P u b l i s h e d f o r SISSA b y S p r i n g e r Re c e i v e d: December 13, 2017
Ac c e p t e d: December 26, 2017
Pu b l i s h e d: January 9, 2018
Further studies of isolated photon production with a jet in deep inelastic scattering at H ERA
T h e ZEU S collaboration
E -m a il: m.wing@ucl.ac.uk
A b s t r a c t : Iso la te d p h o to n s w ith hig h tra n sv e rs e en e rg y have b ee n s tu d ie d in d eep in
e la stic ep s c a tte rin g w ith th e ZE U S d e te c to r a t H E R A , u sin g a n in te g ra te d lu m in o sity o f 326 p b- 1 in th e ra n g e of e x c h a n g e d -p h o to n v irtu a lity 10-350 G e V 2. O u tg o in g iso lated p h o to n s w ith tra n s v e rs e en e rg y 4 < E ^ < 15 G eV a n d p se u d o ra p id ity - 0 . 7 < < 0.9 w ere m easu red w ith ac co m p a n y in g je ts h av in g tra n s v e rs e en e rg y a n d p s e u d o ra p id ity 2.5 <
E ^ < 35 G eV a n d - 1 . 5 < rjjet < 1.8, respectiv ely. D ifferen tial cross sectio n s a re p re se n te d fo r th e follow ing variables: th e fra c tio n of th e in co m in g p h o to n en e rg y a n d m o m e n tu m t h a t is tra n s fe rre d to th e o u tg o in g p h o to n a n d th e lead in g je t; th e fra c tio n of th e in com ing p ro to n en e rg y tra n s fe rre d to th e p h o to n a n d lead in g je t; th e differences in a z im u th a l an g le an d p se u d o ra p id ity b etw e en th e o u tg o in g p h o to n a n d th e lead in g j e t a n d b etw e en th e o u tg o in g p h o to n a n d th e s c a tte re d elec tro n . C o m p ariso n s are m a d e w ith th e o re tic a l p re d ic tio n s: a le a d in g -lo g a rith m M o n te C arlo sim u la tio n , a n e x t-to -le a d in g -o rd e r Q C D p re d ic tio n , a n d a p re d ic tio n u sin g th e k y -fa c to ris a tio n a p p ro a c h .
Ke y w o r d s: L ep to n -N u cleo n S c a tte rin g (e x p e rim e n ts), P h o to n p ro d u c tio n , Q C D
ArXiv ePr i n t: 1712.04273
Op e n Ac c e s s, © The Authors.
Article funded by SCOAP3. https://doi.org/10.1007/JH E P01(2018)032
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
C o n te n ts
1 I n tr o d u c tio n 1
2 E x p e r im e n ta l s e t- u p 2
3 E v e n t s e le c tio n a n d r e c o n s tr u c tio n 2
4 V a r ia b le s s tu d ie d 4
5 E v e n t s im u la tio n 5
6 T h e o r e tic a l c a lc u la tio n s 5
7 E x t r a c tio n o f t h e p h o t o n sig n a l 6
8 S y s t e m a t ic u n c e r ta in t ie s 8
9 R e s u lts 9
10 S u m m a r y 19
T h e Z E U S c o lla b o r a tio n 28
1 In tr o d u c tio n
T h e iso la te d h ig h -en e rg y p h o to n s t h a t a re e m itte d in h ig h -en e rg y collisions involving h a d ro n s are p re d o m in a n tly u n affec te d by p a r to n h a d ro n is a tio n . T h e ir p ro d u c tio n p ro b es th e u n d e rly in g p a rto n ic p rocess a n d c a n p ro v id e in fo rm a tio n o n th e s tr u c tu r e of th e p ro to n . P ro ce sse s of th is ty p e h ave b ee n s tu d ie d in a n u m b e r of fix e d -ta rg e t a n d h a d ro n -c o llid e r e x p e rim e n ts [1- 10]. T h e p ro d u c tio n of iso lated p h o to n s in p h o to p ro d u c tio n , w h ere th e in co m in g p h o to n is q u asi-real, w as p re v io u sly s tu d ie d a t H E R A by th e ZE U S a n d H1 col
la b o ra tio n s [11- 15]. D eep in e la stic n e u tra l c u rre n t (N C ) ep s c a tte rin g (D IS), in w hich th e ex c h an g ed p h o to n h as v irtu a lity Q2 > 1 G eV 2, h as also b ee n m e a su re d in a v a rie ty of Q2 ra n g es [16- 18]. T h e an aly sis p re se n te d h ere e x te n d s a n ea rlie r Z E U S m e a s u re m e n t of iso la te d p h o to n s a n d je ts in D IS [19].
F ig u re 1 show s le a d in g -o rd e r d ia g ra m s for h ig h -en e rg y p h o to n p ro d u c tio n in D IS. Such
“p ro m p t” p h o to n s a re e m itte d e ith e r by th e in co m in g o r o u tg o in g q u a rk o r by th e in co m ing o r o u tg o in g lep to n . In th e first case, th e p h o to n s are classified as “Q Q ” p h o to n s, a n d th e h a d ro n ic p rocess h as tw o h a rd scales: th e v irtu a lity Q2 of th e in cid en t ex c h an g ed p h o to n a n d th e sq u a re o f th e tra n s v e rs e m o m e n tu m of th e p ro m p t p h o to n . In th e second case, th e p h o to n s a re d e n o te d as “L L ” a n d are e m itte d from th e inco m in g o r o u tg o in g le p to n . T h e p re se n t an a ly sis re q u ires th e o b se rv a tio n of a s c a tte re d elec tro n , a h ig h -en e rg y o u tg o in g
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p h o to n a n d a h a d ro n ie je t. P ro c e sse s in w hich th e final s ta te co n sists solely o f a h a rd o u tg o in g e le c tro n a n d a h a rd o u tg o in g p h o to n are th e re b y ex clu d ed . B y re q u irin g th e o u tg o in g p h o to n to be iso lated , a fu r th e r class of p rocesses in w hich th e p h o to n is p ro d u c e d w ith in a je t is su p p re sse d .
In th e p re v io u s Z E U S p u b lic a tio n o n th is to p ic [19], k in e m a tic d is trib u tio n s o f th e o u tg o in g p h o to n a n d th e je t w ere stu d ie d . U sing th e sam e d a t a set, th e an a ly sis is ex te n d e d here by m e a su rin g v aria b les t h a t involve tw o of th e o u tg o in g p h o to n , th e j e t a n d th e s c a tte re d elec tro n . R e s u lts from a le a d in g -lo g a rith m p a rto n -sh o w e r M o n te C arlo [20] are c o m p a re d to th e m e a su re m e n ts. C o m p a riso n is also m a d e w ith tw o th e o re tic a l m o d els:
one a t n e x t-to -le a d in g o rd e r (N L O ) in Q C D [2 1 , 22], a n d o ne b ase d o n a k T-fa c to ris a tio n a p p ro a c h [23].
2 E x p e r im e n ta l s e t-u p
T h e d a t a sam p le used for th e m e a su re m e n t c o rre sp o n d s to an in te g ra te d lu m in o sity of 326 ± 6p b- 1 a n d w as ta k e n w ith th e Z E U S d e te c to r in th e y ears 2 00 4-2007. D u rin g th is p erio d , H E R A ra n w ith an e le c tro n /p o s itro n b e a m en e rg y of 27.5 GeV a n d a p ro to n b e a m en e rg y o f 920 GeV; 138 ± 2 p b- 1 of e + p d a t a a n d 188 ± 3 p b- 1 o f e - p d a t a1 w ere used in th e p re se n t analy sis.
A d e ta ile d d e sc rip tio n o f th e Z E U S d e te c to r c a n b e fo u n d elsew here [24]. C h arg e d p a r ticles w ere reco rd e d in th e c e n tra l tra c k in g d e te c to r (C T D ) [25- 27] a n d a silicon m icro v e rtex d e te c to r [28] w hich o p e ra te d in a m a g n e tic field of 1.43 T p ro v id ed by a th in s u p e rc o n d u c t
ing solenoid. T h e h ig h -re so lu tio n u ra n iu m -s c in tilla to r c a lo rim e te r (C A L ) [29- 32] co n sisted o f th re e p a rts : th e fo rw ard (F C A L ), th e b a rre l (B C A L ) an d th e re a r (R C A L ) c a lo rim e te rs.
T h e B C A L covered th e p s e u d o ra p id ity ra n g e - 0 .7 4 to 1.01 as seen from th e n o m in al in
te ra c tio n p o in t. 2 T h e F C A L a n d R C A L e x te n d e d th e ra n g e to - 3 . 5 to 4.0. T h e sm allest su b d iv isio n o f th e C A L is called a cell. T h e b a rre l e le c tro m a g n e tic c a lo rim e te r (B E M C ) cells h a d a p o in tin g g e o m e try aim ed a t th e n o m in al in te ra c tio n p o in t, w ith a cross sectio n a p p ro x im a te ly 5 x 20 c m 2, w ith th e finer g ra n u la rity in th e Z -d ire c tio n . T h is fine g ra n u la rity allow s th e use of sh o w er-sh ap e d is trib u tio n s to d is tin g u is h iso lated p h o to n s from th e p ro d u c ts of n e u tra l m eson d ecays such as n0 ^ 7 7.
T h e lu m in o sity w as m e a su re d u sin g th e B e th e -H e itle r re a c tio n ep ^ e y p by a lu m i
n o sity d e te c to r w hich co n sisted o f tw o in d e p e n d e n t sy stem s: a le a d -s c in tilla to r ca lo rim e
te r [33- 35] a n d a m a g n e tic s p e c tro m e te r [36].
3 E v en t s e le c tio n an d r e c o n str u c tio n
T h e Z E U S e x p e rim e n t o p e ra te d a th ree -lev el trig g e r sy ste m [2 4 , 3 7 , 38]. A t th e first level, ev e n ts w ere selected if th e y h a d a n en e rg y d e p o s it in th e C A L c o n sis te n t w ith a n iso lated
1Hereafter, “electron” refers to both electrons and positrons unless otherwise stated.
2The ZEUS coordinate system is a right-handed Cartesian system, with the Z axis pointing in the nominal proton beam direction, referred to as the “forward direction” , and the X axis pointing towards the centre of HERA. The coordinate origin is at the centre of the central tracking detector. The pseudorapidity is defined as n = — ln (tan | ) , where the polar angle, 0, is measured with respect to the Z axis. The azimuthal angle, 7, is measured with respect to the X axis.
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elec tro n . A t th e second level, a re q u ire m e n t o n th e en e rg y a n d lo n g itu d in a l m o m e n tu m o f th e ev en t w as used to select N C D IS ev en ts. A t th e th ir d level, th e full ev en t was re c o n s tru c te d a n d tig h te r re q u ire m e n ts fo r a D IS e le c tro n w ere m ad e. Offline selections, sim ila r to th o se of th e e a rlie r ZE U S an a ly sis [19], w ere th e n ap p lied .
O u tg o in g ele c tro n s w ere selected w ith p o la r an g le 9e > 140° in o rd e r to p ro v id e a good m e a su re m e n t in th e R C A L , k in e m a tic a lly s e p a ra te d from th e selected o u tg o in g p h o to n s.
T h e ir im p a c t p o in t ( X ,Y ) o n th e su rface o f th e R C A L w as re q u ire d to lie o u ts id e a re c t
a n g u la r region ± 1 4 .8 cm in X a n d [ - 1 4 .6 , +12.5] cm in Y , to give a well u n d e rs to o d a c c e p ta n c e . T h e o u tg o in g elec tro n s w ere id entified u sin g a n e u ra l n etw o rk [39], a n d th e en e rg y o f th e o u tg o in g elec tro n , E'e, c o rre c te d for a p p a r a tu s effects, w as re q u ire d to b e la rg e r th a n 10 GeV. T h e k in e m a tic v a ria b le Q2 w as re c o n s tru c te d as Q2 = — (k — k ') 2, w h ere k (k ') is th e fo u r-m o m e n tu m of th e in com ing (o u tg o in g ) elec tro n . T h e k in e m a tic region 10 < Q2 < 350 G eV2 w as selected.
A re q u ire m e n t t h a t th e ev en t v e rte x p o sitio n , Z ^ x , sh o u ld be w ith in th e ra n g e |Z vtx| <
40 cm red u ces th e b a c k g ro u n d from n o n -ep collisions. A f u r th e r re q u ire m e n t for a well- c o n ta in e d D IS ev en t, 35 < E —p Z < 65 GeV, w as im p o sed w h ere E —p Z = ^ E ^ 1 — cos 9i);
i
E i is th e en e rg y of th e i- th C A L cell, 9i is its p o la r an gle a n d th e su m ru n s over all cells [40].
P h o to n c a n d id a te s w ere iden tified as energy-flow o b je c ts (E F O s) 3 w ith o u t an asso ci
a te d tra c k , for w hich a t le a st 90% of th e re c o n s tru c te d en e rg y w as d e p o site d in th e B E M C . T h e c a lib ra tio n of th e energies of th e p h o to n a n d s c a tte re d e le c tro n w as ta k e n from an ea rlie r Z E U S an a ly sis an d used d ee p ly v irtu a l C o m p to n s c a tte rin g ev en ts [44]. T h e re
c o n s tru c te d tra n s v e rs e en e rg y of th e p h o to n c a n d id a te , E j , w as re q u ired to lie w ith in th e ra n g e4 4 < E j < 15 GeV a n d th e p se u d o ra p id ity , p7 , h a d to sa tisfy —0.7 < p7 < 0.9.
J e ts w ere re c o n s tru c te d w ith th e k y c lu ste rin g a lg o rith m [45] in th e E schem e in th e lo n g itu d in a lly in v a ria n t inclusive m o d e [46] w ith th e R p a r a m e te r set to 1.0. Since all E F O s o f th e ev en t w ere used ex c ep t for th e e le c tro n signal, one o f th e je ts fo u n d by th is p ro c e d u re co rre sp o n d s to or includes th e p h o to n c a n d id a te . A t le a st one ac c o m p a n y in g je t w as re q u ire d w ith tra n s v e rs e en e rg y E j4 > 2.5 G eV a n d p se u d o ra p id ity , pjet, in th e ra n g e
— 1.5 < pJet < 1.8; if m ore th a n one j e t w as fo un d, t h a t w ith th e h ig h est E j4 w as used.
P h o to n s ra d ia te d from fin a l-sta te e lec tro n s w ere su p p re sse d by re q u irin g t h a t A R >
0.2, w h ere A R = y / ( A 0) 2 + (A p) 2 is th e d is ta n c e to th e n e a re s t re c o n s tru c te d tra c k w ith m o m e n tu m g re a te r th a n 250 M eV in th e p — 0 p lan e. Iso la tio n from h a d ro n ic a c tiv ity was im p o sed by re q u irin g t h a t th e p h o to n c a n d id a te possessed a t least 90% o f th e t o ta l en erg y o f th e je t-lik e o b je c t of w hich it fo rm ed a p a r t. T h is also re d u ced th e b a c k g ro u n d o f p h o to n c a n d id a te s arisin g from n e u tra l m eson decay.
A p p ro x im a te ly 6000 ev e n ts w ere selected a t th is stag e; th is sam p le w as d o m in a te d by b a c k g ro u n d ev e n ts in w hich one o r m o re n e u tra l m esons such as n0 a n d p, d ec ay in g to p h o to n s, p ro d u c e d a p h o to n c a n d id a te in th e B E M C .
3Energy-flow objects [41- 43] were constructed from calorimeter-cell clusters and tracks, associated when possible.
4The upper limit was selected to retain distinguishable shower shapes between the hadronic background and the photon signal.
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4 V a ria b les s tu d ie d
In th e p re v io u s Z E U S p u b lic a tio n [19], d is trib u tio n s of p h o to n a n d je t v aria b les w ere s tu d ied. In th e p re se n t an aly sis, v aria b les t h a t d e p e n d o n tw o of th e th re e m e a su re d o u tg o in g p h y sical o b je c ts w ere stu d ie d , n a m e ly th e h ig h -p T p h o to n , th e lead in g j e t a n d th e s c a tte re d elec tro n . T h e y w ere defined as follows:
• x i p8 is a m e a su re of th e fra c tio n of th e e x c h a n g e d -p h o to n en e rg y a n d lo n g itu d in a l m o m e n tu m t h a t is given to th e o u tg o in g p h o to n a n d th e je t:
„ m a . = E Y - PZ + E Jet - j
Y 2 E ey jb ’
w h ere E7 a n d E Jet d e n o te th e energ ies of th e o u tg o in g p h o to n a n d th e je t, re sp ec
tively, pZ a n d p f d e n o te th e co rre sp o n d in g lo n g itu d in a l m o m e n ta , E e = 27.5 G eV , a n d th e Ja c q u e t-B lo n d e l v aria b le y JB is given by ^ 3 e f o ( E EFO — P FFO) / 2 E e , su m m in g over all energy-flow o b je c ts in th e ev en t ex c ep t th e s c a tte re d elec tro n , each o b je c t b ein g tr e a te d as eq u iv ale n t to a m assless p a rtic le . T h is v aria b le is sen sitiv e to h ig h e r-o rd e r processes t h a t g e n e ra te a d d itio n a l p a rtic le s in th e ev e n t;
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• „pbs e stim a te s th e fra c tio n o f th e p ro to n en e rg y tra n s fe rre d to th e o u tg o in g p h o to n a n d je t:
„obs = EY + P z + EJet + J
„ 2Ep ’
w h ere E p = 920 G eV . T h is v a ria b le is sen sitiv e to th e p a rto n ic s tru c tu r e of th e p ro to n ;
• A3 is th e a z im u th a l angle b etw e en th e je t a n d th e o u tg o in g p h o to n : A3 = |3Jet — 3Y1, w h ere 3*et a n d 3Y d e n o te th e a z im u th a l angles of th e je t a n d p h o to n , respectively.
T h is v aria b le is sen sitiv e to th e p resen ce of h ig h e r-o rd e r g lu o n ra d ia tio n from th e o u tg o in g q u a rk , w hich g e n e ra te s a c o n trib u tio n to th e n o n -c o llin e a rity b etw e en th e p h o to n a n d th e lead in g je t;
• A n is th e difference in p se u d o ra p id ity b etw e en th e j e t a n d th e o u tg o in g p h o to n : A n = nJet — nY, w h ere n*et a n d n Y d e n o te th e p s e u d o ra p id ity o f th e je t a n d th e p h o to n , respectively. T h is v aria b le is sensitiv e to th e d y n a m ic a l p ro p e rtie s o f th e s c a tte rin g process;
• A3 e ’7 is th e a z im u th a l angle b etw e en th e s c a tte re d e le c tro n a n d th e o u tg o in g p h o to n : A3 e ’7 = |3e — 3 7 1, w h ere 3e d e n o te s th e a z im u th a l an gle of th e electro n ; th is a n d th e follow ing v aria b le a re sen sitiv e to h ig h e r-o rd e r processes an d to w h e th e r th e p ro cess is LL or QQ ;
• A ne ’7 is th e difference in p s e u d o ra p id ity b etw e en th e s c a tte re d e le c tro n an d th e p h o to n : A ne ’7 = n e — nY, w h ere ne d e n o te s th e p s e u d o ra p id ity of th e electro n .
A sim ilar Z E U S an aly sis h as b ee n p re v io u sly p erfo rm ed for p h o to p ro d u c tio n [44], s tu d y in g all th e p re se n t v aria b les ex c e p t th o s e asso c ia te d w ith th e s c a tte re d elec tro n .
5 E v en t sim u la tio n
M o n te C arlo (M C ) ev en t sam p les w ere g e n e ra te d to e v a lu a te th e d e te c to r a c c e p ta n c e an d to p ro v id e signal an d b a c k g ro u n d d is trib u tio n s . T h e p ro g ra m Py t h ia 6.416 [20] w as used to sim u la te p ro m p t-p h o to n em ission for th e s tu d y o f th e e v e n t-re c o n stru c tio n efficiency. In Py t h i a, th is pro cess is sim u la te d as a D IS pro cess w ith a d d itio n a l p h o to n ra d ia tio n from th e q u a rk line to ac c o u n t for Q Q p h o to n s. R a d ia tio n from th e le p to n is n o t sim u la te d .
T h e LL p h o to n s t h a t w ere ra d ia te d in to th e d e te c to r a n d w ere iso lated fro m th e o u t
going e le c tro n w ere s im u la te d usin g th e g e n e ra to r D j a n g o h 6 [47], a n in terfa ce to th e M C p ro g ra m H e r a c l e s 4.6.6 [48]; h ig h e r-o rd e r Q C D effects w ere in clu d ed u sin g th e co lou r d ip o le m o d el of A r i a d n e 4.12 [49]. H a d ro n is a tio n of th e p a rto n ic final s ta te w as in each case p erfo rm ed by J e t s e t 7.4 [50] usin g th e L u n d s trin g m o d el [51]. In te rfe re n c e b etw een th e LL a n d Q Q te rm s w as n eg lected .
T h e m a in b a c k g ro u n d to th e Q Q a n d LL p h o to n s cam e from p h o to n ic d ecays o f n e u tra l m esons p ro d u c e d in g en e ral D IS processes. T h is b a c k g ro u n d w as sim u la te d usin g D j a n g o h
6, w ith in th e sam e fram ew o rk as th e LL ev en ts. T h is p ro v id ed a re a listic s p e c tru m of single a n d m u ltip le m esons w ith well m odelled k in e m a tic d is trib u tio n s .
T h e g e n e ra te d M C ev e n ts w ere p assed th ro u g h Z E U S d e te c to r a n d trig g e r sim u la tio n p ro g ra m s b ase d o n Ge a n t 3.21 [52]. T h e y w ere th e n re c o n s tru c te d a n d an a ly se d by th e sam e p ro g ra m s as th e d a ta .
6 T h e o r e tic a l c a lc u la tio n s
T h e P y t h i a p re d ic tio n s a n d th e p re d ic tio n s o f tw o p a rto n -le v e l m o dels w ere co m p a re d to th e re su lts of th e p re se n t analy sis. T h e N L O Q C D c a lc u la tio n o f A u ren ch e, F o n ta n n a z an d G u illet (A F G ) [21], w as p e rfo rm e d in th e M S schem e. U n c e rta in tie s on th e Q C D scale a t th is o rd e r c o n trib u te a n o rm a lisa tio n u n c e rta in ty of ty p ic a lly ±8%. T h is c a lc u la tio n w as p erfo rm ed in th e ce n tre-o f-m ass fram e a n d tra n s fo rm e d in to th e la b o ra to ry fram e, w hich in tro d u c e s u n c e rta in tie s on th e cross sectio n s in som e regions o f th e p a r a m e te r space d u e to n o n -p e rtu rb a tiv e effects [2 2]. T h e A F G p re d ic tio n s w ere c a lc u la te d w ith a c u t o f 2.5 G eV o n th e p h o to n tra n s v e rs e m o m e n tu m in th e ce n tre-o f-m ass fram e, an d d o n o t in clu d e an LL c o n trib u tio n , w hich w as e v a lu a te d u sin g th e D j a n g o h - H e r a c l e s sim u la tio n a n d a d d e d s e p a ra te ly to th e A F G c a lc u la tio n for c o m p a riso n w ith th e d a ta . T h e u n c e rta in tie s on th e A F G p re d ic tio n s show n in th e p re se n t p a p e r re p re se n t th e Q C D scale u n c e rta in tie s.
A c a lc u la tio n by B a ra n o v , L ip a to v a n d Z o to v (B LZ) [23] u sed u p d a te d p a ra m e te rs for th e p re se n t p a p e r. I t is b ase d on th e k T-fa c to ris a tio n m e th o d . T h is a p p ro a c h uses u n in te g ra te d p a r to n d e n sitie s a n d ta k e s in to ac c o u n t b o th Q Q a n d LL p h o to n s, n eg lec tin g th e sm all in terfe ren c e c o n trib u tio n . T h e final re su lt is o b ta in e d as th e co n v o lu tio n o f th e off-shell s c a tte rin g m a tr ix elem e n t w ith th e u n in te g ra te d q u a rk d is trib u tio n in th e p ro to n . In th e k x -fa c to ris a tio n th eo ry , som e p a r t o f th e fin a l-s ta te je ts c a n o rig in a te n o t o nly from th e h a rd su b p ro c ess b u t also from th e p a r to n e v o lu tio n c a scad e in th e in itia l s ta te . T h e q u o te d u n c e rta in tie s o n th e B LZ p re d ic tio n s re p re se n t th e Q C D scale u n c e rta in tie s .
- 5 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
In th e prev io u s Z E U S an a ly sis of p ro m p t p h o to n s in D IS , th e m e a su re d v aria b les w ere a sso c ia te d w ith th e e n tire ev en t, w ith th e o u tg o in g p h o to n , a n d w ith je ts . C o m p ariso n s w ere m a d e to a n ea rlie r N L O Q C D th e o ry [53- 55] a n d to B LZ. B o th th e o rie s d esc rib ed th e sh a p e s of th e sin g le-p artic le cross sectio n s well, b u t failed to re p ro d u c e th e n o rm a lisa tio n of th e d a ta . A la te r versio n of th e o rig in al A F G c a lc u la tio n ag reed well w ith th e re s u lts [56], a n d h as b een used in th e p re se n t study .
T h e p re d ic tio n s of A F G a n d B LZ w ere c a lc u la te d a t th e p a r to n level a n d in c o rp o ra te d k in e m a tic a n d iso latio n c rite ria co rre sp o n d in g to th e d a ta . C o rre c tio n s to th e h a d ro n level w ere m a d e u sin g Py t h ia to d e te rm in e th e ra tio of th e h ad ro n -lev el cross sectio n s to th o se a t th e p a r to n level for each v a ria b le in each bin. T h e Py t h ia ev e n ts w ere w eig h ted a t th e p a r to n level to re p re s e n t th e sh ap e s o f th e A F G a n d B LZ d is trib u tio n s in in o rd e r to c a lc u la te th e h a d ro n is a tio n c o rre c tio n s for all th e o th e r m e a su re d v ariab les. T h e c o rre c tio n s for A F G a n d B LZ w ere sim ilar to w ith in 10%. T h is p ro c e d u re w as also ap p lied se p a ra te ly to th e A F G p re d ic tio n s for th e d ifferen t Q2 ranges.
F o r th e B LZ d is trib u tio n , 98% of th e p a rto n -le v e l cross sec tio n is in th e (0.9,
1.0) bin; consequently, for th is v aria b le a tra n s f e r m a trix from th e p a r to n to th e h a d ro n level w as c a lc u la te d u sin g P y t h i a . T h e sam e p ro c e d u re w as u sed for th e A F G x!)16^
d is trib u tio n . T h e re le v an t tra n s f e r m a tric e s for th e o th e r v aria b les gave sim ila r re s u lts to th e re w eig h tin g p ro c ed u re .
7 E x tr a c tio n o f th e p h o to n sig n a l
T h e ev en t sam p le selected acco rd in g to th e c rite ria d esc rib ed in sec tio n 3 w as d o m in a te d by b a c k g ro u n d from n e u tra l m eson decays; th u s th e p h o to n signal w as e x tra c te d s ta tis tic a lly follow ing th e a p p ro a c h used in prev io u s Z E U S an a ly se s [11- 13, 16, 17].
T h e p h o to n signal w as e v a lu a te d m a k in g use of th e w id th of th e B E M C e n e rg y -c lu ste r co rre sp o n d in g to th e p h o to n c a n d id a te . T h is w as c a lc u la te d as th e v aria b le
w h ere Z is th e Z p o s itio n of th e c e n tre o f th e i- th cell, Z clust6r is th e ce n tro id of th e E F O c lu ste r, w c6ii is th e w id th of th e cell in th e Z d ire c tio n , a n d E j is th e en e rg y reco rd e d in th e cell. T h e sum ru n s over all B E M C cells in th e E F O .
T h e d is trib u tio n s of ( S Z ) for th e full d a t a set a n d th e fitte d M C are show n in figure 2. T h e (S Z ) d is trib u tio n e x h ib its a d o u b le -p e a k e d s tru c tu r e w ith th e first p e a k a t « 0.1, asso c ia te d w ith th e p h o to n signal, a n d a second p e a k a t « 0.5, d o m in a te d by th e n0 ^ 7 7
b a c k g ro u n d .
T h e c o n trib u tio n of iso la te d -p h o to n ev e n ts w as d e te rm in e d for each b in in each m ea
su re d v aria b le by a x2 fit to th e (S Z ) d is trib u tio n in th e ra n g e 0.05 < (S Z ) < 0.8, u sin g th e LL an d Q Q signal a n d b a c k g ro u n d M C d is trib u tio n s as d e sc rib e d in sec tio n 5 . T h e m ean valu e of x2/ n .d . f w as 1.2. C o m p a re d to th e e a rlie r Z E U S p u b lic a tio n [19], im p ro v em en ts have b ee n m a d e in th e m o d ellin g of th e sh a p e s of th e (S Z ) d is trib u tio n s o f th e Q Q an d LL c o n trib u tio n s , u sin g a c o m p a riso n b etw e en th e sh ap e s asso c ia te d w ith th e s c a tte re d
- 6 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
(a) (b)
(c) (d)
F ig u r e 1. Lowest-order diagram s for photon production in ep scattering. (a), (b): quark radiative diagram s (QQ); (c), (d): lepton radiative diagram s (LL).
e le c tro n in M C sim u la tio n of D IS a n d in re al d a ta . B y tr e a tin g th e LL a n d Q Q p h o to n s sep a rately , ac c o u n t is ta k e n o f th e effect o f th e ir differing k in e m a tic d is trib u tio n s on th e a c c e p ta n c e , a n d th e effect o f th e ir differing (n, E T ) d is trib u tio n s on th e s h a p e o f th e p h o to n signal.
In p erfo rm in g th e fit, th e th e o re tic a lly well d e te rm in e d LL c o n trib u tio n w as k ep t co n s ta n t a t its M C -p re d ic te d value a n d th e o th e r co m p o n e n ts w ere varied . O f th e 6149 ev en ts selected, 2451 ± 102 co rre sp o n d to th e e x tra c te d signal, in clu d in g 526 LL p h o to n s. T h e fitte d scale fa c to r ap p lied to th e Q Q c o n trib u tio n in figure 2 w as 1.6, c o n siste n t w ith th e ea rlie r Z E U S analy sis.
F o r a given o b serv ab le Y , th e p ro d u c tio n cross sec tio n w as d e te rm in e d for each b in using
d v = a q q • N ( Y qq) + d a fL '
d Y £ • A Y d Y ’
w h ere N (y q q) is th e n u m b e r of Q Q p h o to n s e x tra c te d from th e fit, A Y is th e b in w id th , L is th e to ta l in te g ra te d lum ino sity, is th e p re d ic te d cross sec tio n for LL p h o to n s from
- 7 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
F ig u r e 2. D istribution of (JZ) for the full d a ta sample. The error bars represent the statistical uncertainties on the d a ta points. The solid line shows a fit to the d a ta of three com ponents with fixed shapes as described in the text. The hatched histogram s represent the LL and fitted QQ com ponents of the fit and the fitted hadronic background (BG).
D j a n g o h - H e r a c l e s a n d A q q is th e a c c e p ta n c e c o rre c tio n for Q Q p h o to n s. T h e value o f A q q w as c a lc u la te d , u sin g th e P y t h i a M C , from th e ra tio o f th e n u m b e r of events g e n e ra te d to th o se re c o n s tru c te d in a given bin; it lies in th e ra n g e 0.91-2.28. To im prove th e re p re s e n ta tio n of th e d a ta , a n d h ence th e a c c u ra c y o f th e a c c e p ta n c e c o rrec tio n s, th e M C p re d ic tio n s w ere rew eighted. T h is w as d o n e u sin g p a ra m e te ris e d fu n c tio n s o f Q2 an d o f nY, a n d also b in -b y -b in as a fu n c tio n of p h o to n energy; th e th re e rew eig h tin g fa cto rs w ere a p p lie d m u ltip licativ ely . T h e ir n e t effect o n th e a c c e p ta n c e s w as sm all.
8 S y s te m a tic u n c e r ta in tie s
T h e sources of sy s te m a tic u n c e rta in ty on th e m easu red cross sectio n s a re as in th e p rev iou s p a p e r [19]. T h e p rin c ip a l sources of u n c e rta in ty w ere e v a lu a te d as follows:
• th e en e rg y scale of th e p h o to n c a n d id a te w as v aried by ± 2 % . T h e m e a n ch a n g e of th e cross sec tio n w as ±6%;
• th e en e rg y scale o f th e je ts w as v aried by ± 1 .5 % fo r je ts w ith Ejet > 10 GeV, ± 2 .5 % for je ts w ith E j ? in th e ra n g e [6, 10] GeV a n d ± 4 % for je ts w ith E j ? < 6 GeV. T h e u n c e rta in ty w as ty p ic a lly ± 7 % ;
• th e en e rg y scale of th e s c a tte re d e le c tro n w as v aried by ± 2 % . T h e overall av erage effect on th e cross sectio n s w as less th a n ±1%.
- 8 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
S y ste m a tic u n c e rta in tie s re la te d to th e M C g e n e ra to rs w ere e v a lu a te d as follows:
• th e d e p e n d e n c e o n th e m o d ellin g of th e h a d ro n ic b a c k g ro u n d by m ean s o f Dj a n g o h- He r a c l e s w as in v e stig a te d by v a ry in g th e u p p e r lim it for th e (5 Z ) fit in th e ra n g e [0.6,1.0], givin g v a ria tio n s t h a t w ere ty p ic a lly ± 5 % ;
• u n c e rta in tie s in th e a c c e p ta n c e d u e to th e P y t h i a m o del w ere a c c o u n te d for by ta k in g h a lf o f th e ch a n g e a ttr ib u ta b le to th e rew eig h tin g d esc rib ed in sec tio n 7 as a sy ste m a tic u n c e rta in ty ; for m o st b in s th e effect w as a p p ro x im a te ly 1%.
O th e r sources of sy s te m a tic u n c e rta in ty w ere fo u n d to b e negligible a n d w ere ig nored [17, 57]: th e se in clu d ed v a ria tio n s o n th e c u ts o n A R , th e tra c k m o m e n tu m , E — p Z , Z vtx an d th e e le c tro m a g n e tic fra c tio n of th e p h o to n show er, a n d a v a ria tio n o f 5% o n th e LL fractio n .
T h e sy ste m a tic u n c e rta in tie s w ere sy m m e trise d by ta k in g th e m e a n of th e p o sitiv e an d n e g a tiv e u n c e rta in ty values a n d w ere co m b in ed in q u a d r a tu re . T h e co m m o n u n c e rta in ty o f 1.8% on th e lu m in o sity m e a su re m e n t is n o t in clu d ed in th e ta b le s a n d figures.
9 R e su lts
D ifferen tial cross sectio n s for th e p ro d u c tio n of a n iso la te d p h o to n in D IS w ith a n a d d itio n a l je t have b ee n m e a su re d in th e la b o ra to ry fram e in th e k in e m a tic regio n d efined by 4 <
EY < 15 GeV, —0.7 < p7 < 0.9, E j4 > 2.5 GeV a n d —1.5 < pJet < 1.8. T h e D IS elec tro n w as c o n stra in e d to b e in th e a n g u la r ra n g e de > 140°, w ith en e rg y g re a te r th a n 10 G eV a n d 10 < Q2 < 350 G eV 2, w h ere Q2 w as d e te rm in e d fro m th e e le c tro n s c a tte rin g angle.
T h e je ts w ere form ed acco rd in g to th e k y -c lu ste rin g a lg o rith m w ith th e R p a r a m e te r set to 1.0. P h o to n iso latio n w as im p o sed such t h a t a t le a st 90% o f th e en e rg y of th e jet-lik e o b je c t c o n ta in in g th e p h o to n belo n g ed to th e p h o to n .
T h e d iffe ren tial cross sectio n s for th e full Q2 ra n g e as fu n c tio n s o f xY eas, x ° bs, A 0 , A p, A 0e ’7 a n d A p e,Y are show n in figure 3 a n d a re given in ta b le s 1- 6 , w hich also list th e values o f th e LL c o n trib u tio n s a n d th e h a d ro n is a tio n c o rrec tio n s. T h e cross sec tio n d ecreases w ith in cre asin g xpbs, h av in g a p e a k a ro u n d 0.0 1, a n d rises a t h ig h values of xY eas, A0 a n d A0e’7 . T h e p re d ic tio n s for th e sum of th e e x p e c te d LL c o n trib u tio n from D j a n g o h - H e r a c l e s a n d a fa c to r of 1.6 tim e s th e e x p e c te d Q Q c o n trib u tio n from P y t h i a ag ree well w ith th e m e a su re m e n ts. T h e success of th e P y t h i a c a lc u la tio n c a n b e a ttr i b u t e d to its use o f a le a d in g -lo g a rith m a p p ro a c h to g lu o n em ission to a u g m e n t its L O p a r to n - s c a tte rin g c a lc u la tio n .
T h e d iffe ren tial cross sectio n s for th e s e p a ra te ra n g es 10 < Q2 < 30 G eV2 a n d 30 <
Q2 < 350 G eV2 a re show n in figures 4 a n d 5 . In b o th th e s e ran g es, a g o o d d e sc rip tio n of th e d a ta is given by th e c o m b in a tio n of th e LL a n d P y t h i a M C s. T h e LL c o n trib u tio n is sm all in th e low er Q2 region, as w as a lre a d y seen in figure 3 (a) of th e e a rlie r ZE U S p u b lic a tio n [19]. In th e h ig h er Q2 ra n g e, th e LL c o m p o n e n t c o n trib u te s significantly, as c a n b e seen in th e x ° bs, A 0 , A p , an d A p e,Y d is trib u tio n s w h ere it is d o m in a n t a t h ig h values o f th e s e v ariab les. T h is reflects th e ch an g es w ith Q2 in th e s tru c tu r e of th e c o n trib u tin g p rocesses.
- 9 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
Z E U S
(a) (b)
(c) (d)
(e) (f)
F ig u r e 3. Differential cross sections in (a) x meas, (b) Xpbs, (c) A^>, (d) An, (e) A ^ e’7, and (f) A n6’7, for the full range 10 < Q2 < 350 GeV2. The inner and outer error bars show, respectively, the statistical uncertainty and the statistical and system atic uncertainties added in quadrature.
The solid histogram s are the M onte C arlo predictions from the sum of Q Q photons from P y t h i a normalised by a factor 1.6 plus Dj a n g o h- He r a c l e s LL photons. The dashed (dotted) lines show the QQ (LL) contributions.
- 10 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
xmeas
ra n g e dx-meas ( p b ) dx;yeasdaLL (P b )
h ad . cor.
10 < Q2 < 350 G eV2
0.0 - 0.4 0.94 ± 0 .2 0 (sta t. ± 0.1 1(sys.) 0.06 ± 0.0 1( s ta t.) 0.63 0.4 - 0.6 2.73 ± 0 .4 3 (s ta t. ) ± 0 .3 2 (sy s.) 0.29 ± 0 .0 4 (s ta t.) 0.90 0.6 - 0.7 7.06 ± 1 .1 4 (sta t. ) ± 0.38(sys.) 0.65 ± 0 .0 9 (sta t.) 1.27 0.7 - 0.8 9.64 ± 1 .2 4 (sta t. ) ± 1.06(sys.) 1.17 ± 0 .1 2 (s ta t.) 1.93 0.8 - 0.9 23.40 ± 1 .7 5 (sta t. ) ± 3.51(sys.) 3.67 ± 0 .2 2 (s ta t.) 2.06 0.9 - 1.0 42.34 ± 2 .2 6 (sta t. ) ± 8.54(sys.) 13.49 ± 0 .4 2 (s ta t.) 0.64
1 0 < Q2 < 30 G eV2
0.0 - 0.4 0.45 ± 0 .1 5 (sta t. ± 0.09(sys.) 0 . 0 1 ± 0.0 1( s ta t.) 0 . 6 8
0.4 - 0.6 1.19 ± 0 .3 1 (s ta t. ± 0.18(sys.) 0.07 ± 0 .0 2 (s ta t.) 1 . 0 0
0.6 - 0.7 4.30 ± 0 .8 8 (sta t. ) ± 0.49(sys.) 0.23 ± 0 .0 6 (s ta t.) 1.30 0.7 - 0.8 5.58 ± 0 .8 8 (sta t. ) ± 0.69(sys.) 0.16 ± 0 .0 4 (sta t.) 2 . 0 2
0.8 - 0.9 9.27 ± 1 .2 0 (sta t. ) ± 1.32(sys.) 0.54 ± 0 .0 8 (s ta t.) 2 . 1 1
0.9 - 1.0 17.76 ± 1 .3 7 (sta t. ± 3.73(sys.) 1.89 ± 0 .1 6 (s ta t.) 0.63 30 < Q2 < 350 G eV2
0.0 - 0.4 0.38 ± 0 .1 5 (sta t. ± 0.05(sys.) 0.06 ± 0.0 1( s ta t.) 0.60 0.4 - 0.6 1.55 ± 0 .3 0 (s ta t. ± 0.23(sys.) 0.22 ± 0 .0 4 (sta t.) 0.82 0.6 - 0.7 2.50 ± 0 .7 3 (sta t. ± 0.36(sys.) 0.42 ± 0 .0 7 (sta t.) 1.25 0.7 - 0.8 4.15 ± 0 .8 9 (sta t. ± 0.53(sys.) 1 . 0 1 ± 0.1 1( s ta t.) 1 . 8 6
0.8 - 0.9 13.90 ± 1 .2 7 (sta t. ± 2.0 1(sys.) 3.14 ± 0 .2 0 (s ta t.) 2 . 0 2
0.9 - 1.0 25.81 ± 1 .8 9 (sta t. ± 4.74(sys.) 11.61 ± 0 .3 8 (s ta t.) 0.65
T a b le 1. Measured differential cross-section dsdZ,as. The quoted system atic uncertainty includes all the com ponents added in quadrature. The calculated LL contribution which was added to the P y t h i a and A FG calculations is also listed, and the hadronisation correction calculated for the AFG predictions. Differences between cross sections in the first section and the sum of the corresponding values in the second and th ird sections are of statistical origin.
- 11 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
xobsx p
ra n g e 4 b (P b ) ^ (P b )
h ad . cor.
10 < Q 2 < 350 G eV2
0.000 - 0.005 344.3 ± 3 1 .7 (s ta t.) ± 22.9(sys.) 35.2 ± 3 .0 (s ta t.) 0.69 0.005 - 0.010 661.8 ± 4 5 .3 (s ta t.) ± 56.6(sys.) 110.8 ± 5 .3 (s ta t.) 0.81 0.010 - 0.015 467.1 ± 3 8 .9 (s ta t.) ± 35.5(sys.) 80.0 ± 4 .5 (s ta t.) 0.91 0.015 - 0.025 164.5 ± 1 6 .5 (sta t.) ± 16.1(sys.) 46.6 ± 2 .4 (s ta t.) 0.99 0.025 - 0.040 46.7 ± 6 . 8 ( s ta t.) ± 2.7 (sys.) 18.7 ± 1 .3 (s ta t.) 1.06 0.040 - 0.070 3.3 ± 0.6 ( s ta t.) ± 2.1 (sys.) 3.3 ± 0 .4 (s ta t.) 1 . 0 0
10 < Q2 < 30 G eV2
0.000 - 0.005 201.8 ± 2 5 .0 (s ta t.) ± 11.1(sys.) 8.4 ± 1 .4 (sta t.) 0.71 0.005 - 0.010 319.6 ± 3 1 .4 (s ta t.) ± 31.8(sys.) 19.4 ± 2 .2 (s ta t.) 0.84 0.010 - 0.015 195.5 ± 2 4 .5 (s ta t.) ± 20.5(sys.) 12.7 ± 1 .8 (s ta t.) 0.98 0.015 - 0.025 68.1 ± 1 0 .4 (sta t.) ± 9.8 (sys.) 5.6 ± 0 .9 (s ta t.) 1.03 0.025 - 0.040 18.7 ± 4.1 ( s ta t.) ± 9.5 (sys.) 2.1 ± 0 .4 (s ta t.) 1.08 0.040 - 0.070 0 . 2 ± 0 . 1 ( s ta t.) ± 0 .1 (sys.) 0 . 2 ± 0.1(s ta t.) 0.95
30 < Q2 < 350 G eV2
0.000 - 0.005 149.3 ± 2 0 .0 (s ta t.) ± 9.1 (sys.) 26.8 ± 2.6(s ta t.) 0 . 6 8
0.005 - 0.010 340.7 ± 3 2 .9 (s ta t.) ± 25.0(sys.) 91.4 ± 4 .8 (s ta t.) 0.78 0.010 - 0.015 271.7 ± 3 0 .5 (s ta t.) ± 17.4(sys.) 67.3 ± 4 .1 (s ta t.) 0 . 8 8
0.015 - 0.025 97.7 ± 1 2 .8 (sta t.) ± 8.1 (sys.) 41.0 ± 2 .3 (s ta t.) 0.97 0.025 - 0.040 37.5 ± 5.3 ( s ta t.) ± 3.1 (sys.) 16.6 ± 1.2(s ta t.) 1.06 0.040 - 0.070 3.0 ± 1.0 ( s ta t.) ± 2.1 (sys.) 3.0 ± 0 .4 (s ta t.) 1 .0 1
T a b le 2. Measured differential cross-section dX0bs. Details as in table 1.
- 12 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
A 3 ra n g e
(deg)
d f e ( p b / d e g )
S
* (P b / d e g )h ad . cor.
10 < Q2 < 350 G eV2
0 - 9 0 90 - 130 130 - 140 140 - 150 150 - 160 160 - 170 170 - 180
0.020 ± 0 .0 0 2 (s ta t.) ± 0.003(sys.) 0.063 ± 0 .0 0 5 (s ta t.) ± 0.005(sys.) 0.093 ± 0 .0 1 2 (s ta t.) ± 0.008(sys.) 0.080 ± 0 .0 1 2 (s ta t.) ± 0.007(sys.) 0.117 ± 0 .0 1 3 (s ta t.) ± 0.006(sys.) 0.129 ± 0 .0 1 1 (s ta t.) ± 0.005(sys.) 0.108 ± 0 .0 1 2 (s ta t.) ± 0.007(sys.)
0.004 ± 0 .0 0 1 (s ta t.)
0 . 0 1 2 ± 0.0 0 1(s ta t.) 0.017 ± 0 .0 0 2 (sta t.)
0 . 0 2 1 ± 0.0 0 2(s ta t.)
0 . 0 2 1 ± 0.0 0 2(s ta t.) 0.027 ± 0 .0 0 2 (sta t.) 0.026 ± 0.0 0 2(s ta t.)
0 . 6 8
0.82
0 . 8 8
0.92 0.95 0.95 0.94 10 < Q2 < 30 G eV2
0 - 9 0 90 - 130 130 - 140 140 - 150 150 - 160 160 - 170 170 - 180
0.004 ± 0 .0 0 1 (s ta t.) ± 0.001(sys.) 0.023 ± 0 .0 0 3 (s ta t.) ± 0.002(sys.) 0.042 ± 0 .0 1 0 (s ta t.) ± 0.007(sys.) 0.047 ± 0 .0 0 9 (s ta t.) ± 0.005(sys.) 0.057 ± 0 .0 1 0 (s ta t.) ± 0.003(sys.) 0.079 ± 0 .0 0 9 (s ta t.) ± 0.004(sys.) 0.064 ± 0 .0 0 9 (s ta t.) ± 0.005(sys.)
0 . 0 0 0 ± 0.0 0 1(s ta t.)
0 . 0 0 1 ± 0.0 0 1(s ta t.) 0.003 ± 0 .0 0 1 (s ta t.) 0.004 ± 0 .0 0 1 (s ta t.) 0.005 ± 0 .0 0 1 (s ta t.) 0.007 ± 0 .0 0 1 (sta t.) 0.007 ± 0 .0 0 1 (sta t.)
0 . 6 8
0.78 0.79 0.85 0.91 0.93 0.93 30 < Q2 < 350 G eV2
0 - 9 0 90 - 130 130 - 140 140 - 150 150 - 160 160 - 170 170 - 180
0.015 ± 0 .0 0 2 (s ta t.) ± 0.002(sys.) 0.040 ± 0 .0 0 4 (sta t.) ± 0.003(sys.) 0.049 ± 0 .0 0 8 (sta t.) ± 0.002(sys.) 0.030 ± 0 .0 0 8 (sta t.) ± 0.001(sys.) 0.064 ± 0 .0 0 9 (sta t.) ± 0.007(sys.) 0.046 ± 0 .0 0 7 (sta t.) ± 0.005(sys.) 0.045 ± 0 .0 0 9 (s ta t.) ± 0.003(sys.)
0.004 ± 0 .0 0 1 (s ta t.)
0 . 0 1 1 ± 0.0 0 1(s ta t.) 0.014 ± 0 .0 0 1 (s ta t.) 0.017 ± 0 .0 0 2 (s ta t.) 0.016 ± 0.0 0 1(s ta t.)
0 . 0 2 0 ± 0.0 0 2(s ta t.) 0.019 ± 0 .0 0 2 (s ta t.)
0 . 6 8
0.83 0.96 0.99
1 . 0 1 1 . 0 1
0.97 T a b le 3. M easured differential cross-section . Details as in table 1.
- 13 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
A n
ra n g e d f e (P b ) d
s
( p b ) h ad .cor.10 < Q2 < 350 G eV2
-2 .2 - - 1 . 5 -1 .5 - - 0 . 8 -0 . 8 - -0 .1
-0 . 1 - 0 . 6
0.6 - 1.3 1.3 - 2.0
0.32 ± 0 .0 8 (s ta t.) ± 0.05(sys.) 1.41 ± 0 .1 5 (s ta t.) ± 0.14(sys.) 2.38 ± 0 .2 2 (s ta t.) ± 0.21(sys.) 3.36 ± 0 .2 7 (s ta t.) ± 0.23(sys.) 3.88 ± 0 .2 8 (s ta t.) ± 0.22(sys.)
1 . 8 8 ± 0.2 1(s ta t.) ± 0.1 2(sys.)
0 . 0 1 ± 0.0 1( s ta t.) 0.06 ± 0.0 1( s ta t.)
0 . 2 1 ± 0.0 2( s ta t.) 0.45 ± 0 .0 3 (sta t.) 0.87 ± 0 .0 4 (s ta t.) 0.92 ± 0 .0 4 (sta t.)
0.76
0 . 6 6
0.74 0.87 1.04
1 . 1 1
10 < Q2 < 30 G eV2
-2 .2 - - 1 . 5 -1 .5 - - 0 . 8 -0 . 8 - -0 . 1
-0 . 1 - 0 . 6
0.6 - 1.3 1.3 - 2.0
0.14 ± 0 .0 5 (s ta t.) ± 0.03(sys.) 0.51 ± 0 .1 2 (s ta t.) ± 0.04(sys.) 1.16 ± 0 .1 5 (s ta t.) ± 0.09(sys.) 1.70 ± 0 .1 9 (s ta t.) ± 0.15(sys.) 1.67 ± 0 .1 9 (s ta t.) ± 0.13(sys.) 0.71 ± 0 .1 3 (s ta t.) ± 0.07(sys.)
0 . 0 0 ± 0.0 1( s ta t.)
0 . 0 0 ± 0.0 1( s ta t.) 0.04 ± 0 .0 1 (sta t.) 0.08 ± 0.0 1( s ta t.) 0.14 ± 0 .0 2 (s ta t.) 0.13 ± 0 .0 2 (s ta t.)
0.63
0 . 6 8
0.77 0.90 1.08 1.07 30 < Q2 < 350 G eV2
-2 .2 - - 1 . 5 -1 .5 - - 0 . 8 -0 . 8 - -0 .1
-0 . 1 - 0 . 6
0.6 - 1.3 1.3 - 2.0
0.20 ± 0 .0 7 (s ta t.) ± 0.03(sys.) 0.86 ± 0 .0 9 (s ta t.) ± 0.09(sys.) 1.25 ± 0 .1 6 (s ta t.) ± 0.13(sys.) 1.68 ± 0 .1 9 (s ta t.) ± 0.08(sys.) 2.23 ± 0 .2 2 (s ta t.) ± 0.19(sys.) 1.16 ± 0 .1 6 (s ta t.) ± 0.06(sys.)
0 . 0 0 ± 0.0 1( s ta t.) 0.05 ± 0 .0 1 (s ta t.) 0.16 ± 0.0 2( s ta t.) 0.37 ± 0 .0 3 (sta t.) 0.72 ± 0 .0 4 (s ta t.) 0.80 ± 0 .0 4 (s ta t.)
0.83 0.65 0.72 0.85
1 . 0 2
1.14 T a b le 4. M easured differential cross-section -4^ - . Details as in table 1.
- 14 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
A0 e >7
ra n g e (deg)
(P b / d e S) (P b / d e g )
h ad . cor.
10 < Q2 < 350 G eV2
0 - 4 5 45 - 80 80 - 1 1 0
110 - 135 135 - 155 155 - 180
0.025 ± 0 .0 0 3 (s ta t.) ± 0.002(sys.) 0.042 ± 0 .0 0 4 (s ta t.) ± 0.003(sys.) 0.047 ± 0 .0 0 4 (s ta t.) ± 0.003(sys.) 0.068 ± 0 .0 0 6 (s ta t.) ± 0.006(sys.) 0.093 ± 0 .0 0 9 (s ta t.) ± 0.007(sys.) 0.085 ± 0 .0 0 8 (s ta t.) ± 0.008(sys.)
0.009 ± 0 .0 0 1 (s ta t.)
0 . 0 1 0 ± 0.0 0 1(s ta t.)
0 . 0 1 0 ± 0.0 0 1(s ta t.)
0 . 0 1 2 ± 0.0 0 1(s ta t.) 0.015 ± 0 .0 0 1 (s ta t.) 0.013 ± 0 .0 0 1 (s ta t.)
0.95 0.94 0.92 0.85 0.79 0.73 10 < Q2 < 30 G eV2
0 - 4 5 45 - 80 80 - 1 1 0
110 - 135 135 - 155 155 - 180
0.013 ± 0 .0 0 2 (sta t.) ± 0.002(sys.) 0.018 ± 0 .0 0 3 (s ta t.) ± 0.001(sys.) 0.024 ± 0 .0 0 3 (s ta t.) ± 0.002(sys.) 0.033 ± 0 .0 0 5 (sta t.) ± 0.002(sys.) 0.031 ± 0 .0 0 6 (sta t.) ± 0.002(sys.) 0.038 ± 0 .0 0 5 (s ta t.) ± 0.004(sys.)
0 . 0 0 2 ± 0.0 0 1(s ta t.)
0 . 0 0 2 ± 0.0 0 1(s ta t.)
0 . 0 0 1 ± 0.0 0 1(s ta t.)
0 . 0 0 2 ± 0.0 0 1(s ta t.)
0 . 0 0 1 ± 0.0 0 1(s ta t.)
0 . 0 0 2 ± 0.0 0 1(s ta t.)
0.95 0.94 0.91 0.85 0.78 0.80 30 < Q2 < 350 G eV2
0 - 4 5 45 - 80 80 - 1 1 0
110 - 135 135 - 155 155 - 180
0 . 0 1 2 ± 0.0 0 2( s ta t.) ± 0.0 0 1(sys.) 0.024 ± 0 .0 0 2 (sta t.) ± 0.002(sys.) 0.023 ± 0 .0 0 3 (sta t.) ± 0.002(sys.) 0.036 ± 0 .0 0 4 (sta t.) ± 0.003(sys.) 0.063 ± 0 .0 0 7 (sta t.) ± 0.005(sys.) 0.047 ± 0 .0 0 6 (sta t.) ± 0.004(sys.)
0.007 ± 0 .0 0 1 (s ta t.) 0.009 ± 0 .0 0 1 (s ta t.) 0.009 ± 0 .0 0 1 (s ta t.)
0 . 0 1 0 ± 0.0 0 1(s ta t.) 0.014 ± 0 .0 0 1 (s ta t.)
0 . 0 1 1 ± 0.0 0 1(s ta t.)
0.95 0.95 0.93
0 . 8 6
0.80 0.70 T a b le 5. M easured differential cross-section dA ^ ,Y . Details as in table 1.
- 15 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
A n e>Y
ra n g e dA ^C (P b ) ddA r,Y (P b )
h ad . cor.
10 < Q2 < 350 G eV2
- 3 .6 - -3 .0 - 3 .0 - -2 .4 - 2 . 4 - -1 . 8
-1.8 - - 1 .2
-1 . 2 - - 0 . 6
0.94 ± 0 .2 1 (s ta t.) ± 0.12(sys.) 3.57 ± 0 .3 0 (s ta t.) ± 0.30(sys.) 5.44 ± 0 .3 6 (s ta t.) ± 0.45(sys.) 3.79 ± 0 .3 1 (s ta t.) ± 0.26(sys.) 1.90 ± 0 .2 1 (s ta t.) ± 0.11(sys.)
0 . 0 2 ± 0.0 1( s ta t.) 0.08 ± 0.0 1( s ta t.) 0.45 ± 0 .0 3 (s ta t.) 1.33 ± 0 .0 5 (s ta t.) 1.24 ± 0 .0 5 (s ta t.)
0.80 0.82 0.83 0.85 0.89 10 < Q2 < 30 G eV2
- 3 .6 - -3 .0 - 3 .0 - -2 .4 - 2 . 4 - -1 . 8 -1.8 - - 1 .2
0.93 ± 0 .2 1 (s ta t.) ± 0.12(sys.) 2.60 ± 0 .2 5 (s ta t.) ± 0.19(sys.) 2.69 ± 0 .2 5 (s ta t.) ± 0.19(sys.) 0.86 ± 0 .1 5 (s ta t.) ± 0.07(sys.)
0 . 0 2 ± 0.0 1( s ta t.) 0.06 ± 0.0 1( s ta t.)
0 . 2 2 ± 0.0 2( s ta t.) 0.19 ± 0 .0 2 (sta t.)
0.81 0.85 0.89 0.92 30 < Q2 < 350 G eV2
- 3 .0 - -2 .4 - 2 . 4 - -1 . 8
-1.8 - - 1 .2
-1 . 2 - -0 . 6
1.00 ± 0 .1 7 (s ta t.) ± 0.11(sys.) 2.72 ± 0 .2 6 (s ta t.) ± 0.25(sys.) 3.00 ± 0 .2 7 (s ta t.) ± 0.18(sys.) 1.90 ± 0 .2 1 (s ta t.) ± 0.11(sys.)
0 . 0 2 ± 0.0 1( s ta t.) 0.23 ± 0 .0 2 (s ta t.) 1.14 ± 0 .0 5 (s ta t.) 1.24 ± 0 .0 5 (s ta t.)
0.77 0.80 0.84 0.89 T a b le 6. Measured differential cross-section . Details as in table 1.
- 16 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
Z E U S
(a) (b)
(c) (d)
(e) (f)
F ig u r e 4. Differential cross sections for the regions 10 < Q2 < 30 and 30 < Q2 < 350 GeV2:
(a, b) x ^ 8, (c, d) xpbs, and (e, f) A ^ . The inner and outer error bars show, respectively, the statistical uncertainty and the statistical and system atic uncertainties added in quadrature.
The solid histogram s are the Monte Carlo predictions from the sum of QQ photons from Py t h i a
normalised by a factor 1.6 plus Dj a n g o h- He r a o l e s LL photons. The dashed (dotted) lines show the QQ (LL) contributions.
- 1 7 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
Z E U S
(a) (b)
(c) (d)
(e) (f)
F ig u r e 5. Differential cross sections for the regions 10 < Q2 < 30 and 30 < Q2 < 350 GeV2:
(a, b) An, (c, d) A 3 e,Y, and (e, f) A n6’7 . The inner and outer error bars show, respectively, the statistical uncertainty and the statistical and system atic uncertainties added in quadrature.
The solid histogram s are the Monte C arlo predictions from the sum of QQ photons from P y t h i a normalised by a factor 1.6 plus Dj a n g o h- He r a c l e s LL photons. The dashed (dotted) lines show the QQ (LL) contributions.
- 18 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
T h e in cre ased im p o rta n c e of th e LL co m p o n e n t a t h ig h er Q2 is also reflected in th e
^meas d is trib u tio n . F ig u re 6 p re se n ts th e a n d xpbs cross sectio n s on a lo g a rith m ic scale. T h e d a ta in th e low -xmeas reg ion a re s a tis fa c to rily d e sc rib e d by Py t h ia w ith o u t th e n eed for f u r th e r h ig h e r-o rd e r processes.
C o m p ariso n s of th e d a t a w ith th e A F G a n d B LZ p re d ic tio n s are p re se n te d for th e e n tire Q2 ra n g e in figure 7 . T h e u p d a te d B LZ p re d ic tio n s d esc rib e th e sh a p e of m o st o f th e d is trib u tio n s re a so n a b ly well, b u t th e re is a n o v e re stim a tio n of a b o u t 2 0% in th e overall cross sectio n , a n d th e e x tre m e ly p e a k ed p re d ic tio n for th e x meas d is trib u tio n is n o t in a g reem en t w ith th e d a ta . T h e A F G p re d ic tio n s d esc rib e all th e d is trib u tio n s well an d also ag ree in th e overall n o rm a lisa tio n .
C o m p ariso n s o f th e d a t a w ith th e A F G m od el in th e tw o s e p a ra te Q2 ran g es are show n in figures 8- 9 . In th e h ig h er Q2 ran g e, th e d e sc rip tio n by A F G is ex cellent. In th e low er ra n g e, th e o n ly d e v ia tio n o b serv ab le is in th e A n d is trib u tio n , w h ere th e d a t a show a te n d e n c y to w a rd s h ig h er values th a n th e th eo ry . T h is m ig h t b e re la te d to th e c u t of 2.5 G eV o n th e tra n s v e rs e p h o to n m o m e n tu m ap p lied in th e A F G c a lc u la tio n [2 1].
10 S u m m a ry
T h e p ro d u c tio n of iso lated p h o to n s ac co m p an ied by je ts h as b ee n m e a su re d in d eep in
e la stic s c a tte rin g w ith th e Z E U S d e te c to r a t H E R A , u sin g a n in te g ra te d lu m in o sity of 326 p b -1. E x p a n d in g on e a rlie r Z E U S re su lts [19], w h ich s tu d ie d sin g le-p artic le d is tri
b u tio n s, d iffe ren tial cross sectio n s h av e b ee n e v a lu a te d as fu n c tio n s o f p a irs of m easu red v aria b les in c o m b in a tio n . T h e k in e m a tic reg ion in th e la b o ra to ry fram e w as defined by 4 < E T < 15 GeV, - 0 . 7 < nY < 0.9, E ^* > 2.5 GeV a n d - 1 . 5 < n et < 1.8. T h e D IS e le c tro n w as c o n stra in e d to b e in th e a n g u la r ra n g e de > 140°, w ith en e rg y g re a te r th a n 10 G eV a n d 10 < Q2 < 350 G eV2, w h ere Q2 w as d e te rm in e d from th e e le c tro n s c a tte rin g angle. T h e je ts w ere form ed ac co rd in g to th e k x -c lu ste rin g a lg o rith m w ith th e R p a r a m e te r set to 1.0. P h o to n iso latio n w as im p o sed such t h a t a t le a st 90% o f th e en e rg y o f th e je t-lik e o b je c t c o n ta in in g th e p h o to n belo n g ed to th e p h o to n . D ifferen tial cross section s a re p re se n te d for th e follow ing variables: th e fra c tio n of th e in co m in g p h o to n en e rg y an d m o m e n tu m t h a t is tra n s fe rre d to th e o u tg o in g p h o to n an d th e lead in g je t; th e fra c tio n of th e in co m in g p ro to n en e rg y tra n s fe rre d to th e p h o to n a n d lead in g je t; th e differences in a z im u th a l angle a n d p s e u d o ra p id ity b etw e en th e o u tg o in g p h o to n a n d th e lead in g je t an d b etw e en th e o u tg o in g p h o to n a n d th e s c a tte re d electro n .
T h e P y t h i a p re d ic tio n for th e q u a r k -ra d ia te d p h o to n c o m p o n e n t plus th e D j a n g o h - H e r a c l e s c a lc u la tio n for th e le p to n -ra d ia te d co m p o n e n t d esc rib es all th e d is trib u tio n s well if th e P y t h i a p re d ic tio n is scaled u p by a fa c to r o f 1.6. T h is is also tr u e if th e d a t a are d iv id ed in to ra n g es ab o v e a n d below a value of Q2 = 30 G eV2. P re d ic tio n s from tw o th e o re tic a l m odels w ere also c o m p a re d to th e d a ta . T h e B LZ m o del gives a fair d e sc rip tio n of th e d a t a b u t d o es n o t give a go o d d e sc rip tio n of th e o verall n o rm a lis a tio n o r th e s h a p e of som e of th e d is trib u tio n s . T h e A F G m od el gives a n excellen t d e s c rip tio n of th e n o rm a lisa tio n a n d a lm o st all th e d is trib u tio n s , b o th for th e e n tire d a t a set a n d for th e s e p a ra te Q2 ranges.
- 19 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
(e) (f)
F ig u r e 6 . Differential cross sections in (a, c, e) x ^ eas and (b, d, f) x . bs for (a, b) 10 < Q 2 <
350 GeV2, (c, d) 10 < Q 2 < 30 GeV2, and (e, f) 30 < Q 2 < 350 GeV2. The distributions are as shown in figures 3- 5 b u t with logarithm ic vertical scale.
- 20 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
Z E U S
(a) (b)
(c) (d)
(e) (f)
F ig u r e 7 . Differential cross sections for selected variables in the full Q 2 range 10 < Q 2 < 350 GeV2: as in figure 3. Theoretical predictions from Aurenche et al. (AFG) and Baranov et al. (BLZ) are shown, with scale uncertainties indicated by the bands.
- 21 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
Z E U S
(a) (b)
(c) (d)
(e) (f)
F ig u r e 8 . Differential cross sections for selected variables in the region 10 < Q2 < 30 GeV2 as in figures 4, 5. Theoretical predictions from Aurenche et al. (AFG) are shown, w ith associated uncertainties indicated by the bands.
- 22 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
Z E U S
(a) (b)
(c) (d)
(e) (f)
F ig u r e 9 . Differential cross sections for selected variables in the region 30 < Q 2 < 350 GeV2 as in figures 4, 5. Theoretical predictions from Aurenche et al. (AFG) are shown, w ith associated uncertainties indicated by the bands.
- 23 -
J H E P 0 1 ( 2 0 1 8 ) 0 3 2
A c k n o w le d g m e n ts
W e a p p re c ia te th e c o n trib u tio n s to th e c o n s tru c tio n a n d m a in te n a n c e o f th e Z E U S d e te c to r o f m an y p eo p le w ho are n o t liste d as a u th o rs . T h e H E R A m ach in e g ro u p a n d th e D E S Y c o m p u tin g s ta ff are esp ecially acknow ledged for th e ir success in p ro v id in g excellent o p e r
a tio n of th e co llid er an d th e d a ta -a n a ly s is e n v iro n m e n t. W e th a n k th e D E S Y d ire c to ra te for th e ir s tro n g s u p p o rt a n d e n c o u ra g e m e n t.
W e also th a n k P. A u ren ch e, M. F o n ta n n a z a n d A. L ip a to v for p ro v id in g th e o re tic a l re su lts a n d ex p ress o u r a p p re c ia tio n for th e c o n trib u tio n s from o u r m uch -m issed la te col
league, N ikolai Zotov.
O p e n A c c e s s . T h is a rtic le is d is trib u te d u n d e r th e te rm s o f th e C re a tiv e C o m m o ns A ttr ib u tio n L icense ( C C -B Y 4.0) , w hich p e rm its an y use, d is trib u tio n a n d re p ro d u c tio n in an y m ed iu m , p ro v id ed th e o rig in al a u th o r(s ) a n d so u rce are c re d ite d .
R e fe r e n c e s
[1] E. Anassontzis et al., High p t direct photon production in pp collisions, Z. Phys. C 13 (1982) 277 [i nSPIRE].
[2] W A70 collaboration, M. Bonesini et al., Production of high transverse m om entum prom pt photons and neutral pions in proton proton interactions at 280 G eV/c, Z. Phys. C 38 (1988) 371 [i nSPIRE].
[3] F E R M IL A B -E 7 0 6 collaboration, G. Alverson et al., Production of direct photons and neutral mesons at large transverse m om enta by n - and p beams at 500 G eV/c, Phys. Rev. D 48 (1993) 5 [i nSPIRE].
[4] C D F collaboration, F. Abe et al., A Precision measurement o f the prom pt photon cross-section in pp collisions at y S = 1.8 TeV, Phys. Rev. Lett. 73 (1994) 2662 [Erratum ibid. 74 (1995) 1891] [i nSPIRE].
[5] C D F collaboration, D. Acosta et al., Measurement of the cross section fo r prom pt diphoton production in pp collisions at y S = 1.96 TeV, Phys. Rev. Lett. 95 (2005) 022003
[hep-ex /0 4 1 2 0 5 0 ] [i nSPIRE].
[6] D0 collaboration, B. A bbott et al., The isolated photon cross-section in pp collisions at VS = 1.8 TeV, Phys. Rev. Lett. 84 (2000) 2786 [hep -ex /9 9 1 2 0 1 7 ] [i nSPIRE].
[7] D0 collaboration, V.M. Abazov et al., M easurement o f the isolated photon cross section in pp collisions at VS = 1.96 TeV, Phys. Lett. B 639 (2006) 151 [Erratum ibid. B 658 (2008) 285]
[hep-ex /0 5 1 1 0 5 4 ] [i nSPIRE].
[8] A T L A S collaboration, High-Et isolated-photon plus jets production in pp collisions at Vs = 8 T eV with the A T L A S detector, Nucl. Phys. B 918 (2017) 257 [a rX iv :1 6 1 1 .0 6 5 8 6 ] [i nSPIRE].
[9] A T L A S collaboration, M easurement of the cross section fo r inclusive isolated-photon production in pp collisions at y S = 1 3 T eV using the A T L A S detector, Phys. Lett. B 770 (2017) 473 [a rX iv :1 7 0 1 .0 6 8 8 2 ] [i nSPIRE].
- 24 -
