Search for the Standard Model Higgs boson decaying into $b\bar{b}$ produced in association with top quarks decaying hadronically 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 SISSA b y £ } S p r i n g e r R e c e i v e d : April 14, 2016 A c c e p t e d : May 13, 2016 P u b l i s h e d : May 27, 2016

Search for the Standard Model Higgs boson decaying into bb produced in association with top quarks

decaying hadronically in pp collisions at √ S = 8 T eV with the A T L A S detector

T h e A T L A S collaboration

E -m a il: a t l a s . p u b l i c a t i o n s @ c e r n . c h

A b s t r a c t : A search for H iggs b o so n p ro d u c tio n in a sso c ia tio n w ith a p a ir of to p q u a rk s ( t t H ) is p erfo rm ed , w h ere th e H iggs b o so n d ecay s to bb, an d b o th to p q u a rk s d ecay h a d ro n - ically. T h e d a t a used co rre sp o n d to a n in te g ra te d lu m in o sity of 20.3 fb -1 of p p collisions a t √ s = 8 T eV co llected w ith th e A T L A S d e te c to r a t th e L arg e H a d ro n C ollider. T h e sea rch selects ev en ts w ith a t le a st six en e rg etic je ts a n d uses a b o o s te d d ecisio n tre e al­

g o rith m to d isc rim in a te b etw e en sign al a n d S ta n d a rd M odel b a c k g ro u n d . T h e d o m in a n t m u ltije t b a c k g ro u n d is e s tim a te d u sin g a d e d ic a te d d a ta -d riv e n tec h n iq u e . F or a H iggs b o so n m ass of 125 G eV , a n u p p e r lim it of 6.4 (5.4) tim e s th e S ta n d a rd M odel cross sectio n is o b serv ed (e x p e c te d ) a t 95% confidence level. T h e b e s t-fit value for th e sig nal s tre n g th is p = 1.6 ± 2.6 tim e s th e S ta n d a rd M odel e x p e c ta tio n for m H = 125 G eV . C o m b in in g all t t H searches c a rrie d o u t by A T L A S a t √ s = 8 a n d 7 TeV , an o b serv ed (e x p ected ) u p p e r lim it o f 3.1 (1.4) tim e s th e S ta n d a rd M odel e x p e c ta tio n is o b ta in e d a t 95% confidence level, w ith a signal s tre n g th p = 1.7 ± 0.8.

Ke y w o r d s: H a d ro n -H a d ro n s c a tte rin g (e x p e rim e n ts)

ArXiy ePr i n t: 1604.03812

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Contents

1 In tr o d u ctio n 2

2 T h e A T L A S d e te c to r 3

3 O b ject rec o n str u c tio n 3

4 E ven t selec tio n 4

5 Signal and backgrou n d m o d ellin g 4

5.1 S ignal m odel 4

5.2 S im u la te d b a c k g ro u n d s 5

5.3 C o m m o n tr e a tm e n t of M C sam p les 6

5.4 M u ltije t b a c k g ro u n d e s tim a tio n usin g d a ta : th e T R Fm j m e th o d 7 5.5 V a lid a tio n of th e T R F m j m e th o d in d a t a a n d sim u la tio n 8

6 M u ltijet trig g e r efficien cy 10

7 E ven t cla ssification 10

8 A n a ly sis m eth o d 10

9 S y ste m a tic u n certa in ties 14

10 S ta tistic a l m eth o d s 19

11 R e su lts 19

12 C om b in ation o f ££H resu lts at / s = 7 and 8 TeV 24 12.1 In d iv id u a l t t H m e a su re m e n ts a n d re su lts 24 12.1.1 H ^ bb (single le p to n a n d d ile p to n t t decays) 25

12.1.2 H ^ ( W W (*) ,t t, Z Z (*)) ^ le p to n s 25

12.1.3 H ^ yy 25

12.2 C o rre la tio n s 26

12.3 R e su lts of th e c o m b in a tio n 26

12.3.1 S ignal s tre n g th 26

12.3.2 C ou p lin g s 26

13 C o n clu sio n 28

T h e A T L A S co lla b o ra tio n 35

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1 Introduction

A fte r th e discovery of a new boso n w ith a m ass of a ro u n d 125 GeV in J u ly 2012 by th e A T L A S [1] a n d C M S [2] c o lla b o ra tio n s, th e focus h as now sh ifted to co n firm in g w h e th e r th is p a rtic le is th e S ta n d a rd M odel (SM ) H iggs b o so n [3- 6] o r a n o th e r boso n. W h ile an y d e v ia tio n from SM p re d ic tio n s w ould in d ic a te th e p resen ce of new physics, all m e a su re m e n ts o f th e p ro p e rtie s of th is new b o so n th u s fa r p erfo rm ed a t th e L arg e H a d ro n C o llid er (L H C ), in clu d in g spin, p a rity , to ta l w id th , a n d co u p lin g to SM p a rtic le s, are co n siste n t w ith th e SM p re d ic tio n [7- 12].

B ecau se o f its larg e m ass, th e to p q u a rk is th e ferm io n w ith th e la rg e st Y ukaw a co u ­ p lin g (yt ) to th e H iggs field in th e SM , w ith a value close to unity . T h e co u p lin g y t is e x p e rim e n ta lly accessible by m e a su rin g th e g lu o n fusion (ggF ) p ro d u c tio n p ro cess o r th e H ^ y y decay, w h ere a sizeable c o n trib u tio n derives from a to p -q u a rk loop. T h is case re q u ires th e a s s u m p tio n t h a t n o new physics c o n trib u te s w ith a d d itio n a l in d u ced loops in o rd e r to m e a su re yt . C u rre n tly , th e o n ly p ro cess w h ere yt c a n b e accessed d ire c tly is th e p ro d u c tio n of a to p -q u a rk p a ir in a sso c ia tio n w ith a H iggs bo so n ( t i H ).

T h e re s u lts of searches for th e H iggs bo so n are u su ally ex p ressed in te rm s o f th e signal- s tre n g th p a r a m e te r y , w hich is defined as th e ra tio of th e o b serv ed to th e e x p e c te d n u m b e r o f signal ev en ts. T h e la tt e r is c a lc u la te d u sin g th e SM cross sec tio n tim e s b ra n c h in g r a ­ tio [13]. T h e com b in ed t t H signal s tre n g th m e a su re d by th e C M S C o lla b o ra tio n [14], o b ta in e d by m erg in g searches in several final s ta te s , is y = 2.8 ± 1.0. T h e A T L A S C ol­

la b o ra tio n h as search ed for a tttH sig nal in ev e n ts en ric h ed in H iggs b o so n d ecays to tw o m assive v e c to r b o sons o r t le p to n s in th e m u ltile p to n c h a n n el [15], fin d in g y = 2 .1 + 1 2 , for t t H ( H ^ bb) [16] in final s ta te s w ith a t le a st one le p to n o b ta in in g y = 1.5 ± 1.1, a n d for t t H ( H ^ y y ) [17] m e a su rin g y = 1 .3 + 1 +

A m o n g all t t H final s ta te s , th e on e w h ere b o th W b o son s from t ^ W b d ecay h a d ro n - ically an d th e H iggs b oson d ecays in to a btb p a ir h as th e la rg e st b ra n c h in g ra tio , b u t also th e le a st signal p u rity . T h is p a p e r d escrib es a sea rch for th is all-h a d ro n ic t t H ( H ^ bb) d ecay m ode. T h e an a ly sis uses p ro to n -p ro to n collision d a t a co rre sp o n d in g to a n in te g ra te d lu m in o sity of 20.3 fb -1 a t ce n te r-o f-m ass en e rg y + s = 8 TeV reco rd e d w ith th e A TLA S d e te c to r a t th e L H C .

A t B o rn level, th e signal s ig n a tu re is eig h t je ts , fo u r o f w hich are b -q u a rk je ts . T h e d o m in a n t b ac k g ro u n d is th e n o n -re s o n a n t p ro d u c tio n o f m u ltije t ev en ts. F o r th is analy sis, a d a ta -d riv e n m e th o d is ap p lied to e s tim a te th e m u ltije t b a c k g ro u n d by e x tra p o la tin g its c o n trib u tio n from a c o n tro l region w ith th e sam e je t m u ltip licity , b u t a low er m u ltip lic ity of je ts c o n ta in in g b -h ad ro n s th a n th e sig nal process. T h e p a ra m e te rs u sed for th e e x tra p o la ­ tio n are m e a su re d from a c o n tro l regio n a n d checked u sin g M o n te C arlo (M C ) sim u la tio n s.

O th e r s u b d o m in a n t b a c k g ro u n d p rocesses are e s tim a te d u sin g M C sim u la tio n s. To m a x ­ im ise th e signal sen sitiv ity , th e ev e n ts are c a te g o rised acco rd in g to th e ir n u m b e r of je ts a n d je ts iden tified as c o n ta in in g b -h ad ro n s (b -tag g ed ). A b o o s te d decisio n tre e (B D T ) al­

g o rith m , b ase d on ev en t sh a p e a n d k in e m a tic v ariab les, is used to d is c rim in a te th e signal fro m th e b a c k g ro u n d . T h e e x tra c tio n of y is p erfo rm ed th ro u g h a fit to th e B D T d isc rim ­ in a n t d is trib u tio n . A fte r th e fit th e d o m in a n t u n c e rta in ty is th e t t + bb p ro d u c tio n cross

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sectio n . T h e se n sitiv ity is also lim ited by sy s te m a tic u n c e rta in tie s fro m th e d a ta -d riv e n m e th o d used for th e m o d ellin g o f th e larg e n o n -re so n a n t m u ltije t p ro d u c tio n .

2 The ATLAS detector

T h e A T L A S d e te c to r [18] co n sists o f a n in n e r tra c k in g d e te c to r s u rro u n d e d by a th in su ­ p e rc o n d u c tin g solenoid m a g n e t p ro v id in g a 2 T ax ial m a g n e tic field, e le c tro m a g n e tic an d h a d ro n c a lo rim e te rs, a n d a m u o n sp e c tro m e te r in c o rp o ra tin g th re e larg e s u p e rc o n d u c tin g to ro id m a g n e ts. T h e in n e r d e te c to r (ID ) co m p rises th e h ig h -g ra n u la rity silicon pixel d e te c ­ t o r a n d th e silicon m ic ro s trip tra c k e r covering th e p s e u d o ra p id ity1 ra n g e |n| < 2.5, a n d th e s tra w -tu b e tra n s itio n ra d ia tio n tra c k e r covering |n| < 2.0. T h e e le c tro m a g n e tic c a lo rim e te r covers |n| < 3.2 a n d co n sists of a b a rre l a n d tw o e n d c a p h ig h -g ra n u la rity le a d /liq u id -a rg o n (L A r) c a lo rim e te rs. A n a d d itio n a l th in L A r p re sa m p le r covers |n| < 1.8. H a d ro n ca lo rim e­

t r y is p ro v id ed by a s te e l/s c in tilla to r-tile c a lo rim e te r, w h ich covers th e regio n |n| < 1.7, an d tw o c o p p e r/L A r h a d ro n e n d c a p c a lo rim e te rs. To co m p lete th e p s e u d o ra p id ity coverage, c o p p e r/L A r a n d t u n g s te n /L A r fo rw ard c a lo rim e te rs cover u p to |n| = 4.9. M u o n tra c k in g c h a m b e rs precisely m easu re th e deflectio n of m uo ns in th e m a g n e tic field g e n e ra te d by su ­ p e rc o n d u c tin g air-co re to ro id s in th e reg ion |n| < 2.7. A th ree -lev el trig g e r sy ste m selects ev e n ts for offline an a ly sis [19]. T h e h a rd w a re -b a s e d Level-1 trig g e r is used to re d u ce th e ev en t r a te to a m ax im u m of 75 kH z, w hile th e tw o so ftw are-b ased trig g e r levels, Level-2 a n d E v e n t F ilte r (E F ), re d u ce th e ev en t r a te to a b o u t 400 Hz.

3 O bject reconstruction

T h e a ll-h a d ro n ic t t H final s ta te is co m p o sed of je ts o rig in a tin g from (u , d, s )-q u a rk s o r g luons (lig h t je ts ) a n d je ts from c- o r b-q uark s (heav y -flav o u r je ts ). E le c tro n s a n d m uons, selected in th e sam e w ay as in ref. [16], a re u sed o n ly to v eto ev en ts t h a t w ould ov erlap w ith th e t t H searches in final s ta te s w ith lep to n s.

A t least one re c o n s tru c te d p rim a ry v e rte x is re q u ired , w ith a t le a st five asso c ia te d tra c k s w ith p T > 400 M eV , a n d a p o s itio n co n siste n t w ith th e lu m in o u s reg ion o f th e b e a m s in th e tra n s v e rse p lan e. If m ore th a n on e v e rte x is fo u n d , th e p rim a ry v e rte x is ta k e n to b e th e one w hich h as th e la rg e st sum of th e sq u a re d tra n s v e rs e m o m e n ta of its asso c ia te d tra c k s.

J e ts a re re c o n s tru c te d w ith th e a n ti-k t a lg o rith m [20- 22], w ith a ra d iu s p a r a m e te r R = 0.4 in th e (n, ) p lan e. T h e y are b u ilt from c a lib ra te d to p o lo g ic al clu ste rs o f en e rg y d e p o sits in th e c a lo rim e te rs [18]. P rio r to je t finding, a local c lu s te r c a lib ra tio n schem e [2 3 , 24]

is ap p lied to co rre c t th e to p o lo g ic al c lu s te r energies for th e effects of n o n -c o m p e n sa tin g c a lo rim e te r re sp o n se, d e a d m a te ria l, a n d o u t-o f-c lu ste r leakage. A fte r en e rg y c a lib ra tio n

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 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 (t,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). Transverse momentum and energy are defined as p t = p sin 6 and E T = E sin 6 respectively.

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base d o n in -situ m e a su re m e n ts [25], je ts are re q u ire d to h ave tra n s v e rs e m o m e n tu m p T >

25 G eV a n d |n| < 2.5. D u rin g je t re c o n s tru c tio n , no d is tin c tio n is m a d e b etw e en identified e le c tro n s a n d je t en e rg y d e p o sits. To avoid d o u b le c o u n tin g e le c tro n s as je ts , an y je t w ith in a cone o f size A R = ^ / ( A ^ )2 + ( A n )2 = 0.2 a ro u n d a re c o n s tru c te d e le c tro n is d iscard ed . A fte r th is, e le c tro n s w ith in a A R = 0.4 o f a re m a in in g je t a re rem oved.

To avoid selectin g je ts fro m a d d itio n a l p p in te ra c tio n s in th e sam e ev en t (p ile-u p ), a loose selectio n is ap p lied to th e je t v e rte x fra c tio n (J V F ), defined as th e ra tio o f th e sca la r sum of th e p t o f tra c k s m a tc h e d to th e je t a n d o rig in a tin g from th e p rim a ry v e rte x to t h a t o f all tra c k s m a tc h e d to th e je t. T h is c rite rio n , J V F > 0.5, is o n ly ap p lie d to je ts w ith p T < 50 GeV a n d |n| < 2.4.

J e ts are b-tagged by m ean s of th e M V1 a lg o rith m [26]. I t co m bines in fo rm a tio n from tra c k im p a c t p a ra m e te rs a n d to p o lo g ic al p ro p e rtie s o f se c o n d a ry a n d te r t i a r y d ecay v ertices w hich a re re c o n s tru c te d w ith in th e je t. T h e w orkin g p o in t u sed for th is sea rch c o rresp o n d s to a 60% efficiency to ta g a b-qu ark je t, a lig h t-je t re je c tio n fa c to r of a p p ro x im a te ly 700 an d a c h a rm -je t re je c tio n fa c to r o f 8, as d e te rm in e d for je ts w ith p T > 25 G eV a n d |n| < 2.5 in sim u la te d R ev e n ts [26]. T h e ta g g in g efficiencies o b ta in e d in sim u la tio n are a d ju s te d to m a tc h th e re su lts o f th e c a lib ra tio n s p erfo rm ed in d a t a [26].

4 Event selection

T h is search is b ase d on d a t a collected usin g a m u ltije t trig g e r, w h ich re q u ires a t least five je ts p assin g th e E F stag e, each h av in g p T > 55 GeV a n d |n| < 2.5. E v e n ts a re d isc a rd e d if an y je t w ith p T > 20 GeV is iden tified as o u t-o f-tim e a c tiv ity from a p re v io u s pp collision o r as c a lo rim e te r noise [27].

T h e five lead in g je ts in p T are re q u ire d to h ave p T > 55 GeV w ith |n| < 2.5 a n d all o th e r je ts are re q u ired to have p T > 25 GeV a n d |n| < 2.5. E v e n ts are re q u ired to h ave a t le a st six je ts , of w hich a t le a st tw o m u st b e b -tagged. E v e n ts w ith w ell-identified iso lated m uons o r ele c tro n s w ith p T > 25 GeV a re d isc a rd e d in o rd e r to avoid o v erlap w ith o th e r

R

H analyses.

To e n h a n c e th e sen sitiv ity , th e selected ev e n ts are ca te g o rise d in to v ario u s d is tin c t regions, a c co rd in g to th e ir je t a n d b -tag m u ltip licitie s: th e reg ion w ith m je ts , o f w hich n a re b-jets, is referred to as “( m j ,n b ) ” .

5 Signal and background m odelling

5.1 Signal m o d el

T h e

R

H signal p rocess is m o delled u sin g m a trix elem e n ts c a lc u la tio n s o b ta in e d from th e H E L A C -O n elo o p package [28] w ith n e x t-to -le a d in g o rd e r (N L O ) a c c u ra c y in a s. Po w h e g-

b o x [29- 31] serves as a n in terfa ce to th e M C p ro g ra m s u sed to s im u la te th e p a r to n show er a n d h a d ro n isa tio n . T h e sam ples c re a te d u sin g th is a p p ro a c h are re ferred to as Po wHe l sam p les [32]. T h e y in clu d e all SM H iggs b o so n a n d to p -q u a rk decays a n d use th e C T 1 0 N L O [33] p a r to n d is trib u tio n fu n c tio n (P D F ) sets w ith th e fa c to ris a tio n ( y F) a n d re n o rm a lisa tio n ( y R) scales set to y F = y R = m t + m H /2 . T h e Po wHe l

R

H sam ples

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use Py t h ia 8.1 [34] to sim u la te th e p a r to n show er w ith th e C T E Q 6 L 1 [35] P D F a n d th e AU2 u n d e rly in g -e v e n t set of g e n e ra to r p a ra m e te rs (tu n e ) [36], w hile HERW ig [37] is u sed to e s tim a te s y s te m a tic u n c e rta in tie s d u e to th e fra g m e n ta tio n m odelling.

F o r th e se t t H sam p les th e cro ss-sectio n n o rm a lisa tio n s a n d th e H iggs b o so n d ecay b ra n c h in g fra c tio n s are ta k e n from th e N L O Q C D a n d from th e N L O Q C D + E W th e o ­ re tic a l c a lc u la tio n s [13] respectively. T h e m asses of th e H iggs b o so n a n d th e to p q u a rk are set to 125 GeV a n d to 172.5 GeV respectively.

5.2 S im u la ted b ackgrounds

T h e d o m in a n t b a c k g ro u n d to th e all-h a d ro n ic ttt H sig nal is m u ltije t p ro d u c tio n , followed by t t + je ts p ro d u c tio n . S m all b a c k g ro u n d c o n trib u tio n s com e from th e p ro d u c tio n o f a single to p q u a rk a n d from th e a sso c ia te d p ro d u c tio n o f a v e c to r b o son a n d a t t p air, t t V (V = W, Z ). T h e m u ltije t b a c k g ro u n d is d e te rm in e d from d a t a u sin g a d e d ic a te d m e th o d d esc rib ed in sec tio n 5 .4 . T h e o th e r b ac k g ro u n d c o n trib u tio n s a re e s tim a te d u sin g M C sim u la tio n s.

T h e m u ltije t events, w hich are used for je t trig g e r stu d ie s a n d for th e v a lid a tio n of th e d a ta -d riv e n m u ltije t b a c k g ro u n d e s tim a tio n , are sim u la te d w ith Py t h ia 8.1 u sin g th e N N P D F 2 .3 LO [38] P D F s.

T h e m a in t t sam p le is g e n e ra te d u sin g th e P o w H E g N L O g e n e ra to r w ith th e C T 1 0 N L O P D F set, a ssu m in g a value of th e to p -q u a r k m ass o f 172.5 GeV. I t is in terfa ced to P y t h i a 6.425 [39] w ith th e C T E Q 6 L 1 P D F set a n d th e P eru g ia2 0 1 1 C [40] u n d erly in g - ev en t tu n e ; th is c o m b in a tio n of g e n e ra to r a n d show ering p ro g ra m s is h e re a fte r re ferred to as P o w H E g + P Y T H iA . T h e sam p le is n o rm alised to th e t o p + + 2 .0 th e o re tic a l c a lc u la tio n p e r­

fo rm ed a t n e x t-to -n e x t-to lead in g o rd e r (N N L O ) in Q C D a n d includ es re s u m m a tio n o f n ex t- to -n e x t-to lead in g lo g a rith m ic (N N L L ) soft g lu o n te rm s [41- 46]. A second t t sam p le is g en ­ e r a te d usin g fully m a tc h e d N L O p re d ic tio n s w ith m assiv e b -q uarks [47] w ith in th e S h e r p a w ith O p e n L o o p s fram ew o rk [4 8 , 49] h e n c e fo rth re ferred to as S h e r p a + O p e n L o o p s . T h e S h e r p a + O p e n L o o p s N L O sam p le is g e n e ra te d follow ing th e fo ur-flav o u r schem e u sing th e S h e r p a 2.0 p re-release a n d th e C T 1 0 N L O P D F set. T h e re n o rm a lisa tio n scale is set to P r = r u , jb b E j /4, w h ere E T;i is th e tra n s v e rs e en e rg y o f p a r to n i, a n d th e fa c to risa tio n a n d re su m m a tio n scales a re b o th set to ( E T ,t + E t ,j)/2 .

T h e p re d ic tio n from S h e r p a + O p e n L o o p s is e x p e c te d to m o del th e tt+ b b c o n trib u tio n m o re a c c u ra te ly th a n P o w H E g + P Y T H iA , since th e la t t e r M C p ro d u c es t t + bb exclusively v ia th e p a r to n show er. T h e S h e r p a + O p e n L o o p s sam p le is n o t p assed th ro u g h full d e te c ­ t o r sim u la tio n . T h u s, t t + je ts ev e n ts from P o w H E g + P Y T H iA are ca te g o rise d in to th re e n o n -o v e rlap p in g sam ples, t t + bb, t t + cc, a n d t t + lig h t-je ts, h e re a fte r called t t + light, usin g a lab ellin g b ase d o n a n a lg o rith m t h a t m a tc h e s h a d ro n s to p a rtic le je ts . T h e n , t t + bb ev en ts from P o w H E g + P y t h i a a re rew eig h ted to re p ro d u c e th e S h e r p a + O p e n L o o p s N L O t t + bb p re d ic tio n . T h e re w eig h tin g is d o n e a t g e n e ra to r level usin g a fin er c a te g o ri­

sa tio n to d istin g u is h ev e n ts w h ere one p a rtic le j e t is m a tc h e d to tw o b-h a d ro n s, o r w here o n ly one b-h a d ro n is m a tc h e d . T h e rew eig h tin g is a p p lie d u sin g several k in e m a tic v aria b les such as th e to p -q u a r k p T , th e t t sy ste m p T , an d , w h ere th is ca n b e defined, A R a n d p T of th e d ije t sy ste m n o t o rig in a tin g from th e to p -q u a rk d ecay [16].

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U nlike t t + bb, no fully m a tc h e d N L O p re d ic tio n s ex ist for t t + c i a n d t t + ligh t events.

A d e d ic a te d re w eig h tin g is th e re fo re ap p lie d to th e to p -q u a r k p T s p e c tra as well as to th e p T sp e c tr a of th e t t sy stem of t t + light a n d t t + c i ev e n ts in P o w h e g + P y t h i a , b ase d o n th e ra tio of d a t a to sim u la tio n of th e m e a su re d d iffe ren tial cross sectio n s a t a /s = 7 TeV [50].

N o such rew eig h tin g is ap p lie d to th e ttt + btb sam ple, w hich is a lre a d y c o rre c te d to m a tc h th e b e s t available th e o ry c a lc u la tio n .

S am ples of sin g le -to p -q u a rk ev e n ts p ro d u c e d in th e s- an d W t-c h a n n e ls a re g e n e ra te d w ith Po w h e g-b o x 2.0 u sin g th e C T 1 0 N L O P D F set. T h e sam p les are in terfa ced to Py t h ia 6.425 w ith th e C T E Q 6 L 1 set of p a r to n d is trib u tio n fu n c tio n s an d P eru g ia2 0 1 1 C u n d e rly in g -e v e n t tu n e . T h e t-c h a n n e l p ro d u c tio n m o d e is g e n e ra te d w ith A c E r M C [51]

in terfa ced to Py t h ia 6.425 w ith th e C T E Q 6 L 1 P D F set an d th e P eru g ia2 0 1 1 C u n d erly in g - ev en t tu n e . O v e rlap s b etw e en th e t t a n d W t final s ta te s are rem oved [52]. T h e sing le-to p - q u a rk sam ples a re n o rm alised to th e a p p ro x im a te N N L O th e o re tic a l cross sectio n s [53, 54]

usin g th e M S T W 2 0 0 8 N N L O P D F set [55, 56].

T h e sam p les of t t V (V = W, Z ) ev en ts a re g e n e ra te d w ith th e M A d G rA p H v 5 LO g en ­ e r a to r [57] a n d th e C T E Q 6 L 1 P D F set. Py t h ia 6.425 w ith th e A U E T 2 B tu n e is used to g e n e ra te th e p a r to n show er. T h e t t V sam p les a re n o rm alised to N L O cro ss-sectio n s [58 , 59].

F inally, ev en t sam p les for single to p q u a rk p lu s H iggs b o so n p ro d u c tio n , tH q b an d t H W , a re g e n e ra te d . T h e cross sectio n s a re c o m p u te d u sin g th e M G 5_aM C @ N L O g en ­ e r a to r [60] a t N L O in Q C D . F or tHqb, sam p les a re g e n e ra te d w ith M A d G rA p H in th e fo ur-flav o u r schem e an d y F = y R = 75 G eV th e n show ered w ith P y t h i a 8.1 w ith th e C T E Q 6 L 1 P D F a n d th e AU2 u n d e rly in g -e v e n t tu n e . F o r tH W , c o m p u te d w ith th e five- flavour schem e, d y n a m ic y F a n d y R scales a re used a n d ev en ts are g e n e ra te d a t N L O w ith M G 5 _ A M C @ N L O + H E rw iG + + [6 1 , 62]. T h ese tw o processes to g e th e r are re ferred to as t H .

A su m m a ry of th e cro ss-sectio n values a n d th e ir u n c e rta in tie s for th e sign al as well as for th e M C sim u la te d b a c k g ro u n d p rocesses is given in ta b le 1.

5.3 C om m on tre a tm en t o f M C sam p les

All sam p les u sin g H e w i g are also in terfa ced to Jim m y v4.31 [63] to s im u la te th e u n ­ d e rly in g event. W ith th e ex c e p tio n of SH ErpA , all M C sam p les use P h o t o s 2 .1 5 [64]

to sim u la te p h o to n ra d ia tio n a n d T a u o l a 1 .2 0 [65] to sim u la te t decays. T h e sam p les a re th e n p ro cessed th ro u g h a s im u la tio n [66] of th e d e te c to r g e o m e try a n d resp o n se usin g G E A nT 4 [67]. T h e sin g le -to p -q u a rk sam p le p ro d u c e d in th e t-c h a n n e l is sim u la te d w ith a p a ra m e te ris e d c a lo rim e te r re sp o n se [68].

All sim u la te d ev e n ts are p ro cessed th ro u g h th e sam e re c o n s tru c tio n so ftw are as th e d a ta . S im u lated ev e n ts a re c o rre c te d so t h a t th e le p to n an d j e t id en tific a tio n efficiencies, en e rg y scales a n d en e rg y re so lu tio n s m a tc h th o se in d a ta .

W h e n selec tin g b ase d on th e o u tp u t value o f th e b-tag ging alg o rith m , th e n u m b e r of selected sim u la te d ev e n ts is sig n ifican tly red u ced , lead in g to larg e s ta tis tic a l flu c tu a tio n s in th e re su ltin g d is trib u tio n s for sam p les w ith a h ig h b -tag m u ltip licity . T h erefo re, ra th e r th a n ta g g in g th e je ts ind iv id u ally , th e n o rm a lisa tio n a n d th e sh a p e of th e s e d is trib u tio n s a re p re d ic te d by c a lc u la tin g th e p ro b a b ility t h a t a j e t w ith a given flavour, p T , a n d n is

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

P ro ce ss a [pb]

t t H 0.129-0.016

t t 253+15

Single to p W t-c h a n n e l 22.4 ± 1.5 Single to p t-c h a n n e l 87.7+1.9 Single to p s-c h an n el 5.61 ± 0.22

t t + W 0.232 ± 0.070

t t + Z 0.205 ± 0.061

tH q b 0 01 72+0.0012 ° . °1 7 2_0.0011 W t H 0 0047+0.0010_{0 .0047} _0.0009

T a b le 1. P roduction cross sections for signal t t H , at m H = 125 GeV, and various sim ulated back­

ground processes. The quoted errors arise from variations of the renorm alisation and factorisation scales and uncertainties in the parton distribution functions.

b-tag ged [69]. T h e m e th o d is v a lid a te d by v erifyin g t h a t th e p re d ic tio n s re p ro d u c e th e n o rm a lisa tio n a n d sh a p e o b ta in e d for a given w orking p o in t of th e b -tagg in g a lg o rith m . T h e m e th o d is ap p lied to all sim u la te d signal a n d b a c k g ro u n d sam ples.

5.4 M u ltijet b ackground e stim a tio n u sin g data: th e T R F^{m j} m eth o d

A d a ta -d riv e n tec h n iq u e , th e ta g r a te fu n c tio n for m u ltije t ev e n ts ( T R F^{m j}) m e th o d , is used to e s tim a te th e m u ltije t b ac k g ro u n d . A fte r m e a su rin g e MJ, th e p ro b a b ility of b -tag ging a th ir d j e t in a sam p le o f ev e n ts w ith a t least tw o b-tagg ed je ts , th e T R Fm j m e th o d uses e MJ to e x tra p o la te th e m u ltije t b a c k g ro u n d from th e regions w ith low er b -tag m u ltip lic ity to th e sea rch regions w ith h ig h er b -tag m u ltip lic ity b u t o th e rw ise id e n tic a l ev en t selection.

In th e first step , th e b -tagging r a te is m easu red in d a t a sam p les selected w ith variou s sin g le-jet trig g ers, w hich a re en ric h ed in m u ltije t ev e n ts a n d hav e lim ited ( ^10%) o v erlap w ith th e search region. T h e ev e n ts in th is T R F m j e x tra c tio n regio n are re q u ire d to have a t least th re e je ts w ith p T > 25 G eV a n d |n| < 2.5, w ith a t le a st tw o b-tagged je ts . E x c lu d in g th e tw o je ts w ith th e h ig h est b -tagg in g w eight in th e ev en t, e MJ is d efined as th e r a te of b-tagging an y o th e r je t in th e ev en t. I t is p a ra m e te ris e d as a fu n c tio n of th e je t p T a n d n, a n d also of th e averag e A R b etw e en th is je t a n d th e tw o je ts in th e event w ith h ig h est b-tagging w eight, ( A R j , hMV1)). T h e p T a n d n d e p e n d e n c e o f e MJ reflects th e co rre sp o n d in g se n sitiv ity o f th e b-tag ging efficiency to th e s e v aria b les. In m u ltije t events, th e A R d e p e n d e n c e o f e MJ is c o rre la te d w ith th e m u lti-b -je t p ro d u c tio n m ech an ism . T h is affects e MJ, show n in figure 1, w hich d ecreases by u p to a fa c to r tw o as A R in creases for fixed p T a n d n.

In th e search region th e T R F m j m e th o d s ta r ts from th e d a t a sam p le w ith e x a c tly tw o b-tag ged je ts s u b tra c tin g th e c o n trib u tio n s from all o th e r b a c k g ro u n d s o b ta in e d from M C sim u la tio n . M u ltije t b a c k g ro u n d sam p les c o n ta in in g m je ts (m > 6), o u t of w hich n are

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⁷

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5

“ 0 .0 8

0 .0 6

0 .0 4

0 .0 2

0 2 5 9 0 0 2 5 9 0 0 2 5 9 0 0 2 5 9 0 0 2 5 9 0 0 2 5 9 0 0 2 5 9 0 0 2 5 9 0 0 2 5 9 0 0 2 5 9 0 0 2 5 9 0 0 2 5 9 0 0

PT [GeV]

F ig u r e 1. Dependence of eMJ on the je t transverse m om entum p T, in regions of je t pseudorapidity n and average A R between this je t and the two jets in the event w ith highest 6-tagging weight, (AR(j hMVi)}. The p T bin boundaries are 25 (lowest), 40, 55, 70, 100, 200, 400, 600, 900 GeV (highest), chosen such as to have uniform num ber of events across bins of ( A R j , hMV1)}.

b -tagged (n > 3) are th e n c o n s tru c te d , u sin g a n ev en t w eight w ( m j, n b ), w hich is c a lc u la te d from £Mj a n a lo g o u sly to th e m e th o d d e sc rib e d in ref. [69], a c c o u n tin g for th e fa ct t h a t th e s ta r tin g sam p le c o n ta in s tw o 6-ta g g e d je ts . In each m u ltije t ev en t e m u la te d usin g T R F MJ by m ean s of e MJ, (m — 2) je ts n o t o rig in ally 6-ta g g e d c a n b e used for th e e m u la tio n of th e p ro p e rtie s of a d d itio n a l b-tagged je ts . T h is p ro c e d u re allow s to e m u la te o b serv ab les t h a t d e p e n d on th e n u m b e r of b-tagged je ts.

5.5 V alid a tion o f th e T R F^{m j} m eth o d in d a ta and sim u la tio n

V a lid a tio n of th e T R F MJ m e th o d is p erfo rm ed by a ‘closu re t e s t ’, s e p a ra te ly in d a t a an d sim u la tio n . T h is is p erfo rm ed u sin g th e sam e d a t a sam p les t h a t w ere em ployed to e s tim a te e MJ. In th e se low je t m u ltip lic ity sam ples, th e T R F MJ m e th o d , w hich is a p p lie d to th e ev e n ts w ith e x a c tly tw o 6-ta g g e d je ts , is u sed to p re d ic t d is trib u tio n s in ev e n ts w ith a t le a st th re e 6-ta g g e d je ts . U sin g e MJ d eriv e d in d e p e n d e n tly in d a t a a n d sim u la tio n , th e p re d ic te d d is trib u tio n s a re c o m p a re d to th o s e re su ltin g w h en d ire c tly a p p ly in g 6-tag g in g . T h is is d o n e for a n u m b e r of v ariab les, such as 6-ta g g e d je t p T , a n g u la r d is ta n c e b etw een 6-ta g g e d je ts , a n d ev en t sh ap e s. As a n ex a m p le, for ev en ts w ith a t le a st th re e je ts a n d a t le a st th re e 6-ta g g e d je ts (> 3 j, > 3 b ), figure 2 show s th e clo su re te s t in d a t a for th e th ird - le a d in g -je t p T , H T (th e sc a la r sum o f th e p T of all je ts ), a n d C e n tra lity Mass (defined as H T d iv id ed by th e in v a ria n t m ass o f th e je ts ). F ig u re 3 show s th e re su lts of th e clo sure te s t in sim u la te d m u ltije t ev e n ts for d is trib u tio n s of th e le a d in g -je t pT, th e m in im u m m ass of all je t p a irs in th e ev en t (m min), a n d th e th ird -le a d in g 6-ta g g e d j e t p T . T h e d efin itio n s of th e se v aria b les c a n b e fo u n d in ta b le 3 . In b o th d a t a a n d s im u la te d m u ltije t ev e n ts w ith a t le a st th re e 6-ta g g e d je ts , th e p re d ic te d a n d o b serv ed n u m b e r of ev en ts agree w ith in 5%. In ev e n ts w ith a h ig h er 6-ta g g e d je t m u ltip lic ity th e n u m b e rs agree w ith in th e larg e s ta tis tic a l u n c e rta in ty . F o r th is re a so n th e s y s te m a tic u n c e rta in tie s re la te d to th e T R F MJ m e th o d a re n o t e s tim a te d in th e v a lid a tio n regions.

— A T L A S 2 0 .3 fb -1 Vs = 8 T e V

< A R(jhMV1)>: [0 0 " 1 9 ] 2 L < A R(jhMV1)>: [1 .9 - 2 .5] ^ <A R (jhMV1)>: [2 ^ - 5 .0] —

— |n|: [0 .0 -0 .5 ] ; [0 .5 -1 .0 ] ; [1 .0 -1 .5 ] ; [1 .5 -2 .5 ] | |n|: [0 .0 -0 .5 ] ; [0 .5 -1 .0 ] ; [1 .0 -1 .5 ] ; [1 .5 -2 .5 ] |n|: [0 .0 -0 .5 ] ; [0 .5 -1 .0 ] ; [1 .0 -1 .5 ] ; [ 1 . 5 - 2 .5 ] -

_ _{4 4} ¹ _{1 AA} ¹ ₁ ¹ ₁ ^I _I ¹ ₁ ¹₁

_ + ^{1 , 1} ♦ ^{1 ■ ♦ ♦ ■}

—^{A T 1 1 ■ i 1 1 1 1}

1 1 4- ' + ' a . -4 1 .1+ + , 1

. f 'J* V h i : ♦ + <

!■ ' T ■*- + i**- +

■ i i i ■ }■ i T

■ i i j i i i

— i i i i i i

+ V -f +

4-1

‘i i i i i hjt-

1

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

Figure 2. Comparison of the shapes predicted by the T R Fmj m ethod (red histogram s) and direct b-tagging (black circles) in d a ta events w ith at least three jets and at least three b-tagged jets for (a ) the third-leading b-tagged je t p T, (b) H T, and (c) CentralityMass. The definitions of the variables are listed in table 3. Events were selected with various single-jet triggers. The T R Fmj prediction is normalised to the same num ber of events as the data. The uncertainty band for the T R Fmj

predictions shown in the ratio plot represents statistical uncertainties only.

Figure 3. Comparison of the shapes predicted for the T R Fmj m ethod (red histogram s) and direct b-tagging (black circles) in P y t h i a 8.1 m ultijet events with at least three jets and at least three b-tagged jets for (a) leading-jet p t, (b) m mjin and (c) the third-leading b-tagged je t p t in the event.

The definitions of the variables are listed in table 3. Distributions are normalised to the same area. The uncertainty band for the T R Fmj predictions shown in the ratio plot represents statistical uncertainties only.

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6 M ultijet trigger efficiency

N o t all je ts are re c o n s tru c te d a t th e trig g e r level, m a in ly d u e to th e Level-1 slidin g w indow alg o rith m a n d th e Level-1 re so lu tio n [70]. T h e m u ltije t trig g e r efficiency w ith re sp e c t to th e offline selectio n is d eriv e d in te rm s of th e efficiency for a single je t to be asso c ia te d w ith a c o m p le te j e t trig g e r ch ain , i.e., a co m p lete sequ ence o f je ts re c o n s tru c te d a t Level-1, Level-2 a n d E F sa tisfy in g th e re q u ire m e n ts d esc rib ed in sec tio n 4 . T h is sin g le-jet trig g e r efficiency, etrlg, is e v a lu a te d in in terv a ls of offline re c o n s tru c te d p T a n d n

/ \ _ N trlg(pT ,n ) ,p -i \

e trlg (p T ,n )= N ( p T ,n ) , ( )

w h ere N trlg(pT ,n ) is th e n u m b e r o f je ts m a tc h e d w ith a trig g e r ch a in a n d N ( p T ,n ) is th e t o ta l n u m b e r of je ts w ith in a given offline re c o n s tru c te d p t a n d n in terv a l. F ig u re 4 shows t h a t for larg e je t p T , etrlg reach es a p la te a u close to unity.

F o r b o th d a t a a n d sim u la tio n , etrlg(pT , n) is deriv ed u sin g ev e n ts trig g e re d by a single­

je t trig g e r w ith a p t th re s h o ld of 110 G eV , a n d o nly th e offline je ts w hich are in th e h em isp h ere o p p o site to th e trig g e r j e t a re used . To avoid a d d itio n a l trig g e r bias, ev en ts a re d isc a rd e d if m ore th a n one je t w ith p T > 110 G eV is re c o n s tru c te d . T h e ra tio of etrlga (pT ,n ) to eJMg,dljet, w h ere th e la t t e r is e s tim a te d in s im u la te d d ije t even ts, is referred to as S F trlg(pT ,n ) . In th e an aly sis, for each M C sam p le a co n sid ered , th e final n u m b e r o f ev e n ts p assin g th e m u ltije t trig g e r is e s tim a te d by w e ig h tin g each je t by th e p ro d u c t of etrlg’a (pT , n) a n d S F trlg(pT , n). T h e p a ra m e te rs etrlg(pT ,n ) a n d S F trlg(pT ,n ) are e s tim a te d for je t p T u p to 100 G eV . F ig u re 4 show s th e p T d e p e n d e n c e of edr£lga (pT , n), ej^lg,ttH (pT , n), etrlg’dljet(pT , n) a n d S F trlg(pT ,n ) for je ts w ith in |n| < 2.5, to g e th e r w ith th e u n c e rta in ­ tie s from th e difference b etw e en ejglg,ttH (pT ,n ) a n d ejglg,dljet(pT , n), w hich is ta k e n as th e sy s te m a tic u n c e rta in ty o f th e m e th o d .

7 Event classification

Six in d e p e n d e n t an aly sis regio ns are co n sid ered for th e fit u sed in th e an alysis: tw o c o n tro l regions (6j, 3b), (6j, > 4 b ) a n d four signal regions (7j, 3b ), (7j, > 4 b ), ( >8j, 3b) a n d ( >8j,

> 4 b ). In a d d itio n , th e th re e regions w ith e x a c tly tw o 6-ta g g e d je ts , (6j, 2b), (7j, 2b) an d ( >8j, 2b ), a re used to p re d ic t th e m u ltije t c o n trib u tio n to h ig h er 6-ta g g in g m u ltip lic ity regions, u sin g th e T R F MJ m e th o d , as d e sc rib e d above. T h e ev en t yields in th e differen t an a ly sis regions p rio r to th e fit a re su m m a rise d in ta b le 2.

T h e regions are a n a ly se d s e p a ra te ly a n d com b in ed s ta tis tic a lly to m ax im ise th e overall sen sitiv ity . T h e m o st sensitiv e regions, ( >8j, 3b) a n d ( >8j, > 4 b ), a re e x p e c te d to c o n trib u te m o re th a n 50% of th e to ta l significance.

8 Analysis m ethod

T h e T o o lk it for M u ltiv a ria te D a ta A n aly sis (T M V A ) [71] is used to t r a in a B D T to s e p a ra te th e t t H sig n al from th e b ac k g ro u n d . A d e d ic a te d B D T is defined a n d o p tim ise d in each of

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

F ig u r e 4. Single-jet trigger efficiencies, etrig, (top) for data, sim ulated dijet events, and t t H events, as a function of je t p T for jets w ith |n| < 2.5; (bottom ) SFtrig (pT,n ) = £triga(PT, n ) / etri'g’dijet(PT, n).

The uncertainty on SFtrig, shown as the green shaded area, is estim ated from the difference between the efficiencies in dijet and t t H sim ulated events in the denom inator of SFtrig.

6j, 3b 6j, > 4 b 7j, 3b 7j, > 4 b > 8 j, 3b > 8 j, > 4 b M u ltijet 16380 ± 130 1112 ± 33 12530 ± 110 1123 ± 34 10670 ± 100 1324 ± 36

ii+ lig h t 1530 ± 390 48 ± 18 1370 ± 430 45 ± 18 1200 ± 520 40 ± 23

tt + cc 280 ± 180 17 ± 12 390 ± 240 21 ± 15 560 ± 350 48 ± 33

tt + bb 330 ± 180 44 ± 26 490 ± 270 87 ± 51 760 ± 450 190 ± 110

ti + V 14.2 ± 6.3 1.8 ± 1.5 22.0 ± 9.0 3.5 ± 2.3 40 ± 15 8.0 ± 4.2

Single to p 168 ± 63 6.0 ± 3.7 139 ± 55 8.3 ± 4.6 110 ± 49 10.6 ± 5.9

T o tal background 18700 ± 480 1229 ± 48 14940 ± 580 1288 ± 66 13330 ± 780 1620 ± 130 t i H [ m j = 125 GeV) 14.3 ± 4.6 3.3 ± 2.1 23.7 ± 6.4 7.2 ± 3.3 48 ± 11 16.8 ± 6.1

D a ta events 18508 1545 14741 1402 13131 1587

S / B < ^{0.001 0.003 0.002 0.006 0.004 0.010}

s/Vb 0.10 0.095 0.194 0.20 0.415 0.417

T a b le 2. Event yields from sim ulated backgrounds and the signal as well as d a ta in each of the analysis regions prior to the fit (pre-fit). The quoted uncertainties are the sum in quadrature of the statistical and system atic uncertainties in the yields for all samples bu t the m ultijet background.

The m ultijet norm alisation and its system atic uncertainty are determ ined by the fit, so only its statistical uncertainty is quoted here. Since the num bers are rounded, the sum of all contributions m ay not equal th e to tal value. The signal-to-background ratio, S /B , and the significance, S /\/B , are also given. The t H background is not shown as it am ounts to fewer th an 1.5 events in each region.

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th e six an a ly sis regions. T h e v aria b les e n te rin g th e B D T a n d th e ir d efin itio n s a re liste d in ta b le 3 .

T h e in p u t v aria b les in clu d e e v e n t-sh a p e v aria b les such as C e n tra lity Mass a n d ap la n a rity , g lobal ev en t v ariab les, such as S T (th e m o d u lu s of th e v e c to r sum of th e j e t p T ), HT 5 (th e sc a la r sum of th e je t p T s ta r tin g from th e fifth je t in p T o rd e r), m “ m (th e sm allest in v a ria n t m ass of all d ije t co m b in a tio n s), a n d th e m in im u m A R b etw e en je ts . T h e p T of th e so ftest je t in th e ev en t is th e only in d iv id u a l k in e m a tic v aria b le t h a t e n te rs th e B D T d irectly.

O th e r v aria b les a re c a lc u la te d from p a irs o f o b je c ts: A R ( b , b)pmax (th e A R b etw e en th e tw o b-tagged je ts w ith h ig h est v e c to r sum p T ), m ^ R(b,b) (th e in v a ria n t m ass of th e tw o b-tag ged je ts w ith th e sm allest A R ), ( ET 1 + E T2) / ^ E ; T ts (th e su m of th e tra n sv e rse energies of th e tw o lead in g je ts d iv id ed by th e su m of th e tra n s v e rs e energies o f all je ts ), m2 jets (th e m ass of th e d ije t p air, w hich, w h e n co m b in ed w ith an y b-tagged je t, m ax im ises th e m a g n itu d e of th e v e c to r sum of th e p T of th e th re e -je t sy stem ) a n d m2b-jets (th e in v a ria n t m ass o f th e tw o b-tagged je ts w hich a re selected by re q u irin g t h a t th e in v a ria n t m ass o f all th e re m a in in g je ts is m a x im a l). T w o v aria b les a re c a lc u la te d as th e in v a ria n t m ass of th re e je ts : m top,i is c o m p u te d from th e th re e je ts w hose in v a ria n t m ass is n e a re st to th e to p q u a rk m ass, ta k in g in to a c c o u n t th e je t en e rg y re so lu tio n s; th e mtop,2 c a lc u la tio n uses th e sam e a lg o rith m b u t ex cludes th e je ts w hich e n te r m top>1. F inally, a log-likelihood r a tio v aria b le, A, is used; it is re la te d to th e p ro b a b ility of an ev en t to be a sig n al c a n d id a te , c o m p a re d to th e p ro b a b ility of b ein g a b a c k g ro u n d c a n d id a te .

T h e A v aria b le is th e sum of th e lo g a rith m s of ra tio s o f re la tiv e p ro b a b ility d en sities for W boson, to p q u a rk a n d H iggs b o so n reso n an ces to b e re c o n s tru c te d in th e even t. F o r a

P ' / ' ') given re so n an ce X d ec ay in g to tw o je ts , th e A co m p o n e n t is b u ilt as A x ( m 77) = ln B ^s /mj j ) P^{b k g}\mjj ) w ith in a m ass w indow wx = ± 3 0 G eV a ro u n d th e given p a rtic le m ass:

( s ■ G (m j j \ m x , ° x ) , for \m j j - m x \ < w x , .

P sig(m j j ) = < , (8.1)

( 1 — s, for \m jj — m x \ > w x .

\ b ■ R e c t ( m x , w x ), for \m jj — m x \ < w x ,

p bkg(m j j ) = < (8 .2)

( 1 — b, for \ m jj — m x \ > wx .

H ere s a n d b a re th e p ro b a b ilitie s to find a je t p a ir w ith an in v a ria n t m ass w ith in ± w x o f m x . T h e y a re c a lc u la te d from th e sig nal sim u la tio n a n d from th e m u ltije t b a c k g ro u n d respectively. T h e signal m ass d is trib u tio n is m o d elled w ith a G a u ssia n G ( m j j \ m x , a x ), w hile th e b a c k g ro u n d is m odelled w ith a u n ifo rm d is trib u tio n R e c t( m x , w x ) b etw e en m x — w x a n d m x + wx . B o th fu n c tio n s P sig( m j j ) a n d P bkg( m j j ) a re n o rm alised to un ity. F o r th e to p q u a rk re so n an ce th e th re e -p a rtic le m ass, m jjb , is u sed. T h e w id th of th e G a u ssia n is set to a x = 18 G eV for all resonances; th is v alu e c o rre sp o n d s to th e e x p e c te d e x p e rim e n ta l w id th of a H iggs b o so n w ith no c o m b in a to ric b a c k g ro u n d .

T h e ex p ressio n for th e co m p lete ev en t A is:

A (m j j , m jjb , m bb) — A W ( m j j \ m W , & x ) + -^op^T,,;.;'^ m jjb \m top, ^ x ) . (8.3) + Ah(pT,bb, m b b \m u , o x ).

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V ariable D efinition B D T ra n k

6j, 3b 6j, > 4b 7j, 3b 7 j ,> 4b > 8j, 3b > 8 j ,> 4b

C 'entralityMass S calar sum of th e je t p x divided by th e in v arian t m ass of th e je ts 1 1 1 1 9 6

A p ian a rity l.SAp, w here Ap is th e second eigenvalue of th e m o m en tu m

ten s o r b u ilt w ith all je ts

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¹¹

- -

⁶

-

Ax T h e m o d u lu s of th e vector sum of je t px 2 2 2 4 2 2

t?T5 S calar sum of j e t p x s ta rtin g from th e fifth je t 8 — — ⁷ — —

... "ii i

mn Sm allest in v arian t m ass of any co m b in atio n of two je ts 9 — 6 10 11 12

A Amin M inim um A R betw een tw o je ts 6 5 9 — 8 4

softest iet

PT p x of th e softest je t — ^{6 10} — — ¹⁰

A A (M )p" ax A R betw een tw o fc-tagged je ts w ith th e larg est vector sum p x 11 — ^{7 5 5 3} AR(b,b)™°

mbb In v a ria n t m ass of th e c o m b in atio n of two fc-tagged je ts w ith th e sm allest A R 3 3 8 9 3 9

ib p 1 + t t p 2

Y,

j e t s

Sum of th e f?x of th e tw o je ts w ith leading f?x divided by th e sum of th e f?x of all je ts T h e m ass of th e d ije t p air, which, w hen com bined w ith any fc-tagged je t,

m axim ises th e m ag n itu d e of th e vector sum of th e p x of th e tlire e-jet system

5

10

8 4 2

8

7 5

b - j e t s

T h e in v arian t m ass of th e tw o fc-tagged je ts w hich are selected b y requiring

t h a t th e in v arian t m ass of all th e rem ain in g je ts is m axim al ¹² 7

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⁶

-

⁸

nrtop.l M ass of th e re co n stru c te d to p q u a rk 13 10 — — 4 11

nrtop,2 M ass of th e re co n stru c te d to p q u a rk c alcu lated from th e je ts n o t en terin g m top,i 7 9 5 — 10 7

A T h e lo g arith m of th e ra tio of event p ro b ab ilities u n d e r th e signal and 4 4 3 3 1 1

b a ckground hypo th eses

T a b le 3. List of variables used in the BDT in the six analysis regions. The num bers indicate the ranking of the corresponding variables, ordered by decreasing discrim inating power. Variables not used in the BDT of a specific region are m arked by a dash.

JH EP

05 (2 01

6)

16

0

T h e th re e te rm s refer to W, to p , a n d H iggs re so n an ces resp ectively . F or th e to p q u a rk a n d H iggs b o so n reso n an ce s th e m asses, m jjb a n d m bb, as well as th e p T , d efined as th e m a g n itu d e of th e v e c to r sum of th e p T of th e je ts u sed to re c o n s tru c t th e to p q u a rk , p T ,jjb, a n d to re c o n s tru c t th e H iggs boson, p T ,bb, are used. T h e value o f A is c a lc u la te d for all p o ssib le j e t c o m b in a tio n s a n d th e m ax im u m A of th e ev en t is chosen.

T h e v aria b les e n te rin g th e B D T a re selected a n d ra n k e d ac co rd in g to th e ir s e p a ra tio n pow er w ith an ite ra tiv e p ro c e d u re , w hich sto p s w h en a d d in g m o re v aria b les d oes n o t signif­

ic a n tly im prove th e se p a ra tio n b etw e en signal a n d b a c k g ro u n d . T h e cu t-o ff c o rre sp o n d s to th e p o in t w h en a d d in g a v aria b le increases th e significance, defined as y ^ i S / B i2 w here S i a n d B i are th e e x p e c te d signal a n d b a c k g ro u n d yield s in th e ith b in of th e B D T d is­

c rim in a n t, by less th a n 1%.

Signal a n d b a c k g ro u n d sam ples are classified as d esc rib ed in sec tio n 7 , a n d th e n each s u b ­ s am p le is fu r th e r su b d iv id e d ra n d o m ly in to tw o su b sam p les of eq u a l size for tra in in g an d fo r te stin g .

T h e ra n k in g of th e in p u t v aria b les in te rm s of s e p a ra tio n pow er for each an aly sis region is show n in ta b le 3 . T h e d is trib u tio n s of th e B D T o u tp u ts for sim u la te d signal a n d b a c k g ro u n d ev e n ts are show n in figure 5 for each an a ly sis region. T h e figure show s a b e tt e r s e p a ra tio n b etw e en sig n al a n d b ac k g ro u n d for low je t m u ltip lic itie s th a n for h ig h je t m u ltip licitie s. T h is is ex p lain e d by th e n u m b e r o f p o ssib le je t p e rm u ta tio n s . T h e n u m b e r of je t p e rm u ta tio n s increases givin g th e b ac k g ro u n d m o re co n fig u ratio n s to m im ic th e signal.

9 System atic uncertainties

T h e sources of sy s te m a tic u n c e rta in ty co n sid ered in th is an a ly sis c a n be g ro u p e d in to six m a in c a te g o ries as su m m a rise d in ta b le 4 . E a c h sy s te m a tic u n c e rta in ty is re p re se n te d by an in d e p e n d e n t p a ra m e te r, re ferred to as a n u isan ce p a ra m e te r, a n d is p a ra m e te ris e d w ith a G a u ssia n fu n c tio n for th e s h a p e u n c e rta in tie s a n d a lo g -n o rm al d is trib u tio n for th e n o rm a lisa tio n s [72]. T h e y a re c e n tre d a ro u n d zero a n d one, re sp ectiv ely , w ith a w id th t h a t c o rre sp o n d s to th e given u n c e rta in ty . T h e u n c e rta in tie s in th e in te g ra te d lum inosity, re c o n s tru c tio n of th e physics o b je c ts, a n d th e sig n al a n d b ac k g ro u n d M C m od els are tre a te d as in ref. [16]. T h e u n c e rta in tie s re la te d to th e j e t trig g e r as well as th o se re la te d to th e d a ta -d riv e n m e th o d to e s tim a te th e m u ltije t b a c k g ro u n d a re d iscu ssed below . In to ta l, 99 fit p a ra m e te rs are co n sid ered . T h e d e te r m in a tio n a n d tr e a tm e n t of th e sy ste m a tic u n c e rta in tie s are d e ta ile d in th is sectio n. T h e ir im p a c t o n th e fitte d sign al s tre n g th is s u m m a rise d in ta b le 8 in sec tio n 1 1.

T h e s y s te m a tic u n c e rta in ty in th e lu m in o sity for th e d a t a sam p le is 2.8% . I t is d eriv ed follow ing th e sam e m e th o d o lo g y as t h a t d e ta ile d in ref. [73]. T h e trig g e r u n c e rta in ty is d e te rm in e d from th e difference b etw e en etrig, e s tim a te d u sin g t t H a n d d ije t M C ev ents.

E a c h j e t in th e ev en t is w eigh ted acco rd in g to S F trig(pT , n), th e u n c e rta in ty o f w h ich is p ro p a g a te d to th e s h a p e a n d n o rm a lisa tio n o f th e B D T o u tp u t d is trib u tio n , as show n in figure 6(a).

T h e u n c e rta in tie s in physics o b je c ts a re re la te d to th e re c o n s tru c tio n a n d b-tag gin g o f je ts . T h e je t en e rg y re so lu tio n (J E R ) a n d th e je t en e rg y scale (JE S ) u n c e rta in tie s are

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S y ste m a tic u n c e rta in ty source T y p e N u m b e r of c o m p o n e n ts

L u m in o sity N 1

T rigger SN 1

P h y sic s Objects

J e t en e rg y scale SN 21

J e t v e rte x fra c tio n SN 1

J e t en e rg y re so lu tio n SN 1

6-ta g g in g efficiency SN 7

c-ta g g in g efficiency SN 4

L ig h t-je t ta g g in g efficiency SN 12

B a ck g ro u n d M C M odel

t t cross sec tio n N 1

t t m odelling: p T rew eig h tin g SN 9

t l m odelling: p a r to n show er SN 3

tl+ h e a v y -fla v o u r: n o rm a lis a tio n N 2

t i + c i : heavy -flav o u r rew eig h tin g SN 2

t i + c i : g e n e ra to r SN 4

t i +66: N L O S h ap e SN 8

t i V cross sectio n N 1

t l V m o d ellin g SN 1

Single to p cross sectio n N 1

D a ta d riven background

M u ltije t n o rm a lis a tio n N 6

M u ltije t T R Fm j p a ra m e te ris a tio n S 6

M u ltije t Ht c o rre c tio n S 1

M u ltije t S T c o rre c tio n S 1

Sig n a l M odel

t i f f scale SN 2

t i f f g e n e ra to r SN 1

t i f f h a d ro n is a tio n SN 1

t i f f p a r to n show er SN 1

T a b le 4. Sources of system atic uncertainty considered in the analysis grouped in six categories.

“N” denotes uncertainties affecting only th e norm alisation for the relevant processes and channels, whereas “S” denotes uncertainties which are considered to affect only the shape of normalised distributions. “SN” denotes uncertainties affecting bo th shape and norm alisation. Some sources of system atic uncertainty are split into several components. The num ber of com ponents is also reported.

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

(a) (b) (c)

(d) (e) (f)

F ig u r e 5. Response of the BDT algorithm for sim ulated signal [dashed red), tt+ je ts background [solid blue) and m ultijet background [dotted green) events in the (top) regions w ith 3 b-tags [(a) 6, (b) 7 and (c) > 8 jets) and in the (bottom ) regions with > 4 b-tags [(d) 6, (e) 7 and (f) > 8 jets).

The binning is the same as th a t used in the fit.

d eriv e d co m b in in g th e in fo rm a tio n from te s t-b e a m d a t a a n d sim u la tio n [25]. T h e J E S u n c e rta in tie s are sp lit in to 21 u n c o rre la te d c o m p o n e n ts. T h e la rg e st of th e se u n c e rta in tie s is d u e to th e je t flavour co m p o sitio n . T h e J V F u n c e rta in ty is d eriv e d from Z [ ^ ^- } + 1-je t ev en ts in d a ta a n d sim u la tio n by v ary in g th e n o m in al c u t valu e by 0.1 u p a n d dow n.

T h e u n c e rta in ty re la te d to th e b -tagg ing is m o delled w ith six in d e p e n d e n t p a ra m e te rs , w hile fo u r p a ra m e te rs m o d el th e c-ta g g in g u n c e rta in ty [26]. T h ese a re eigenvalues o b ta in e d by d ia g o n alisin g th e m a trix w hich p a ra m e te rise s th e ta g g in g efficiency as a fu n c tio n of p x , ta k in g in to ac c o u n t b in -to -b in c o rre la tio n s. T w elve p a ra m e te rs , w hich d e p e n d o n p x an d n, are used to p a ra m e te ris e th e lig h t-je t-ta g g in g s y s te m a tic u n c e rta in tie s [74]. T h e p e r-je t b -tag g in g u n c e rta in tie s are 3% -5% , a b o u t 10% for c-ta g g in g a n d 20% for ligh t je t tag g in g . A n a d d itio n a l u n c e rta in ty is assigned to th e b-tag ging efficiency for je ts w ith p x > 300 G eV , w hich lacks s ta tis tic s for a n a c c u ra te c a lib ra tio n from d a ta .

A com b in ed u n c e rta in ty of ± 6 .0 % is assign ed to th e t l + j e t s p ro d u c tio n cross sectio n, in clu d in g m o d ellin g c o m p o n e n ts d u e to th e value o f a s, th e P D F used , th e p ro cess en erg y scale, a n d th e to p q u a rk m ass. O th e r sy ste m a tic u n c e rta in tie s re la te d to t l + j e t s p ro d u c ­ tio n are d u e to th e m o d ellin g of p a r to n show ers a n d h a d ro n is a tio n .

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Figure 6. (a) Per event trigger scale factor SF^{t r ig} (black dots) versus the BDT ou tp u t of t t H events, shown with its corresponding system atic uncertainty (green band) for the (>8j, >4b) region. (b) Comparison of the BDT outp u t of the m ultijet background predicted w ith different sets of T R F . The nominal T R F^{M J} is represented by the red points. The b ottom panel shows th e ratios of the alternative T R F^{M J} predictions to the nominal set.

The systematic uncertainties arising from the reweighting procedure to improve tt background description by simulation (section 5.2), have been extensively studied in ref. [16]

and adopted in this analysis. The largest uncertainties in the tti background description arise from radiation modelling, the choice of generator to simulate tti production, the JES, JER, and flavour modelling. These systematic uncertainties are applied to the tt+light and tt + ci components. Two additional systematic uncertainties, the full difference between applying and not applying the reweightings of the tti system p

^T

and top quark p

^T

, are assigned to the tt + ci component.

Four additional systematic uncertainties in the tti + cci estimate are derived from the simultaneous variation of factorisation and renormalisation scales in

M a d g r a p h + P y t h i a .

For the tt

+ 66

background, three scale uncertainties are evaluated by varying the renormali­

sation and resummation scales. The shower recoil model uncertainty and two uncertainties due to the PDF choice in the

s h e r p a + O p e n L o o p s

NLO calculation are also taken into account.

The tt+ jets background is parameterised to allow a varying percentage of heavy flavours c and

6

in the additional jets not originating from the top quark decay prod­

ucts. An uncertainty of ±50% is assigned to the tt +

66

and tt + ci components of the tt+ jets cross section, which are treated as uncorrelated and are derived by comparing

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