Measurement of the double-differential high-mass Drell-Yan cross section in $\mathit{pp}$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector

(1)

Published fo r SISSA by Spr in g e r

Received: J u n e 7, 2016 A ccepted: J u ly 18, 2016 Published: A u g u s t 1, 2016

M e a s u r e m e n t o f t h e d o u b l e - d i f f e r e n t i a l h i g h - m a s s

D r e l l - Y a n c r o s s s e c t i o n i n p p c o l l i s i o n s a t √s = 8 T e V w i t h t h e A T L A S d e t e c t o r

T h e A T L A S c o l l a b o r a t i o n 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 : T h is p a p e r p re se n ts a m e a s u re m e n t o f th e d o u b le-d iffere n tia l cross sectio n for th e D rell-Y an Z /7 * ^ a n d p h o to n -in d u c e d 7 7 ^ t+ l~ processes w here I is an e le c tro n o r m uon. T h e m e a su re m e n t is p erfo rm ed for in v a ria n t m asses of th e le p to n p airs, m u , b etw e en 116 G eV a n d 1500 G eV u sin g a sam p le of 20.3 fb- 1 of pp collisions d a ta a t cen tre-o f-m ass en e rg y of y fs = 8 TeV collected by th e A TLA S d e te c to r a t th e LH C in 2012.

T h e d a t a a re p re se n te d d o u b le d iffe ren tially in in v a ria n t m ass a n d a b so lu te d ile p to n ra p id ity as well as in in v a ria n t m ass a n d a b so lu te p s e u d o ra p id ity s e p a ra tio n o f th e le p to n p air. T h e single-d ifferen tial cross sec tio n as a fu n c tio n o f m u is also re p o rte d . T h e e le c tro n a n d m u on c h a n n e l m e a su re m e n ts are co m b in ed a n d a to ta l e x p e rim e n ta l precisio n of b e t t e r th a n 1%

is achieved a t low m u . A co m p ariso n to n e x t-to -n e x t-to -le a d in g o rd e r p e r tu r b a tiv e Q C D p re d ic tio n s u sin g several re c e n t p a r to n d is trib u tio n fu n c tio n s a n d in clu d in g n e x t-to -le a d in g o rd e r electro w eak effects in d ic a te s th e p o te n tia l of th e d a t a to c o n s tra in p a r to n d is trib u tio n fu n c tio n s. In p a rtic u la r, a larg e im p a c t of th e d a t a o n th e p h o to n P D F is d e m o n s tra te d .

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: 1606.01736

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(2)

C o n te n ts

1 I n tr o d u c tio n 2

2 A T L A S d e t e c t o r 3

3 S im u la te d e v e n t s a m p le s 4

4 E v e n t s e le c tio n 5

4.1 E le c tro n c h a n n e l 5

4.2 M u o n ch a n n el 6

5 B a c k g r o u n d e s tim a t e 7

5.1 M u ltije t a n d W + je ts b a c k g ro u n d e s tim a te in th e e le c tro n ch a n n el 7 5.2 M u ltije t a n d W + je ts b a c k g ro u n d e s tim a te in th e m u o n c h a n n e l 11

6 C r o s s -s e c tio n m e a s u r e m e n t 12

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

7.1 E le c tro n c h a n n e l 13

7.1.1 M u ltije t a n d W + je ts b ac k g ro u n d 14

7.1.2 E n e rg y scale a n d re so lu tio n 15

7.1.3 R e c o n stru c tio n , id e n tific a tio n a n d iso latio n efficiency 15

7.1.4 T rig g er efficiency 16

7.2 M u o n ch a n n el 16

7.2.1 R e c o n s tru c tio n efficiency 16

7.2.2 M o m e n tu m scale a n d re so lu tio n 16

7.2.3 Iso la tio n a n d im p a c t p a r a m e te r efficiency 16

7.2.4 M u ltije t a n d W + je ts b ac k g ro u n d 16

7.2.5 T rig g er efficiency 17

7.3 S y ste m a tic u n c e rta in tie s co m m o n to b o th ch a n n els 17

7.3.1 T op a n d d ib o so n b a c k g ro u n d 17

7.3.2 L u m in o sity 18

7.3.3 M C s ta tis tic s a n d M C m o d ellin g 18

7.3.4 B in -b y -b in c o rre c tio n 18

7.3.5 P D F u n c e rta in ty 18

8 R e s u lts 18

9 C o m p a r iso n t o t h e o r e t ic a l p r e d ic tio n s 26

10 C o n c lu s io n 32

A T a b le s: s e p a r a te c r o ss s e c tio n s in t h e e le c tr o n a n d m u o n c h a n n e ls 33

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(3)

T h e A T L A S c o lla b o r a tio n 44

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

T h e D rell-Y an (D Y ) p rocess [1] o f le p to n p a ir p ro d u c tio n in h a d ro n ic in te ra c tio n s , p p ^ Z /y* + X w ith Z /y * ^ l + l - , is a pow erful to o l in u n d e rs ta n d in g th e n a tu r e of p a rto n ic in te ra c tio n s a n d of h a d ro n ic s tr u c tu r e in d e ta il. T h e s tu d y of th is p ro cess h as b ee n fu n d a m e n ta l in dev elo p in g th e o re tic a l p e r tu r b a tiv e c a lc u la tio n s of q u a n tu m ch ro m o d y n a m ic s (Q C D ) w hich a re now p erfo rm ed a t n e x t-to -n e x t-to -le a d in g -o rd e r (N N L O ) a c c u ra c y [2

5]. M e a su re m e n ts from th e L arg e H a d ro n C o llid er (L H C ) of n e u tra l- a n d c h a rg e d -c u rre n t D rell-Y an processes m e d ia te d by Z /y * a n d W ex ch an g e re sp ectiv ely a t cen tre-o f-m ass energ ies of y fs = 7 TeV a n d 8 TeV have b een recen tly pu b lish ed by th e A TLA S [6- 8], C M S [9- 12] a n d L H C b [13- 17] co lla b o ra tio n s. T h ese d a t a p ro v id e new c o n s tra in ts on th e p a r to n d is trib u tio n fu n c tio n s (P D F s ) of th e p ro to n , som e of w h ich have b een used in re cen t g lobal P D F fits [18- 20].

A lth o u g h on-shell Z a n d W boso n m e a su re m e n ts p ro v id e th e g re a te s t e x p e rim e n ta l p recision, th e y a re re s tric te d in th e k in e m a tic ra n g e o f p a rto n ic m o m e n tu m fra c tio n x, a n d fo u r-m o m e n tu m tra n s f e r Q = m ^ , th e in v a ria n t m ass o f th e d ile p to n p air. Off- shell m e a su re m e n ts p ro v id e c o m p le m e n ta ry c o n s tra in ts in a w id er ra n g e o f x a n d Q . In th e n e u tra l-c u rr e n t case, th e off-shell m e a su re m e n ts a re d o m in a te d by th e ele c tro m a g n e tic q u a rk couplings to th e v irtu a l p h o to n y*, w h e reas th e on -shell m e a su re m e n ts a re d o m in a te d by th e w eak ax ial a n d v e c to r co u p lin g s of th e q u a rk s to th e Z bo son . T h erefo re, th e m e a su re m e n ts have d ifferent se n sitiv ity to th e u p -ty p e a n d d o w n -ty p e q u a rk s. A t larg e m u th e m e a su re m e n ts offer c o n s tra in ts on th e larg e -x a n tiq u a r k P D F s w h ich a re p o o rly know n.

In a d d itio n , off-shell m e a su re m e n ts m ay also b e sen sitiv e to th e largely u n c o n stra in e d p h o to n P D F [7 , 8 , 2 1 , 22] th ro u g h th e p h o to n -in d u ce d (P I) process YY ^ l + l - .

N e u tra l-c u rre n t D Y d a t a a t h ig h er m asses c a n also b e used to d e te rm in e th e ru n n in g of th e electro w eak (E W ) gau g e co u p lin g s ab ove th e w eak scale, a n d to set m o d e l-in d e p e n d e n t lim its o n new s ta te s w ith electro w eak q u a n tu m n u m b e rs [23]. In p a rtic u la r, a t th e h ig h est in v a ria n t m asses accessible a t th e L H C , th e o b serv ed d ile p to n s p e c tru m m ay b e sen sitiv e to n ew physics, w hich could m an ife st itse lf as a re so n an ce o r a b ro a d m o d ificatio n to th e co n tin u u m s p e c tru m . Such searches p erfo rm ed by th e A T L A S a n d C M S e x p e rim e n ts [24- 26]

h av e so fa r n o t fo u n d an y significant d e v ia tio n s from th e S ta n d a rd M odel, a n d th e larg e st s y s te m a tic u n c e rta in ty o n th e deriv ed exclusion lim its arises from th e lack o f know ledge o f th e P D F s a t high x. Since a t lead in g o rd e r th e p a r to n m o m e n tu m fra c tio n s from th e tw o p ro to n s (1 or 2) are given by x 1,2 = ( m u / y / s ) e±W^£, w h ere y u is th e d ile p to n ra p id  ity, it c a n be seen t h a t th e larg e x regio n is accessible a t larg e m u in th e case o f c e n tra l p ro d u c tio n ( y ^ = 0), as well as a t low er m u a n d larg e y u . T h erefo re, a d o u b le-d iffere n tia l m e a s u re m e n t o f th e D rell-Y an cross sec tio n in m u a n d y u p rov id es P D F c o n s tra in ts in a n ew k in e m a tic reg ion w hich is e x p e c te d to b e u n affec te d by th e m a n ife sta tio n of p o te n tia l n ew physics a t th e h ig h est in v a ria n t m ass.

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(4)

T h is a rtic le re p o rts tw o inclusive d o u b le-d iffere n tia l cro ss-sectio n m e a su re m e n ts for th e p rocess p p ^ £+£- + X . T h e first m e a s u re m e n t is re p o rte d as a fu n c tio n o f m u an d a b so lu te d ile p to n ra p id ity |y££|, a n d th e second as a fu n c tio n of m u a n d a b s o lu te d ile p to n p se u d o ra p id ity s e p a ra tio n |A % £|. T h ese m e a su re m e n ts a re sen sitiv e to th e p ro to n P D F s, th e P I process, a n d h ig h e r-o rd e r electro w eak c o rrec tio n s, w h ich have d ifferen t k in e m a tic d ep e n d en cies. In p a rtic u la r, th e t-c h a n n e l P I p ro cess is e x p e c te d to c o n trib u te a t large

|A n ££|, sm all |y££| a n d larg e m u . T h erefo re, m e a su re m e n ts as a fu n c tio n o f v ario u s k in e m a tic d is trib u tio n s are n eed ed to d ise n ta n g le th e d ifferen t c o n trib u tio n s [27]. F o r co m p leten e ss th e inclusive single-differential m e a su re m e n t d a / d m ££ is also pro v id ed . T h e m e a su re m e n ts a re p erfo rm ed u sin g p p collision d a t a co llected a t y fs = 8 TeV in b o th electro n a n d m uon ch an n els. T h e d a t a cover th e k in e m a tic reg ion of 116 < m ££ < 1500 GeV a n d access p a rto n ic m o m e n tu m fra c tio n s from 10-3 u p to x ~ 1. T h e in te g ra te d lu m in o sity of th e d a ta sam p le is 20.3 fb - 1 , a fa c to r five la rg e r th a n u sed in th e p re v io u s A T L A S m e a su re m e n t [7]

a t ^ /s = 7 TeV p erfo rm ed in th e e le c tro n c h a n n el only. T h erefo re, th e re su lts re p o rte d here h ave a s u b s ta n tia lly b e tte r precisio n th a n ea rlie r re su lts.

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

T h e A T L A S d e te c to r [28] co n sists of a n in n e r tra c k in g 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, 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 a m u o n sp ec

tro m e te r (M S ). C h arg e d p a rtic le s in th e p s e u d o ra p id ity1 ran g e |n| < 2.5 are re c o n stru c te d w ith th e ID , w hich co n sists of layers of silicon pixel a n d m ic ro s trip d e te c to rs a n d a straw - tu b e tra n s itio n -ra d ia tio n tra c k e r h av in g coverage w ith in |n| < 2.0. T h e ID is im m ersed in a 2 T m a g n e tic field p ro v id ed by th e solenoid. T h e la t t e r is s u rro u n d e d by a h e rm e tic c a lo rim e te r t h a t covers |n| < 4.9 a n d p ro vides th re e -d im e n sio n a l re c o n s tru c tio n of p a rtic le show ers. T h e e le c tro m a g n e tic c a lo rim e te r is a liq u id -arg o n sa m p lin g c a lo rim e te r, w hich uses lead a b so rb e rs for |n| < 3.2 a n d c o p p e r a b so rb e rs in th e v ery fo rw ard region. T h e h a d ro n ic sa m p lin g c a lo rim e te r uses p la s tic s c in tilla to r tile s as th e ac tiv e m a te ria l a n d steel a b so rb e rs in th e region |n| < 1.7. In th e regio n 1.5 < |n| < 4.9, liqu id arg o n is used as ac tiv e m a te ria l, w ith c o p p e r o r /a n d tu n g s te n a b so rb e rs. O u tsid e th e c a lo rim e te rs, air-co re to ro id s s u p p ly th e m a g n e tic field for th e MS. T h e re , th re e s ta tio n s of precisio n c h a m b e rs allow th e a c c u ra te m e a su re m e n t of m u o n tra c k c u rv a tu re in th e reg ion |n| < 2.7. T h e m a jo rity of th e se p recisio n c h a m b e rs a re co m p o sed of d rift tu b e s , w hile c a th o d e -s trip c h a m b e rs p rov ide coverage in th e in n e r s ta tio n s of th e fo rw ard regio n fo r 2 .0 < |n| < 2.7. A d d itio n al m uon c h a m b e rs in sta lle d b etw e en th e in n e r a n d m id d le s ta tio n s of th e fo rw ard reg ion a n d co m m issioned p rio r to th e 2012 ru n im p ro ve m e a s u re m e n ts in th e tra n s itio n reg ion o f 1.05 <

|n| < 1.35 w h ere th e o u te r s ta tio n s h ave n o coverage. M u o n trig g e rin g is p o ssib le in th e ra n g e |n| < 2.4, using re sistiv e -p la te c h a m b e rs in th e c e n tra l regio n t h a t also p ro v id e a m ea

1ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the interaction point to the centre of the LHC ring, and the y-axis points upward. Cylindrical coordinates (r, 0) are used in the transverse plane, 0 being the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angle 6 as n = — ln tan (6 /2).

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(5)

su re m e n t of th e c o o rd in a te o u t of th e b e n d in g p lan e, a n d th in -g a p c h a m b e rs in th e fo rw ard region. A th ree-lev el trig g e r sy stem [29] selects ev en ts to be reco rd e d for offline an aly sis.

3 S i m u la t e d e v e n t s a m p le s

M o n te C arlo (M C ) sim u la tio n sam p les a re u sed to m o d el th e e x p e c te d sig nal a n d b ack g ro u n d yields, w ith th e ex c e p tio n of c e rta in d a ta -d riv e n b a c k g ro u n d e s tim a te s . T h e M C sam p les are n o rm alised usin g th e h ig h e st-o rd e r cro ss-sectio n p re d ic tio n s availab le in p e r

tu r b a tio n th eo ry .

T h e D Y p rocess is g e n e ra te d a t n e x t-to -le a d in g o rd e r (N L O ) u sin g P o w h e g [30- 33]

a n d th e C T 1 0 P D F [34], w ith P y t h i a 8 [35] to m odel p a rto n show ering a n d h a d ro n isa tio n . To e s tim a te sy s te m a tic u n c e rta in tie s in th e ev en t m o d ellin g a n a lte r n a tiv e sam p le is sim u la te d u sin g th e sam e P D F b u t th e M C @ N L O [36- 38] g e n e ra to r w ith H e r w i g + + [39].

T h e Z / y * d iffe ren tial cross sec tio n as a fu n c tio n of m ass h as b ee n c a lc u la te d a t n e x t-to - n e x t-to -le a d in g o rd e r (N N L O ) in p e r tu r b a tiv e Q C D (p Q C D ) u sin g F E W Z 3.1 [5, 40 , 41]

w ith th e M S T W 2 0 0 8 N N L O P D F [42]. T h e c a lc u la tio n in clu des N L O electro w eak (E W ) c o rre c tio n s b ey o n d fin a l-s ta te p h o to n ra d ia tio n (F S R ). A m a s s -d e p e n d e n t K -f a c to r used to scale th e Z /y * M C sam p le is o b ta in e d from th e ra tio o f th e c a lc u la te d N N L O p Q C D cross sec tio n w ith th e a d d itio n a l E W c o rrec tio n s, to th e cross sec tio n fro m th e P o w h e g sam p le. I t is fo u n d to d e v ia te from u n ity by 3 .5 -2 .0 % across th e m e a su re d ra n g e in m ^ .

T h e p h o to n -in d u c e d (P I) process, YY ^ l + l - , is sim u la te d a t le a d in g -o rd e r u sing P y t h i a 8 a n d th e M R S T 2004qed P D F [21]. T h e M C yield is scaled by a fa c to r of 0.7 in o rd e r to m a tc h th e N L O c a lc u la tio n s of SA N C [4 3 , 44].

T h e b a c k g ro u n d from t t p ro d u c tio n is th e d o m in a n t b a c k g ro u n d w ith iso lated p ro m p t le p to n s from electro w eak b o so n decays. I t is e s tim a te d a t N L O u sin g P o w h e g a n d th e C T 1 0 P D F , w ith P y t h i a 6 [45] for p a rto n show ering a n d h a d ro n isa tio n . T w o fu rth e r M C sam p les for t t a n d single to p (W t) p ro d u c tio n in a sso c ia tio n w ith a W b o so n a re m od elled by M C @ N L O a n d th e C T 1 0 P D F , w ith H e r w i g [4 6 , 47] for p a r to n show ering a n d h a d ro n isa tio n . T h e M C @ N L O t t sam p le is u sed for e s tim a tin g s y ste m a tic u n c e rta in tie s only.

T h e t t M C sam ples are n o rm alised to a cross sec tio n o f 0¾ = 253-15 p b for a to p -q u a rk m ass of 172.5 GeV. T h is is c a lc u la te d a t N N L O in Q C D in clu d in g re s u m m a tio n o f n ex t- to -n e x t-to -le a d in g lo g a rith m ic soft-g lu o n te rm s w ith T o p + + 2 . 0 [48- 53]. T h e P D F a n d a s u n c e rta in tie s o n th e t t cross sec tio n 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 [54]

w ith th e M S T W 2 0 0 8 68% CL N N L O [42, 55], C T 1 0 N N LO [3 4 , 56] a n d N N P D F 2 .3 [57]

P D F e rro r sets ad d e d in q u a d r a tu r e to th e scale u n c e rta in ty . V a ry in g th e to p -q u a r k m ass by ± 1 GeV leads to a n a d d itio n a l s y s te m a tic u n c e rta in ty o f + 8 p b a n d - 7 pb, w hich is also ad d e d in q u a d r a tu re . T h e sin g le-to p b a c k g ro u n d in a sso c ia tio n w ith a W b o so n h as a cross sec tio n of a w t = 22.4 ± 1.5 p b [58]. G iven t h a t th e W t c o n trib u tio n is sm all c o m p a re d to th e t t cross sectio n , a n overall u n c e rta in ty of 6% is e s tim a te d on th e to p -q u a rk b ackg ro und .

F u r th e r im p o rta n t b a c k g ro u n d c o n trib u tio n s are d u e to d ib o so n ( W W , W Z a n d Z Z ) p ro d u c tio n w ith d ecays to final s ta te s w ith a t least tw o lep to n s. T h e d ib o so n processes a re g e n e ra te d a t lead in g o rd e r (LO ) w ith He r w ig, usin g th e C T E Q 6 L 1 P D F [59]. T h e W Z a n d Z Z cro ss-sectio n values used are 20.3 ± 0.8 p b a n d 7.2 ± 0.3 p b respectively, as

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(6)

Process G enerator P arton shower G enerator P D F Model param eters ( “Tune” )

Drell-Yan P o w h e g P y t h i a 8.162 CT10 AU2 [67]

Drell-Yan M C@ NLO 4.09 H e r w ig + + 2.6.3 CT10 UE-EE-3 [39]

PI P y t h i a 8.170 P y t h i a 8.170 MRST2004qed 4C [68]

tt P o w h e g P y t h i a 6.427.2 CT10 AUET2 [69]

tt M C@ NLO 4.06 H e rw ig 6.520 CT10 AUET2

W t M C@ NLO 4.06 H e rw ig 6.520 CT10 AUET2

Diboson H e rw ig 6.520 H e rw ig 6.520 CTEQ6L1 AUET2

T a b le 1. Overview of sim ulated event samples used.

c a lc u la te d a t N L O w ith M C F M [6 0 , 61] a n d th e C T 1 0 P D F . T h e W W cross sec tio n is assu m ed to be 70.4 ± 7 p b , d eriv e d by scaling th e M C F M value of 58.7 p b by a fa c to r of 1.20 ± 0.12. T h is scale fa c to r a n d its u n c e rta in ty co rre sp o n d to a n a p p ro x im a te m ean o f th e tw o scale fa c to rs for W W p ro d u c tio n w ith zero a n d one e x tr a je t, as d iscu ssed in ref. [62].

T h e y a re c o n siste n t w ith th e re c e n t A T L A S m e a su re m e n t of th e W W cross sec tio n a t v 's = 8 TeV, w hich yields a value of 71.1 ± 1.1 (s ta t) (sys) ± 1 .4 p b [63].

All M C sam p les used in th e an a ly sis in clu d e th e effects of F S R , m u ltip le in te ra c tio n s p e r b u n c h crossing ( “p ile -u p ” ) , a n d d e te c to r sim u la tio n . F S R is sim u la te d u sin g P h o t o s [64], ex c e p t for sam ples h a d ro n ise d by H e r w i g + + w h ich inclu des a n a tiv e F S R sim u la tio n . T h e effects of p ile-u p are a c c o u n te d for by o verlaying s im u la te d m in im u m -b ias ev e n ts [65].

T h e in te ra c tio n s of p a rtic le s w ith th e d e te c to r are m o d elled u sin g a full A T L A S d e te c to r sim u la tio n [65] b ase d on G e a n t 4 [66]. F inally, several co rrectio n s are applied to th e sim u la te d sam p les, a c c o u n tin g for differences b etw e en d a t a a n d sim u la tio n in th e le p to n trig g e r, re c o n stru c tio n , id en tificatio n , a n d iso la tio n efficiencies as well as le p to n re so lu tio n a n d m u o n m o m e n tu m scale.

A n overview of th e sim u la te d ev en t sam p les is given in ta b le 1 .

4 E v e n t s e l e c t i o n

E v e n ts are re q u ired to b e reco rd e d d u rin g s ta b le b e a m c o n d itio n p e rio d s a n d m u st pass d e te c to r a n d d a ta - q u a lity re q u ire m e n ts. D u e to differences in th e d e te c to r re sp o n se to e le c tro n s a n d m uons th e selectio n is o p tim ise d s e p a ra te ly for each c h a n n e l a n d is d esc rib ed in th e follow ing.

4 .1 E le c tr o n c h a n n e l

T h e e le c tro n d a ta are co llected by a trig g e r w hich uses c a lo rim e tric in fo rm a tio n to id en tify tw o c o m p a c t e le c tro m a g n e tic en e rg y d e p o sitio n s. Id e n tific a tio n a lg o rith m s use c a lo rim e te r show er sh a p e in fo rm a tio n to find c a n d id a te e le c tro n p a irs w ith a m in im u m tra n s v e rs e en e rg y of 35 GeV a n d 25 GeV for th e lead in g a n d s u b le a d in g elec tro n . T h e c a n d id a te e le c tro n p a irs are n o t m a tc h e d to in n e r d e te c to r tra c k s in th e trig g e r allow ing th e sam e trig g e r to b e u sed for th e m u ltije t a n d W + je ts d a ta -d riv e n b a c k g ro u n d e s tim a tio n stu d ies, w h ere a b a c k g ro u n d -e n ric h e d sam p le is re q u ired .

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(7)

E le c tro n s a re re c o n s tru c te d by c lu s te rin g en e rg y d e p o s its in th e ele c tro m a g n e tic c a lo rim e te r u sin g a sliding-w indow alg o rith m . T h ese c lu ste rs are th e n m a tc h e d to tra c k s re c o n s tru c te d in th e in n e r d e te c to r. T h e c a lo rim e te r p ro vides th e en e rg y m e a su re m e n t an d th e tra c k is used to d e te rm in e th e a n g u la r in fo rm a tio n of th e e le c tro n tra je c to ry . A n en erg y scale c o rre c tio n d e te rm in e d from Z ^ e + e - , W ^ e v , a n d J / 0 ^ e + e - decays [70] is a p p lied to d a ta . C a n d id a te s are re q u ire d to have a p s e u d o ra p id ity w ith in th e in n e r d e te c to r tra c k in g region, |n e | < 2.47, ex c lu d in g a region, 1.37 < |n e | < 1.52, w h ere th e tra n s itio n b etw e en th e b a rre l a n d e n d c a p e le c tro m a g n e tic c a lo rim e te rs is n o t well m o d elled in th e sim u la tio n . E a c h c a n d id a te is re q u ired to satisfy th e “m e d iu m ” e le c tro n id en tific a tio n [7 1 , 72]

c r ite ria b ase d on c a lo rim e tric show er sh ap e s a n d tra c k p a ra m e te rs .

L e p to n s p ro d u c e d in th e D rell-Y an p ro cess a re e x p e c te d to b e well iso la te d from en e rg y d e p o sitio n s n o t a sso c ia te d w ith th e lep to n . T h e deg ree o f iso la tio n for ele c tro n s is defined as th e sc a la r sum of tra n s v e rs e energy, ^ E t , o f a d d itio n a l en e rg y c o n ta in e d in a con e of size A R = ( A ^ )2 + (A n )2 a ro u n d th e electron, o m ittin g th e elec tro n tra n sv e rse energy E f . T h is c a lo rim e tric iso la tio n is re q u ire d to sa tisfy E t (A R = 0.4) < 0.007■ E f + 5 GeV fo r th e lead in g elec tro n , a n d E t (A R = 0.4) < 0.022 ■ E f + 6 GeV for th e su b lead in g elec tro n , in o rd e r to re ta in a h ig h efficiency of a p p ro x im a te ly 99% p e r e le c tro n over a large ra n g e in E f .

C a n d id a te ev e n ts are re q u ired to hav e a t le a st tw o e le c tro n s w ith E f > 30 GeV an d a t least one of th e e lec tro n s satisfy in g E f > 40 GeV to e n su re th e selected e le c tro n is on th e efficiency p la te a u o f th e trig g e r. T h e in v a ria n t m ass o f th e p a ir is re q u ired to b e in th e ra n g e 116 < m ee < 1500 GeV. T h e a b so lu te d ifference in p s e u d o ra p id ity b etw e en th e tw o elec tro n s, |A n ee|, is re s tric te d to be less th a n 3.5 in o rd e r to su p p re ss th e m u ltije t b a c k g ro u n d w hich is d o m in a te d by t-c h a n n e l p rocesses. N o ch a rg e re q u ire m e n ts a re p laced o n th e le p to n p a ir d u e to p o ssible ch a rg e m isid e n tific atio n , w hich c a n o cc u r e ith e r d u e to b re m ss tra h lu n g , o r d u e to th e lim ite d m o m e n tu m re so lu tio n of th e ID a t v ery high p f . 4 .2 M u o n c h a n n e l

C a n d id a te ev e n ts in th e m u o n ch a n n el are co llected u sin g tw o trig g e rs, each re q u irin g a single m uon, b u t w ith differen t tra n s v e rs e m o m e n tu m th re sh o ld s as m easu red in th e h igher-level trig g e r sy stem . A h ig h -th re sh o ld trig g e r d e m a n d s t h a t th e m u o n tra n s v e rs e m o m e n tu m be above 36 GeV a n d co llects m o st o f th e d a t a sam p le. A s u p p le m e n ta ry lo w -th re sh o ld trig g e r re q u ires a n iso lated m u o n w ith tra n s v e rs e m o m e n tu m ab o v e 24 GeV.

T h e iso la tio n for m uons is defined u sin g th e sc a la r sum o f tra n s v e rs e m o m e n ta , p f , of a d d itio n a l tra c k s d iv id ed by p f , th e tra n s v e rs e m o m e n tu m of th e m uon. T h is p ro v id es a g o o d d isc rim in a n t a g a in st th e m u ltije t b a c k g ro u n d arisin g from th e sem ilep to n ic decays o f h ea v y q u a rk s. T h is iso latio n d e fin itio n is im p le m e n te d in th e lo w -th re sh o ld trig g e r in w hich th e c a n d id a te m uo ns a re re q u ire d to satisfy p f (A R = 0 . 2 ) / p f < 0.12.

M uons a re iden tified by tra c k s re c o n s tru c te d in th e m u o n s p e c tro m e te r m a tc h e d to tra c k s re c o n s tru c te d in th e in n e r d e te c to r a n d m u st satisfy |n^| < 2.4. In a d d itio n th e y m u st p ass th e “m e d iu m ” id e n tific a tio n c r ite ria [73], b ase d o n re q u ire m e n ts on th e n u m b e r o f h its in th e d ifferent in n e r d e te c to r a n d m u o n s p e c tro m e te r su b sy stem s, as well as th e significance of th e ch a rg e / m o m e n tu m ra tio im b alan ce b etw e en th e ID a n d M S m e a su re

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(8)

m en ts. B a c k g ro u n d from m u ltije t ev en ts is efficiently su p p re sse d by im p o sin g th e iso latio n c o n d itio n P t ( A R = 0 .2 )/p T < 0.1. A sm all c o n trib u tio n of cosm ic-ray m u on s is re

m oved by re q u irin g th e m a g n itu d e of th e lo n g itu d in a l im p a c t p a r a m e te r to th e p rim a ry in te ra c tio n v erte x , z 0, to b e less th a n 10 m m . T h e p rim a ry in te ra c tio n v e rte x is ta k e n to b e th e one w ith th e la rg e st sum of sq u a re d tra n s v e rs e m o m e n ta of all a sso c ia te d tra c k s.

E v e n ts a re selected if th e y c o n ta in a t least tw o o p p o site ly c h a rg ed m uo ns w ith pT >

30 GeV a n d a t le a st one o f th e m uon s satisfies pT > 40 GeV in o rd e r to h ave th e sam e p h a se space as in th e e le c tro n ch a n n e l m e a su re m e n t. F in a lly th e d ile p to n in v a ria n t m ass is re q u ire d to be in th e ra n g e 116 < m w < 1500 GeV. N o re q u ire m e n t is p laced o n |A n w |.

5 B a c k g r o u n d e s t i m a t e

T h e b a c k g ro u n d from p rocesses w ith tw o o r m ore iso lated fin a l-s ta te lep to n s of th e sam e flavo ur is d eriv e d from M C sim u la tio n . T h e processes w ith n o n-n eg ligible c o n trib u tio n s a re tt, W t (h e re a fte r te rm e d th e to p -q u a r k b a c k g ro u n d ) a n d d ib o so n ( W W , W Z a n d Z Z ) p ro d u c tio n , see ta b le 1. T h e b a c k g ro u n d arisin g from th e Z / y * ^ t t p ro cess is p re d ic te d u sin g M C sim u la tio n a n d fo u n d to be negligible.

B a c k g ro u n d c o n trib u tio n s fro m ev en ts w h ere a t least one fin a l-s ta te je t o r p h o to n passes th e e le c tro n or m u o n selectio n c r ite ria are d e te rm in e d u sin g d a ta . T h is includ es co n tr ib u tio n s from light- a n d heavy -flav o u r m u ltije t processes, a n d y + je t p ro d u c tio n , referred to h e re a fte r as th e m u ltije t b a c k g ro u n d . A d d itio n a l c o n trib u tio n s a re d u e to W + j e t s p ro cesses a n d t t a n d W t p ro d u c tio n w ith less th a n tw o iso lated fin a l-s ta te lep to n s, re ferred to h e re a fte r as W + j e t s b ac k g ro u n d . T h e d a ta -d riv e n e s tim a te s are d e sc rib e d in d e ta il below .

T h e n u m b e r of e x p e c te d ev en ts is c a lc u la te d as th e su m o f th e d a ta -d riv e n a n d sim u

la te d b a c k g ro u n d e stim a te s, a n d th e e x p e c te d ev en t yield p re d ic te d by th e D Y a n d P I M C sim u la tio n s. As c a n be seen in figures 1- 5 , g o o d a g reem en t is fo u n d in b o th th e ee an d p p c h a n n els co m p a rin g d a t a a n d e x p e c ta tio n for th e p£ a n d pT d is trib u tio n s of th e lep  to n s, as well as for th e d is trib u tio n s in in v a ria n t m ass, ra p id ity a n d A p u . T h e b a c k g ro u n d c o n trib u tio n s are stack e d in o rd e r of in cre asin g im p o rta n c e . In th e e le c tro n ch a n n el th e to p -q u a rk , m u ltije t a n d d ib o so n c o n trib u tio n s to th e e x p e c ta tio n a re fo u n d to b e a p p ro x i

m a te ly 9%, 4% a n d 2% re sp ectiv ely in th e p h a se sp ace o f th e m e a su re m e n t. In th e m uo n c h a n n e l th e to p -q u a rk a n d d ib o so n b a c k g ro u n d s c o n s titu te a b o u t 9% a n d 2% o f th e to ta l e x p e c ta tio n , w h e reas th e m u ltije t c o n trib u tio n is below 1% ev eryw h ere. T h e p re d ic te d P I c o n trib u tio n is 1% for b o th chann els b u t ca n reach as m uch as 16% in th e bin a t high est m u a n d larg e st A p u .

5.1 M u ltije t a n d W + j e t s b a c k g r o u n d e s tim a t e in t h e e le c tr o n c h a n n e l

T h e p ro b a b ility t h a t a je t is m isid en tified as a n e le c tro n (th e “fake r a te ” ) is d e te rm in e d as a fu n c tio n o f tra n s v e rs e energy, E T a n d p se u d o ra p id ity , n, of th e e le c tro n c a n d id a te u sin g b ac k g ro u n d -e n rich ed d a t a sam p les. T h ese sam p les are reco rd e d u sin g a set o f single

je t trig g e rs w ith E T th re s h o ld s in th e ra n g e 2 5 -3 6 0 GeV. In each o f th e s e sam ples, th e fake ra te f \ ( f2) is c a lc u lated as th e fractio n of leadin g (sub leading ) electro n c a n d id a te s t h a t pass th e n o m in al e le c tro n id en tific a tio n a n d lead in g (su b lea d in g ) e le c tro n iso latio n

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(9)

F ig u r e 1. D istribution of electron pseudorapidity r/e (upper plots) and transverse energy E f (lower plots) for invariant masses m ee > 116 GeV (left plots), and m ee > 300 GeV (right plots), shown for d a ta (solid points) and expectation (stacked histogram ) after the complete selection. The lower panels show the ratio of d a ta w ith its statistical uncertainty to the expectation.

re q u ire m e n ts, w ith re s p e c t to th e e n tire sam p le of “loose” e le c tro n c a n d id a te s. T h e loose c a n d id a te s sa tisfy o nly a su b se t of th e n o m in al e le c tro n id e n tific a tio n c rite ria . To re je ct p ro m p t-e le c tro n c o n trib u tio n s from W d ecays o r th e D Y process, ev en ts a re v eto ed in th e follow ing cases: if th e m issing tra n s v e rs e m o m e n tu m [74] is la rg e r th a n 25 GeV, if th e y c o n ta in tw o iden tified ele c tro n s sa tisfy in g s tric t c r ite ria o r if th e y c o n ta in tw o elec tro n s sa tisfy in g less s tric t c r ite ria b u t w ith a n in v a ria n t m ass b etw e en 71 GeV a n d 111 GeV. A w eig h ted av erag e of th e fake ra te s o b ta in e d from th e j e t sam p les is th e n c a lc u la te d .

In a d d itio n to th e fake ra te , th e p ro b a b ility r1 ( r 2) t h a t a p ro m p t electro n in th is loose selectio n satisfies th e n o m in a l e le c tro n id e n tific a tio n a n d lead in g (su b lea d in g ) iso latio n re q u ire m e n ts is used in e v a lu a tin g th is b ac k g ro u n d . T h is p ro b a b ility is ta k e n from th e M C sim u la tio n as a fu n c tio n of E t a n d n. P o te n tia l differences b etw e en d a t a a n d s im u la te d sam p les in le p to n id e n tific a tio n an d iso la tio n efficiencies are a c c o u n te d for by a p p ly in g scale fa c to rs [72] to th e sim u la tio n , w hich a re g en e rally close to unity.

A sy stem of e q u a tio n s is used to solve for th e u n k n o w n c o n trib u tio n to th e b a c k g ro u n d fro m ev e n ts w ith one o r m o re fake e le c tro n s in th e sam p le trig g e re d w ith th e d e fa u lt analy sis trig g e r. T h e re la tio n b etw e en th e n u m b e r of tr u e p a ire d o b je c ts N ab, w ith E f > E f an d

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(10)

F ig u r e 2. D istribution of muon pseudorapidity (upper plots) and transverse m om entum pT (lower plots) for invariant masses m MM > 116 GeV (left plots), and m MM > 300 GeV (right plots), shown for d ata (solid points) and expectation (stacked histogram ) after the complete selection. The lower panels show the ratio of d a ta with its statistical uncertainty to the expectation.

F ig u r e 3. The invariant mass (m « ) distribution after event selection for the electron selection (left) and muon selection (right), shown for d a ta (solid points) com pared to the expectation (stacked his

togram ). The lower panels show the ratio of d a ta with its statistical uncertainty to the expectation.

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(11)

F ig u r e 4. D istribution of absolute dielectron rapidity |yee| (upper plots) and absolute dielectron pseudorapidity separation |A nee| (lower plots) for invariant mass m ee > 116 GeV (left plots), and m ee > 300 GeV (right plots), shown for d a ta (solid points) and expectation (stacked histogram ) after the complete selection. The lower panels show the ratio of d a ta w ith its statistical uncertainty to the expectation.

a, b € {R, F }, and th e num ber of m easured pairs N xy , w ith x, y € {T, L}, can be w ritte n as:

( N^{t t}^ N^{t l} N^{l t}

(

_{r i r}₂

r i(1 - r 2) (1 - r i ) r 2

r i^{/ 2} r i (1 - /2) (1 - r i ) f 2

/ i r2 f i(1 - r 2) (1 - f i ) r 2

/ i/2 / i(1 - / 2) (1 - / i )/2

^ ^ Nr r^ N^{r f} N^{f r}

\ N^{l l}J \ ( 1 - r i)(1 - r²) (1 - r i) (1 - /²) (1 - / i) ( 1 - ^ ) (1 - / i ) ( 1 - /²) / \ N^{f f}J (5.1) T he subscripts R and F refer to pro m p t electrons and fake electrons (jets) respectively.

T he subscript T refers to electrons th a t pass th e nom inal selection. T he subscript L corresponds to electrons th a t pass th e loose requirem ents described above b u t fail th e nom inal requirem ents.

T he background originating from pairs of objects w ith a t least one fake electron (NTTultljet&W+jets) in th e to ta l num ber of pairs, w here b o th objects are reco n structed as signal-like (i.e. c o n trib u te to N TT) is given by:

NTTultljet&W+jets = r i /2NRF + / i r 2 Nf r + / i /2N f f . (5.2)

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(12)

F ig u r e 5. D istribution of absolute dimuon rapidity |yMM| (upper plots) and absolute dimuon pseudorapidity separation |AnMM| (lower plots) for invariant mass m MM > 116 GeV (left plots), and m MM > 300 GeV (right plots), shown for d a ta (solid points) and expectation (stacked histogram ) after the complete selection. T he lower panels show the ratio of d a ta w ith its statistical uncertainty to the expectation.

T he num ber of tru e paired objects on th e right-hand side of equation ( 5.2) can be expressed in term s of m easurable q u antities (N TT, N TL, N LT, N LL) by inverting th e m atrix in equ atio n (5.1) . T he n o rm alisation and shape of th e background in each variable of interest are au to m atically derived by using th e m easurable q u an tities as a function of th a t same variable. T he estim ated m u ltijet background over th e full invariant m ass range is found to be ab o u t 3%.

5 .2 M u ltije t a n d W + j e t s b a c k g r o u n d e s tim a t e in t h e m u o n c h a n n e l

T he m ultijet background rem aining after th e com plete event selection in th e m uon chan

nel is largely due to heavy flavour b- and c-quark decays, and is estim ated using a d a ta - driven technique in two s-eps-converted-to.pdf. T his m eth od also accounts for any p o ten tial W + je ts background, however, th e co n trib u tio n of this com ponent is expected to be negli

gible. F irst th e n o rm alisation of th e m u ltijet background in each m w bin is determ ined, and th e n th e shape in th e |yw | and in |A nw | variables is estim ated.

T he background in each invariant m ass region is determ ined using th re e orthogo

nal control regions w ith inverted m uon isolation requirem ents, a n d /o r inverted m uon-pair

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(13)

ch a rg e re q u ire m e n ts. T h e tw o v aria b les are larg ely u n c o rre la te d for th e m u ltije t b ac k g ro u n d . In each c o n tro l region th e c o n ta m in a tio n fro m signal, to p -q u a rk , a n d d ib o so n b a c k g ro u n d is s u b tra c te d usin g sim u la tio n . T h e yield of m u ltije t ev e n ts in th e sign al re gion is p re d ic te d u sin g th e c o n s tra in t t h a t th e yield ra tio o f o p p o site -c h a rg e to sam e-ch arg e m u o n p a irs is id e n tic a l in th e iso la te d a n d n o n -iso lated regions. A co m p ariso n o f th e iso

la tio n d is trib u tio n for m uons in ev e n ts w ith e ith e r sam e-ch arg e a n d o p p o site -c h a rg e m uo n p a irs show s a sm all lin e a r d e v ia tio n of u p to 10% w hen e x tra p o la te d in to th e iso lated sig

n al region. T h is is fo u n d to b e in d e p e n d e n t of m w , a n d is c o rre c te d for. F o r th e region m w > 500 GeV th e re a re insufficient sam e-ch arg e iso lated m u o n p a irs to give a reliab le e s tim a te . T h erefo re, th e b a c k g ro u n d yield in th e regio n m w < 500 GeV is fitte d to tw o a lte r n a tiv e fu n c tio n a l form s a n d e x tra p o la te d to la rg e r m w w h ere th e av erag ed p re d ic tio n is ta k e n as th e e s tim a te of th e b a c k g ro u n d yield. T h e |yw | a n d |A ^ W | d e p e n d e n c e of th e b a c k g ro u n d in each m w region is o b ta in e d from a m u ltije t-e n ric h e d d a t a c o n tro l regio n in w hich p a irs of sam e-ch arg e a n d o p p o site -c h a rg e m uo ns sa tisfy ^ p T ( A R = 0 .2 )/p T > 0.1.

Signal, to p -q u a r k a n d d ib o so n c o n ta m in a tio n in th is c o n tro l reg ion is s u b tra c te d u sin g M C sim u la tio n . T h e re s u ltin g |yw | a n d |A ^ W | s p e c tr a in each m w regio n are n o rm alised to th e yield o b ta in e d in th e first step . F o r m w > 500 GeV th e |yw | o r |A ^ W | sh a p e is ta k e n from th e region 300 < m w < 500 GeV. O v erall th e to ta l m u ltije t b a c k g ro u n d varies from 1% to 0.1% over th e co m p lete in v aria n t m ass range.

6 C r o s s - s e c t i o n m e a s u r e m e n t

T h e D rell-Y an cross sectio n, in clu d in g th e irre d u cib le c o n trib u tio n from th e P I process, is m e a su re d d iffe ren tially in 12 bins of m u from 116 G eV to 1500 G eV , as well as double- d iffe ren tially in five bins of m u as a fu n c tio n of |y ^ | a n d |A % ^|. T h e re su lts are p re se n te d in th e fiducial region of th e m e a su re m e n t, in w hich th e lead in g (su b lea d in g ) le p to n has a pT > 40 G eV (pT > 30 G eV ) a n d b o th le p to n s are w ith in |p^| < 2.5. T h e k in e m a tic v aria b les are defined by th e lep to n s b efore F S R , i.e. th e re s u lts are given a t th e B o rn - level in Q E D . R e su lts a t th e “d re sse d ” level, w h ere lep to n s a fte r F S R are re co m b in ed w ith ra d ia te d p h o to n s w ith in a cone of A R = 0.1, are o b ta in e d by m u ltip ly in g th e B orn-level re su lts w ith th e d re sse d c o rre c tio n fa c to rs kdressed, p ro v id ed in ta b le s 6- 11 in th e ap p e n d ix . T h ese c o rre c tio n fa c to rs are o b ta in e d from th e P o w h e g a n d P y t h i a 8 M C sam ples for th e D Y a n d P I processes, respectively.

T h e d o u b le-d iffere n tia l cross sec tio n as a fu n c tio n o f in v a ria n t m ass a n d ra p id ity is c a lc u la te d as

d 2a = Ndata - Nbkg 1 (6 1)

d m « A V tA C DY L int A mu 2A |y«| ’

w h ere N data is th e n u m b e r of c a n d id a te ev en ts o b serv ed in a given b in o f m u a n d |y ^ | of w id th A TO££ a n d A |y££| respectively. T h e t o ta l b a c k g ro u n d in t h a t b in is d e n o te d as N bkg a n d L int is th e in te g ra te d lum ino sity. T h e fa c to r of tw o in th e d e n o m in a to r a c c o u n ts for th e m o d u lu s in th e ra p id ity b in w id th . T h e d o u b le-d iffere n tia l cross sec tio n as a fu n c tio n o f m ass a n d |A p ^ | a n d th e sing le-differential m e a su re m e n t as a fu n c tio n of in v a ria n t m ass a re d efined accordingly.

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(14)

T h e fa c to r, Cdy , ta k e s in to a c c o u n t th e efficiency o f th e signal selectio n a n d b in m i

g ra tio n effects. I t is defined as th e n u m b e r o f M C g e n e ra te d ev en ts t h a t p ass th e signal selectio n in a c e rta in m e a su re m e n t b in c a lc u la te d from th e re c o n s tru c te d le p to n k in em atics d iv id ed by th e to ta l n u m b e r of g e n e ra te d ev e n ts w ith in th e fid ucial region, in th e c o rre sp o n d in g bin, c a lc u la te d from B o rn-level o r d ressed -lev el le p to n k in em atics. It is o b ta in e d from th e D rell-Y an a n d P I M C sam p les a fte r c o rre c tio n for differences in th e re c o n s tru c tio n , id en tificatio n , trig g e r, a n d iso latio n efficiencies b etw e en d a t a a n d sim u la tio n , as well as for m o m e n tu m scale a n d re so lu tio n m ism o d e llin g effects. In g en e ral th e Cdy fa c to rs are fo u n d to b e in th e ra n g e 6 0-80% across th e m e a su re d k in e m a tic ran ge.

T h e C DY fa c to r also includ es e x tra p o la tio n s over th e sm all regions t h a t are ex clu ded for re c o n s tru c te d e le c tro n (1.37 < |n e | < 1.52 a n d 2.47 < |n e | < 2.5) o r m u o n (2.4 <

| < | < 2.5) c a n d id a te s . In th e e le c tro n ch a n n el, th e fiducial cross sec tio n m e a su re m e n ts as a fu n c tio n of m ee a n d |yee|, a n d th e sing le-differential m e a su re m e n t, a re e x tra p o la te d over th e u n m e a su re d region |A r ee| > 3.5. T h e e x tra p o la tio n c o rre c tio n is in clu d ed in th e C DY fa cto r. N o such e x tra p o la tio n is re q u ire d for th e d o u b le-d iffere n tia l m e a su re m e n t as fu n c tio n of m ass a n d |A r ee| w hich only e x te n d s to |A r ee | = 3.

T h e B orn-level b in p u rity is defined as th e fra c tio n o f re c o n s tru c te d M C signal ev e n ts in a given b in w hich w ere also g e n e ra te d in th e sam e b in u sin g B orn-lev el le p to n k in em atics.

A n a n a la g o u s d efin itio n is used for th e d ressed-lev el b in p u rity . T h e b in p u ritie s are fo u n d to b e ty p ic a lly above 85%, a n d abo v e 75% ev eryw here. T h is en su res t h a t th e b in m ig ra tio n effects are sm all, a n d th e c o rre c tio n s a p p lie d to ac c o u n t for b in m ig ra tio n s have sm all u n c e rta in tie s .

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

T h e sy ste m a tic u n c e rta in tie s o n th e m e a su re m e n ts are discu ssed s e p a ra te ly for th o se sources w hich arise o n ly in th e e le c tro n ch a n n el, th o se w hich arise o n ly in th e m u o n c h a n nel, a n d th o se w hich are co m m o n to b o th m e a su re m e n ts. In each sec tio n th e sources are discu ssed in o rd e r o f im p o rta n c e , w ith th e la rg e st sources o f u n c e rta in ty liste d first. E a c h so urce is classified as b ein g c o rre la te d o r u n c o rre la te d b etw e en m e a s u re m e n t b in s in a single ch a n n el. T h e u n c o rre la te d sources a re p ro p a g a te d u sin g th e p se u d o -e x p e rim e n t m e th o d in w hich th e c o rre c tio n fa cto rs u sed to im prov e th e m o d ellin g o f d a t a by th e sim u la tio n a re ra n d o m ly sh ifted in an ensem b le of p seu d o -e x p e rim e n ts ac co rd in g to th e m e a n an d s ta n d a r d d e v ia tio n of th e c o rre c tio n fa c to r. T h e re s u ltin g u n c e rta in ty o n th e m easu red cross sec tio n is d e te rm in e d from th e v a ria n c e o f th e m e a su re m e n ts for th e ensem ble. T h e c o rre la te d c o n trib u tio n s are p ro p a g a te d by th e offset m e th o d in w hich th e values from each so urce are c o h e re n tly sh ifted u p w a rd s a n d d o w n w ard s by on e s ta n d a r d d e v ia tio n a n d th e m a g n itu d e of th e ch a n g e in th e m e a su re m e n t is c o m p u te d . T h e sign o f th e u n c e rta in ty c o rre sp o n d s to a o ne s ta n d a r d d e v ia tio n u p w a rd sh ift of th e u n c e rta in ty source.

7.1 E le c tr o n c h a n n e l

T h e s y s te m a tic u n c e rta in tie s o n th e cross sec tio n t h a t are u n iq u e to th e e le c tro n c h a n nel are d o m in a te d by th e u n c e rta in tie s in th e d e te r m in a tio n o f th e m u ltije t a n d W + je ts

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(15)

b a c k g ro u n d d e sc rib e d in sec tio n 5 .1 , a n d in th e e le c tro n en e rg y scale. In a d d itio n , a larg e c o n trib u tio n to th e u n c e rta in ty also arises from th e to p -q u a rk a n d d ib o so n b a c k g ro u n d s u b tra c tio n , a n d is discu ssed in sec tio n 7 .3 .

A ll c o rre la te d a n d u n c o rre la te d c o n trib u tio n s to th e s y s te m a tic u n c e rta in tie s a re given in each b in of th e m e a su re m e n t in ta b le s 6 , 7 , a n d 8 of th e ap p en d ix .

7 .1 .1 M u ltije t a n d W + j e t s b a c k g r o u n d

In o rd e r to d eriv e th e u n c e rta in ty o n th e d a ta -d riv e n b a c k g ro u n d e s tim a te d e sc rib e d in sec tio n 5 .1 , th e d e fa u lt “m a trix m e th o d ” is a lte re d by a ssu m in g n = r2 = 1. T h is second m a tr ix m e th o d leads to a sim p lifica tio n o f th e m a trix in e q u a tio n ( 5.1) , b u t also n e c e ssita te s th e use of M C c o rre c tio n s to ac c o u n t for th e id e n tific a tio n a n d iso latio n inefficiencies o f real e lec tro n s. L arg e M C c o rre c tio n s c a n be avoided in a th ir d m a trix m e th o d w h ere th e c o n ta m in a tio n from re al e le c tro n s is red u ced . T h e s u b s c rip t L in e q u a tio n ( 5.1) now c o rresp o n d s to e lec tro n s t h a t p ass th e loose re q u ire m e n ts b u t fail th e re q u ire m e n t on th e m a tc h in g b e tw ee n tra c k a n d c lu ste r, in s te a d of failing th e full id en tific a tio n a n d iso la tio n re q u ire m e n ts.

In a d d itio n , tw o a lte r n a tiv e b a c k g ro u n d -e n ric h e d sam p les a re o b ta in e d u sin g a ta g -a n d - p ro b e te c h n iq u e on th e je t-trig g e re d sam p le a n d o n th e sam p le trig g e re d by th e d e fa u lt an a ly sis trig g ers, re q u irin g th e ta g to fail c e rta in a s p e c ts o f th e e le c tro n id en tific a tio n d e

p e n d in g on th e trig g e r. F u rth e rm o re , th e ev en t sh o u ld have a m issin g tra n s v e rs e m o m e n tu m sm aller th a n 25 G eV , th e p ro b e need s to have th e sam e c h a rg e as th e ta g a n d th e in v a ria n t m ass of th e ta g -a n d -p ro b e p a ir needs to b e o u ts id e th e Z m ass w indow from 71 to 111 G eV .

T h e d e fa u lt a n d th e tw o a d d itio n a l m a trix m e th o d s are each used in c o n ju n c tio n w ith th e d e fa u lt a n d th e tw o a lte r n a tiv e b a c k g ro u n d -e n ric h e d sam p les, lead in g to a d e fa u lt an d eig h t a lte r n a tiv e b a c k g ro u n d e stim a te s. O u t of th e eig h t a lte rn a tiv e b a c k g ro u n d e stim a te s th o se tw o a re iden tified t h a t in gen eral, i.e. in a lm o st all b in s ex c e p t for flu c tu a tio n s, yield th e la rg e st a n d sm allest b a c k g ro u n d c o n trib u tio n . In each bin, th e av erag e a b so lu te difference b etw e en th o se tw o an d th e d e fa u lt b a c k g ro u n d e s tim a te is u sed as a sy s te m a tic u n c e rta in ty o n th e m e th o d .

A n o th e r sy s te m a tic u n c e rta in ty c a n arise if fake ra te s are d ifferen t for th e v ario u s p ro cesses c o n trib u tin g to th is b ac k g ro u n d , a n d if th e re la tiv e c o n trib u tio n s o f th e s e p rocesses differ b etw e en th e d a ta sam p les from w hich th e fake ra te s a re m e a su re d an d th e d a t a sa m ple to w hich th e fake ra te s a re ap p lied . F or ex am p le, je ts o rig in a tin g from b o tto m q u a rk s have a h ig h er fake r a te th a n lig h t-q u a rk je ts , b u t th e effect o f th is is negligible as th e n u m b e r of b-jets is sm all a n d sim ilar in b o th sam ples. H ow ever, as a n a d d itio n a l check th e b a c k g ro u n d is re c a lc u la te d u sin g all n in e m e th o d s discu ssed above, b u t w ith s e p a ra te fake ra te s for differen t b a c k g ro u n d processes. As th e m ean of th e se n in e m e th o d s is in a g reem en t w ith th e d e fa u lt b a c k g ro u n d e s tim a te no a d d itio n a l s y ste m a tic u n c e rta in ty is ap p lied .

T h e u n c e rta in ty on th e d e fa u lt fa k e -ra te c a lc u la tio n is deriv ed by v ary in g th e re q u ire m e n ts used to su p p re ss real e le c tro n c o n ta m in a tio n in th e d a t a sam p le u sed to m easu re th e fake ra te . T h e la rg e st d e v ia tio n of a b o u t 5% on th e b a c k g ro u n d o cc u rs w h e n th e value o f th e m issin g tra n s v e rs e en e rg y re q u ire m e n t is ch an g ed . I t is ad d e d in q u a d r a tu r e to th e sy s te m a tic u n c e rta in ty on th e m e th o d to o b ta in th e full s y s te m a tic u n c e rta in ty (^C0r lt') on

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(16)

th e cross sec tio n t h a t is c o rre la te d b etw e en bins. T h e v alu e of ^COr^' is fo u n d to be aro u n d 1%, risin g to a lm o st 4% a t larg e |A n ee|.

T h e u n c o rre la te d p a r t c o n sists of th e s ta tis tic a l u n c e rta in ty o n th e fake ra te s , w hich re su lts in a n u n c e rta in ty o n th e b ac k g ro u n d of a t m o st 5%, a n d of th e s ta tis tic a l u n c e rta in ty from th e sam p le to w hich th e fake ra te s are ap p lied . T h e se tw o sources a re ad d e d in q u a d r a tu r e a n d yield th e u n c e rta in ty ( ^ n c ^ ) on th e cross sec tio n t h a t is u n c o rre la te d b etw e en bins a n d is ty p ic a lly less t h a n 0.5% , in cre asin g to 3% a t larg e |A n ee|.

7 .1 .2 E n e r g y s c a le a n d r e s o lu tio n

T h e e le c tro n en e rg y scale a n d re so lu tio n as well as th e co rre sp o n d in g u n c e rta in tie s are d e te rm in e d usin g Z ^ e + e - , W ^ ev, a n d J / 0 ^ e + e - d ecay s [70]. T h e u n c e rta in ty on th e en e rg y scale is s e p a ra te d in to 14 u n c o rre la te d s y s te m a tic sources as well as one s ta tis tic a l co m p o n e n t. T h e s ta tis tic a l u n c e rta in ty on th e en e rg y scale is fo u n d to b e negligible.

A d d in g th e effects o f th e 14 sources of u n c e rta in ty on th e en e rg y scale in q u a d r a tu r e a fte r p ro p a g a tin g to th e m e a su re d cross sectio ns, th e co m b in ed u n c e rta in ty is d e n o te d as £C0SrCale, a n d is 1-4% for m ee > 200 GeV, b u t is b e tte r th a n 0.5% a t low er m ee a n d c e n tra l ra p id ity .

T h e u n c e rta in ty on th e en e rg y re so lu tio n is s e p a ra te d in to seven u n c o rre la te d sys

te m a tic sources w hich are p ro p a g a te d to th e cro ss-sectio n m e a su re m e n ts in d iv id u a lly an d th e n q u a d ra tic a lly su m m ed . T h is com b in ed u n c e rta in ty is d e n o te d as 5C0rres a n d is ty p ic a lly 0 .1- 0 .2% everyw here ex cep t a t large |yee| o r large |A n ee|.

7 .1 .3 R e c o n s t r u c t io n , id e n tific a tio n a n d is o la tio n e ffic ie n c y

T h e re c o n s tru c tio n a n d id e n tific a tio n efficiencies of e lec tro n s a re d e te rm in e d from d a t a for e le c tro n s w ith E T u p to a b o u t 100 GeV, usin g vario u s ta g -a n d -p ro b e m e th o d s in Z a n d J / 0 decays, follow ing th e p re sc rip tio n of ref. [71] w ith c e rta in im p ro v em en ts a n d a d ju s tm e n ts for th e 2012 c o n d itio n s [72]. In o rd e r to e x te n d th e m e a su re m e n t ra n g e o f th e id e n tific a tio n efficiency, th e ta g -a n d -p ro b e m e th o d u sin g th e iso la tio n d is trib u tio n of th e p ro b e for th e d isc rim in a tio n b etw e en signal a n d b a c k g ro u n d in Z ^ e + e - d ecays [72] is c a rrie d o u t u p to a b o u t 500 GeV in Et. W ith in s ta tis tic a l u n c e rta in tie s , th e id e n tific a tio n efficiencies are fo u n d to be s ta b le a n d c o n s iste n t w ith th e one d eriv ed in th e la st b in (E T I 80 GeV) in ref. [72].

T h e differences b etw e en th e m e a su re d re c o n stru c tio n a n d id e n tific a tio n efficiencies an d th e ir values in M C sim u la tio n are ta k e n as n- a n d E T -d e p e n d e n t scale fa c to rs w ith w hich th e Cdy fa c to r deriv ed from sim u la tio n is co rrec te d . Sim ilarly, scale fa c to rs for th e isola

tio n re q u ire m e n ts on th e lead in g a n d su b le a d in g e le c tro n are d eriv ed u sin g a ta g -a n d -p ro b e m e th o d in Z ^ e + e - decays. T h e y a re a p p lie d as a fu n c tio n of E T only, as th e n d e p e n d en ce is negligible.

T h e u n c e rta in tie s o n th e cross sec tio n d u e to th e sy s te m a tic u n c e rta in tie s on th e scale fa c to rs for th e e le c tro n re c o n s tru c tio n , id en tific a tio n a n d iso la tio n as well as th e s ta tis tic a l u n c e rta in ty o n th e iso latio n are d e n o te d as 5£0C°, ^Cor, ^C00 a n d 5 ^ 0 respectively. O f th ese, th e la rg e st co m p o n e n t is ^Cot, w hich is fo u n d to b e 0 .5 -1 % ev eryw here. T h e u n c e rta in ty AC0Co is g en e rally below 0.3% a n d b e tte r th a n 1% ev eryw here. B o th c o m p o n e n ts of th e iso la tio n efficiency u n c e rta in ty are fo u n d to b e 0 .2% o r b e tte r for m ee < 300 GeV.

J H E P 0 8 ( 2 0 1 6 ) 0 0 9

(17)

7 .1 .4 T rig g er e ffic ie n c y

T h e trig g e r efficiency is m e a su re d in d a t a a n d in th e M C sim u la tio n u sin g a ta g -a n d -p ro b e m e th o d in Z ^ e + e - decays. T h e differences as a fu n c tio n of E T a re fo u n d to b e sm aller th a n 1% everyw here, w ith n o d e p e n d e n c e on p. T h erefo re, E T -d e p e n d e n t scale fa c to rs are u sed to co rre c t C D Y. T h e u n c e rta in ty o n th e cross sec tio n d u e to th e s ta tis tic a l (£Ung) an d s y s te m a tic ( $ £ / ) u n c e rta in tie s o n th e trig g e r efficiency are each fo u n d to b e 0 .1% or b e tte r for m ee < 300 GeV.

7 .2 M u o n c h a n n e l

U n c e rta in tie s re la te d to th e m u o n trig g e r, re c o n stru c tio n , iso latio n a n d im p a c t p a r a m e te r efficiencies, as well as th e m u o n m o m e n tu m scale a n d re so lu tio n are all s tu d ie d u sin g th e Z ^ p + p - p rocess a n d a ta g -a n d -p ro b e m e th o d . O f th e se , th e la rg e st c o n trib u tio n to th e m e a su re m e n t precisio n arises from th e re c o n s tru c tio n efficiency m od ellin g, a n d th e m u on m o m e n tu m scale c a lib ra tio n . H ow ever, th e to p -q u a r k a n d d ib o so n b a c k g ro u n d s u b tra c tio n is also a d o m in a n t source o f u n c e rta in ty , a n d is discu ssed in sec tio n 7 .3 . A d e ta ile d b re a k d o w n o f th e u n c e rta in tie s is p ro v id ed in ta b le s 9 , 10 a n d 11 in th e ap p e n d ix .

7 .2 .1 R e c o n s t r u c t io n e ffic ie n c y

T h is is th e d o m in a n t source of m u o n -re la te d c o rre la te d sy s te m a tic u n c e rta in ty a n d is d o m in a te d a t larg e pT by th e u n c e rta in ty in c o n trib u tio n s from c a ta s tro p h ic m u o n en e rg y loss v ia b re m s s tra h lu n g [73] . W h e n p ro p a g a te d to th e cross sec tio n th is source is fo u n d to be ty p ic a lly 0.5% , risin g to 1% a t th e h ig h est pT. T h is c o n trib u tio n is d e n o te d as ££°£°.

7 .2 .2 M o m e n tu m s c a le a n d r e s o lu tio n

T h e c o rre c tio n s on m u o n m o m e n tu m scale a n d re so lu tio n are o b ta in e d fro m fits to th e Z ^ p + p - lin e-sh ap e w ith scale a n d re so lu tio n p a ra m e te rs in local a n d regions, se p a ra te ly for m u o n tra c k s re c o n s tru c te d in th e ID a n d th e M S [ 73] . U n c e rta in tie s arisin g from th e m e th o d o lo g y re su lt in a c o rre la te d sy ste m a tic u n c e rta in ty on th e m e a su re d cross sectio n s of ty p ic a lly 0.4% . T h e se c o n trib u tio n s are listed as for th e m o m e n tu m scale, a n d ^Corres a n d ^ 0/ 618 for th e M S a n d ID reso lu tio n u n c e rta in tie s respectively.

7 .2 .3 I s o la tio n a n d im p a c t p a r a m e te r e ffic ie n c y

M odelling o f th e m u o n iso la tio n a n d im p a c t p a r a m e te r selectio n efficiencies c a n give rise to a d d itio n a l s y s te m a tic u n c e rta in tie s a n d a re e s tim a te d to g e th e r. T h e sources co n sid ered in clu d e th e re m a in in g b a c k g ro u n d c o n ta m in a tio n , th e re sid u a l v a ria tio n in rj^, a n d a p o ssib le b ias from th e ev en t to p o lo g y e s tim a te d by v a ry in g th e a z im u th a l o p en in g an g le b etw een th e tw o m uons used in th e ta g -a n d -p ro b e m e th o d . T h e re su ltin g c o rre la te d cro ss-sectio n u n c e rta in ty is fo u n d to b e ty p ic a lly 0.1% , risin g to 0.5% a t larg e m w . T h is c o n trib u tio n is lab elled as £8° .

7 .2 .4 M u ltije t a n d W + j e t s b a c k g r o u n d

T h e u n c e rta in ty o n th e m u ltije t b a c k g ro u n d e s tim a tio n co n sists of sev eral sources. T h e s ta tis tic a l u n c e rta in ty of th e c o n tro l regions is p ro p a g a te d in th e a p p r o p ria te w ay a n d ca n