Search for resonances in diphoton events at $\sqrt{s}=13$ TeV with the ATLAS detector

Pu b l i s h e d f o r S IS S A b y Sp r i n g e r Re c e i v e d: June 14, 2016 Ac c e p t e d: August 20, 2016 Pu b l i s h e d: September 1, 2016

Search for resonances in diphoton events at

√

s = 13 T e V with the A T L A S detector

T h e A T L A S collaboration

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

A b s t r a c t : Searches for new resonances decaying into two photons in th e ATLAS experi­

m ent a t th e C E R N Large H adron Collider are described. T he analysis is based on proton- p ro to n collision d a ta corresponding to an in teg rated lum inosity of 3.2 fb -1 a t √ s = 13 TeV recorded in 2015. Two searches are perform ed, one targ e te d at a spin-2 particle of m ass larger th a n 500 GeV, using R an dall-S un drum graviton sta te s as a b enchm ark model, and one optim ized for a spin-0 particle of m ass larger th a n 200 GeV. V arying b o th th e m ass and th e decay w idth, th e m ost significant deviation from th e background-only hypothesis is ob­

served a t a dip h o to n invariant m ass arou nd 750 GeV w ith local significances of 3.8 and 3.9 sta n d a rd deviations in th e searches optim ized for a spin-2 and spin-0 particle, respectively.

T he global significances are estim ated to be 2.1 sta n d a rd deviations for b o th analyses. T he consistency betw een th e d a ta collected a t 13 TeV and 8 TeV is also evaluated. L im its on th e p ro d u ction cross section tim es branching ratio to two photons for th e two resonance types are reported.

K

: Beyond S ta n d ard M odel, H adron-H adron scatterin g (experim ents), H ard scatterin g, P a rtic le and resonance production, p ro to n -p ro to n scatterin g

A

X

P

: 1606.03833

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

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 2

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

4 P h o t o n s e le c tio n 5

5 E v e n t s e le c tio n a n d s a m p le c o m p o s it io n 7

5.1 P rim a ry v ertex selection 7

5.2 E vent selection

5.3 Sam ple com position

5.4 Signal acceptance and efficiency 9

6 S ig n a l m o d e llin g 11

7 B a c k g r o u n d e s tim a t e s 12

7.1 M onte C arlo e x tra p o la tio n approach 13

7.2 Functional-form ap proach 15

7.3 C om parison of th e two m etho ds for th e background e stim ate 16

8 S t a tis tic a l p r o c e d u r e 16

9 R e s u lts 18

9.1 Sum m ary of system atic un certainties 18

9.2 C om patib ility w ith background-only hypothesis 19

9.3 K inem atic d istrib u tio n s for events w ith arou nd 750 GeV 22

9.4 C om patib ility w ith

TeV d a ta 23

9.5 C ross-section lim its 25

10 C o n c lu s io n 26

T h e A T L A S c o lla b o r a tio n 33

1 In tr o d u c tio n

New high-m ass states decaying into two photons are predicted in m any extensions of th e S ta n d ard M odel (SM ). T he d ip h oto n final s ta te provides a clean experim ental signature w ith excellent invariant m ass resolution and m o d erate backgrounds. Searches for new high-m ass resonances decaying into two photons are described, using C E R N Large H adron Collider (LHC) [1] p ro to n -p ro to n (pp) collision d a ta a t yfs= 13 TeV recorded in 2015 by th e ATLAS d etecto r. T he d a ta correspond to an in teg rated lum inosity of 3.2 fb - 1 .

T he decay photons would have different kinem atic p roperties depending on w h ether th e h yp othetical particle has spin-0 or spin-2. These are exploited by applying two different

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

selections, w ith looser kinem atic selection requirem ents for th e spin-2 resonance search. T he p h oto n identification c riteria and th e event pre-selection are com m on to b o th searches.

T he search for a spin-2

resonance uses th e R andall-S un dru m (RS) m odel [2] graviton as a benchm ark. T his entails a lightest K aluza-K lein [3] spin-2 g raviton ex citatio n (G*) w ith a dim ensionless coupling k /M p i, w here M Pl = M p i / \ /

n is th e reduced P lan ck scale and k th e cu rv atu re scale of th e e x tra dim ension. T he lightest graviton excitatio n is expected to be a fairly narrow resonance for k / M Pl < 0.3 [4], w ith th e w idth given by 1 .4 4 (k /M Pl )2m G*, w here m G* is th e m ass of th e lightest graviton sta te . For k / M Pl = 0.1, th e n a tu ra l w idth increases from 11G eV a t m G* = 800 GeV to 3 0G eV at m G* = 2200 GeV. For m G* = 800 GeV, th e contrib u tio ns of th e n a tu ra l w idth and of th e experim ental m ass resolution to th e w id th of th e resonance are com parable. T he shape of th e invariant m ass d istrib u tio n of th e m ain background from th e p ro d uction of pro m p t p ho ton pairs is estim ated from th eoretical com putations, and th e co n trib u tio n from th e reducible background of events w here at least one je t is m isidentified as a photon is added from d ata-d riv en estim ates.

T his app roach works well up to th e highest invariant m asses w here a small num ber of background events are expected. T he search is perform ed in th e m ass range above 500 GeV and in th e k / M Pl range 0.01 to 0.3, searching for an excess over th e estim ated background d ip h o to n invariant m ass d istrib u tio n . To m odel such an excess, th e RS graviton resonance shape is convolved w ith th e experim ental resolution.

Spin-0

resonances are predicted in theories w ith an extended Higgs sector [5- 11].

T he search for a spin-0 resonance uses a restricted kinem atic range for th e p hoton selection, tak in g advantage of th e isotropic d istrib u tio n of th e decay p ro d u cts in th e centre-of-m ass fram e of th e new particle. T he background is estim ated by fittin g th e d ip ho ton invariant m ass d istrib u tio n to an an alytical function, searching for an excess m odelled by a spin

resonance convolved w ith th e experim ental resolution. T he search is perform ed in th e mass range 200-2000 GeV, w here th ere are enough events to co n strain th e background shape, and for w idth values up to

% of th e m ass of th e hypothesized particle.

Searches for d ip ho to n resonances in LHC R un-1 d a ta have been rep o rted by th e A T­

LAS and CMS collaborations [12- 16]. A sim ilar analysis was perform ed by th e CMS collaboration using th e 2015 LHC pp d a ta [17].

T his p a p e r is organized as follows. A fter a description of th e ATLAS d e te c to r in section 2 and of th e d a ta and sim ulated event sam ples in section 3, th e p h o ton selection and energy m easurem ents are presented in section 4 . In sections 5 to

th e event selection, th e m odelling of th e signal and th e estim atio n of th e background as well as th e sta tistic a l procedure to analyse th e d a ta are presented. T he results are discussed in section 9 .

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

T he ATLAS d etecto r [18] is a m ulti-purpose d e te c to r w ith a forw ard-backw ard sym m etric cylindrical geom etry

A t sm all radii, th e inner d e te c to r (ID ), im m ersed in a 2 T m ag­

1The ATLAS experiment 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 upward. Cylindrical coordinates (r, 7) are used in

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

netic field produced by a th in su p erconducting solenoid located in front of th e calorim eter, is m ade up of fine-granularity pixel and m icrostrip detectors. These silicon-based detec­

to rs cover th e pseudorapidity range |n| < 2.5. A gas-filled straw -tu b e tra n sitio n rad ia ­ tio n track er (T R T ) com plem ents th e silicon track er at larger radii and also provides elec­

tro n identification capabilities based on tra n sitio n rad iation . T he electrom agnetic (EM ) calorim eter is a lead /liq u id-arg o n sam pling calorim eter w ith accordion geom etry. T he calorim eter is divided into a b arrel section covering |n| < 1.475 and two end-cap sections covering 1.375 < |n| < 3.2. For |n| < 2.5 it is divided into th re e layers in d epth , which are finely segm ented in n and ¢. A th in presam pler layer, covering |n| < 1.8, is used to correct for fluctuations in u p stream energy losses. H adronic calorim etry in th e region |n| < 1.7 uses steel absorbers and scintillator tiles as th e active m edium . Liquid-argon calorim etry w ith copper absorbers is used in th e hadronic end-cap calorim eters, which cover th e region 1.5 < |n| < 3.2. A forw ard calorim eter using copper or tu n g ste n absorbers w ith liquid a r­

gon com pletes th e calorim eter coverage up to |n| = 4.9. T he m uon sp ectrom eter m easures th e deflection of m uon tracks w ithin |n| < 2.7, using th re e statio n s of precision drift tubes, w ith cath o d e strip cham bers in th e innerm ost layer for |n| > 2.0. T he deflection is provided by a toroidal m agnetic field from air-core superconducting m agnets, w ith an integral of ap ­ proxim ately 3 T-m and

T-m in th e central and end-cap regions, respectively. T he m uon sp ectrom eter is in stru m en ted w ith trigger cham bers covering |n| < 2.4. E vents are selected using a first-level trigger im plem ented in custom electronics, which reduces th e event rate to a design value of 100 kHz using a subset of d etecto r inform ation. Software algorithm s w ith access to th e full d e te c to r inform ation are th e n used in th e high-level trigg er to yield a recorded event ra te of ab o u t 1 kHz [19].

3 D a ta an d sim u la te d e v e n t sa m p les

D a ta were collected by th e ATLAS d e te c to r in 2015 using pp collisions at a centre-of-m ass energy of ^/s = 13 TeV w ith a m inim um bunch spacing of 25 ns, an average num ber of pp interactions per bunch crossing of ab o u t 13, and a peak instan tan eo u s lum inosity of 5 x 10

cm -

s- 1 . E vents from pp collisions were recorded using a dip h o to n trigger w ith transverse energy E T = E sin(0) thresholds of 35 GeV and 25 GeV for th e E T-ordered leading and subleading p hoton cand id ates, respectively. In th e high-level trigger, clusters of energy in th e EM calorim eter are reco n structed and required to satisfy loose c riteria according to th e p roperties of showers in itiated by photons. T he trigg er has a signal efficiency close to 99% for events fulfilling th e final event selections. O nly events taken in stable beam conditions, and in which th e d e te c to r is fully operatio nal, are considered. A fter d a ta - q u ality requirem ents, th e d a ta sam ple corresponds to an integ rated lum inosity of 3.2 fb - 1 . T he m easurem ent of th e in teg rated lum inosity has an u n certain ty of ± 5% . It is derived, following a m ethodology sim ilar to th a t detailed in ref. [

], from a p relim inary calib ratio n of th e lum inosity scale using van der M eer scans perform ed in A ugust 2015.

the transverse plane, 0 being the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angle

as n = — lntan(

/

).

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

Sim ulated M onte C arlo (MC) sam ples are used to optim ize th e search stra te g y and to stu d y background sources. Interference effects betw een signal and background processes are neglected. Signal sam ples for th e RS graviton m odel are generated using P y t h i a

[

], version 8.186, w ith th e N N PD F23LO [22] p a rto n d istrib u tio n functions (P D F ) and th e A14 [23] set of tu n ed param eters (tune) for th e underlying event, for different choices of th e graviton m ass and th e p a ra m ete r k / M pi , spanning a m ass range from 500 GeV to 5000 GeV and k / M Pl values from 0.01 to 0.3. Only th e lowest-mass RS graviton sta te is generated. Sam ples for any m ass or k / M Pl value are obtained by rew eighting an event sam ple generated w ith a uniform m ass d istrib u tio n using th e B reit-W igner and p a rto n lum inosity term s. T he la tte r sam ple is o b tain ed using th e P y t h i a

configuration as de­

scribed above w ith m G* = 5 TeV and k / M Pl = 0.1, w ith an m YY-dependent factor th a t modifies th e p ro d u ctio n cross section to remove th e effect of th e B reit-W igner term and th e p a rto n lum inosity. T he validity of this procedure is verified using sam ples generated a t discrete values of m G* and k / M Pl. B ecause th e graviton coupling increases w ith th e energy of th e decay pro d u cts, th e invariant m ass d istrib u tio n for a large-w idth graviton signal exhibits a high-m ass tail which is not present for a spin

particle w ith properties like those of a Higgs boson.

T he signal in th e spin-0 particle search is sim ulated as if it were a SM Higgs boson produced in pp collisions via gluon fusion and decaying into two photons. O th er p ro duc­

tio n processes are investigated to assess th e im pact of th e p ro d u ctio n m ode on th e signal modelling. MC sam ples are produced for different hypotheses of th e spin-0 boson m ass (m X ) in th e range 200 GeV to 2000 GeV and of th e decay w id th ( r X ) up to 10% of m X . For th e n arrow -w idth approx im atio n (NW A), th e w idth of th e particle is set to 4M eV . G luon fusion events are generated w ith P o w h e g - b o x [24, 25], version

, interfaced w ith P y t h i a

for th e underlying event, p a rto n showering and h adronization. To m odel signals w ith large decay w idths, a function param eterizing th e th eoretical line-shape of th e reso­

nance is used [15, 16]. T he P o w h e g - b o x im plem entation of a large-w idth spin-0 resonance w ith couplings like those of th e Higgs boson in th e SM is chosen for th is function. T he line-shape is m odelled w ith a B reit-W igner d istrib u tio n based on a ru nning-w idth scheme, including th e dependence of th e cross section on th e gluon-gluon p a rto n luminosity. In order to reduce th e sensitivity to m odelling effects from th e off-shell region, th e sam ple g eneration is restricted to th e region m X ± 2 r X . T he validity of th is procedure is checked by com paring th e result of th is im plem entation w ith sim ulated sam ples g enerated w ith a large w idth in P o w h e g - b o x . E vents produced via vector-boson fusion are generated using P o w h e g - b o x [26] interfaced w ith P y t h i a

. A ssociated prod u ction w ith a vector-boson or a tt p air is g enerated w ith P y t h i a

. T he C T 1 0 [27] P D F set is used for th e samples g en erated w ith P o w h e g - b o x , while C T E Q 6 L 1 [28] is used for th e sam ples generated w ith P y t h i a

. T he underlying-event g eneration for th e gluon fusion and vector-boson fusion sam ples is based on th e P y t h i a

AZNLO tu n e [29], while for th e o th er sam ples, th e A14 tu n e is used.

E vents containing two p ro m p t photons, representing th e largest irreducible background to th e search, are sim ulated using th e SHErpA [30] g en erato r version 2.1.1. M atrix elem ents are calculated w ith up to two p arto n s at leading order in QCD and m erged w ith th e SHErpA

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

p a rto n shower [31] using th e M E+PS@ LO prescription [32]. T he gluon-induced box process is also included. T he C T 1 0 P D F set is used in conjunction w ith a d edicated parton-show er tu n e of S h e r p a . Sam ples of th e p h o to n + je t reducible background com ponent are also gen­

e ra ted using S h e r p a . For com parisons, P y t h i a

is also used to generate S ta n d ard M odel d ip h o to n production, based on th e leading-order q u a rk -an tiq u ark t-channel an nihilation diagram and th e gluon-induced box process, and p h o to n + je t production.

T he generated events are passed th ro u g h a full d e te c to r sim ulation [33] based on G e a n t 4 [34]. P ile-up from additio nal pp collisions in th e same and neighbouring bunch crossings is sim ulated by overlaying each MC event w ith a variable num ber of sim ulated inelastic pp collisions generated using P y t h i a

w ith th e A2 tu n e [35]. T he MC events are weighted to reproduce th e d istrib u tio n of th e average num ber of interactions per bunch crossing observed in th e d a ta .

4 P h o to n se le c tio n

P h o to n and electron can did ates are reconstructed from clusters of energy deposited in th e electrom agnetic calorim eter. C andidates w ithout a m atching tra c k or reconstructed conversion v ertex in th e inner d e te c to r are classified as unconverted photons. Those w ith a m atching reconstru cted conversion vertex or a m atching track, consistent w ith originating from a p hoton conversion, are classified as converted photons. Those m atched to a track consistent w ith originating from an electron produced in th e beam in teractio n region are kept as electrons.

Only p hoton can d id ates w ith |n| < 2.37 are considered, not including th e tra n sitio n re­

gion 1.37 < |n| < 1.52 betw een th e barrel and end-cap calorim eters. T he calorim eter g ran u ­ larity in th e excluded tra n sitio n region is reduced, and th e presence of significant addition al inactive m aterial degrades th e ph oton identification capabilities and energy resolution.

P h o to n identification is based prim arily on shower shapes in th e calorim eter [36], w ith th e selection c riteria re-optim ized for th e conditions expected for th e 2015 d a ta . An initial loose selection is derived using only th e inform ation from th e hadronic calorim eter and th e lateral shower shape in th e second layer of th e electrom agnetic calorim eter, which contains m ost of th e energy. T he final tig h t selection applies tig h ter c riteria to these variables, different for converted and unconverted p h oto n candid ates. It also places requirem ents on th e shower shape in th e finely segm ented first calorim eter layer to ensure th e co m patibility of th e m easured shower profile w ith th a t originating from a single ph oton im pacting th e calorim eter. W hen applying th e photon identification c riteria to sim ulated events, th e shower shapes are corrected for small differences in th eir average values betw een d a ta and sim ulation. T he efficiency of th e p h oton identification increases w ith E

from 85% at 50 GeV to 95% a t 200 GeV. For E T > 50 GeV, th e u n certain ty in th e p h o ton identification efficiency varies betw een ±1% and ±5% depending on n and E T . T his u n certain ty is estim ated from th e effect of differences betw een show er-shape variable distrib u tio n s in d a ta and sim ulation. From th e studies done in ref. [36], th is procedure is found to provide a conservative estim ate of th e un certainties.

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

To fu rth e r reject th e background from je ts m isidentified as photons, th e p h oton candi­

d ates are required to be isolated using b o th calorim eter and track ing d e te c to r inform ation.

T he calorim eter isolation variable, ET°, is defined as th e sum of th e E t of energy clusters deposited in a cone of size A R = \ J (A n )

+ ( A ^ )

= 0.4 aro un d th e p h o to n cand idate, excluding an area of size A n x A 0 = 0.125 x 0.175 centred on th e p h oto n cluster; th e expected p h o to n energy deposit outside th e excluded area is su b tra c te d . T he pile-up and underlying-event co n trib u tio n to th e calorim eter isolation variable is su b tra c te d from th e isolation energy event-by-event [37- 39]. T he selection requirem ent on th e calorim eter iso­

latio n variable is defined by ET° < 0 .0 2 2 E t + 2.45 GeV, w here E t is th e transv erse energy of th e p h oto n can d id ate. T h e tra c k isolation variable (pT°) is defined as th e scalar sum of th e transverse m om enta of th e track s in a cone of A R = 0.2 around th e p h oto n candid ate.

T he tracks are required to have p t > 1.0 GeV and to be consistent w ith originating from th e d ip ho ton p rim ary vertex, defined in section 5.1. For converted photons, th e one or two tracks associated w ith th e p ho to n conversion are excluded from th e pT° co m p u tation . T he requirem ent applied for th e tra c k isolation variable is pT° < 0 .0 5 E t.

T he efficiency of th e isolation requirem ents is studied using several d a ta control sam ­ ples. E lectrons from Z -boson decays are used to validate th e isolation variables up to E

= 100 GeV. Inclusive p h o to n sam ples are used to check th e efficiency of th e isolation requirem ent in a wide E

range from 50 GeV up to 1000 GeV. Small differences betw een d a ta and sim ulation in th e average value of th e calorim eter isolation variable are observed as a function of E

and n of th e p h oton candidates. T he size of th is difference is used as a sy stem atic uncertainty. T he efficiency of th e com bined isolation requirem ent for photons fulfilling tig h t identification selection in signal MC sam ples is 90% to 96% in th e E

range 100 GeV to 500 GeV, w ith an u n certain ty betw een 1% and 2%. T he isolation requirem ent reduces th e ra te at which je t are m isidentified as photons by a b o u t one o rder of m agnitude.

T he m easurem ent of th e electron or p h oto n energy is based on th e energy collected in calorim eter cells in an area of size A n x A 0 = 0.075 x 0.175 in th e barrel and 0.125 x 0.125 in th e end-caps. A m u ltiv ariate regression algorithm [40] to calib rate electron and photon energy m easurem ents was developed and optim ized on sim ulated events. C orrections are m ade for th e energy deposited in front of th e calorim eter and outside th e cluster, as well as to account for th e v ariatio n of th e energy response as a function of th e im pact point on th e calorim eter. T he in p u ts to th e energy calib ratio n algorithm are th e m easured energy per calorim eter layer, including th e presam pler, th e n of th e cluster and th e local position of th e shower w ithin th e second-layer cell corresponding to th e cluster centroid. In addition, for converted photons, th e tra c k tran sverse m om enta and th e conversion radius are used to fu rth e r im prove th e energy resolution, especially at low energy. T he calib ratio n of th e layer energies in th e calorim eter is based on th e m easurem ent perform ed w ith

d a ta at yfs =

TeV [40]. T he overall energy scale in d a ta and th e difference in th e co n stan t term of th e energy resolution betw een d a ta and sim ulation are estim ated w ith a sam ple of Z -boson decays to electrons recorded in

and reprocessed using th e sam e conditions as used for th e 2015 d a ta tak in g and event processing. At E t values larger th a n w 200 GeV, th e energy resolution is dom in ated by th e c o n stan t term of th e calorim eter energy resolution, which am ounts to 0.6% -1.5% depending on n. T he energy scale and resolution corrections are

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

checked using Z -boson decays to electrons recorded in th e 2015 d a ta se t. U ncertain ties in th e m easurem ents perform ed w ith th is sam ple are estim ated following a procedure sim ilar to th a t discussed in ref. [40]. T he difference betw een th e values m easured w ith th e 2015 d a ta and those predicted from th e reprocessed

d a ta is also tak e n into account in th e u ncertainties. T he u n certain ty in th e p hoton energy scale a t high E t is typically

± (0 .5 -2 .0 )% depending on n, and th e relative u n certain ty in th e ph oton energy resolution for E t = 300 GeV is ± (3 0 -4 5 )% depending on n. A dditional un certainties related to th e e x tra p o la tio n of th e energy scale to photons of very high energies, in ad d itio n to those described in ref. [40], were considered and found to be small. In p articu lar, detailed checks of th e validity of th e calibratio n for th e lowest gain range of th e electronic read o u t [41] of th e electrom agnetic calorim eter, which is used in th e E t range above 350 GeV in th e central p a rt of th e electrom agnetic b arrel calorim eter, were perform ed, including checks w ith high- E t electrons from Z -boson decays. These checks show th a t th e relative calibration of th e low-gain read o ut w ith respect to th e o th er gains is b e tte r th a n ±

%.

5 E v en t s e le c tio n an d sa m p le c o m p o s itio n

S ta rtin g from th e triggered events, two photon candidates fulfilling th e tig h t identification c riteria are required, w ith E T above 40 GeV and 30 GeV, respectively. T he p rim ary vertex corresponding to th e pp collision th a t produced th e d ip h oton can d id a te is identified. In addition, th e calorim eter- and track-based isolation requirem ents are applied to fu rth er reduce th e background from je ts m isidentified as photons, th us increasing th e expected sensitivity of th e analyses. Different additional selections are th e n applied, separately in th e spin

and spin

resonance searches.

5.1 P r im a r y v e r t e x s e le c tio n

T he d ip h o to n m ass reco n struction requires th e recon structed prim ary v ertex corresponding to th e pp collision th a t produced th e d iphoton candid ate. T he correct identification of th e track s originating from th is pp collision is also necessary to avoid pile-up co ntributions to th e tra c k isolation. To keep th e co n trib u tio n of th e opening angle resolution to th e mass resolution sm aller th a n th e con trib u tio n of th e energy resolution, a position resolution for th e prim ary vertex of ab o u t 15 m m in th e z-direction is required. B e tte r resolution is needed to correctly m atch tracks to th e pp collision vertex of th e d iph oto n candid ate. T he directions of b o th p hoton can did ates are m easured using th e longitudinal and transverse segm entation of th e electrom agnetic calorim eter, w ith a resolution of ab o u t 60 m r a d / v E w here E is th e p hoton energy in GeV. An estim ate of th e z-position of th e d iph oto n prim ary v ertex is ob tained by com bining th e average beam -spot position w ith this ‘p h o ton p o in tin g ’.

It m ay be enhanced using th e track s from photon conversions w ith conversion radii before or in th e volum e of th e silicon detectors. T his estim ate gives a resolution of ab o u t 15 mm in th e z-direction. In order to select th e correct p rim ary vertex for th e dip h o to n event, a neural-netw ork discrim inant, sim ilar to th e one used in ref. [42], is co n stru cted using b o th th e z-position of th e d ip h oto n p rim ary vertex estim ated by th e p h o ton pointing including its u n certain ty and additio nal inform ation from th e tracks associated w ith each reconstru cted

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

p rim ary vertex. A fter applying th is procedure, th e con trib u tio n of th e opening angle resolution to th e m ass resolution is negligible. T he efficiency to reco nstru ct th e correct p rim ary v ertex w ithin ± 0.3 m m is ab o u t

%.

5 .2 E v e n t s e le c tio n

In th e selection used to search for a spin-2 resonance, th e tran sverse energy of each photon is required to satisfy E T > 55 GeV. W ith th is selection, 5066 d iph o ton events w ith a d ip h o to n invariant m ass m

> 200 GeV are selected in th e d a ta .

T he search for a spin-0 resonance applies tig h ter selections which were optim ized on sim ulated background and signal sam ples. Given th e isotropic d istrib u tio n of th e decay, th e average tran sv erse energy of th e two photons is expected to be higher th a n th a t of photons from background processes a t th e sam e invariant m ass. For a given value of m 77, th e transverse energy is required to be E T > 0.4m

for th e p h o ton w ith th e highest E T and E t > 0.3m

for th e p h oton w ith th e second-highest E T . T his selection improves th e expected sensitivity by m ore th a n 20% for m asses larger th a n 600 GeV com pared to the initial requirem ent. W ith these requirem ents, 7391 (2878) events are selected in th e d a ta w ith m

> 1 5 0 GeV (> 2 0 0 GeV). T he highest invariant m ass value observed in th e d a ta is 1933 GeV (1606 GeV) for th e spin

(spin-0) search selection.

5 .3 S a m p le c o m p o s it io n

T he selected sam ples m ainly consist of events from d ip h o to n production, followed by pho- to n + je t production, w ith one je t m isidentified as a photon, and dijet p ro d uctio n w ith two je ts m isidentified as photons. B ackground sources from Drell-Yan, W y or Z y production, w ith eith er one or two isolated electrons m isidentified as photons, are negligible. A q u a n ­ tita tiv e u n d erstan d in g of th e sam ple com position is required for th e background estim ate in th e spin-2 resonance search. It is also used in th e studies for th e choice of background function in th e spin

resonance search.

Two m ethods based on control regions built from events failing th e isolation require­

m ent a n d /o r some of th e tig h t p h oton identification requirem ents are used to e stim ate th e relative co n trib u tio n of th e various sources of background directly from d a ta . To avoid sig­

nificant correlation w ith th e isolation variable, only some of th e tig h t p h o to n identification requirem ents using th e first layer of th e calorim eter are inverted

In th e first m etho d [43], denoted th e 2 x 2 sidebands m ethod, four regions for each ph oto n can d id ate are co nstru cted , one region corresponding to th e signal selection and th e others to can d idates failing th e isolation requirem ent only, failing p a rt of th e tig h t identification requirem ent only or failing b oth. For dip h o to n candidates, 16 control regions are thu s obtained. T he in p u ts to th e m eth od are th e num bers of events in th e 16 regions and th e signal efficiencies of th e tig h t identification and isolation requirem ents. T he correlation betw een these two requirem ents is assum ed to be negligible for background events. T he m etho d allows th e sim ultaneous e x tractio n of th e num bers of genuine d ip hoto n events, p h o to n + je t, je t+ p h o to n and dijet background events, and of th e efficiencies of th e tig h t identification and isolation requirem ents for p h o ton can did ates from m isidentified jets.

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

P h o to n + je t events correspond to th e cases w here th e sub-leading p h o ton can d id ate in E

is a je t m isidentified as a photon, and vice versa for je t+ p h o to n events.

T he second m eth od [44], denoted th e m a trix m ethod, classifies th e d ip h o to n candid ates passing tig h t identification requirem ents into four categories depending on w hether both, only th e leading, only th e sub-leading or none of th e photons pass th e isolation cut. T he num bers of observed events in d a ta in these categories are related to th e num bers of genuine diphoton, p h o to n + je t, je t+ p h o to n and dijet events th ro u g h isolation efficiencies for signal and background. T he efficiency for background is estim ated in control regions of th e d a ta , using events failing a subset of th e tig h t identification requirem ents. E vents satisfying th e tig h t identification are used to e stim ate th e efficiency for genuine photons, after su b tra c tin g th e background com ponent, whose am ount is estim ated by com paring th e num ber of events passing w ith th e num ber failing a subset of th e tig h t identification requirem ents, in control region of th e d a ta w ith large tra c k isolation value, p f ° > 0.05E

+ 10 GeV. Once these efficiencies are known, th e sam ple com position can be ex tra cte d by th e inversion of a 4 x 4 m atrix.

B o th m etho d s can be applied over th e full selected kinem atic range, or in bins of m 77, th u s providing inclusive as well as differential yields. F igure 1 shows th e decom position of th e selected d a ta sam ple into th e co ntributions from diphoton, p h o to n + je t or je t+ p h o to n , and dijet events for b o th selections and th e corresponding purities, defined as th e ratio of dip h o to n events to th e to ta l num ber of events in th e sam ple. T he p u rity is (94+:+% for th e spin-2 selection and (93+8)% for th e spin-0 selection. U ncertainties in these p u rity estim ates originate from th e sta tistic a l u n certain ty in th e d a ta sam ple, th e definition of th e control region failing th e tig h t identification requirem ent, th e m odelling of th e isolation d istrib u tio n and possible correlations betw een th e isolation variable and th e inverted identification criteria. T he two m ethods give consistent results w ithin th eir u ncertainties. T he e stim ate of these un certain ties is sensitive to th e small num ber of events in some of th e control regions.

5 .4 S ig n a l a c c e p ta n c e a n d e ffic ie n c y

T he expected signal yield can be expressed as th e p ro d u ct of th re e term s: th e production cross section tim es branching ratio to two photons, th e acceptance (A) of th e kinem atic requirem ents, and th e reco n stru ctio n and identification efficiency (C). T he acceptance is expressed as th e fraction of decays satisfying th e fiducial acceptance a t th e g en erato r level.

T he factor C is defined as th e ratio of th e num ber of events fulfilling all th e selections placed on reco nstru cted q u an tities to th e num ber of events in th e fiducial acceptance. T he fiducial acceptance closely follows th e selection c riteria applied to th e reconstru cted d ata:

|nY| < 2.37, E t > 55 GeV for th e spin-2 resonance search selection and E t > 0.4m

(leading

), E t > 0.3m

(sub-leading

) for th e spin-0 resonance search. A n isolation requirem ent is applied in th e fiducial acceptance definition using all particles w ith lifetime g reater th a n 10 ps at th e g en erato r level in a cone of A R = 0.4 arou nd th e p h oto n direction ET° < 0.05ET +

GeV. T he value of th e isolation requirem ent applied a t th e particle level is ad ju sted to reproduce th e selection applied a t th e reconstruction level.

For th e spin-2 resonance search, th e acceptance for th e benchm ark RS graviton m odel varies from

% at a m ass of 500 GeV, to 91% a t a m ass of 5000 GeV. T he factor C is

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

Figure 1. T he d ip h o to n in v arian t m ass d istrib u tio n s (u p p er panels) of th e d a ta for th e spin-2 and spin- 0 selections an d th e ir decom position into co n trib u tio n s from genuine dip h o to n , p h o to n + je t plus je t+ p h o to n and je t + j e t events, d eterm in ed as described in th e te x t. T he b o tto m panels show th e p u rity of d ip h o to n events as d ete rm in ed from th e tw o m ethods. T he to ta l u n certain ties are shown, including s ta tistic a l and sy stem atic com ponents.

alm ost co n stan t a t

% in th is m ass range. T h e value of A x C for th e selection th u s ranges from 45% to 61% for masses betw een 500 GeV and 5000 GeV w ith a small dependence on th e w idth.

For th e spin-0 resonance search, A ranges from 52% to 62% in th e m ass range from 200 GeV to 700 GeV for a particle sim ilar to a Higgs boson produced by gluon fusion and is alm ost co n stan t above 700 GeV. T he gluon fusion prod uction m ode is used to com pute th e value of C , which ranges from 65% for a particle of m ass 200 GeV to 71% a t 700 GeV and is alm ost c o n stan t above 700 GeV. For th e generator-level fiducial acceptance definition, th e generated d ip ho to n invariant m ass is required to be w ithin ±

r of th e resonance mass.

Different prod u ctio n m odes (vector-boson fusion, associated p rod uction w ith a W or Z boson or w ith a tt pair) yield differences in C values of a t m ost ± 3% , which is tak en as an uncertainty. In th e case of a decay w id th larger th a n th e d e te c to r resolution, th e correction factor C varies by up to ±5% depending on th e assum ed decay w idth. T his v ariation is tak en as an additio n al uncertainty.

E x perim en tal un certainties in C arise from uncertain ties in th e ph oton identification efficiency (±3% to ±2% d epending on th e assum ed m ass and on th e selection), th e ph oton isolation efficiency (± 4% to ±1% depending on th e assum ed m ass and on th e selection), and th e trig ger efficiency (± 0.6% ). U ncertainties in C related to th e p h o to n energy scale and resolution have a negligible im pact on th e u n certain ty in th e expected signal yield.

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

6 S ig n a l m o d e ll in g

T he invariant m ass d istrib u tio n of th e dip h o to n p air for th e signal is expected to peak near th e assum ed m ass of th e new particle, w ith a spread given by th e convolution of its intrinsic decay w id th w ith th e experim ental resolution. For b o th searches, th e experim ental resolution of th e invariant m ass is m odelled w ith a double-sided C ry stal Ball (DSCB) function. Interference effects betw een signal and background are ignored.

T he DSCB function is defined as:

w here t = (m YY — ^ CB) / o CB, N is a norm alization p aram eter, ^ CB is th e peak of th e G aussian d istrib u tio n , o CB represents th e w id th of th e G aussian p a rt of th e function, a low ( a high) param eterizes th e m ass value w here th e d istrib u tio n of th e invariant m ass becomes a power-law function on th e low-mass (high-m ass) side, w ith n low (n high) th e exponent of th is function. For sam ples w ith small decay w idth, th e w idth of th e DSCB G aussian core o

param eterizes th e entire effect of th e experim ental invariant m ass resolution.

T he dip h o to n invariant m ass resolution for a narrow resonance, as m easured by th e o CB p aram eter, varies from ab o u t

GeV a t a m ass of

GeV to ab o u t 13 GeV a t a m ass of 2000 GeV. T h e relative u n certain ty in th e signal m ass resolution is m ostly driven by th e u n certain ty in th e co n stan t term of th e energy resolution, which is th e d om inant c o n trib u tio n a t high energy and varies from -30% to -40% as a function of th e mass, in th e range from 200 GeV to 1000 GeV and stays alm ost c o n stan t above 1000 GeV.

For th e spin-2 resonance search, th e signal m ass d istrib u tio n for any value of th e m ass and k / M

is obtained by a convolution of th e intrinsic d e te c to r resolution, m odelled by a DSCB function, w ith th e predicted d istrib u tio n of th e m ass line-shape a t g enerato r level, as discussed in section 3 . T he p aram eters of th e DSCB function are determ ined from RS g raviton signal sam ples of various m asses w ith k / M Pl = 0.01, corresponding to a w idth of 1.14 ■ 10- 4 m G*, which is negligible com pared to th e d e te c to r resolution. T he convolution approach takes into account th e high-m ass tail predicted for th e benchm ark RS graviton m odel for large coupling values. It is validated by com paring th e predicted m ass d istrib u tio n to th e one derived in fully sim ulated sam ples w ith different k / M Pl values and good agreem ent is found.

W hen considering spin-0 resonances w ith larger n a tu ra l w idths, sim ulated as discussed in section 3 , th e recon stru cted line-shapes for a spin-0 signal are well described by DSCB functions. T he function effectively param eterizes th e com bined effects of th e theo retical line-shape and th e d e te c to r response. T he p aram eters of th e DSCB fit function are th en expressed as an alytical functions of th e m ass and w idth of th e hypothesized resonance.

T his approach provides ad eq u ate m odelling of th e invariant m ass d istrib u tio n of th e signal for w id th values up to

% of th e resonance m ass.

(

e if a low — t — a high

N • < e- °.5aiow Osw - aiow - t ) ” Iow if t < -aiow

—0.5a2- , [ahigh ( nhigh i A

nhigh . ­

l e high .nhgh - "high + 1) if t > a high,

(6 . 1)

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

Figure 2. T he d istrib u tio n s for different signal hypotheses for an RS grav ito n w ith a m ass of 1000 G eV an d (a) k / M pi = 0.01, (b) k / M pi = 0.2, and for a scalar resonance w ith a m ass of 600 G eV an d (c) a narrow decay w id th a n d (d) w ith r / m = 0.06. A fit is su p erim p o sed using th e convolution of th e grav ito n m ass line-shape w ith th e d e te c to r resolution for th e g rav ito n signal case a n d using a double-sided C ry stal B all function for th e scalar resonance case.

F igure 2 illu strates th e signal m odelling for a 1000 GeV RS graviton w ith k / M Pl = 0.01 ( r G* /m G* = 0.01%) or

( r G* / m G* =

%) and for a 600 GeV scalar particle w ith eith er a narrow w id th or a w id th equal to

% of th e m ass. For b o th analyses, a possible bias from th e m odelling of th e signal m ass resolution has a negligible im pact on th e ex tracted signal yield.

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

Tw o different m etho d s are used to e stim ate th e background co n tribu tion s to th e m YY d istri­

b ution. In th e spin-2 search, which aim s to reach m asses up to 5000 GeV, th e sm all num ber of d a ta events at high masses does not effectively co n strain th e d istrib u tio n of th e invari­

a n t m ass d istrib u tio n . T he shape of th e invariant m ass d istrib u tio n of th e m ain diphoton

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

background is thus predicted using th e next-to-leading (NLO) order in QCD D ip h o x [45]

co m p utatio n , version 1.3.2. T he background from p h o to n + je t and dijet p ro d u ction is added using control sam ples from th e d a ta . T he second approach, m ore a p p ro p riate for th e m ass range in which th ere are enough d a ta events close to th e investigated resonance m ass, is based on using a sm ooth functional form , w ith fully d ata-d riv en param eters to m odel th e to ta l background. In th is approach, used for th e spin-0 resonance search, th e m ass d istrib u tio n from d a ta is fitted in th e range above 150 GeV and th e search range for th e signal is 200-2000 GeV.

7.1 M o n te C a rlo e x tr a p o la t io n a p p r o a c h

T he background is sep arated into th e d iphoton irreducible com ponent and th e reducible co n tributions from p h o to n + je t and dijet events. To properly norm alize each com ponent, th e com position of th e d a ta sam ple in th e invariant m ass interval from 200 GeV to 500 GeV is d eterm ined following a procedure sim ilar to t h a t described in section 5.3. T he norm alized d istrib u tio n of th e to ta l background can th e n be estim ated over th e full m ass range from 200 GeV to 5000 GeV, sum m ing th e different background com ponents w ith th e ir relative norm alizations from th e 200-500 GeV range.

T he D ip h o x NLO co m p u tatio n is used to predict th e shape of th e invariant m ass d istrib u tio n of th e irreducible d ip h oto n background a t th e p a rto n level. K inem atic selec­

tio n requirem ents corresponding to th e analysis selection (E T > 55 GeV, |n| < 2.37) are applied. This co m p u tatio n includes th e co n trib u tio n of photons produced in th e fragm en­

ta tio n of quarks or gluons. T he C T E Q

.

M P D F set [46] is used and th e factorization, renorm alization and frag m en tation scales are set to th e m ass of th e d ipho to n system . Fully sim ulated d ip h oton events gen erated w ith S h e r p a are rew eighted using th e ratio of th e D ip h o x and S h e r p a calculations a t th e p a rto n level, as a function of th e d ip h oton in­

variant m ass. T he rew eighting factor varies by ab o u t 20% over th e d ip h oton m ass range from 200 GeV to 5000 GeV. T he u n certain ty in th e D ip h o x co m p u tatio n is estim ated by considering th e following effects: un certainties in th e P D F from variations of th e 22 eigen­

vectors th a t are provided w ith th e C T E Q

.

M P D F (from ±2% a t a m ass of 200 GeV,

±35% a t a m ass of 3500 GeV and up to ±140% at a m ass of 5000 GeV on th e shape of the norm alized invariant m ass d istrib u tio n ), in th e choice of P D F set from a com parison w ith th e M S T W 2 0 0 8 N L O P D F set [47] (up to ± 5 % ), from th e p h oto n isolation applied at th e p a rto n level in D ip h o x (±10% ), and from th e choice of factorization, renorm alization and frag m entatio n scales used in D ip h o x (±5% in th e shape of th e norm alized invariant m ass d istrib u tio n ).

To predict th e shape of th e p h o to n + je t and dijet backgrounds, control sam ples where one or two of th e photons fail to m eet th e tig h t identification c riteria b u t fulfil looser selections are used. T he shape of th e invariant m ass d istrib u tio n in these control samples is fitted w ith a function of th e form

w here x = / ^ / s and p are free param eters. T he u n certain ty in th e shape of this background is estim ated by varying th e identification c riteria used to select th e photons in

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

F i g u r e 3. R elative pre-fit u n c erta in ties in th e sh ap e of th e d istrib u tio n of th e p re d icted back­

gro u n d for th e spin-2 resonance search. T he u n c e rtain ties are show n in th e m ass range 500 G eV to 3500 GeV. T he reducible b ackground u n c e rta in ty corresponds to th e u n c e rta in ty in th e shape of th e reducible b ackground com ponent. T h e u n c e rta in ty in th e shape of th e irreducible background resu lts from u n ce rtain tie s affecting th e NLO d ip h o to n c o m p u ta tio n (p a rto n d is trib u tio n functions an d facto rizatio n an d ren o rm alizatio n scales). T he u n c e rta in ty in th e p u rity corresponds to th e im p a ct of th e relative n o rm alizatio n of th e reducible background com pared to th e irreducible back­

ground. T he u n c e rta in ty in isolation resu lts from th e u n c e rta in ty due to th e choice of parton-level isolation c u t in th e D ip h o x NLO co m p u tatio n .

th e control sam ple. Given th e high p u rity of th e selected sam ple, this is a small co n trib utio n to th e to ta l uncertainty.

T he u n certain ty in th e norm alized m YY d istrib u tio n of th e to ta l background results from un certain ties in b o th th e shape and th e relative norm alization of each com ponent.

Four independent sources of system atic u n certain ty are considered, each of th em w ith an im pact varying w ith th e invariant m ass b u t fully correlated across th e full m ass range.

T hese sources are th e shape of th e reducible background, th e relative n orm alization of th e reducible and irreducible backgrounds, th e im pact of th e parton-level isolation requirem ent in D ip h o x and th e effect of th e un certainties in th e scales and P D F in th e D ip h o x com ­ p u tatio n . Figure 3 shows th e evolution of th e uncertainties in th e background prediction, before th e fit to th e invariant m ass d istrib u tio n described in section

, as a function of m YY in th e region m YY > 500 GeV, which is th e search range for th e spin-2 resonance. T he sum of these un certain ties is co n strained by th e fit and reduced significantly com pared to th e individual com ponents. A t masses larger th a n 1000 GeV, th e m ain con trib u tio n to th e u n certain ty originates from th e shape of th e irreducible background, which in tu rn m ostly arises from th e P D F uncertainty. T he im pact of these uncertain ties in th e range 200 GeV to 500 GeV is also tak e n into account. In addition, MC sta tistic a l uncertainties, which range from ±5% to ±10% in a 5 GeV m ass interval, are also considered, uncorrelated betw een bins.

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

7 .2 F u n c tio n a l-fo r m a p p r o a c h

A fam ily of functions, a d a p te d from those used by searches for new physics signatures in dijet final sta te s [48], is chosen to describe th e shape of th e invariant m ass distribu tion :

/ ( fc)(x; b, {a k}) = N (1 — x

/

)bx Ek=°aj(logx)J , (7.2) w here x = m YY/ y's, b and ak are free p aram eters, and N is a norm alization factor. T he num ber of free p aram eters describing th e norm alized m ass d istrib u tio n is thu s k +

.

To validate th e choice of th is functional form and to derive th e corresponding uncer­

tainties, th e m etho d detailed in ref. [49] is used to check th a t th e functional form is flexible enough to accom m odate different physics-m otivated underlying d istrib utio ns. A large sam ­ ple of d ip hoto n p seud o -d ata is produced using th e D ip h o x NLO co m p utatio n, w here th e p h oton four-vectors are sm eared w ith th e d etecto r resolution, and also w ith S h e r p a gen­

e ra ted sam ples which are th e n passed th ro u g h th e full d e te c to r sim ulation and th e event reconstruction. T he im pact of th e P D F uncertainties on th e invariant m ass d istrib u tio n is also tak en into account. T he shape of th e m ass d istrib u tio n for th e reducible p h o to n + je t and dijet backgrounds is estim ated w ith d a ta control sam ples selected w ith one or two of th e photons failing th e tig h t identification c riteria b u t fulfilling a looser set of requirem ents.

T hese sam ples are dom in ated by events w ith one or two je ts m isidentified as photons. As th e lim ited num ber of d a ta events does not directly allow a precise estim ate of th e mass d istrib u tio n for m asses above 500 GeV, th e invariant m ass d istrib u tio n of these sam ples is fitted w ith various sm ooth functions providing an ad eq u ate fit to th e d a ta . T he final p seud o-d ata set is obtained by sum m ing th e d iph oto n c o n trib u tio n and th e sm oothed esti­

m ate of th e p h o to n + je t and dijet backgrounds. T he bias related to th e choice of functional form is estim ated as th e fitted “spurious” signal [49] yield in these pseudo-data, which con­

sist only of background events, w hen perform ing a signal-plus-background fit for various signal m ass hypotheses. To be selected for th e analysis, th e functional form is required to have a fitted “spurious” signal of less th a n

% of th e sta tistic a l u n certain ty in th e fitted signal yield over th e full investigated m ass range. A m ong th e forms fulfilling th is criteria, th e one w ith th e lowest num ber of degrees of freedom is preferred. B ased on these criteria, th e functional form defined in eq. (7.2) w ith k = 0 is selected. T he u n certain ty in th e background is estim ated from th e fitted “spurious” signal. For a narrow -signal hypothesis, it varies from 7 events a t 200 GeV to 0.006 events at 2000 GeV. For larger hypothesized signal w idths, th e signal is in teg rated over a w ider m ass range and th e background un ­ c e rtain ty is larger, varying from 20 events a t 200 GeV to 0.04 events a t 2000 GeV, for a hypothesized signal w ith a relative w idth r / m of

%. For a signal m ass of 750 GeV, it varies from

events for a small w idth to

events for r / m of

%.

To decide w hether a function w ith increased com plexity is needed to describe th e d a ta , an F -te st is perform ed. Tw o background-only fits, using th e sim plest validated function and a m ore com plex version using a larger value of k, are perform ed on th e selected d a ta , binned according to th e expected num ber of background d ip h oton events. A test sta tistic F is com puted from th e resulting x

values, and its prob ability is com pared w ith th a t expected from a F isher d istrib u tio n w ith th e corresponding num ber of degrees of freedom.

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

T he hypothesis th a t th e addition al degree of freedom is not needed to adeq u ately describe th e d a ta is rejected if th e prob ab ility to have an F value higher th a n th e one observed in th e d a ta is less th a n 5%. T he te sts do not indicate a need for add ition al degrees of freedom w ith respect to th e sim plest function (k =

).

7 .3 C o m p a r iso n o f t h e tw o m e t h o d s for t h e b a c k g r o u n d e s tim a t e

T he two m ethods used for th e background estim ate were com pared in th e m ass range where th ey are b o th used. Because of th e different event selection, th e functional form used to de­

scribed th e background for th e spin

search selection, determ ined following th e procedure discussed in section 7.2, is different from th e spin-0 search selection and can be expressed as f (x; a o ,a i) = N e (“o+«ilog(x))log(x), w here x = m YY/V s , a

and a

are free p aram eters and N is a norm alization factor. To e stim ate th e background in one selection scenario and for a specific approach, an unconditional signal-plus-background m axim um -likelihood fit w ith th e corresponding signal hypothesis is perform ed on th e d a ta . T he com parison of th e different background estim ates is shown in tab le

for two different d ip ho ton invariant m ass windows. For th e MC e x tra p o la tio n m ethod, th e sta tistic a l u n certain ty is directly related to th e to ta l num ber of events in th e d a ta sam ple and th u s is a t th e level of ±1.5%

for th e spin-2 resonance search selection. For th e functional-form approach, th e sta tistic a l u n certain ty originating from th e u n certain ty in th e determ in atio n of th e p aram eters of th e function from th e fit to th e d a ta is larger, especially a t high masses. T he sy stem atic uncer­

ta in ty in th e MC e x tra p o la tio n m eth od originates from th e sources of u n certain ty discussed in section 7.1. T hese uncertain ties are th e n constrained when fitting th e background m odel to th e d a ta . For instance, in th e spin-2 search selection for a m ass aro u nd 750 GeV, th e to ­ ta l background u n certain ty before th e fit is ±12% . This is reduced to ±3.5% after th e fit to th e d a ta . For th e functional-form approach, th e system atic u n certain ty is given directly by th e “spurious” signal uncertainty, which depends on th e signal hypothesis being considered.

T his sy stem atic u n certain ty is lower th a n th a t of th e MC e x tra p o la tio n approach.

At high m ass th e MC e x tra p o la tio n gives a sm aller uncertainty. For m asses around 750 GeV th ey are found to be com parable, while a t low m ass, w here th e sta tistic a l com po­

nent of th e u n certain ty using th e functional-form approach is small, this approach has a lower to ta l uncertainty. For all masses, th e to ta l u ncertain ty in th e background estim ate is significantly sm aller th a n th e expected sta tistic a l fluctuations of th e background yield in th e different signal regions being considered. O verall th ere is good agreem ent betw een th e background predictions from th e two m ethods.

8 S ta tis tic a l p ro c ed u r e

T he num bers of signal and background events are obtained from m axim um -likelihood fits of th e m YY d istrib u tio n of th e selected events, for (m x , k / M Pl ) hypotheses w here a spin

resonance from th e b en chm ark RS m odel is probed, or for ( m x , a ) hypotheses w here the presence of a spin

resonance of m ass m x and w idth r = a m x is probed.

T he function used to describe th e d a ta can be w ritte n as

N Sf S(m YY) + N Bf B( m YY) , (8.1)

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

Investigated signal region B ackground from B ackground from MC ex tra p o la tio n functional form m = 750 GeV, r / m =

%

720-780 GeV, spin

selection 20.1 ± 0.3 ± 0.7 21.9 ± 1.2 ± 0.4 720-780 GeV, spin-0 selection 6.7 ± 0.1 ± 0.4

± 0.7 ± 0.3 m = 1500 GeV, r / m =

%

1440-1560 GeV, spin

selection 1.14 ± 0.02 ± 0.09 1.51 ± 0.27 ± 0.08 1440-1560 GeV, spin-0 selection 0.32 ± 0.01 ± 0.04 0.33 ± 0.11 ± 0.04

T a b le 1. E stim a te d num bers of b ackground events for different signal hypotheses, in a m ass w indow corresponding to ± 1 .5 tim es th e resolution of th e signal. T he resu lts o b tain ed by applying th e two m eth o d s to co m p u te th e b ackground are com pared. T he s ta tistic a l an d sy stem atic u n c e rtain ties in th e background e stim ates are show n se p arately w ith th e s ta tistic a l u n c e rta in ty first.

w here N S is th e fitted num ber of signal events, / S(m 77) is th e norm alized invariant mass d istrib u tio n for a given signal hypothesis, N B is th e fitted num ber of background events and / B (m 77) is th e norm alized invariant m ass d istrib u tio n of th e background events. In th e spin-2 resonance search, /B is th e sum of th e d iphoto n N L O -based co m p u tatio n and th e reducible background contrib u tio n. In th e spin-0 resonance search, /B is described by a functional form w ith two free p aram eters. T he fitted num ber of signal events is related to th e assum ed signal cross section tim es branching ratio to two photons via th e integ rated lum inosity and th e acceptance and d e te c to r efficiency correction factors.

U ncertain ties in th e signal p aram eterizatio n , th e acceptance and d e te c to r efficiency cor­

rection factors for th e signal and in th e description of th e background shape are included in th e fit via nuisance p aram eters. U ncertainties in th e signal m odelling are constrained w ith G aussian or log-norm al p en alty term s. In th e case of th e M onte Carlo approach, discussed in section 7.1, th e u n certain ty in th e shape of each background com ponent and in th e relative n orm alization of th e different com ponents corresponds to a different nui­

sance p a ra m ete r affecting th e to ta l background shape, as illu strated in figure 3 . These nuisance param eters are also co n strained w ith G aussian p en alty term s. In th e case of th e functional-form ap proach to describe th e background, th e p aram eters of th e function are nuisance p aram eters w ith ou t p en alty term s, and th e system atic u n certain ty in th e back­

ground description is im plem ented by th e “spurious” signal term , which is constrained by a G aussian p en alty term and, for a given (m X , a ) hypothesis, has th e sam e invariant m ass d istrib u tio n as th e signal. T his “spurious” signal u n certain ty is considered separately for each (m X , a ) hypothesis w ith o u t any correlation betw een th e different investigated m ass ranges.

Each fit allows for a single signal com ponent. T he whole m ass spectru m (sta rtin g at 150 GeV for th e spin-0 resonance search and at 200 GeV for th e spin

resonance search) is used for all probed m ass hypotheses.

T he local p-value (p

) for th e com patibility w ith th e background-only hypothesis when testin g a given signal hypothesis (m X , a ) is based on scanning th e q

(m X , a ) te st s ta tis ­

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