of th e cosine of the) stop-pair p ro d uction angle, | c o s 9*|, w ith respect to th e beam line in th e centre-of-m ass reference fram e 3 distinguishes betw een centrally produced m assive particles and high-m ass forw ard-scattering events from QCD. It provides efficient d iscrim ination and does not exhibit significant variation w ith th e stop mass.
3. In addition, a requirem ent on th e subjets is applied to each of th e leading large-R je ts in th e event. T he p T of each su b jet a and b relative to th e o th er is referred to
as th e su b jet p T2/ p T1, defined by
su b jet PT2/ m = . (5 2)
m ax[pT ( a ) ,p T (b)]
T he A , | cos 9*|, and su b jet p T2/ p T1 variables provide good d iscrim ination betw een sig
nal and background and are m otivated by an ATLAS search for scalar gluons a t ^ /s = 7T eV [93] as well as by refs. [38, 94].
In ad d itio n to th e kinem atic observables described above, b-tagging applied to an ti-kt R = 0.4 je ts provides a very powerful d iscrim inant for defining b o th th e signal and th e control regions, and one th a t is ap proxim ately uncorrelated w ith th e kinem atic features discussed above. Using these kinem atic observables and th e presence of a t least two b- tagged jets per event, th e signal region is defined by (for th e leading two large-R jets)
A < 0.1,
| cos 9*| < 0.3, (5.3)
su b je t p T2/ p T1 > 0.3.
D istrib u tio n s of th e d iscrim inating variables are shown in figure 3 . Insofar as th e d a ta p oints are dom in ated by background in these plots, even in th e case of a p o ten tial signal, th e d a ta points should be u n d ersto od to represent th e background.
3This scattering angle, 0*, is formed by boosting the two stop large-R jets to the centre-of-mass frame and measuring the angle of either stop large-R jet with respect to the beam line.
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Figure 3. Distributions of the discriminating variables for events in which the other three selections are applied for each subfigure. The signal region is indicated with a red arrow. All distributions are normalised to unity. Overflows are included in the last bin for subfigures (a) and (b). (a) Number of b-tags/event, n. (b) Large-R jet mass asymmetry, A. (c) Stop-pair centre-of-mass frame production angle, | cos0*|. (d) Subjet p t 2/ p t i for the leading jet in each event.
J H E P 0 6 ( 2 0 1 6 ) 0 6 7
Following these selections, th e d istrib u tio n of th e average m ass of th e leading two large-R jets, miVg = (m i6* + m J2et) /2 , is used to search for an excess of events above th e background prediction. T he search is done in regions of miVg th a t are optim ised to give th e best significance. As shown in figure 4 , th e stop signal is expected as a peak th a t would a p p e ar on to p of a sm oothly falling background spectrum . A G aussian d istrib u tio n is fitted to th e stop signal miVg peak. T he m ean of th e fit, (miVg), is consistent w ith m j in each case. T he resolution of th e miVg peak is given approxim ately by s/(m£Vg) ~ 5 — 7%
(where s is th e sta n d a rd deviation of th e fit), and has only a weak dependence on th e stop m ass in th e range probed by th is analysis. M ass w in d o w s in miVg are determ ined by tak in g into account th e effect of je t energy scale (JE S) and je t energy resolution (JE R ) m easurem ent uncertain ties on th e expected signal miVg d istrib u tio n and th e estim ated background. T he size of each m ass window is defined to be equal to or larger th a n th e full w idth of th e miVg m ass spectrum for th e m j m odel th a t best corresponds to th a t range. T he definitions of these m ass windows and th e signal efficiency in each window are given in ta b le 1. F igure 4(a) shows th e m ass windows overlaid on to p of th e signal miVg d istrib u tio n s for a few stop masses. T he efficiency of th e m ass windows (relative to th e SR cu ts of eq. (5.3) ) varies from 79% a t 100 GeV to 19% a t 400 GeV. T he low efficiency at high m ass is due to th e fact th a t th e decay p ro du cts are often not fully contained in th e large-R je t, as can be seen in figure 4 (b ). F igure 5 shows th e p ro d u ct of acceptance and efficiency, after th e SR cu ts and m ass windows, as a function of m j. T he significantly lower acceptance tim es efficiency for light stop masses in figure 5 is alm ost entirely due to th e efficiency of th e trig g er selections which are for 100, 250, and 400 GeV stop m asses 0.56%, 22%, and 96%, respectively. This low efficiency is com pensated by th e large cross section for low stop masses, retain in g sensitivity to these m ass values.
J H E P 0 6 ( 2 0 1 6 ) 0 6 7
(b) Logarithmic scale.
F ig u re 4. Distributions of the average jet mass mJaVg for signal samples with m(- = 100, 150, 200, 250, and 300 GeV, in linear (a) and logarithmic (b) scales (solid lines). A Gaussian distribution is fitted to the mass peak of each sample (dashed lines). The resolution, s/(m Ja<Vtg), is quoted for each stop mass value. The mass windows are highlighted with the shaded rectangles in (a). The long tail peaking around m^/2 for high-mass stops shown in (b) is due to events where not all stop decay products are clustered within the large-R jets.
J H E P 0 6 ( 2 0 1 6 ) 0 6 7
r n { [G eV ] W in d o w [GeV] S e le c tio n e ffic ie n c y in m a s s w in d o w
100 [95,115] 79%
125 [115,135] 77%
150 [135,165] 83%
175 [165,190] 72%
200 [185, 210] 6 8%
225 [210, 235] 56%
250 [235, 265] 55%
275 [260, 295] 49%
300 [280, 315] 44%
325 [305, 350] 30%
350 [325, 370] 29%
375 [345, 395] 25%
400 [375,420] 19%
Table 1. Definition of the signal mass windows and selection efficiency in each window relative to the SR cuts of eq. (5.3).
Figure 5. Total acceptance times efficiency (A x e) of the SR cuts of eq. (5.3), and SR cuts combined with the mass window selection in table 1, as a function of my The denominator of the efficiency (in %) is the total number of events, i.e. the top row in table 3.
J H E P 0 6 ( 2 0 1 6 ) 0 6 7
6 B a ck g ro u n d e stim a tio n
T he estim atio n of th e d om inant SM m ultijet background in th e signal region, including b o th th e expected num ber of events and th e shape of th e miVg background spectrum , is perform ed directly from th e d a ta . MC sim ulations are used to stu d y th e background estim atio n m eth o d itself and to assess th e co n trib u tio n from t i p roduction. For th e back
ground estim ation, addition al kinem atic regions are defined by inverting th e A and | c o sd*\
selections as shown in tab le 2 . These are labelled An, B n , C n , w here n indicates th e num b er of b-tags (n = 0, = 1, > 2). T he signal region kinem atic selection c riteria of eq. ( 5.3) are com prised by th e D n requirem ents and sum m arised in th e last row of tab le 2 , where S R = D 2 w ith n > 2 b-tags, and D1 w ith n = 1 6-tag is a validation region. Signal event yields are sum m arised in tab le 3 for th ree stop masses.
T he m ethod relies on th e assum ption th a t th e shape of th e miVg spectru m is indepen
d ent of th e various b-tagging selections, as figure 6(a) indicates, in each of th e kinem atic regions (A n, B n , C n , and D n ) defined in tab le 2 . T he advantage of th e approach adopted here is th a t events w ith fewer th a n two b-tagged jets can be used as control and validation regions for in s i t u studies of these kinem atic regions. An estim atio n of th e norm alisation and shape of th e spectrum in th e signal region D 2 can therefore be teste d and validated using events w ith n = 1 as well as regions A (A > 0.1, \ cos 0*\ > 0.3) and C (A > 0.1,
\ cos 0*| < 0.3). Region B (A < 0.1, \ cos0*| > 0.3) is prim arily used to evaluate shape differences in th e predicted miVg sp ectra (see section 7.2) .
T he A and \ cos d* \ variables are found to have a correlation coefficient of a t m ost 1% in d a ta events for n = 0. In sim ulated m ultijet events, th e correlation is also consistent w ith zero in events w ith n > 2, w ithin th e large sta tistic a l u ncertainties. Consequently, th e ratio of n > 2 (or n = 1) to n = 0 in regions A, B , and C should be approxim ately th e sam e as th e ratio in region D . T he average je t m ass spectrum , miVg, is com pared across th e various n selections for region A, as well as betw een each of th e regions in events w ith n = 0. These com parisons are shown in figure 6 along w ith th e ratio of th e spectru m in each region to th a t which m ost closely m atches th e final signal region in each figure (region D for n = 0 and n > 2 for region A). T he results d em o n stra te th a t th e miVg sp ectra in regions C and D are reliably reproduced by regions A and B , respectively, as shown in figure 6 (b ).
T he p o ten tial for events from t t pro d u ctio n to co n trib u te increases w ith th e ad d itio n of b-tag-m ultiplicity selections. Table 4 presents th e num ber of events in th e d a ta and th e c o n trib u tio n from ti, as determ ined by MC sim ulation, in regions A, B , C , and D for n = 0, = 1, > 2. T he expected signal and tic o n trib u tio n s are also given for a few m ass windows.
T he ttt c o n trib u tio n is at th e few p er mille level in th e events w ith n = 0. C ontributions rise slightly in events w ith n = 1 to a m axim um of < 4% in region D 1. Lastly, regions A2 and C 2 (A > 0.1) have a m axim um t t con trib u tio n of aro u nd < 10%. Consequently, w hen validating th e m eth o d and in th e final background estim ate, th e con trib u tio n from t i is su b tra c te d in each of th e regions. T he corrected to ta l num ber of events in a given region is defined as N Xn = — NXn and th e corrected miVg spectrum is defined as N X n ,i = N ^ n ^ — Nj^n i , w here i represents th e ith bin of th e histogram (X = A, B , C, or D, and n refers to th e num ber of b-tags). T he two qu an tities are related by N Xn = S iN Xn,i .
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Region A | cos 0*| S ubjet PT2/P T1 n
A n > 0.1 > 0.3 > 0.3 = 0, = 1, > 2 B n < 0.1 > 0.3 > 0.3 = 0, = 1, > 2 C n > 0.1 < 0.3 > 0.3 = 0, = 1, > 2 D n < 0.1 < 0.3 > 0.3 = 0, = 1, > 2
T able 2. Definitions of the kinematic regions defined by A, | cos 0* |, subjet pT 2 / p t i, and the b-tag multiplicity (n = 0, = 1, > 2). The letters A , B, C, and D label the A and | cos0*| selections, whereas n indicates the number of b-tags. D2 = S R is the signal region of the analysis.
Selection my = 100 GeV my = 250 GeV my = 400 GeV
T otal events (9.72 ± 0.01) x 106 (9.54 ± 0.02) x 104 (6.202 ± 0.002) x 103 J e t + Ht trigger (5.47 ± 0.08) x 104 (2.07 ± 0.01) x 104 (5.98 ± 0.02) x 103
L arge-R je t ta g (1.68 ± 0.04) x 104 (4.76 ± 0.06) x 103 (1.29 ± 0.01) x 103 n > 2 (6.35 ± 0.23) x 103 (1.70 ± 0.03) x 103 515 ± 6
A2 416 ± 58 194 ± 11 68.7 ± 2.2
B 2 639 ± 71 199 ± 11 33.3 ± 1.6
C 2 419 ± 62 149 ± 9 71.2 ± 2.2
D2 711 ± 74 240 ± 12 41.5 ± 1.8
T ab le 3. The expected number of signal events in 17.4 fb-1 from MC simulation for each of the selections applied to the n > 2 region. Stop masses of my = 100 GeV, 250 GeV and 400 GeV are shown. The statistical uncertainty of the MC simulation is shown for each selection. The jet + H t trigger selection includes the offline selection. The large-R jet tag includes both the kinematic preselections and the splitting criteria defined by eq. (4.1) and eq. (4.2). No selections are placed on the masses of the candidate stop jets. The region definitions of A2-D2 are summarised in table 2.
All regions used for th e background estim atio n (A0, C 0, D 0, A2, and C 2) exhibit p o ten tial signal co n trib u tio n of less th a n 10%. Region B 2 (A < 0.1, | cos 0*\ > 0.3) is not used to derive th e background estim ate, since th e expected signal con trib u tio n is m uch higher here th a n in A2 and C 2 (for my = 100 GeV th e signal c o n trib u tio n is 50% in B 2, com pared w ith 2.2% in A2 and 8.2% in C 2). T he expected signal co n trib u tio n in th e validation regions (n = 1) is only significant in B 1 and D1 (b o th require A < 0.1). D ue to th is level of expected signal contribu tion, and th e m Ja<Vg dependence of th a t contrib utio n, th e background estim atio n procedure obtain s th e m jaVg spectrum from th e n = 0 regions
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Figure 6. Shape comparisons of the mJaVg spectrum for the data (a) in region A for events with n = 0, = 1, > 2 and (b) in regions A, B , C, D for events with n = 0. In each case, the lower panel shows the ratio of the spectrum in each region to that which most closely matches the final signal region (n > 2 for region A and region D for n = 0). Only statistical uncertainties are shown.
for the final background spectrum estim ate. The background estim ation procedure itself is summarised in the following steps:
1. The miV g shape ( ND 0 ,i) and to tal number of events (ND 0) are extracted from the D0 region.
2. A projection factor is derived between events with n = 0 and events w ith n > 2 for the signal-depleted regions A (A > 0.1, | cos d*\ > 0.3) and C ( A > 0.1, | cos d*| < 0.3).
As explained above, the number of t t events is subtracted in regions A0, C 0, A2, and C 2 before evaluating the projection factor ( kA,o )2:
N X 2
(kA , c )2 = ( kA2+ kc 2) / 2 , where kx 2 = , X = A, C. (6.1) NX 0
3. The projection factor is used to estim ate the to tal number of events,
ND 2 = (kA ,C)2 X ND 0 + ND 2, (6.2) and shape (bin-by-bin),
ND 2 ,i = (kA ,C)2 X ND 0 ,i + ND 2 x (6.3)
in the signal region, D2 (where the contribution from t t in D2 has been added).
This procedure is performed in the entire mass range and the mass windows are then defined from the estim ated background spectrum . The projection factors kA 2 and kC2
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Region N d a ta N tj ( ± st at. ± syst.)
[95,115
Ns
Nd a ta
] GeV N«
Nd a ta
[135, 165
Ns Nd a ta
] GeV N»:
Nd a ta
[165, 190] GeV
Ns N »t
Nd a ta Nd a ta
[375, 420] GeV
Ns Nn
Nd a ta Nd a ta
n = 0
Na o 296 226 390 ± 1 0 + 1 00- 9 5 0.21% 0.27% 0.048% 0.14% 0.019% 0.072 % 0.11% 0.037%
Nb o 115671 176 ± 7 + 50 - 4 2 0.64% 0.20% 0.90% 0.17% 0.50% 0.14% 0.68% 0.13%
Nc o 114186 221 ± 8 + 59 - 5 2 0.42 % 0.39% 0.088% 0.20% 0.020% 0.093% 0.24% 0.18%
Nd o 44 749 110 ± 6 + 2 7 - 2 7 4.0% 0.27% 2.0% 0.29% 2.3% 0.24% 2.4% 0.%
n = 1
Na i 79 604 1 110 ± 1 0 + 1 90 - 1 8 0 1.2% 2.6% 0.46 % 1.5% 0.48% 0.74% 0.22% 0.71%
Nb i 31045 517 ± 1 1 + 8 4 - 8 3 14% 1.9% 9.7% 2.3% 8.0% 1.9% 10% 0.089%
N c i 32 163 620 ± 1 0 + 1 1 0 - 1 0 0 4.8% 3.4% 1.6% 2.1 % 1.3% 0.99% 0.28% 0.76 %
Nd i 12 350 306 ± 8 + 52 - 4 5 29% 2.3% 31% 3.6% 21% 3.7% 43% 0.000 10%
n > 2
Na2 22 259 1050 ± 1 0 + 1 90 - 1 7 0 2.2% 6.8% 1.7% 5.7% 1.2% 2.8% 1.0% 1.9%
N b 2 8416 556 ± 1 0 + 9 4- 8 6 50% 7.2% 29% 10.0% 24% 8.8% 26% 0.24%
NC2 9 384 570 ± 1 0 + 1 00 - 9 4 8.2% 8.8% 4.1% 7.5% 2.8% 2.9% 2.8% 2.7%
ND2 3 688 311 ± 7 + 60 - 4 7 120% 8.4% 73% 14% 72% 11 % 160% 0.51%
T ab le 4. The observed event yields for 17.4 fb-1 in each of the regions for each b-tag multiplicity are shown, as well as the expected fractional signal contribution for the mass windows (as defined in table 1) corresponding to m t- = 100, 150, 175, and 400 GeV, and the t t contribution in the same mass windows. The t t systematic uncertainties include both the detector-level uncertainties and the theoretical uncertainties, as described in section 7.
are com patible a t th e level of ab o u t 4% (including th e t i su b tra c tio n as in eq. (6.1) ) and th is difference is included as a system atic u n certain ty on th e background e stim ate (see section 7) . T he validity of th e background estim atio n m eth o d can be d e m o n strated in th e n = 1 regions by deriving a pro jection factor analogously to eq. (6.1) for n = 0 and n = 1,
(kA,C )t = (kA1 + kc i ) / 2 . (6.4)
T he expected num ber of events in th e full range of D 1 is th e n estim ated by N 'd 1 = ( k A ,o)i x N do + N t]t)1
= 12400 ± 130. (6.5)
T he sam e e stim ate for D 2 gives
N D2 = (kA,C)2 X N D0 + N D2
= 3640-90. (6.6)
In eq. (6.5) and eq. (6.6) th e u n certain ty q uoted includes th e sta tistic a l u n certain ty and th e uncertainties related to th e t t e stim ate (see section 7) . These num bers should be com pared
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w ith th e observed num bers of events in tab le 4 , 12350 in D1 and 3688 in D 2. T he observed num bers of events are consistent w ith th e estim ated values.
7 S y s te m a tic u n c e r ta in tie s
Several sources of sy stem atic u n certain ty are considered when determ ining th e estim ated co n tributions from signal and background. T he background estim ate un certain ties p e rta in p rim arily to th e m eth o d itself. T he control and validation regions defined in section 6 are used to evaluate th e size of these u ncertainties. A description of th e p rim ary sources of u n certain ty follows.
7.1 b -je t-m u ltip lic ity m j^g s h a p e u n c e r ta in ty
Regions A (A > 0.1, | cos 0*\ > 0.3) and C (A > 0.1, | cos 0*\ < 0.3) are used to di
rectly com pare th e shape of th e m Ja<Vg spectrum in events w ith b-jet-m ultiplicities of n = 0 and n > 2 (the tt-corrected m Ja<Vg spectrum is used, as defined in section 6) . T he b- jet-m u ltip licity mi'Vg shape system atic u n certain ty is calculated as th e m axim um of th e bin-by-bin difference of region A2 com pared to A0 (figure 6 (a)) and C 2 com pared to C 0,
^{,-jet-multi. syst. = m ax [|1 - v^2,i/VA0,i|, |1 - VC2,i/vc0,i|] , (7.1) w here th e norm alised miVg spectru m are defined as vx n ,i = Nx n ,i/ Nx n (X = A, C ). T he expression in eq. (7.1) is th e n added in q u a d ra tu re w ith th e sta tistic a l u n certain ty to form th e to ta l system atic u n certain ty for th a t p a rticu la r bin. A fixed bin w id th of 50 GeV is used in o rder to reduce effects due to sta tistic a l un certainties. T he size of th e b-jet-m ultiplicity m Ja<Vg shape system atic u n certain ty varies from approxim ately 7-12% a t low miVg to 20%
near m Ja<Vg ~ 300 GeV, and to aro u nd 90% for mivg ~ 400 GeV. T he large system atic u n certain ty in th e high-m ass tail is due to th e low num ber of events in th e n > 2 regions.
F igure 8 shows th e b-jet-m ultiplicity miVg shape system atic u n certain ty as well as th e to ta l system atic u n certain ty w hen com bined w ith th e c o n stan t system atic u n certain ty due to th e 4% difference betw een pro jectio n factors kA2 and kC2 m entioned in section 6 , and th e background estim atio n miVg shape system atic u n certain ty described below in section 7.2.
7 .2 B a c k g r o u n d e s tim a t io n m j^g s h a p e u n c e r ta in ty
E vents w ith n = 1 are used to te s t th e validity of th e background estim atio n m eth od in d a ta and to derive a system atic u n certain ty on th e approach. Figure 7 shows several results of th is te s t by com paring th re e estim ated sp e ctra w ith th e observed spectrum in each of th e four regions. T he estim ated sp ectra of figure 7 are determ ined using projectio n factors,
k x i = N x i /N x o , (7.2)
from events w ith n = 0 to those w ith n = 1, in each of th e th ree regions X = A, B , and C in order to d eterm ine th e ex ten t to which th e prediction varies w ith each choice. Region D1 was used to v alidate th e sy stem atic u n certain ty derived from A1, B 1, and C 1. Because of th e th re e projectio n factors (k ^, kB , and kC) th ere are th re e estim ates (N Y1/ ,i , NYp ,i ,
J H E P 0 6 ( 2 0 1 6 ) 0 6 7
and Ny i i ) of the mjaVg spectrum in each of the regions Y 1 = A1, B1, and C 1. Thus, in total there are nine estim ates of the actual spectra, these are w ritten succinctly as
N y 1/^i = k x 1 x Nyoi , where X = {A, B , C } and Y = {A, B , C }. (7.3) These estim ates provide a test of the shape com patibility as well as the overall normalisation of the background estim ate (the special cases N ^p ,,, N B1/ ,,, and N C1/ ,, are normalised to the d ata by construction and thus only provide a shape comparison of n = 1 and n = 0). A system atic uncertainty for the background projection is then derived by taking, bin-by-bin, the largest deviation of the ratio of estim ated to actual yield from unity in the mJaVg spectra in each of the regions A, B, and C according to
^bkg. syst. = ^ | 1 _ N y^ , . / N y 1)i | , (7.4)
where Ny 1,, are the observed d ata points and N y p ,, are the estim ated spectra defined by eq. (7.3) . A bin w idth of 5 0 GeV is used, ju st as above with the 6-jet multiplicity maVg shape system atic uncertainty. This is added in quadrature with the statistical uncertainty of th a t ratio in order to form the total systematic uncertainty for th a t particular bin. The size of the background estim ation mJaVg shape system atic uncertainty varies from less th an 10% at low ~ 100 GeV to 20% near mJavg ~ 400 GeV. Figure 8 shows the background estim ation shape system atic uncertainty as well as the to tal system atic uncertainty when combined with the two above-mentioned systematic uncertainties.
7 .3 B a c k g r o u n d ££ c o n tr ib u tio n s y s t e m a t ic u n c e r ta in ty
Since POWHEG+ PYTHIA MC simulation is used to determ ine the contribution from ti events in the signal region and each of the control regions, systematic uncertainties related to the MC simulation of the process itself are included in the to tal systematic uncertainty for the background estimation. The theoretical uncertainties include renormalisation and factori
sation scale variations, parton distribution function uncertainties, the choice of MC genera
to r using comparisons with MC@NLO [95], the choice of parton shower models using compar
isons with Herwig [96], and initial- and final-state radiation (FSR) modelling uncertainties.
The size of the theoretical system atic uncertainties for tt production vary from approxi
m ately 40% to 70% in the relevant kinematic regions and are dom inated by the uncertainties from the MC generator and IS R /F S R variations. The detector-level uncertainties include the JES and JE R uncertainties [83] as well as the 6-tagging efficiency and m istag-rate un
certainties [87]. U ncertainties associated with the large-R jet mass scale and resolution are taken into account by the JES and JE R uncertainties of the input small-R jets [88].
The size of the to tal tt system atic uncertainty varies in the mass range ma^g = 100
200 GeV from approxim ately 50% to 80%. In the range mJaetg = 300-400 GeV the tt system atic uncertainties are of the order of 100%, but the tt background is completely negligible in this range. Lastly, an uncertainty of 2.8% is applied to the measured integrated luminosity of 17.4 fb-1 following the methodology described in ref. [97].
J H E P 0 6 ( 2 0 1 6 ) 0 6 7
F ig u re 7. The mJaVg distribution is shown in four validation regions with n = 1. In each case the data (A1, B1, C1, and D1) are compared to estimates based on projection factors derived between n = 0 and n = 1 in A, B, and C (see section 7.2).
7 .4 S ig n a l s y s t e m a t ic u n c e r ta in tie s
In addition to the system atic uncertainties associated with the background estim ate, the MC simulation of the signal model is subject to system atic uncertainties. Much like the contribution from tt, these uncertainties include experimental uncertainties as well as theo
retical uncertainties. The detector-level uncertainties include the JES and JE R uncertain
ties, and the b-tagging uncertainties as described for the estim ate of tt. The theoretical uncertainties include renormalisation and factorisation scale variations, parton distribu
tion function uncertainties, and ISR and FSR modelling uncertainties. The nominal signal
J H E P 0 6 ( 2 0 1 6 ) 0 6 7
F ig u re 8. Systematic uncertainty for the data-driven multijet background estimation. The blue dashed line represents the background estimation systematic uncertainty estimated from compar
isons of the predicted mjeJg spectra in regions A1, B 1 , and C 1 to the actual spectra. The red dotted line represents the estimated systematic uncertainty due to shape differences between events with n = 0 and n > 2. The green line represents a systematic uncertainty due to the level of compatibil
ity of kA 2 and kC2. Finally, the black line with a filled yellow area shows the combined systematic uncertainty of all three contributions added in quadrature. The systematic uncertainty curves were smoothed with a Gaussian filter of spread 20 GeV.
cross-section and its uncertainty are taken from an envelope of cross-section predictions us
ing different P D F sets and factorisation and renormalisation scales, as described in ref. [66].
Each signal model is varied according to these systematic uncertainties and the impact on the acceptance in each mass window is then propagated to the final result. The largest contribution to the total signal system atic uncertainty comes from the JES and b-tagging, both in the range 10-18%. The size of the theoretical uncertainty grows from around 5%
for low-mass stops to around 10% for higher-mass stops.
To evaluate the IS R /F S R system atic uncertainty, separate samples of tt* pair events are generated using MadGraph + PYTHIA, and the rate of IS R /F S R production is varied. These are used to reweight the pT (tt*) distribution of the nominal signal samples to estim ate the change in signal acceptance x efficiency. The effect ranges from 0-17%, with the largest im pact at high my.
J H E P 0 6 ( 2 0 1 6 ) 0 6 7
m-t [GeV] Window [GeV] N"data driven est.
nB est. NBot. est. N obs.
Ndata Ns
100 [95,115] 465 ± 56 39 ± 26 504 ± 61 460 560 ± 140
125 [115,135] 496 ± 49 68 ± 37 564 ± 61 555 570 ± 130
150 [135,165] 680 ± 61 105 ± 49 785 ± 78 761 560 ± 110
175 [165,190] 471 ± 46 63 ± 19 534 ± 50 583 421 ± 96
200 [185, 210] 395 ± 46 16.5 ± 9.6 412 ± 47 416 293 ± 50
225 [210, 235] 266 ± 37 2.4 ± 2.4 269 ± 37 283 178 ± 36
250 [235, 265] 176 ± 27 1.1 ± 1.1 177 ± 27 195 127 ± 29
275 [260, 295] 104 ± 19 0.59 ± 0.55 104 ± 19 96 71 ± 20
300 [280, 315] 69 ± 16 0.93 ± 0.29 70 ± 16 51 48 ± 10
325 [305, 350] 43 ± 14 0.73 ± 0.53 43 ± 14 44 29.4 ± 6.9
350 [325, 370] 26 ± 10 0.23 ± 0.15 26 ± 10 37 20.2 ± 4.3
375 [345, 395] 18.6 ± 9.8 0.076 ± 0.076 18.7 ± 9.8 22 12.6 ± 2.8
400 [375,420] 9.5 ± 7.7 0.026 ± 0.026 9.5 ± 7.7 5 8.1 ± 1.8
T able 5. Summary of the observed number of events in the data and the estimated number of signal and background events with total uncertainties (i.e. all listed uncertainties are the combined statistical and systematic uncertainties) th at fall within each of the optimised mass windows in region D2. The total number of estimated background events in each window is the sum of the estimated background from the data-driven method and the t t simulation. The columns, from left to right indicate: NBata-drlven est', the data-driven background estimate; Ng est', the background contribution from tt; N_Bot' est', the total estimated background; N ^ g,, the number of observed events in the data; and NS, the number of expected signal events.
8 R e su lts
Table 5 sum m arises th e observed and expected num ber of events th a t fall w ithin each of th e optim ised m ass windows in th e signal region, D 2 . Figure 9 shows th e observed m ’Bvg d istri
b u tio n in th e d a ta , along w ith th e estim ated background sp ectru m , including b o th th e sys
tem a tic and sta tistic a l u ncertainties. No excess over th e background prediction is observed.
M odel-independent u p p er lim its a t 95% confidence level (CL) on th e num ber of beyond- the-SM (BSM) events for each signal region are derived using th e C L s prescription [98] and neglecting any possible co n trib u tio n in th e control regions. D ividing these by th e in teg rated lum inosity of th e d a ta sam ple provides up p er lim its on th e visible BSM cross-section, a vis., which is defined as th e p ro d u ct of acceptance (A), reco nstructio n efficiency (e), branching ratio (B R ), and p ro d u ctio n cross-section ( a prod.). T his search specifically targ e ts low-mass t ^ bs decays, assum ing 100% BR. T he resulting lim its on th e num ber of BSM events and on th e visible signal cross-section are shown in ta b le 6 . T he significance of an excess can be quantified by th e prob ab ility (p0) th a t a background-only experim ent has a t least as m any events as observed. This p-value is also rep o rted for each region in tab le 6 , where
J H E P 0 6 ( 2 0 1 6 ) 0 6 7
Figure 9. The observed mJaVg spectrum in the signal region is shown as black points with statistical uncertainties. Also shown is the total SM background estimate, and the separate contributions from the data-driven multijet and MC t t backgrounds. The red hatched band represents the combined statistical and systematic uncertainty on the total SM background estimate. Signal mass spectra are shown with statistical uncertainties only. The bottom panel shows the ratio of the data relative to the total SM background estimate.
p0 = 1 — CLb and CLb is the confidence level observed for the background-only hypothesis.
The p-value is truncated at 0.5 for any signal region where the observed number of events is less th an the expected number.
Exclusion limits are set on the signal model of interest. A profile likelihood ratio com
bining Poisson probabilities for signal and background is computed to determ ine the 95%
CL for com patibility of the d ata with the signal-plus-background hypothesis (CLs+b) [99].
A similar calculation is performed for the background-only hypothesis (CL&). From the ratio of these two quantities, the confidence level for the presence of signal (CLs) is deter
mined [98]. Systematic uncertainties are treated as nuisance param eters assuming Gaussian distributions and pseudo-experiments are used to evaluate the results. This procedure is implemented using a software framework for statistical d ata analysis, H istF itter [100]. The observed and expected 95% CL upper limits on the allowed cross-section are shown in fig-
