Search for flavour-changing neutral current top quark decays $t\rightarrow Hq$ in $\mathit{pp}$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector

P u b l i s h e d f o r S I S S A b y S p r i n g e r

R e c e i v e d: S e p te m b e r 22, 2015

R e v i s e d: N o v e m b e r 9, 2015

A c c e p t e d: N o v e m b e r 12, 2015

P u b l i s h e d: D ecem ber 10, 2015

Search for flavour-changing neutral current top quark decays t → H q in pp collisions at √ s = 8 TeV with the ATLAS detector

T h e A T LA S collaboration

E-mail: 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 flavour-changing n e u tra l c u rren t decays of a to p qu ark to an up- ty p e q u ark (q = u, c) and th e S ta n d ard M odel Higgs boson, w here th e Higgs boson decays to bb, is presented. T he analysis searches for to p q u ark pair events in which one to p q uark decays to Wb, w ith th e W boson decaying leptonically, and th e o th er to p qu ark decays to Hq. T he search is based on pp collisions at yfs = 8TeV recorded in 2012 w ith the ATLAS d etecto r at th e C E R N Large H adron Collider and uses an in tegrated lum inosity of 20.3 fb- 1 . D a ta are analysed in th e lepton-plus-jets final sta te , characterised by an isolated electron or m uon and a t least four jets. T he search exploits th e high m ultiplicity of b- q u ark je ts ch aracteristic of signal events, and employs a likelihood discrim inant th a t uses th e kinem atic differences betw een th e signal and th e background, which is dom in ated by t t ^ W b W b decays. No significant excess of events above th e background ex p ectatio n is found, and observed (expected) 95% CL up p er lim its of 0.56% (0.42%) and 0.61% (0.64%) are derived for th e t ^ H c and t ^ H u branching ratios respectively. T he com bination of th is search w ith o th er ATLAS searches in th e H ^ 7 7 and H ^ W W * , r r decay m odes significantly improves th e sensitivity, yielding observed (expected) 95% CL u p per lim its on th e t ^ H c and t ^ H u branching ratios of 0.46% (0.25%) and 0.45% (0.29%) respectively. T he corresponding com bined observed (expected) u p p er lim its on th e |AtcH | and lAtuH| couplings are 0.13 (0.10) and 0.13 (0.10) respectively. These are th e m ost restrictive direct bounds on tq H in teractions m easured so far.

Ke y w o r d s: H adron-H adron S cattering, Top Physics, Higgs Physics, FC N C In teractio n s ArXiy ePr in t: 1509.06047

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C o n te n ts

1 I n t r o d u c t i o n 2

2 A T L A S d e t e c t o r 4

3 O b j e c t r e c o n s t r u c t i o n 4

4 D a t a s a m p le a n d e v e n t p r e s e l e c t io n 6

5 B a c k g r o u n d a n d s ig n a l m o d e llin g 6

6 A n a ly s is s t r a t e g y 10

6.1 E vent catego risatio n 10

6.2 D iscrim ination of signal from background 10

6.2.1 Signal prob ab ility 12

6.2.2 B ackground prob ab ility 13

6.2.3 F in al d iscrim inant 15

7 S y s t e m a t i c u n c e r t a i n t i e s 15

7.1 Lum inosity 15

7.2 R eco n stru cted objects 18

7.3 B ackground m odelling 19

7.4 Signal m odelling 20

8 S t a t i s t i c a l a n a ly s is 21

9 R e s u l t s 22

9.1 H ^ bb 22

9.2 H ^ 7 7 24

9.3 H ^ W + W - , r + t - 29

9.4 C om bination of searches 30

10 C o n c l u s io n 34

A P r e - f i t a n d p o s t- f it e v e n t y ie ld s in t h e t t ^ W b H q , H ^ bb s e a r c h 36 B P r e - f i t e v e n t y ie ld s in t h e t t ^ W b H q , H ^ W W * , r r s e a r c h 39

T h e A T L A S c o l l a b o r a t i o n 47

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1 In tr o d u c tio n

Following th e observation of a Higgs boson by th e ATLAS and CMS collaborations [1, 2], a com prehensive program m e of m easurem ents of its properties is underw ay looking for deviations from th e S tan d ard M odel (SM) predictions. An interesting possibility is th e presence of flavour-changing n e u tra l cu rren t (FC N C ) interactions betw een th e Higgs boson, th e to p quark, and a u- or c-quark, t q H (q = u, c). Since th e Higgs boson is lighter th a n th e to p quark, w ith a m easured m ass m H = 125.09 ± 0.24 GeV [3], such interactions would m anifest them selves as FC N C to p q uark decays, t ^ Hq. In th e SM, such decays are extrem ely suppressed relative to th e dom inant t ^ W b decay m ode, since tq H interactions are forbidden a t th e tre e level and even suppressed a t higher-orders in th e p e rtu rb ativ e expansion due to th e G lashow -Iliopoulos-M aiani (GIM ) m echanism [4]. As a result, th e SM predictions for th e t ^ H q branching ratios are exceedingly small: B R (t ^ H u ) ~ 10-1 7 and B R (t ^ Hc) ~ 10-15 [5- 8]. On th e o th er hand, large enhancem ents in these branching ratios are possible in some beyond-SM scenarios, w here th e GIM suppression can be relaxed a n d /o r new particles can c o n trib u te to th e loops, yielding effective couplings orders of m ag n itude larger th a n those of th e SM. E xam ples include quark-singlet m odels [9], two- H iggs-doublet m odels (2HDM ) of ty p e I, w ith explicit flavour conservation, and of ty p e II, such as th e m inim al supersym m etric SM (MSSM) [10- 12], or supersym m etric m odels w ith R -p arity violation [13]. In those scenarios, typical branching ratios can be as high as B R (t ^ Hq) ~ 10- 5 . A n even larger branching ratio of B R (t ^ Hc) ~ 10- 3 can be reached in 2HDM w itho u t explicit flavour conservation (type III), since a tree-level FC N C coupling is not forbidden by any sym m etry [14- 16]. W hile o th er FC N C to p couplings, tqq, t q Z , tqg, are also enhanced relative to th e SM prediction in those scenarios beyond th e SM, th e largest enhancem ents are typically for th e t q H couplings, and in p a rticu la r th e t c H coupling. See ref. [7] for a review.

Searches for t ^ H q decays have been perform ed by th e ATLAS and CMS collabora­

tions, tak in g advantage of th e large sam ples of t t events collected during R u n 1 of th e LHC.

In these searches, one of th e to p quarks is required to decay into W b , while th e o th er top q u ark decays into Hq, yielding t t ^ W b H q .1 A ssum ing SM decays for th e Higgs boson and m n = 125 GeV, th e m ost sensitive single-channel searches have been perform ed in th e H ^ 7 7 decay m ode which, d espite th e tin y branching ratio of B R (H ^ 7 7) ~ 0.2%, is ch aracterised by very small background and excellent d ip hoto n m ass resolution. T he resulting observed (expected) 95% confidence level (CL) u p p er lim its on B R (t ^ Hq) are 0.79% (0.51%) and 0.69% (0.81%), respectively from th e ATLAS [17] and CMS [18] collab­

orations. T hese searches are insensitive to th e difference betw een t ^ H u and t ^ Hc, and th u s th e above lim its can be in terp reted as applying to th e sum B R (t ^ H u ) + B R ( t ^ H c).

T he CMS C ollaboration has also rein terp reted searches in m ultilep to n (three or four lep- tons) final sta te s [18] in th e context of t t ^ W b H q w ith H ^ W W * , r r , resulting in an observed (expected) u p p er lim it of B R (t ^ Hc) < 1.28% (1.17%) a t th e 95% CL. M ulti- lepton searches are able to exploit a significantly larger branching ratio for th e Higgs boson

Tn the following WbHq is used to denote both W+bHq and its charge conjugate, HqW- b. Similarly, WbWb is used to denote W+bW- b.

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decay com pared to th e H ^ 7 7 decay m ode, and are also characterised by relatively small backgrounds. However, in general th ey do not have good m ass resolu tion,2 so any excess would be h ard to in terp ret as originating from t ^ H q decays. T he com bination of CMS searches in dip h o to n and m ultilep ton (th ree or four leptons) final sta te s yields an observed (expected) u p p er lim it of B R (t ^{^} Hc) < 0.56% (0.65%) a t th e 95% CL [18].

U p per lim its on th e branching ratios B R (t ^{^} Hq) (q = u, c) can be tra n sla te d to up p er lim its on th e non-flavour-diagonal Yukawa couplings AtqH ap p earin g in th e following L agrangian:

L f c n c = AtcH t H c + AtuH t H u + h.c. (1.1)

T he branching ratio B R (t ^{^} H q) is estim ated as th e ratio of its p a rtia l w id th [8] to th e SM t ^ W b p a rtial w idth [19], which is assum ed to be dom in ant. B o th predicted p artial w idths include next-to-leading-order (NLO) QCD corrections. Using th e expression derived in ref. [17], th e coupling ^|AtqH^| can be ex tra cte d as ^|AtqH^| = (1.92 ^± 0 .0 2 )^ /B R (t ^{^} H q).

T he results presented in th is p a p e r fill a gap in th e c u rren t program m e of searches for t ^ H q decays a t th e LHC by considering th e d om inan t decay m ode H ^ bb, which has B R (H ^{^} bb) ^~ 58%. This search is focused on th e t t ^ W b H q (q = u ,c ) process, w ith W ^ £v (I = e, ^ , ^t ) and H ^ bb, resulting in a lepton-plus-jets final s ta te w ith high b-jet m ultiplicity, which can be effectively exploited to suppress th e overw helm ing tb background.

E arly studies of th e prospects for th is search a t th e LHC were perform ed in ref. [20]. Only events w ith an electron or m uon, including those produced via leptonically decaying tau s, are considered. T he lepton-plus-jets final s ta te also allows th e kinem atic recon stru ctio n of th e final s ta te and in p a rticu la r th e dijet invariant m ass spectrum from th e H ^ bb decay, providing ad d ition al handles th a t would help in detectin g t t ^ W b H q events. M ost of th is p a p e r is devoted to th e discussion of th is p a rticu la r search, for which background es­

tim atio n techniques, system atic uncertainties and sta tistic a l tre a tm e n t closely follow those used in recent ATLAS searches using th e sam e final-state sign ature [21, 22]. T his p a­

p er also includes a rein terp re ta tio n of th e ATLAS search for t t H associated production, w ith H ^{^} W W^*, Z Z^{* , t t}, resulting in m ultilepto n final sta te s [23]. T his rein terp re ta tio n only considers th e final sta te s w ith a significant expected co n trib u tio n from t t ^ W b H q , H ^ W W^{* , t t} signal, nam ely two sam e-charge leptons w ith and w ith o u t an identified hadronic ta u lepton and th re e leptons. A com bination of th e th re e ATLAS searches for t t ^ W b H q , probing th e H ^ bb, H ^ W W * , t t, and H ^ 7 7 decay m odes, is perform ed and bounds are set on B R (t ^{^} Hc) and B R (t ^{^} H u ) , as well as on th e corresponding non-flavour-diagonal Yukawa couplings.

T his p ap er is organised as follows. A brief description of th e ATLAS d e te c to r is provided in section 2 . Subsequent sections are devoted to a detailed discussion of th e t t ^ W b H q , H ^ bb search, covering th e object recon struction (section 3) , th e d a ta sam ple and event preselection (section 4) , th e m odelling of th e backgrounds and th e signal (section 5) , th e analysis stra te g y (section 6) , and th e system atic uncertain ties (section 7) . Section 8 provides a discussion of th e sta tistic a l m ethods used. Section 9 presents th e

2 An exception is the H ^ ZZ* ^ f - (t, t! = e, y) decay mode, which has a very small branching ratio and thus is not promising for this search.

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results obtain ed by th e th re e individual ATLAS searches as well as th eir com bination.

Finally, th e conclusions are given in section 10.

2 A T L A S d e te c to r

T he ATLAS d etecto r [24] consists of th e following m ain subsystem s: an inner tracking system , electrom agnetic and hadronic calorim eters, and a m uon spectrom eter. T he inner d e te c to r provides trackin g inform ation from silicon pixel and m icrostrip detectors in th e p seu do rap idity3 range |n| < 2.5 and from a straw -tu b e tra n sitio n rad iatio n tracker cover­

ing |n| < 2.0, all im m ersed in a 2 T axial m agnetic field provided by a superconducting solenoid. T he electrom agnetic (EM ) sam pling calorim eter uses lead as th e abso rb er m ate ­ rial and liquid-argon (LAr) as th e active m edium , and is divided into b arrel (|n| < 1.475) and end-cap (1.375 < |n| < 3.2) regions. H adron calorim etry is also based on th e sam ­ pling technique, w ith eith er scintillator tiles or LA r as th e active m edium , and w ith steel, copper, or tu n g ste n as th e abso rb er m aterial. T he calorim eters cover |n| < 4.9. T he m uon sp ectro m eter m easures th e deflection of m uons w ith |n| < 2.7 using m ultiple layers of high-precision track in g cham bers located in a to ro idal field of approxim ately 0.5 T and 1 T in th e cen tral and end-cap regions of ATLAS, respectively. T he m uon sp ectro m eter is also in stru m en ted w ith sep arate trigger cham bers covering |n| < 2.4. A three-level trigger system [25] is used to select interesting events. T he first-level trig ger is im plem ented in custom electronics and uses a subset of d etecto r inform ation to reduce th e event ra te to a t m ost 75 kHz. T his is followed by two softw are-based trigger levels exploiting th e full d e te c to r inform ation and yielding a typical recorded event ra te of 400 Hz d u rin g 2012.

3 O b je c t r e c o n str u c tio n

E lectron can d idates [26] are reco nstructed from energy clusters in th e EM calorim eter th a t are m atched to reco n stru cted track s in th e inner d etecto r. E lectro n clusters are required to have a tran sv erse energy E T g reater th a n 25 GeV and |nciuster| < 2.47, excluding th e tra n sitio n region 1.37 < |% luster| < 1.52 betw een sections of th e EM calorim eter. T he lon­

g itud in al im pact p a ra m ete r of th e electron tra c k w ith respect to th e e v en t’s p rim ary vertex (see section 4) , z0, is required to be less th a n 2 m m. E lectrons are required to satisfy

“tig h t” q u ality requirem ents [26] based on calorim eter, trackin g and com bined variables th a t provide good sep aratio n betw een p ro m p t electrons and jets. To reduce th e back­

ground from n on-prom pt electrons resulting from sem ileptonic decays of b- or c-hadrons, and from jets w ith a high fraction of th e ir energy deposited in th e EM calorim eter, elec­

tro n candid ates m ust also satisfy calorim eter- and track-based isolation requirem ents. T he calorim eter isolation variable is based on th e energy sum of cells w ithin a cone of size

3ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis coinciding with the axis of the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upward. Cylindrical coordinates (r,0) are used in the transverse plane, 0 being the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angle 6 as n = — lntan(6/2).

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A R = \ / ( A^ ) 2 + (A n) 2 = 0.2 aro un d th e direction of each electron candid ate, and an n-dependent requirem ent is m ade, giving an average efficiency of 90% across n for p ro m pt electrons from Z boson decays. T his energy sum excludes cells associated w ith th e electron cluster and is corrected for leakage from th e electron cluster itself as well as for energy de­

posits from ad ditio nal pp in teractions w ithin th e sam e bunch crossing ( “pileup” ). A fu rth e r 90%-efficient isolation requirem ent is m ade on th e tra c k transverse m om entum (px) sum aroun d th e electron (excluding th e electron tra c k itself) in a cone of size A R = 0.3.

M uon can didates [27, 28] are reconstructed from tra c k segm ents in th e various layers of th e m uon sp ectrom eter th a t are m atched w ith tracks found in th e inner d etector. T he final can d idates are refitted using th e com plete tra c k inform ation from b o th d etecto r system s and are required to have p x > 25 GeV and |n| < 2.5. T he longitudinal im pact p a ra m ete r of th e m uon tra c k w ith respect to th e p rim ary vertex, z0, is required to be less th a n 2 mm.

M uons are required to satisfy a p x -dependent track-based isolation requirem ent: th e scalar sum of th e p x of th e tracks w ithin a cone of variable size A R = 10 GeV /pT arou n d th e m uon (excluding th e m uon tra c k itself) m ust be less th a n 5% of th e m uon px (pX). This requirem ent has good signal efficiency and background rejection even un der high-pileup conditions, as well as in boosted configurations w here th e m uon is close to a je t. For m uons from W boson decays in sim ulated ttt events, th e average efficiency of th e isolation requirem ent is ab o u t 95%.

J e ts are reco n stru cted w ith th e a n ti - k algorithm [29- 31] w ith a radius p aram eter R = 0.4, using calib rated topological clusters [32, 33] built from energy deposits in th e calorim eters. P rio r to je t finding, a local cluster calib ratio n scheme [34] is applied to correct th e topological clu ster energies for th e non-com pensating response of th e calorim e­

ter, as well as for th e energy lost in dead m aterial and via out-of-cluster leakage. T he corrections are obtain ed from sim ulations of charged and n e u tra l particles. A fter energy calib ration [35], jets are required to have p x > 25 GeV and |n| < 2.5. To reduce th e con­

ta m in a tio n due to je ts originating from pileup interactions, a requirem ent on th e absolute value of th e je t v ertex fraction (JV F ) variable above 0.5 is applied to je ts w ith p x < 50 GeV and |n| < 2.4. T his requirem ent ensures th a t at least 50% of th e scalar sum of th e p x of th e tracks w ith px > 1 GeV associated w ith a je t comes from track s originating from th e p rim ary vertex. D uring je t reconstruction, no d istinctio n is m ade betw een identified elec­

tro n s and je t energy deposits. Therefore, if any of th e je ts lie w ithin A R = 0.2 of a selected electron, th e closest je t is discarded in order to avoid double-counting of electrons as jets.

Finally, any electron or m uon w ithin A R = 0.4 of a selected je t is discarded.

J e ts containing b-hadrons are identified (b-tagged) via an algorithm [36] th a t uses m u ltiv ariate techniques to com bine inform ation from th e im pact p aram eters of displaced tracks as well as topological properties of secondary and te rtia ry decay vertices recon­

stru c te d w ithin th e je t. For each jet, a value for th e m ultivariate b-tagging discrim inant is calculated. T he je t is considered b-tagged if th is value is above a given threshold. T he thresh o ld used in th is search corresponds to 70% efficiency to ta g a b-quark je t, w ith a light-jet4 rejection factor of ^ 1 3 0 and a charm -jet rejection factor of 5, as determ ined for je ts w ith pT > 20 GeV and |n| < 2.5 in sim ulated t t events.

4Light-jet denotes a jet originating from the hadronisation of a light quark (u, d, s) or gluon.

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T he m issing tran sv erse m om entum (E™ ss) is co n stru cted [37] from th e vector sum of all calorim eter energy deposits contained in topological clusters. All topological cluster energies are corrected using th e local cluster calibration scheme discussed previously in th e context of th e je t energy calibration. Those topological clusters associated w ith a high-pT ob ject (e.g. je t or electron) are fu rth e r calibrated using th e ir respective energy corrections.

In addition, co ntrib u tio ns from th e p T of selected m uons are included in th e calculation of E p iss.

4 D a ta sa m p le and e v e n t p r e se le c tio n

T his search is based on pp collision d a ta at y/s = 8 TeV collected by th e ATLAS experim ent betw een A pril and D ecem ber 2012. O nly events recorded w ith a single-electron or single­

m uon trig g er under stable beam conditions and for which all d e te c to r subsystem s were o p erational are considered. T he corresponding integ rated lum inosity is 2 0 .3 ± 0.6 fb-1 [38].

Single-lepton triggers w ith different p t thresholds are com bined in a logical O R in o rder to increase th e overall efficiency. T he p t thresholds are 24 or 60 GeV for th e electron triggers and 24 or 36 GeV for th e m uon triggers. T he triggers w ith th e lower p t threshold include isolation requirem ents on th e c an d id ate lepton, resulting in inefficiencies a t high p t th a t are recovered by th e triggers w ith higher p t threshold.

E vents satisfying th e trigg er selection are required to have a t least one reconstructed v ertex w ith a t least five associated tracks w ith pT > 400 MeV, consistent w ith originating from th e beam collision region in th e x - y plane. T he average num ber of pp interactions per bunch crossing is ap proxim ately 20, resulting in several vertices reconstructed p er event.

If m ore th a n one v ertex is found, th e h a rd -sc atte r prim ary v ertex is tak en to be th e one which has th e largest sum of th e squared transv erse m om enta of its associated tracks. For th e event topologies considered in th is paper, this requirem ent leads to a probab ility to reconstru ct and select th e correct h a rd -sc a tte r p rim ary v ertex larger th a n 99%.

Preselected events are required to have exactly one electron or m uon, as defined in section 3 , th a t m atches, w ithin A R = 0.15, th e lepton can d id a te reco nstructed by th e trigger. In addition, a t least four je ts are required, of which a t least two m ust be b-tagged.

5 B a ck g ro u n d and sig n a l m o d e llin g

A fter th e event preselection, th e m ain background is t t ^ W b W b production, possibly in association w ith jets, denoted by tt+ je ts in th e following. Single to p q u ark prod uctio n and p ro d u ctio n of a W boson in association w ith je ts (W + je ts) c o n trib u te to a lesser extent.

Small contribu tion s arise from m u ltijet, Z + je ts and diboson (W W , W Z, Z Z ) production, as well as from th e associated pro d u ction of a vector boson V (V = W, Z ) or a Higgs boson and a t t p air ( t t V and t t H ). Signal and all backgrounds are estim ated from sim ulation and norm alised to th e ir th eoretical cross sections, w ith th e exception of th e m u ltijet background, which is estim ated w ith d ata-d riv en m ethods [39].

Sim ulated sam ples of ttt events are generated w ith th e NLO gen erato r P o w h e g - B o x 2.0 [40- 43] using th e CT10 [44] set of p a rto n d istrib u tio n functions (P D F ). T he nom inal

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sam ple is interfaced to P y t h i a 6.425 [45] for p a rto n showering and h ad ronisatio n w ith th e CTEQ 6L1 P D F set and th e Perugia2011C [46] set of optim ised p aram eters for th e underlying event (UE) description, referred to as th e “U E tu n e ” . An a ltern ativ e sam ­ ple, used to stu d y th e u n certain ty related to th e h adron isation model, is interfaced to H e r w ig v6.520 [47] w ith th e CTEQ 6L1 P D F set and Jim m y v4.31 [48] to sim ulate th e UE. All sam ples are g en erated assum ing a to p q u ark m ass of 172.5 GeV and to p q u ark decays exclusively th ro u g h t ^ Wb. T he t t process is norm alised to a cross section of 253+16 pb, com puted using T o p + + v2.0 [49] a t next-to -nex t-to -lead ing order (NNLO) in QCD, including resum m ation of next-to -n ext-to-leadin g logarithm ic (NNLL) soft gluon term s [50- 54], and using th e M ST W 2008 NNLO [55, 56] P D F set. T heoretical uncer­

tain tie s result from variations of th e factorisatio n and renorm alisation scales, as well as from un certain ties on th e P D F and a s . T he la tte r two represent th e largest con trib u tio n to th e overall th eo retical u n certain ty on th e cross section and were calculated using th e PD F 4L H C prescription [57] w ith th e M ST W 2008 68% CL NNLO, CT10 NNLO [44, 58]

and N N PD F2.3 5f F F N [59] P D F sets. In th e case w here a non-zero B R (t ^ Hq) is as­

sum ed, an additio n al factor of [1 — B R (t ^ H q)]2 is applied to th e sam ple norm alisation.

It is not possible to g enerate th e t t ^ W b H q signal w ith P o w h e g - B o x , and a different event g en erator is used instead, as discussed below.

T he t t sam ples are generated inclusively, b u t events are categorised depending on th e flavour content of ad d ition al particle je ts not originating from th e decay of th e tt sy stem.5 D etails ab o u t this categorisation scheme can be found in ref. [21]. In th is way, a distin ction is m ade betw een t t + bb, tt + cc and ti+ lig h t-je ts events. T he first two categories are generically referred to as tt+ H F events (w ith H F stan d in g for “heavy flavour”), while th e la tte r category also includes events w ith no ad d ition al jets. T he m odelling of tt+ H F in P o w h e g - B o x + P y t h i a is via th e parton-show er evolution. To stu d y uncertainties related to th is simplified description, an a ltern ativ e tt+ je ts sam ple is generated w ith M a d g r a p h 5 1.5.11 [60] using th e CT10 P D F set. It includes tree-level diagram s w ith up to three ad d itio nal p arto n s (including b- and c-quarks) and is interfaced to P y t h i a 6.425.

Since th e best possible m odelling of th e tt+ je ts background is a key aspect of this search, a correction is applied to sim ulated ttt events in P o w h e g - B o x + P y t h i a based on th e ratio of th e differential cross sections m easured in d a ta and sim ulation a t yfs = 7 TeV as a function of to p q u ark pT and t t system p T [61]. T his correction significantly improves agreem ent betw een sim ulation and d a ta at yfs = 8 TeV in d istrib u tio n s such as th e je t m ultiplicity and th e p T of decay p ro ducts of th e t t system [21], and is applied only to ti+ lig h t-je ts and t t + cc events. T he m odelling of th e t t + bb background is im proved by rew eighting th e P o w h e g - B o x + P y t h i a prediction to an NLO prediction of t i + bb w ith massive b quarks and including p a rto n showering [62], based on S h e r p a + O p e n L o o p s [63, 64] using th e CT10 P D F set. Such tre a tm e n t is not possible for th e t t + cc background since a corresponding NLO prediction is not cu rrently available. M ore d etails ab o u t th e m odelling of th e tt+ je ts background can be found in ref. [21].

5Particle jets are reconstructed by clustering stable particles excluding muons and neutrinos using the anti-kt algorithm with a radius parameter R = 0.4.

J H E P 1 2 ( 2 0 1 5 ) 0 6 1

Sam ples of single-top-quark backgrounds corresponding to th e t-channel, s-channel, and W t p ro d u ctio n m echanism s are g enerated w ith P o w h e g - B o x 2.0 [65, 66] using th e CT10 P D F set and interfaced to P y t h i a 6.425 w ith th e CTEQ 6L1 P D F set in com bination w ith th e Perugia2011C U E tu n e. O verlaps betw een th e t i and W t final sta te s are avoided using th e “diagram rem oval” scheme [67]. T he single-top-quark sam ples are norm alised to th e appro xim ate NNLO th eo retical cross sections [68- 70], calculated using th e M ST W 2008 NNLO P D F set.

Sam ples of W /Z + je ts events are g enerated w ith up to five add ition al parto n s us­

ing th e A l p g e n v2.14 [71] LO g en erator w ith th e CTEQ 6L1 P D F set and interfaced to P y t h i a 6.426. To avoid double-counting of parto n ic configurations generated by b o th th e m atrix-elem ent calculation and th e p a rto n shower, a p a rto n -je t m atching scheme ( “MLM m atch ing” ) [72] is employed. T h e W + je ts sam ples are generated sep arately for W + lig h t- jets, W bb+ jets, W cc+ jets, and W c + je ts. T he Z + je ts sam ples are generated separately for Z + lig h t-je ts, Z bb+ jets, and Z c c + je ts. O verlap betw een V Q Q + je ts (V = W, Z and Q = b, c) events gen erated from th e m atrix-elem ent calculation and those generated from parton-show er evolution in th e W /Z + lig h t-je ts sam ples is avoided via an algorithm based on th e angular sep aratio n betw een th e e x tra heavy quarks: if A R (Q , Qt ) > 0.4, th e m atrix- elem ent prediction is used, otherw ise th e parton-show er prediction is used. B o th th e W + je ts and Z + je ts background contributions are norm alised to th e ir inclusive NNLO th e ­ oretical cross sections [73]. F u rth e r corrections are applied to W /Z + je ts events in o rder to b e tte r d escribe d a ta in th e preselected sam ple. N orm alisation factors for each of th e W + je ts categories (W bb+ jets, W cc+ jets, W c + je ts and W + lig h t-je ts) are derived for events w ith one lepton and a t least four je ts by sim ultaneously analysing six different event categories, defined by th e b-tag m ultiplicity (0, 1 and > 2) and th e sign of th e lepton charge [74]. T he b-tag m ultiplicity provides inform ation ab o u t th e heavy-flavour com position of th e W + je ts background, while th e lepton charge is used to determ in e th e n orm alisation of each com ­ ponent, exploiting th e expected charge asym m etry for W + je ts pro du ction in pp collisions as predicted by A l p g e n . In th e case of Z + je ts events, a correction to th e heavy-flavour fraction is derived to reproduce th e relative rates of Z + 2 -je ts events w ith zero and one b-tagged je t observed in d a ta . In addition, th e Z boson p x spectru m is com pared betw een d a ta and th e sim ulation in Z +2-jets events, and a rew eighting function is derived in or­

d er to im prove th e m odelling. This rew eighting function is also applied to th e W + je ts sim ulated sam ple and it was verified th a t th is correction fu rth e r improves th e agreem ent betw een d a ta and sim ulation for W + je ts events. In any case, W /Z + je ts events co n stitu te a very small background in th is analysis after final event selection.

T he W W /W Z /Z Z + je ts sam ples are generated w ith up to th re e ad ditio nal p arto n s using Al p g e n v2.13 and th e CTEQ 6L1 P D F set, interfaced to Her w ig v6.520 and Jim m y

v4.31 for p a rto n showering, h ad ro nisation and U E m odelling. T he MLM p a rto n -je t m atch ­ ing scheme is used. T he W W + je ts sam ples require a t least one of th e W bosons to decay leptonically, while th e W Z /Z Z + je ts sam ples require one Z boson to decay leptonically and th e o th er boson decays inclusively. A dditionally, W Z + je ts sam ples requiring th e W boson to decay leptonically and th e Z boson to decay hadronically, are generated w ith up to th re e addition al p arto n s (including m assive b- and c-quarks) using Sh e r p a v1.4.1 and th e CT10 P D F set. All diboson sam ples are norm alised to th e ir NLO th eo retical cross

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Sam ples of tiV events, including W W W , are generated w ith up to two additional p a r­

to ns using MAdGRAPH5 1.3.28 w ith th e CTEQ 6L1 P D F set, and interfaced to Py t h ia

6.425 w ith th e A U ET2B U E tu n e [76]. A sam ple of t t f f events is generated w ith th e Po wHel fram ew ork [77], which com bines th e Po w h e g- Bo x g enerator and NLO m atrix elem ents o b tain ed from th e H E LA C -O neloop package [78]. T he sam ple is g en erated us­

ing th e C T10nlo P D F set [44]. Showering is perform ed w ith Py t h ia 8.1 [79] using th e CTEQ 6L1 P D F set and th e AU2 U E tu n e [76, 80]. Inclusive decays of th e Higgs boson are assum ed in th e g eneration of th e t t f f sam ple. T he tiV sam ples are norm alised to th e NLO cross-section predictions [81]. T he t t f f sam ple is norm alised using th e NLO cross section [82- 84] and th e Higgs decay branching ratios [85- 88] collected in ref. [89].

T he m ultijet background co n tributes to th e selected d a ta sam ple via several production and m isreconstruction m echanism s. In th e electron channel, it consists of n on-prom pt elec­

tro n s (from sem ileptonic b- or c-hadron decays) as well as m isidentified photons (e.g. from a conversion of a p hoton into an e + e - pair) or je ts w ith a high fraction of th e ir energy deposited in th e EM calorim eter. In th e m uon channel, th e m ultijet background is predom ­ in an tly from n on-prom pt m uons. Its n orm alisation and shape are estim ated directly from d a ta by using th e “m a trix m eth o d ” technique [39], which exploits differences in lepton- identification-related p roperties betw een pro m p t and isolated leptons and leptons th a t are eith er non-isolated or result from th e m isidentification of photons or jets. F u rth e r details can be found in ref. [22].

T he t i ^ W bH q signal process is m odelled using th e P r o t o s v2.2 [90, 91] LO g en erator w ith th e C T E Q 6 L 1 P D F set, and interfaced to P y t h i a 6.426 and th e Peru- gia2011C U E tu n e. Two sep arate sam ples are generated corresponding to tt ^ W b H c and t i ^ W bH u , w ith th e W boson forced to decay leptonically, W ^ t v ( t = e, ^ , t ), T he to p q u ark and Higgs boson masses are set to 172.5 GeV and 125 GeV, respectively. T he Higgs boson is allowed to decay to all SM particles w ith branching ratios as given in ref. [89]. T he signal sam ple is norm alised to th e same NNLO cross section as used for th e t t ^ W bW b sam ple, and th e corresponding branching ratios: ^ ( t i ^ W ( ^ tv )b H q ) = 2B R (t ^ Hq)[1 - B R (t ^ H q )]B R (W ^ t v ) a tf, w ith B R (W ^ t v ) = 0.324 and B R (t ^ H q) depending on th e branching ratio being tested . Typically a reference branching ratio of B R (t ^ H q) = 1% is used. T he case of b o th to p quarks decaying into H q is neglected in th e analysis given existing u p p er lim its on B R (t ^ H q) (see section 1) . In order to improve th e m odelling of th e signal kinem atics, a tw o-step rew eighting procedure is applied: th e first step is designed to correct th e sp ectrum of to p q u ark p x and t i system p x to m atch th a t of th e uncorrected t i ^ W bW b P o w h e g - B o x + P y t h i a sample; th e second step in­

volves th e sam e correction to th e to p q uark p x and t i system p x applied to th e tt+ je ts background (see discussion above).

Finally, all gen erated sam ples are processed th ro u g h a sim ulation [92] of th e d etecto r geom etry and response using Ge a n t4 [93]. A dditional m inim um -bias pp in teractions are sim ulated w ith th e Py t h ia 8.1 gen erato r w ith th e M ST W 2008 LO P D F set and th e A2 U E tu n e [94]. T hey are overlaid on th e sim ulated signal and background events according to th e lum inosity profile of th e recorded d a ta . T he contributions from these pileup interactions are m odelled b o th w ithin th e sam e bunch crossing as th e h ard -sc atte rin g process and

J H E P 1 2 ( 2 0 1 5 ) 0 6 1

in neighbouring bunch crossings. All sim ulated sam ples are processed th ro u g h th e same reco nstruction software as th e d a ta . Sim ulated events are corrected so th a t th e object identification efficiencies, energy scales, and energy resolutions m atch those determ ined from d a ta control samples.

6 A n a ly sis s tr a te g y

T his section presents an overview of th e analysis stra te g y followed by th e tt ^ W b H q , H ^ btb search.

6 .1 E v e n t c a t e g o r i s a t i o n

Given th e focus on th e W ^ £v and H ^ bb decay m odes, th e t t ^ W b H q signal is expected to have typically four jets, of which th re e or four are b-tagged. T he la tte r case corresponds to th e t t ^ W b H c signal w here th e charm quark, as well as th e th re e b-quark jets, are b-tagged. A dditional je ts can also be present because of initial- or final-state rad i­

ation. In o rder to optim ise th e sensitivity of th e search, th e selected events are categorised into different channels depending on th e num ber of je ts (4, 5 and >6) and on th e num ber of b-tagged jets (2, 3 and > 4 ). Therefore, th e to ta l num ber of analysis channels considered in th is search is nine: (4 j, 2 b), (4 j, 3 b), (4 j, 4 b), (5 j, 2 b), (5 j, 3 b), (5 j, > 4 b), ( > 6 j, 2 b), ( > 6 j, 3 b), and (> 6 j, > 4 b), w here (n j, m b) indicates n selected je ts and m b-tagged jets.

T he overall ra te and com position of th e ttt+ je ts background strongly depends on th e je t and b-tag m ultiplicities, as illu strated in figure 1. T he ttt+ lig h t-jets background is dom inant in events w ith exactly two or th re e b-tagged jets, w ith th e two b-quarks from th e to p q uark decays being tagged in b o th cases, and a charm q u ark from th e hadronic W boson decay also being tagged in th e la tte r case. C o n tributions from t t+ c e and t t+bb become significant as th e je t and b-tag m ultiplicities increase, w ith th e t t + bb background being do m in ant for events w ith > 6 je ts and > 4 b-tags.

In th e channels w ith four or five jets and th re e or a t least four b-tags, which dom inate th e sensitivity of this search, selected signal events have a H ^ bb decay in m ore th a n 95%

of th e events. T he channels m ost sensitive to th e t t ^ W b H u and t t ^ W b H c signals are (4 j, 3 b) and (4 j, 4 b) respectively. Because of th e b e tte r signal-to-background ratio in th e (4 j, 4 b) channel, th is analysis is expected to have b e tte r sensitivity for t t ^ W b H c th a n for t t ^ W b H u signal. T he rest of th e channels have significantly lower signal-to- background ratios, b u t th ey are useful for calibrating th e tt+ je ts background prediction and constraining th e related sy stem atic uncertainties (see section 7) th ro u g h a likelihood fit to d a ta (see section 8) . T his stra te g y was first used in th e ATLAS search for t i H associated production, w ith H ^ bb [21], and is ad opted in this analysis. A tab le sum m arising th e observed and expected yields before th e fit to d a ta in each of th e analysis channels can be found in appen d ix A .

6 .2 D i s c r i m i n a t i o n o f s ig n a l f r o m b a c k g r o u n d

A fter event categorisation, th e signal-to-background ratio is very low even in th e m ost sensitive analysis channels, and a su itable discrim inating variable betw een signal and back-

J H E P 1 2 ( 2 0 1 5 ) 0 6 1

F ig u re 1. Comparison between the data and background prediction for the yields in each of the analysis channels considered before the fit to data (pre-fit). Backgrounds are normalised to their nominal cross sections discussed in section 5. The expected tt ^ WbHc and tt ^ Wb Hu signals (dashed histograms) are shown separately normalised to BR(t ^ Hq) = 1%. The tt ^ WbWb background is normalised to the SM prediction. The small contributions from W / Z +jets, single top, diboson and multijet backgrounds are combined into a single background source referred to as

“Non-tt” . The bottom panel displays the ratio of data to the SM background ( “Bkg” ) prediction.

The hashed area represents the total uncertainty on the background.

ground needs to be co n stru cted in order to im prove th e sensitivity of th e search. A powerful discrim inant betw een signal and background can be defined as:

P sig(x )

D (x ) = P s^ (x ) + P bkg(x) , (6.1)

w here P sig(x) and P bkg(x) represent th e probability d ensity functions (pdf) of a given event un der th e signal hypothesis (tt ^ W b H q ) and u nd er th e background hypothesis (tt ^ W b W b ) respectively. B o th pdfs are functions of x, representing th e four-m om entum vectors of all final-state particles a t th e reconstruction level: th e lepton (£), th e n eu trin o (v;

reco nstru cted as discussed below), and th e Njets selected je ts in a given analysis channel.

Since b o th signal and background result from th e t t decay, th ere are few experim ental handles available to d iscrim inate betw een them . T he m ost prom inent features are th e dif­

ferent resonances present in th e decay (i.e. th e Higgs boson in th e case of t t ^ W b H q and a h adronically decaying W boson in th e case of t t ^ W b W b ) , and th e different flavour content of th e jets form ing those resonances. T his is th e m ain inform ation exploited in th e con­

stru c tio n of P sig(x) and P bkg(x) in this analysis, so th a t x is extended to include not only th e four-m om enta of je ts pjet, b u t also th e value of th eir m u ltivariate b-tagging discrim inant w jet, i.e., x = {p£,pv , (pjeti, wj et.)} (i = 1 , . . . ,N jets). T here is also some angu lar inform a­

J H E P 1 2 ( 2 0 1 5 ) 0 6 1

tio n from th e different spins of th e d a u g h te r resonances (Higgs and W boson) th a t could be exploited, b u t it is expected to be subleading in im po rtance and is neglected in this analysis.

T he calculation of P sig(x) and P bkg(x) is discussed in d etail in sections 6.2.1 and 6.2.2 respectively. In th e following, be denotes th e b-quark je t from th e sem ileptonic to p quark decay, qh and bh d enote th e light-quark je t (qh = u or c) and b-quark je t from th e hadronic to p q u ark decay in background and signal events respectively, qi and q2 denote th e up-type- q u ark je t (u or c) and dow n-type-quark je t (d or s) from th e W boson decay respectively, and b1 and b2 denote th e two b-quark je ts from th e Higgs boson decay. T he level of sep aratio n achieved betw een signal and background w ith th e resulting d iscrim inant D is illu strated in section 6.2.3.

6 .2 .1 S ig n a l p r o b a b i l i t y

T he co n stru ction of P sig(x) will now be described step by step to illu strate th e m ethod.

If th e p arto n ic origin of each je t were known [see figure 2 (a)], P sig(x) would be defined in th is analysis as th e p ro d u ct of th e norm alised pdfs for each of th e recon structed invariant m asses in th e event: th e sem ileptonic to p q u ark m ass (M evb|), th e hadronic to p q u ark m ass (M blb2qh) and th e Higgs boson m ass (M blb2). Since M blb2qh and Mblb2 are correlated, th eir difference in q u a d ra tu re , X blb2qh = M blb2qh 0 M blb2, is used instead of M blb2qh. Therefore th e expression for P sig ju s t m aking use of th e above kinem atic inform ation, denoted by PSig, is:

Pkig (x) = P slg (M,„b, ) P slg (Xbl b„ h ) P slg (Mblb2). (6.2) T he distrib u tio n s of these invariant masses are obtained from sim ulated signal events using th e recon structed lepton a n d /o r jets corresponding to th e correct p a rto n -je t assign­

m ent, d eterm ined by m atching a given q u ark (before final-state rad iation ) to th e clos­

est je t w ith A R < 0.3. T he corresponding pdfs are con stru cted as unit-norm alised one­

dim ensional histogram s. To com pute Mevbl , th e neu trin o four-m om entum is needed, which is reco nstru cted as follows. Initially, th e x and y com ponents of th e neu trin o m om entum , p x,v and py,v, are identified w ith those of th e reco nstru cted EXpiss vector. T h e z com ­ ponent of th e neu trin o m om entum , p z,v, is inferred by solving M / = (pe + p v)2, w ith M w = 80.4 GeV being th e W boson m ass. If two real solutions ( “2sol” ) exist, th ey are sorted according to th eir absolute value of |pz,v | i.e., |pz,v 1| < |pz,v2|. It is found th a t in 62% of th e cases p z,v1 is closer th a n p z,v2 to th e generator-level n eu trin o p z,v. In th is case, two different pdfs are co nstructed , one for each solution, and P2sl0i(M evb£) is defined as th e average of th e two pdfs weighted by th eir fractions (0.62 for p z,v1 and 0.38 for p z,v2). If no real solution ( “nosol”) exists, which h appens in ab o u t 30% of th e cases, th e p x,v and p y,v com ponents are scaled by a com m on factor un til th e discrim inant of th e q u a d ra tic eq u ation is exactly zero, yielding only one solution for p z,v. This solution for p z,v is used to com pute M evbl, , from which th e corresponding PgOsol(M evb£) is co n stru cted . In th e cal­

culation of Pklg(x) from equ atio n (6.2) , P sig(M evb|) is identified w ith P ^ O ^ M ^ ) or w ith PgOsol(M evb|), depending on how m any neu trin o solutions can be found for th e event.

In practice, th e p arto n ic origin of th e jets is not known, so it is necessary to evalu­

a te P sig(x) by averaging over th e N p possible p arto n -je t assignm ents, which dilutes th e

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kinem atic inform ation. At this point b-tagging inform ation can be used to suppress th e im pact from p arto n -je t assignm ents th a t are inconsistent w ith th e correct p a rto n flavours as follows:

w ith je tj (i = 1 , . . . , 4) representing th e p a rto n -je t assignm ent being evaluated, and Pf( j e t j denoting th e probab ility th a t je t i, characterised by its four-m om entum p

jet

. and b-tagging weight value w

jet

., originates from a p a rto n w ith flavour f (b, c, or l; l for light p a rto n ). T he calib ration of th e b-tagging algorithm is perform ed for fixed thresholds on th e m ultivariate b-tagging discrim inant variable, corresponding to different average b-tagging efficiencies in t t events of 60%, 70%, and 80%, also referred to as “op eratin g p o in ts” (O P ). T he corresponding thresholds are denoted by w

°Up

, w ith O P = 60%, 70%, or 80%. P aram eteri- sations of th e b-tagging efficiencies for different je t flavours as functions of je t p T and n are available for each of these o p eratin g points, e

®p

(pT ,n), which can be used to com pute Pf as follows: if th e je t b-tagging weight falls betw een th e thresholds for op eratin g points O P

i

and O P

2

^{, w}

CUt

^{1 < w}

jet <

^w

°Up

2, th e n Pf = e

^P

^l

—

^e

^P

2; alternatively, if th e je t b-tagging weight is below (above) th e th resho ld corresponding to th e 80% (60%) o p eratin g point,

6.2.2 Background probability

T he calculation of P bkg follows a sim ilar approach to th a t discussed in section 6.2.1, al­

th o u g h it is slightly m ore com plicated to account for th e varying fraction and different kinem atic features of th e tt+ lig h t-je ts , tt + c t and t t + bb backgrounds as a function of th e analysis channel. This is p articu larly relevant in th e (4 j, 3 b) and (4 j, 4 b) channels, which d om inate th e sensitivity of th e search. W hile tt+ lig h t-je ts events often have b o th je ts from th e hadronic W boson decay am ong th e four selected je ts [see figure 2 (b)], this is seldom th e case for t t + bb and t t + c t events, especially in th e (4 j, 4 b) channel. In this case th e four b-tagged jets typically originate from th e two b-quarks from th e to p q u ark decays, th e charm q u ark from th e W boson decay, and an e x tra heavy-flavour q u ark (b or c) produced in association w ith th e t t system , while th e je t associated w ith th e dow n-type q u ark from th e W boson decay is not reconstructed [see figure 2 (c)].

To account for th is, th e following kinem atic variables are considered: M f vbe, X qij bh and M qij , w ith X qijbh = M qijbh 0 M qij , were j denotes an e x tra q u ark -jet which can either o riginate from th e W boson decay (q2) or from an e x tra heavy-quark (b or c) produced in association w ith th e t t system . For each of these possibilities, occurring in a fraction f j of th e cases, corresponding pdfs are constructed. As a generalisation of equ ation (6.3) , th e

Np

e pb;g,g ( x k ) PkH( xk )

P sig (x) = ,

e P

i v

⁾

k=l

w here p kig(x) is given by eq u atio n (6.2) and Pbtag(x) is defined as:

P bteg(x ) = P b( je tl ) p b(je t2)P b(je t3)P qh (jet4) ,

(6.3)

(6.4)

th e n Pf = 1 — e80% (P f = e60%).

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O Q i - h

b < D

(a) (b)

b f < ^ Q jet.!

¢1 < J ) ieti

92

bh < 0

b, c je t .

b h j e t 4

F ig u re 2. Representative Feynman diagrams illustrating the partonic configurations and parton- jet assignments considered in the construction of (a) the signal probability and (b) and (c) the background probability used in the definition of the final discriminant (see text for details).

g

g

I

expression for P bkg(x) becomes:

Np

E E t - P b S ' (x fiP k ’M x b

P bkg (x) = 1=1 , (6.5)

U 1

E E f , Pb£gJ (x k) k= 1 j€{b,c,q2}

w ith

P kingj (x) = P bkg (M,vb£ ) P bkg(Xqx j bh ) P bkg (M q j ), (6.6) and

P btag,j (x) = P b(je t1)P qi (je t2)P j (je t3)P b(jet4) . (%7) w here P f ( j e t j are com puted as discussed in section 6.2.1. In th e above expression, P , = P for j = q2, th e dow n-type q u ark in th e W boson decay, and P qi = f cP c + (1 — f c) P , where f c is th e fraction of events w here th e up-typ e q u ark from th e W boson decay assigned to th e je t is a charm quark. T his fraction is different in each analysis channel, prim arily depending on th e b-tag m ultiplicity requirem ents. It varies from ~ 50% for events in th e (4 j, 2 b) channel to ~ 90% for events in th e (4 j, 4 b) channel.

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6 .2 .3 F i n a l d i s c r im in a n t

T he final discrim inant D is com puted for each event as given in equ ation (6.1) , using th e definitions for P slg and P bkg given in equations (6.3) and (6.5) , respectively. Since this analysis has higher expected sensitivity to a t t ^ W b H c signal th a n to a t t ^ W b H u signal and, in order to allow probing of th e B R (t ^ H u ) versus B R (t ^ Hc) plane, th e d iscrim inant optim ised for t t ^ W b H c is used for b o th th e H c and H u decay m odes. It was verified th a t using th e t t ^ W b H c discrim inant for th e t t ^ W b H u search does not result in a significant sensitivity loss. F igure 3 com pares th e shape of th e D d istrib u tio n betw een th e t t ^ W b H c and t t ^ W b H u signals and th e t t ^ W b W b background in each of th e channels considered in this analysis.

7 S y s te m a tic u n c e r ta in tie s

Several sources of system atic u n certain ty are considered th a t can affect th e norm alisation of signal and background a n d /o r th e shape of th eir corresponding final d iscrim inant dis­

trib u tio n s. Each source of system atic u n certain ty is considered to be uncorrelated w ith th e o th er sources. C orrelations of a given system atic u n certain ty are m ain tained across processes and channels. Table 1 presents a list of all system atic uncertain ties considered in th e analysis and indicates w h eth er th ey are tak en to be norm alisation-only, or to affect b o th shape and norm alisation.

T he leading sources of sy stem atic u n certain ty vary depending on th e analysis channel considered, b u t th ey typically originate from tt+ je ts m odelling (including tt+ H F ) and b- tagging. For exam ple, th e to ta l sy stem atic u n certain ty in th e background norm alisation in th e (4 j, 4 b) channel, which dom inates th e sensitivity in th e case of th e t t ^ W b H c search, is approxim ately 20%, w ith th e largest co ntrib u tio n s originating from t t+ H F nor­

m alisation, b-tagging efficiency, c-tagging efficiency, light-jet tagging efficiency and ttt cross section. However, as shown in section 9, th e fit to d a ta in th e nine analysis channels al­

lows th e overall background u n certain ty to be reduced significantly, to ap proxim ately 4.4%.

T he reduced u n certain ty results from th e significant co n strain ts provided by th e d a ta on some system atic uncertainties, as well as th e anti-correlations am ong sources of system atic u n certain ty resulting from th e fit to th e d a ta . T he to ta l system atic u n certain ty on th e t t ^ W b H c signal no rm alisation in th e (4 j, 4 b) channel is approxim ately 17%, w ith sim ilar contrib u tio n s from un certainties related to b-tagging and overall signal m odelling.

A fter th e fit, th is u n certain ty is reduced to 7.8%. Table 2 presents a sum m ary of th e sys­

tem a tic uncertainties for th e t t ^ W b H c search and th e ir im pact on th e no rm alisation of th e signal and th e m ain backgrounds in th e (4 j, 4 b) channel.

T he following sections describe each of th e system atic uncertain ties considered in th e analyses.

7.1 L u m in o s ity

T he u n certain ty on th e in teg rated lum inosity is 2.8%, affecting th e overall norm alisation of all processes estim ated from th e sim ulation. It is estim ated from a calib ratio n of th e lu-

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D

(a) (b) (c)

D D

(d) (e) (f)

D D D

D

(g) (h) (i)

D D

F ig u re 3. Comparison of the shape of the D discriminant distribution between the tt ^ WbHc (red dashed) and tt ^ W bHu (blue dotted) signals, and the tt ^ WbWb background (black solid) in each of the channels considered in the analysis: (a) (4 j, 2 b), (b) (4 j, 3b), (c) (4 j, 4 b), (d) (5 j, 2 b), (e) (5 j, 3 b), (f) (5 j, >4 b), (g) (> 6 j, 2 b), (h) (> 6 j, 3 b), and (i) (> 6 j, >4 b).

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Systematic uncertainty Type Components

L u m in o sity N 1

R e c o n s tru c te d O b je c ts

Electron SN 5

Muon SN 6

Jet reconstruction SN 1

Jet vertex fraction SN 1

Jet energy scale SN 22

Jet energy resolution SN 1

Missing transverse momentum SN 2

b-tagging efficiency SN 6

c-tagging efficiency SN 4

Light-jet tagging efficiency SN 12

High-pT tagging SN 1

B a c k g ro u n d M o del

tt cross section N 1

tt modelling: p T reweighting SN 9

tt modelling: parton shower SN 3

tt+H F: normalisation N 2

tl^+cH: p T reweighting SN 2

t t + ct: generator SN 4

t t +bb: NLO shape SN 8

W +jets normalisation N 3

W p T reweighting SN 1

Z +jets normalisation N 3

Z p T reweighting SN 1

Single top normalisation N 3

Single top model SN 1

Diboson normalisation N 3

t t V cross section N 1

t W model SN 1

t t H cross section N 1

t t H model SN 2

Multijet normalisation N 4

S ignal M o d el

tt cross section N 1

Higgs boson branching ratios N 3

tt modelling: p T reweighting SN 9

tt modelling: p T reweighting non-closure N 1

tt modelling: parton shower N 1

T able 1. List of systematic uncertainties considered. An “N” means th at the uncertainty is taken as affecting only the normalisation for all relevant processes and channels, whereas “SN” means that the uncertainty is taken on both shape and normalisation. Some of the systematic uncertainties are split into several components for a more accurate treatment.

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WbHc

Pre-fit

tt+ L J tt + ^{c c} ttt + btb WbHc

Post-fit

tt+ L J tt + ^{c c} tt + bb

Luminosity ±2.8 ±2.8 ±2.8 ±2.8 ±2.6 ±2.6 ±2.6 ±2.6

Lepton efficiencies ±1.5 ±1.5 ±1.5 ±1.5 ±1.5 ±1.5 ±1.5 ±1.5

Jet energy scale ±3.3 ±2.9 ±2.3 ±5.8 ±1.4 ±1.2 ±1.8 ±4.1

Jet efficiencies ±1.2 — ±1.9 ±1.7 ±0.9 — ±1.4 ±1.2

Jet energy resolution — ±1.2 ±2.8 ±2.9 — — ±1.0 ±1.1

b-tagging eff. ±7.9 ±5.5 ±5.2 ± 10 ±5.7 ±3.9 ±3.7 ±6.6

c-tagging eff. ±7.0 ±6.6 ±13 ±3.5 ±6.3 ±6.0 ± 1 1 ±3.2

Light-jet tagging eff. ±0.8 ±18 ±3.2 ±1.5 ±0.6 ±13 ±2.3 ±1.1

tt: reweighting ±5.9 ±2.7 ±4.2 — ±3.8 ±1.9 ±2.3 —

tt: parton shower ±5.4 ±4.8 ±10 ±4.9 ±1.7 ±1.5 ±6.5 ±3.1

tt+ H F : normalisation — — ±50 ±50 — — ±32 ±16

tt+ H F : modelling — — — ±7.7 — — — ±7.4

Signal modelling ±6.9 — — — ±6.9 — — —

Theor. cross sections ±6.2 ±6.2 ±6.2 ±6.2 ±3.9 ±3.9 ±3.9 ±3.9

Total ±17 ±22 ±54 ±53 ±7.8 ±14 ±28 ±15

T ab le 2. tt ^ WbHc, H ^ bb search: summary of the systematic uncertainties considered in the (4 j, 4 b) channel and their impact (in %) on the normalisation of the signal and the main backgrounds, before and after the fit to data. The tt ^ WbHc signal and the tt+light-jets background are denoted by “WbHc ” and “tt+ L J ” respectively. Only sources of systematic uncertainty resulting in a normalisation change of at least 0.5% are displayed. The total post-fit uncertainty can differ from the sum in quadrature of individual sources due to the anti-correlations between them resulting from the fit to the data.

m inosity scale derived from b eam -separation scans perform ed in N ovem ber 2012, following th e sam e m ethodology as th a t detailed in ref. [38].

7 .2 R e c o n s t r u c t e d o b j e c t s

U ncertain ties associated w ith leptons arise from th e reconstruction, identification and trig ­ ger. These efficiencies are m easured using tag -an d -p ro b e techniques on Z ^ t +t - (I = e, p) d a ta and sim ulated sam ples. T he small differences found are corrected for in th e sim ula­

tion. Negligible sources of u n certain ty originate from th e corrections applied to ad just th e lepton m om entum scale and resolution in th e sim ulation to m atch those in d a ta . T he com bined effect of all these un certain ties results in an overall norm alisation u n certain ty on th e signal and background of approxim ately 1.5%.

U ncertain ties associated w ith je ts arise from th e efficiency of je t reco nstructio n and identification based on th e JV F variable, as well as th e je t energy scale and resolution. T he largest c o n trib u tio n results from th e je t energy scale, whose un certain ty dependence on je t p T and n is split into 22 u ncorrelated sources th a t are tre a te d independently in th e analysis.

It affects th e norm alisation of signal and backgrounds by approxim ately 3-4% in th e m ost sensitive search channels, (4 j, 3 b) and (4 j, 4 b), and up to 12% in th e channels w ith > 6 jets.

U ncertain ties associated w ith energy scales and resolutions of leptons and je ts are prop­

ag ated to E™ ss. A dditional un certainties originating from th e m odelling of th e underlying

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