Measurement of the inclusive isolated prompt photon cross section in $\mathit{pp}$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector

P u b l i s h e d f o r S IS S A b y S p r i n g e r R e c e i v e d : M ay 12, 2016 A c c e p t e d : July 15, 2016 P u b l i s h e d : A ugust 1, 2016

Measurement of the inclusive isolated prompt photon cross section in pp collisions at √ s = 8 T e V with the A T L A S detector

T h e A T L A S collaboration

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A b s t r a c t : A m e a s u r e m e n t o f t h e c ro ss s e c tio n fo r t h e in c lu siv e p r o d u c tio n o f is o la te d p r o m p t p h o to n s in p r o to n - p r o to n c o llisio n s a t a c e n tre -o f-m a s s e n e rg y o f y fs = 8 T e V is p r e s e n te d . T h e m e a s u r e m e n t c o v ers t h e p s e u d o r a p id ity r a n g e s |n Y| < 1.37 a n d 1.56 <

|n Y| < 2 .3 7 in t h e tr a n s v e r s e e n e rg y ra n g e 25 < < 1500 G e V . T h e r e s u lts a r e b a s e d o n a n in te g r a te d lu m in o s ity o f 20.2 f b - 1 , re c o rd e d b y t h e A T L A S d e t e c t o r a t t h e L H C . P h o t o n c a n d id a te s a r e id e n tifie d b y c o m b in in g in f o r m a tio n fro m t h e c a lo r im e te r s a n d th e in n e r tr a c k e r . T h e b a c k g r o u n d is s u b t r a c t e d u s in g a d a ta - d r iv e n te c h n iq u e , b a s e d o n th e o b s e rv e d c a lo r im e te r s h o w e r-s h a p e v a ria b le s a n d t h e d e p o s itio n o f h a d r o n ic e n e rg y in a n a r r o w c o n e a r o u n d th e p h o to n c a n d id a te . T h e m e a s u r e d c ro ss s e c tio n s a r e c o m p a re d w ith le a d in g - o r d e r a n d n e x t- to - le a d in g o r d e r p e r t u r b a t i v e Q C D c a lc u la tio n s a n d a r e fo u n d t o b e in a g o o d a g re e m e n t o v e r t e n o r d e r s o f m a g n itu d e .

Ke y w o r d s: H a d r o n - H a d r o n s c a tte r in g ( e x p e r im e n ts ) , P h o t o n p r o d u c tio n , p r o to n - p r o to n s c a tte r in g

ArXiy ePr i n t: 1605.03495

J H E P 0 8 ( 2 0 1 6 ) 0 0 5

C o n te n ts

1 I n tr o d u c tio n 1

2 A T L A S d e t e c t o r a n d d a ta 2

3 T h e o r e tic a l p r e d ic tio n s 3

4 P h o t o n s e le c tio n 6

4.1 P h o t o n id e n tif ic a tio n 7

4.2 P h o t o n is o la tio n 7

5 B a c k g r o u n d s u b tr a c tio n 8

6 C r o ss s e c t io n 10

7 U n c e r t a in t ie s 11

8 R e s u lts a n d d is c u ss io n 14

9 C o n c lu s io n 18

A T a b le s o f m e a s u r e d c r o ss s e c tio n s 19

T h e A T L A S c o lla b o r a tio n 26

1 In tr o d u c tio n

P r o m p t p h o to n s , e x c lu d in g th o s e o r ig in a tin g fro m h a d r o n d e c a y s , a r e p r o d u c e d a t t h e L H C in t h e h a r d p ro c e s s p p ^ 7 + X . T h e m e a s u r e m e n t o f th i s in c lu siv e p r o d u c tio n p ro v id e s a p r o b e o f p e r t u r b a t i v e Q u a n tu m C h r o m o d y n a m ic s (p Q C D ) a n d sp ecifically , th r o u g h th e d o m in a n t le a d in g - o r d e r (L O ) p ro c e s s qg ^ q y , c a n b e u s e d t o s tu d y t h e g lu o n p a r t o n d i s t r i b u t i o n f u n c tio n ( P D F ) [1- 6] o f t h e p r o to n . I n a d d itio n , a n im p ro v e d u n d e r s ta n d in g o f p r o m p t p h o to n p r o d u c tio n is p o te n tia lly i m p o r t a n t in a id in g a n a ly s e s o f p ro c e s s e s fo r w h ic h th e y a r e a n i m p o r t a n t b a c k g r o u n d (fo r in s ta n c e , m e a s u r e m e n ts o f t h e H ig g s b o s o n in t h e d ip h o to n d e c a y c h a n n e l) .

In c lu s iv e p r o m p t p h o to n p r o d u c tio n is m a d e u p o f tw o c o n tr ib u tio n s : d ir e c t a n d fr a g ­ m e n ta tio n p h o to n s . D ir e c t p h o to n s a re th o s e a s s o c ia te d w ith t h e h a r d s u b -p ro c e s s , w h e re a s f r a g m e n ta tio n p h o to n s a r e p r o d u c e d fro m t h e f r a g m e n ta tio n o f a c o lo u re d p a r t o n . A n is o la tio n re q u ir e m e n t is u s e d t o re d u c e b o t h t h e p o o r ly u n d e r s to o d n o n - p e r tu r b a tiv e fr a g ­ m e n ta tio n c o n tr ib u tio n a n d t h e c o n ta m in a tio n fro m t h e d o m in a n t b a c k g r o u n d o f p h o to n s o r ig in a tin g fro m h a d r o n d e c a y s , m a in ly lig h t n e u t r a l m e s o n s (i.e. n 0 , n ).

J H E P 0 8 ( 2 0 1 6 ) 0 0 5

In c lu s iv e m e a s u r e m e n ts o f p r o m p t p h o to n s h a v e b e e n m a d e a t h a d r o n c o llid e rs b y A T L A S [7- 9], C M S [1 0 , 11] , C D F [12] , D 0 [13 , 14] , U A 1 [15] a n d U A 2 [16]. T h e a n a ly ­ sis p r e s e n te d h e re u se s 20.2 f b - 1 o f p r o to n - p r o to n c o llisio n d a t a re c o rd e d b y t h e A T L A S d e t e c t o r a n d is p e rf o rm e d a t a h ig h e r c e n tre -o f-m a s s e n e rg y (8 TeV ) t h a n t h e p re v io u s m e a s u r e m e n ts . S im ila r m e a s u r e m e n ts h a v e a lso b e e n m a d e p re v io u s ly in d e e p in e la s tic s c a tte r in g a n d p h o to p r o d u c tio n e x p e r im e n ts a t H E R A [17- 20] .

T h e fid u c ia l re g io n o f t h e m e a s u r e m e n t p r e s e n te d is d e fin e d in te r m s o f t h e p h o to n k in e m a tic q u a n t i t i e s:1 tr a n s v e r s e e n e rg y E ^ , p s e u d o r a p id ity n7 a n d tr a n s v e r s e is o la tio n e n e rg y E T ° . T h e d iffe re n tia l c ro ss s e c tio n is m e a s u r e d a s a f u n c tio n o f E ^ , fo r t h e h ig h e s t- e n e rg y p h o to n in t h e e v e n t, a n d s p a n s t h e 25 < E ^ < 1500 G eV ra n g e . T h e n7 ra n g e is s p lit t o g iv e fo u r in te rv a ls fo r t h e c ro s s -s e c tio n m e a s u r e m e n t: |n 7 1 < 0.6, 0.6 < |n 7 1 < 1.37, 1.56 < |n 7 1 < 1.81 a n d 1.81 < |n 7 1 < 2.3 7 . T h e fin a l c o n s tr a in t is th e p h o to n is o la tio n , w h e re E T ° is c a lc u la te d w ith in a c o n e o f size A R = 0.4, c e n tr e d a r o u n d t h e p h o to n , a n d is c h o se n t o b e E T ° < 4 .8 G eV + 4.2 x 1 0-3 x E ^ . T h is fid u c ia l re g io n is id e n tic a l in b o t h t h e th e o r e tic a l c a lc u la tio n s a n d t h e e x p e r im e n ta l m e a s u r e m e n t; h o w ev er, th e r e a re d iffe re n c e s in t h e c a lc u la tio n o f E T °:

• A t d e t e c t o r level it is t h e s u m o f e n e rg y d e p o s its in t h e c a lo r im e te r, c o r r e c te d fo r th e d e p o s its r e la te d t o t h e p h o to n c a n d id a te itself.

• A t p a r tic le level it is t h e s u m o f e n e rg y fro m all p a r tic le s , e x c e p t fo r m u o n s, n e u tr in o s a n d t h e p h o to n itse lf.

• A t p a r t o n level it is t h e s u m o f e n e rg y fro m all c o lo u re d p a r to n s .

A n a d d itio n a l c o r r e c tio n t o re m o v e e n e rg y fro m th e u n d e r ly in g e v e n t (U E ) o r a d d itio n a l p r o to n - p r o to n in te r a c tio n s is a p p lie d a t d e t e c t o r a n d p a r tic le level, a s d e ta ile d in s e c tio n 4 .2 . T h e r e a r e s e v e ra l d iffe re n c e s b e tw e e n t h e m e a s u r e m e n t p r e s e n te d h e re a n d t h e p re v io u s A T L A S in c lu siv e p h o to n m e a s u r e m e n ts [7- 9]. I n a d d itio n t o t h e c h a n g e in c e n tre -o f-m a s s e n e rg y a n d E ^ re a c h , it a lso p r o b e s fo r t h e firs t tim e t h e re g io n 25 < E ^ < 45 G eV fo r 1.81 < |n 7 1 < 2 .3 7 . T h e m e a s u r e m e n t is a lso c o m p a r e d t o d iffe re n t th e o r e tic a l p re d ic tio n s t h a n u s e d p re v io u sly , as d e ta ile d in s e c tio n 3 . A n E ^ - d e p e n d e n t is o la tio n re q u ir e m e n t is in tr o d u c e d fo r t h e fir s t tim e , e ffe c tiv e ly r e la x in g t h e m a x im u m E T ° a t h ig h E ^ , as o u tlin e d in s e c tio n 4 a lo n g w ith t h e d is c u s s io n o f c h a n g in g t h e u p p e r e d g e o f t h e e x c lu d e d n7 re g io n fro m 1.52 t o 1.56. O t h e r d iffe re n c e s in t h e b a c k g r o u n d e s tim a tio n , u n fo ld in g a n d u n c e r ta in ty c a lc u la tio n s a re h ig h lig h te d in s e c tio n s 5 , 6 a n d 7 re s p e c tiv e ly , a n d t h e r e s u lts a r e s h o w n in s e c tio n 8.

2 A T L A S d e te c to r an d d a ta

T h e A T L A S e x p e r im e n t [21] a t t h e L H C is a m u lti- p u r p o s e p a r tic le d e t e c t o r w ith a fo rw a rd - b a c k w a rd s y m m e tr ic c y lin d r ic a l g e o m e tr y a n d a n e a r 4 n c o v e ra g e in so lid a n g le . I t c o n s is ts

1ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upwards. Cylindrical coordinates (r, R) are used in the transverse plane, R being the azimuthal angle around the z-axis. The pseudorapidity is defined in terms of the polar angle 0 as y = — ln ta n (0 /2 ). Angular distance is measured in units of A R = \ J (A y)² + (AR)².

J H E P 0 8 ( 2 0 1 6 ) 0 0 5

o f a n in n e r tr a c k in g d e t e c t o r s u r r o u n d e d b y a t h i n s u p e r c o n d u c tin g so le n o id p r o v id in g a 2 T a x ia l m a g n e tic field, e le c tr o m a g n e tic a n d h a d r o n ic c a lo r im e te rs , a n d a m u o n s p e c tr o m e te r . T h e in n e r tr a c k in g d e t e c t o r c o v ers t h e p s e u d o r a p id ity r a n g e |n| < 2.5. I t c o n s is ts o f silic o n p ix e l, silic o n m ic r o s tr ip , a n d t r a n s i t i o n r a d ia tio n tr a c k in g d e te c to r s . W i t h i n th e re g io n |n | < 3.2, E M c a lo r im e tr y is p ro v id e d b y h ig h - g r a n u la r ity l e a d /liq u id - a r g o n (L A r) s a m p lin g c a lo r im e te rs , w ith a n a d d itio n a l t h i n L A r p r e s a m p le r c o v e rin g |n | < 1.8, t o c o r r e c t fo r e n e rg y loss in m a te r ia l u p s tr e a m o f t h e c a lo r im e te rs . A h a d r o n ic ( s te e l/s c in tilla to r - tile ) c a lo r im e te r c o v e rs th e c e n tr a l p s e u d o r a p id ity ra n g e ( |n | < 1.7). T h e e n d - c a p a n d fo rw a rd re g io n s a re in s tr u m e n te d w ith L A r c a lo r im e te r s fo r b o t h t h e E M a n d h a d r o n ic e n e rg y m e a s u r e m e n ts u p t o |n | = 4.9. T h e m u o n s p e c tr o m e te r s u r r o u n d s t h e c a lo r im e te rs a n d is b a s e d o n th r e e la rg e a ir-c o re to r o id s u p e r c o n d u c tin g m a g n e ts w ith e ig h t co ils e a c h . I t in c lu d e s a s y s te m o f p re c is io n tr a c k in g c h a m b e r s a n d f a s t d e te c to r s fo r tr ig g e r in g . A th r e e -le v e l tr ig g e r s y s te m is u s e d t o s e le c t e v e n ts . T h e firs t-le v e l tr ig g e r is im p le m e n te d in h a r d w a r e a n d u se s a s u b s e t o f t h e d e te c to r in f o r m a tio n t o re d u c e th e a c c e p te d r a t e t o a t m o s t 75 k H z. T h is is fo llo w ed b y tw o s o ftw a r e -b a s e d h ig h -le v e l tr ig g e r s t h a t t o g e t h e r re d u c e t h e a c c e p te d e v e n t r a t e t o 400 H z o n a v e ra g e , d e p e n d in g o n t h e d a t a - t a k i n g c o n d itio n s d u r in g 2012.

T h e d a t a s e t u s e d in t h is a n a ly s is w as o b ta in e d u s in g p r o to n - p r o to n c o llisio n s re c o rd e d in 2012 b y t h e A T L A S d e te c to r , w h e n t h e L H C o p e r a te d a t a c e n tre -o f-m a s s e n e r g y o f y fs = 8 TeV . T h e in te g r a te d lu m in o s ity o f t h e d a t a s e t u s e d in t h is m e a s u r e m e n t is 20.2 f b - 1 w ith a n u n c e r ta in ty o f 1.9% [22] . T h e e v e n ts u s e d in t h e a n a ly s is w e re re c o rd e d b y t h e tr ig g e r s y s te m u s in g s in g le - p h o to n tr ig g e r s [2 3 ], w h ic h u se id e n tif ic a tio n c r ite r ia lo o s e r t h a n t h e s e le c tio n d e s c rib e d in s e c tio n 4 .1 . F o r th e h ig h -le v e l trig g e r s , E ^ th r e s h o ld s a r e d e fin e d in 20 G eV s te p s fro m 20 G eV t o 120 G eV . M u ltip le tr ig g e r th r e s h o ld s a r e r e q u ir e d b e c a u s e t h e tr ig g e r s a r e p re s c a le d t o re d u c e t h e i r r a te , e x c e p t fo r t h e u n p re s c a le d 120 G eV th r e s h o ld . E a c h th r e s h o ld is u s e d in t h e a n a ly s is w ith in a n e x c lu siv e E ^ ra n g e , d e te r m in e d t o b e w h e re th e tr ig g e r h a s a n efficien cy g r e a te r t h a n 9 9 .5 % , w ith r e s p e c t t o th e fu ll s e le c tio n d e ta ile d in s e c tio n 4 . O n ly e v e n ts ta k e n d u r in g p e r io d s o f g o o d d a t a q u a lity , w h e re th e c a lo r im e te rs a n d in n e r tr a c k in g d e te c to r s a r e in n o m in a l o p e r a tio n , a re r e ta in e d in t h e d a t a s e t . T o re m o v e a n y n o n -c o llis io n b a c k g ro u n d , e a c h e v e n t is r e q u ir e d t o h a v e a r e c o n s tr u c te d v e r te x c o n s is te n t w ith t h e a v e ra g e b e a m - s p o t p o s itio n , w h e re t h e v e r te x is r e q u ir e d t o h a v e a t le a s t tw o a s s o c ia te d tr a c k s . T h is c o n d itio n is c lo se t o 100% efficien t fo r r e ta in in g e v e n ts w ith p h o to n s w ith in t h e d e t e c t o r a c c e p ta n c e .

3 T h e o r e tic a l p r e d ic tio n s

T h e th e o r e tic a l c a lc u la tio n s u s e d in t h e a n a ly s is c o n s is t o f L O M o n te C a r lo (M C ) e v e n t g e n e r a to r s a n d c a lc u la tio n s a t n e x t- to - le a d in g - o r d e r (N L O ) o r h ig h e r. T w o e v e n t g e n e r a ­ to r s a r e u s e d a t L O : Py t h i a 8.1 6 5 [24] a n d Sh e r p a 1.4.0 [25] . T h e s e e v e n t g e n e r a to r s a re in te r f a c e d w ith a d e ta ile d d e t e c t o r s im u la tio n [2 6 ] (b a s e d o n G E A N T 4 [27]), t h e o u t p u t o f w h ic h is r e c o n s tr u c te d in th e s a m e w a y as t h e d a t a . T h e L O p r e d ic tio n s a re u s e d t o s tu d y m a n y a s p e c ts o f t h e a n a ly s is a n d a re a ls o c o m p a r e d t o t h e fin a l c ro ss s e c tio n . T h e fin al

J H E P 0 8 ( 2 0 1 6 ) 0 0 5

c ro ss s e c tio n s a re a lso c o m p a r e d t o th r e e c a lc u la tio n s : Je tPh o x [28] , PeTeR [2 9 , 3 0 ]2 a n d M C F M [3 1 ].3

E v e n t g e n e r a tio n w ith Py t h i a in c lu d e s: t h e d e s c r ip tio n o f t h e P D F s u s in g C T E Q 6 L 1 [3 2 ], t h e s im u la tio n o f in itia l- a n d f in a l- s ta te r a d ia tio n , t h e s im u la tio n o f t h e U E u s in g t h e A T L A S A U 2 s e t o f tu n e d p a r a m e te r s ( tu n e ) [3 3 ] b a s e d o n t h e m u ltip le p a r t o n in te r a c tio n m o d e l [3 4 ], a n d t h e m o d e llin g o f t h e h a d r o n is a tio n b a s e d o n t h e L u n d s tr in g m o d e l [3 5 ]. T h e L O d ir e c t c o n tr ib u tio n t o t h e p r o m p t p h o to n p r o d u c tio n is fu lly in c lu d e d in t h e m a in m a tr ix - e le m e n t c a lc u la tio n . I n c o n tr a s t, t h e f r a g m e n ta tio n c o n tr ib u tio n is m o d ­ e lle d b y f in a l- s ta te Q E D r a d ia tio n a r is in g fro m c a lc u la tio n s o f all 2 ^ 2 Q C D p ro c e sse s.

Py t h i a is u s e d t o e x t r a c t t h e c e n tr a l v a lu e s o f t h e m e a s u r e m e n t, w h ile Sh e r p a is u s e d as a s e c o n d L O g e n e r a to r a s it sh o w e d e x c e lle n t a g r e e m e n t w ith t h e r e s u lts in th e A T L A S p h o to n p lu s j e t m e a s u r e m e n t [36] . T h e Sh e r p a p re d ic tio n s a re u s e d t o c ro s s ­ c h e c k t h e r e s u lts a n d d e te r m in e u n c e r ta in tie s a ris in g fro m t h e u se o f M C s im u la tio n s in p a r t s o f th e a n a ly s is . T h e Sh e r p a c a lc u la tio n s a re p e rfo r m e d w ith u p t o fo u r p a r t o n e m is s io n s a n d t h e r a d ia tio n o f g lu o n s a n d p h o to n s is d o n e c o h e re n tly . T h is m e a n s t h a t th e f r a g m e n ta tio n c o n tr ib u tio n is p r o d u c e d d iffe re n tly t o t h e c o n tr ib u tio n in Py t h i a a n d is a lso in d is tin g u is h a b le fro m t h e d ir e c t c o n tr ib u tio n , u n lik e Py t h i a w h e re t h e c o n tr ib u tio n s c a n b e s e p a r a te d . T h e Sh e r p a e v e n ts a r e p r o d u c e d w ith : t h e C T 1 0 [37] P D F , t h e U E m o d e l b a s e d o n t h e r e c o m m e n d e d t u n e p ro v id e d b y t h e Sh e r p a a u th o r s , a n d h a d r o n is a tio n m o d e lle d u s in g a m o d ifie d v e rs io n o f t h e c lu s te r m o d e l [38] .

T h e L O s im u la te d e v e n ts u s e d in t h e a n a ly s is a r e re w e ig h te d in o r d e r t o m a tc h as w ell a s p o s s ib le t h e e x p e r im e n ta l c o n d itio n s o f th e d a t a s e t . O n e o f th e s e c o r r e c tio n s is t o r e p r o d u c e t h e p ile -u p ( a d d itio n a l p r o to n - p r o to n in te r a c tio n s in t h e s a m e b u n c h c ro ssin g ) c o n d itio n s , w h e re t h e w e ig h ts a re d e r iv e d fro m th e d i s t r i b u t i o n o f a v e ra g e in te r a c tio n s p e r b u n c h c ro s s in g ( ^ ) in d a t a a n d M C s im u la tio n s w ith a n a d d itio n a l c o n s ta n t t o im p ro v e t h e a g r e e m e n t o f t h e n u m b e r o f p r im a r y v e rtic e s . A s e c o n d w e ig h t is u s e d t o e n s u r e a n a c c u r a te n7 m e a s u r e m e n t b y r e p r o d u c in g in t h e M C s im u la tio n s t h e z - v e r te x p o s itio n o f t h e h a r d i n te r a c tio n m e a s u r e d in d a t a .

T h e fin a l c ro ss s e c tio n s a re c o m p a r e d t o th e s e L O g e n e r a to r s a n d a lso t o p a rto n -le v e l c a lc u la tio n s . T h e k in e m a tic s e le c tio n u s e d in a ll o f t h e p re d ic tio n s m a tc h e s t h e fid u c ia l re g io n d e fin e d in s e c tio n 1 . F o r t h e h ig h e r o r d e r p r e d ic tio n s t h e n o m in a l r e n o r m a lis a tio n ( ^r), f a c to r is a tio n ( ^ p ) a n d f r a g m e n ta tio n ( ^ f ) sc a le s w ere s e t t o t h e p h o to n tr a n s v e r s e e n e rg y ( ^r = = = E ^ ).

J e t P h o x , a w e ll- e s ta b lis h e d N L O p a r to n - le v e l g e n e r a to r fo r t h e p r e d ic tio n o f p r o ­ c e sse s w ith p h o to n s in t h e fin a l s t a t e , is u s e d as t h e b a s e lin e t o c o m p a r e t h e r e s u lts . J e t P h o x is c a p a b le o f c a lc u la tin g t h e d o u b le -d iff e re n tia l in c lu siv e p r o m p t p h o to n c ro ss s e c tio n d2a / ( d E ^ d n 7 ) a t p a r t o n level t o N L O a c c u r a c y fo r b o t h t h e d ir e c t a n d f r a g m e n ta ­ tio n p h o to n p ro c e sse s. T h e c a lc u la tio n c a n b e c o n fig u re d t o u se a n E ^ - d e p e n d e n t is o la tio n

2We thank M atthew Schwartz for providing theoretical predictions for the inclusive photon cross section using the PeTeR calculation; http://peter.hepforge.org.

3We thank Ciaran Williams and John Campbell for their help in the ongoing investigation of the unex­

pected differences seen in the MCFM.

J H E P 0 8 ( 2 0 1 6 ) 0 0 5

re q u ir e m e n t4 a n d u se s t h e N L O p h o to n f r a g m e n ta tio n f u n c tio n o f B F G s e t I I [3 9 , 4 0 ]. T o c h e c k t h e effect o f t h e P D F c h o ice o n t h e p r e d ic tio n s , th e y a r e g e n e r a te d w ith d iffe re n t P D F s e ts ( C T 1 0 , M S T W 2 0 0 8 N L O [4 1 ], N N P D F 2 .3 [4 2 ] a n d H E R A P D F 1 .5 [4 3 ]), p r o v id e d b y t h e L H A P D F p a c k a g e [44] . T h e s tr o n g c o u p lin g c o n s ta n t ( a s ) is a ls o o b ta in e d fo r e a c h P D F u s in g L H A P D F a n d t h e f in e - s tr u c tu r e c o n s ta n t ( g e m ) is s e t t o t h e J e t P h o x d e f a u lt o f 1 /1 3 7 .

T h e fo llo w in g s y s te m a tic u n c e r ta in tie s (c o m b in e d in q u a d r a t u r e ) a r e a s s ig n e d t o th e Je tPh o x c a lc u la tio n s a n d a r e e s tim a te d b y m e a n s o f p r o c e d u r e s [4 5 ] u s e d in t h e p re v io u s m e a s u r e m e n ts :

• T h e u n c e r ta in ty o n t h e sc a le c h o ic e is e v a lu a te d fro m t h e e n v e lo p e o f v a r y in g th e th r e e sc ales b y a f a c to r o f tw o a r o u n d t h e n o m in a l v a lu e , b o t h s im u lta n e o u s ly a n d in d e p e n d e n tly (k e e p in g tw o fix e d a t th e n o m in a l v a lu e ). T h e im p a c t o n t h e p r e d ic te d c ro ss s e c tio n v a rie s b e tw e e n 12% a n d 20%.

• T h e P D F u n c e r ta in ty is o b ta in e d b y r e p e a tin g th e J e t P h o x c a lc u la tio n fo r t h e 52 e ig e n v e c to r s e ts o f t h e C T 1 0 P D F a n d a p p ly in g a s c a lin g f a c to r in o r d e r t o p ro d u c e t h e u n c e r ta in ty fo r t h e 68% c o n fid e n c e -le v e l (C L ) in te rv a l. T h e c o r r e s p o n d in g u n ­ c e r ta in ty in t h e c ro ss s e c tio n in c re a s e s w ith E ^ a n d v a rie s b e tw e e n 5% a t 100 G eV a n d 15% a t 900 G eV .

• T h e u n c e r ta in ty d u e t o a s is e v a lu a te d , fo llo w in g t h e r e c o m m e n d a tio n o f ref. [3 7 ], b y r e p e a tin g t h e c a lc u la tio n w ith a s v a rie d b y ±0.002 a r o u n d t h e c e n tr a l v a lu e o f 0 .1 1 8 a n d s c a lin g in o r d e r t o o b t a i n t h e u n c e r ta in ty fo r t h e 68% C L in te rv a l. T h e u n c e r ta in ty d u e t o a s is s m a lle r t h a n t h a t fro m t h e sc a le o r P D F u n c e r ta in tie s fo r t h e w h o le p h a s e s p a c e ; it slo w ly d e c r e a s e s fro m 9% w ith in c re a s in g E ^ , w ith th e e x c e p tio n o f a b o v e 900 G eV w h e re it in c re a s e s t o 15% .

• T o b e a b le t o c o r r e c t fro m p a r t o n level t o p a r tic le level, a d d itio n a l h a d r o n is a tio n - p lu s -U E c o r r e c tio n fa c to rs w e re e v a lu a te d u s in g t h e tw o a l te r n a tiv e h a d r o n is a tio n a n d U E m o d e ls in P y t h i a a n d S h e r p a . T h e s tu d y w as p e rfo rm e d b y r e p e a tin g th e c a lc u la tio n w ith a n d w ith o u t th e h a d r o n is a tio n a n d U E c o n tr ib u tio n s a n d r e s u lte d in a c o r r e c tio n clo se t o u n ity fo r b o t h M C m o d e ls w ith a s m a ll d e v ia tio n o f a t m o s t 2% a t low E Y . T h e re fo re , as in t h e p re v io u s a n a ly s e s , n o c o r r e c tio n f a c to r is a p p lie d t o th e c e n tr a l v a lu e ; h o w ev er, in th is m e a s u r e m e n t a n E ^ - d e p e n d e n t u n c e r ta in ty is a s s ig n e d t o t h e th e o ry , b a s e d o n t h e la r g e s t d e v ia tio n fro m u n ity b e tw e e n t h e tw o m o d e ls.

PeTeR is u s e d a s a se c o n d p a r to n - le v e l g e n e r a to r t o p r e d ic t t h e d iffe re n tia l is o la te d p r o m p t p h o to n c ro ss s e c tio n a t N L O in c lu d in g t h e r e s u m m a tio n o f th r e s h o ld lo g a r ith m s a t t h e n e x t- to - n e x t- to - n e x t- to - le a d in g - lo g a r ith m ic (N N N L L ) level. PeTeR is r o u g h ly e q u iv ­ a le n t t o a fix e d - o rd e r c a lc u la tio n a t n e x t- n e x t- to - le a d in g - o r d e r (N N L O ); th e r e is c u r r e n tly n o e x a c t c a lc u la tio n a v a ila b le fo r in c lu siv e p h o to n s a t th i s o r d e r . T o a c c o u n t fo r t h e iso la ­ tio n c r ite r ia a p p lie d in t h e m e a s u r e m e n t, t h e PeTeR r e s u lt a t N L O is n o rm a lis e d t o t h a t 4The ET° requirement selected in this analysis is chosen to not be too restrictive for the NLO calculations, to avoid potential unphysical values in these predictions [28].

J H E P 0 8 ( 2 0 1 6 ) 0 0 5

fro m Je tPh o x. T h e PeTeR p re d ic tio n s a re s u p p le m e n te d w ith t h e r e s u m m a tio n o f la rg e e le c tro w e a k S u d a k o v lo g a r ith m s a c c o rd in g t o ref. [4 6 , 47] . T h e s e e le c tr o w e a k c o rre c tio n s , n o t in c lu d e d in t h e p r e d ic tio n s fro m Je tPh o x, p ro v id e e s tim a te s o f e le c tro w e a k u n c e r t a i n ­ tie s t h a t a re i m p o r t a n t fo r h ig h E ^ a n d a lso m e a n t h a t , u n lik e Je tPh o x, PeTeR u se s a r u n n in g a EM. T h e sc a le u n c e r ta in ty is c a lc u la te d s im ila rly t o Je tPh o x, b y v a ry in g th e s c a le s a r o u n d t h e c e n tr a l v a lu e , b u t in PeTeR th e r e a r e fo u r sc a le s [48] : h a r d m a tc h in g , j e t , so ft a n d f a c to r is a tio n . F in a lly t h e P D F u n c e r ta in ty is t a k e n d ir e c tly fro m Je tPh o x.

A n a d d itio n a l s t u d y w a s m a d e u s in g M C F M , fo llo w in g o n fro m t h e s tu d ie s in ref. [4 9 ], w ith p a r a m e te r s (C T 1 0 P D F , p h o to n is o la tio n , sc a le c h o ice a n d a EM) m a tc h in g th o s e in Je tPh o x. M C F M c a lc u la te s t h e f r a g m e n ta tio n p ro c e s s o n ly t o L O a n d th e r e f o r e d e v ia ­ tio n s fro m Je tPh o x p r e d ic tio n s w e re e x p e c te d b e lo w a p p r o x im a te ly 200 G eV . S u r p r is ­ ingly, h o w ev e r, e v e n a t h ig h e r E ^ t h e p re d ic tio n s fro m M C F M w e re fo u n d t o b e c o n s is ­ t e n t l y b e lo w t h e p r e d ic tio n s fro m Je tPh o x, a lth o u g h w ith in t h e th e o r e tic a l u n c e r ta in tie s . T h is t r e n d is u n d e r in v e s tig a tio n b y t h e c a lc u la tio n s a u th o r s a n d t h e p re d ic tio n s a re n o t p r e s e n te d h e re .

4 P h o to n se le c tio n

T h e p h o to n s e le c tio n , in b o th d a t a a n d M C s im u la tio n , is b a s e d o n t h e r e c o n s tr u c tio n [50]

o f a n E M c lu s te r in t h e c a lo r im e te r as a p h o to n c a n d id a te . T h e a b s e n c e o f a n a s s o c i­

a t e d tr a c k in th e in n e r d e t e c t o r c lassifies t h e p h o to n c a n d id a te a s a n u n c o n v e r te d p h o to n , w h e re a s it is c la ssifie d as a c o n v e r te d p h o to n if t h e c lu s te r is m a tc h e d t o tw o tr a c k s c o m in g fro m a c o n v e rs io n v e r te x o r t o o n e tr a c k w h ic h h a s n o h its in t h e in n e r m o s t la y e r o f th e in n e r tr a c k in g d e te c to r . B o t h th e c o n v e rte d a n d u n c o n v e r te d c a n d id a te s a r e k e p t in th e a n a ly s is . A f u r t h e r tr a c k - b a s e d c la s s ific a tio n [51] is u s e d t o m in im is e t h e n u m b e r o f ele c ­ t r o n s r e c o n s tr u c te d a s p h o to n s , a lth o u g h th is in tr o d u c e s a s lig h t d e c re a s e in e fficien cy fo r r e c o n s tr u c tin g c o n v e rte d p h o to n s . T h e c o n v e rs io n c la s s ific a tio n is u s e d b o t h t o d e te r m in e t h e size o f t h e p h o to n c lu s te r in t h e b a r r e l c a lo r im e te r a n d a lso a s a n i n p u t t o t h e d e d ic a te d e n e rg y c a lib r a tio n [52], w h ic h is a p p lie d t o a c c o u n t fo r e n e rg y loss b e fo re t h e E M c a lo rim e ­ te r . T h is c a lib r a tio n s t a r t s b y c o r r e c tin g th e re s p o n s e fro m e a c h o f th e la y e rs in t h e E M c a lo r im e te r a n d t h e n a p p lie s a re s p o n s e c a lib r a tio n fro m M C s im u la tio n s t o t h e c lu s te r e n e rg ie s. A f te r a c c o u n tin g fo r d e t e c t o r re s p o n s e v a r ia tio n s n o t in c lu d e d in t h e s im u la tio n , s u c h a s h ig h -v o lta g e in h o m o g e n e itie s in so m e s e c to rs , e n e rg y s c a le fa c to r s a r e t h e n a p p lie d fro m t h e c o m p a r is o n o f t h e d e t e c t o r re s p o n s e t o Z b o s o n d e c a y s t o e le c tr o n - p o s itr o n p a ir e v e n ts in d a t a a n d M C s im u la tio n s .

F o llo w in g th is c a lib r a tio n , o n ly p h o to n c a n d id a te s w ith E ^ > 25 G eV a n d a c lu s te r b a r y c e n tr e (in t h e s e c o n d la y e r o f t h e E M c a lo r im e te r ) ly in g w ith in |n Y| < 1 .3 7 o r 1.56 <

|n Y| < 2 .3 7 a re r e ta in e d fo r t h e a n a ly s is . T h e t r a n s i t i o n re g io n b e tw e e n t h e b a r r e l a n d e n d - c a p c a lo r im e te rs (1 .3 7 < |n Y| < 1.56) is e x c lu d e d d u e t o th e d e g r a d e d p e r f o r m a n c e in d u c e d b y t h e in c re a s e d a m o u n t o f in a c tiv e m a te r ia l in f r o n t o f t h e c a lo r im e te r. T h is re g io n is e x p a n d e d in t h e m e a s u r e m e n t p r e s e n te d h e re t o 1.56, c o m p a r e d t o t h e v a lu e o f 1.52 u s e d p re v io u sly , t o im p ro v e t h e a c c u r a c y o f t h e p h o to n e n e rg y m e a s u r e m e n t a s it a v o id s u s in g c lu s te r s c a lib r a te d b y s c in tilla to r s t h a t a r e p a r t o f t h e h a d r o n ic c a lo r im e te r.

J H E P 0 8 ( 2 0 1 6 ) 0 0 5

F in a lly , p h o to n s r e c o n s tr u c te d n e a r re g io n s o f t h e c a lo r im e te r a ffe c te d b y r e a d - o u t o r h ig h - v o lta g e fa ilu re s a r e n o t in c lu d e d in th e a n a ly s is . T h e r e m a in in g p h o to n c a n d id a te s a re t h e n u s e d in th i s a n a ly s is if th e y s a tis f y f u r t h e r s e le c tio n a n d q u a lity c r ite r ia b a s e d o n t h e i r c a lo r im e te r sh o w e r s h a p e s a n d is o la tio n en e rg y .

4 .1 P h o t o n id e n tific a tio n

I n o r d e r t o r e d u c e th e p re v io u s ly m e n tio n e d la r g e s t b a c k g r o u n d , n a m e ly n o n - p r o m p t p h o ­ to n s o r ig in a tin g m a in ly fro m d e c a y s o f e n e r g e tic n0 a n d n m e so n s, n in e s h o w e r-s h a p e v a ri­

a b le s [50] a re e x p lo ite d , s im ila rly t o t h e p re v io u s A T L A S in c lu siv e p h o to n m e a s u r e m e n ts . T h e s e s h o w e r-s h a p e v a r ia b le s a r e fo rm e d b a s e d o n t h e r e la tiv e a n d a b s o lu te e n e r g y d e p o ­ s itio n w ith in t h e c a lo r im e te r cells u s in g t h e fu ll g r a n u la r ity o f t h e d iffe re n t la y e rs o f th e c a lo r im e te r s y s te m . T h e p a r t i c u l a r s e le c tio n c r ite r ia fo r e a c h o f th e n in e v a ria b le s a r e tu n e d fo r c o n v e rte d a n d u n c o n v e r te d p h o to n s s e p a ra te ly , a s w ell as b e in g a d ju s te d d e p e n d in g o n n7 (in in te r v a ls m a tc h in g t h e fo u r n7 re g io n s o f th is m e a s u r e m e n t) . I n t h e M C s im u la tio n s t h e s a m e c r ite r ia a re a p p lie d a s in d a t a , b u t w ith tw o c o rre c tio n s . F ir s tly , t h e s h o w e r-s h a p e v a ria b le s a r e s h if te d [50] t o m a tc h t h e m e a s u r e d d is tr ib u tio n s in d a t a . S eco n d ly , a d d itio n a l c o r r e c tio n fa c to rs ( a t m o s t a few p e r c e n t fro m u n ity ) t o m a tc h t h e id e n tif ic a tio n efficien cy in t h e M C s im u la tio n s a n d t h a t in d a t a a r e a p p lie d , c a lc u la te d in e a c h E ^ a n d n7 in te rv a l.

T o q u a n tif y t h e effect o f th e id e n tif ic a tio n c r ite r ia , t h e id e n tif ic a tio n e fficien cy fo r p r o m p t p h o to n s is d e fin e d in M C s im u la tio n s as:

N MC

MC id,matched (A

£id = n MC . ( 4 . 1)

particle

w h e re r e c o n s tr u c te d p h o to n s h a v e t o s a tis fy t h e id e n tif ic a tio n c r ite r ia a n d b e g e o m e tr i­

c a lly m a tc h e d , w ith A R < 0.2, t o is o la te d p h o to n s g e n e r a te d a t p a r tic le level. T h is eMC is s h o w n in fig u re 1 a lo n g w ith th e efficien cies fo r c o n v e rte d a n d u n c o n v e r te d p h o to n s .5 T h e u n c o n v e r te d p h o to n efficien cy is h ig h a n d a p p r o x im a te ly c o n s ta n t fo r m o re e n e rg e tic p h o to n s , a s e x p e c te d sin c e th e y s h o u ld leav e a m o re p r o n o u n c e d sh o w e r in th e d e te c to r . H o w ev er, a d r o p in efficien cy is o b s e rv e d w h e n c o m b in in g w ith c o n v e r te d p h o to n s . T h e e ffic ien cy t o r e c o n s tr u c t c o n v e rs io n s d e c re a s e s a t h ig h E ^ ( > 150 G eV ) w h e re it b e c o m e s m o re d iffic u lt t o s e p a r a te t h e tw o tr a c k s fro m t h e c o n v e rsio n s. T h e s e v e ry c lo se -b y tr a c k s a r e m o re lik e ly t o fail t h e t i g h t e r se le c tio n s , in c lu d in g a t r a n s i t i o n r a d ia tio n r e q u ir e m e n t, a p p lie d t o s in g le -tra c k c o n v e rs io n c a n d id a te s .

4 .2 P h o t o n is o la tio n

T h e p h o to n c a n d id a te s a r e r e q u ir e d t o b e is o la te d t o d is tin g u is h b e tw e e n p r o m p t p h o ­ to n s a n d h a d r o n ic b a c k g r o u n d . A s s t a t e d in s e c tio n 1, E ^ is c a lc u la te d fro m to p o lo g ic a l c lu s te r s o f c a lo r im e te r cells in a c o n e o f size A R = 0 .4 a r o u n d t h e p h o to n a n d c o r r e c te d fo r t h e d e p o s its r e la te d t o t h e p h o to n c a n d id a te itse lf. A s th is q u a n t i t y is s u s c e p tib le to

5 At particle level the conversion classification is based on information from the detailed detector simu­

lation of the photon, by searching for a conversion of the photon into an electron-positron pair within the geometrical region of the inner tracking detector.

J H E P 0 8 ( 2 0 1 6 ) 0 0 5

F i g u r e 1. T he p h o to n identification efficiency (w ith s ta tistic a l u n c e rta in ty ) as a function of £ ^ d eterm in ed in P y t h i a M C sim ulations, along w ith th e se p a ra te d efficiencies for un co n v erted and converted photons. T he efficiency is show n for th e region |nY | < 0.6, w ith sim ilar resu lts found in o th e r |nY | regions.

c o n tr ib u tio n s fro m t h e U E a n d p ile -u p , a c o r r e c tio n b a s e d o n t h e j e t a r e a m e th o d [53] is a p p lie d . T h is e s tim a te s o n a n e v e n t-b y -e v e n t b a s is t h e a m b ie n t e n e r g y d e n s ity , w h ic h is t h e n s u b t r a c t e d fro m t h e £)So b e fo re a p p ly in g th e is o la tio n r e q u ir e m e n t. T h e s e c o rre c tio n s a r e ty p ic a lly b e tw e e n 1.5 a n d 2 G eV . I n o r d e r fo r t h e d e te c to r - le v e l d i s t r i b u t i o n t o r e p r o d u c e t h e d i s t r i b u t i o n fro m d a t a , it is c o r r e c te d in e a c h £ p a n d in te rv a l b y th e d iffe re n c e b e tw e e n t h e m e a n v a lu e o f £iS ° in d a t a a n d M C s im u la tio n s . T h e s e c o rr e c ­ tio n s r a n g e fro m a few h u n d r e d M eV u p t o 3-4 G eV a n d a re c o n s is te n t fo r b o t h Py t h i a

a n d Sh e r p a.

T h e m e a s u r e m e n t p r e s e n te d h e re u se s a n £ ^ - d e p e n d e n t is o la tio n re q u ire m e n t:

£ f ° < 4 .8 G eV + 4.2 x 1 0-3 x £ Y. (4.2) I n c o n t r a s t t o t h e fix e d v a lu e (3 o r 7 G eV ) u s e d in t h e p re v io u s a n a ly s e s , th is r e q u ir e m e n t h a s b e e n o p tim is e d t o r e t a i n m o re o f t h e p h o to n s s a tis fy in g t h e id e n tif ic a tio n c r ite r ia in s e c tio n 4.1 w h ils t a lso o b ta in in g th e b e s t s ig n a l- to - b a c k g r o u n d r a t i o th r o u g h o u t t h e la rg e

£ T ra n g e o f t h e m e a s u r e m e n t. I n a d d itio n , th e f r a c tio n o f p h o to n c a n d id a te s t h a t h a v e s a tis fie d t h e id e n tif ic a tio n c r ite r ia a n d s u b s e q u e n tly a lso s a tis f y t h e is o la tio n r e q u ir e m e n t, s ta y s h ig h a n d c o n s ta n t. T h is is d u e t o t h e is o la tio n r e q u ir e m e n t b e in g r e la x e d a t h ig h e r

£ T , c o m p a r e d t o u s in g a fix ed c u t.

5 B a ck g ro u n d su b tr a c tio n

T h e n u m b e r o f e v e n ts w ith a p h o to n c a n d id a te (N T fiata) s a tis fy in g t h e k in e m a tic , id e n ­ tif ic a tio n a n d is o la tio n s e le c tio n c r ite r ia , a s d e ta ile d in s e c tio n 4 , h a s c o n tr ib u tio n s fro m h a d r o n ic b a c k g r o u n d a n d e le c tro n s . T h e s e c o n tr ib u tio n s a re re m o v e d s ta tis tic a lly b y te c h ­ n iq u e s d e ta ile d b e lo w .

T h e h a d r o n ic b a c k g r o u n d (fro m m e s o n d e c a y s a n d je t s ) is re m o v e d b y a d a ta - d r iv e n te c h n iq u e , as d o n e in t h e p re v io u s A T L A S a n a ly s e s . T h is te c h n iq u e u se s a tw o -d im e n s io n a l

J H E P 0 8 ( 2 0 1 6 ) 0 0 5

s id e b a n d s m e th o d b a s e d o n t h e is o la tio n a n d id e n tif ic a tio n c r ite r ia . F o r t h e id e n tific a ­ tio n , p h o to n s e ith e r s a tis fy t h e fu ll c r ite r ia o f a ll t h e s h o w e r-s h a p e v a ria b le s o u tlin e d in s e c tio n 4.1 o r a n o r th o g o n a l s e le c tio n w h ic h a im s t o m a x im is e th e h a d r o n ic b a c k ­ g r o u n d . T h is o r th o g o n a l s e le c tio n is a c h ie v e d b y in v e r tin g fo u r v a ria b le s r e la te d t o th e firs t la y e r o f t h e E M c a lo r im e te r , w h ic h h a s cells w ith a v e ry s m a ll w id th in n. F o r is o la tio n , p h o to n s a r e e ith e r is o la te d a s d e fin e d in s e c tio n 4.2 o r n o n - is o la te d b y h a v in g E^S° > 7.8 G eV + 4.2 x 1 0-3 x E ^ . T h e fo u r re g io n s a re t h e n d e fin e d in d a t a t o be:

• N A,data: p h o to n c a n d id a te s s a tis f y in g b o t h t h e is o la tio n a n d id e n tif ic a tio n c r ite r ia , i e 7,data

• N B ,data: p h o to n c a n d id a te s t h a t a r e n o n -is o la te d , b u t s a tis fy th e id e n tif ic a tio n c r ite r ia .

• n C,data: p h o to n c a n d id a te s t h a t o n ly s a tis fy t h e o r th o g o n a l id e n tif ic a tio n c r ite r ia b u t a re is o la te d .

• n D,d ata: p h o to n c a n d id a te s t h a t o n ly s a tis f y t h e o r th o g o n a l id e n tif ic a tio n c r ite r ia a n d a r e n o n - is o la te d .

A s d e fin e d a b o v e , th e r e is a 3 G eV s e p a r a tio n b e tw e e n t h e n o n - is o la te d re g io n a n d th e is o la te d re g io n . T h is s e p a r a tio n is u s e d t o lim it t h e n u m b e r o f p a rtic le -le v e l s ig n a l p h o to n s t h a t fall in to t h e b a c k g r o u n d re g io n s. T o q u a n tif y th is effect, sig n a l le a k a g e f r a c tio n s a re c a lc u la te d in M C s im u la tio n s :

N K,MC fK,MC _ signal

f = NA,MC ’ ( 5 . 1)

signal

w ith K = B , C , D . T h e s e le a k a g e f r a c tio n s a r e fo u n d t o b e s m a ll a n d a re c a lc u la te d in P y T H ia fo r t h e c e n tr a l v a lu e , w ith S H E r p a u s e d as a c ro ss-c h e c k .

T h e tw o -d im e n s io n a l s id e b a n d s m e th o d a s s u m e s t h a t t h e tw o c h o s e n v a ria b le s a re in d e p e n d e n t fo r t h e b a c k g r o u n d . T h e is o la tio n a n d id e n tif ic a tio n c r ite r ia a r e c h o s e n t o m in im is e a n y s u c h d e p e n d e n c e , b u t a n y d e v ia tio n fro m th is a s s u m p tio n c a n b e a c c o u n te d fo r b y u s in g M C s im u la tio n s t o c a lc u la te t h e ra tio :

n a,m c n d,m c

R = N bkg • N bkg ( _ 2)

R bkg = N B,MC nC,MC , ( 5 .2)

N bkg • N bkg

w h e re a re th e n u m b e r o f b a c k g r o u n d e v e n ts in e a c h o f t h e re g io n s K = A , B , C , D . F o r t h e c e n tr a l v a lu e t h e a s s u m p tio n , c o n firm e d in a c o n tr o l re g io n , t h a t th e y a r e in d e ­ p e n d e n t ( R bkg = 1) is u se d ; h o w e v er, R bkg is v a r ie d in s e c tio n 7 t o o b t a i n t h e s y s te m a tic u n c e r ta in ty o f a n y p o t e n tia l d e p e n d e n c e .

T h e fo u r s id e b a n d re g io n s, sig n a l le a k a g e f r a c tio n s a n d R bkg a re t h e n u s e d t o so lv e fo r

7» T A, data ♦

N signal v ia:

(

(N C ,d a ta fC ,M C n A,data) \

/ ^{Ą r}B,data /B,MC ^ątA,d a t^ ( f signal ) \ f r. o\

( N - f N si!gnal ) • ) . ( 5 .3)

J H E P 0 8 ( 2 0 1 6 ) 0 0 5

T h is s o lu tio n is u s e d in t h e c r o s s -s e c tio n m e a s u r e m e n t v ia th e sig n a l p u rity , w h ic h is d e ­ fin e d as:

N A,data

Psignal = N-Agdata . ( 5 .4)

I n a ll fo u r re g io n s, P signal is fo u n d t o rise w ith £ / fro m 60% a t 25 G eV t o 100%

a t a r o u n d 300 G eV . I n t h e h ig h e s t £ / in te rv a l t h e m e th o d is i n a c c u r a te d u e t o a la c k of e v e n ts in t h e b a c k g r o u n d re g io n s so h e re t h e c e n tr a l v a lu e o f P signal fro m t h e p re v io u s £ / in te r v a l is u s e d in th e c ro s s - s e c tio n c a lc u la tio n .

F in a lly , a f te r t h e a b o v e s u b t r a c t i o n a r e m a in in g b a c k g r o u n d o f fa k e p h o to n s fro m e le c tr o n s is a c c o u n te d fo r. A s in p re v io u s m e a s u r e m e n ts , th i s is e s tim a te d u s in g M C s im u la tio n s , s c a le d t o t h e m e a s u r e d in te g r a te d lu m in o s ity in d a t a , o f Z a n d W b o s o n d e c a y s t o e le c tro n s . R e c o n s tr u c te d p h o to n s fro m th e s e s im u la tio n s p a s s in g t h e s e le c tio n of s e c tio n 4 a r e c o u n te d if th e y a r e g e o m e tric a lly m a tc h e d t o a p a rtic le -le v e l e le c tro n . T h e n u m b e r o f fa k e p h o to n s re m o v e d ( N e^ 7) is less t h a n 0.2% o f t h e r e m a in in g sig n a l p h o to n s ( N Y,dataP signai) in all fo u r re g io n s a n d fo r m o s t o f t h e £ / r a n g e — o n ly re a c h in g a m a x im u m o f 0.7% in so m e low £ / in te rv a ls . A s th i s is s u c h a s m a ll effect n o s y s te m a tic u n c e r ta in ty is a s s ig n e d t o th i s s u b tr a c tio n .

6 C ro ss se c tio n

T h e d iff e re n tia l is o la te d p r o m p t p h o to n c ro ss s e c tio n as a f u n c tio n o f £ / ( c a lc u la te d in fo u r |n Y| re g io n s) in c lu d e s e le m e n ts d e s c rib e d in t h e p re v io u s s e c tio n s a n d ta k e s t h e fo rm :

A = t

A

w h e re £ / is t h a t o f t h e h ig h e s t tr a n s v e r s e e n e r g y p h o to n s a tis fy in g t h e k in e m a tic , id e n tif ic a tio n a n d is o la tio n c r ite r ia (s e c tio n 4 ) . T h e tr ig g e r e fficien cy (etrig) c o r r e c ts N Y,data fo r a n y e v e n ts t h a t w o u ld s a tis f y t h e s e le c tio n c r ite r ia b u t w ere n o t r e c o rd e d in t h e d a t a s e t ( s e c tio n 2) . T h e n u m b e r o f e v e n ts ( N Y,data) w ith a p h o to n s a tis fy in g t h e s e le c tio n c r ite r ia is c o r r e c te d fo r b a c k g r o u n d u s in g t h e p re v io u s ly in tr o d u c e d s u b t r a c t i o n fa c to r s P signal a n d N e^7 ( s e c tio n 5) . F u r th e r , t h e o v e ra ll size o f t h e s tu d ie d d a t a s e t is a c c o u n te d fo r b y d iv id in g b y t h e t o t a l in te g r a te d lu m in o s ity ( / L d t) a n d th e c ro ss s e c tio n is n o rm a lis e d t o in v e rse G eV b y d iv id in g e a c h m e a s u r e d £ / in te rv a l b y its size ( A £ / ).

T h e r e m a in in g f a c to r , ecorr, is t h e u n fo ld in g c o r r e c tio n f a c to r u s e d t o c o r r e c t th e m e a ­ s u r e m e n t t o p a r tic le level t o allo w fo r d ir e c t c o m p a r is o n s t o th e o r e tic a l p r e d ic tio n s . T h e u n fo ld in g fa c to rs a r e d e riv e d u s in g Py t h i a, w ith Sh e r p a u s e d a s a c ro ss-c h e c k . T h e u n ­ fo ld in g c o r r e c tio n fa c to r s a r e e x tr a c t e d b y u s in g a b in - b y - b in u n fo ld in g p r o c e d u r e a n d a re d e fin e d as:

N m c l

f = signal (6 2)

tcorr = N MC , ( 2)

particle

w h e re N sMCal a n d N M C icle re fe r t o t h e n u m b e r o f e v e n ts w ith a n is o la te d p h o to n a t d e te c to r level a n d p a r tic le level re s p e c tiv e ly .

J H E P 0 8 ( 2 0 1 6 ) 0 0 5

T h e m a in c o n tr ib u tio n t o ec°rr is t h e id e n tif ic a tio n efficien cy (s e c tio n 4 .1 ) , r e s u ltin g in a v e ry s im ila r s h a p e in c lu d in g t h e s lig h t d e c re a s e a t h ig h E T . H o w ev er, ec°rr d iffers a s it a ls o c o n ta in s t h e effe cts fro m p h o to n m ig r a tio n s b e tw e e n d iffe re n t E T in te rv a ls a n d t h e is o la tio n e fficien cy (s e c tio n 4 .2 ) . T h e o v e ra ll c o r r e c tio n lies b e tw e e n 0 .8 a n d 0.9 a n d th e r e f o r e in d ic a te s t h a t d e t e c t o r effe c ts a r e r a t h e r sm a ll.

T h e r e s u lts o f t h e b in -b y -b in u n fo ld in g p r o c e d u r e a r e c ro ss-c h e c k e d u s in g a n ite r a tiv e u n fo ld in g m e th o d , w h ic h re d u c e s th e re lia n c e o n t h e s h a p e o f t h e M C s im u la tio n d i s t r i b u ­ tio n s o f E T a t p a r tic le o r d e t e c t o r level. T h e m e th o d is b a s e d o n B a y e s T h e o r e m [54] a n d ite r a tiv e ly6 u n fo ld s th e s p e c tr u m b y c h a n g in g t h e p r io r o f t h e p a rtic le -le v e l d i s t r i b u t i o n t o t h e p re v io u s ly u n fo ld e d s p e c tr u m fo r th e n e x t ite r a tio n . T h e r e s u lts sh o w t h a t t h e tw o u n fo ld in g p r o c e d u r e s a re in v e ry g o o d a g r e e m e n t, c o n s id e rin g s t a t i s t i c a l u n c e r ta in tie s only.

7 U n c e r ta in tie s

T o e s tim a te t h e s y s te m a tic u n c e r ta in tie s , t h e c ro s s -s e c tio n c a lc u la tio n w as r e p e a te d v a ry in g t h e s e le c tio n p r o c e d u r e , b a c k g r o u n d s u b t r a c t i o n te c h n iq u e s o r t h e u n fo ld in g c o r r e c tio n fa c ­ to r . O n e d iffe re n c e c o m p a r e d t o th e p re v io u s a n a ly s e s is t h a t th is m e a s u r e m e n t m a k e s u se o f th e B o o t s t r a p te c h n iq u e [55] t o e v a lu a te t h e s ta t i s t i c a l in flu e n c e o n s y s te m a tic u n c e r t a i n ­ tie s , a c h ie v e d b y p r o d u c in g a la rg e n u m b e r o f w e ig h te d (b a s e d o n a P o is s o n d is tr ib u tio n ) r e p lic a s fo r e a c h e v e n t. T h e r e s u lt is t h e n u s e d t o re d u c e th e s t a t i s t i c a l f lu c tu a tio n s b y a p p ly in g a tw o - s te p s m o o th in g te c h n iq u e ; firs tly c o m b in in g E T in te rv a ls u n til t h e p r o p a ­ g a te d u n c e r ta in ty h a s a s u ffic ie n tly la rg e s ta t i s t i c a l sig n ific a n c e , fo llo w ed b y p e r f o r m in g a G a u s s ia n k e rn e l s m o o th in g o n t h e o r ig in a l E T in te rv a ls .

T h e fo llo w in g t e x t d e s c rib e s t h e in c lu d e d u n c e r ta in ty s o u rc e s ( q u a n tif y in g th o s e t h a t a r e s m a lle r):

• T h e p h o to n e n e rg y sc a le is a lte r e d b y v a r y in g s y s te m a tic s o u rc e s u p a n d d o w n , w ith t h e r e s u ltin g s h ifts b e in g s u m m e d in q u a d r a t u r e t o p ro v id e t h e t o t a l u n c e r ta in ty . T h e s o u rc e s a re s p lit t o a c c o u n t fo r c o r r e la tio n s a n d r a n g e fro m b e in g r e la te d to : d e te c to r m a te r ia l a n d r e a d - o u t; s im u la tio n o f t h e d e te c to r ; e x tr a p o la tio n s fro m d a ta - d r iv e n m e a s u r e m e n ts ; a n d fin a lly d e ta ils r e la te d t o t h e d iffe re n c e s b e tw e e n u n c o n v e r te d o r c o n v e r te d p h o to n sh o w e rs in t h e c a lo r im e te r. T h e u n c e r ta in ty in t h e p h o to n e n e rg y sc a le is a r o u n d 1% , e x c e p t fo r t h e re g io n 1.56 < |n Y| < 1.81, b u t t h e u n c e r ta in ty in t h e m e a s u r e m e n t is la r g e r d u e t o th e s te e p ly fa llin g c ro ss s e c tio n .

• T h e a d m ix tu r e o f d ir e c t a n d f r a g m e n ta tio n p h o to n s in a g iv e n E T in te r v a l affe c ts t h e c a lc u la tio n o f b o t h P signal a n d ecOTr. I n s te a d o f u s in g t h e d e f a u lt M C s im u la tio n fr a c tio n , a fit o f th e E T d i s t r i b u t i o n is p e rfo r m e d in P y T H ia t o fin d t h e o p tim a l a d m ix tu r e (a s d o n e in th e r e c e n t p h o to n p lu s j e t p a p e r [36]). T h e u n c e r ta in ty is d e ­ riv e d b y c o m p a r in g t h e r e s u lts fro m th is o p tim a l a d m ix tu r e w ith t h e d e f a u lt P y T H ia s im u la tio n . T h is re p la c e s t h e s y s te m a tic u n c e r ta in ty o b ta in e d p re v io u s ly fro m a n a r b i t r a r y re m o v a l o r d o u b lin g o f t h e f r a g m e n ta tio n c o m p o n e n t.

6In this analysis the result converges after four iterations.

J H E P 0 8 ( 2 0 1 6 ) 0 0 5

• R bkg is s e t t o u n ity w h e n P signal is c a lc u la te d . A s d e s c r ib e d in s e c tio n 5 , th is follow s t h e a s s u m p tio n t h a t th e r e a r e n o c o r r e la tio n s b e tw e e n t h e is o la tio n a n d id e n tif ic a tio n c r ite r ia fo r t h e b a c k g ro u n d . A t e s t o f t h is a s s u m p tio n is p e rfo rm e d b y s u b d iv id in g t h e b a c k g r o u n d - d o m in a te d re g io n w ith a n a d d itio n a l n o n -is o la te d c r ite r io n a n d th e n r e p e a tin g t h e tw o -d im e n s io n a l s id e b a n d s in b a c k g r o u n d o n ly re g io n s. A 10% d iffe r­

e n c e fro m u n ity is fo u n d in th is t e s t , w h ic h is t h e n a p p lie d t o R bkg t o c a lc u la te th e u n c e r ta in ty .

• A s d e s c r ib e d in s e c tio n 4 .1 , t h e p h o to n id e n tif ic a tio n e fficien cy in t h e M C s im u la tio n s u se s c o r r e c tio n f a c to r s a n d t h e a s s o c ia te d u n c e r ta in ty in th e s e a lte r s t h e c ro ss s e c tio n b y 0.5% fo r m o s t o f th e E T r a n g e . I n t h e lo w est E T in te r v a ls it re a c h e s 2% a n d a b o v e 550 G eV it r a n g e s fro m 1% t o 4% ( in c r e a s in g w ith n Y).

• F o r t h e a b o v e p h o to n id e n tif ic a tio n c o r r e c tio n fa c to r s a n e x t r a u n c e r ta in ty is re q u ire d , o b ta in e d fro m M C s im u la tio n s , t o a c c o u n t fo r a s m a ll d iffe re n c e in t h e p h o to n iso la ­ tio n r e q u ir e m e n t a p p lie d in t h is a n a ly s is fro m t h a t u s e d fo r t h e m e a s u r e m e n t o f th e p h o to n id e n tif ic a tio n efficiency. T h is im p a c ts t h e c ro ss s e c tio n by 0.5% b u t rise s t o 1% fo r t h e h ig h e s t E T in te rv a ls .

• T h e o r th o g o n a l id e n tif ic a tio n s e le c tio n in s e c tio n 5 re lie s o n in v e r tin g t h e s e le c tio n c r ite r ia o f fo u r o f t h e s h o w e r-s h a p e v a ria b le s . T h e u n c e r ta in ty in t h is p r o c e d u r e is e s tim a te d b y in v e r tin g e ith e r o n ly tw o o f th e s e v a ria b le s o r b y in v e r tin g a n e x t r a v a r ia b le . A d a ta - d r iv e n te c h n iq u e is u s e d t o d is e n ta n g le t h is u n c e r ta in ty fro m t h a t a lr e a d y in c lu d e d in t h e R bkg u n c e r ta in ty a b o v e . T h e r e s u ltin g u n c e r ta in ty is 2% fo r E T < 100 G eV b u t q u ic k ly fa lls t o z e ro fo r h ig h e r E T .

• T h e is o la tio n r e q u ir e m e n t u s e d t o d e fin e t h e b a c k g r o u n d re g io n in th e P signal c a l­

c u la tio n w as a lte r e d so t h a t t h e c o n s ta n t p a r t o f t h e r e q u ir e m e n t (7 .8 G eV ) w as v a rie d b y ± 1 G eV (c h o se n a s it is la r g e r t h a n a n y d iffe re n c e in th e M C s im u la tio n s b e tw e e n p a rtic le -le v e l a n d d e te c to r - le v e l is o la tio n ) . T h e r e s u ltin g u n c e r ta in ty is less t h a n 0.5% .

• T h e p h o to n e n e rg y r e s o lu tio n is c a lc u la te d fro m se v e ra l in d e p e n d e n t s o u rc e s in a s im ila r m a n n e r t o t h e e n e rg y scale, b u t t h e r e s o lu tio n is f o u n d t o b e o f m u c h less im p o r ta n c e t h a n t h e sc a le a s it o n ly p r o d u c e s a n u n c e r ta in ty o f 0 .5 % , w h ic h rises t o 1% fo r t h e h ig h e s t E T in te rv a ls .

• T h e effect o f u n fo ld in g is in v e s tig a te d b y u s in g a s m o o th f u n c tio n t o re w e ig h t th e M C s im u la tio n s t o m a tc h th e d a t a E T d is tr ib u tio n . U n fo ld in g t h e d a t a u s in g th is re w e ig h te d M C p r e d ic tio n g iv es a d iffe re n c e o f less t h a n 0.5% c o m p a r e d t o t h e n o m in a l v a lu e .

• T h e u n c e r ta in ty in th e c o r r e c tio n fa c to r s fro m t h e c h o ic e o f Q C D - c a s c a d e a n d h a d ro - n is a tio n m o d e l is d e riv e d fro m c o m p a r in g S H E r p a w ith P y T H ia . T o a v o id d o u b le c o u n tin g t h e effe c ts fro m t h e f r a g m e n ta tio n c o n tr ib u tio n , t h e P y T H ia s im u la tio n

J H E P 0 8 ( 2 0 1 6 ) 0 0 5

F i g u r e 2. S u m m ary of th e relative size of th e com bined sy stem atic u n c e rta in ty (which excludes th e lum inosity) and its four m ain co n trib u tio n s, show n as a function of E T .

with the optim al adm ixture of direct and fragm entation photons is used again. The resulting uncertainty is 2% at low £ / but quickly falls to zero as £ / increases.

• The integrated luminosity has an uncertainty measured to be ±1.9%. It is derived, following the same methodology as th a t detailed in ref. [22], from a calibration of the luminosity scale derived from beam -separation scans performed in November 2012.

• O ther uncertainties were studied, but are not included in the system atic uncertainty as they were found to be negligible. Examples of these studies include: investi­

gating the trigger efficiency (statistical uncertainties are < 0.1%), pile-up (splitting the dataset by number of interactions per bunch crossing) and the MC simulation isolation shift (correcting the MC simulation by twice the fit accuracy).

The systematic uncertainties except for the luminosity uncertainty are combined. This is done by treating each of the sources as uncorrelated in each £ / interval. However, the sources are treated as correlated across different intervals in £ / . This combination is shown in figure 2 along with several of the main system atic uncertainties detailed above.

The energy scale uncertainty dominates the h ig h -£ / region, especially in the region 1.56 <

In7 1 < 1.81. At low £ / the uncertainties from the Rbkg variation and adm ixture of direct and fragm entation photons are of similar m agnitude and dom inate the uncertainty. In the

£ / range 80-200 GeV the main system atic uncertainties are of similar order and, in all but the region 1.56 < |n7 1 < 1.81, this leads to the luminosity uncertainty being larger than this combination of the other systematic uncertainties.

The statistical uncertainty is mainly from the data, but also has a component due to the MC simulation. This component is from the reliance on MC simulations in the calculation of Psignal and ecorr. The resulting total statistical uncertainty is 1-2% for most of the measured £ / range, until it rises steeply in the highest £ / intervals.

J H E P 0 8 ( 2 0 1 6 ) 0 0 5

Figure 3. D ifferential cross sections from d a ta an d J e t P h o x (using th e C T10 P D F ), show n as a function of E ^ for th e four |n7 | regions. T he d istrib u tio n s are scaled, by specified factors, to se p a ra te th e d istrib u tio n s visually.

8 R e su lts and d isc u ssio n

The final cross sections are measured following eq. (6.1) in the fiducial region given in section 1. The system atic uncertainties, as described in section 7, are combined with the statistical uncertainty, b u t do not include the luminosity uncertainty. The measured cross sections are compared to theoretical predictions, as detailed in section 3, along with uncertainties from the combination of the scale, PD F, 0 ¾ and hadronisation plus UE un­

certainties. Figure 3 shows a summary of the results (with the measured cross sections also being tabulated in appendix A) , where it can be seen th a t the measurement is well described overall by J e t P h o x over ten orders of m agnitude in cross section. The total cross sections shown in table 1 are integrated over the entire ET for each n7 region. As seen in the previous measurement [9] the total cross sections are 20% higher in d ata th an those predicted by J e t P h o x , but the results are consistent within the uncertainties. It can also be seen th a t the measurement uncertainty, dom inated by the system atic uncertainty, is smaller than the theoretical uncertainty.

The difference between d ata and J e t P h o x is explored further in figure 4 where the cross-section ratios are shown in each of the four n7 regions as a function E T . Each n7 region shows a similar trend at low E T , in th a t the J e t P h o x NLO predictions are up to 20% lower th an those measured. This difference remains constant, especially in the central n7 region, for ET < 500 GeV where the fragm entation contribution decreases with ET from being

J H E P 0 8 ( 2 0 1 6 ) 0 0 5

|n7 1 range £

p

0-0.6 0.6-1.37 1.56-1.81 1.81-2.37

25-1500 25-1100 25-650 25-650

15.6-1'4(syst) ± 0.0 2 (stat) ± 0.3(lum i) 2 0 .2 -2 'i(sy st) ± 0.0 3 (stat) ± 0.4(lum i)

6.7-0'][(syst) ± 0.0 2 (stat) ± 0.1(lum i) 14.3-1 ' 4(syst) ± 0.0 3 (stat) ± 0.3(lum i)

13.3 ± 2.6(theory) 17.1 ± 3.2(theory)

5.2 ± 1.0(theory) 11.4 ± 2.3(theory) Table 1. M easured an d p red icte d to ta l cross sections show n for each of th e four |nY | ranges. T he J e t P h o x p red ictio n s are m ade using th e C T10 P D F .

Figure 4. R atio of th e o ry ( J e t P h o x using th e C T10 P D F ) to d a ta for th e differential cross sections as a function of £ - for th e four \rp | regions. T he s ta tistic a l com ponent of th e u n c e rta in ty in th e d a ta is in d icated b y th e horizontal tick m arks w hereas th e whole error b a r corresponds to th e com bined s ta tistic a l and sy stem atic u n c e rta in ty (the ad d itio n al sy stem atic u n c e rta in ty arising from th e u n c e rta in ty in th e in te g ra te d lu m in o sity is displayed se p arate ly as a d o tte d line). T he N L O to ta l u n c e rta in ty from J e t P h o x is displayed as a b an d , w hich corresponds to th e com bination of th e scale, a S, P D F an d h ad ro n isatio n -p lu s-U E uncertain ties. In th e highest £ - interval of th e

|nY| < 0.6 region th e th eo re tic al p red ictio n an d u n c e rta in ty is n o t show n as it is above th e range of th e figure.

a large contribution to the cross section, showing th a t

models this contribution well ap art from the normalisation. The normalisation difference decreases above this £ ^ and in the range 1100 < £ ^ < 1500 GeV the prediction overestimates the measurement, although this is where the experimental and PD F uncertainties are largest. The results are shown using the CT10 PD F, but there is very little difference when comparing the central value to those from MSTW2008, NNPDF2.3 and HeraPDF1.5, with any difference at high

£T being covered by the large theoretical uncertainty.

The overall trend in differences between d ata and theory is similar to th a t seen in the measurement using 2011 data. However, a significant increase in the experimental

J H E P 0 8 ( 2 0 1 6 ) 0 0 5