Pu b l i s h e d f o r SISSA b y —1 Sp r i n g e r Re c e i v e d: D ecem ber 10, 2018
Re v i s e d: M arch 3, 2019
Ac c e p t e d: M arch 20, 2019
Pu b l i s h e d: A p r il 15, 2019
Study of the rare decays of B0 and B 0 mesons into muon pairs using data collected during 2015 and 2016 with the ATLAS detector
T h e A T L A S collaboration
E - m a i l : a t l a s .p u b l i c a t i o n s @ c e r n .c h
A b s t r a c t : A stu d y of th e decays B°s → ß + ß ~ and ß ° → ß + ß ~ has been perform ed using 26.3 fb-1 of 13TeV LHC p ro to n -p ro to n collision d a ta collected w ith th e ATLAS d etecto r in 2015 and 2016. Since th e d e te c to r resolution in ß + ß ~ invariant m ass is com parable to th e B 0-B 0 m ass difference, a single fit determ ines th e signal yields for b o th decay modes.
T his results in a m easurem ent of th e branching fraction B (B ° → ß + ß - ) = (3.2— q) x 10-9 and an u p p er lim it B ( B 0 → ß + ß - ) < 4.3 x 10-10 a t 95% confidence level. T he result is com bined w ith th e R u n 1 ATLAS result, yielding B (B ° → B + B - ) = (2. 8— ) x 10-9 and
B ( B 0 → ß + ß - ) < 2.1 x 10-10 a t 95% confidence level. T h e com bined result is consistent w ith th e S ta n d ard M odel prediction w ithin 2.4 sta n d a rd deviations in th e B ( B 0 → ^ + ^ - )- B (B ° → B + B - ) plane.
Ke y w o r d s: H adron-H adron scatterin g (experim ents)
ArXiy ePr in t: 1812.03017
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C on ten 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 , d a ta a n d s im u la tio n s a m p le s 3
3 D a t a s e le c tio n 5
4 B a c k g r o u n d c o m p o s it io n 6
5 H a d r o n m is id e n tific a tio n 8
6 C o n tin u u m b a c k g r o u n d r e d u c tio n 9
7 D a t a - s im u la t io n c o m p a r is o n s 11
8 B + ^ J / ÿ K + y ie ld e x t r a c t io n 13
9 E v a lu a tio n o f t h e B + ^ J / ÿ K + t o ^ M+M- e ffic ie n c y r a tio 15
10 E x t r a c tio n o f t h e sig n a l y ie ld 17
10.1 Signal and background m odel 17
10.2 R elative signal efficiency betw een B D T bins 19
10.3 System atic un certainties in th e fit 19
10.4 R esults of th e signal yield e x tractio n 22
11 B r a n c h in g fr a c tio n e x t r a c t io n 22
12 C o m b in a tio n w it h t h e r u n 1 r e su lt 24
13 C o n c lu s io n s 26
T h e A T L A S c o lla b o r a tio n 30
1 Introd u ction
Flavour-changing n eu tral-cu rren t processes are highly suppressed in th e S ta n d ard M odel (SM). T he branching fractions of th e decays B 0s) ^ ß + ß - are, in addition, helicity sup
pressed in th e SM, and are predicted to be B (B 0 ^ ß + ß - ) = (3.65 ± 0.23) x 10-9 and
8 ( B ° ^ ß + ß - ) = (1.06 ± 0.09) x 10-10 [1]. T he sm allness and precision of these pre
dicted branching fractions provide a favourable environm ent for observing contributions from new physics: significant deviations from SM predictions could arise in m odels in
volving non-SM heavy particles, such as those predicted in th e M inim al S upersym m etric
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S ta n d ard M odel [2- 6] and in extensions such as M inim al F lavour V iolation [7, 8], Two- H iggs-D oublet M odels [6], and oth ers [9 , 10]. T he CMS and LH C b collaborations rep orted th e observation of B ° ^ ß + ß - [11, 12] and evidence of B0 ^ ß + ß - w ith com bined values B ( B 0 ^ ß + ß - ) = (2.8-0:7) x 10-9 and B ( B 0 ^ ß + ß - ) = (3.9+1.4) x 10-10 [13]. T he LH C b C o llaboration u p d a te d its R u n 1 result w ith p a rt of th e d a ta collected in R u n 2, m easuring B (B ° ^ ß + ß - ) = (3.0 ± 0 .6 + °-) x 10-9 (where th e first u n certain ty is sta tistic a l and th e second system atic) and determ ining B (B0 ^ ß + ß - ) < 3.4 x 10-10 a t 95% confidence level (CL) [14]. ATLAS has m easured, w ith th e R un 1 d a ta se t [15], B (B0 ^ ß + ß - ) = (0.9-0.1) x 10- 9 , while settin g an u p p er lim it on B0 ^ ß + ß - of 4.2 x 10-10 a t 95% CL.
T his p ap er rep o rts th e result of a search for B0 ^ ß + ß - and B0 ^ ß + ß - decays perform ed using pp collision d a ta corresponding to an effective integ rated lum inosity of 26.3 fb- 1 , collected at 13TeV centre-of-m ass energy during th e first two years of th e LHC R u n 2 d a ta -ta k in g period using th e ATLAS detecto r. T he analysis stra te g y follows th e approach employed in th e previous ATLAS m easurem ent [15], b u t uses d a ta collected w ith one ra th e r th a n th re e sep arate sets of trigger thresholds, applies sta n d a rd ATLAS muon selection c riteria (section 3) ra th e r th a n a d edicated m uon m u ltiv ariate discrim inant, and em ploys an im proved sta tistic a l tre a tm e n t of th e result (section 10) .
T he n o tatio n used th ro u g h o u t th e p a p e r refers to th e com bination of processes and th e ir charge-conjugates, unless otherw ise specified. T he B0 ^ ß + ß - and B0 ^ ß + ß - branching fractions are m easured relative to th e reference decay m ode B + ^ J / —( ^ ß + ß - ) K + which is a b u n d a n t and has a well-m easured branching fraction B (B + ^ J / —K +) x B ( J / — ^ ß + ß - ). T he B0 ^ ß + ß - (B0 ^ ß + ß - ) branching fraction can be ex tra cte d as:
B ( B ° s) ^ ß + ß - ) = - ¾ x [ B ( B + ^ J / ÿ K +) x B ( J / ÿ ^ ß + ß - )] x f ^
£ ß + ß - N J /ß K + Jd(s)
N B (B + ^ J / ÿ K +) x B ( J / ^ ^ ß + ß - ) f ( 11)
= Nd(s)--- Dre,--- x f c , ■ (L1) w here N d ( N s ) is th e B 0 ^ ß+ß - (B ° ^ ß + ß - ) signal yield, N J / ^ K + is th e B + ^ J / ÿ K + reference channel yield, £ ß +ß - and e J / ß K + are th e corresponding values of acceptance tim es efficiency (m easured in fiducial regions defined in section 9) , and f u / f d ( f u / f s ) is th e ratio of th e h adro nisatio n probabilities of a b-quark into B + and B 0 (B °) . In th e q u a n tity D ref = N j / ^ k + x ( e ß +ß - / e J /p K+ ), th e - ratio takes into account relative differences in efficiencies, in teg rated lum inosities and th e trigger selections used for th e signal and th e reference m odes Signal and reference channel events are selected w ith sim ilar dim uon triggers O ne half of th e reference channel sam ple is used to determ in e th e norm alisation and th e o th er half is used to tu n e th e kinem atic distrib u tio n s of sim ulated events
T h e event selection uses variables related to th e B c an d id ate decay tim e, th us in tro d u c
ing a dependence of th e efficiency on th e signal lifetime T h e relation betw een th e m easured branching fraction and th e corresponding value a t p ro d uction is established assum ing th e decay tim e d istrib u tio n predicted in th e SM, w here th e decay occurs m ainly th ro u g h th e heavy eigen state B°s, H of th e B°s)-B°s) system . Some m odels of new physics [16, 17] pre
dict m odifications to th e decay tim e d istrib u tio n of B ° ^ ß + ß - and a com parison w ith
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th e experim ental result requires a correction to th e ratio of th e tim e-in teg rated efficiencies en tering D ref.
T he ATLAS inner tracking system , m uon sp ectro m eter and, for efficient identification of muons, also th e calorim eters, are used to reconstruct and select th e event candidates.
D etails of th e detecto r, trigger, d a ta sets, and prelim inary selection c riteria are discussed in sections 2 and 3. A blind analysis was perform ed in which d a ta in th e dim uon invariant mass range from 5166 to 5526 MeV were removed until th e procedures for event selection and the d etails of signal yield e x tra ctio n were com pletely defined. Section 4 introduces th e three m ain categories of background. Section 5 describes th e stra te g y used to reduce th e probabil
ity of h ad ro n m isidentification. T he final sam ple of cand idates is selected using a m ultivari
a te classifier, designed to enhance th e signal relative to th e d om inant dim uon background com ponent, as discussed in section 6. Checks on the distributions of th e variables used in th e m u ltivariate classifier are sum m arised in section 7. T hey are based on th e com parison of d a ta and sim ulation for dim uon events, for B + ^ J / ÿ K + can did ates and for events selected as B ° ^ J / ÿ ÿ ^ ß + ß - K + K - , which provide an ad d ition al validation of th e pro
cedures used in th e analysis. Section 8 details the fit procedure used to ex tract th e yield of B + ^ J / ÿ K + events. T he d eterm in atio n of th e ratio of efficiencies in th e signal and th e reference channels is presented in section 9 . Section 10 describes th e e x tractio n of th e signal yield, obtain ed w ith an unbinned m axim um -likelihood fit perform ed on th e dim uon invari
an t m ass distrib u tio n . In th is fit, events are separated into classifier intervals to m axim ise th e fit sensitivity. T he results for th e branching fractions B (B ° ^ ß + ß - ) and B (B0 ^
ß + ß - ) are repo rted in section 11 and com bined w ith th e full R u n 1 results in section 12.
2 A TLA S d etecto r, d ata and sim ulation sam ples
T he ATLAS d ete c to r1 consists of th ree m ain com ponents: an inner detector (ID) track ing system im m ersed in a 2 T axial m agnetic field, surrounded by electrom agnetic and hadronic calorim eters and by th e m uon sp ectrom eter (MS). A full description can be found in ref. [18], com plem ented by ref. [19] for details ab o u t th e new innerm ost silicon pixel layer th a t was installed for R u n 2.
T his analysis is based on th e R u n 2 d a ta recorded in 2015 and 2016 from p p collisions a t th e LHC at y f s = 13 TeV. D a ta used in th e analysis were recorded durin g stable LHC beam periods. D a ta q u ality requirem ents were im posed, n o tab ly on th e perform ance of th e MS, ID and calorim eter system s. T he to ta l integ rated lum inosity collected by ATLAS in th is period is 36.2 fb -1 w ith an uncertainty of 2.1%. These values are determ ined using a m ethodology sim ilar to th a t detailed in ref. [20], based on calibration of th e lum inosity scale using x - y beam -sep aration scans, and use th e LUCID-2 d etecto r [21] for th e baseline lum inosity m easurem ent. T he to ta l effective integ rated lum inosity used in th is analysis —
"ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point. The z-axis is along the beam pipe, the x-axis points to the centre of the LHC ring and the y-axis points upward.
Cylindrical coordinates (r, 0) are used in the transverse plane, r being the distance from the origin and 0 being the azimuthal angle around the beam pipe. The pseudorapidity n is defined as n = — ln[tan(6/2)]
where 6 is the polar angle.
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accounting for trigg er prescales — am ounts to 26.3 fb-1 for th e signal and 15.1 fb-1 for the reference channel.
Sam ples of sim ulated M onte C arlo (MC) events are used for train in g and validation of th e m u ltiv ariate analyses, for th e d eterm in atio n of th e efficiency ratios, and for developing th e procedure used to determ in e th e signal. Exclusive MC sam ples were produced for th e signal channels B0 ^ ß + ß - and B 0 ^ ß + ß - , th e reference channel B + ^ J / ÿ K + ( J / ÿ ^ ß + ß - ), and th e control channel B0 ^ J / ÿ ÿ ( J / ÿ ^ ß + ß - , ÿ ^ K + K - ). In addition, background studies em ploy MC sam ples of inclusive bb ^ ß + ß - X decays, exclusive sam ples of B0 ^ K - ß + v , B 0 ^ n - ß + v , Ab ^ p ß - v, B 0s) ^ h h ' decays w ith h (/) being a charged pion or kaon, and inclusive decays B ^ J / ÿ X as well as th e exclusive B + ^ J / ÿ n + decay.
M ost of th e dim uon can d idates in th e d a ta sam ple originate from th e decays of hadrons produced in th e h adro nisatio n of bb pairs. T he inclusive bb ^ ß + ß - X MC sam ple used to describe this background requires th e presence of two m uons in th e final sta te , w ith b o th m uons originating from th e bb decay chain. T he size of th is sam ple is equivalent to roughly th re e tim es th e in teg rated lum inosity of th e d a ta .
T he MC sam ples were g en erated w ith P y t h i a 8 [22]. T he ATLAS detector and its response were sim ulated using G e a n t 4 [23, 24]. A dditional pp interactions in th e same and nearby bunch crossings (pile-up) are included in th e sim ulation. M uon reconstruction and triggering efficiencies are corrected in th e sim ulated sam ples using d ata-d riv en scale factors. T he scale factors for th e trig ger efficiencies are obtained by com paring d a ta and sim ulation efficiencies d eterm ined w ith a tag -an d -p ro b e m ethod on inclusive pro m pt and non-prom pt J / ÿ candid ates. T his procedure yields scale factors as a function of th e muon transverse m om entum and pseudorapidity, which are applied th ro u g h o u t th e analysis [25].
R eco n struction and selection efficiencies are obtain ed from sim ulation and sim ilarly cor
rected according to data-d riv en com parisons. In ad d itio n to these efficiency corrections, sim ulated events are rew eighted to reproduce th e pile-up m ultiplicity observed in d a ta , and according to th e equivalent in teg rated lum inosity associated w ith each trig ger selection.
Using th e iterativ e rew eighting m ethod described in ref. [26], th e sim ulated sam ples of th e exclusive decays considered are ad ju sted w ith tw o-dim ensional d ata-d riv en weights (DDW ) to correct for th e differences betw een sim ulation and d a ta observed in th e B m e
son transverse m om entum and p seudorapidity d istrib utio ns. D D W ob tained from B + ^ J / ÿ K + decays are used to correct th e sim ulation sam ples in th e signal and reference chan
nels. D D W obtain ed from th e B0 ^ J / ÿ ÿ control channel are found to agree w ith those from B + ^ J / ÿ K +, showing th a t th e sam e corrections are applicable to B0 and B 0 decays.
R esidual differences betw een d a ta and sim ulation studied in th e B + ^ J / ÿ K + and B0 ^ J / ÿ ÿ signals are tre a te d as sources of system atic uncertainty in th e evaluation of th e signal efficiency, as discussed in section 9 . T he only exception to th is tre a tm e n t is th e B m eson isolation ( / 0.7 in section 6 and table 1) , where residual differences are used to reweight th e signal MC events and th e corresponding uncertain ties are p ro p ag ated to account for residual sy stem atic u n certain ty effects.
Sim ilarly to th e exclusive decays, th e kinem atic d istrib u tio n s of th e inclusive bb ^ ß + ß - X MC sam ple are rew eighted w ith corrections obtain ed from th e dim uon invariant m ass sidebands in d a ta .
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3 D a ta selection
For d a ta collected durin g th e LHC R un 2, th e ATLAS d etecto r uses a two-level trigger system , consisting of a hardw are-based first-level trigg er and a softw are-based high-level trigger. A first-level dim uon trigger [27] selects events requiring th a t one m uon has p T >
4 GeV and th e o th er has p T > 6 GeV. A full track reconstruction of th e m uon candidates is perform ed by th e high-level trigger, w here an additio nal loose selection is im posed on th e dim uon invariant m ass m w , accepting can did ates in th e range 4 GeV to 8.5 GeV. Due to th e increased pile-up in 2016 d a ta , an ad d ition al selection was added a t this trigger stage, requiring th e vector from th e p rim ary vertex to th e dim uon vertex to have a positive com ponent (L xy) along th e dim u o n ’s transv erse m om entum direction. T he effect of this selection is accounted for in th e analysis b u t has no consequence since stricte r requirem ents are applied in th e full event selection (see section 6) .
T he signal channel, th e reference channel B + ^ J / —K + and th e control channel B0 ^ J / —'' were selected w ith trigger prescale factors th a t vary during th e data-tak in g period. In th e 36.2 fb-1 of d a ta analysed, th e prescaling of th e trigger approxim ately averages to a reduction by a factor 1.4, giving an effective in tegrated lum inosity for th e signal sam ple of 26.3 fb- 1 , while for th e reference and control channels 15.1 fb-1 were collected due to an effective prescale of 2.4. These effects are tak en into account in th e e x tra ctio n of th e signal branching fraction, th ro u g h th e e factors in eq. (1 .1) .
Using inform ation from th e full offline reconstruction, a prelim inary selection is p er
form ed on can didates for B 0s) ^ ß + ß - , B + ^ J / —K + ^ ß + ß - K + and B0 ^ J / —' ^ ß + ß - K + K - decays. In th e ID system , m uon candidates are required to have a t least one m easured hit in th e pixel d e te c to r and two m easured h its in th e sem iconductor tracker.
T hey are also required to be reco n structed in th e MS, and to have |n| < 2.5. T he offline m uon p air m ust pass th e p T > 4 GeV and p T > 6 GeV requirem ents im posed by th e trigger.
Furtherm ore, th e m uon cand id ates are required to fulfil t i g h t m uon quality c riteria [28]; this requirem ent is relaxed to lo o s e for th e h ad ro n m isidentification studies in section 5. K aon can did ates m ust satisfy sim ilar requirem ents in th e ID, except for a looser requirem ent of p T > 1 GeV.
T he com puted B m eson prop erties are based on a decay vertex fitted to two, th ree or four tracks, depending on th e decay process to be reconstructed. T he B candid ates are required to have a x2 per degree of freedom below 6 for th e fit to th e B vertex, and below 10 for th e fit to th e J / — ^ ß + ß - vertex. T he selections 2915 < m (ß + ß - ) < 3275 MeV and 1005 < m ( K + K - ) < 1035 MeV are applied to th e J / — ^ ß + ß - and th e ' ^ K + K - vertices, respectively. In th e fits to th e B + ^ J / —K + and B0 ^ J / — ' channels, the reco n structed dim uon m ass is con strained to th e world average J / — m ass [29].
R econ structed B can d id ates are retain ed if th e y satisfy pB > 8.0 GeV and |nB | < 2.5.
T he invariant m ass of each B can d id a te is calculated using m uon tra jec to rie s m easured by com bining th e inform ation from th e ID and MS to im prove upon th e m ass resolution o b tained from ID inform ation only [30].
T he invariant m ass range considered for th e B0s) ^ ß + ß - decay s ta rts at 4766 MeV and is 1200 MeV wide. W ith in th is range a 360-MeV-wide signal region is defined, sta rtin g
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a t 5166 MeV. T he rem ainder of th e range defines th e u p p er and lower m ass sidebands of th e analysis.
For th e reference and control channels, th e m ass range considered is 4930-5630 (5050
5650) MeV for B + ^ J / ÿ K + (B0 ^ J / ÿ ÿ ) , where 5180-5380 (5297-5437) MeV is the peak region and higher and lower m ass ranges com prise th e m ass sidebands used for back
ground su b tractio n .
T he co ordinates of p rim ary vertices (PV ) are obtain ed from charged-particle tracks not used in th e decay vertices, and th a t are constrained to th e lum inous region of th e colliding beam s in th e transverse plane. T he m atching of a B can d id a te to a P V is m ade by e x tra p o la tin g th e c an d id ate tra je c to ry to th e point of closest approach to th e beam axis, and choosing th e P V w ith th e sm allest distance along z. Sim ulation shows th a t th is m ethod m atches th e correct vertex w ith a probability above 99% for all relevant pile-up conditions.
To reduce th e large background in th e B 0^ ^ ß + ß - channel before applying th e final selection based on m u ltiv ariate classifiers, a loose collinearity requirem ent is applied betw een th e m om entum of th e B can d id a te (~pB) and th e vector from th e P V to th e decay v ertex (A x ). T he absolute value of th e azim uthal angle a 2D betw een these two vectors is required to be sm aller th a n 1.0 radians. T he com bination A R flight = \ /a2D2 + (A n )2, w here A n is th e difference in pseudorapidity, is required to satisfy A R flight < 1.5.
A fter th e p relim inary selection, approxim ately 3.5 x 106 candidates are found in the B0s) ^ ß + ß - fit region, w ith ab o u t 1.0 x 106 falling in th e blinded range [5166, 5526] MeV.
4 B ackground com p osition
T he background to th e B 0^ ^ ß + ß - signal originates from th re e m ain sources:
C o n t i n u u m background, th e d om inant com binatorial com ponent, which consists of m uons originating from u ncorrelated h adron decays and is characterised by a weak depen dence on th e dim uon invariant mass;
P a r t i a l l y r e c o n s t r u c t e d decays, w here one or m ore of th e final-state particles ( X ) in a b- h ad ro n decay is not reconstructed, causing these candid ates to accum ulate in th e low dim uon invariant m ass sideband (this background includes a significant co n trib utio n from sem ileptonic decays w here one of th e m uons is a m isidentified hadron, discussed below);
P e a k i n g background, due to B0s) ^ h h ' decays, w ith b o th hadrons m isidentified as muons.
T he continuum background consists m ainly of m uons produced ind ependently in th e frag m en tatio n and decay chains of a b-quark and a b-quark. It is studied in th e signal mass sidebands, and it is found to be well described by th e inclusive bb ^ ß + ß - X MC sample.
T he p a rtially recon stru cted decays consist of several topologies: (a) s a m e - s i d e com b in atorial background from decay cascades (b ^ c ß - v ^ s (d ) ß + ß - vv); (b) s a m e - v e r t e x background from B decays containing a m uon p air (e.g. B0 ^ K *°ß + ß - or B ^ J / 0 ß + X ^ ß + ß - ß + X ); (c) B + decays (e.g. B + ^ J / 0 ß + v ^ ß + ß - ß + v ); (d) sem ileptonic b-hadron decays w here a final-state h adro n is m isidentified as a muon. T he
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Dimuon invariant mass [MeV] Mass of two misidentified muons [MeV]
(a) (b)
F ig u re 1. (a) Dimuon invariant mass distribution for the partially reconstructed background (as categorised in section 4), from simulation, before the final selection against continuum is applied but after all other requirements. The different components are shown as stacked histograms, normalised according to world-averaged measured branching fractions. The SM expectations for the B0.) ^ ß + ß - signals are also shown for comparison. Continuum background is not included here. (b) Invariant mass distribution of the B 0 s) ^ hh' peaking background components after the complete signal selection is applied. The B 0 ^ n + n - and B 0 ^ K + K - contributions are negligible on this scale. In both plots the vertical dashed lines indicate the blinded analysis region. Distributions are normalised to the expected yield for the integrated luminosity of 26.3 fb- 1 .
rem ainder of this p ap er im plicitly excludes categories (c) and (d) w hen referring to partially reco nstructed or b ^ ß + ß - X decays, since these categories are tre a te d separately.
T he bb ^ ß + ß - X MC sam ple is used to investigate th e background com position after th e analysis selection. All backgrounds in this sam ple have a dim uon invariant mass d istrib u tio n m ainly below th e m ass range considered in th is analysis, w ith a high-m ass tail extending th ro u g h th e signal region. T he sim ulation does not con tem plate sources o th er th a n m uons from bb decays: cc and pro m p t contributio n s are not included 2. All possible origins of two m uons in th e bb decay tre e are, however, analysed, after classification into th e m utu ally exclusive continuum and p a rtially reconstructed categories described above. This sam ple is used only to identify suitable functional m odels for th e corresponding background com ponents, and as a b enchm ark for these models. No shape or norm alisation co n strain ts are derived from th is sim ulation. T his makes th e analysis largely insensitive to m ism atches betw een background sim ulation and d a ta .
T he sem ileptonic decays w ith final-state hadrons m isidentified as m uons consist m ainly of th ree-b o d y charm less decays B0 ^ n - ß + v, B 0 ^ K - ß + v and Ab ^ p ß - v in which th e tail of th e invariant m ass d istrib u tio n extends into th e signal region. D ue to branching fractions of th e order of 10- 6 , this background is not large, and is furth er reduced by
2These sources are suppressed by the final analysis selections introduced in section 6. Potential residual contributions are found to be consistent with the continuum background models used in the final fit (sec
tion 10.1), where systematic uncertainties for background model inconsistencies between data and MC are taken into account (section 10.3).
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th e m uon identification requirem ents, discussed in section 5. T he MC invariant m ass d istrib u tio n s of these p artially reconstru cted decay topologies are shown to g eth e r w ith th e SM signal predictions in figure 1(a) after applying th e prelim inary selection c riteria described in section 3 .
Finally, th e peaking background is due to B0s) ^ h h ' decays containing two hadrons m isidentified as m uons. T he d istrib u tio n s in figure 1(b), obtain ed from sim ulation, show th a t these decays p o p u late th e signal region. T his com ponent is fu rth e r discussed in sec
tio n 5.
5 H adron m isidentification
In th e prelim inary selection, m uon candidates are form ed from th e com bination of tracks recon stru cted independently in th e ID and MS. T he perform ance of th e m uon recon stru c
tio n in ATLAS is presented in ref. [28]. A dditional studies were perform ed to evaluate th e am oun t of background related to hadrons erroneously identified as muons.
D etailed sim ulation studies were perform ed for th e B0s) ^ h h ' channel w ith a full
G E A N T 4-based sim ulation [23] of all system s of th e ATLAS detecto r. T he vast m ajo rity of background events from particle m isidentification are due to decays in flight of kaons and pions, in which th e m uon receives m ost of th e energy of th e p aren t meson. Hence th is background is generally related to tru e m uons m easured in th e MS, b u t not produced pro m p tly in th e decay of a B meson.
T he m uon c an d id ate is required to pass t i g h t m uon requirem ents in th e prelim inary selection, which are based on th e profile of energy deposits in th e calorim eters as well as on tig h ter ID-M S m atching c riteria th a n those used for th e lo o s e requirem ents. Two- bo dy B decays in control regions show th a t t i g h t selections have, relative to th e lo o s e
c o u n te rp art, an average had ron m isidentification probability reduced by a factor 0.39 w ith a m uon reconstruction efficiency of 90%. T he resulting final value of th e m isidentification probab ility is 0.08% for kaons and 0.1% for pions. Efficiencies and fake rates are relative to th e analysis preselections, including tracking b u t excluding any m uon requirem ent.
T he background due to B 0s) ^ h h ', w ith double m isidentification of h h ' as ß + ß - , has a reco nstru cted invariant m ass d istrib u tio n th a t peaks a t 5240 MeV, close to th e B0 mass, and is effectively indistinguishable from th e B 0 signal (see figure 1(b)). The expected num ber of peaking-background events can be estim ated in a way analogous to th a t for th e signal, from th e num ber of observed B + ^ J / ÿ K + events using eq. ( 1.1) , after tak in g into account th e expected differences from m uon identification variables and trigger selections. W orld average [29] values for th e branching fractions of B0 and B 0 into K n , K K and n n are used, to g eth e r w ith th e had ro n m isidentification probabilities obtained from sim ulation. This results in 2.7 ± 1.3 to ta l expected peaking-background events, after th e reference m u ltivariate selection.3
3This selection, corresponding to 54% signal efficiency, was also applied to derive all other quantities quoted in this section and includes a selection against the ß + ß - continuum background based on the BDT discussed in section 6.
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W hen selecting lo o s e m uons and inverting th e ad d ition al requirem ents im posed in th e
t i g h t m uon selection, th e num ber of events containing real m uons is su b stan tially reduced, while th e num ber of peaking-background events is approxim ately two tim es larger th a n in th e sam ple obtained w ith th e nom inal selection. A fit to d a ta for th is background-enhanced sam ple retu rn s 6.8 ± 3.7 events, which tra n sla tes into a peaking-background yield in th e signal region of 2.9 ± 2.0 events w hen tak in g into account th e relative rejection of th e m uon q u ality selections. T he predicted yield is in good agreem ent w ith th e sim ulation.
Besides th e peaking background, th e t i g h t m uon selection also reduces th e sem ileptonic co n tributions w ith a single m isidentified hadron. Sim ulation yields 30 ± 3 events expected from B 0 ^ n - ß + v and B 0 ^ K - ß + v in th e final sam ple, w ith a d istrib u tio n kinem atically co nstrained to be m ostly below th e signal region. T he Ab ^ p ß - v con trib u tio n is negligible due to th e sm aller p ro d uction cross section and th e low ra te a t which protons fake muons.
6 C ontinuum background reduction
A m ultivariate analysis, im plem ented as a boosted decision tree (B D T ), is employed to enhance th e signal relative to th e continuum background. T his B D T is based on th e 15 variables described in ta b le 1. T he d iscrim inating variables can be classified into th ree groups: (a) B m eson variables, related to th e reconstructio n of th e decay v ertex and to th e collinearity betw een B and th e flight vector betw een th e produ ctio n and decay vertices A x; (b) variables describing th e m uons th a t form th e B m eson candidate; and (c) variables related to th e rest of th e event. T he selection of th e variables aim s to m axim ise th e d iscrim ination power of th e classifier w ithout introducing significant dependence on th e invariant m ass of th e m uon pair.
T he sam e discrim inatin g variables were used in th e previous analysis based on th e full R u n 1 d a ta s e t [15]. T he rem oval of individual variables was explored to sim plify th e B D T in p u t, however, th is results inevitably in a significant redu ction of th e B D T separation power. To m inim ise th e dependence of th e classifier on th e effects of pile-up, th e addition al track s considered to com pute th e variables / 0.7, D O C A xtrk and are required to be com patible w ith th e p rim ary v ertex m atched to th e dim uon candid ate.
T he correlations am ong th e d iscrim inating variables were studied in th e MC sam ples for signal and continuum background discussed in section 2 , and in d a ta from th e sidebands of th e ß + ß - invariant m ass distrib u tio n . T here are significant linear correlations am ong th e variables x P V,DVxy, Lxy, |d0|max-sig., |d>|min-sig. and xjj,xPV. T he variables IPBD, D O C A ^ and / 0.7 have negligible correlation w ith any of th e others used in th e classifier.
T he sim ulated signal sam ple and th e d a ta from th e dim uon invariant m ass sideband regions are used for tra in in g and testin g th e classifier. As discussed in section 2, sim ulated signal sam ples are corrected for m uon reconstructio n efficiency differencies betw een sim u
latio n and d a ta , and rew eighted according to th e distrib u tio n s of p T and |n| of th e dim uon and of th e pile-up observed in d a ta . T he B D T train in g is done using th e TM VA toolkit [31].
Sideband d a ta are used for th e B D T tra in in g and optim isation. T he sam ple is sub
divided into th re e random ly selected sep arate and equally p o p u lated subsam ples used in tu rn to tra in and validate th e selection efficiency of th re e in dependent B D T s. T he resulting
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Variable Description
p B Magnitude of the B candidate transverse momentum p TB.
XPV,DV xy Compatibility of the separation Ax between production (i.e. associated PV) and decay (DV) vertices in the transverse projection: A xT-S- —1 • A x t , where S- y is
A x t AxT
the covariance matrix.
A R flight Three-dimensional angular distance between " B and Ax: y/a 2D2 + (An)2
|« 2d| Absolute value of the angle in the transverse plane between p T B and A xT.
Lxy Projection of A xT along the direction of " B : (AxT •—TB) / | - t B |.
Tp3DB Three-dimensional impact parameter of the B candidate to the associated PV.
D O C A ^ Distance of closest approach (DOCA) of the two tracks forming the B candidate (three-dimensional).
A PW Azimuthal angle between the momenta of the two tracks forming the B candidate.
|d0|max_sig. Significance of the larger absolute value of the impact parameters to the PV of the tracks forming the B candidate, in the transverse plane.
|do|min-sig. Significance of the smaller absolute value of the impact parameters to the PV of the tracks forming the B candidate, in the transverse plane.
P Lpmin The smaller of the projected values of the muon momenta along p T B.
Io.7 Isolation variable defined as ratio of | - t B | to the sum of | - t B | and the trans
verse momenta of all additional tracks contained within a cone of size A R =
\ J(A ^)2 + (An)2 = 0.7 around the B direction. Only tracks matched to the same PV as the B candidate are included in the sum.
DOCAxtrk DOCA of the closest additional track to the decay vertex of the B candidate. Only tracks matched to the same PV as the B candidate are considered.
NClor Number of additional tracks compatible with the decay vertex (DV) of the B candidate with ln(xXtrk DV) < 1. Only tracks matched to the same PV as the B candidate are considered.
Ag,xPVX2 Minimum x2 for the compatibility of a muon in the B candidate with any PV reconstructed in the event.
T ab le 1. Description of the 15 input variables used in a BDT classifier to discriminate between signal and continuum background. When the BDT classifier is applied to B+ " J/-0 K + and Bj? " J / P P candidates, the variables related to the decay products of the B mesons refer only to the muons from the decay of the J / p . Horizontal lines separate the classifications into groups (a), (b) and (c) respectively, as described in the text. For category (c), additional tracks are required to have p T > 500 MeV.
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Figure 2. BDT output distribution for the signal and background events after the preliminary se
lection and before applying any reweighting to the BDT input variables: (a) simulation distributions for B 0 ^ g + g - signal, continuum, partially reconstructed b ^ g + g - X events and B c decays; (b) dimuon sideband candidates (which also include prompt contributions, mainly at lower BDT values and not simulated in the continuum MC sample), compared with the continuum MC sample and the simulated signal. All distributions are normalised to unity in (a) and to data sidebands in (b).
B D T s are found to produce results th a t are statistically com patible, and are com bined in one single classifier in such a way th a t each B D T is applied only to th e p a rt of th e d a ta sam ple not involved in th e B D T tra in in g .
F igure 2 shows th e d istrib u tio n of th e B D T o u tp u t variable for sim ulated signal and backgrounds, separately for continuum background and p artially recon stru cted events.
Also shown is th e B D T d istrib u tio n for dim uon can d id ates from th e sidebands of th e invariant m ass d istrib u tio n in d a ta . T he B D T o u tp u t was found to not have any sig
nificant correlation w ith th e dim uon invariant m ass. T he final selection requires a B D T o u tp u t value larger th a n 0.1439, corresponding to signal and continuum background effi
ciencies of 72% and 0.3% respectively. T he analysis uses all can d idates after th is selection;
however, accepted events w ith B D T values close to th e selection threshold are effectively only constraining th e background m odels.4 For this reason, signal and reference channel yields and efficiencies are m easured relative to th e signal reference selection discussed in section 9 , while th e events in th e final selection w ith lower B D T values are used to improve th e background m odelling.
7 D a t a - s i m u l a t i o n c o m p a r i s o n s
D espite th e lack of correlation betw een th e B D T variable and th e can didates invariant m ass, th e change in relative co n trib u tio n of different background com ponents as a function
4T he ^ g + g - signal fit was found to be insensitive to th e signal for candidates w ith B D T o u t
p u t value sm aller th a n 0.2455 (corresponding to 54% and 0.03% efficiencies for signal and background respectively).
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Figure 3. Data and continuum MC distributions of the (a) |a 2D| and (b) ln (x%,xPv) variables (defined in table 1). The points correspond to the sideband data, while the continuous-line his
togram corresponds to the continuum MC distribution, normalised to the number of data events.
The filled-area histogram shows the signal MC distribution for comparison. The bottom insets report the data/M C ratio, zoomed-in in order to highlight discrepancies in the region th at is most relevant for the analysis.
of th e B D T o u tp u t can produce a variation of th e background shape in sep arate B D T bins.
T he shape p aram eters and norm alisations of th e backgrounds are for this reason d e te r
m ined purely from d ata: th e bb ^ ß + ß - X MC sim ulation is not used for B D T trainin g, co m p u tatio n of efficiencies or n orm alisation purposes. T he only role of th e bb ^ ß + ß - X M C is th e validation of th e functional forms em ployed to param eterise th e backgrounds on d a ta , as discussed in section 10.1. T he dependence of th e background param eterisatio n on th e B D T o u tp u t variable was investigated in d a ta and shown to be consistent w ith sim ula
tion, even for lower B D T values w here pro m p t backgrounds c o n trib u te significantly. This observation is su p p o rted by th e fair agreem ent of th e B D T in p u t variables d istrib u tio n betw een th e sim ulated bb ^ ß + ß - X background and w h at observed on d a ta sidebands.
F igure 3 com pares th e d istrib u tio n s of two of th e m ost discrim inating variables in th e con
tin u u m background MC sam ple w ith d a ta in th e dim uon m ass sidebands. A greem ent w ith th e sideband d a ta is fair.
T he d istrib u tio n s of th e d iscrim inating variables are also used to com pare sim ulation and d a ta in th e B + ^ J / ÿ K + and B°s ^ J / ÿ ÿ sam ples. To perform these com parisons, for each variable th e co n trib u tio n of th e background is su b tra c te d from th e B + ^ J / ÿ K + (B0 ^ J / ÿ ÿ ) signal. For th is purpose, a m axim um -likelihood fit is perform ed to th e invariant m ass d istrib u tio n , sep arately in bins of rap id ity and transv erse m om entum . T he fit m odel used is sim pler th a n th e one employed for th e e x tra ctio n of th e B + signal for n orm alisation as described in section 8, b u t is sufficient for th e purpose discussed here.
F igure 4 shows exam ples of th e d istrib u tio n s of th e discrim inating variables obtained from d a ta and sim ulation for th e reference sam ples. Observed differences are used to e stim ate sy stem atic un certainties on th e efficiency ratio R £ = e (B + ^ J / ÿ K + )/e (B ° s) ^ ß + ß - ) w ith th e procedure described in section 9 . T he discrepancy visible for th e isolation
J H E P 0 4 ( 2 0 1 9 ) 0 9 8
Figure 4. Data and MC distributions in B+ ^ J / ÿ K + events for the discriminating variables:
(a) |a2 D|, (b) ln (xP v d v x y ) and (c) I 0 7. The variable I 0.7 is also shown in (d) for B° ^ J / ÿ ^ events. The points correspond to the sideband-subtracted data, while the line corresponds to the MC distribution, normalised to the number of data events. The highest bin in (c) and (d) accounts for the events with I0.7 = 1. The bottom insets report the data/M C ratio, zoomed-in in order to highlight discrepancies in the region that is most relevant for the analysis.
variable I0.7 in th e B + ^ J / ÿ K + channel is th e m ost significant am ong all variables and b o th reference channels.
8 B + ^ J / ÿ K + y i e l d e x t r a c t i o n
T h e reference channel yield is ex tra cte d w ith an unbinned extended m axim um -likelihood fit to th e J / ÿ K + invariant m ass d istrib u tio n . T he functional forms used to m odel bo th th e signal and th e backgrounds are obtained from studies of M C sam ples. All th e yields are e x tra cte d from th e fit to d a ta , while th e shape p a ra m ete rs are determ ined from a sim ultaneous fit to d a ta and MC sam ples. Free p aram eters are introduced for th e m ass scale and m ass resolution to accom m odate d ata-M C differences. T he best-fit values indicate a negligibly poorer resolution and a m ass shift at th e level of 2 MeV.
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F ig u re 5. Result of the fit to the J/-0 K + invariant mass distribution for all B+ candidates in half of the data events. The various components of the spectrum are described in the text. The inset at the bottom of the plot shows the bin-by-bin pulls for the fit, where the pull is defined as the difference between the data point and the value obtained from the fit function, divided by the error from the fit.
T he fit includes four com ponents: B + ^ J / 0 K + decays, C abibbo-suppressed B + ^ J /- 0 n + decays in th e right tail of th e m ain peak, p a rtially recon structed B decays (P R D ) w here one or m ore of th e final-state particles are missing, and th e non-resonant background com posed m ostly of bb ^ J / 0 X decays. All com ponents o th er th a n th e last one have shapes constrain ed by MC sim ulation as described below, w ith th e d a ta fit in
cluding an ad d ition al G aussian convolution to account for possible d ata-M C discrepancies in m ass scale and resolution. T he shape of th e B + ^ J / 0 K + m ass d istrib u tio n is pa- ram eterised using a Johnson S u function [32, 33]. T he final B + ^ J / 0 K + yield includes th e co n trib u tio n from rad iativ e effects (i.e. w here photons are em itted from th e B decay p ro d u cts). T he B + ^ J / ^ n + decays are m odelled by th e sum of a Johnson S u function and a G aussian function, w here all p aram eters except th e n orm alisation are determ ined from th e sim ulation. T he decay m odes c o n trib u tin g to th e P R D are classified in sim ulation on th e basis of th eir m ass dependence. Each of th e th re e resulting categories co n tribu tes to th e overall P R D shape w ith com binations of Ferm i-D irac and exponential functions, con
trib u tin g differently in th e low-mass region. T h eir shape p aram eters are determ ined from sim ulation. Finally, th e non-resonant background is m odelled w ith an exponential function w ith th e shape p a ra m ete r ex tra cte d from th e fit. T he n orm alisation of each com ponent is uncon strain ed in th e fit, which is therefore m ostly independent of ex tern al in p u ts for th e branching fractions. T he residual dependence of th e P R D m odel shapes on th e relative branching fractions of th e c o n trib u tin g decays is considered as a source of sy stem atic un
certainty. T he resulting fit, shown in figure 5, yields 334 351 B + ^ J / 0 K + decays w ith a sta tistic a l u n certain ty of 0.3%. T he ratio of yields of B + ^ J / ^ n + and B + ^ J / 0 K + is (3.71 ± 0.09)% (where th e u n certain ty rep o rted is sta tistic a l only), in agreem ent w ith th e e x p ectatio n from th e world average [29] of (3.84 ± 0.16)%.
J H E P 0 4 ( 2 0 1 9 ) 0 9 8
Some system atic uncertain ties are included by design in th e fit. For exam ple, th e effect of th e lim ited MC sam ple size is included by perform ing a sim ultaneous fit to d a ta and MC sam ples. Scaling factors determ ined in th e fit to d a ta account for th e differences in m ass scale and resolution betw een d a ta and sim ulation. A dditional system atic uncertain ties are evaluated by varying th e default fit m odel described above. T hey tak e into account th e kinem atic differences betw een d a ta and th e MC sam ples used in th e fit, differences in effi
ciency betw een B + and B - decays and uncertain ties in th e relative fractions and shapes of P R D and in th e shape of th e various fit com ponents. T he stab ility of this large sam ple fit is verified by rep eatin g th e fit w ith different initial p a ra m ete r values. In each case, th e change relative to th e default fit is recorded, sym m etrised and used as an e stim ate of th e system atic uncertainty. T he m ain con trib ution s to th e system atic u n certain ty come from th e func
tio nal m odels of th e background com ponents, th e com position of th e P R D and th e signal charge asym m etry. T he to ta l sy stem atic u n certain ty in th e B + yield am ounts to 4.8%.
9 E valuation o f th e B+ ^ J / ÿ K + to ^ ß+ß- efficiency ratio T he ratio of efficiencies R e = e (B + ^ J / 0 K + )/£ (B 0 s) ^ ß + ß - ) enters th e D ref term defined in section 1: D ref = N j / ^ k + / R e. B o th channels are m easured in th e fiducial ac
ceptance for th e B meson, defined as p B > 8.0 GeV and |nB | < 2.5. Correspondingly, e (B + ^ J / 0 K +) and ^ (B 0s) ^ ß + ß - ) are m easured w ithin th e B m eson fiducial accep
tan ce and include ad d itio nal final s ta te particles acceptance as well as trigger, recon struc
tio n and selection efficiencies. T he final s ta te particles acceptance is defined by th e selection placed on th e particles in th e final state: |n^| < 2.5 and pT > 6.0 (4.0) GeV for th e leading (trailing) m uon p T , pK > 1.0 GeV and |nK | < 2.5 for kaons. T he s i g n a l r e f e r e n c e B D T selection, defined as B D T > 0.2455, has an efficiency of ab o u t 54% (51%) in th e signal (ref
erence) channel. T he overall efficiency ratio R e is 0.1176 ± 0.0009 (sta t.) ± 0.0047 (syst.), w ith uncertain ties d eterm ined as described below.
T he ratio R e is com puted using th e m ean lifetime of B0 [29, 34] in th e MC generator.
T he sam e efficiency ratios apply to th e B 0 ^ ß + ß - and B 0 ^ ß + ß - decays, w ithin th e M C sta tistic a l u n certain ty of 0.8%. T h e sta tistic a l uncertain ties in th e efficiency ratios come from th e finite num ber of events available for th e sim ulated sam ples. T he system atic u n certain ty affecting R e comes from five sources.
T he first co n trib u tio n is due to th e uncertainties in th e data-d riv en weights introduced in section 2 , and am ounts to 0.8%. T his term is assessed by creating a ltern ativ e d a ta se ts using correction factors th a t are random ly sam pled in accord w ith th eir nom inal values and uncertainties. T he RM S value of th e d istrib u tio n of R e obtained from these d a ta se ts is tak en as th e sy stem atic uncertainty.
A second co n trib u tio n of 1.0% is related to th e m uon trigger and reconstruction effi
ciencies. T he effect of th e uncertainties in th e d ata-d riv en efficiencies is evaluated using random sam pling, as above.
A 3.2% system atic u n certain ty co n trib u tio n arises from th e differences betw een d a ta and sim ulation observed in th e m odelling of th e discrim in atin g variables used in th e B D T classifier (tab le 1) . For each of th e 15 variables, th e MC sam ples for B0s) ^ ß + ß - and
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Source C on trib u tio n [%]
S tatistical 0.8
K inem atic rew eighting (DDW ) 0.8 M uon trigger and reconstruction 1.0
B D T in p u t variables 3.2
K aon track in g efficiency 1.5
P ile-up rew eighting 0.6
T ab le 2. Summary of the uncertainties in R£.
B + ^ J / 0 K + are rew eighted w ith th e ratio of th e B + ^ J / 0 K + event d istrib u tio n s in sideb an d -su b tracted d a ta and th e MC sim ulation. T he isolation variable / 0.7 is com puted using charged-particle tracks only, and differences betw een B + and B0 are expected and were observed in previous studies [26]. Hence for this variable th e rew eighting procedure for th e B0 ^ ß + ß - MC sam ple is based on B 0 ^ J / ^ ^ d ata. For all discrim inating variables except / 0.7, th e value of th e efficiency ratio is modified by less th a n 2% by th e reweighting procedure and each variation is tak en as an independent con trib u tio n to th e system atic u n certain ty in th e efficiency ratio. For / 0.7 th e rew eighting procedure changes th e efficiency ratio by ab o u t 6%. Because of th e significant m is-modelling, th e MC samples obtained after rew eighting on th e d istrib u tio n of / 0.7 are taken as a reference, thus correcting th e central value of th e efficiency ratio . T he 1% u n certain ty in th e / 0.7 correction is added to th e sum in q u a d ra tu re of th e uncertain ties assigned to th e o th er d iscrim inating variables. T he to ta l u n certain ty in th e m odelling of th e d iscrim inating variables is th e dom inant co n tribution to th e sy stem atic u n certain ty in R e.
A fo u rth source of system atic u n certain ty arises from differences betw een th e B0 ^ ß + ß - and th e B + ^ J / 0 K + channel related to th e reco nstructio n efficiency of th e kaon tra c k and of th e B + decay vertex. These un certainties are m ainly due to inaccuracy in th e m odelling of passive m aterial in th e ID. T h e corresponding system atic u n certain ty is estim ated by varying th e d e te c to r m odel in sim ulations, which results in changes betw een 0.4% and 1.5% depending on th e n range considered. T he largest value is used in th e full e ta range.
Finally, th e un certain ty associated w ith rew eighting th e sim ulated events as a function of th e pile-up m ultiplicity d istrib u tio n co ntribu tes 0.6%.
Table 2 sum m arises these system atic uncertainties.
T he efficiency ratio enters in eq. ( 1.1) w ith th e D ref term defined in section 1, m ultiplied by th e num ber of observed B ± candidates. T he to ta l u n certain ty in D ref is ±6.3% .
A correction to th e efficiency ratio for B0 ^ ß + ß - is needed because of th e w idth difference A r s betw een th e B0 eigenstates. According to th e SM, th e decay B 0 ^ ß + ß - proceeds m ainly th ro u g h th e heavy s ta te B s,H [1, 16], which has w id th r s,H = r s — A r s/2 , which is 6.6% sm aller th a n th e average r s [29]. T he variation in th e value of the B 0 ^ ß + ß - m ean lifetime was tested w ith sim ulation and found to change th e B0 efficiency, and
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consequently th e B 0 to B + efficiency ratio, by +3.3% . T his correction is applied to th e cen tral value of D ref used in section 11 for th e determ in atio n of B (B 0 ^ ^ + ^ - ) .5 D ue to th e sm all value of A r d, no correction needs to be applied to th e B 0 ^ ^ + + - decay.
10 E xtraction o f th e signal yield
D im uon candid ates passing th e prelim inary selection and th e selections against hadro n m isidentification and continuum background are classified according to four intervals (w ith boundaries a t 0.1439, 0.2455, 0.3312, 0.4163 and 1) in th e B D T o u tp u t. R ep eating th e R u n 1 analysis approach, each interval is chosen to give an equal efficiency of 18% for signal MC events, and th e y are ordered according to increasing signal-to-background ratio.
A n unbinned extended m axim um -likelihood fit is perform ed on th e dim uon invariant m ass d istrib u tio n sim ultaneously across th e four B D T intervals, each including m odels for th e respective signal and background contributions. T he first two bins (covering th e lowest B D T values considered) co n trib u te m ostly to background m odelling: it has been verified w ith MC pseudo-experim ents th a t th ey have negligible im pact on th e signal ex tractio n.
T he result of th e fit is param eterised w ith th e to ta l yield of B ° ^ ^ + + - and B 0 ^ B + + - events in th e th ree highest intervals of B D T o u tp u t. Section 10.1 describes th e signal and background fit models. T he p aram eters describing th e background are allowed to vary freely and are determ ined by th e fit. T he norm alisations of th e individual fit com ponents, including th e signals, are com pletely unconstrained and allowed to take negative values.
T he ratios of th e signal yields in different B D T bins are con strained to equal th e ratios of th e signal efficiencies in those sam e bins. T he system atic uncertain ties due to variations in th e relative signal and background efficiencies betw een B D T intervals, to th e signal p aram eterisatio n and to th e background m odel are discussed in sections 10.2 and 10.3.
E ach is m odelled in th e likelihood as a m ultiplicative G aussian d istrib u tio n whose w idth is equal to th e corresponding system atic uncertainty.
1 0.1 S ig n a l a n d b a c k g r o u n d m o d e l
T he signal and background m odels are derived from sim ulations and from d a ta collected in th e m ass sidebands of th e search region.
T he invariant m ass d istrib u tio n of th e B 0s) ^ ^ + + - signal is described w ith two double-G aussian distrib u tio n s, centred respectively a t th e B 0 or B°? mass. T he shape p aram eters are ex tra cte d from sim ulation, w here th ey are found to be uncorrelated w ith th e B D T o u tp u t. System atic uncertainties in th e m ass scale and resolutions are considered separately. F igure 6 shows th e invariant m ass distrib u tio n s for B 0 and B 0, obtain ed from M C events and norm alised to th e SM expectations.
5The decay time distribution of B0 ^ ß+ ß - is predicted to be different from the one of Bs,H in scenarios of new physics, with the effect related to the observable A [16, 17]. The maximum possible deviation from the SM prediction of A = +1 is for A = -1 , for which the decay time distribution of B0 ^ ß+ß- corresponds to the distribution of the Bs,L eigenstate. In the comparison with new-physics predictions, the value of B (B S ^ ß+ ß - ) obtained from this analysis should be corrected by +3.6% or +7.8% respectively for A = 0 and -1.
J H E P 0 4 ( 2 0 1 9 ) 0 9 8
D im uon in va rian t m ass [M eV]
F ig u re 6. Dimuon invariant mass distribution for the B 0 and B 0 signals from simulation. The results of the double-Gaussian fits are overlaid. The two distributions are normalised to the SM prediction for the expected yield with an integrated luminosity of 26.3 fb- 1 .
T he background in th e signal fit is com posed of th e types of events described in sec
tio n 4: ( a ) th e continuum background; ( b ) th e background from p a rtially reconstructed b ^ ß + ß ~ X events, which is present m ainly in th e low m ass sideband; (c) th e peaking background.
T he non-peaking co n trib u tio n s have a com m on m ass shape m odel, w ith p aram eters co nstrained across th e B D T bins in th e fit as described below, and independent yields across B D T bins and com ponents. S y stem atic uncertainties arising from m odel assum ptions will be discussed in section 10.3, including effects due to th e presence of B + ^ J / ^ ß + v and sem ileptonic B°s)/A0 ^ h ß v decays.
B o th in sim ulation and sideband d a ta , th e continuum background has a small linear dependence on th e dim uon invariant m ass. In th e sim ulation, th e slope p a ra m ete r has a roughly linear dependence versus B D T interval; th e m ass sidebands in d a ta confirm this tre n d , albeit w ith large sta tistic a l uncertainty. T his dependence is included in th e fit model.
T he small system atic uncertain ties due to deviations from th is assum ption are discussed below in section 10.3.
T he b ^ ß + ß ~ X background has a dim uon invariant m ass d istrib u tio n th a t falls m onotonically w ith increasing dim uon m ass. T he m ass dependence is derived from d a ta in th e low m ass sideband, and described w ith an exponential function w ith th e sam e shape in each B D T interval. T he value of th e shape p a ra m ete r is ex tra cte d from th e fit to d a ta .
T he invariant m ass d istrib u tio n of th e peaking background is very sim ilar to th e B0 signal, as shown in figure 1(b). T he description of th is com ponent is o b tained from MC sim ulation, which indicates th a t th e shape and norm alisation are th e sam e for all B D T bins.
In th e fit, th is co n trib u tio n is included w ith fixed m ass shape and w ith a n orm alisation of 2.9 ± 2.0 events, as discussed in section 5. T his co n trib u tio n is equally d istrib u ted am ong th e th re e highest intervals of th e B D T o u tp u t.
T he fittin g procedure is tested w ith MC pseudo-experim ents, as discussed in sec
tio n 10.3.
