P u b l i s h e d f o r SISSA b y S p r i n g e r
Received: November 30, 2018 Revised: March 11, 2019 Accepted: March 28, 2019 Published: April 4, 2019
Measurements of inclusive and differential fiducial cross-sections of tt production with additional heavy-flavour jets in proton-proton collisions at / s = 13 TeV with the A TLA S detector
ATLAS
E X P E R I M E N T
T h e A T L A S collaboration
E-m ail: 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 : T his p a p e r presents m easurem ents of t t p ro d uction in association w ith add i
tion al b-jets in pp collisions a t th e LHC a t a centre-of-m ass energy of 13 TeV. T he d a ta were recorded w ith th e ATLAS d e te c to r and correspond to an integ rated lum inosity of 36.1 fb- 1 . F iducial cross-section m easurem ents are perform ed in th e dilep to n and lepton-plus-jets tt decay channels. R esults are presented a t particle level in th e form of inclusive cross-sections of t t final sta te s w ith th re e and four b-jets as well as differential cross-sections as a function of global event p roperties and prop erties of b-jet pairs. T he m easured inclusive fiducial cross-sections generally exceed th e tibb predictions from various next-to-leading-order m a
trix elem ent calculations m atched to a p a rto n shower b u t are com patible w ithin th e to ta l uncertainties. T he experim ental un certainties are sm aller th a n th e un certainties in th e predictions. Com parisons of state-o f-th e-art th eoretical predictions w ith th e differential m easurem ents are shown and good agreem ent w ith d a ta is found for m ost of them .
Ke y w o r d s: H adron-H adron scatterin g (experim ents), H eavy q u ark production
ArXiv ePr in t: 1811.12113
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C o n te n ts
1 In tr o d u ctio n 2
2 A T L A S d e te c to r 4
3 M o n te C arlo sim u la tio n 5
4 O b ject rec o n stru ctio n and id en tifica tio n 9
4.1 D etector-level ob ject recon structio n 9
4.2 Particle-level ob ject definitions 10
5 E ven t selec tio n and d efin ition o f th e fiducial p h ase sp ace 11
5.1 D a ta event selection 11
5.2 Fiducial phase-space definition 11
6 B ack grou n d estim a tio n 12
6.1 B ackground from single-top, Z /y*+ je ts and W + je ts events 12
6.2 B ackground from n o n-prom pt and fake leptons 13
6.3 D a ta and prediction com parison of baseline selection 16
7 E x tr a c tio n o f th e fiducial cro ss-sectio n s 16
7.1 D ata-driven correction factors for flavour com position of ad d itio n al jets in
t t events 16
7.2 Unfolding 20
8 S y ste m a tic u n certa in ties 21
8.1 E x perim ental un certain ties 21
8.2 M odelling sy stem atic uncertainties 23
8.3 U n certain ty in ttc and ttl background 23
8.4 U n certain ty in n o n -ti background estim atio n 24
8.5 P ro p a g atio n of uncertain ties 24
9 In clu siv e and d ifferential fid u cial cro ss-sectio n resu lts 25
10 S u m m ary 30
T h e A T L A S co lla b o ra tio n 49
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F ig u re 1. Example Feynman diagrams of processes leading to a ttbb final state, including (a) QCD ttbb production, (b) t t H (H ^ bb), and (c) ttZ ( Z ^ bb).
1 I n tr o d u c t io n
M easurem ents of th e p ro d uctio n cross-section of to p -a n tito p q u ark pairs (tb) w ith additio nal je ts provide im p o rta n t tests of q u an tu m chrom odynam ics (Q CD ) predictions. Am ong these, th e process of t t produced in association w ith je ts originating from b-quarks (b-jets) is particu larly im p o rta n t to m easure, as th ere are m any uncertain ties in th e calculation of th e process. For exam ple, calculating th e am plitude for th e process shown in figure 1a is a challenge due to th e non-negligible m ass of th e b-quark. It is therefore im p o rta n t to com pare th e predictions w ith b o th inclusive and differential experim ental cross-section m easurem ents of tb p rod u ctio n w ith addition al b-jets. S tate-o f-th e-art QCD calculations give predictions for th e t t pro d u ctio n cross-section w ith up to two ad ditio nal massless p a r
ton s a t next-to-leading o rder (NLO) in p e rtu rb a tio n th eo ry m atched to a p a rto n shower [1], and th e QCD prod u ction of ttbb is calculated a t NLO m atched to a p a rto n shower [2- 5].
Moreover, since th e discovery of th e Higgs boson [6 , 7], th e d ete rm in a tio n of th e Higgs coupling to th e heaviest elem entary particle, th e to p quark, is a crucial te s t of th e S tan d ard M odel (SM). D irect m easurem ents of th e to p -q u ark Yukawa coupling are perform ed in events w here a Higgs boson is produced in association w ith a to p -q u a rk pair ( t t H ) [8, 9].
T he Higgs branching ratio s are dom inated by th e H ^ bb decay [10, 11], and therefore th e t t H process can be m easured w ith th e best sta tistic a l precision using events where th e Higgs boson decays in th is m anner, leading to a ttbb final sta te as shown in figure 1b.
However, th is channel suffers from a large background from QCD ttbb prod uction indicated in figure 1a [12, 13].
M easurem ents of t t H ( H ^ bb) would benefit from a b e tte r u n d erstan d in g of th e QCD pro d u ction of ttbb as predicted by th e SM and, in p articu lar, im proved M onte C arlo (MC) modelling. T he m easurem ents presented in th is p a p e r were chosen in order to provide d a ta needed to improve th e QCD MC m odelling of th e ttbb process. T he differential observables are particu larly interestin g as th ey are sensitive to th e relative co n trib u tio n of events from tb-associated Higgs p ro d u ctio n ( t t H ) w ith H ^ bb decays to Q C D -produced ttbb events in various phase space regions. Even th o ug h th e aim is to im prove th e m odelling of QCD pro d u ction of additio nal b-jets in t t events, this analysis m easures th eir produ ctio n w ith out sep aratin g th e different p ro d u ctio n channels such as t t H or tt in association w ith a vector boson ( t t V ), for exam ple th e t t Z process shown in figure 1c.
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In this paper, m easurem ents of fiducial cross-sections are presented using d a ta recorded by th e ATLAS d e te c to r during 2015 and 2016 in p ro to n -p ro to n (pp) collisions a t a centre- of-mass energy yfs = 13 TeV, corresponding to a to ta l integ rated lum inosity of 36.1 fb- 1 . In addition, differential m easurem ents a t th is centre-of-m ass energy are presented as a function of various observables. Previous m easurem ents of ttt p ro d u ctio n w ith additional heavy-flavour jets have been rep orted by ATLAS a t yfs = 7 TeV [14] and b o th CMS and ATLAS a t yfs = 8 TeV [15- 17]. CMS has also rep o rted a m easurem ent of th e inclusive ttbb cross-section using 2.3 fb-1 a t / s = 13 TeV [18].
Since th e to p q u ark decays into a b-quark and W boson nearly 100% of th e tim e, tt events are typically classified according to how th e two W bosons decay. In th is analysis, two channels are considered: th e eß channel, in which b o th W bosons decay leptonically, one into a m uon and m uon n eu trino and th e o th er into an electron and electron neutrino, and th e lepton-plus-jets channel (lepton + jets), in which one W boson decays into an isolated charged lepton (an electron or m uon) and corresponding n eutrin o and th e o th er W boson decays into a p air of quarks. E lectrons and m uons produced eith er directly in th e decay of th e W boson or via an interm ediate T-lepton are included in b o th channels.
T he decay of a to p -q u ark pair results in two b-quarks and therefore a final s ta te which includes th e p ro d u ctio n of two ad ditional b-quarks m ay contain up to four b-jets. T he inclusive fiducial cross-sections are presented for events w ith a t least th re e b-jets and for events w ith a t least four b-jets. T he differential cross-sections are presented for events w ith a t least th re e b-jets in th e eß channel and w ith at least four b-jets in th e lepton + jets channel. T he results are o b tain ed as a function of th e transverse m om entum (p t) 1 of each of th e b-jets, th e scalar sum of th e p T of th e lepton(s) and je ts in th e events (Ht) and of only je ts in th e events (HTad) and as a function of th e b-jet m ultiplicity (N b_jets).
T his analysis does not a tte m p t to identify th e origin of th e b-jets, i.e. it does not distinguish betw een additio n al b-jets and b-jets th a t come from th e to p -q u ark decays. This is to avoid using sim ulation-based inform ation to a ttrib u te b-jets to a p a rticu la r production process, which would lead to significant m odelling uncertainties. Instead , differential cross
sections are m easured as a function of kinem atic d istrib u tio n s of pairs of b-jets. T he rep o rted d istrib u tio n s could be used to distinguish th e co n trib u tio n of specific prod uctio n m echanism s: th e p air m ade from th e two b-jets closest in angular distance is expected to be form ed by b-jets from gluon sp littin g and th e p air m ade from th e two highest-pT b-jets is expected to be dom in ated by to p -p air production. For each of these pairs, th e d istrib u tio n s are m easured for th e angular separation betw een th e b-jets (A R (b, b)), th e invariant m ass (m bb) and transverse m om entum (pT,bb). It should be noted th a t for events w ith a t least th re e b-jets, it is likely th a t one of th e two closest b-jets originates from th e to p quark. Hence th e sim ple picture th a t th e two closest b-jets are usually from gluon sp littin g m ay not apply.
1ATLAS 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 along 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 z-axis. The pseudorapidity is defined in terms of the polar angle 6 as n = — lntan(6/2). The angular separation between two points in n and 0 is defined as A R = %(An)2 + (A0)2.
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However, A R , m bb and p T ,bb are used for recon struction of th e final sta te in analyses w ith m ultiple b-jets and therefore probing th e m odelling of these observables is im p o rta n t.
T he cross-sections are o b tain ed by su b tra c tin g th e estim ated num ber of no n-rt back
ground events from th e d a ta d istrib u tions. At d e te c to r level, je ts are identified as containing b-hadrons ( “b-tagging” ) by a m ultiv ariate algorithm [19]. T he t t background resulting from a d d itio nal light-flavour and charm -quark je ts wrongly identified as b-jets is evaluated using a te m p la te fit, in which th e tem p lates are con stru cted from th e o u tp u t discrim inant of th e b-tagging algorithm . T he b ack g ro un d -subtracted distrib u tio n s are corrected for acceptance and d e te c to r effects using an unfolding technique th a t includes corrections for th e tt-re late d backgrounds.
T his p ap er is laid o ut as follows. T he experim ental set-up for th e collected d a ta is de
scribed in section 2 . D etails of th e sim ulation used in th is analysis are provided in section 3.
T he recon struction and identification of leptons and jets, th e b-tagging of je ts a t d etecto r level, and th e definitions of objects a t particle level are described in section 4 . T he selection of reco nstru cted events and th e definition of th e fiducial phase space are given in section 5.
E stim atio n of th e background from non-rt processes is described in section 6 . T h e m ethod to estim ate th e t t background w ith add ition al je ts m isidentified as b-jets and th e unfolding p rocedure to correct th e d a ta to particle level for fiducial cross-section m easurem ents are explained in section 7. Sources of system atic uncertainties and th eir pro p ag atio n to th e m easured cross-sections are described in section 8. T he m easured inclusive and norm alised differential fiducial cross-sections and th e com parison w ith various th eo retical predictions are presented in section 9. Finally, th e results are sum m arised in section 10.
2 A T L A S d e t e c t o r
T he ATLAS d e te c to r [20] a t th e LHC covers nearly th e entire solid angle around th e colli
sion point. It consists of an in ner-tracking d e te c to r su rrounded by a th in superconducting solenoid, electrom agnetic and hadronic calorim eters, and a m uon sp ectro m eter in co rp o rat
ing th re e large su p erconducting toroidal m agnets.
T he inner d etecto r (ID) system is im m ersed in a 2 T axial m agnetic field and provides charged-particle track in g in th e pseudorapidity range |n| < 2.5. T he ID is com posed of silicon d etecto rs and th e tra n sitio n rad iatio n tracker. T he high-granularity silicon pixel d e te c to r covers th e in teraction region and is followed by th e silicon m icrostrip tracker. T he innerm ost silicon pixel layer, added to th e inner d e te c to r before th e s ta rt of R un-2 d a ta tak in g [21, 22], improves th e identification of b-jets. T he track ing capabilities of th e silicon d etectors are augm ented by th e tra n sitio n rad iatio n tracker, which is located a t a larger radius and enables tra c k recon stru ction up to |n| = 2.0. It also provides signals used to sep arate electrons from pions.
T he calorim eter system covers th e range |n| < 4.9. W ith in th e region |n| < 3.2, electrom agnetic calorim etry is provided by barrel and endcap h igh-granularity lea d /liq u id argon (LAr) electrom agnetic calorim eters, w ith an addition al th in LA r presam pler covering
|n| < 1.8 to correct for energy loss in m aterial u p stream of th e calorim eters. H adronic calorim etry is provided by th e steel/scin tillatin g -tile calorim eter, segm ented into th ree
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barrel stru c tu re s w ithin |n| < 1.7, and two c o p p e r/L A r hadronic endcap calorim eters. T he solid angle coverage is com pleted w ith forw ard c o p p e r/L A r and tu n g ste n /L A r calorim eter m odules optim ised for electrom agnetic and hadronic m easurem ents, respectively.
T he m uon sp ectrom eter (MS) com prises sep arate trigger and high-precision tracking cham bers m easuring th e deflection of m uons in a m agnetic field generated by th e supercon
d u ctin g air-core toroids. T he field integral of th e toroids ranges betw een 2.0 and 6.0 T m across m ost of th e d etecto r. A set of precision cham bers covers th e region |n| < 2.7 w ith th re e layers of d rift tu b es, com plem ented by cath o d e strip cham bers in th e forw ard region, w here th e background is highest. T he m uon trigger system covers th e range |n| < 2.4 w ith resistive p late cham bers in th e barrel, and th in gap cham bers in th e endcap regions.
A two-level trigger system is used for event selection [23, 24]. T he first trigg er level 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 100 kHz. This is followed by a softw are-based trigg er th a t reduces th e event ra te to ab o u t 1 kHz.
3 M o n t e C a r lo s im u la t io n
M onte C arlo sim ulations are used in th ree ways in th is analysis: to e stim ate th e signal and background com position of th e selected d a ta sam ples, to determ ine correction factors for d e te c to r and acceptance effects for unfolding, and finally to estim ate system atic uncer
tain ties. In addition, th eo retical predictions are com pared w ith th e unfolded d a ta . T he com p u ter codes used to g enerate th e sam ples and how th ey were configured are described in th e following. T he signal MC sam ples used in th e analysis are listed in tab le 1.
T he nom inal t t sam ple was gen erated using th e P o w h e g - B o x g en erato r (version 2, r3026) [25- 28] at next-to-leading-order (NLO) in a s w ith th e N N PD F3.0N L O set of p a r
to n d istrib u tio n functions (P D F ) in th e m atrix elem ent calculation. T he p a rto n shower, fragm en tatio n, and th e underlying event were sim ulated using P y t h i a 8.210 [29] w ith th e N N PD F2.3L O P D F sets [30, 31] and th e corresponding A14 set of tu n ed p aram eters [32].
T he h damp p aram eter, which controls th e p T of th e h ard est ad d ition al p a rto n emission beyond th e B orn configuration, was set to 1.5m t [33], w here m t denotes th e to p -q u ark m ass. T he P o w h e g hardness criterion used in th e m atching (POWHEG:pTdef) is set to 2 following a stu d y in ref. [33]. T he renorm alisation and factorisatio n scales were set to ß = ^ m t + Pt t, w here p T,t is th e transverse m om entum of th e to p quark. A dditional jets, including b-jets, were generated by th e h ard est ad ditio nal p a rto n em ission and from
p a rto n showering. T his sam ple is called P o w h e g + P y t h i a 8 in th e following.
Processes involving th e pro d u ctio n of a W ,Z or Higgs boson in ad ditio n to a tt pair were sim ulated using th e MADGRAPH5_aMC@NLO g en erato r [34, 35] a t NLO in a s in th e m atrix elem ent calculation. T he p a rto n shower, frag m en tatio n and underlying event were sim ulated using P y t h i a 8 w ith th e A 14 p a rto n shower tune. A dynam ic renorm al
isation and facto risatio n scale set to H T /2 was used, w here H T is defined as th e scalar sum of th e tran sv erse m ass, m T = ^ / m 2 + pT, of all p arto n s in th e p arto n ic final state.
T he N N P D F 3 .0 N L O P D F set was used in th e m a trix elem ent calculation while th e N N P D F 2 .3 L O P D F set was used in th e p a rto n shower. In th e case of t t H , th e Higgs
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Generator sample Process Matching Tune Use
PowHEg-Box v2 + tt NLO Powheg A14 nom.
PYtHia 8.210 hdamp = 1.5mt
MaDGRaph5_ aMC@NLO + tt + V/H NLO MC@NLO A14 nom.
P y th ia 8.210
PowhEg-Box v2 + tt NLO Powheg A14Var3cDown syst.
P y th ia 8.210 RadLo hdamp = 1.5mt
PowhEg-Box v2 + ttt NLO Powheg A14Var3cUp syst.
P y th ia 8.210 RadHi hdamp — 3.°m£
PowhEg-Box v2 + ttt NLO Powheg H7UE syst.
Herwig 7.01 hdamp — 1.5mt
Sherpa 2.2.1 tt tt +0,1 parton at NLO +2,3,4 partons at LO
MePs@Nio Sherpa syst.
MadGraph5_aMC@NLO + tt NLO MC@NLO A14 comp.
P y th ia 8.210
Sherpa 2.2.1 ttbb (4FS) ttbb NLO MC@NLO Sherpa comp.
PowHe i + ttbb NLO Powheg A14 comp.
P y th ia 8.210 (5FS) hdamp — HT/2
PowHe i + ttbb NLO Powheg A14 comp.
P y th ia 8.210 (4FS) hdamp — HT/2
PowhEg-Box v2 + ttbb NLO Powheg A14 comp.
P y th ia 8.210 ttbb (4FS) hdamp — HT/2
T ab le 1. Summary of the MC sample set-ups used for modelling the signal processes (tt + ttV + t tH ) for the data analysis and for comparisons with the measured cross-sections and differential distributions. All samples used the NNPDF3.0NLO PDF set with the exception of the two S h e rp a samples, which used NNPDF3.0NNLO. The different blocks indicate from top to bottom the samples used as nominal MC (nom.), systematic variations (syst.) and for comparison only (comp.). For details see section 3.
boson m ass was set to 125 GeV and all possible Higgs decay m odes were allowed, w ith th e branching fractions calculated w ith H D E C A Y [36, 37]. T he ttW and t t Z sam ples are norm alised to cross-sections calculated to NLO in a s w ith M aD G raph5_aM C @ N L O . T he t t H sam ple is norm alised to a cross-section calculated to NLO accuracy in QCD, including N L O electrow eak corrections [36].
A ltern ativ e tt sam ples were generated to assess th e uncertain ties due to a p a rticu la r choice of QCD MC m odel for th e productio n of th e add ition al b-jets and to com pare w ith unfolded d a ta , as listed in tab le 1. In order to investigate th e effects of initial- and final-state radiation , two sam ples were generated using P o w h e g + P y t h i a 8 w ith th e renorm alisation and factorisatio n scales varied by a factor of 2 (0.5) and using low -radiation (high-radiation) v ariations of th e A14 tu n e and an h damp value of 1.5m t (3.0m t ), corresponding to less (more) p a rto n shower rad iatio n [33]. These sam ples are called P o w h e g + P y t h i a 8 (RadLo) and P o w h e g + P y t h i a 8 (R adH i) in th e following. To estim ate th e effect of th e choice of p a rto n shower and h ad ro n isatio n algorithm s, a MC sam ple was g enerated by interfacing P o w h e g w ith H e r w ig 7 [38, 39] (v7.01) using th e H 7U E set of tu n e d p aram eters [39].
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In o rder to estim ate th e effects of QCD scales, and m atching and m erging algorithm s used in th e NLO t t m a trix elem ent calculation and th e p a rto n shower to predict additional b-jets, events were gen erated w ith th e S h e r p a 2.2.1 g en erator [40], which m odels th e zero and one ad d itio n al-p arto n process a t NLO accuracy and up to four ad ditio nal p arto n s at LO accuracy, using th e M e P s @ N lo prescription [41]. A dditional b-quarks were tre a te d as massless and th e N N P D F 3 .0 N N L O P D F set was used. T he calculation uses its own p a rto n shower tune. T his sam ple is referred to as S h e r p a 2.2 tt.
In ad d itio n to th e t t sam ples described above, a t t sam ple was generated using th e MAdGRAPH5_aMC@NLO [34] (v2.3.3) generator, interfaced to P y t h i a 8.210 and is referred to as M A dG RA PH^aM C@ N LO+PY THiA 8 hereafter. As w ith th e nom inal P o w h e g + P y t h i a 8 t t sam ple, th e N N P D F 3 .0 N L O P D F set was used in th e m atrix elem ent calculation and th e N N P D F 2 .3 L O P D F set was used in th e p a rto n shower. This sam ple is used to calculate th e fraction of t t + V / H events in t t events and to com pare w ith th e d a ta . T he A14 set of tu n ed p aram eters was used for P y t h i a .
T he t t sam ples are norm alised to a cross-section of a tt = 8 3 2 + ^ pb as calculated w ith th e T o p + + 2 .0 program to next-to -n ext-to -leading order (NNLO) in p e rtu rb a tiv e QCD, including soft-gluon resum m ation to next-to-next-to-leading-log (NNLL) order (see ref. [42]
and references th erein ), and assum ing m t = 172.5 GeV. T he u n certain ty in th e theoretical cross-section comes from in dependent variations of th e factorisatio n and renorm alisation scales and variations in th e P D F and a s , following th e P D F 4 L H C p rescription w ith th e M ST W 2008 NNLO, CT10 NNLO and N N PD F2.3 5f F F N P D F sets (see ref. [43] and references therein, and refs. [44- 46]).
Four m ore predictions were calculated only for com parisons w ith d a ta and are all based on ttt btb m a trix elem ent calculations. T hese predictions all use th e sam e renorm alisation and facto risation scale definitions as th e stu d y presented in ref. [36]. T he renorm alisation scale, ß R, is set to ß R = ]Qi=t t b b E t /4 , w here E Ti refers to th e transverse energy of th e p a rto n i in th e p arto n ic final sta te , and th e factorisation scale, ß F , is set to H T /2 which is defined as
ßF = Ht/2 = 2 ^ E t ,i , i=t , ï, b, b , j
w here j refers to th e additio n al Q C D -radiated p a rto n s at NLO.
T hree of th e four predictions are based on th e P o w h e g m ethod, and use th e P y t h i a 8 p a rto n shower w ith th e sam e p a rto n shower tu n e and th e sam e m atching settings as the nom inal P o w h e g + P y t h i a 8 sam ple, w ith th e exception of th e hdamp p aram eter, which is set to th e sam e value as th e facto risation scale, i.e. H t / 2 . In th e ttbb m atrix elem ent calculations w ith m assive b-quarks, th e b-quark m ass is set to m b = 4.75 GeV. T he set-up of th e four ded icated sam ples are described below.
A sam ple of ttbb events was generated using SH ER PA +O PEnLoops [2]. T he ttbb m atrix elem ents were calculated w ith m assive b-quarks a t NLO, using th e C o m ix [47] and OPEn- L o o p s [48] m a trix elem ent generators, and m erged w ith th e S h e r p a p a rto n shower, tu n ed by th e au th o rs [49]. T he four-flavour NNLO N N PD F3.0 P D F set was used. T he resum m a
tio n scale, ßQ, was set to th e same value as ß F . T his sam ple is referred to as S h e r p a 2.2 ttbb (4FS). A sam ple of ttbb events was g enerated using th e P o w H e l g en erator [3], w here th e
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m a trix elem ents were calculated a t NLO assum ing massless b-quarks and using th e five- flavour NLO N N PD F3.0 P D F set. E vents were required to have th e invariant m ass, mbb, of th e bb system to be larger th a n 9.5 GeV and th e pT of th e b-quark larger th a n 4.75 GeV as described in ref. [36]. These events were m atched to th e P y t h i a 8 p a rto n shower using th e P o w h E g m ethod. This sam ple is referred to as P o w H E L + P y t m a 8 tibb (5FS).
A sam ple of tibb events using th e Po wHel g en erato r w here th e m atrix elem ents were calculated at NLO w ith m assive b-quarks and using th e four-flavour NLO N N PD F3.0 P D F set [4]. E vents were m atched to th e P y t h i a 8 p a rto n shower using th e P o w h E g m ethod.
T his sam ple is referred to as P o w H e L + P y t h i a 8 tibb (4FS).
A sam ple of tibb events using th e P o w h E g g enerator w here tibb m atrix elem ents were calculated at NLO w ith m assive b-quarks and using th e four-flavour NLO N N PD F3.0 P D F set [5]. E vents were m atched to th e P y t h i a 8 p a rto n shower using th e P o w h E g m ethod.
T his sam ple is referred to as P o w h e g + P y t h i a 8 tibb (4FS) to distinguish it from th e nom inal P o w h e g + P y t h i a 8 sam ple m entioned above.
For all sam ples involving to p quarks, m t was set to 172.5 GeV and th e E v t G e n v1.2.0 program [50] was used for p roperties of th e b o tto m and charm had ro n decays except for th e S h e r p a sam ples. To preserve th e spin correlation inform ation, to p q uarks were decayed following th e m eth od of ref. [51] which is im plem ented in P o w h E g - B o x and by M a d S p in [52] in th e M a D G R a P h 5 _ a M C @ N L O + P y th Ia 8 sam ples. S h e r p a perform s its own calculation for spin correlation. B o th of th e P o w H e L + P y t h i a 8 tibb sam ples used P y t h i a to decay th e to p quarks, w ith a to p -q u ark decay w id th of 1.33 GeV, and hence these predictions do not include t i spin correlations.
T he p ro d uctio n of single top-q uarks in th e tW - and s-channels was sim ulated using th e P o w h e g - B o x (v2, r2819) NLO g enerator w ith th e CT10 P D F set in th e m atrix elem ent calculations. E lectrow eak t-channel single-top-quark events were g enerated using th e P o w h e g - B o x (v1, r2556) g enerator. T his g enerato r uses th e four-flavour scheme for th e NLO m atrix elem ents calculation to g eth er w ith th e fixed four-flavour P D F set CT10f4.
For all to p processes, to p -q u a rk spin correlations are preserved (in th e case of th e t-channel, to p quarks were decayed using M a d S p in ). T he interference betw een t i and tW pro d uctio n is accounted for using th e diagram -rem oval scheme [53]. T he p a rto n shower, fragm entation, and th e underlying event were sim ulated using P y t h i a 6.428 [54] w ith th e CTEQ 6L1 P D F sets and th e P erugia 2012 tu n e (P2012) [55, 56]. T he single-top MC sam ples for th e t- and s-channels are norm alised to cross-sections from NLO predictions [57, 58], while th e tW - channel MC sam ple is norm alised to approx im ate NNLO [59].
E vents containing W or Z bosons w ith associated je ts were sim ulated using th e S h e r p a 2.2.1 g enerator. M atrix elem ents were calculated for up to two p arto n s a t NLO and up to four p a rto n s a t leading order (LO) using th e C o m ix and O p e n L o o p s m atrix elem ent g enerators and m erged w ith th e S h e r p a p a rto n shower using th e MePs@Nlo
prescription. T he N N PD F3.0N N LO P D F set was used in conjunction w ith p a rto n shower tu n in g developed by th e S h e r p a authors. T h e W /Z + je ts events are norm alised to NNLO cross-sections, com puted using F e w z [60] w ith th e M ST W 2008 NNLO P D F set.
D iboson processes were sim ulated using th e S h e r p a 2.1.1 generator. M atrix elem ents were calculated using th e C o m ix and O p e n L o o p s m a trix elem ent generators and m erged
J H E P 0 4 ( 2 0 1 9 ) 0 4 6
w ith th e S h e r p a p a rto n shower using th e M e P s @ N lo prescription. In th e case of b o th bosons decaying leptonically, m a trix elem ents contain all diagram s w ith four electroweak vertices and were calculated for up to one (four charged leptons or two charged leptons and two neutrinos) or zero p a rto n s (three charged leptons and one neutrino) a t NLO, and up to th re e parto n s a t LO. In th e cases w here one of th e bosons decays hadronically and the o th er leptonically, m a trix elem ents were calculated w ith up to one ( Z Z ) or zero (W W , W Z ) a d d ition al p a rto n s a t NLO and up to th re e ad ditio nal p a rto n s a t LO. T he CT10 P D F set was used in conjunction w ith p a rto n shower tu n in g developed by th e S h e r p a au tho rs. In all M C sim ulation sam ples, th e effect of m ultiple pp interactions p er bunch crossing (pile-up) was m odelled by adding m ultiple m inim um -bias events sim ulated w ith P y t h i a 8.186 [29], th e A2 set of tu n ed p aram eters [61] and th e M STW 2008LO set of P D F s [62]. T he MC sim ulation sam ples are re-weighted to reproduce th e d istrib u tio n of th e m ean num ber of interactions per bunch crossing observed in th e d a ta .
4 O b je c t r e c o n s t r u c t io n a n d id e n t if ic a t io n 4.1 D e te c to r -le v e l o b ject reco n stru ctio n
A description of th e m ain reconstruction and identification c riteria applied for electrons, m uons, jets and b-jets is given below.
E lectrons are reco nstru cted [63] by m atching ID track s to clusters in th e electrom ag
netic calorim eter. E lectrons m ust satisfy th e tight identification criterion, based on a likelihood discrim inant com bining observables related to th e shower shape in th e calorim e
te r and to th e tra c k m atching th e electrom agnetic cluster, and are required to be isolated in b o th th e ID and th e EM calorim eter using th e px -d ep en d en t isolation w orking point.
E lectrons are required to have p T > 25 GeV and |nciuster| < 2.47. E lectrons th a t fall in th e tra n sitio n region betw een th e barrel and endcap calorim eters (1.37 < |ncluster| < 1.52) are poorly m easured and are therefore not considered in th is analysis.
M uon can d idates are recon stru cted [64] by m atching ID tracks to tracks in th e m uon spectrom eter. Track reco n struction is perform ed independently in th e ID and MS before a com bined tra c k is form ed w ith a global re-fit to hits in th e ID and MS. M uon cand idates are required to have p T > 25 GeV and |n| < 2.5, m ust satisfy th e m edium identification c riteria and are required to be isolated using th e p T-dependent isolation w orking point.
E lectro n and m uon track s are required to be associated w ith th e p rim ary vertex. This association requires th e electron (m uon) tra c k to have |d o |/^ do < 5 (3) and |A z0 sin d| <
0.5 m m, w here d0 and z 0 are th e transverse and longitudinal im pact param eters of th e electron (m uon) track, respectively, ado is th e u n certain ty in th e m easurem ent of d0, and d is th e angle of th e tra c k relative to th e axis parallel to th e beam line.
R econstruction, identification and isolation efficiencies of electrons (muons) are cor
rected in sim ulation to m atch those observed in d a ta using Z ^ e + e - ( ß + ß - ) events, and th e position and w id th of th e observed Z boson peak is used to calib rate th e electron (m uon) energy (m om entum ) scale and resolution.
T he an ti-kt algorithm [65] w ith a radius p a ra m ete r of R = 0.4 is used to reconstruct jets w ith a four-m om entum recom bination scheme, using energy deposits in topological clusters
J H E P 0 4 ( 2 0 1 9 ) 0 4 6
in th e calorim eter as in p u ts [66]. Je ts are calib rated using a series of sim ulation-based corrections and in situ techniques [67]. C alibrated je ts are required to have p T > 25 GeV and |n| < 2.5 so th a t d a ta from th e ID is available for determ in in g w h eth er th ey contain b-hadrons. Je ts w ith pT < 60 GeV and |n| < 2.4 are required to be identified as originating from th e p rim ary vertex using a jet-v erte x tag ger (JV T ) algorithm [68].
Je ts containing b-hadrons are identified exploiting th e lifetimes of b-hadrons and th eir masses. A m ultivariate algorithm , MV2c10, th a t combines tra c k and secondary-vertex inform ation is used to distinguish b-jets from o th er je ts [69]. Four working points are defined by different b-tagging discrim inant o u tp u t thresholds corresponding to efficiencies of 85%, 77%, 70% and 60% in sim ulated t i events for b-jets w ith p T > 20 GeV and rejection factors ranging from 3-35 for c-jets and 30-1500 for light-flavour je ts [19, 69].
A fter selecting electrons, m uons and je ts as defined above, several c riteria are applied to ensure th a t objects do not overlap. If a selected electron and m uon share a tra c k th en th e electron is rejected. If an electron is w ithin A R = 0.2 of one or m ore jets th e n the closest je t to th e electron is removed. If th ere are rem aining je ts w ithin A R = 0.4 of an electron th e n th e electron is removed. W hen a je t is w ithin A R = 0.4 of a m uon, it is removed if it has fewer th a n th re e tracks, otherw ise th e m uon is removed.
4.2 P a rticle -lev el o b je ct d efin itio n s
Particle-level objects are selected in sim ulated events using definitions th a t closely m atch th e detector-level objects defined in section 4.1. Particle-level objects are defined using stable particles having a prop er lifetime g reater th a n 30 ps.
T his analysis considers electrons and m uons th a t do not come from had ro n decays for th e fiducial definition.2 In o rder to take into account final-state p h oto n rad iation , th e four-m om entum of each lepton is modified by adding to it th e four-m om enta of all photons, n ot originating from a hadron, th a t are located w ithin a A R = 0.1 cone aro un d th e lepton.
E lectrons and m uons are required to have pT > 25 GeV and |n| < 2.5.
J e ts are clustered using th e anti-k t algorithm w ith a radius p a ra m ete r of 0.4. All stable particles are included except those identified as electrons and m uons, and th e photons added to them , using th e definition above and neutrinos not from h adron decays. These jets do n ot include particles from pile-up events b u t do include those from th e underlying event.
T he decay p ro d u cts of hadronically decaying t-leptons are therefore included. Je ts are required to have p T > 25 GeV and |n| < 2.5.
Je ts are identified as b-jets by requiring th a t a t least one b-hadron w ith p T > 5 GeV is m atched to th e je t by ghost association [70]. Here, th e ghost-association procedure includes b-hadrons in th e je t clustering after scaling th eir p T to a negligible value. A sim ilar procedure is followed to define c-jets, w ith th e b-jet definition tak in g precedence, i.e. a je t containing one b-hadron and one c-hadron is defined as a b-jet. Je ts th a t do not contain eith er a b-hadron or a c-hadron are considered to be light-flavour jets.
2Electrons and muons from t decays are thus included.
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E lectrons and m uons th a t m eet th e selection c riteria defined above are required to be sep arated from selected je ts by A R (lep to n , jet) > 0.4. T his ensures com patibility w ith th e detector-level selection defined in section 4.1.
5 E v e n t s e le c t io n a n d d e fin itio n o f t h e fid u c ia l p h a s e s p a c e 5.1 D a ta even t se lec tio n
T he d a ta analysed were collected by th e ATLAS d e te c to r in 2015 and 2016 during stable pp collisions a t yfs = 13 TeV while all com ponents of th e ATLAS d e te c to r were fully operation al. T he to ta l in teg rated lum inosity recorded in this period is 36.1 fb- 1 .
In order to ensure events originate from pp collisions, events are required to have at least one p rim ary vertex w ith a t least two tracks. T he p rim ary vertex is defined as th e v ertex w ith th e highest ^ pT of tracks assigned to it.
Single-electron or single-m uon triggers are used to select th e events. T hey require a p x of at least 20 (26) GeV for m uons and 24 (26) GeV for electrons for th e 2015 (2016) d a ta set and also include requirem ents on th e lepton q u ality and isolation. These triggers are com plem ented by oth ers w ith higher px requirem ents b u t loosened isolation requirem ents to ensure m axim um efficiencies at higher lepton px.
In th e eß channel, events are required to have exactly one electron and one m uon of p x > 27 GeV and w ith opposite electric charge. A t least one of th e two leptons m ust be m atched in flavour and angle to a trigger object. In th e lepton + je ts channel, exactly one selected lepton of p x > 27 GeV is required and m ust be m atched to th e trig g er object th a t triggered th e event.
In th e eß channel, at least two je ts are required and a t least two of these m ust be b-tagged at th e 77% efficiency b-tagging working point for th e baseline selection. T he m easurem ent of th e fiducial cross-section w ith one (two) ad d itio n al b-jets requires a t least th re e (at least four) je ts to be b-tagged. For th e m easurem ent of th e b-jet m ultiplicity d istrib u tio n , a t least two je ts are required and at least two of th em m ust be b-tagged. All o th er differential cross-section m easurem ents in th e eß channel require a t least th re e jets and at least th re e of these m ust be b-tagged.
In th e lepton + je ts channel, a t least five jets are required and a t least two of these m ust be b-tagged for th e baseline selection. For th e m easurem ent of th e fiducial cross-section w ith one (two) add itio nal b-jets, five (six) je ts are required, of which at least th re e (at least four) m ust be b-tagged. For th e m easurem ent of th e differential cross-sections, at least six jets, a t least four of which are b-tagged, are required. In this channel, b-jets are identified using th e tig h te r 60% efficiency b-tagging working point to b e tte r suppress c-jets from W - ^ t s or W + ^ cs decays.
5.2 F id u cia l p h a se-sp a ce d efin ition
T he phase space in which th e fiducial cross-section is m easured is defined using particle- level objects w ith kinem atic requirem ents sim ilar to those placed on reconstru cted objects in th e event selection. T he definitions of th e fiducial phase spaces used for th e cross
sections m easurem ents are given below. T he d a ta are corrected to particle level using
J H E P 0 4 ( 2 0 1 9 ) 0 4 6
slightly different definitions of th e fiducial phase space depending on th e to p -p a ir decay channel and on th e observable.
In th e channel, fiducial cross-sections are determ ined by requiring exactly one elec
tro n and one m uon w ith opposite-sign charge a t particle level and a t least th re e (at least four) b-jet(s) for th e fiducial cross-section w ith one (two) ad ditio nal b-jets. T he norm alised differential cross-sections are m easured in th e fiducial volum e containing th e leptons and a t least two b-jets for th e d istrib u tio n differential in num ber of b-jets and at least th ree b-jets for all o th er differential m easurem ents.
In th e lepton + je ts channel, th e fiducial phase space for th e m easurem ent of th e in teg rated cross-section w ith one (two) ad ditio nal b-jet(s) is defined as containing exactly one particle-level electron or m uon and five (six) jets, at least th re e (four) of which are b-jets. D ifferential cross-sections are m easured in a fiducial volum e containing a t least six je ts and w here at least four of th em are required to be b-jets.
6 B a c k g r o u n d e s t im a t io n
T he baseline selection w ith at least two b-tagged je ts results in a sam ple w ith only small backgrounds from processes o th er th a n t t production. As m entioned before, events w ith a d ditional b-jets produced in tiV or t t f f p ro d u ction are tre a te d as signal. T he estim atio n of t t p ro d u ctio n in association w ith additional light-flavour je ts or c-jets is described in section 7.1 and is perform ed sim ultaneously w ith th e e x tra ctio n of fiducial cross-sections.
T he rem aining background events are classified into two types: those w ith pro m pt leptons from single top, W or Z decays (including those produced via leptonic t decays), which are discussed in section 6.1, and those w here a t least one of th e reco nstru cted lepton can d idates is n o n-prom pt or “fake” (N P & fake lep.), i.e. a n on-prom pt lepton from th e decay of a b- or c-hadron, an electron from a p ho ton conversion, hadronic je t activity m isidentified as an electron, or a m uon produced from an in-flight decay of a pion or kaon. T his is estim ated using a com bined data-d riv en and sim ulation-based approach in th e e ^ channel, and a data-d riv en approach in th e lepton + je ts channel, b o th of which are described in section 6.2.
6.1 B ack grou n d from sin g le-to p , Z /7* + je ts and W + j e t s ev en ts
T he background from single to p -q u ark p ro d u ctio n is estim ated from th e MC sim ulation predictions in b o th th e e ^ and lepton + je ts channels. This background co n tribu tes 3%
of th e event yields in b o th channels, w ith slightly sm aller contribu tion s in th e four b-jets selections.
In th e e ^ channel, a very small num ber of events from D rell-Yan p rod uction and Z /y* ( ^ t t) + je ts fulfil th e selection criteria. T his background is estim ated from MC sim ulation scaled to th e d a ta w ith sep arate scale factors for th e tw o-b-tagged jets and three- b-tagged je ts cases. T he scale factors are derived from d a ta events th a t have a reconstructed m ass of th e dilepton system corresponding to th e Z boson m ass and th a t fulfil th e sta n d a rd selection except th a t th e lepton flavour is ee or ^ . T he fraction of background events from Z /y* ( ^ t t) + je ts is below two p er mill for all b-tagged je t m ultiplicities. A small num ber
J H E P 0 4 ( 2 0 1 9 ) 0 4 6
of Z /Y * + jets events, w here th e Z /y* is decaying into any lepton flavour pair, can en ter in th e lepton + jets channel and is estim ated from MC sim ulation.
In th e lepton + je ts channel, a small background from W + je ts rem ains after th e event selection; however, th is co n trib u tio n is below 2% in events th a t have a t least th re e b-tagged jets. This background is estim ated directly from MC sim ulation.
6.2 B ack grou n d from n o n -p rom p t and fake lep to n s
In th e eß channel, th e n orm alisation of this background is estim ated from d a ta using events in which th e electron and m uon have th e sam e-sign electric charge. T he m ethod is described in ref. [71]. Know n sources of sam e-sign pro m p t leptons are su b tra c te d from th e d a ta and th e non-prom pt and fake background is e x tra cte d by scaling th e rem aining d a ta events by a tran sfer factor d eterm ined from MC sim ulation. This tran sfer factor is defined as th e ratio of predicted opposite-sign to predicted sam e-sign n on-prom pt and fake leptons.
In th e lepton + je ts channel, th e background from no n-prom pt and fake leptons is estim ated using th e m a trix m ethod [72]. A sam ple enriched in n o n-prom pt and fake leptons is o b tain ed by rem oving th e isolation and im pact p a ra m ete r requirem ents on th e lepton selections defined in section 4. T he efficiency for these leptons, hereafter referred to as loose leptons, to m eet th e identification c riteria defined in section 4.1 is th e n m easured separately for p ro m p t and fake lep to n s.3 For b o th electrons and m uons th e efficiency for a prom pt loose lepton to pass th e identification c riteria defined in section 4.1 is m easured using a sam ple of Z boson decays. T he efficiency for fake loose leptons to pass th e identification c riteria is m easured using events th a t have low m issing transverse m om entum for electrons and high lepton im p a c t-p a ra m ete r significance for m uons. These efficiencies allow the num ber of fake leptons selected in th e signal region to be estim ated.
3Here fake leptons also include non-prompt leptons.
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Figure 2. Comparison of the data distributions with predictions for the number of b-tagged jets, in events with at least 2 b-tagged jets, in the (a) ep and (b) lep to n + je ts channels. The systematic uncertainty band, shown in grey, includes all uncertainties from experimental sources.
Figure 3. Comparison of the data distributions with predictions for the leading b-tagged jet p T, in events with at least 3 b-tagged jets, in the (a) ep and (b) lep to n + je ts channels. The systematic uncertainty band, shown in grey, includes all uncertainties from experimental sources. Events that fall outside of the range of the x-axis are not included in the plot.
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Process 2b > 3b > 4b Signal (tt + t t H + t t V ) 74 400 ± 2 900 3 200 ± 310 210 ± 29
tt 74 200 ± 2 900 3 100 ± 310 190 ± 29
t t H 45. 3 ± 6.6 36.5 ± 7.0 9.4 ± 3.3
t t V 190 ± 16 33.5 ± 6.7 4.4 ± 2.2
B ackground 3150 ± 810 140 ± 53 9.2 ± 5.6
Single to p 2 460 ± 540 96 ± 32 4.1 ± 2.5
N P and fake lep. 600 ± 600 43 ± 43 5.1 ± 5.1
Z /y* + je ts 53 ± 13 1.3 ± 0.3 0.07 ± 0.02
D iboson 38 ± 20 1.0 ± 1.1 < 0.01
E xpected Observed
77 600 76 425
± 3 000 3320 3 809
± 3 2 0 216 267
± 30
T ab le 2. Predicted and observed ep, channel event yields in 2b, > 3b and > 4b selections. The quoted errors are symmetrised and indicate total statistical and systematic uncertainties in predic
tions due to experimental sources.
Process > 5 j, > 2b > 5 j, > 3b > 5j, = 3b > 6 j, > 4b Signal
(tt + ttH + ttV ) 429000 ± 42000 23700 ± 2 200 22 300 ± 2100 1 130 ± 110
t i 426000 ± 42000 23000 ± 2 200 21 700 ± 2100 1 030 ± 110
ttH 1250 ± 58 437 ± 23 351 ± 18 68.3 ± 5.8
ttV 2020 ± 110 250 ± 16 215 ± 14 28.3 ± 2.8
Background 39 500 ± 7900 2 230 ± 470 2110 ± 450 87 ± 23
Single top 16400± 2000 856 ± 99 803 ± 94 35.7 ± 6.5
NP and fake lep. 11000 ± 5 500 740 ± 380 710 ± 360 32 ± 21
W +jets 8 600 ± 5300 440 ± 270 410 ± 260 11.0 ± 6.9
Z /y* +jets 2 960 ± 480 164 ± 26 155 ± 26 5.9 ± 1.5
Diboson 529 ± 80 34.0 ± 5.6 32.0 ± 5.5 1.79 ± 0.58
Expected 469000 ± 42000 26000 ± 2 300 24 400 ± 2 200 1 220 ± 110
Observed 469 793 28167 26 389 1316
T ab le 3. Predicted and observed lepton + jets event yields in the > 5j > 2b, > 5j > 3b, > 5j = 3b, and > 6j > 4b selections. The quoted uncertainties are symmetrised and indicate total statistical and systematic uncertainties in predictions due to experimental sources.
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6.3 D a ta and p red ic tio n co m p arison o f b a selin e selec tio n
T he overall num ber of events fulfilling th e baseline selection is well described by th e pre
diction in b o th channels, as seen in tables 2 and 3 and figure 2, w here b and j denote a b-jet and a je t of any flavour, respectively. However, th e num ber of events w ith more th a n two b-tagged jets is slightly u n d erestim ated, as shown in figures 2 and 3. Therefore, data-d riv en scale factors are derived to correct th e predictions of addition al c-jets or light je ts in th e t t MC sim ulation, as described in th e next section.
7 E x t r a c t io n o f t h e fid u c ia l c r o s s - s e c t io n s
F iducial cross-sections in th e phase spaces defined in section 5.2 for th e different observables are ex tra cte d from detector-level d istrib u tio n s obtained after th e event selections described in section 5.1 and su b tra c tin g th e num ber of background events produced by th e n o n -ti processes described in section 6. A fter th e su b tra c tio n of n o n -ti background, th e d a ta suffer from backgrounds from t t events w ith ad d ition al light-flavour jets (til) or c-jets (tic) th a t are m isidentified as b-jets by th e b-tagging algorithm . T he correction factors for these backgrounds are m easured in d a ta , as presented in section 7.1. T he d a ta are th e n unfolded using th e corrected MC sim ulation as described in section 7.2.
7.1 D a ta -d r iv en co rrectio n factors for flavour co m p o sitio n o f a d d itio n a l je ts in i i ev en ts
T he m easurem ent of t t + b-jets p ro d u ctio n is d ependent on th e d eterm in atio n of th e back
ground from o th er t t processes. For exam ple, according to sim ulation studies in th e eß channel, only ab o u t 50% of th e events selected a t d e te c to r level w ith a t least th re e b-tagged je ts a t th e 77% efficiency w orking point and w ithin th e fiducial phase space of th e analysis, also have a t least th re e b-jets at particle level. T he oth er events contain at least one c-jet or light-flavour je t which is m isidentified as a b-jet. T he cross-section of t i w ith addition al je t p ro d uction has been m easured w ith 10% (16%) u n certain ty for events w ith two (three) ad d ition al jets [73]. However, these m easurem ents did not d eterm ine th e flavours of th e ad d ition al jets. D ue to th e lack of precise m easurem ents of these processes, te m p la te fits to d a ta are perform ed to e x tra ct th e ttb signal yields and e stim ate th e ttc and til backgrounds as described in th e following. T he tem p lates are con stru cted from tt, t t H and t t V MC sim ulated sam ples, as th e signal includes th e contribution s from t t V and t t H .
T he events in th e eß channel are selected w ithin an analysis region consisting of at least th re e b-tagged je ts a t th e 77% b-tagging w orking point as specified in section 5.1. This avoids e x tra p o la tio n of th e background shapes d eterm ined outside th e selected region into th e analysis region. T he fit in th e lepton + jets channel is perform ed on a sam ple w ith at least five jets, a t least two of which are b-tagged w ith a b-tagging efficiency of 60%. W hile th is m eans th a t th e MC sim ulation is needed to e x tra p o la te th e results of th e fit into th e signal regions, it allows th e ttt l background to be ex tra cte d in w h at is effectively a control region. T he lepton + je ts channel suffers from an ad ditio n al background due to W + ^ c i or corresponding W - decays in th e inclusive t i process, w here th e c-jet is m isidentified as
J H E P 0 4 ( 2 0 1 9 ) 0 4 6
C ategory e^ lepton + jets
tt6 > 3 6-jets > 3 6-jets
tic < 3 6-jets and > 1 c-jet < 3 6-jets and > 2 c-jets tti events th a t do not m eet above c riteria events th a t do not m eet above c riteria T able 4. Event categorisation (for the definition of the MC templates) based on the particle-level selections of b-jets, c-jets and light-flavour jets.
a b-jet. In order to sep arate th is background from tt+ c -je ts events, events containing only one particle-level c-jet are a ttrib u te d to this background and grouped into a tti class, while those w ith two particle-level c-jets are placed into a tic class, as sum m arised in tab le 4.
In this sam ple, 85% of th e events w ith exactly one particle-level c-jet are found to contain W ^ cs(cs) decays, according to t i MC sim ulation. T em plates are created for events in th e different categories described in tab le 4 using th e 6-tagging discrim inant value of th e je t w ith th e th ird -high est 6-tagging discrim inant in th e channel, and th e two jets w ith th e th ird - and fourth-highest b-tagging discrim inant values in th e lepton + jets channel.
T he d iscrim inant values are divided into five 6-tagging discrim inant bins such th a t each bin corresponds to a certain range of 6-tagging efficiencies defined by th e w orking points.
T he bins range from 1 to 5, corresponding to efficiencies of 100% -85% , 85% -77% , 77% - 70%, 70% -60% , and < 60% respectively. In th e e ^ channel, one-dim ensional tem p lates w ith th re e bins are form ed corresponding to 6-tagging efficiencies betw een 77% and 0% for th e je t w ith th e th ird highest 6-tagging discrim inant value. In th e lepton + je ts channel, tw o-dim ensional tem p lates are created using th e 6-tagging discrim inant values of th e two je ts w ith th e th ird - and fourth-highest 6-tagging discrim inant values, corresponding to
6-tagging efficiencies betw een 100% and 0% for th e two jets.
In b o th channels, one te m p la te is created from th e sum of all backgrounds described in section 6 and th re e tem p lates are created from tt, ttV and t t H MC sim ulations, to account for tt6, tic and tti events, as detailed in tab le 4 . These tem p lates are th e n fitted to th e d a ta using a binned m axim um -likelihood fit, w ith a Poisson likelihood
r t ^ ^
A
e -Vk( a ( a ) xk L ( a |x i , . . . ,Xn) = ;--- ,V
Xk-w here x k is th e num ber of events in bin k of th e d a ta te m p la te and vk ( a ) is th e expected n um ber of events, and depends upon a num ber of free p aram eters, a .
In th e e ^ channel, two free p aram eters are used, such th a t th e expected num ber of events in bin k is
vk( a b, a cl) = a bN tfb + a cl { N ttc + N ttl) + N non-tf ,
w here N ^ , N tkc, N k and Nkon_tj are th e num bers of events in bin k of th e tt6, tic, tii and n o n -tt background tem p lates, respectively. T he scale factors o b tain ed from th e fit are a b = 1.37 ± 0.06 and a cl = 1.05 ± 0.04, w here th e quoted un certainties are sta tistic a l only.
J H E P 0 4 ( 2 0 1 9 ) 0 4 6
Figure 4. The 6-tagging distribution of the third-highest 6-tagging discriminant-ranked jet for the (a) eß channel, and of the third and fourth 6-tagging discriminant-ranked jet for the (b) lepton+jets channel. For clarity, the two-dimensional lepton + jets templates have been flattened into one dimension. The ratios of total predictions before and after the fit to the data are shown in the lower panel. The vertical bar in each ratio represents only the statistical uncertainty, and the grey bands represent the total error including systematic uncertainties from experimental sources. The extracted scale factors a b, a c, a l, a cl are given considering only statistical uncertainties.
F igure 4a shows th e d istrib u tio n s of th e tem p lates before and after scaling th e tem plates by these scale factors.
In th e lepton + je ts channel, th re e free param eters, a b, a c and a l , are used in th e m axim um -likelihood fit, such th a t th e expected num ber of events in bin k is
vk ( a b, a c, a l) = a bN ttb + a cN ttc + a lN ttl + N non-tf . (7^ ) T he best-fit values of th e free p aram eters are a b = 1.11 ± 0.02, a c = 1.59 ± 0.06 and a l = 0.962 ± 0.003 w here th e quoted un certainties are sta tistic a l only. Including system atic uncertainties, th e values of a b ex tra cte d in th e eß and lepton + jets channels are found to be com patible a t a level b e tte r th a n 1.5 sta n d a rd deviations. Some of th e d om inant com m on system atic uncertain ties have small correlations betw een th e two channels, while th e u n certain ty in a b due to th e m odelling of th e ttc tem p la te in th e eß channel, as discussed in section 8.3 is un correlated betw een th e two channels. Taking only this u n certain ty as uncorrelated, th e values of a b e x tra cte d from th e two channels are found be com patible a t a level b e tte r th a n 1.7 sta n d a rd deviations. Figure 4b shows th e d istrib u tio n of th e 6- tagging discrim inant before and after th e fit. For clarity, th e tw o-dim ensional le p to n + je ts tem p lates are flatten ed into a single dim ension. Figures 5 and 6 show th e com parison of d a ta and predictions for th e 6-tagged je t m ultiplicity and th e leading 6-tagged je t p T in th e eß and lepton + jets channels after th e ttb signal, and th e ttc and ttl backgrounds, are
J H E P 0 4 ( 2 0 1 9 ) 0 4 6
Figure 5. Comparison of the data distributions with predictions, after applying scale factors, for the number of b-tagged jets, in events with at least 2 b-tagged jets, in the (a) ep and (b) lepton + jets channels. The systematic uncertainty band, shown in grey, includes all uncertainties from experimental sources.
Figure 6. Comparison of the data distributions with predictions for the leading b-tagged jet p T, after applying scale factors, in events with at least 3 b-tagged jets, in the (a) ep and (b) lepton + jets channels. The systematic uncertainty band, shown in grey, includes all uncertainties from experimental sources. Events that fall outside of the range of the x-axis are not included in the plot.
J H E P 0 4 ( 2 0 1 9 ) 0 4 6
scaled by th e e x tra cte d scale factors. T he d a ta are described m uch b e tte r by th e prediction after th e scaling is applied.
7.2 U n fo ld in g
T he m easured d istrib u tio n s a t d e te c to r level are unfolded to th e particle level. T he unfold
ing procedure corrects for resolution effects and for d e te c to r efficiencies and acceptances.
F irst, th e num ber of n o n -tt background events in bin j (N j on tt bkg), described in section 6, is su b tra c te d from th e d a ta d istrib u tio n at th e d e te c to r level in bin j ( N jata). T his re
tain s a m ix tu re of signal and tt-re late d backgrounds, th e la tte r com ing from m is-tagged events as described in section 7.1. A series of corrections are th e n applied, w ith all correc
tions derived from sim ulated tt, t t H and t t V events. Following th e su b tra c tio n of n o n -tt background, th e d a ta are first corrected for m is-tagged events by applying a correction
f j = abN ttb,reco ttb = a b N jtb b ttb, reco+ Bj ’
w here a b is defined in th e previous section, Nj^breco is th e num ber of detector-level ttb events predicted by MC sim ulation, and Bj is th e num ber of detector-level ttc and ttl events in bin j , after being scaled by th e fit param eters, a cl or a c and ai, defined in th e previous section. In th e eß channel,
Bj - a cl ( N jt cl y tte,reco + N j ttl,recoJ ’1 , and in th e lepton + je ts channel,
B j - a cN j c tttc, reco + ai N j i ttti, reco ,
w here N jt tic,reco and N j tw,reco are th e num bers of reco nstructed ttc and ttl events in bin j,J ’ as predicted by MC sim ulation, respectively. N ext, an acceptance correction, faccept, is applied, which corrects for th e fiducial acceptance and is defined as th e prob ability of a ttt b event passing th e detector-level selection in a given bin j ( N t reco) to also fall w ithin th e fiducial particle-level phase space (Nj^brecoApart). It is estim ated as
j N jtttb,recoApart
f accept N j *
tttb,reco
T he detector-level objects are required to be m atched w ithin A R — 0*4 to th e corresponding particle-level objects. This requirem ent leads to a b e tte r correspondence betw een th e particle and d e te c to r levels and improves th e unfolding perform ance. T he m atching factor /matching is defined as
j>j N jttb,reco Apart Amatched
f matching N j ,
tib,reco Apart
w here N j b recoApartAmatched is th e subset of reconstructed events falling in th e particle-level fiducial volum e which are m atched to th e corresponding particle-level objects.
