Measurement of the production cross-section of a single top quark in association with a $\mathit{W}$ boson at 8 TeV with the ATLAS experiment

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 : October 14, 2015

R e v i s e d : December 7, 2015 A c c e p t e d : December 20, 2015 P u b l i s h e d : January 11, 2016

Measurement of the production cross-section of a single top quark in association with a W boson at 8 T e V with the A T L A S experiment

T h e A T L A S collaboration

E-m ail: atlas.publications@cern.ch

A b s t r a c t : T h e cro ss-sectio n for th e p ro d u c tio n of a single to p q u a rk in a sso c ia tio n w ith a W b o so n in p ro to n -p ro to n collisions a t yfs = 8 T eV is m easu red . T h e d a ta s e t c o rresp o n d s to an in te g ra te d lu m in o sity of 20.3 f b - 1 , co llected by th e A T L A S d e te c to r in 2012 a t th e L arg e H a d ro n C o llid er a t C E R N . E v e n ts c o n ta in in g tw o le p to n s a n d one c e n tra l b-jet are selected. T h e W t signal is s e p a ra te d from th e b a c k g ro u n d s u sin g b o o ste d decision tree s, each o f w hich com bines a n u m b e r o f d is c rim in a tin g v aria b les in to o ne classifier. P ro d u c tio n o f W t ev en ts is o b serv ed w ith a significance of 7.7a. T h e cro ss-sectio n is e x tra c te d in a profile likelihood fit to th e classifier o u tp u t d is trib u tio n s . T h e W t cro ss-sectio n , inclusive o f d ecay m odes, is m easu red to b e 2 3 .0 ± 1 .3 (s ta t.)+ 3 's (s y s t.)± 1 .1 (lu m i.) p b . T h e m easu red cro ss-sectio n is used to e x tra c t a value for th e C K M m a tr ix elem en t \Vtb\ of 1.01 ± 0.10 a n d a low er lim it of 0.80 a t th e 95% confid ence level. T h e cro ss-sectio n for th e p ro d u c tio n o f a to p q u a rk a n d a W b o so n is also m e a su re d in a fidu cial a c c e p ta n c e re q u irin g tw o le p to n s w ith p T > 2 5 G e V a n d \n\ < 2.5, one je t w ith p T > 2 0 G e V a n d \n\ < 2.5, an d

> 2 0 G e V , in clu d in g b o th W t a n d to p -q u a rk p a ir ev en ts as signal. T h e m easu red value of th e fiducial cro ss-sectio n is 0.85 ± 0 .0 1 (s ta t.) + o o 7 (sy s t.)± 0 .0 3 (lu m i.) pb.

Ke y w o r d s: H a d ro n -H a d ro n s c a tte rin g , T op physics

ArXiy ePr i n t: 1510.03752

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C o n te n ts

1 I n tr o d u c tio n 1

2 T h e A T L A S d e t e c t o r a n d o b je c t r e c o n s tr u c tio n 3

3 D a t a a n d s im u la te d s a m p le s 5

4 E v e n t s e le c tio n 7

5 A n a ly s is 8

6 S y s t e m a t ic u n c e r ta in t ie s 13

7 R e s u lts 18

7.1 M e a su re m e n t of th e inclusive cro ss-sectio n 18

7.2 C o n s tra in ts o n \ f LVVtb\ a n d \Vtb| 20

8 C r o s s -s e c tio n m e a s u r e m e n t in s id e a fid u cia l a c c e p ta n c e 21

8.1 F id u c ia l selectio n 22

8.2 S y ste m a tic u n c e rta in tie s 22

8.3 R e su lts 23

9 C o n c lu s io n 24

T h e A T L A S c o lla b o r a tio n 32

1 In tr o d u c tio n

T h e p ro d u c tio n of a single to p q u a r k a t th e L a rg e H a d ro n C o llid er (L H C ) p ro c e e d s v ia th e w eak in te ra c tio n in th e S ta n d a rd M odel (S M ). T h e th re e m a in m od es of single to p - q u a rk p ro d u c tio n are: t-ch a n n el, th e ex ch an g e of a W b oso n b etw e en a ligh t q u a rk an d a h ea v y q u a rk ; s-c h an n el, v ia a v irtu a l W boson; a n d W t , th e p ro d u c tio n o f a to p q u a rk in a sso c ia tio n w ith a W boso n . Single to p -q u a r k p ro d u c tio n d e p e n d s on th e to p -q u a rk co u p lin g to th e W boson, w hich is p a ra m e te ris e d by th e fo rm fa c to r f LV a n d th e C a b ib b o - K o b a y ash i-M ask aw a (C K M ) m a tr ix elem e n t Vtb [1- 3]. T h e cro ss-sectio n for each of th e th re e p ro d u c tio n m o d es is p ro p o rtio n a l to th e sq u a re o f \ f LVVtb\ [4 , 5]. P h y sic s b ey o n d th e SM c a n c o n trib u te to th e single to p -q u a rk final s ta te a n d m o d ify th e p ro d u c tio n cro ss­

sectio n s [6 , 7] as well as th e k in e m a tic d is trib u tio n s , for ex a m p le th ro u g h a re so n an ce t h a t d ecay s to W t [8 , 9].

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F ig u r e 1. Representative leading-order Feynm an diagram for the production and decay of a single top quark in association w ith a W boson.

T h e p ro d u c tio n of single to p q u a rk s h as b ee n o b serv ed a t th e T e v a tro n p ro to n - a n tip ro to n co llid er in th e t-c h a n n e l [10, 11] a n d s-c h a n n e l [12- 14], as well as th e ir com b i­

n a tio n [15- 17]. T h e W t p rocess h as a sm all e x p e c te d cro ss-sectio n a t th e T e v a tro n an d w as n o t o b served. T h e t-c h a n n e l m o d e h as b ee n o b served by b o th th e A TLA S [18, 19] an d C M S [2 0 , 21] c o lla b o ra tio n s a t th e L H C . T h e s -c h a n n e l m o d e h as n o t yet b ee n m easu red a t th e L H C b ec au se o f its sm all p ro d u c tio n cro ss-sectio n [22]. E v id e n c e for W t p ro d u c tio n w as re p o rte d by A T L A S [23] a n d C M S [24] in p ro to n -p ro to n (pp) collisions a t 7 TeV. T h e o b se rv a tio n of W t p ro d u c tio n in pp collisions a t 8 TeV h as b ee n re p o rte d by C M S [25].

P r o d u c tio n of W t ev en ts p ro c eed s v ia b -q u a rk -in d u ce d p a rto n ic ch a n n els such as gb ^ W t ^ W - W +b. A le a d in g -o rd e r (LO ) F e y n m a n d ia g ra m in th e 5 -flav o u r-n u m b er schem e (5F N S , c o n sid erin g th e q u a rk s u, d, s, c, a n d b in th e in itia l s ta te ) is show n in figure 1.

T h e p resen ce of o nly a single b-q u ark in th e final s ta te re p re se n ts a d is tin c tiv e fe a tu re w ith re sp e c t to th e W + W - bb final s ta te o f to p -q u a rk p a ir (tt) p ro d u c tio n . T h e W t final s ta te c o n ta in s an a d d itio n a l b-q u ark in h ig h e r-o rd e r Q u a n tu m C h ro m o d y n a m ic s (Q C D ) c o rre c tio n d ia g ra m s in th e 5FN S, as well as in th e le a d in g -o rd e r p rocess in th e 4-flavour- n u m b e r schem e (4F N S , co n sid erin g o n ly th e q u a rk s u , d, s, c in th e in itia l s ta te ), m ak in g it ch allen g in g to e x p e rim e n ta lly s e p a ra te W t p ro d u c tio n from t t p ro d u c tio n .

T h e th e o re tic a l p re d ic tio n for th e W t p ro d u c tio n cro ss-sectio n a t n e x t-to -le a d in g o rd e r (N L O ) w ith n e x t-to -n e x t-to -le a d in g lo g a rith m ic (N N L L ) soft g lu o n c o rre c tio n s is 22.37 ± 1.52 p b [26] a t a ce n tre-o f-m ass en e rg y of yfs = 8 TeV for a to p -q u a r k m ass of m t = 172.5 GeV [27]. In th is c a lc u la tio n , th e u n c e rta in ty o n th e th e o re tic a l cro ss-sectio n a c c o u n ts for th e v a ria tio n of th e re n o rm a lisa tio n a n d fa c to ris a tio n scale b etw e en m t /2 a n d 2 m t a n d for th e p a r to n d is trib u tio n fu n c tio n (P D F ) u n c e rta in tie s (u sing th e 90%

confidence level erro rs of th e M S T W 2 0 0 8 N N L O P D F set [28]). T h is cro ss-sectio n re p ­ re se n ts a b o u t 20% of th e t o ta l cro ss-sectio n for all single to p -q u a rk p ro d u c tio n m od es a t th e L H C . A second th e o re tic a l p re d ic tio n for th e W t p ro d u c tio n cro ss-sectio n is 18.8 ± 0.8 (scale) ± 1 .7 (P D F ) pb, c o m p u te d a t N L O w ith H a th o r v2.1 [2 9 , 30]. T h e P D F u n c e rta in tie s a re c a lc u la te d u sin g th e P D F 4 L H C p re sc rip tio n [31] w ith th re e d ifferen t P D F sets ( C T 1 0 , M S T W 2 0 0 8 n l o 6 8 c l [28] a n d N N P D F 2 .3 [32]). T h e re n o rm a lisa tio n an d fa c to ris a tio n scales are set to 65 GeV a n d th e b-q u ark from in itia l- s ta te ra d ia tio n is re q u ired to have a tra n s v e rs e m o m e n tu m of less th a n 60 GeV.

T h is p a p e r p re se n ts a m e a su re m e n t o f th e cro ss-sectio n for W t p ro d u c tio n in p p col­

lisions a t yfs = 8 TeV, b ase d on th e an a ly sis of 20.3 fb -1 of d a t a co llected by th e A TLA S

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d e te c to r in 2012. T h e m e a s u re m e n t is c a rrie d o u t in th e d ile p to n final s ta te show n in fig­

u re 1 w h ere each W b o so n decays to a n e le c tro n o r a m u o n a n d a n e u trin o (e v o r p v ). T h is a n a ly sis re q u ires tw o o p p o site -sig n h ig h -tra n sv e rse -m o m e n tu m (px ) le p to n s (ee, ep , p p ), m issing tra n s v e rs e m o m e n tu m (E ™ ss), a n d o ne h ig h -p x c e n tra l je t, w h ich is re q u ire d to c o n ta in a b -h a d ro n (b -jet). T h e m a in b a c k g ro u n d to th is s ig n a tu re is from t t p ro d u c tio n , w ith sm aller b a c k g ro u n d s co m in g from d ib o so n s ( W W , W Z , Z Z ), Z + je ts , a n d ev en ts w h ere one o r b o th le p to n s a re m isid en tified (fak e-le p to n events) o r n o n -p ro m p t. C o n tro l regions en ric h ed in tb a n d o th e r b a c k g ro u n d ev en ts a re also defined. E v e n ts in th e tb- en ric h ed regions fulfil th e sam e le p to n a n d m issin g tra n s v e rs e m o m e n tu m re q u ire m e n ts, a n d have e x a c tly tw o je ts , w ith one o r b o th o f th e je ts re q u ire d to be iden tified as a b-jet.

E v e n ts in th e o th e r b ac k g ro u n d -e n rich ed regions have on e or tw o je ts w h ich are re q u ired to n o t b e iden tified as b-jets. T h e b a c k g ro u n d s are e s tim a te d w ith sim u la tio n , ex c e p t th e n o n -p ro m p t o r fa k e-lep to n b a c k g ro u n d , w h ich is e s tim a te d from d a ta . B o o ste d decision tre e s (B D T ) a re used to o p tim ise th e d isc rim in a tio n b etw e en sign al a n d b a c k g ro u n d [33].

T h e cro ss-sectio n is e x tra c te d u sin g a profile likelihood fit of th e B D T resp o n se. T h e b a c k g ro u n d n o rm a lisa tio n a n d th e s y s te m a tic u n c e rta in tie s are c o n s tra in e d by s im u lta n e ­ o u sly a n a ly sin g p h ase -sp ace regions w ith s u b s ta n tia l W t signal c o n trib u tio n s a n d regions w h ere th e W t c o n trib u tio n s are negligible. T h e ra tio of th e m e a su re d cro ss-sectio n to th e th e o re tic a l p re d ic tio n (w hich assu m es Vtb = 1) is used to e x tra c t a valu e o f \ / LVVtb\.

In th e 5F N S , th e W t single to p -q u a rk p rocess o verlap s a n d in terfe res w ith t t p ro d u c tio n a t N L O w h ere d ia g ra m s involving tw o to p q u a rk s are p a r t o f th e re al em issio n co rrec tio n s to W t p ro d u c tio n [3 4 , 35]. A c a lc u la tio n in th e 4 F N S schem e includ es W t a n d tb as well as n o n -to p -q u a rk d ia g ra m s [36] a n d th e in terfe ren c e b etw e en W t a n d tb e n te rs a lre a d y a t tre e level. A m e a su re m e n t o f th e cro ss-sectio n insid e a fid ucial ac ce p ta n c e , d esig n ed to red u ce th e d e p e n d e n c e on th e th e o ry assu m p tio n s, is also p re se n te d . T h e fid ucial a c c e p ta n c e is d efined u sin g physics o b je c ts c o n s tru c te d of s ta b le p a rtic le s to a p p ro x im a te th e W t d e te c to r ac c e p ta n c e . T h e cro ss-sectio n for th e sum of W t a n d tb p ro d u c tio n is m easu red in th is fiducial a c cep tan c e.

T h is p a p e r is o rg a n ise d as follow s: sec tio n 2 p ro v id es a b rief overview of th e A TLA S d e te c to r a n d th e d efin itio n of physics o b je c ts . S ectio n 3 d esc rib es th e d a t a a n d M o n te C arlo sam p les used for th e analy sis. S ectio n 4 d esc rib es th e ev en t selectio n a n d b a c k g ro u n d e s tim a tio n . S ection 5 p re se n ts th e p ro c e d u re d efined to d is c rim in a te th e sig n al from th e b ac k g ro u n d s usin g B D T s. T h e d o m in a n t s y s te m a tic u n c e rta in tie s are discu ssed in sec tio n 6 . S ectio n 7 p re se n ts th e re su lts for th e inclusive cro ss-sectio n m e a su re m e n t a n d for |Vtb| an d discusses th e im p a c t of sy s te m a tic u n c e rta in tie s. S ectio n 8 defines th e fid ucial a c c e p ta n c e a n d p re se n ts th e fiducial cro ss-sectio n m e a su re m e n t. F in ally , a s u m m a ry is p re se n te d in sec tio n 9 .

2 T h e A T L A S d e te c to r and o b je c t r e c o n str u c tio n

T h e A T L A S d e te c to r [37] is a m u lti-p u rp o s e p a rtic le d e te c to r w ith a fo rw ard -b ack w ard sy m m e tric c y lin d rica l g e o m e try a n d a n e a r 4 n coverage in solid a n g le .1 A T L A S co m p rises

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

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a n in n e r d e te c to r (ID ) s u rro u n d e d by a th in s u p e rc o n d u c tin g solenoid p ro v id in g a 2 T ax ial m a g n e tic field, a c a lo rim e te r sy stem a n d a m u o n sp e c tro m e te r in a to ro id a l m a g n e tic field.

T h e ID tra c k in g sy ste m covers th e p se u d o ra p id ity ra n g e |n| < 2.5 a n d co n sists of silicon pixel, silicon m ic ro strip , a n d tra n s itio n ra d ia tio n tra c k in g d e te c to rs . T h e ID prov id es p recise p o s itio n an d m o m e n tu m m e a su re m e n ts for ch a rg ed p a rtic le s a n d allow s efficient id en tific a tio n of je ts c o n ta in in g b-h ad ro n s. L e a d /liq u id -a rg o n (L A r) sa m p lin g c a lo rim e te rs p ro v id e e le c tro m a g n e tic (E M ) en e rg y m e a su re m e n ts w ith h ig h g ra n u la rity u p to |n| = 2.5.

A h a d ro n (s te e l/s c in tilla to r-tile ) c a lo rim e te r covers th e c e n tra l p s e u d o ra p id ity ra n g e (|n | <

1.7). T h e e n d -c a p a n d fo rw ard region s a re in s tru m e n te d w ith L A r c a lo rim e te rs for b o th th e E M a n d h a d ro n ic en e rg y m e a su re m e n ts u p to |n| = 4.9. T h e m u o n s p e c tro m e te r su rro u n d s th e c a lo rim e te rs. I t co n sists of th re e larg e air-co re to ro id s u p e rc o n d u c tin g m a g n e t sy stem s, s e p a ra te trig g e r d e te c to rs a n d h ig h -p recisio n tra c k in g c h a m b e rs p ro v id in g a c c u ra te m uo n tra c k in g for |n| < 2.7 a n d m u o n trig g e rin g fo r |n| < 2.4.

A th ree -lev el trig g e r sy ste m [38] is used to select even ts. T h e first-level trig g e r is im p le m e n te d in h a rd w a re a n d uses a su b se t of th e d e te c to r in fo rm a tio n to re d u ce th e ev ent r a te to less th a n 75 kH z. T w o so ftw are-b ased trig g e r levels, Level-2 a n d th e E v e n t F ilte r, re d u ce th e r a te of Level-1 ac c e p ts to a b o u t 400 Hz o n average.

C a n d id a te ev e n ts a re c h a ra c te rise d by e x a c tly tw o le p to n s (ee, ^ , e ^ ) , m issin g t r a n s ­ verse m o m e n tu m EXpiss d u e to th e n e u trin o s fro m th e le p to n ic d ecay s o f th e tw o W bosons, a n d a b-jet o rig in a tin g from th e to p -q u a rk decay. E le c tro n c a n d id a te s are re c o n s tru c te d from en e rg y clu ste rs in th e c a lo rim e te r w hich a re m a tc h e d to ID tra c k s [39]. S elected e le c tro n s m u st have E x > 25 GeV a n d |n| < 2.47, ex c lu d in g th e b a r re l/e n d -c a p tra n s itio n region of 1.37 < |n| < 1.52. A h it in th e in n e rm o st layer o f th e ID is re q u ired , to re je ct p h o to n conversions. E le c tro n c a n d id a te s a re re q u ire d to fulfil c a lo rim e te r-b a se d an d tra c k - b ase d iso la tio n re q u ire m e n ts in o rd e r to su p p re ss b ac k g ro u n d s from h a d ro n decays. T h e c a lo rim e te r tra n s v e rs e en e rg y w ith in a cone o f size A R = 0.2 a n d th e sc a la r su m o f tra c k p x w ith in A R of 0.3 a ro u n d th e elec tro n , in each case ex c lu d in g th e c o n trib u tio n from th e elec­

tr o n itself, are each re q u ired to b e sm aller th a n E x - a n d n -d e p e n d e n t th re s h o ld s c a lib ra te d to give n o m in al selectio n efficiencies o f 90% fo r p ro m p t e le c tro n s from Z ^ ee decays.

M u o n c a n d id a te s a re re c o n s tru c te d by co m b in in g m a tc h in g tra c k s re c o n s tru c te d in b o th th e ID a n d th e m u o n sp e c tro m e te r [40]. S elected m u on s have a p x > 25 GeV a n d

|n| < 2.5. A n iso la tio n c rite rio n [41] is a p p lie d in o rd e r to re d u ce b a c k g ro u n d c o n ta m in a tio n from ev en ts in w hich a m u o n c a n d id a te is ac co m p an ied by h a d ro n s. T h e ra tio of th e sum of p x of a d d itio n a l tra c k s in a variab le-size cone a ro u n d th e m uon, to th e p x of th e m u o n [41], is re q u ire d to b e less th a n 0.05, y ield in g a selectio n efficiency o f 97% for p ro m p t m uons from Z ^ r r decays.

J e ts are re c o n s tru c te d usin g th e a n t i - k je t c lu ste rin g a lg o rith m [42] w ith a ra d iu s p a ­ r a m e te r of R = 0.4, u sin g locally c a lib ra te d to p o lo g ic al c lu s te rs as in p u ts [43]. J e t energies a re c a lib ra te d u sin g energy- a n d n -d e p e n d e n t c o rre c tio n fa c to rs d eriv e d from s im u la tio n a n d w ith re sid u a l c o rre c tio n s from in -situ m e a su re m e n ts [44]. J e ts are re q u ire d to b e re­

of the LHC ring, and the y-axis points upwards. 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 0 as y = — lntan(0/2). Angular separation is measured in units of AR = \ J (Ay)² + (A0)².

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c o n s tru c te d in th e ra n g e \n\ < 2.5 a n d to have p x > 20 GeV. To re d u ce th e c o n ta m in a tio n d u e to je ts from a d d itio n a l pp in te ra c tio n s in th e sam e o r n e ig h b o u rin g b u n c h crossings (p ileu p ), tra c k s o rig in a tin g from th e p rim a ry v e rte x m u st c o n trib u te a larg e fra c tio n to th e sc a la r sum of th e p x of all tra c k s in th e je t. T h is je t v e rte x fra c tio n (J V F ) [45] is re q u ired to be a t le a st 50% for je ts w ith p x < 50 GeV a n d \ n \ < 2.4.

To avoid d o u b le -c o u n tin g o b je c ts in a n ev en t a n d to su p p re ss le p to n s from heavy- flavour decays, overlap s b etw e en re c o n s tru c te d o b je c ts are resolved in th e follow ing ord er:

(1) je ts o v e rla p p in g w ith a selected e le c tro n w ith in A R of 0.2 are rem oved; (2) e lec tro n s t h a t are w ith in A R of 0.4 of a je t a re rem oved; (3) ev e n ts a re re je c te d if a selected e le c tro n sh ares a n ID tra c k w ith a selected m uon; a n d (4) m u on s t h a t are w ith in A R o f 0.4 o f a je t a re rem oved.

T h e id en tific a tio n of b-jets relies o f th e long lifetim e o f b -h ad ro n s a n d th e to p o lo g ic al p ro p e rtie s of se c o n d a ry a n d t e r tia r y d ecay v ertices re c o n s tru c te d w ith in th e je t. A co m bi­

n a tio n of m u ltiv a ria te a lg o rith m s is used to id en tify b-jets (b-tag) [46]. T h e b-tag a lg o rith m h as an av erag e efficiency of 70% for b-jets from t t d ecay s a n d a n av erage m is-ta g ra te of 0.8% [4 7 , 48] for lig h t-q u a rk je ts .

T h e m issin g tra n s v e rs e m o m e n tu m (E ™ ss) is c a lc u la te d as th e m a g n itu d e o f th e v ec to r sum over th e energies of all clu ste rs in th e c a lo rim e te rs, a n d is refined by a p p ly in g o b je c t- level c o rre c tio n s to th e c o n trib u tio n s arisin g from iden tified elec tro n s, m uons, a n d je ts [49].

3 D a ta an d sim u la te d sa m p les

T h e d a ta s e t used for th is an a ly sis w as co llected a t a/s = 8 TeV in 2012 by th e A T L A S d e te c to r a t th e L H C , a n d c o rresp o n d s, a fte r d a t a q u a lity re q u ire m e n ts, to a n in te g ra te d lu m in o sity of 20.3 fb - 1 . E v e n ts are re q u ired to have fired e ith e r a sin g le-ele ctro n o r single­

m u o n trig g e r. T h e e le c tro n a n d m u o n trig g e rs im p o se a p x th re s h o ld of 24 GeV, along w ith iso la tio n re q u ire m e n ts o n th e le p to n . To recov er efficiency for h ig h er p x lep to n s, th e iso la te d le p to n trig g e rs a re co m p lem en ted by trig g e rs w ith o u t iso la tio n re q u ire m e n ts, b u t w ith p x th re sh o ld s of 60 GeV a n d 36 GeV fo r e lec tro n s a n d m u on s respectively.

S am ples of sig n al a n d b a c k g ro u n d ev e n ts a re s im u la te d usin g v ario u s M o n te C arlo (M C ) g e n e ra to rs, as su m m a rise d in ta b le 1. T h e g e n e ra to rs u sed for th e e s tim a tio n of th e m o d ellin g u n c e rta in tie s are liste d to g e th e r w ith th e referen ce s im u la tio n for th e W t signal a n d th e t i b a c k g ro u n d . In a d d itio n , P D F s used by each g e n e ra to r a n d th e p e r tu r - b a tiv e o rd e r in Q C D of th e re sp e c tiv e c a lc u la tio n s a re p ro v id ed . All sim u la tio n sam p les a re n o rm alised to th e o re tic a l cro ss-sectio n p re d ic tio n s. A to p -q u a rk m ass of 172.5 GeV is used [27].

T h e W t ev e n ts are s im u la te d u sin g th e N L O g e n e ra to r P o w H E g - B o x [50 , 51], in te r­

faced to Py t h ia [52] for p a r to n show ering w ith th e P e ru g ia 2011C set of tu n e d p a ra m e ­ te rs [53]. In th e P o w H E g - B o x ev en t g e n e ra to r, th e C T 1 0 [54] P D F s a re used, w hile th e C T E Q 6 L 1 [55] P D F s are used for Py t h i a. T h e g e n e ra tio n o f W t ev en ts is p e rfo rm e d in th e 5F N S . T h e ov erlap a n d in terfe ren c e b etw e en W t a n d t i is h a n d le d usin g th e d ia g ra m - rem oval schem e (D R ), w h ere all d o u b ly re s o n a n t N L O W t d ia g ra m s are rem oved [56]. A n a d d itio n a l sam p le, g e n e ra te d w ith th e d ia g ra m -s u b tra c tio n schem e (D S ), w h ere th e cross-

J H E P 0 1 ( 2 0 1 6 ) 0 6 4

P ro ce ss G e n e ra to r P D F N o rm a lisa tio n

W t Po w h e g- Bo x v1.0

+ P y t H i a v6.426, D R

C T 1 0 C T E Q 6 L 1

W t t Po w h e g- Bo x v1.0

+ P y t H i a v6.426, DS

C T 1 0

C T E Q 6 L 1 22.37 pb

W t t Po w h e g- Bo x v1.0 C T 1 0 (N L O + N N L L )

+ He r w ig v6.520.2, D R C T 1 0

W t t M C @ N L O v4.06

+ He r w ig v6.520.2, D R

C T 1 0 C T 1 0

t t Po w h e g- Bo x v1.0

+ P y t H i a v6.426

C T 1 0 C T E Q 6 L 1

t t t Po w h e g- Bo x v1.0

+ He r w ig v6.520.2

C T 1 0 C T 1 0

253 p b (N N L O + N N L L )

t t t M C @ N L O v4.06

+ He r w ig v6.520.2

C T 1 0 C T 1 0

W W , W Z , Z Z A LpG En v2.1.4

+ He r w ig v6.520.2

C T E Q 6 L 1 C T 1 0

88 p b (N L O ) Z ( ^ ee, ^ , t t) + je ts A LpG En v2.1.4

+ P y t H i a v6.426

C T E Q 6 L 1 C T E Q 6 L 1

3450 pb (N N L O )

T a b le 1. Monte Carlo generators used to model the W t signal and the background processes at

a/ s = 8 TeV. The samples m arked w ith a f are used as alternatives for W t or tt to evaluate modelling uncertainties. DR refers to the diagram-removal scheme and DS to the diagram -subtraction scheme to handle the overlap and interference between W t and tt, as discussed in the text.

sec tio n c o n trib u tio n from F e y n m a n d ia g ra m s c o n ta in in g tw o to p q u a rk s is s u b tra c te d , is u sed to e v a lu a te th e u n c e rta in ty asso c ia te d w ith th e m o d ellin g of th e o v erlap b etw e en W t a n d t t [56]. T w o a lte r n a tiv e sam p les a re u sed to d e te rm in e th e o ry m o d ellin g u n c e rta in ­ ties: one usin g M C @ N L O [57] a n d th e o th e r u sin g P o w h e g - B o x , b o th in terfa ced to H e r w i g [58], w ith Jim m y for u n d e rly in g -e v e n t m o d ellin g [59].

T h e d o m in a n t a n d larg ely irre d u c ib le t t b a c k g ro u n d is s im u la te d w ith P o w h e g - B o x , u sin g th e C T 1 0 N L O P D F set, w ith p a r to n show ering an d h a d ro n is a tio n p erfo rm ed w ith P y t H i a . T h e t t p ro d u c tio n cro ss-sectio n is o ti = 253+H p b , c o m p u te d a t N N L O in Q C D , in clu d in g re su m m a tio n o f N N L L soft g lu o n te rm s [60- 66].

S m aller b a c k g ro u n d s arise from d ib o so n a n d Z + j e t s p ro d u c tio n . T h e A LpG En LO g en ­ e r a to r [67], in terfa ced to H e r w i g , is u sed to g e n e ra te d ib o so n ev en ts, w ith th e C T E Q 6 L 1 P D F set. D ib o so n ev e n ts are n o rm alised to th e N L O p re d ic tio n [68]. T h e Z + je ts b ac k ­ g ro u n d is g e n e ra te d w ith A LpG En, in terfa ced to P y t H i a , w ith th e C T E Q 6 L 1 P D F set.

T h e d ib o so n e s tim a te also ac co u n ts for lower cro ss-sectio n d ib o so n pro cesses, in clu d in g H ^ W W . T h e Z + j e t s ev e n ts a re n o rm alised to th e N N L O p re d ic tio n [69].

J H E P 0 1 ( 2 0 1 6 ) 0 6 4

T h e n o n -p ro m p t o r fa k e-lep to n b a c k g ro u n d arises fro m n o n -p ro m p t ele c tro n s o r m uons from th e w eak d ec ay of m esons ev en ts, o r fro m ev e n ts w h ere one o r b o th lep to n s are m is- identified. T h is b a c k g ro u n d c o n trib u tio n in clu d es th e t-c h a n n e l a n d s -c h a n n e l single to p - q u a rk p ro d u c tio n m odes. T h e n o rm a lis a tio n an d s h a p e o f th e n o n -p ro m p t o r fak e-lep to n b a c k g ro u n d is d e te rm in e d d ire c tly from d a ta , u sin g th e m a trix m e th o d [70]. In a d d itio n to ev e n ts from th e signal d a t a sam p le (lab elled as “t ig h t” ev e n ts), a second ( “loose” ) set en ric h ed w ith fake le p to n s is defined by rem o v in g th e le p to n iso la tio n re q u ire m e n t. G iven th e p ro b a b ilitie s for re al a n d fake le p to n s t h a t a lre a d y p assed th e loose selectio n to also pass th e tig h t selection, th e n u m b e r of tig h t ev e n ts w ith a fake le p to n is d e te rm in e d from a lin e a r sy ste m o f e q u a tio n s.

G e n e ra te d ev en ts a re p assed th ro u g h a sim u la tio n [71] o f th e A T L A S d e te c to r based o n G EA nT 4 [72] a n d re c o n s tru c te d u sin g th e sam e p ro c e d u re as for collision d a ta . T h e a lte r n a tiv e t t sam p les used to e v a lu a te th e o ry m o d ellin g u n c e rta in tie s a re in s te a d p rocessed w ith th e A T L F A S T -II [71] sim u la tio n , w h ich em ploys a p a ra m e te ris a tio n of th e re sp o n se o f th e e le c tro m a g n e tic a n d h a d ro n ic c a lo rim e te rs, a n d G E A nT 4 for th e o th e r d e te c to r c o m p o n e n ts. T h e sim u la tio n s also in clu d e th e effect of m u ltip le p p collisions p e r b u n ch cro ssin g (p ileu p ).

4 E v en t se le c tio n

T h e d ile p to n selectio n re q u ires t h a t each ev en t h as a h ig h -q u a lity re c o n s tru c te d p rim a ry v e rte x , w hich m u st be form ed from a t least five tra c k s w ith p x > 0.4 GeV. E a c h selected ev en t m u st c o n ta in e x a c tly tw o iso lated o p p o site -sig n lep to n s (e, ^ ) t h a t o rig in a te from th e p rim a ry v erte x , a t le a st one of w hich m u st b e a sso c ia te d w ith a le p to n t h a t trig g e re d th e ev en t. In a d d itio n , since th e W t s ig n a tu re c o n ta in s a h ig h -p x q u a rk from th e to p -q u a rk decay, ev e n ts are re q u ired to hav e e ith e r one je t o r tw o je ts .

E v e n ts from Z -b o so n d ecays (in clu d in g Z ^ ee, Z ^ ^ , a n d Z ^ t t w ith t ^ e o r ^ ) a re su p p re sse d th ro u g h re q u ire m e n ts on th e in v a ria n t m ass of th e d ile p to n sy ste m as well as o n ETpiss a n d th e p s e u d o ra p id ity o f th e le p to n s + je t(s ) sy stem . E v e n ts c o n ta in in g sam e- flavour le p to n s (ee o r ^ ) are re je c te d if th e in v a ria n t m ass of th e le p to n p a ir is b etw een 81 GeV a n d 101 GeV. E v e n ts are also re q u ired to have ETpiss > 40 GeV, w ith th e th re s h o ld ra ise d to 70 GeV if th e in v a ria n t m ass of th e le p to n p a ir is below 120 GeV. E v e n ts c o n ta in in g one e le c tro n a n d one m u o n are re q u ire d to h ave E “ iss > 20 GeV, w ith th e th re s h o ld raised to 50 GeV if th e in v a ria n t m ass of th e le p to n p a ir is below 80 GeV. Since W t ev en ts are m o re c e n tra l th a n Z + je ts ev en ts, th e p se u d o ra p id ity of th e sy ste m o f b o th le p to n s a n d all je ts , re c o n s tru c te d from th e v e c to ria l sum of le p to n a n d j e t m o m e n ta , is re q u ire d to be

\ nsys \ < 2.5.

E v e n ts are c a te g o rised in to five regio ns d e p e n d in g o n th e je t a n d b -tag m u ltip licitie s.

T h e la rg e st n u m b e r o f e x p e c te d signal ev e n ts is in th e 1-jet regio n w ith one b-tagg ed je t, w hile ev en ts in th e tw o -jet regio ns w ith one o r tw o b-tags are d o m in a te d by tt . T h ese th re e regions a re in clu d ed in th e cro ss-sectio n fit. T w o a d d itio n a l regions a re u sed to v a lid a te th e m o d ellin g of th e o th e r b ac k g ro u n d s b u t a re n o t in clu d ed in th e fit. O n e -jet a n d tw o -jet ev e n ts t h a t have zero b-tagged je ts co m p o se th e 0 -ta g c o n tro l regions, w hich a re e n h a n c e d

J H E P 0 1 ( 2 0 1 6 ) 0 6 4

Process 1-jet 1-tag 2-jet 1-tag 2-jet 2-tag 1-jet 0-tag 2-jet 0-tag W t

tt Diboson Z + jets

Non-prompt or fake lepton

1000(140) 4500(700) 40(30) 70(40) 24(15)

610(70) 7600(900)

35(15) 60(40) 27(15)

160(50) 5000(900)

1(1) 7(4) 13(7)

660(100) 2600(400) 1600(500) 2600(1400)

130(70)

290(30) 2660(330)

670(270) 900(500) 80(50) Total background

Signal+Background

4600(700) 5600(800)

7700(900) 8300(900)

5000(900) 5200(900)

6900(1400) 7600(1500)

4300(600) 4600(600)

Observed 5585 8371 5273 7530 4475

T a b le 2. Numbers of expected events for the W t signal and th e various background processes and observed events in d a ta in the five regions, w ith their predicted uncertainties. Uncertainties shown include all sources of statistical and system atic uncertainty, summed in quadrature.

in th e o th e r b ac k g ro u n d s. O bserv ed yields a n d k in e m a tic d is trib u tio n s in th e 0 -ta g c o n tro l regions a re s tu d ie d w hile ch oosing th e selectio n cu ts; th e th re e regions in clu d ed in th e cro ss-sectio n fit are n o t p a r t of th is o p tim is a tio n p ro c ed u re .

T h e p re d ic te d ev en t yields for sig nal a n d b ac k g ro u n d s, a n d th e ir u n c e rta in tie s , are su m m a rise d in ta b le 2 . U n c e rta in tie s from d ifferen t sources are ad d e d in q u a d r a tu re , n o t ta k in g in to ac c o u n t po ssib le c o rre la tio n s. M an y of th e sources of s y s te m a tic u n c e rta in ty a re co m m o n to th e W t signal a n d t i b a c k g ro u n d p rocesses, a n d c o rre la te d b etw e en regions (see sec tio n 6) . T h e n u m b e rs of ev e n ts o b serv ed in d a t a a n d th e to ta l p re d ic te d yields are c o m p a tib le w ith in th e u n c e rta in tie s. T h e W t sig nal co m p rises 21% of th e t o ta l e x p e c te d ev en t yield in th e 1-jet 1 -tag region. T h e m a in b a c k g ro u n d o rig in a te s from th e p ro d u c tio n o f to p -q u a r k p a ir events, w hich a c co u n ts for a lm o st 80% o f th e to ta l ev en t yield in th e 1-jet 1 -tag region. F or th e o th e r regions in clu d ed in th e fit, th e e x p e c te d fra c tio n of signal ev e n ts is sm aller, 9% in th e 2-jet 1 -tag reg ion a n d 3% in th e 2 -jet 2 -ta g region, w hich is th e m o st en ric h ed in ti. T h e o th e r b ac k g ro u n d s are sm all in th e 1-jet 1 -tag a n d 2-jet regions w h ere th e y ac c o u n t for 2% o f th e to ta l ev en t yield. T h e 0 -ta g c o n tro l regions are en rich ed in o th e r b a c k g ro u n d s (d ib o so n , Z + j e t s a n d n o n -p ro m p t o r fake le p to n ), w h ich c o n trib u te 4 0-60% of th e t o ta l ev en t yield.

T h e ETpiss d is trib u tio n s of ev e n ts in th e 0 -ta g regio ns a re show n in figure 2 to d e m o n ­ s tr a te th e g o o d m o d ellin g of th e o th e r b ac k g ro u n d s. T h e b e h a v io u r of th is d is trib u tio n a t low E ™ ss values is a re su lt of th e d ifferen t re q u ire m e n ts for sam e-flavou r a n d o p p o site- flav o u r lep to n s. F ig u re s 3 a n d 4 show th e d is trib u tio n s of k in e m a tic v aria b les o f re co n ­ s tru c te d o b je c ts for th e th re e b-tagged regions. T h e d a t a d is trib u tio n s a re well m o delled by th e b a c k g ro u n d a n d signal e x p e c ta tio n s in all regions.

5 A n a ly sis

T h e s e p a ra tio n of th e W t signal from th e d o m in a n t b a c k g ro u n d fro m to p -q u a rk p a irs is a c co m p lish e d th ro u g h th e use of a B D T a lg o rith m [33] in th e T M V A fram ew o rk [73].

T h e B D T s are tra in e d s e p a ra te ly in th re e regions, 1-jet 1 -tag, 2-jet 1 -tag a n d 2-jet 2- ta g , u sin g sim u la te d W t ev e n ts as sig n al a n d sim u la te d t i ev en ts as b a c k g ro u n d . T h re e

J H E P 0 1 ( 2 0 1 6 ) 0 6 4

Figure 2. D istributions of the missing transverse m om entum Emiss in (a) 1-jet and (b) 2-jet events w ith 0 b-tags. The sim ulated signal and background contributions are scaled to their expectations.

T he hatched area represents the sum in qu adratu re of the statistical and system atic uncertainties.

The last bin includes the overflow.

Figure 3. D istributions, in the 1-jet 1-tag region, of (a) p t of the leading lepton (fi), (b) p t

of the second-leading lepton ( ^ ) , (c) p t of the je t (ji), and (d) E ^ lss. The sim ulated signal and background contributions are scaled to their expectations. The hatched area represents the sum in qu adratu re of the statistical and system atic uncertainties. The last bin includes the overflow.

J H E P 0 1 ( 2 0 1 6 ) 0 6 4

Figure 4. D istributions of the p T of the leading je t (ji) and the second-leading je t ( j 2) in the (a,b) 2-jet 1-tag and (c,d) 2-jet 2-tag regions. The sim ulated signal and background contributions are scaled to their expectations. The hatched area represents the sum in q uadrature of the statistical and system atic uncertainties. The last bin includes th e overflow.

equal-size W t samples are combined to reduce sensitivity to the modelling uncertainties and to maximise the number of events available for training: the P o w h e g -B o x + P y th ia sample with the DR scheme, the P o w h e g -B o x + P y th ia sample with the DS scheme, and the P o w h e g -B o x + H e rw ig sample with the DR scheme. The A d a B o o s t boosting algorithm is used [74]. This algorithm increases the event weight for mis-classified events for consecutive trees in the training. The final BDT is then the weighted average over all trees. The list of variables entering the BDT algorithm is chosen based on the power to discriminate the W t signal from the ti background and is derived from a large set of kinematic variables th at show good agreement between data and MC simulation. The number of input variables is a compromise between the achievable discrimination power and possible overtraining. As a result of this optimisation procedure, 13, 16, and 16 variables are selected for the 1-jet 1-tag, 2-jet 1-tag, and 2-jet 2-tag regions, respectively.

The BDT input variables used in the three regions are explained below and are listed in table 3 together with their importance ranking. The objects (denoted o i , . . . , on) used to define these kinematic variables are the leading- and second-leading lepton (^1 and ^ ) and jet ( j1 and j 2) as well as ETpiss. The kinematic variables are defined as follows.

J H E P 0 1 ( 2 0 1 6 ) 0 6 4

pTys(o 1, . . . , o n ), m a g n itu d e of th e v e c to r su m of th e tra n s v e rs e m o m e n ta of th e o b je c ts.

• ^ E T , th e sc a la r sum of tra n s v e rs e en e rg y o f c a lo rim e te r cells. F o r cells a sso c ia te d w ith ele c tro n s a n d je ts , th e co rre sp o n d in g c o rre c tio n s are ap p lied .

• a (pTys(o1, . . . , on )), th e ra tio of p^ys to (H T + ^ E T ), w h ere H T is th e sc a la r sum of th e tra n s v e rs e m o m e n ta o f th e o b je c ts.

• A p T (o1, o2), th e difference in p T b etw e en th e tw o o b je c ts.

• A R ( o1, o2), th e s e p a ra tio n of th e tw o o b je c ts in 0 - n space.

• m T (o1,o2), th e tra n s v e rs e m ass, given by ^ /2 p T (o1)p T (o2)(1 — c o s A 0 ) .

• C e n tra lity (o1, o2), th e ra tio o f th e sc a la r su m o f th e p T of th e tw o o b je c ts to th e sum of th e ir energies.

• m (o1, o2), th e in v a ria n t m ass of th e sy stem of th e tw o o b je c ts.

• m T2, w hich c o n ta in s in fo rm a tio n a b o u t th e p resen ce o f th e tw o n e u trin o s from th e tw o W -b o so n d ecay s [75- 77]. T h e mT 2 a lg o rith m c re a te s c a n d id a te s for th e tr a n s ­ verse m o m e n ta of th e tw o n e u trin o s, w h ich m u st su m to give th e m issing tra n sv e rs e m o m e n tu m . T h ese a re co m b in ed w ith th e m o m e n ta o f th e tw o lep to n s to form th e tra n s v e rs e m ass of tw o c a n d id a te W bo son s, w ith each also fulfilling a W -b o so n m ass c o n s tra in t. F o r each such c a n d id a te p a ir, th e la rg e r of th e tw o tra n s v e rs e m asses is k ep t. T h e n mT 2 is given by th e sm allest tra n sv e rs e m ass in all p o ssib le c a n d id a te pairs.

• E / m ( o1,o2 , 0 3), th e ra tio of th e en e rg y of th e sy ste m of th e th re e o b je c ts to th e in v a ria n t m ass of th is sy stem .

F ig u re 5 c o m p ares th e sh ap e s o f th e m o st im p o rta n t v aria b les in th e 1-jet 1 -tag region for W t a n d t t ev en ts a n d show s a c o m p a riso n of th e d a t a a n d th e SM p re d ic tio n s. T h e m o st im p o rta n t v a ria b le is pTys( f1, f2, ETpiss, j O , w h ich is sen sitiv e to th e u n id en tified b -q u ark in t i ev en ts. T h is v aria b le p ea k s a t low er values for W t a n d h as a lo n g er ta il for ti . T h e second m o st im p o rta n t v aria b le is th e s e p a ra tio n o f th e lead in g le p to n a n d th e je t, in 0 -n space. T h e se tw o o b je c ts o rig in a te from th e sam e to p q u a rk in W t ev en ts, lead in g to a s h a r p e r p e a k th a n in t i ev en ts. F ig u re 6 show s th e m o st im p o rta n t d is c rim in a tin g v ariab les in th e 2 -jet regions. H ere, th e p T s d is trib u tio n also p ea k s a t lower values for W t th a n for ti , b u t th e d is trib u tio n is also b ro a d e r for W t, re su ltin g in a long ta il. T h e in v a ria n t m ass v aria b les are im p o rta n t for 2 -jet events, w h ere h a lf o f th e p o ssib le le p to n -je t p airin g s co rre sp o n d to th e o b je c ts from th e d ecay of o ne of th e to p q u a rk s in t i ev en ts lead in g to a p e a k a t low er in v a ria n t m ass. F o r W t, on ly one q u a r te r o f th e p ossible p airin g s o f je ts an d le p to n s co rre sp o n d to th e o b je c ts from th e to p -q u a rk decay.

T h e B D T re sp o n se for th e th re e regions is show n in figure 7 . T h e W t sig n al is larg e r a t p o sitiv e B D T resp o n se values, w hile th e t i b a c k g ro u n d d o m in a te s for n eg a tiv e B D T

J H E P 0 1 ( 2 0 1 6 ) 0 6 4

Variable 1-jet, 1-tag 2-jet 1-tag 2-jet 2-tag

pTys (fi,f2 ,E m iss, j i ) 1

pTys ( ^ 2 , j i ) 7

pTys (^1,^2) 13

pTys (ji,j2 ) 10 1

pTys ( f j ^ E ^ ) 12 2

pTys (fi,f2 ,E m iss,j i ,j 2 ) 13

pTys ( f i j i ) 13

a(pTys) (fi,f2 ,E m lss, j i ) 4 5

PT (j2) 8

Apx (^i, ) 8

Apt ( ( f i,f 2 ,ji) , (Emlss)) 9

Apt (Emlss, j i ) 9

a p t (fi,^2, Emlss, j i ) 16

A p t (^2, j’2) 14

A R ( f i , j i) 2 5

A R (^2,j i) 4 10

A R (^2,j2) 6

A R (^2,j i ) 11

A R (4 /2) 14

A R ( ( f j ^ j 9

m (^2, j i ) 10 3 3

m (fi, j'2) 1 4

m (ji, j'2) 2

m (^2, j'2) 7 7

m ( f i , j i ) 8 6

m (fi,f2 ) 15

m (f2, j i , j'2) 11

m ( f i , f2, j i , j'2) 15

m T (j'i ,ET?lss) 5

mT2 11

E / m (fi,f2 , j'2) 16

S e t 3

C entrality(fi , f 2) 6

C entrality(f i , j i ) 12

C entrality(f 2, j’2) 12

T a b le 3. Discriminating variables used in the training of the BDT for each region. The num ber indicates the relative im portance of this variable, w ith 1 referring to the m ost im portant variable.

An em pty field means th a t this variable is not used in this region.

J H E P 0 1 ( 2 0 1 6 ) 0 6 4

Figure 5. D istributions of the two most im portant BDT input variables for the 1-jet 1-tag region.

The distributions are shown for (a, b) the p T of the system of the leptons, je t and Emlss and (c, d) the A R between the leading lepton and the jet. Each contribution is normalised to unit area in (a, c) and to its expectation in (b, d). The hatched area represents the sum in qu adratu re of the statistical and system atic uncertainties. The last bin includes the overflow.

response values. The BDT range in each region is chosen to ensure sufficient simulation statistics in each bin. The BDT separates the signal from the background in all three regions, although even for high BDT response values in the 1-jet 1-tag region, there remains a large expected background from

events. The BDT responses from figure 7 are used in the profile likelihood fit swith this binning.

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

Systematic uncertainties affect the acceptance estimates for the signal and background processes. Some of the systematic uncertainties also affect the shape of the BDT response.

Experimental sources of uncertainty arise from the modelling of jets, leptons and ETplss.

The impact of the uncertainty in the jet energy scale (JES) on the acceptance and shape of the BDT response for

and

is evaluated in 22 uncorrelated components, each of which can have a pT and n dependence [44, 78]. The largest components are related

J H E P 0 1 ( 2 0 1 6 ) 0 6 4

Figure 6. D istributions of the m ost im portant BDT input variables in the (a, b) 2-jet 1-tag and (c, d) 2-jet 2-tag regions. The distributions are shown for (a, b) the invariant mass of the system of the leading lepton and the second-leading je t and (c, d) the p T of the system of the two jets.

Each contribution is normalised to unit area in (a, c) and to its expectation in (b, d). The hatched area represents the sum in quadrature of the statistical and system atic uncertainties. The last bin includes the overflow.

to the modelling and the heavy-flavour correction, with an acceptance uncertainty for W t and

events of 1-2%. The shape uncertainty is taken into account for the JES component with the largest impact on the fit result (JES modelling component 1). The jet energy resolution uncertainty is evaluated by smearing the energy of each jet in the simulation and symmetrising the resulting change in acceptance and BDT response shape [79]. The resulting acceptance uncertainty for W t and

events is 1-3%, and the shape uncertainty is taken into account.

The uncertainties in the modelling of the jet reconstruction and the jet vertex fraction requirement are evaluated by randomly discarding jets according to the difference in jet reconstruction efficiency between the data and MC simulation and by varying the the jet vertex fraction requirement, respectively. These uncertainties have an impact on the acceptance for W t and

events of less than 1%. They do not change the shape of the BDT response.

Further uncertainties arise from the modelling of the trigger, reconstruction, and iden­

tification efficiencies for electrons [80] and muons [40], as well as from the modelling of

J H E P 0 1 ( 2 0 1 6 ) 0 6 4

Figure 7. BDT response for (a, b) 1-jet 1-tag, (c, d) 2-jet 1-tag and (e, f) 2-jet 2-tag events. Each contribution is norm alised to unit area in (a, c, e) and to its expectation in (b, d, f). The hatched area represents the sum in qu adrature of the statistical and system atic uncertainties. The first bin includes the underflow and the last bin the overflow.

the electron and muon energy scale and resolution [40, 81]. These have an effect on the acceptance for W t and

events of less than 1%, except for the electron identification un­

certainty, which has an acceptance uncertainty for W t and

of 2%. These uncertainties do not change the shape of the BDT response.

J H E P 0 1 ( 2 0 1 6 ) 0 6 4

U n c e rta in tie s in th e m o d ellin g o f th e b-tag ging efficiency a n d m is-ta g ra te s are e s ti­

m a te d from d a t a [4 7 , 48]. T h ese u n c e rta in tie s d e p e n d on th e je t flav ou r a n d p T , a n d for m is-ta g ra te s also o n je t n. T h e u n c e rta in ty for b-jets is e v a lu a te d in six c o m p o n e n ts, w ith th e la rg e st c o m p o n e n t h av in g a n a c c e p ta n c e u n c e rta in ty for W t a n d t i ev en ts of 1-4% , d e p e n d in g o n th e an a ly sis region [48]. T h e b -tag m o d ellin g u n c e rta in tie s d o n o t ch a n g e th e sh a p e of th e B D T response.

T h e v a ria tio n s in le p to n a n d je t en ergies are p ro p a g a te d to th e E ™ ss value. T h is u n c e rta in ty h as a d d itio n a l c o n trib u tio n s from th e m o d ellin g o f th e en e rg y d e p o sits w hich a re n o t asso c ia te d w ith an y re c o n s tru c te d o b je c t [49]. B o th a n en e rg y scale a n d a n en e rg y re so lu tio n c o m p o n e n t are co n sid ered . T h e co rre sp o n d in g a c c e p ta n c e u n c e rta in ty for W t a n d t t ev en ts is less th a n 0.3% . T h e E ™ ss scale co m p o n e n t also a lte rs th e sh a p e o f th e B D T resp onse.

T h e o re tic a l u n c e rta in tie s a re e v a lu a te d for th e signal as well as th e tti p re d ic tio n s.

F ig u re 8 show s th e re la tiv e shift o f th e B D T re sp o n se asso c ia te d w ith fo u r of th e th e o ry m o d ellin g u n c e rta in tie s. T h e u n c e rta in ty o n th e W t sign al a n d th e tti b a c k g ro u n d asso ­ c ia te d w ith in itia l- a n d fin a l-s ta te ra d ia tio n (IS R /F S R ) is e v a lu a te d u sin g P o w h e g - B o x in terfa ced to P y t h i a . T h e re n o rm a lisa tio n scale asso c ia te d w ith th e s tro n g co u p lin g a S is v aried u p a n d do w n by a fa c to r of tw o in th e m a trix -e le m e n t c a lc u la tio n a n d a P y t h i a P e ru g ia 2012 tu n e is used to c re a te sam p les w ith in cre ased a n d d ec rea sed levels of ra d i­

a tio n t h a t a re c o m p a tib le w ith 7 TeV A TLA S d a t a [82]. F o r ti, th e h d a m p p a r a m e te r of P o w h e g - B o x [51], w hich affects th e a m o u n t of Q C D ra d ia tio n , is v aried to g e th e r w ith IS R /F S R . T h is u n c e rta in ty is tr e a te d as u n c o rre la te d b etw e en W t a n d t t ev en ts. F ig u re 8 show s t h a t th is u n c e rta in ty has a larg e effect o n th e a c c e p ta n c e a n d also a lte rs th e sh a p e o f th e B D T response.

T h e u n c e rta in ty asso c ia te d w ith th e N L O m a tc h in g m e th o d is e v a lu a te d by co m p a rin g P o w h e g - B o x w ith M C @ N L O , b o th in terfa ced to H e r w i g . F ig u re 8 show s t h a t th is u n c e rta in ty h as a d e p e n d e n c e on th e sh a p e of th e B D T re sp o n se. F o r W t p ro d u c tio n , th e la rg e st im p a c t of th is u n c e rta in ty is to sh ift ev en ts b etw e en th e 1-jet 1 -tag a n d 2 -jet 2 -ta g regions. F or t i ev en ts, th e im p a c t of th is u n c e rta in ty is on th e a c c e p ta n c e , w h ere it is 11-12% . T h is u n c e rta in ty is tr e a te d as c o rre la te d b etw e en W t a n d t t events.

T h e u n c e rta in ty asso c ia te d w ith th e m o d ellin g of th e h a d ro n is a tio n a n d p a r to n show er is e v a lu a te d by c o m p a rin g sam p les w h ere P o w h e g - B o x is in terfa ced w ith P y t h i a to th o se w h ere it is in terfa ced w ith H e r w i g . T h is u n c e rta in ty a lte rs th e sh a p e of th e B D T resp on se.

F o r th e W t signal, th e u n c e rta in ty a sso c ia te d w ith th e schem e used to rem ove o verlap w ith t t is e v a lu a te d by co m p a rin g th e tw o d ifferen t schem es: th e n o m in al sam p le, g e n e ra te d w ith th e D R schem e, is c o m p a re d to a sam p le g e n e ra te d w ith th e D S schem e. T h e re la tiv e sh ift o f th e B D T re sp o n se is show n in figure 8 . T h e re la tiv e sh ift o f th is u n c e rta in ty is a b o u t 5% in th e signal regio n for 1-jet 1 -tag ev en ts, a n d grow s to larg e values in th e b a c k g ro u n d -d o m in a te d region for 2-jet ev en ts, w h ere its e v a lu a tio n is lim ited by sim u la tio n s ta tis tic s a n d th e p re d ic te d ev en t yield is v ery sm all. T h is u n c e rta in ty a lte rs th e s h a p e of th e B D T response.

T h e e v a lu a tio n of th e P D F u n c e rta in ty follows th e P D F 4 L H C p re sc rip tio n [31] u sing th re e differen t P D F sets ( C T 1 0 , M S T W 2 0 0 8 m o 6 8 c L [28] a n d N N P D F 2 .3 [32]). T h e

J H E P 0 1 ( 2 0 1 6 ) 0 6 4

Figure 8. Relative shift of the BDT response associated w ith system atic variations of ISR /FSR , NLO m atching m ethod, D R /D S and hadronisation for (a) 1-jet 1-tag, (b) 2-jet 1-tag, and (c) 2-jet 2-tag events. DR refers to the diagram-removal scheme, DS to the diagram -subtraction scheme.

uncertainty on the acceptance for W t and ti events is evaluated in each of the three analysis regions. The PDF uncertainty is considered correlated between W t and

events, except for ti 1-jet events, for which it is considered to be uncorrelated. The PDF uncertainty com­

ponents th at affect the ti acceptance in this region differ from the uncertainty components th at affect the ti acceptance in the other regions [83].

The normalisation of the ti background has an uncertainty of 6% [65, 66]. The diboson background process has an uncertainty of 30% for 1-jet events and 40% for 2-jet events [84], which is treated as uncorrelated between different regions. The Z +jets and non-prompt or fake-lepton backgrounds have normalisation uncertainties of 60% to account for possible mismodelling of the jet multiplicity and the acceptance of these small backgrounds [85, 86]. The Z +jets and non-prompt or fake-lepton normalisation uncertainties are treated as uncorrelated between background sources and regions.

The uncertainty on the integrated luminosity is 2.8%. It is derived, following the same methodology as that detailed in ref. [87], from a preliminary calibration of the luminosity scale derived from beam-separation scans performed in November 2012. The luminosity uncertainty enters in the extraction of the cross-section as well as in the normalisation

J H E P 0 1 ( 2 0 1 6 ) 0 6 4

o f th e b a c k g ro u n d p ro cesses t h a t are n o rm alised to th e o ry p re d ic tio n s. T h e s ta tis tic a l u n c e rta in ty d u e to th e fin ite size of th e s im u la tio n sam p les is also ta k e n in to ac co u n t.

7 R e su lts

7.1 M e a s u r e m e n t o f t h e in c lu s iv e c r o s s -s e c tio n

A profile likelihood fit to th e B D T classifier d is trib u tio n s is p erfo rm ed , u sin g th e R o o S ta ts so ftw are [8 8 , 89], in o rd e r to d e te rm in e th e inclusive W t cross-sectio n , u tilisin g th e 1-jet 1 -tag, 2-jet 1-tag, a n d 2 -jet 2 -ta g regions. T h e inclusio n o f th e 2-jet regions p ro vides a d d itio n a l signal se n sitiv ity a n d also helps to c o n s tra in th e ttt b a c k g ro u n d n o rm a lis a tio n a n d sy ste m a tic u n c e rta in tie s .

T h e b in n e d likelihood fu n c tio n is c o n s tru c te d as th e p ro d u c t of P o isso n p ro b a b ility te rm s over all bins co n sid ered in th e an aly sis. T h is lik eliho od d e p e n d s on th e s ig n a l-stre n g th p a r a m e te r / , w hich is a m u ltip lic a tiv e fa c to r on th e u n c o n s tra in e d W t y ield p re d ic tio n . N u isan c e p a ra m e te rs (d e n o te d 9) a re used to en c o d e th e effects of th e v ario u s sources o f sy ste m a tic u n c e rta in ty on th e signal a n d b a c k g ro u n d e x p e c ta tio n s . T h ese n u isan ce p a ra m e te rs are im p le m e n te d in th e likelihood fu n c tio n w ith m u ltip lic a tiv e G a u ssia n or lo g -n o rm al c o n s tra in ts w ith m e a n 90 a n d s ta n d a r d d e v ia tio n A 9 . T h e likelihood is th e n m ax im ise d w ith re s p e c t to th e full set o f / a n d 9 p a ra m e te rs . T h e values o f th e s e p a ra m e te rs a fte r m a x im is a tio n a re re ferred to as / , 9, a n d A 9.

T h e e x p e c te d cro ss-sectio n is o b ta in e d from a fit to th e so-called A sim ov d a ta s e t [90], w ith th e signal a n d all b ac k g ro u n d s scaled to th e ir p re d ic te d sizes [26]. T h e ex­

p e c te d m e a su re m e n t is / exp = 1.0 0-° } 7. T h e o b serv ed re su lt for th e signal s tre n g th is / obs = 1 .0 3 -° -7 , w hich c o rre sp o n d s to a m easu red cro ss-sectio n of 23.0 ± 1.3 ( s t a t.) + 3 ' 5 (sy st.) ± 1.1 (lu m i.) pb. In c lu d in g s y s te m a tic u n c e rta in tie s , th e o b ­ served (e x p ected ) significance of th e sign al c o m p a re d to th e b a c k g ro u n d -o n ly h y p o th e sis is 7.7 (6.9) s ta n d a r d d e v ia tio n s, o b ta in e d usin g an a s y m p to tic a p p ro x im a tio n [90].

T h e p o st-fit (p re-fit) effect o f each in d iv id u a l sy ste m a tic u n c e rta in ty o n /t is c a lc u la te d by fixing th e co rre sp o n d in g n u isan ce p a r a m e te r a t 9 + A 9 (9 + A 9 ), a n d p erfo rm in g th e fit ag ain . T h e difference b etw e en th e d e fa u lt a n d th e m odified / , A / , re p re se n ts th e effect on / of th is p a r tic u la r u n c e rta in ty . T h e p u ll ((9 — 9 o )/A 9 ), a n d th e p re-fit an d p o st-fit im p a c ts for th e n u isan ce p a ra m e te rs w ith th e la rg e st im p a c t o n / are show n in figure 9 . Since th e to ta l n u m b e r of o b serv ed ev en ts in th e 2 -jet regio ns is a b o u t 14000, w ith a W t signal fra c tio n of a b o u t 6%, th e n u isan ce p a ra m e te rs t h a t have a ttt a c c e p ta n c e u n c e rta in ty of m o re th a n a b o u t 2% c a n b e c o n s tra in e d in th e fit. T h is ap p lies to th e je t en e rg y re so lu tio n an d t t n o rm a lisa tio n u n c e rta in tie s, a m o n g s t o th e rs . T h e E “ lss scale u n c e rta in ty h as a s h a p e d e p e n d e n c e in th e 1-jet 1 -tag regio n for W t a n d tt , w hich re su lts in th e co rre sp o n d in g n u isan ce p a r a m e te r b ein g sh ifted b u t n o t m u ch c o n stra in e d . T h e th e o ry m o d ellin g u n c e rta in tie s d u e to IS R /F S R , D R /D S , a n d N L O m a tc h in g m e th o d have larg e p re-fit a n d p o st-fit im p a c ts. T h e n u isan ce p a r a m e te r for I S R /F S R W t is sh ifted a n d c o n s tra in e d in th e fit d u e to its B D T re sp o n se sh a p e d e p e n d en ce , show n in figure 8 . T h is u n c e rta in ty has th e la rg e st im p a c t on / , b o th p re-fit a n d p o st-fit. T h e I S R /F S R t t u n c e rta in ty h as a sm aller p o st-fit im p a c t on /t an d is c o n s tra in e d d u e its a c c e p ta n c e an d

J H E P 0 1 ( 2 0 1 6 ) 0 6 4

F ig u r e 9. Effect on the uncertainty on th e fitted value of the signal strength / (A f) and pull of the dom inant nuisance param eters, ordered by their im pact on / . The shaded and hashed areas refer to the top axis: the shaded bands show the initial im pact of th a t source of uncertainty on the precision of / ; the hatched areas show th e im pact on the m easurem ent of th a t source of uncertainty, after the profile likelihood fit, at the ±1<r level. The points and associated error bars show the pull of the nuisance param eters and their uncertainties and refer to the b otto m axis. A m ean of zero and a width of 1 would imply no constraint due to th e profile likelihood fit. Only the 11 uncertainties w ith the largest im pact on / are shown.

shape dependence. In a test where the ISR/FSR uncertainty is considered to be correlated between W t and

events, the expected uncertainty on t is reduced to ±0.16. The nuisance parameter for the NLO matching method uncertainty is constrained by the

background because of the large acceptance component and shape dependence of the NLO matching method uncertainty.

Table 4 summarises the contributions from the various sources of systematic uncer­

tainty to the uncertainties on the observed fit result. The total uncertainty in the table is the uncertainty obtained from the full fit, and is therefore not identical to the sum in quadrature of the components, due to correlations that the fit induces between the uncer-

J H E P 0 1 ( 2 0 1 6 ) 0 6 4

U n c e rta in ty Im p a c t on f [%]

S ta tis tic a l ± 5 .8

L u m in o sity ± 4 .7

T h e o ry m o d ellin g

I S R /F S R +8.2

-9.4

H a d ro n is a tio n ± 1 .7

N L O m a tc h in g m e th o d ± 2 .5

P D F ± 0 .6

D R /D S +2.2

-4.8 D e te c to r

J e t +9.0

-9.9

L e p to n ± 3 .0

zumiss

Et ± 5 .5

b-tag ± 1 .0

B a c k g ro u n d n o rm . +2.9

-2.6

T o ta l +16

-17

T a b le 4. Sum m ary of the relative uncertainties on the W t cross-section m easurem ent. Detector uncertainties are grouped into categories. All sources of uncertainty within a category are added in quadrature to obtain the category uncertainty.

ta in tie s . T h e la rg e st c o n trib u tio n s to th e cro ss-sectio n u n c e rta in ty are from th e m od ellin g o f I S R /F S R a n d from th e j e t en e rg y re so lu tio n a n d scale.

T h e B D T re sp o n se for each reg ion is show n n o rm alised to th e fit re su lt in figure 10.

T h e d e p e n d e n c e o f th e cro ss-sectio n o n th e to p -q u a rk m ass is e v a lu a te d u sin g W t a n d t t sim u la tio n sam p les w ith v ario u s to p -q u a rk m asses. T h e cro ss-sectio n d e p e n d s lin e a rly on th e to p -q u a r k m ass d u e to ch an g es in ac ce p ta n c e , w ith a slop e o f 1.11 p b /G e V .

7 .2 C o n s tr a in ts o n |fLvVtb| a n d |Vtb|

T h e inclusive cro ss-sectio n m e a su re m e n t p ro v id es a d ire c t d e te rm in a tio n of th e m a g n itu d e o f th e C K M m a trix elem e n t Vtb. T h e ra tio of th e m e a su re d cro ss-sectio n to th e th e o re tic a l p re d ic tio n is eq u a l to | / LVVtb | 2, w h ere th e form fa c to r / LV could b e m odified by new physics o r ra d ia tiv e c o rre c tio n s th ro u g h an o m alo u s co u p lin g c o n trib u tio n s , for ex a m p le th o se in refs. [3 , 91 , 92]. T h e W t p ro d u c tio n a n d to p -q u a rk decays th ro u g h |Vt s | a n d |Vtd | are assu m ed to b e sm all. A low er lim it on |Vtb| is o b ta in e d for / LV = 1 as in th e SM, w ith o u t assu m in g C K M u n ita r ity [5 , 93]. A n a d d itio n a l s y ste m a tic u n c e rta in ty d u e to a v a ria tio n o f th e to p -q u a r k m ass by 1 GeV is in clu d ed in th e Vtb e x tra c tio n . T h e u n c e rta in tie s o n th e th e o re tic a l cro ss-sectio n d u e to th e v a ria tio n of th e re n o rm a lisa tio n a n d fa c to ris a tio n scale (0.6 p b ), th e P D F u n c e rta in ty (1.4 p b ), a n d th e b e a m -e n e rg y u n c e rta in ty [94] (0.38 pb) a re also a c c o u n te d for.

T h e v alue for | / LVVtb| is e x tra c te d from th e | / LVVtb|2 likelihood, w hich is a ssu m ed to b e G a u ssia n . T h e low er lim it o n |Vtb|2 c o rre sp o n d s to 95% of th e in te g ra l o f th is likelihood,

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