P u b l i s h e d f o r SISSA b y S p r i n g e r
Received: January 25, 2019 Revised: June 25, 2019 Accepted: July 2, 2019 Published: July 19, 2019
Search for scalar resonances decaying into
µ + µ- in events w ith and w ith o u t
b-tagg ed je ts produced in p roton -p roton collisions at
√ S =13 T e V with the A T L A S d etecto r
T h e A T L A S collaboration E-m ail: atlas.publications@cern.ch
A b s t r a c t : A search for a narrow scalar resonance decaying into an opposite-sign m uon p air produced in events w ith and w ith o u t b-tagged je ts is presented in this paper. T he search uses 36.1 fb- 1 of √ s = 13 TeV p ro to n -p ro to n collision d a ta recorded by th e ATLAS experim ent a t th e LHC. No significant excess of events above th e expected S tan d ard M odel background is observed in th e investigated m ass range of 0.2 to 1.0 TeV. T he observed u p p er lim its a t 95% confidence level on th e cross section tim es branching ratio for b-quark associated p ro d u ction and gluon-gluon fusion are betw een 1.9 and 41 fb and 1.6 and 44 fb respectively, which is consistent w ith expectations.
Ke y w o r d s: H adron-H adron scatterin g (experim ents)
ArXiv ePr in t: 1901.08144
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C o n t e n t s
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 3
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 4
4 E v e n t r e c o n s tr u c tio n 6
5 S ig n a l a n d b a c k g r o u n d e s tim a t e 7
6 S t a tis tic a l a n a ly s is 9
7 S y s t e m a t ic u n c e r ta in tie s 10
7.1 E xperim ental uncertainties 10
7.2 T heoretical uncertainties 12
8 R e s u lts 15
9 C o n c lu s io n 17
T h e A T L A S c o lla b o r a tio n 24
1 I n t r o d u c t i o n
T his p ap er presents a search, in p ro to n -p ro to n (pp) collision d a ta a t a centre-of-m ass energy of 13 TeV, targ e tin g a scalar particle Ф w ith a m ass in th e range 0.2-1.0 TeV decaying into two opposite-sign m uons. T he n a tu ra l w id th of th e particle is assum ed to be m uch narrow er th a n th e experim ental resolution, such th a t it is th e la tte r th a t d om inates th e d istrib u tio n of th e dim uon invariant m ass in signal events. To m axim ize th e sensitivity to th e presence of b-quarks, th e analysis is perform ed in two d a ta categories. T he first search category requires a t least one je t tagged as containing b-hadrons (b-tagged) in th e final sta te . T he second category requires exactly zero b-tagged je ts in th e event. Sim ultaneous fits to these two categories are used to search for b o th th e gluon-gluon fusion and b-associated production m echanism s of th e scalar particle. T his work is prim arily m otivated as a signature-based search; th e event selection is not designed to ta rg e t any specific m odel and instead facilitates th e com parison of th e d a ta w ith predictions from various th eoretical models.
T he discovery of th e 125 GeV Higgs boson a t th e Large H adron Collider (LHC) [1, 2]
was a significant step in u n d erstan d in g th e m echanism of electrow eak sym m etry breaking (EW SB ). M easurem ents of th e prop erties of th is particle [3- 7] are so far consistent w ith exp ectatio n s for th e S tan d ard M odel (SM) Higgs boson [8- 13]. However, th e observed Higgs
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F ig u re 1. Feynman diagrams for (a) the b-quark associated production mode and (b) the gluon
gluon fusion production mode.
boson could be only a p a rt of an extended scalar sector, as predicted by several theo retical m odels beyond th e SM. For exam ple, such an extended scalar sector is predicted by a class of extensions of th e SM known as th e tw o-H iggs-doublet m odels (2HDM ) [14, 15].
T h e 2HDM posit th e existence of th re e n eu tral bosons w ith properties and coupling stre n g th s differing from those of th e SM Higgs particle. One of th e higher-m ass n eu tral Higgs bosons m ay couple to m uons a t a higher ra te th a n to T-leptons, in co n trad iction to th e SM Yukawa ordering. T his is th e case in th e Flavourful Higgs m odel [16], for exam ple.
T he search described in th is p ap er sets lim its on th e cross-section tim es branching ratio of Φ decaying into m uon pairs which are m ore string ent th a n th e equivalent lim its for Φ decaying into T-lepton pairs [17]. T his is due to higher identification efficiency and lower background ra te for m uons th a n for T-leptons, and th e invariant-m ass resolution being b e tte r for m uon pairs th a n for T-lepton pairs. Similarly, th e coupling of these higher-m ass n e u tra l Higgs bosons to b-quarks could be enhanced relative to th e SM Higgs boson coupling. Hence, th e p ro d u ction of Φ in association w ith b-quarks (bbΦ), shown in figure 1(a ), could be m ore a b u n d a n t th a n th e pro d uctio n of $ by gluon-gluon fusion (ggF), shown in figure 1 (b ). T he Φ ^ bb decay m ode, w here $ is produced in associations w ith 6-quarks, is investigated by CMS in ref. [18].
A dditional in terest for th e search for an excess of events w ith respect to th e SM predictions in th e dim uon plus b-tagged jets final s ta te arises from Z ' and lepto qu ark m odels [19], which could result in eith er resonant or non-resonant co ntrib u tio n s to th e
p p ^ t t p + p - ^ W b W b p + p - final sta te . This work com plem ents th e search for Z ' candi
d ates decaying into m uon pairs presented in ref. [20]: by classifying events in term s of th e presence or absence of a b-tagged je t, it m ay be sensitive to signatures not observable w ith an inclusive selection.
Previous sim ilar searches focused explicitly on beyond-the-SM Higgs bosons decaying into m uon pairs, in th e m ass range 90-500 GeV [21, 22] using y f s = 7 and 8 TeV d a ta . This work extends th e exclusion lim its for new scalar resonances w ith m asses up to 1.0 TeV.
T he analysis described in th is p ap er makes use of a fit to th e observed dim uon invariant m ass (m w ) spectra. T he presence of a signal produced eith er in association w ith b-quarks
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or via gluon-gluon fusion is tested w ith sim ultaneous fits to th e two d a ta regions (w ith and w ith ou t a b-tagged jet) sep arately for ЬЬФ and ggF prod uction m odes. No assum ptions are m ade a b o u t th e relative co n tribu tio n s of th e ЬЬФ and ggF cross-sections.
T his p ap er is stru c tu re d as follows. Section 2 describes th e ATLAS d etecto r. Sec
tio n 3 discusses th e d a ta and th e sim ulated event sam ples used to m odel th e signal and th e background processes. T he event reco nstruction is discussed in section 4 , while sec
tio n 5 describes th e background e stim ate and introduces th e signal interp o latio n procedure used to m odel th e d istrib u tio n for resonance m ass hypotheses for which no sim ulated sam ple was generated. T he event yields and th e description of th e sta tistic a l analysis are discussed in section 6 , followed by section 7 , which provides an overview of th e system atic uncertainties. Section 8 sum m arizes th e results.
2 A T L A S d e te c to r
ATLAS [23- 25] is a m ultipurpose particle d etecto r w ith a forw ard-backw ard sym m etric cylindrical geom etry and near 4n coverage in solid ang le.1 It consists of an inner tracking d e te c to r surrounded by a th in su perconducting solenoid, electrom agnetic and hadronic calorim eters, and a m uon sp ectrom eter.
T he inner track in g d etecto r (ID) covers th e pseudorapidity range |n| < 2.5, and is surrounded by a sup erconducting solenoid providing a 2 T m agnetic field. A t small radii, a high-granularity silicon pixel d e te c to r covers th e v ertex region and typically provides four m easurem ents per track. It is followed by th e silicon m icrostrip tracker, which provides eight m easurem ent points p er track. T he silicon detectors are com plem ented by a gas-filled straw -tu b e tra n sitio n rad iatio n tracker, which extends th e track ing capability radially w ith typically 35 m easurem ents per tra c k for particles a t |n| = 2.0.
E lectrom agnetic (EM ) calorim etry, w ithin th e region |n| < 3.2, is provided by b a r
rel and endcap high-granularity lead /liq u id -arg o n (LAr) sam pling calorim eters, w ith an ad ditio n al th in LA r presam pler covering |n| < 1.8 to correct for energy loss in th e up
stream m aterial. For |n| < 2.5 th e EM calorim eter is divided into th re e layers in dep th . A steel/scin tillato r-tile calorim eter provides hadronic calorim etry for |n| < 1.7. LA r ioniza
tion, w ith copper as absorber, is used for th e hadronic calorim eters in th e endcap region 1.5 < |n| < 3.2. T he solid-angle coverage is com pleted w ith forw ard c o p p e r/L A r and tu n g ste n /L A r calorim eter m odules in 3.1 < |n| < 4.9, optim ized for EM and hadronic m easurem ents, respectively.
T he m uon spectro m eter (MS) surrounds th e calorim eters and com prises sep arate trig ger and high-precision track in g cham bers m easuring th e deflection of m uons in a m agnetic field provided by one b arrel and two end-cap toroid m agnets. T he precision cham ber sys
tem covers th e region |n| < 2.7 w ith th re e layers of m onitored d rift tu b es, com plem ented
■ATLAS uses a right-handed coordinate system w ith its origin a t th e nom inal in teractio n point (IP) in th e centre of th e detecto r and th e z-axis along th e beam pipe. T he x-axis points from th e IP to th e centre of th e LHC ring, and th e y-axis points upw ard. Cylindrical coordinates (r, ф) are used in th e transverse plane, ф being th e azim uthal angle around th e z-axis. T he pseudorapidity is defined in term s of th e polar angle в as r = — ln ta n ( e /2 ) . T he angular distance is m easured in u n its of A R = \ J ( A n )2 + (Д ф )2.
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by cath o d e-strip cham bers in th e forw ard region. T he m uon trigg er system covers th e range |n| < 2.4 w ith resistive-plate cham bers in th e barrel and th in -g ap cham bers in the endcap regions.
A two-level trigger and d a ta acquisition system is used to record events for offline analysis [26]. T he level-1 trigger is im plem ented in hardw are and uses a subset of th e d e te c to r inform ation to reduce th e event ra te to a value of a t m ost 100 kHz. It is followed by a softw are-based high-level trig ger which filters events using th e full d e te c to r inform ation and o u tp u ts events for p erm an en t storage at an average ra te of 1 kHz.
3 D a t a a n d s i m u l a t e d e v e n t s a m p le s
T his search is perform ed w ith a sam ple of pp collision d a ta recorded at a centre-of-m ass energy y / s = 13 TeV corresponding to an in tegrated lum inosity of 36.1 fb- 1 collected during 2015 and 2016. E vents are considered for fu rth e r analysis only if th ey were collected under stable L H C beam conditions and th e relevant d e te c to r com ponents were fully o perational.
T he d a ta used in th is analysis were collected using a com bination of m uon triggers.
For th e 2015 d a ta s e t an isolated m uon w ith tran sverse m om entum px g reater th a n 20G eV was required, while for 2016 th is requirem ent was raised to 26 GeV. To avoid inefficiencies due to th e isolation requirem ent, these triggers were com plem ented by a trigger requiring a reco n structed m uon w ith p x g reater th a n 50 GeV, w itho u t any isolation requirem ents.
Sim ulated signal events were gen erated sim ilarly to th e SM Higgs boson H , w here H was replaced by a higher-m ass scalar boson Φ w ith a co n stan t w id th of 4 MeV. Nine M onte C arlo (MC) sam ples were gen erated in th e m ass range 0.2-1.0 TeV a t intervals of 100 GeV.
B o th th e ggF and bb$ p ro d u ctio n m odes were considered. E vents were generated at next-to- leading order (NLO) w ith P o w H E G -B o x 2 [27- 30] and Ma dGr a p h5_aM C @ N L O [31, 32], for ggF and bb$ respectively. T he CT10 [33] set of p a rto n d istrib u tio n functions (P D F s) was used in th e generation of ggF events while C T 1 0n l o_n f4 [34] P D F s were used to produce th e b-quark associated signal sam ples in th e four-flavour scheme. In th e gluon-gluon fusion p ro d u ction m ode, P y tH iA 8.210 [35] w ith th e AZNLO [36] set of tu n ed param eters was used to g eth e r w ith th e CTEQ 6L1 [37] P D F set for th e p a rto n shower, underlying event and hadron izatio n sim ulation. For th e b-quark associated production, P y tH iA 8.210 w ith th e A14 [38] set of tu n ed p aram eters was used to g eth e r w ith th e N N PD F2.3LO [39] P D F set for th e p a rto n shower, underlying event, and h ad ro n ization sim ulation. T he E v tG en v1.2.0 program [40] was used to m odel th e properties of th e b o tto m and charm hadron decays in all signal sam ples.
Since th e generated signal sam ples are spaced equally in m $ while th e experim ental resolution increases w ith m $ , signal d istrib u tio n s for in term ed iate m ass hypotheses were o b tain ed using an in terp o latio n procedure, described in section 5.
E vents containing Z /y * + je ts were sim ulated using Po w h e g- Box 2 [29, 41] interfaced to th e P y tH iA 8.186 p a rto n shower m odel and th e CT10 P D F set. T he AZNLO tu n e was used, w ith P D F set CTEQ 6L1 for th e m odelling of n o n -p ertu rb ativ e effects. T he E v tG e n v1.2.0 program was used to m odel th e properties of th e b o tto m and charm hadron decays. P h o to s + + 3.52 [42] was used for photons rad ia te d from electrow eak vertices and
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charged leptons. G enerator-level filters are employed to enhance th e fraction of sim ulated events in th e phase-space region th a t is m ost relevant for th e analysis. E vent yields were corrected w ith a m ass-dependent rescaling a t next-to -n ext-to-leadin g o rder (N N L O ) in th e QCD coupling co n stant, com puted w ith V R A P 0.9 [43] and th e CT14N N LO P D F set [34]. M ass-dependent electro-w eak (EW ) corrections were com puted at NLO w ith mcsanc-1 .2 0 [44], along w ith photon-induced co ntribu tio n s ( 7 7 ^ i t via t- and u-channel processes) com puted w ith th e M R ST2004Q ED P D F set [45].
A dditional Z/Y* + jets events, used to evaluate th e system atic u n certain ty from the m odelling of th e fitted distrib u tio n , were sim ulated w ith S h e r p a 2.2.1 [46] and w ith M a d G ra p h 5 _ a M C @ N L O interfaced w ith P y t h i a 8.186. In S h e r p a , Z/Y* + jets m atrix elem ents were evaluated w ith up to two e x tra parto n s a t NLO, and th ree or four e x tra p a rto n s were included a t LO in QCD. T he m erging of different p a rto n m ultiplicities was achieved th ro u g h a m atching scheme based on th e C K K W -L [47, 48] m erging technique using a m erging scale of Q cut = 20 GeV. T he m odels used for th e p a rto n shower and underlying event are th e ones provided internally by S h e r p a . T he S h e r p a 2.2.1 gener
a to r ad o p ts a full five-flavour scheme, w ith m assless b-quarks and c-quarks in th e m atrix elem ents. These quarks are given m ass in th e final s ta te and m assive quarks can be pro
duced directly via th e p a rto n shower. T h e M a d G ra p h 5 _ a M C @ N L O v2 g en erato r merges th e LO (Q CD ) m atrix-elem ent calculations for Z /7* + jets w ith up to four ad d ition al p a r
to ns (higher je t m ultiplicities are m odelled by th e p a rto n shower algorithm ). T he m erging scheme applied to com bine different p a rto n m ultiplicities is th e CK K W -L scheme w ith a m erging scale of Q cut = 30 GeV. For th e LO m atrix-elem ent calculation th e N N PD F2.3 LO P D F s were used (w ith a S = 0.13). T he A14 tu ne, to g eth er w ith th e N N PD F2.3 LO P D F s, was used for th e p a rto n shower. Sim ilarly to S h e r p a 2.2.1, M a d G ra p h 5 _ a M C @ N L O ad o p ts a full five-flavour scheme.
For th e generation of t t and single to p -q u a rk pro du ction in th e W t- and t-channel, th e P o w H E g -B o x 2 g en erato r w ith th e CT10 P D F set was used for th e m a trix elem ent calculations. T he p a rto n shower, fragm entation, and th e underlying event were sim ulated using P y t h i a 6.428 w ith th e CTEQ 6L1 P D F set and th e corresponding P eru gia 2012 tu n e [49]. T he to p -q u a rk m ass was set to 172.5 GeV. For th e generation of t t events, th e hdamp p a ra m ete r of P o w H E g -B o x , which controls th e transv erse m om entum of th e first ad d itio n al emission beyond th e B orn configuration, was set to th e m ass of th e to p quark. T he m ain effect of th is p a ra m ete r is to regulate th e high tran sverse m om entum em ission against which th e t t system recoils. T he t t p ro d uction sam ple was norm alized to th e predicted p ro d u ctio n cross-section as calculated w ith th e T o p + + 2 .0 program to NNLO in p e rtu rb a tiv e QCD, including soft-gluon resum m ation to next-to-next-to-leading- log (NNLL) order [50]. T he norm alization of th e single to p -q u ark event sam ples used an app roxim ate calculation a t NLO in QCD for th e t-channels [51, 52] while N L O +N N L L predictions were used for th e W t-channel [52]. T he E v tG en v1.2.0 program was used to describe th e prop erties of th e b o tto m and charm had ro n decays.
D iboson processes were m odelled using th e Sh e r pa 2.1.1 [46] g en erator and th ey were calculated for up to one ( Z Z ) or zero (W W , W Z ) ad ditio nal parto n s a t NLO and up to th re e additional p a rto n s a t leading o rder (LO) using th e Com ix [53] and O penLoops [54]
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m atrix-elem ent generators. T he m a trix elem ent calculation was m erged w ith th e Sh e r pa
in tern al p a rto n shower [55] using th e M E+PS@ N LO prescription [56]. T he CT10 P D F set was used in conjunction w ith d edicated p a rto n shower tu n in g developed by th e Sh e r pa
au tho rs. T he g en erator cross-sections, calculated a t N L O , were used in this case.
T he g enerated signal sam ples were sim ulated w ith th e fast sim ulation [57, 58] fram e
work of ATLAS, which replaces th e full sim ulation of th e electrom agnetic and hadronic calorim eters by a p aram eterized model. T he background sam ples were sim ulated using th e full G eant4-based sim ulation of th e d e te c to r [59]. Finally, th e sim ulated events were processed th ro u g h th e sam e reconstruction software as th e d a ta . T he effects of pile-up from m ultiple p ro to n -p ro to n in teractions in th e sam e and neighbouring bunch crossings were accounted for by overlaying m inim um -bias events sim ulated using P y t h i a 8 w ith th e A2 tu n e [60] and interfaced w ith th e M STW 2008LO P D F s. Sim ulated events were th en rew eighted to m atch th e pile-up conditions observed in th e d a ta .
4 E v e n t r e c o n s t r u c t i o n
In te rac tio n vertices are recon stru cted [61] from tracks m easured by th e inner d etecto r. T he p rim ary v ertex is defined as th e vertex w ith th e largest ^ pT of its associated tracks. It m ust have a t least two associated tracks, each w ith transverse m om entum p T > 400 MeV.
M uon can d id ates are reco nstru cted from an ID tra c k com bined w ith a tra c k or track segm ent d etected in th e m uon sp ectro m eter [62]. These two tracks are used as in p u ts to a com bined fit (for p T less th a n 300 GeV) or to a sta tistic a l com bination (for p T g reater th a n 300 GeV) [62]. T he com bined fit takes into account th e energy loss in th e calorim eter and m ultip le-scatterin g effects. T he sta tistic a l com bination for high transv erse m om enta is perform ed to m itig ate th e effects of relative ID and MS m isalignm ents. H igh-px m uon can d id ates are required to have at least th re e hits, one in each of th e th re e layers of precision cham bers in th e MS. For these m uons, specific regions of th e MS w here th e alignm ent is su bop tim al are vetoed as a precaution, as well as th e tra n sitio n region betw een th e MS b arrel and endcap (1.01 < \n\ < 1.10). F u rth e r qu ality requirem ents are applied to th e consistency of th e ID and MS m om entum m easurem ents, and to th e m easured m om entum u n certain ty for th e MS track.
T he recon structed m uon can d id ates are required to have tran sv erse m om entum , p T , g reater th a n 30 GeV and pseudorapidity \n\ < 2.5. T hey are fu rth e r required to be con
sistent w ith th e hypothesis th a t th ey originate from th e p rim ary vertex by applying selec
tions on th e tran sv erse (do) and longitudinal (z0) im pact p aram eters, defined relative to th e p rim ary vertex position: \d0 / a do | < 3 and \z0 sin 9\ < 0.5 mm w here a do denotes th e u n certain ty in th e tran sv erse im pact p aram eter. A loose isolation requirem ent is applied, based on th e sum of th e m om enta of inner d etecto r track s which lie w ithin a variable-sized cone, w ith A R max = 0.3, around th e m uon track. T his isolation requirem ent is tu n ed to yield a 99% efficiency over th e full range of m uon px.
Je ts are recon stru cted from noise-suppressed energy clusters in th e calorim eter [63]
w ith th e anti-k t algorithm [64, 65] w ith radius p a ra m ete r R = 0.4. T he energies of th e jets are calibrated using a je t energy scale (JE S) correction derived from b o th sim ulation and
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in situ studies using d a ta [66]. All jets are required to have p T > 25 GeV and |n| < 4.5. A m u ltivariate selection th a t reduces co n tam in atio n from pile-up [67] is applied to je ts w ith
Pt < 60 GeV and w ith |n| < 2.4 utilizing calorim eter and track in g inform ation to separate h a rd -sc a tte r jets from pile-up jets.
Selected je ts in th e central region can be tagged as containing b-hadrons (b-tagged) by using a m ultivariate discrim inant (MV2c10) [68, 69] th a t combines inform ation from an im p act-p aram eter-b ased algorithm , from th e explicit reco nstru ction of a secondary vertex and from a m ulti-vertex fitte r th a t a tte m p ts to reco nstru ct th e full b- to c-hadron decay chain. A t th e chosen w orking point, th e algorithm provides nom inal light-flavour (u,d,s- q u ark and gluon) and c-jet m isidentification rates of 3% and 32%, respectively, for an average 85% b-jet tagging efficiency, as estim ated from sim ulated t t events for jets w ith
P t > 20 GeV and |n| < 2.5. T he flavour-tagging efficiencies from sim ulation are corrected separately for b-, c- and light-flavour jets, based on th e respective d ata-b ased calibration analyses [70].
Sim ulated events were corrected to reflect th e m uon and je t m om entum scales and reso
lutions, b-jet identification algorithm calibration, as well as th e m uon trigger, identification, and isolation efficiencies m easured in d a ta .
An overlap rem oval procedure is applied to avoid a single particle being reconstructed as two different o bjects as follows. Je ts not tagged as b-jets, b u t which are reconstructed w ithin A R = 0.2 of a m uon, are removed if th ey have fewer th a n th re e associated tracks or if th e m uon energy c o n stitu tes m ore th a n 50% of th e je t energy. M uons reconstructed w ithin a cone of size A R = m in (0.4,0.04 + 10 GeV / p t) arou n d th e je t axis of any surviving je t are rem oved. Je ts are also discarded if th ey are w ithin a cone of size A R = 0.2 around an electron candid ate. E lectrons are recon structed from clusters of energy deposits in th e electrom agnetic calorim eter th a t m atch ID tracks, and are identified as described in ref. [71].
For electrons w ith tran sv erse energy E T > 10 GeV and pseudorapidity of |n| < 2.47, a likelihood-based selection is used a t th e “loose” op eratin g point defined in [71].
Following th e overlap removal, je t cleaning c riteria are applied to identify je ts arising from non-collision sources or noise in th e calorim eters, and any event containing such a je t is removed [72].
T he m issing transverse m om entum , E™ ss, is defined as th e negative vector sum of th e transverse m om enta of m uons, electrons and jets associated w ith th e p rim ary vertex. A soft term [73] is added to include w ell-reconstructed track s m atched to th e p rim ary vertex th a t are not associated w ith any of th e objects.
At least two reco nstructed m uons are required in th e event, and th e two highest-pT m uons of th e event are used to form a dim uon candid ate. If these m uons do not have opposite charges, th e event is rejected.
5 S ig n a l a n d b a c k g r o u n d e s t i m a t e
E vents satisfying th e preselection c riteria of section 4 are considered for fu rth e r analysis.
D epending on th e value of th e recon structed dim uon invariant m ass and th e num ber of b-tagged jets, th ey are classified as being in eith er a control region, used to m easure th e
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ra te of th e d om inant backgrounds (Z/Y* + jets and tf) or a signal region, used to search for th e 4 ^ p p signal. All signal and control regions are designed to be orthogonal.
Selected events are retained in th e signal region if th e dim uon invariant m ass, m w , exceeds 160 GeV, while th ey are retained in th e control region if 100 GeV < < 160 GeV.
T he control regions do not include th e Z -boson peak; this avoids co n strain ts on system atic un certainties in a region of phase space which m ay behave differently w ith respect to th e high m ass tails w here th e signal search is focused.
E vents in th e signal region are fu rth e r classified as “SR bT ag” , if a t least one b-tagged je t is identified in th e event, or “SR bV eto” , otherw ise. No fu rth e r o p tim izatio n of th e signal region definition is considered, in order to m inim ize th e assum ptions m ade ab o u t th e signal kinem atics.
E vents in th e control region are fu rth e r classified as “C R bV eto” if th ere is no b-tagged je t identified in th e event, while rem aining control region events are classified as “C R bT ag” ,
if th e m issing transverse m om entum is less th a n 100 GeV, or “C R ttb a r” otherw ise.
T he dom inant background sources for this sig n atu re are m uon pairs th ro u g h
Z / y* + je ts , to p -q u ark pair, and diboson production. W + je ts and QCD m ulti-jet events co n trib u te less th a n 0.0 1% to th e to ta l background in signal regions, and therefore are neglected. All relevant background co ntributions were m odelled using sim ulated samples as described in section 3 .
Sim ulated Z / y* + jets events were categorized d epending on th e generator-level “t r u t h ” labels of th e jets in th e event. Sim ulated jets were tru th -la b elled according to which hadrons w ith p T > 5 GeV were found w ithin a cone of size A R = 0.3 aro u nd th e je t axis. If a b- h ad ro n was found, th e je t was tru th -la b elled as a b-jet. If no b-hadron was found, b u t a c-hadron was present, th e n th e je t was tru th -la b elled as a c-jet. O therw ise th e je t was tru th -la b elled as a light-flavour (i.e., u ,d,s-qu ark, or gluon) jet. T he Z / y* + je ts events were classified as Z + heavy flavour (Z + H F ) if a b-jet or c-jet was found at g enerator level and Z + light flavour (Z + L F ) otherw ise. These two categories of sim ulated events were tre a te d as different background com ponents.
T he predictions for th e expected num bers of t f , Z + H F and Z + L F events are adjusted to m atch th e num ber of events in d a ta in th e control regions via a global fit (see section 6) , while th e o th er backgrounds are norm alized to th eir expected cross-section, discussed in section 3 .
T he expected invariant m ass d istrib u tio n of th e narrow resonance signal is m odelled w ith a double-sided C ry stal Ball (DSCB) [74] function in th e m ass range 0.2 TeV < <
1.0 TeV for all nine sim ulated MC sam ples. T he w idth of th e d istrib u tio n is do m inated by th e experim ental resolution, which can be described by a G aussian d istrib u tio n . T he power-law asym m etric term s of th e DSCB have enough degrees of freedom to m odel the
tails for signals in th e 0.2-1.0 TeV m ass range. In order to in terp o late th e signal p a ra m eterization to any m ass value in th is fit range, second-order polynom ial param eterization s of all six signal-shape p aram eters as a function of are o b tained from a sim ultaneous fit to all th e generated m ass points m $ , separately for events w ith and w itho ut a t least one b-tagged je t. Since all signal sam ples are scaled to th e sam e a rb itra ry cross-section, any differences in th e num ber of events are due to differences in th e acceptances of th e selec
J H E P 0 7 ( 2 0 1 9 ) 1 1 7
tion. T he fitted n orm alization is param eterized w ith a second-order polynom ial in a sim ilar way to th e o th er DSCB param eters. As a result of th is procedure, th e d istrib u tio n for an a rb itra ry hypothesis m ass can be found by co n stru ctin g a DSCB from p aram eters calculated using th e fitted coefficients and th e hypothesized m ass m $. T he in terp olatio n is perform ed separately for each system atic variation, and for th e gluon-gluon fusion and
b-qu ark associated prod u ctio n signal sam ples. B inned tem p lates are th e n generated from th e DSCB. To validate th e in terp o latio n procedure, one sim ulated sam ple at a tim e is re
moved from th e sim ultaneous fit, and th e tem p la te generated from th e DCSB is com pared w ith th e d istrib u tio n from th e corresponding sim ulated sam ple and th ey agree w ithin 2-5% , th e size of th e bin-by-bin MC sta tistic a l uncertainty. Nine MC sam ples were gener
a te d in th e m ass range 0.2-1.0 TeV, every 100 GeV. T he interp o latio n procedure was used to generate signal tem p lates every 10 GeV betw een 0.2 and 0.3 TeV, every 20 GeV betw een 0.3 and 0.6 TeV, and every 50 GeV betw een 0.6 and 1.0 TeV.
T he acceptance of b-quark associated production in th e SR bTag region varies in th e range 11-19% depending on . T he acceptance in th e SRbVeto region, which is inversely co rrelated w ith th e SR bTag one, varies from 20% to 15%. For th is reason, b o th SR bTag and SRbVeto are included in th e global fit (see section 6) . T he acceptance of gluon-gluon fusion in th e SRbVeto region varies in th e range 31-35% . T he acceptance in th e SR bTag is less th a n 2% for all masses.
6 S t a t i s t i c a l a n a l y s is
T he te s t sta tistic qß as defined in ref. [75] is used to determ ine th e probability th a t th e background-only m odel is com patible w ith th e observed d a ta , to e x tra ct th e local p-value, and, if no hint of a signal is found in th is procedure, to derive exclusion intervals using th e CLs m ethod. T he binned likelihood function is bu ilt as th e p ro d u ct of Poisson probability term s associated w ith th e bins in th e d istrib u tio n in th e 0.16-1.5 TeV range. It depends on th e p a ra m ete r of interest, on th e norm alization factors of th e d om inant backgrounds and on ad ditio n al nuisance p aram eters (representing th e estim ates of th e sy stem atic u n c e rtain ties) th a t are each constrained by a G aussian prior. T h e bin-by-bin sta tistic a l uncertainties of th e sim ulated backgrounds are also considered. S eparate fits are perform ed to te s t th e different hypotheses: only bb$ signal, only ggF signal, and signal com posed of different m ixtures of th e two p ro d uction modes. D a ta are fitted in th e 0.16-1.5 TeV range to check th a t th e background description is correct and to constrain system atic u ncertainties, while th e signal presence is teste d in a narrow er 0.2-1.0 TeV range.
L ogarithm ic binning in is chosen to scale w ith experim ental dim uon m ass resolu
tio n (defined as full-w idth at half-m axim um ), which varies from 5% at = 200 GeV to 14% at = 1 TeV, while ensuring th a t th e num ber of sim ulated background events in each bin is sufficient to reliably predict th e background. T he num bers of events in th e CR- bVeto, C R bTag, and C R ttb a r control regions are also included in th e m axim um -likelihood fit. D a ta in these regions are used to co n strain th e norm alizations of th e d om inant back
ground processes: Z + L F , Z + H F , and t t T he norm alization factors used to scale th e expected num ber of events for each process to m atch th e d a ta are free p aram eters in th e
J H E P 0 7 ( 2 0 1 9 ) 1 1 7
Background Asimov data Observed data Z + H F 1.00 ± 0.23 1.47 ± 0.26 Z + L F 1.00 ± 0.02 1.02 ± 0.02 t t 1.00 ± 0.04 1.02 ± 0.04
T ab le 1. Normalization factors of the dominant backgrounds as measured in a fit to data under the background plus signal hypothesis (480GeV bb$ signal). The uncertainty includes both the statistical and systematic sources: the latter ones dominate. The reduction of the observed relative uncertainty of the Z + HF normalization in the data fit is due to the large increase in the number of Z + HF events when the data in signal regions are included.
fit. T h eir expected u n certain ty is estim ated using an Asimov d a ta se t [75], a pseu do-d ata d istrib u tio n equal to th e background plus signal ex p ectatio n for a given value of th e signal cross-section tim es branching ratio. T he expected and m easured norm alization factors are shown in tab le 1. T hey are m easured in a fit to d a ta u nd er th e background plus signal hypothesis, w here th e signal corresponds to bb$ pro du ctio n w ith m ass = 480 GeV.
As discussed in section 7, th e experim ental uncertain ties are tre a te d as fully corre
lated am ong different processes and regions, while th e th eo retical uncertain ties are m ostly uncorrelated am ong processes.
T he num bers of observed events in th e signal regions to g eth er w ith th e predicted event yields from signal and background processes are shown in tab le 2 . T he num bers are th e results of th e m axim um -likelihood fit to d a ta un d er th e background plus signal hypothesis, w here th e signal corresponds to bb$ p ro d uctio n w ith = 480 GeV. T he num ber of predicted signal events corresponds to th e expected u p p er lim it (UL) tim es th e cross-section: this highlights th e com parison betw een signal and background at th e edge of th e analysis sensitivity.
T he observed num bers of events are com patible w ith those expected from SM processes, w ithin u n certainties. T he d istrib u tio n in th e SR bTag region is shown in figure 2(a) for a bb$-only fit. T he d istrib u tio n in th e SRbVeto region is shown in figure 2 (b ), for a ggF-only fit. E ach background process is norm alized according to its post-fit cross-section.
T he tem p lates for th e = 200 GeV, = 480 GeV and = 1 TeV m ass hypotheses are norm alized to th e expected u p p e r lim it.
7 S y s t e m a t i c u n c e r t a i n t i e s
T he sources of system atic u n certain ty can be divided into th re e groups: those of exper
im ental origin, those related to th e m odelling of th e sim ulated backgrounds, and those associated w ith signal sim ulation. T he finite size of th e sim ulated background sam ples is also an im p o rta n t source of uncertainty.
7.1 E x p e r im e n ta l u n c e r ta in tie s
T he d om inant experim ental uncertainties originate from residual m ism odelling of th e muon reco nstruction and selection after th e sim u latio n -to -d ata efficiency correction factors have been applied. T hey include th e u n certain ty o b tained from Z ^ p p d a ta studies and a
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Sample SRbTag SRbVeto CRbTag CRbVeto CRttbar t t 16490± 240 2 090 ± 300 16 300 ± 600 2 320 ± 350 4 160 ± 70 Single top 1470 ± 100 480 ± 50 1 340 ± 100 530 ± 50 297 ± 22 Diboson 176 ± 23 2 570 ± 180 280 ± 40 4 550 ± 310 19 ± 5 Z + H F 1 920 ± 320 3 400 ± 700 13 300 ± 1900 25000 ± 5 000 18 ± 9 Z + L F 1060 ± 330 57 700 ± 900 6 300 ± 2 000 501 000 ± 5 000 10 ± 9 Total Bkg 21110± 140 66 240 ± 250 37530 ± 200 533 100 ± 700 4 500 ± 60 bb$ (UL)
ggF (UL)
37+ 1 4
37 —10 4+2
45+ 18 45 +13 73+ 2 8
73+21
Data 21154 66300 37 527 533134 4511
T ab le 2. Post-fit numbers of events from the combined fit under the background plus signal hy
pothesis (480 GeV bb$ signal). Here “Total Bkg” represents the sum of all backgrounds. The quoted uncertainties are the combination of statistical and systematic uncertainties. The uncertainty in the total background determined by the fit is smaller than the sum in quadrature of the individual components due to the normalization factors and systematic uncertainties that introduce correlation between them. The number of signal events corresponds to the expected upper limit (UL) times the cross-section. The uncertainties in the expected signal yields are from fits using the Asimov dataset.
F ig u re 2. Distributions of the dimuon invariant mass, mMM, after the combined fit to data are shown normalized: (a) in the SRbTag, under the background plus signal hypothesis (480 GeV bb$
signal) and (b) in the SRbVeto, under the background plus signal hypothesis (480GeV ggF signal).
The fit for a m$ =480 GeV signal corresponds to the largest excess observed above the background expectation. Each background process is normalized according to its post-fit cross-section. The templates for the m$ =200 GeV, m$ =480 GeV and m$ =1 TeV mass hypotheses are normalized to the expected upper limit. The data are shown by the points, while the size of the statistical uncertainty is shown by the error bars. The last bin includes the overflow. The blue arrows represent the data points outside of the frame. The hatched band shows the total systematic uncertainty of the post-fit yield.
J H E P 0 7 ( 2 0 1 9 ) 1 1 7
high-pT e x tra p o la tio n u n certain ty corresponding to th e decrease in th e m uon recon struc
tio n and selection efficiency w ith increasing p t which is predicted by th e MC sim ulation.
T he d eg rad atio n of th e m uon reconstruction efficiency was found to be ap proxim ately 3%
p er TeV as a function of m uon p t . U ncertain ties in th e isolation and trigger efficiencies of m uons [62], along w ith th e u n certain ty in th e ir energy scale and resolution, are estim ated from Z ^ p p d a ta tak en at a/s = 13 TeV. These are found to have only a small im pact (they account for < 0.4% of th e to ta l u n certain ty on th e fitted value of th e signal cross-sections).
O th e r sources of experim ental un certainties are th e residual differences in th e m odelling of th e flavour-tagging algorithm , th e je t energy scale and th e je t energy resolution after th e sim u latio n -to -d ata correction factors are applied. F lavour-tagging sim u latio n-to -data efficiency correction factors are derived [68] separately for b-jets, c-jets, and light-flavour jets. All th re e correction factors depend on je t p T (or p T and |n|) and are affected by uncer
tain tie s from m ultiple sources. These are decom posed into u n correlated com ponents which are th e n tre a te d independently, resulting in th re e uncertain ties for b-jets and for c-jets, and five for light-flavour jets. T he ap pro xim ate size of th e u n certain ty in th e tagging efficiency is 2% for b-jets, 10% for c-jets and 30% for light-flavour jets. A dditional uncertainties are considered in th e e x tra p o la tio n of th e b-jet efficiency calibration above p t = 300 GeV and in th e m isidentification of hadronically decaying T-leptons as b-jets. T he un certainties in th e je t energy scale and resolution are based on th e ir respective m easurem ents in d a ta [66].
T he m any sources of u n certain ty in th e je t energy scale correction are decom posed into 2 1 unco rrelated com ponents which are tre a te d as being independent of one anoth er. An ad ditional u n certain ty th a t specifically affects th e energy calibration of b- and c-jets is considered.
T he un certain ties in th e energy scale and resolution of th e je ts and leptons are prop agated to th e calculation of E™ ss, which also has ad ditio nal un certainties from th e scale, resolution, and efficiency of th e track s used to define th e soft term , along w ith th e m odelling of th e underlying event.
T he pile-up m odelling un certain ty is assessed by varying th e num ber of pile-up in terac
tions in sim ulated events. T he v ariations are designed to cover th e u n certain ty in th e ratio of th e predicted and m easured cross-section of non-diffractive inelastic events producing a hadronic system of m ass m X > 13 GeV [76].
T he uncertain ty in th e com bined 2015+2016 integ rated lum inosity is 2.1%. It is de
rived, following a m ethodology sim ilar to th a t detailed in ref. [77], and using th e LUCID-2 d e te c to r for th e baseline lum inosity m easurem ents [78], from calib ratio n of th e lum inosity scale using x -y beam -sep aratio n scans.
7 .2 T h e o r e t ic a l u n c e r ta in tie s
B a c k g r o u n d p r o c e s s e s . As discussed earlier, th e rates of m ajo r backgrounds are m ea
sured using d a ta control regions, th u s th eoretical uncertain ties in th e predicted cross-section for Z / y * + je ts and t t processes are not considered. Instead , th e effects of th eo retical uncer
tain tie s in th e m odelling of th e d istrib u tio n and in th e ratio of th e event yields in signal regions to those in th e control regions are evaluated. T he d o m in ant theo retical uncertainties are th e shape u n certain ty in th e dim uon m ass sp e ctra of th e ttt and Z + H F contributions.
J H E P 0 7 ( 2 0 1 9 ) 1 1 7
For b o th th e Z + L F and Z + H F processes, th e following sources of th eoretical and m odelling uncertain ties are considered: P D F uncertainties (estim ated via eigenvector vari
ations and by com paring different P D F sets), lim ited accuracy of th e fixed-order calculation (estim ated by QCD scale variations), variations in th e choice of strong coupling co n stan t value ( a S(M Z)), E W corrections, and photon-induced corrections. These variations are tre a te d as fully co rrelated betw een Z + L F and Z + H F processes.
T he P D F variatio n u n certain ty is obtained using th e 90% confidence level (CL) CT14N N LO P D F erro r set and by following th e procedure described in refs. [79, 80].
R a th e r th a n a single nuisance p a ra m ete r to describe th e 28 eigenvectors of this P D F error set, which could lead to an u n d erestim ation of its effect, a re-diagonalized set of 7 P D F eigenvectors was used [34]. T his represents th e m inim al set of P D F eigenvectors th a t m ain
tain s th e necessary correlations, and th e sum in q u a d ra tu re of these eigenvectors m atches th e original CT14N N LO error envelope well. T hey are tre a te d as sep arate nuisance pa
ram eters. T he uncertain ties due to th e variation of P D F scales and a S are derived using VRAP. T he form er is o b tained by varying th e renorm alization and factorization scales of th e nom inal CT14NNLO P D F up and down sim ultaneously by a factor of two. T he value of a S used (0.118) is varied by ±0.002. T he E W correction un certain ty was assessed by com paring th e nom inal additive (1 + £EW + £ q c d ) tre a tm e n t w ith th e m ultiplicative ap proxim ation ((1 + £EW)(1 + £qCD)) tre a tm e n t of th e E W correction in th e com bination of th e higher-order E W and QCD effects. T he u n certain ty in th e photon-induced correction is calculated from th e un certain ties in th e q u ark m asses and th e ph oton P D F . Following th e recom m endations of th e PD F 4L H C forum [80], an additio n al u n certain ty due to th e choice of nom inal P D F set is derived by com paring th e central values of CT14NNLO w ith those from o th er P D F sets, nam ely M M HT14 [81] and N N PD F3.0 [82]. T he m axim um w id th of th e envelope of these com parisons is used as th e P D F choice uncertainty, b u t only if it is larger th a n th e w id th of th e CT14NNLO P D F eigenvector variation envelope.
An add ition al m odelling u n certain ty is considered for th e Z + H F process. T he sp ectrum sim ulated by P o w h e g was com pared w ith those sim ulated w ith S h e r p a 2.2.1 [46]
and w ith M a d G ra p h 5 _ a M C @ N L O interfaced w ith P y tH iA 8.186. A functional form was chosen to describe th e envelope of th e differences in th e d istrib u tio n shape betw een events w ith a t least one b-quark sim ulated by S h e r p a 2.2.1 and M a d - G ra p h 5 _ a M C @ N L O v2.
These system atic un certainties not only im ply uncertainties in th e shape of th e d istrib u tio n in th e signal region, b u t th ey also affect th e ratio of th e expected num ber of events in th e signal region to th e expected num ber in th e control region. T he effect on th e Z + L F norm alization in th e bVeto signal region is 2%, while th e size of th e u n certain ty for Z + H F in th e bTag signal region is 7%.
Moreover, th e ratio of th e expected num ber of Z + L F events in th e bVeto control region to th e events in bTag control and signal regions was estim ated w ith th e nom inal P o w H E G + P y tH iA Z + je t sam ple, and w ith th e a ltern ativ e Ma dGr a p h5_aM C @ N L O v2 sam ple. To cover th e observed difference betw een th e two, an addition al u n certain ty of 27% in th e norm alization of th e Z + L F process in th e bTag signal and control region was applied.
J H E P 0 7 ( 2 0 1 9 ) 1 1 7
For th e t t process, th eo retical uncertainties in th e m odelling of th e sp ectru m and in th e e x tra p o la tio n from control region to signal region are also considered. These are esti
m ated by com paring th e nom inal prediction w ith altern ativ e ones. To e stim ate th e im pact of initial and final s ta te rad iatio n m odelling, two a ltern ativ e P o w h e g + P y t h i a samples were gen erated w ith th e following param eters. In th e first one, th e renorm alization ( p R) and factorizatio n (p F) scale were varied by a factor of 0.5, th e value of h damp was doubled (2m t) and th e corresponding P eru g ia 2012 rad iatio n tu n e variation was used. In th e second sam ple, th e renorm alization and factorization scales were varied by a factor of 2, while th e h damp p a ra m ete r was not changed. T he associated v ariation from th e P eru g ia 2012 tu n e was used. These choices of p aram eters have been shown to encom pass th e cases w here p R and p F are varied independently, and covered th e m easured uncertainties of th e d a ta for u n
folded t t d istrib u tio n s [83, 84]. Differences in p a rto n shower and h ad ron izatio n m odels were investigated using a sam ple w here P o w h e g - B o x was interfaced w ith H e r w i g + + 2.7.1 [85]
w ith th e U E -EE -5 tu n e [38] and th e corresponding CTEQ 6L1 P D F s. T he nom inal sam ple was also com pared w ith a sam ple generated w ith M a d G ra p h 5 _ a M C @ N L O 2.2.1 [31]
interfaced w ith H e r w i g + + . A NLO m atrix elem ent and CT10 P D F were used for th e t t
h ard -sc atte rin g process. T he p a rto n shower, had ro nization and th e underlying events were m odelled using th e H e rw ig + —+ 2.7.1 generator. T he U E -EE-5 tu n e and th e corresponding CTEQ 6L1 P D F were used. A functional form was chosen to encom pass th e differences in th e d istrib u tio n shape betw een th e nom inal sam ple and all these a ltern ativ e sam ples.
T hese sam ples were also used to estim ate th e 3.5% e x tra p o la tio n u n certain ty from C R ttb a r to th e SRbTag.
T heoretical un certain ties th a t arise from higher-order co n trib utio ns to th e cross
sections and P D F s and affect th e values of th e predicted cross-sections for th e diboson and single-top backgrounds are considered.
S ig n a l p r o c e s s e s . U ncertainties related to signal m odelling include th e uncertainties associated w ith th e initial- and final-state radiatio n, th e m odelling of underlying events, th e choice of th e renorm alization and factorizatio n scales, and th e p a rto n d istrib u tio n functions. None of th em has a sizeable effect on th e shape of th e spectra, b u t some of th em do affect th e acceptance in th e signal regions. U ncertain ties for th e different mass hypotheses were evaluated, b u t for simplicity, only th e largest of th e values is used. In th e calculation of th e u n certainties, a p p ro p riate requirem ents on th e m uon and jets kinem atics are applied a t had ro n level for th e SR bTag and SRbVeto regions.
T he factorization and renorm alization scales were varied by a factor of two up and down, including correlated and anti-co rrelated variations, b o th in P o w h e g - B o x and in M G 5 _ aM C @ N L O . For th e b b $ process, th e largest deviation from th e value of th e nom inal acceptance is considered as th e final scale u n certain ty (2% in SRbTag, and 1% in SRbV eto). A 25% u n certain ty for th e acceptance of ggF events in th e SR bTag is consid
ered, as well as its anti-correlated effect in th e SRbVeto region, following th e procedure a d o pted in ref. [86].
T he P D F un certain ties are estim ated by tak in g th e envelope of th e changes in th e acceptance associated w ith th e PDF4LHC15_nlo_100 (PDF4LC15_nlo_nf4_30) [80] error
J H E P 0 7 ( 2 0 1 9 ) 1 1 7
set for th e ggF (b b 4 ) signal process. T hey correspond to changes in acceptances not larger th a n 1%.
System atic variations of th e p aram eters of th e A14 (for b b 4 ) and AZNLO (for ggF) tu n es are used to account for th e uncertainties associated w ith th e initial and final sta te rad iatio n and th e m odelling of underlying events. For b b 4 , these uncertain ties correspond to changes of 3.8% and 3.2% of th e acceptance in th e SR bTag and SRbVeto regions. They are associated w ith a m igration of events from one signal region to th e oth er, hence th ey are tre a te d as anti-correlated betw een th e two signal regions. For ggF, th e u n certain ty in th e SRbVeto is negligible (< 0.5%), while it is 3.8% in th e SRbTag.
As discussed in section 3 , th e signal sam ples were sim ulated w ith th e fast sim ula
tio n fram ew ork of ATLAS, which replaces th e full sim ulation of th e electrom agnetic and hadronic calorim eters by a param eterized model. No significant differences in acceptance and dim uon invariant m ass were observed betw een a lim ited num ber of fast sim ulation sig
nal sam ples and sam ples g en erated w ith full G eant4-based sim ulation, hence no system atic u n certain ty is considered for th e use of fast sim ulation.
T he cu rren t result is d o m inated by th e sta tistic a l u n certain ty of th e d a ta (which ac
counts for 66% of th e to ta l u n certain ty on th e fitted value of th e signal cross-section), and th e system atic u n certain ty due to th e finite size of th e sim ulated background sam ples (which accounts for 25% of th e to ta l u ncertain ty ). A m ongst th e rem aining system atic u n c e rtain ties, th e m odelling of th e shape of th e d istrib u tio n for th e Z + je ts and to p -a n tito p backgrounds dom inates (3% of th e to ta l u n certainty) followed by th e m uon identification efficiency (1.5%). All o th er considered sources of experim ental and theo retical u n c e rtain ties (which individually have an im pact < 0.4%) have a com bined co n trib u tio n of less th a n 5% to th e to ta l u n certain ty on th e u p p e r lim it.
8 R e s u l t s
T he observed p-values as a function of m $ , o b tain ed applying th e sta tistic a l analysis de
scribed in section 6 , are shown in figure 3(a) for th e bb4-only fit and in figure 3(b) for th e ggF-only fit. T he lines in each figure correspond to sep arate fits. T he d o tte d line represents th e p-value for a fit including only SR bTag and all control regions (CRs), th e dashed line represents th e p-value for a fit including only S R bV eto+ C R s, while th e solid line corresponds to th e com bined S R bT ag + S R b V eto + C R s fit. T he d o tte d lines in th e two figures show sim ilar behaviour and so do th e dashed lines, while th e com bined p-values are calculated for sep arate signal production m odes im plying very different co ntributions from th e SRbVeto and SR bTag regions, which lead to su b stan tially different lim its. T he largest excess of events above th e expected background is observed for th e b-quark associ
a te d p ro d uctio n at ab o u t = 480 GeV and am ounts to a local significance of 2.3^, which becomes 0.6ct after considering th e look-elsewhere effect over th e m ass range 0.2-1.0 TeV.
T he look-elsewhere effect is estim ated using th e m etho d described in ref. [87].
Since th e d a ta are in agreem ent w ith th e predicted backgrounds th e results are given in term s of exclusion lim its. T hese are set using th e m odified frequentist CLs m eth o d [88].
U pp er lim its on th e cross section tim es branching ratio for a m assive scalar particle are set
J H E P 0 7 ( 2 0 1 9 ) 1 1 7
Figure 3 . Observed p-values as a function of т Ф for (a) a ЬЬФ-only fit and (b) a ggF-only fit. The dotted line corresponds to the data in the SRbTag only, the dashed line to the data in SRbVeto only, and the solid curve to the combination of the two data categories. All three fits include data from all control regions.
a t th e 95% confidence level (CL) as a function of th e particle m ass. T he u p p er lim its at 95%
CL on Стф x В(Ф ^ (where а Ф is th e cross section and B is th e branching ratio) assum e th e n a tu ra l w id th of th e resonance to be negligible com pared to th e experim ental resolution, and th ey cover th e m ass range 0.2-1.0 TeV. In figure 4(a) and 4(b) th e 95% CL up p er lim its are shown for Ь-q u ark associated production and gluon-gluon fusion, respectively. T he expected lim its are in th e ranges 1.3-25 fb and 1.8-25 fb, respectively. T he observed lim its are in th e ranges 1.9-41 fb and 1.6-44 fb, respectively. B o th th e expected and observed lim its are calculated in th e asy m p to tic approxim ation [75], which was verified w ith MC pseudo-experim ents for th e т Ф = 1000 GeV hypothesis. T he up p er lim it on th e ggF p ro d u ction m ode is d o m in ated by th e SRbVeto, while for th e ЬЬФ p ro d u ctio n m ode b o th th e SR bT ag and SR bV eto regions c o n trib u te to th e result because of th e relative acceptance of th e ЬЬФ pro d uctio n m ode in th e two regions. L im its shown in figure 4 are obtained in sim ultaneous fits of th e SRbVeto and SR bTag d a ta regions and correspond to th e different signal pro duction m odes. Usage of th e sam e d a ta events in b o th th e ЬЬФ-only and th e ggF-only fits explains correlations in th e behaviour of th e observed lim its.
Figures 5(a) and 5(b) show th e observed and expected 95% CL u p p er lim its on th e p ro d u ction cross section tim es branching ratio for Ф ^ ц,ц, as a function of th e fractional c o n trib u tio n from Ь-qu ark associated p ro d uctio n (т ь ь ф/ ^ ььф + ^ ggF]) and th e scalar reso
nance m ass. These fractions are derived assum ing th a t o th er pro d uctio n m echanism s do not affect th e result.
A com plete set of tables and figures are available a t th e D u rh am H ep D ata reposi
to ry [89].
J H E P 0 7 ( 2 0 1 9 ) 1 1 7
F ig u re 4. The observed and expected 95% CL upper limits on the production cross section times branching ratio for a massive scalar resonance produced via (a) b-quark associated production and (b) gluon-gluon fusion.
F ig u re 5. The (a) observed and (b) expected 95% CL upper limit on the production cross section times branching ratio for $ ^ 7 7 as a function of the fractional contribution from b-quark associated production and the scalar boson mass.
9 C o n c l u s i o n
T he ATLAS d e te c to r a t th e LHC has been used to search for a m assive scalar resonance decaying into two opposite-sign m uons, produced via b-quark associated p ro d u ctio n or via gluon-gluon fusion, assum ing th a t th e n a tu ra l w idth of th e resonance is negligible com pared to th e experim ental resolution. T he search is conducted w ith 36.1 fb- 1 of pp collision d a ta a t a/s = 13 TeV, recorded durin g 2015 and 2016. T he observed dim uon invariant m ass sp ectru m is consistent w ith th e S tan d ard M odel prediction w ithin uncertainties for events b o th w ith and w ith ou t a b-tagged je t over th e 0.2-1.0 TeV range. T he observed u p p er lim its a t 95% confidence level on th e cross-section tim es branching ratio for b-quark associated p ro d u ctio n and gluon-gluon fusion are betw een 1.9 and 41 fb and 1.6 and 44 fb respectively, which is consistent w ith expectations.
J H E P 0 7 ( 2 0 1 9 ) 1 1 7
A c k n o w l e d g m e n t s
We th a n k C E R N for th e very successful op eratio n of th e LHC, as well as th e su p p o rt staff from our in stitu tio n s w ith o u t whom ATLAS could not be o p erated efficiently.
We acknowledge th e su p p o rt of A N P C yT , A rgentina; Y erPhI, A rm enia; ARC, A us
tralia; B M W F W and F W F , A ustria; ANAS, A zerbaijan; SSTC, Belarus; C N P q and FA PESP, Brazil; NSERC , NRC and C FI, C anada; CERN; C O N IC Y T , Chile; CAS, M O ST and NSFC, C hina; C O LC IEN C IA S, Colombia; M SM T CR, M PO C R and VSC CR, Czech R epublic; D N R F and DN SRC, D enm ark; IN 2P3-C N R S, C E A -D R F /IR F U , France;
SRNSFG, Georgia; B M B F, H G F, and M PG , G erm any; GSRT, Greece; R G C , H ong K ong SAR, China; ISF and Benoziyo C enter, Israel; IN FN , Italy; M E X T and JS P S , Jap an;
C N R ST , Morocco; N W O , N etherlands; RCN, Norway; M NiSW and NCN, Poland; F C T , P ortu gal; M N E /IFA , R om ania; MES of R ussia and NRC KI, R ussian Federation; JIN R ; M ESTD , Serbia; MSSR, Slovakia; A RRS and MIZS, Slovenia; D S T /N R F , South Africa;
M IN ECO , Spain; SRC and W allenberg F oundation, Sweden; SERI, SNSF and C antons of B ern and Geneva, Sw itzerland; M O ST, Taiwan; TA EK , Turkey; STFC , U nited K ingdom ; D O E and N SF, U nited S tates of A m erica. In addition, individual groups and m em bers have received su p p o rt from B C K D F, C A N A R IE, CRC and C om pute C anada, C anada;
CO ST, ER C , E R D F , Horizon 2020, and M arie Sklodowska-Curie A ctions, E u ro p ean Union;
Investissem ents d ’ Avenir L abex and Idex, ANR, France; D FG and AvH F oundation, G er
m any; H erakleitos, T hales and A risteia program m es co-financed by E U -E S F and th e Greek N SR F, Greece; B SF-N SF and G IF, Israel; C E R C A P rog ram m e G eneralitat de C atalunya, Spain; T he Royal Society and Leverhulm e T rust, U nited K ingdom .
T he crucial com puting su p p o rt from all W LC G p a rtn e rs is acknowledged gratefully, in p a rticu la r from CERN , th e ATLAS Tier-1 facilities at T R IU M F (C anad a), N D G F (D enm ark, Norway, Sweden), CC -IN 2P3 (France), K IT /G rid K A (G erm any), IN FN -C N A F (Italy), N L-T1 (N etherlands), P IC (Spain), ASGC (Taiw an), RAL (U.K.) and BNL (U.S.A .), th e Tier-2 facilities worldwide and large non-W L C G resource providers. M a
jo r con trib u to rs of com puting resources are listed in ref. [90].
O p e n A c c e s s . This article is d istrib u ted under th e term s of th e C reative Com m ons A ttrib u tio n License (CC -B Y 4.0) , which perm its any use, d istrib u tio n and reprodu ction in any m edium , provided th e original au th o r(s) and source are credited.
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