P u b l i s h e d f o r S IS S A b y S p r i n g e r R e c e i v e d: January 14, 2016
R e v i s e d: July 8, 2016 A c c e p t e d: A u gu s t 20, 2016 P u b l i s h e d: A u gu s t 24, 2016
Measurement of the CP-violating phase ϕ s and the B s 0 meson decay width difference with B s 0 → J/ψϕ decays in ATLAS
T h e A T L A S collaboration
E - m a i l : atlas.publications@cern.ch
A b s t r a c t: A measurement o f the B 0 decay param eters in the B 0 ^ channel using an integrated lum inosity o f 14.3 fb -1 collected by the A T L A S detector from 8 T e V pp collisions at the L H C is presented. T h e measured param eters include the C P-violatin g phase 0 s, the decay w idth r s and the w idth difference between the mass eigenstates A r s.
T h e values measured for the physical param eters are statistically com bined w ith those from 4.9 fb -1 o f 7 T e V data, leading to the follow ing:
0 s = -0 .0 9 0 ± 0.078 (sta t.) ± 0.041 (syst.) rad A r s = 0.085 ± 0.011 (sta t.) ± 0.007 (syst.) ps-1
r s = 0.675 ± 0.003 (sta t.) ± 0.003 (syst.) ps- 1 .
In the analysis the param eter A r s is constrained to be positive. Results for <ps and A r s are also presented as 68% and 95% likelihood contours in the 0 s- A r s plane. A lso measured in this decay channel are the transversity am plitudes and corresponding strong phases. A ll measurements are in agreem ent w ith the Standard M o d el predictions.
K e y w o r d s: B physics, C P violation, F la vor physics, H adron-H adron scattering (ex p eri
m ents)
A rXi y ePr i n t: 1601.03297
O p e n A c c e s s , C o p y rig h t C E R N ,
for th e b en efit o f th e A T L A S C ollab oratio n . A r tic le funded b y S C O A P 3.
doi:10.1007/JHEP08(2016)147
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Contents
1 I n t r o d u c t io n 1
2 A T L A S d e t e c to r a n d M o n t e C a r lo s im u la tio n 2
3 R e c o n s tr u c t io n a n d c a n d id a te se lec tio n 3
4 F la v o u r t a g g in g 4
4.1 B± ^ J / 0 K ± event selection 5
4.2 F lavou r taggin g m ethods 5
4.3 U sing ta g inform ation in the B0 fit 8
5 M a x i m u m lik e lih o o d fit 11
5.1 Signal P D F 12
5.2 Background P D F 13
5.3 M uon trig g er proper tim e-dependent efficiency 16
6 R e s u lt s 16
7 S y s te m a tic u n c e rta in tie s 16
8 D is c u s s io n 21
9 C o m b in a t io n o f 7 T e V a n d 8 T e V re su lts 23
10 S u m m a r y 25
T h e A T L A S c o lla b o r a t io n 29
1 Introduction
N e w phenom ena beyond the predictions o f the Standard M o d el (S M ) m ay alter C P v i
olation in b-hadron decays. A channel that is expected to be sensitive to new physics contributions is the decay B 0 ^ J / 0 0 . C P vio lation in the B 0 ^ J / ^ decay occurs due to interference between direct decays and decays w ith B 0- B 0 m ixing. T h e oscillation fre
quency o f B 0 meson m ixing is characterized by the mass difference A m s o f the heavy (B h ) and light ( B L ) mass eigenstates. T h e C P vio la tin g phase <ps is defined as the weak phase difference between the B 0- B 0 m ixing am plitude and the b ^ c c s decay am plitude. In the absence o f C P violation, the B H state would correspond to the C P - o d d state and the B L to the C P -e v e n state. In the SM the phase 0 s is small and can be related to C abibbo- Kobayashi-M askaw a (C K M ) quark m ixing m atrix elements via the relation 0 s ~ — 2^s,
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w ith p s = a rg [—(VtsVtb)/(VCsVCb)]; assuming no physics beyond the SM contributions to B 0 m ixing and decays, a value o f —2^s = -0 .0 3 6 3 + 00010 rad can be predicted by com bining beauty and kaon physics observables [1] .
O ther physical quantities involved in B 0- B 0 m ixing are the decay w idth r s = ( r L + r H )/2 and the w idth difference A r s = r L — r H , where r L and r H are the decay w idths o f the different eigenstates. T h e w idth difference is predicted to be A r s = 0.087 ± 0.021 ps-1 [2] . Physics beyond the SM is not expected to affect A r s as significantly as <ps [3] . How ever, extra ctin g A r s from data is interesting as it allows theoretical predictions to be tested [3] . Previou s measurements o f these quantities have been reported by the D 0 , C D F , L H C b , A T L A S and C M S collaborations [4- 9] .
T h e decay o f the pseudoscalar B 0 to the vector-vector J + 0 (^ + ^ - ) 0 ( K + K - ) final state results in an adm ixture o f C P - o d d and C P -e v e n states, w ith orbital angular m om entum L = 0, 1 or 2. T h e final states w ith orbital angular m om entum L = 0 or 2 are C P -e v e n , w hile the state w ith L = 1 is C P -o d d . T h e same final state can also be produced w ith K + K - pairs in an S-w ave configuration [10] . Th is S-w ave final state is C P -o d d . T h e C P states are separated statistically using an angular analysis o f the final-state particles.
F lavou r taggin g is used to distinguish between the initial B 0 and B 0 states.
T h e analysis presented here provides a measurement o f the B 0 ^ J / + 0 decay pa
ram eters using 14.3 fb -1 o f L H C pp data collected by the A T L A S detector during 2012 at a centre-of-mass energy o f 8 TeV . Th is is an update o f the previous flavour-tagged tim e- dependent angular analysis o f B 0 ^ J / + ^ [8] that was perform ed using 4.9 fb -1 o f data collected at 7 TeV . Electrons are now included, in addition to final-state muons, for the flavour taggin g using leptons.
2 A T L A S detector and M onte C arlo simulation
T h e A T L A S detector [11] is a m ulti-purpose particle physics detector w ith a forw ard- backward sym m etric cylindrical geom etry and nearly 4n coverage in solid an gle.1 T h e inner tracking detector (I D ) consists o f a silicon pixel detector, a silicon m icrostrip detector and a transition radiation tracker. T h e ID is surrounded by a thin superconducting solenoid providing a 2 T axial m agnetic field, and by a high-granularity liquid-argon (L A r ) sam pling electrom agnetic calorim eter. A steel/scintillator tile calorim eter provides hadronic coverage in the central rap idity range. T h e end-cap and forw ard regions are instrumented w ith L A r calorim eters for electrom agnetic and hadronic measurements. T h e muon spectrom eter (M S ) surrounds the calorim eters and consists o f three large superconducting toroids w ith eight coils each, a system o f tracking chambers, and detectors for triggering.
T h e muon and tracking systems are o f particular im portance in the reconstruction o f B meson candidates. O n ly data collected when both these systems were operating
" A T L A S uses a righ t-han ded coo rd in a te system w ith its origin at th e n om in al in teractio n p oin t ( I P ) in th e centre o f th e d etecto r and th e z-axis along th e beam pipe. T h e x-axis poin ts fro m th e I P to th e centre o f th e L H C ring, and th e y-axis poin ts upward. C y lin d ric a l coordin ates (r, 0 ) are used in th e transverse plane, 0 b ein g th e azim u th al angle around th e beam pipe. T h e p seu dora pid ity is defined in term s o f the p o la r an gle 6 as n = — ln ta n (6 / 2 ).
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correctly and when the L H C beams were declared to be stable are used in the analysis.
T h e data were collected during a period o f rising instantaneous luminosity, and the trigger conditions varied over this tim e. T h e triggers used to select events for this analysis are based on identification o f a J / 0 ^ ^ + ^ - decay, w ith transverse m om entum (p T ) thresholds o f either 4 G eV or 6 G eV for the muons. T h e measurement uses 14.3 fb -1 o f pp collision data collected w ith the A T L A S detector at a centre-of-mass energy o f 8 TeV . D a ta collected at the beginning o f the 8 T eV data-taking period are not included in the analysis due to a problem w ith the trig g er tracking algorithm . T h e trigger was subsequently changed to use a different tracking algorithm that did not have this problem .
T o study the detector response, estim ate backgrounds and m odel system atic effects, 12 m illion M on te C arlo (M C ) sim ulated B 0 ^ J / ^ 0 events were generated using Py t h i a
8 [12, 13] tuned w ith A T L A S data [14] . N o pT cuts were applied at the generator level.
T h e detector response was sim ulated using the A T L A S sim ulation fram ew ork based on G E A N T 4 [15, 16] . In order to take into account the varying number o f proton-proton interactions per bunch crossing (pile-u p) and trigger configurations during data-taking, the M C events were w eighted to reproduce the same pile-up and trig g er conditions in data.
A d d itio n a l samples o f the background decay B0 ^ J / 0 K 0*, as w ell as the m ore general bb ^ J / 0 X and pp ^ J / 0 X backgrounds were also sim ulated using Py t h i a 8.
3 Reconstruction and candidate selection
Events must pass the trigger selections described in section 2. In addition, each event must contain at least one reconstructed prim ary vertex, form ed from at least four ID tracks, and at least one pair o f oppositely charged muon candidates that are reconstructed using inform ation from the M S and the ID [17] . A muon identified using a com bination o f M S and ID track param eters is referred to as a c o m b i n e d - m u o n . A muon form ed from a M S track segment that is not associated w ith a M S track but is m atched to an ID track extrapolated to the M S is referred to as a s e g m e n t - t a g g e d m u o n . T h e muon track param eters are determ ined from the ID measurement alone, since the precision o f the measured track param eters is dom inated by the ID track reconstruction in the p t range o f interest for this analysis. Pairs o f op positely charged muon tracks are refitted to a com m on vertex and the pair is accepted for further consideration if the quality o f the fit meets the requirem ent x 2/d.o.f. < 10. T h e invariant mass o f the muon pair is calculated from the refitted track param eters. In order to account for varyin g mass resolution in different parts o f the detector, the J / 0 candidates are divided into three subsets according to the pseudorapidity n o f the muons. A m axim um -likelihood fit is used to extract the J / 0 mass and the corresponding mass resolution for these three subsets. W h en both muons have |n| < 1.05, the dim uon invariant mass must fall in the range 2.959-3.229 G eV to be accepted as a J / 0 candidate. W h en one muon has 1.05 < |n| < 2.5 and the other muon
|n| < 1.05, the corresponding signal region is 2.913-3.273 GeV. For the third subset, where b oth muons have 1.05 < |n| < 2.5, the signal region is 2.852-3.332 G eV. In each case the signal region is defined so as to retain 99.8% o f the J / 0 candidates identified in the fits.
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T h e candidates for the decay $ ^ K + K - are reconstructed from all pairs o f op p o
sitely charged particles w ith pT > 1 G eV and |n| < 2.5 that are not identified as muons.
C andidate events for B ° ^ J / 0 (^ + ^ - ) $ ( K + K - ) decays are selected by fittin g the tracks for each com bination o f J / 0 ^ ^ + ^ - and $ ^ K + K - to a com m on vertex. Each o f the four tracks is required to have at least one hit in the pixel detector and at least four hits in the silicon m icrostrip detector. T h e fit is further constrained by fixing the invariant mass calculated from the tw o muon tracks to the J / 0 mass [18] . A quadruplet o f tracks is accepted for further analysis if the ve rte x fit has a x 2/d.o.f. < 3, the fitted pT o f each track from $ ^ K + K - is greater than 1 G e V and the invariant mass o f the track pairs (assum
ing that th ey are kaons) falls w ithin the interval 1.0085 G eV < m ( K + K - ) < 1.0305 GeV.
I f there is more than one accepted candidate in the event, the candidate w ith the lowest X 2/d.o.f. is selected. In total, 375,987 B ° candidates are collected w ithin a mass range o f 5.150-5.650 GeV.
For each B ° meson candidate the proper decay tim e t is estim ated using the expression:
t = Lx y mB
p t b ’
where pTB is the reconstructed transverse m om entum o f the B ° meson candidate and m B denotes the mass o f the B ° meson, taken from [18] . T h e transverse decay length, L xy, is the displacem ent in the transverse plane o f the B ° meson decay ve rte x w ith respect to the prim ary vertex, projected onto the direction o f the B ° transverse m om entum. T h e position o f the prim ary ve rte x used to calculate this quantity is determ ined from a refit follow ing the rem oval o f the tracks used to reconstruct the B ° meson candidate.
For the selected events the average number o f pile-up proton-proton interactions is 21, necessitating a choice o f the best candidate for the prim ary ve rte x at which the B ° meson is produced. T h e variable used is the three-dim ensional im pact param eter d0, which is calculated as the distance between the line extrapolated from the reconstructed B ° meson ve rte x in the direction o f the B 0 m om entum, and each prim ary vertex candidate. T h e chosen prim ary vertex is the one w ith the smallest d0.
A study [19] m ade using a M C sim ulated dataset has shown that the precision o f the reconstructed B 0 proper decay tim e remains stable over the range o f pile-up encountered during 2012 data-taking. N o B ° meson decay-tim e cut is applied in this analysis.
4 Flavour tagging
T h e initial flavour o f a neutral B meson can be inferred using inform ation from the opposite- side B meson that contains the other pair-produced b-quark in the event [20, 21] . Th is is referred to as opposite-side taggin g (O S T ).
T o study and calibrate the O S T methods, events containing B ± ^ J / 0 K ± decays are used, where the flavour o f the B ±-m eson is provided by the kaon charge. A sample o f B ± ^ J / 0 K ± candidates is selected from the entire 2012 dataset satisfying the data- qu ality selection described in section 2. Since the O S T calibration is not affected by the trig g er problem at the start o f the 8 T e V data-taking period, the taggin g measurement uses 19.5 fb -1 o f integrated lum inosity o f pp collision data.
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4.1
B ± ^ J / ^ K
± even t se lec tio nIn order to select candidate B ± ^ J / 0 K ± decays, firstly J / 0 candidates are selected from pairs o f oppositely charged combined-muons form ing a good vertex, follow in g the criteria described in section 3. Each muon is required to have a transverse m om entum o f at least 4 G eV and pseudorapidity w ithin |n| < 2.5. T h e invariant mass o f the dimuon candidate is required to satisfy 2.8 G eV < m (^ + ^ - ) < 3.4 GeV. T o form the B candidate, an additional track, satisfying the same qu ality requirements described for tracks in section 3, is com bined w ith the dim uon candidate using the charged kaon mass hypothesis, and a ve rte x fit is perform ed w ith the mass o f the dim uon pair constrained to the known value o f the J / 0 mass. T o reduce the prom pt com ponent o f the com binatorial background, a requirem ent is applied to the transverse decay length o f the B candidate o f L xy > 0.1 mm.
A sideband subtraction m ethod is used in order to study param eter distributions cor
responding to the B ± signal processes w ith the background com ponent subtracted. Events are divided into sub-sets into five intervals in the pseudorapidity o f the B candidate and three mass regions. T h e mass regions are defined as a signal region around the fitted peak signal mass position ^ ± 2a and the sideband regions are defined as [^ — 5a, ^ — 3a] and [^ + 3a, ^ + 5a], where ^ and a are the mean and w idth o f the Gaussian function describing the B signal mass. Separate binned extended m axim um -likelihood fits are perform ed to the invariant mass distribution in each region o f pseudorapidity.
A n exponential function is used to m odel the com binatorial background and a hy
perbolic tangent function to param eterize the low-mass contribution from in correctly or pa rtia lly reconstructed B decays. A Gaussian function is used to m odel the B ± ^ J / 0 n ± contribution. T h e contribution from non-com binatorial background is found to have a neg
ligible effect on the taggin g procedure. F igu re 1 shows the invariant mass distribution o f B candidates for all rap idity regions overlaid w ith the fit result for the combined data.
4.2 F la v o u r t a g g in g m e th o d s
Several m ethods that differ in efficiency and discrim inating power are available to infer the flavour o f the opposite-side b-quark. T h e measured charge o f a muon or electron from a sem ileptonic decay o f the B meson provides strong separation power; however, the b ^ £ transitions are diluted through neutral B meson oscillations, as well as by cascade decays b ^ c ^ £, which can alter the charge o f the lepton relative to those from direct b ^ £ decays. T h e separation power o f lepton taggin g is enhanced by considering a w eighted sum o f the charge o f the tracks in a cone around the lepton, where the w eighting function is determ ined separately for each ta g g in g m ethod by op tim izin g the ta g g in g perform ance. I f no lepton is present, a w eighted sum o f the charge o f tracks in a je t associated w ith the opposite-side B meson decay provides some separation. T h e flavour taggin g m ethods are described in detail below.
For muon-based tagging, an additional muon is required in the event, w ith > 2.5 GeV, |n| < 2.5 and w ith |Az| < 5 mm from the prim ary vertex. Muons are classified accord
ing to their reconstruction class, c o m b in e d or s e g m e n t - t a g g e d , and subsequently treated as
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Figure 1. The invariant mass distribution for B ± ^ J/-0K± candidates satisfying the selection criteria, used to study the flavour tagging. Data are shown as points, and the overall result of the fit is given by the blue curve. The contribution from the combinatorial background component is indicated by the red dotted line, partially reconstructed B decays by the green shaded area, and decays of B ± ^ J / ^ n ± , where the pion is mis-assigned a kaon mass, by the purple dashed line.
Figure 2. The opposite-side muon cone charge distribution for B ± signal candidates for s e g m e n t- tagged (left) and c o m b in e d (right) muons. The B ± charge is determined from the kaon charge.
distinct flavour taggin g m ethods. In the case o f m ultiple muons, the muon w ith the highest transverse m om entum is selected.
A muon cone charge variable is constructed, defined as
E
N tracks / \K= i qi • (p T i)
t-^ N tracką \K ’ E i (p T i)K
where q is the charge o f the track, k = 1.1 and the sum is perform ed over the reconstructed ID tracks w ithin a cone, A R = y /( A$)2 + ( An)2 < 0.5, around the muon direction. T h e reconstructed ID tracks must have p T > 0.5 G eV and |n|< 2.5. Tracks associated w ith the B± signal decay are excluded from the sum. In figure 2 the opposite-side muon cone charge distributions are shown for candidates from B± signal decays.
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F ig u r e 3. The opposite-side electron cone charge distribution for B signal candidates.
For electron-based tagging, an electron is identified using inform ation from the inner detector and calorim eter and is required to satisfy the tigh t electron quality criteria [22] . T h e inner detector track associated w ith the electron is required to have p T > 0.5 G eV and |n| < 2.5. It is required to pass w ithin |Az| < 5 mm o f the prim ary vertex to rem ove electrons from non-signal interactions. T o exclude electrons associated w ith the signal- side o f the decay, electrons are rejected that have m om enta w ithin a cone o f size A R = 0.4 around the signal B candidate direction in the lab ora tory fram e and opening angle between the B candidate and electron m om enta, ( b, o f cos(Zb) > 0.98. In the case o f more than one electron passing the selection, the electron w ith the highest transverse m om entum is chosen. A s in the case o f muon tagging, additional tracks w ithin a cone o f size A R = 0.5 are used to form the electron cone charge Q e w ith k = 1.0. I f there are no additional tracks w ithin the cone, the charge o f the electron is used. T h e resulting opposite-side electron cone charge distribution is shown in figure 3 for B + and B - signal events.
In the absence o f a muon or electron, b - t a g g e d jets (i.e. jets that are the product o f a b-quark) are identified using a m ultivariate taggin g algorithm [23] , which is a com bination o f several b-tagging algorithm s using an artificial neural network and outputs a b - t a g weight classifier. Jets are selected that exceed a b - t a g w eight o f 0.7. Th is value is op tim ized to m axim ize the taggin g power o f the calibration sample. Jets are reconstructed from track inform ation using the anti-kt algorithm [24] w ith a radius param eter R = 0.8. In the case o f m ultiple jets, the je t w ith the highest value o f the b-tag w eight is used.
T h e jet c h a r g e is defined as
Q = E f tracks Qi • (P T i)K Qjet E f traCkS(PTi)K ’
where k = 1.1 and the sum is over the tracks associated w ith the je t, excluding those tracks associated w ith a prim ary vertex other than that o f the signal decay and tracks from the signal candidate. F igu re 4 shows the distribution o f the opposite-side jet-ch arge for B ± signal candidates.
T h e efficiency, e, o f an individual taggin g m ethod is defined as the ratio o f the num
ber o f events tagged by that m ethod to the to ta l number o f candidates. A prob ab ility P (B | Q ) (P (B | Q )) that a specific event has a signal decay containing a b-quark (b-quark)
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F ig u r e 4. Opposite-side jet-charge distribution for B ± signal candidates.
given the value o f the discrim inating variable is constructed from the calibration sam
ples for each o f the B + and B - samples, which defines P (Q | B + ) and P (Q | B - ), re
spectively. T h e prob ab ility to ta g a signal event as containing a b-quark is therefore P (B | Q ) = P ( Q | B + ) / ( P( Q \ B+ ) + P (Q | B - ) ) , and correspondingly P (B | Q ) = 1 - P (B | Q ).
It is possible to define a qu antity called the dilution D = P (B | Q ) — P (B | Q ) = 2 P (B | Q ) — 1, which represents the strength o f a particular flavour taggin g m ethod. T h e taggin g power o f a particular taggin g m ethod is defined as T = eD 2 = ^ i e* ■ (2 P i (B |Q i ) — 1 )2, where the sum is over the bins o f the prob ab ility distribution as a function o f the charge variable. A n effective dilution, D = y/T/e, is calculated from the measured taggin g power and efficiency.
T h e flavour taggin g m ethod applied to each B 0 candidate event is taken from the inform ation contained in a given event. B y definition there is no overlap between lepton- tagged and jet-ch arge-tagged events. T h e overlap between muon- and electron-tagged events, corresponding to 0.4% o f all tagged events, is n egligib ly small. In the case o f doubly tagged events, the tagger w ith the highest taggin g power is selected; however, the choice o f hierarchy between muon- and electron-tagged events is shown to have negligible im pact on the final fit results. I f it is not possible to provide a taggin g response for the event, then a prob ab ility o f 0.5 is assigned. A sum m ary o f the taggin g perform ance is given in table 1.
4.3 U s in g t a g in fo rm a tio n in th e B 0 fit
T h e tag-p rob ab ility for each B 0 candidate is determ ined from calibrations derived from a sample o f B ± ^ J / 0 K ± candidates, as described in section 4.2. T h e distributions o f tag- probabilities for the signal and background are different and since the background cannot be factorized out, additional prob ab ility terms, P s(P (B | Q )) and P b(P (B | Q )) for signal and background, respectively, are included in the fit. T h e distributions o f tag-probabilities for the B 0 candidates consist o f continuous and discrete parts (events w ith a tag charge o f
± 1 ) ; these are treated separately as described below.
T o describe the continuous part, a fit is first perform ed to the sideband data, i.e., 5.150 G eV < m (B 0) < 5.317 G eV or 5.417 G eV < m (B 0) < 5.650 GeV, where m (B 0) is the mass o f the B 0 candidate. D ifferent functions are used for the different taggin g m eth
ods. For the combined-m uon taggin g m ethod, the function has the form o f the sum o f a
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Tagger E fficiency [%] D ilu tion [%] T a ggin g P ow er [%]
Com bined ^ E lectron
Segm ent-tagged ^ Jet-charge
4.12 ± 0.02 1.19 ± 0.01 1.20 ± 0.01 13.15 ± 0.03
47.4 ± 0.2 49.2 ± 0.3 28.6 ± 0.2 11.85 ± 0.03
0.92 ± 0.02 0.29 ± 0.01 0.10 ± 0.01 0.19 ± 0.01
T o ta l 19.66 ± 0.04 27.56 ± 0.06 1.49 ± 0.02
T a b le 1. Summary of tagging performance for the different flavour tagging methods described in the text. Uncertainties shown are statistical only. The efficiency and tagging power are each determined by summing over the individual bins of the charge distribution. The effective dilution is obtained from the measured efficiency and tagging power. For the efficiency, dilution, and tagging power, the corresponding uncertainty is determined by combining the appropriate uncertainties in the individual bins of each charge distribution.
fourth-order polyn om ial and tw o exponential functions. A second-order polyn om ial and tw o exponential functions are applied for the electron taggin g algorithm . A sum o f three Gaussian functions is used for the segm ent-tagged muons. For the jet-ch arge taggin g algo
rithm an eighth-order polyn om ial is used. In all four cases unbinned m axim um -likelihood fits to data are used. In the next step, the same function as applied to the sidebands is used to describe the distributions for events in the signal region: the background param eters are fixed to the values obtained from the fits to the sidebands w hile the signal param eters are free in this step. T h e ratio o f background to signal (obtained from a simultaneous m ass-lifetim e fit) is fixed as well. T h e results o f the fits projected onto histograms o f B 0 ta g-p rob ab ility for the different taggin g m ethods are shown in figure 5.
T o account for possible deviations between data and the selected fit m odels a number o f altern ative fit functions are used to determ ine system atic uncertainties in the B 0 fit.
These fit variations are described in section 7.
T h e discrete com ponents o f the ta g-p rob ab ility distribution originate from cases where the ta g is derived from a single track, g ivin g a tag charge o f ex a ctly + 1 or - 1 . T h e fractions o f events / + 1 and / _ w ith charges + 1 and - 1 , respectively, are determ ined separately for signal and background using events from the same B 0 mass signal and sideband regions.
P o sitive and negative charges are equally probable for background candidates form ed from a random com bination o f a J / 0 and a pair o f tracks, but this is not the case for background candidates form ed from a pa rtia lly reconstructed b-hadron. For signal and background contributions, sim ilar fractions o f events that are tagged w ith + 1 or —1 taggin g charge are observed for each o f the taggin g methods. T h e rem aining fraction o f events, 1 — / + i — / _ 1, constitute the continuous part o f the distributions. T able 2 summarizes the fractions /+1 and / _ 1 obtained for signal and background events and for the different ta g methods.
T o estim ate the fractions o f signal and background events which have tagging, a sim
ilar sideband-subtraction m ethod is used to determ ine the relative fraction o f signal and background events tagged using the different methods. These fractions are also included in the m axim um -likelihood fit, described in section 5. T h e results are sum m arized in table 3.
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Figure 5. The continuous part of tag-probability for tagging using combined-muons (top-left), electrons (top-right), segment-tagged muons (bottom-left) and jet-charge (bottom-right). Black dots are data, blue is a fit to the sidebands, purple to the signal and red is a sum of both fits.
T a g m ethod Signal
f + i f - i
Background
f + i f - i
Com bined ^ E lectron
Segm ent-tagged ^ Jet-charge
0.124 ± 0.012 0.127 ± 0.012 0.105 ± 0.020 0.139 ± 0.021 0.147 ± 0.024 0.118 ± 0.023 0.071 ± 0.005 0.069 ± 0.005
0.093 ± 0.003 0.095 ± 0.003 0.110 ± 0.007 0.110 ± 0.007 0.083 ± 0.004 0.084 ± 0.004 0.068 ± 0.002 0.069 ± 0.002
T able 2. Table summarizing the fraction of events /+1 and / _ 1 with tag charges of +1 and — 1, respectively for signal and background events and for the different tag methods. Only statistical errors are quoted.
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J H E P 0 8 (2 0 1 6 )1 4 7
T a g m ethod Signal Background Com bined ^
E lectron
Segm ent-tagged ^ Jet-charge
U ntagged
0.047 ± 0.003 0.012 ± 0.001 0.013 ± 0.001 0.135 ± 0.003 0.793 ± 0.002
0.038 ± 0.001 0.008 ± 0.001 0.015 ± 0.001 0.100 ± 0.001 0.839 ± 0.002
T a b le 3. Table summarizing the relative fractions of signal and background events tagged using the different tag methods. The fractions include both the continuous and discrete contributions.
Only statistical errors are quoted.
5 M axim u m likelihood fit
A n unbinned m axim um -likelihood fit is perform ed on the selected events to extract the pa
ram eter values o f the B 0 ^ J / ^ ( ^ + ^ - ) 0 ( K + K - ) decay. T h e fit uses inform ation about the reconstructed mass m, the measured proper decay tim e t, the measured proper de
cay tim e uncertainty a t , the taggin g probability, and the transversity angles Q o f each B 0 ^ J / ^ 0 decay candidate. T h e measured proper decay tim e uncertainty a t is calcu
lated from the covariance m atrix associated w ith the ve rte x fit o f each candidate event. T h e transversity angles Q = (0T , ^ T , ^ T ) are defined in section 5.1. T h e likelihood is indepen
dent o f the K + K - mass distribution. T h e likelihood function is defined as a com bination o f the signal and background prob ab ility density functions as follows:
N
l n L = £ { w i ■ ln (fs ■ F s (m i, U , a tt , Q i , P ( B | Q ) , P t ) i=1
+ fs ■ fb° - F b c( m i , t i , a t i, Q i,P (B | Q ), p T i) + fs ■ fA b - F a 6( m i , t i , a t i, Qi, P (B | Q ),p T i)
+ (1 — f s ■ (1 + f B0 + f Ab) ) F bkg(m i , ti , a t ;, Qi , P (B | Q ),p T ) ) } , (5 .1)
where N is the number o f selected candidates, wi is a w eighting factor to account for the trigger efficiency (described in section 5.3) , and fs is the fraction o f signal candidates.
T h e background fractions f Bo and fA b are the fractions o f B 0 mesons and A b baryons m is-identified as B 0 candidates calculated relative to the number o f signal events; these param eters are fixed to their M C values and varied as part o f the system atic uncertainties.
T h e mass m i , the proper decay tim e ti and the decay angles Q* are the values measured from the data for each event i. F s, F Bo, F a 6 and F bkg are the prob ab ility density functions (P D F ) m odelling the signal, B 0 background, A b background, and the other background distributions, respectively. A detailed description o f the signal P D F term s in equation ( 5.1) is given in section 5.1. T h e three background functions are described in section 5.2.
J H E P 0 8 (2 0 1 6 )1 4 7
5.1 S ig n a l P D F
T h e P D F used to describe the signal events, F s, has the follow in g com position:
F s (m i,t i,a t i, Q i,P (B | Q ), p T i) = P s (m i) ■ P s ( Q i , t i , P ( B | Q ) , a ^ )
■Ps(ati) ■ P s (P (B | Q )) ■ A (Q i,p T i) ■ P s (P T i). (5.2)
T h e mass function P s(m i ) is m odelled by a sum o f three Gaussian distributions. T h e prob ab ility term s P s(a ti) and P s(p T i) are described by gam m a functions and are unchanged from the analysis described in ref. [25] . T h e taggin g prob ab ility term for signal P s(P (B | Q )) is described in section 4.3.
T h e term P s(Q ^ t i , P (B | Q ), a ti) is a join t P D F for the decay tim e t and the transver
sity angles Q for the B ° ^ J / 0 (^ + ^ - ) 0 ( K + K - ) decay. Ign orin g detector effects, the distribution for the tim e t and the angles Q is given by the differential decay rate [26] :
10
dt dQ = ^ 2 ° (fc)(t)g (fc)(^ T , ^ T , 0 T ^ k=1
where O (k )(t ) are the tim e-dependent functions corresponding to the contributions o f the four different am plitudes ( A 0, A||, A ^ , and A S) and their interference terms, and g (fc)(# T , , 0t) are the angular functions. Table 4 shows these tim e-dependent functions and the angular functions o f the transversity angles. T h e form ulae for the tim e-dependent functions have the same structure for B 0 and B 0 but w ith a sign reversal in the terms containing A m s. In tab le 4, the param eter A ^ ( t ) is the tim e-dependent am plitude for the C P - o d d final-state configuration w hile A 0(t ) and A y (t ) correspond to C P -e v e n final- state configurations. T h e am plitude A S (t ) gives the contribution from the C P - o d d non
resonant B 0 ^ J / 0 K + K - S-w ave state (w hich includes the f 0). T h e corresponding functions are given in the last four lines o f table 4 (k = 7-10). T h e am plitudes are pa
ram eterized by |Ai |ei^i , where i = {0 , ||, ± , S }, w ith A0 = 0 and are norm alized such that
|A0(0)|2 + |A^(0)|2 + |A|| (0)|2 = 1. |A^(0)| is determ ined according to this condition, while the rem aining three am plitudes are param eters o f the fit. T h e form alism used throughout this analysis assumes no direct C P violation.
T h e angles (0T , , 0 T ), are defined in the rest frames o f the final-state particles. T h e x-axis is determ ined by the direction o f the 0 meson in the J / 0 rest frame, and the K + K - system defines the x - y plane, where ( K + ) > 0. T h e three angles are defined as:
• , the angle between p (^ + ) and the norm al to the x - y plane, in the J / 0 meson rest frame,
• 0 T , the angle between the x-axis and (^ + ), the projection o f the ^ + m om entum in the x - y plane, in the J / 0 meson rest frame,
• , the angle between p ( K + ) and —p (J / 0 ) in the 0 meson rest frame.
T h e P D F term P s(Q i , t i , P ( B | Q ) , a ti) takes into account the lifetim e resolution, so each tim e elem ent in tab le 4 is smeared w ith a Gaussian function. Th is sm earing is perform ed
-
12-
J H E P 0 8 (2 0 1 6 )1 4 7
Figure 6. The proper decay time uncertainty distribution for data (black), and the fits to the background (blue) and the signal (purple) contributions. The total fit is shown as a red curve.
num erically on an event-by-event basis where the w id th o f the Gaussian function is the proper decay tim e uncertainty, measured for each event, m ultiplied by a scale factor to account for any mis-measurements. T h e prop er decay tim e uncertainty distribution for data, including the fits to the background and the signal contributions is shown in figure 6.
T h e average value o f this uncertainty for signal events is 97 fs.
T h e angular acceptance o f the detector and kinem atic cuts on the angular distributions are included in the likelihood function through A ( QppT i). Th is is calculated using a 4D binned acceptance m ethod, applying an event-by-event efficiency according to the transver- sity angles (dT , ^ t , <Pt) and the pT o f the candidate. T h e pT binning is necessary, because the angular acceptance is influenced by the pT o f the B0 candidate. T h e acceptance is calculated from the B0 ^ J / ^ $ M C events. Takin g the small discrepancies between data and M C events into account have negligible effect on the fit results. In the likelihood func
tion, the acceptance is treated as an angular acceptance P D F , which is m ultiplied w ith the tim e- and angle-dependent P D F describing the B0 ^ J / ^ ( p + p - )<fi(K+ K - ) decays. As b oth the acceptance and tim e- and angle-dependent decay P D F s depend on the transversity angles th ey must be norm alized together. Th is norm alization is done num erically during the likelihood fit. T h e P D F is norm alized over the entire B0 mass range 5.150-5.650 GeV.
5.2 B a c k g r o u n d P D F
T h e background P D F has the follow in g com position:
F b k g (m i , t i , ati , &i , P (B|Q),pT i ) = Pb (m i) ■ P b(t i\o ti) ■ P b(P (B\Q) )
•Pb( ^i) ■ P b ( ^ti ) ■ Pb(PT i) . ( 5.3)
T h e proper decay tim e function pb(ti |ati ) is param eterized as a prom pt peak m odelled by a Gaussian distribution, tw o positive exponential functions and a negative exponential func
tion. Th ese functions are smeared w ith the same resolution function as the signal decay tim e-dependence. T h e prom pt peak m odels the com binatorial background events, which are expected to have reconstructed lifetim es distributed around zero. T h e tw o positive exponential functions represent a fraction o f longer-lived backgrounds w ith non-prom pt
J H E P 0 8 (2 0 1 6 )1 4 7
k O W ( t ) g {k )(0 T ,1 p T ,0 T ) 1 1 I M 0 ) I 2
(s)
(1 + cos 4>s) e _ r L * + (1 — cos 4>s) e _ r H * ± 2 e ~ Fst s i n ( A m st ) sin cf>s 2 cos2 t p r i 1 — sin2 0t cos2 p ) 2 ^ | | ( 0 ) | 2 (1 + cos (f>s) e _ r L + (1 — cos (f>s) e _ r H ± 2 e ~ rst s i n ( A m st ) sin <f>s sin2 p ( l — sin2 9t sin2 p ) 3 | I P ( o ) | 2
(s) (s)
(1 — cos 4>s) e _ r L * + (1 + cos 4>s) e _ r H * =p 2 e _ r s * s i n ( A m aT ) sin <ps sin2 'ipx sin2 9t
4 i | A o ( 0 ) P
1
(0)| cos(1 + cos (f>s) e _ r L ’* + ( ! — cos (j)s) e —r H)jt ± 2 e _ r s * s i n ( A m aT ) s i n ^
^ sin 2'ipx sin2 9t sin 2p
5 |^4||(0)11 A_l( 0)| [T (e r L — e r H );t) c o s ( P - P s i n ^ — sin2 'ipx sin 29t sin p
± e rs * ( s i n ( p — ^||) c o s (A r n st ) — cos(£j_ — cos (f>s s i n ( A m sT ) ) ]
6 |4o ( 0 ) P _ L ( 0 ) | [ i ( e r L * - e r H t )c o s ó ± s in (f> s ^ sin 2'ipx sin 29t cos <f>r
± e rs *(s in p c o s ( A m st ) — cos p cos <ps s i n ( A m sT ) ) ]
7 | | P ( 0 ) | 2 (1 — cos 4>s) e _ r L * + (1 + cos 4>s) e _ r H * =p 2 e _ r s * s i n ( A m aT ) sin cf>s | ( l — sin2 9t co s2 p ) 8 | P ( 0 ) P | | ( 0 ) | [ i ( e r L — e r H ’*) sin(c>|| - 5S ) s in <j>s | n/6 sin 'ip? sin2 9t sin 2 p
± e rs *(cos(^|| — 5 s ) c o s ( A m st ) — sin(^y — S s ) cos <ps s i n ( A m sT ) ) ]
9 ^ | Ą s ( 0 ) P _ l ( 0 ) | s i n ( P - Ss ) | \/6 sin 'ipx sin 29t cos <f>r (1 — cos 4>s) e r L * + (1 + cos 4>s) e r n * =p 2e rs * s i n ( A m aT ) sin cf>s
10 | 4 o (0 )P < j(0 )| [| (e r HS)* - e pl ’*) sin 5s sin <ps | v/3 cos tpT ( 1 — sin2 9t co s2 p )
± e rs*(c o s Ss c o s ( A m st ) + sin Ss cos 4>s s i n ( A m sT ) ) ]
T a b le 4. Table showing the ten time-dependent functions, 0 ^ k\ t ) and the functions of the transversity angles P P t , V T ;‘/’r )- The amplitudes
|An(0)|2 and |A||(0)|2 are for the CP-even components of the 5 ° —> J / rtp4> decay, |A^(0)|2 is the C P-od d amplitude; they have corresponding strong phases 5n, 51| and S ± . By convention So is set to be zero. The S'-wave amplitude |A,g(0)|2 gives the fraction of 5 ° —> J / i p K + K ~ ( f o ) and has a related strong phase S s- The ± and terms denote two cases: the upper sign describes the decay of a meson that was initially a 5 ° meson, while the lower sign describes the decays of a meson that was initially 5 °.
L f l ( 9 T 0 Z ) 80d3Hr
J/ 0 , com bined w ith hadrons from the prim ary vertex or from a B / D meson in the same event. T h e negative exponential function takes into account events w ith p oor ve rte x res
olution. T h e prob ab ility term s P b(u-ti) and P b(pT i) are described by gam m a functions.
T h e y are unchanged from the analysis described in ref. [25] and explained in detail there.
T h e taggin g prob ab ility term for background P b ( P ( B |Q)) is described in section 4.3.
T h e shape o f the background angular distribution, P b (^ j) arises prim arily from de
tector and kinem atic acceptance effects. These are described by Legendre polyn om ial functions:
V lm ( 0 T) = V ( 2 l + l) / ( 4 n ) V ( J - m )!/ (l + m )!P jm|(c o s0t)
P k(x ) = 2kfc! d x ? (x - 1) (5 .4)
6 6 l | a k ,i,m V 2 Y lm ( 0 T)c o s (m ^ T ) P k (c o s ^ t ) where m > 0 P b(0T , ^ T, 0 T ) = E E E | a k , i , m V2Y l m ( 0 T) sin (m % r)P k (co s ^ t ) where m < 0 k= 0 l= 0 m = ~ l I a k , i , m V2Y l° ( 9 t ) P k( c o s ^ t ) where m = 0
where the coefficients a k,l ,m are adjusted to give the best fit to the angular distributions for events in the B°? mass sidebands. These param eters are then fixed in the main fit. T h e B ° mass interval used for the background fit is between 5.150 and 5.650 G eV excluding the signal mass region | (m (B °) — 5.366 GeV| < 0.110 G eV. T h e background mass m odel, P b (m j) is an exponential function w ith a constant term added.
C ontam ination from Bd ^ J / 0 K °* and A d ^ J / ^ p K - events mis-reconstructed as B ° ^ J / ^ 0 are accounted for in the fit through the FBo and F A b term s in the P D F function described in equation ( 5.1) . T h e fraction o f these contributions, fB 0 = (3.3 ± 0.5)% and /Ab = (1 .8 ± 0.6)% , are evaluated from M C sim ulation using production and branching frac
tions from refs. [18, 27- 31] . M C sim ulated events are also used to determ ine the shape o f the mass and transversity angle distributions. T h e 3D angular distributions o f B ° ^ J / 0 K *°
and o f the conjugate decay are m odelled using input from ref. [32] , w hile angular distribu
tions for A b ^ J / ^ p K - and the conjugate decay are m odelled as flat. These distributions are sculpted for detector acceptance effects and then described by Legendre polyn om ial functions, equation ( 5.4) , as in the case o f the background described by equation ( 5.3) . These shapes are fixed in the fit. T h e Bd and Ab lifetim es are accounted for in the fit by adding additional exponential terms, scaled by the ratio o f B d/ B ° or A b/ B ° masses as ap
propriate, where the lifetim es and masses are taken from ref. [18] . System atic uncertainties due to the background from B d ^ J / 0 K °* and A b ^ J / ^ p K - decays are described in section 7. T h e contribution o f B d ^ J / ^ K n events as w ell as their interference w ith B d ^ J / 0 K °* events is not included in the fit and is instead assigned as a system atic uncertainty.
T o account for possible deviations between data and the selected fit m odels a number o f altern ative fit functions and mass selection criteria are used to determ ine system atic uncertainties in the B ° fit. These fit variations are described in section 7.
J H E P 0 8 (2 0 1 6 )1 4 7
5.3 M u o n t r ig g e r p r o p e r tim e -d e p e n d e n t efficien cy
It was observed that the muon trigger biases the transverse im pact param eter o f muons, resulting in a m inor inefficiency at large values o f the proper decay tim e. Th is inefficiency is measured using M C simulated events, by com paring the B 0 proper decay tim e distribution o f an unbiased sample w ith the distribution obtained including the trigger. T o account for this inefficiency in the fit, the events are re-weighted by a factor w:
w = p0 ■ [1 — p i ■ ( E r f ( (t — p3)/ p 2) + 1)], (5.5)
where p0,p 1,p 2 and p 3 are param eters determ ined in the fit to M C events. N o significant bias or inefficiency due to off-line track reconstruction, ve rte x reconstruction, or track qu ality selection criteria is observed.
6 Results
T h e full simultaneous unbinned m axim um -likelihood fit contains nine physical parameters:
A r s, 0 s, r s, |A0(0)|2, |A|(0)|2, 5||, 0^, |AS (0)|2 and 0 s . T h e other param eters in the likelihood function are the B0 signal fraction f s, param eters describing the J / 0 0 mass distribution, param eters describing the B 0 meson decay tim e plus angular distributions o f background events, param eters used to describe the estim ated decay tim e uncertainty dis
tributions for signal and background events, and scale factors between the estim ated decay tim e uncertainties and their true uncertainties. In addition there are also 353 nuisance param eters describing the background and acceptance functions that are fixed at the tim e o f the fit. T h e fit m odel is tested using pseudo-experim ents as described in section 7. These tests show no significant bias, as well as no system atic underestim ation o f the statistical errors reported from the fit to data.
M u ltip ly in g the to ta l number o f events supplied to the fit w ith the extracted signal fraction and its statistical uncertainty provides an estim ate for the to ta l number o f B 0 meson candidates o f 74900 ± 400. T h e results and correlations o f the physics param eters obtained from the fit are given in tables 5 and 6. F it projections o f the mass, proper decay tim e and angles are given in figures 7 and 8, respectively.
7 Systematic uncertainties
System atic uncertainties are assigned by considering effects that are not accounted for in the likelihood fit. These are described below.
• F la v o u r t a g g in g : there are tw o contributions to the uncertainties in the fit param e
ters due to the flavour taggin g procedure, the statistical and system atic components.
T h e statistical uncertainty due to the size o f the sample o f B ± ^ J / 0 K ± decays is included in the overall statistical error. T h e system atic uncertainty arising from the precision o f the taggin g calibration is estim ated by changing the m odel used to param eterize the prob ab ility distribution, P (B | Q ), as a function o f ta g charge from the third-order polyn om ial function used by default to one o f several altern ative
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J H E P 0 8 (2 0 1 6 )1 4 7
Param eter Value Statistical uncertainty
System atic uncertainty
0s [rad] —0.110 0.082 0.042
A r s[ps- 1 ] 0.101 0.013 0.007
Ts[ps- 1 ] 0.676 0.004 0.004
|A||(0)|2 0.230 0.005 0.006
|Ao(0)|2 0.520 0.004 0.007
|As (0)|2 0.097 0.008 0.022
[rad] 4.50 0.45 0.30
£|| [rad] 3.15 0.10 0.05
— $ s [rad] —0.08 0.03 0.01
T a b le 5. Fitted values for the physical parameters of interest with their statistical and systematic uncertainties.
A r Ts |A||(0)|2 |Ao(0)|2 |As (0)|2 ^11 s ± 1
03 0.097 —0.085 0.030 0.029 0.048 0.067 0.035 —0.008
A r 1 —0.414 0.098 0.136 0.045 0.009 0.008 —0.011
Ts 1 —0.119 —0.042 0.167 —0.027 —0.009 0.018
|A||(0)|2 1 —0.330 0.072 0.105 0.025 —0.018
|Ao(0)|2 1 0.234 —0.011 0.007 0.014
|As (0)|2 1 —0.046 0.004 0.052
^11 1 0.158 —0.006
s ± 1 0.018
T a b le 6. Fit correlations between the physical parameters of interest.
functions. T h e alternatives used are: a linear function; a fifth -order polynom ial; or tw o third-order polynom ials describing the positive and negative regions that share the constant and linear term s but have independent quadratic and cubic terms. For the combined-m uon tagging, an additional m odel consisting o f tw o third-order p o ly nomials sharing the constant term but w ith independent linear, quadratic and cubic term s is also used. T h e B ° fit is repeated using the altern ative m odels and the largest difference is assigned as the system atic uncertainty.
• A n g u l a r a c c e p ta n c e m e th o d : the angular acceptance (from the detector and kinem atic effects m entioned in section 5.1) is calculated from a binned fit to M C simulated data. In order to estim ate the size o f the system atic uncertainty intro
duced from the choice o f binning, different acceptance functions are calculated using different bin w idths and central values. These effects are found to be negligible.
J H E P 0 8 (2 0 1 6 )1 4 7
F ig u re 7. (Left) Mass fit projection for the B 0 ^ J/00 sample. The red line shows the total fit, the dashed purple line shows the signal component, the long-dashed dark blue line shows the B 0 ^ J/-0K0* component, while the solid light blue line shows the contribution from A b ^ J / 0 p K - events. (Right) Proper decay time fit projection for the B ° ^ J/00 sample. The red line shows the total fit while the purple dashed line shows the total signal. The total background is shown as a blue dashed line with a long-dashed grey line showing the prompt J/-0 background. Below each figure is a ratio plot that shows the difference between each data point and the total fit line divided by the statistical uncertainty (a ) of that point.
• In n e r d e t e c to r a lig n m e n t: residual m isalignm ents o f the ID affect the im pact param eter, d0, distribution w ith respect to the prim ary vertex. T h e effect o f a radial expansion on the measured d0 is determ ined from data collected at 8 TeV , w ith a trig g er requirem ent o f at least one muon w ith a transverse m om entum greater than or equal to 4 G eV. T h e radial expansion uncertainties determ ined in this w ay are 0.14% for |n| < 1.5 and 0.55% for 1.5 < |n| < 2.5. These values are used to estim ate the effect on the fitted B 0 param eter values. Sm all deviations are seen in some param eters, and these are included as system atic uncertainties.
• T r ig g e r efficien cy: to correct for the trig g er lifetim e bias the events are re-weighted according to equation ( 5.5) . T h e uncertainty o f the param eters p0, p 1,p 2 and p 3 are used to estim ate the system atic uncertainty due to the tim e efficiency correction.
These uncertainties originate from the follow in g sources: the lim ited size o f the M C simulated dataset, the choice o f bin-size for the proper decay tim e distributions and variations between different triggers. T h e system atic effects are found to be negligible.
• B a c k g r o u n d a n g le s m o d e l, choice o f p t b in s: the shape o f the background angular distribution, P b( $ T , 0 t , ^ t ), is described by the Legendre polyn om ial func
tions given in equation ( 5.4) . T h e shapes arise prim arily from detector and kinem atic acceptance effects and are sensitive to the pT o f the B 0 meson candidate. For this reason, the param eterization using the Legendre polyn om ial functions is perform ed in four pT intervals: 0-13 GeV, 13-18 GeV, 18-25 G eV and > 2 5 GeV. T h e system-
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18-
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F ig u re 8. Fit projections for the transversity angles of events with 5.317 GeV < m ( J / ^ K K) <
5.417 GeV for (top left), cos(0T ) (top right), and cos(^T ) (bottom ). In all three plots the red solid line shows the total fit, the CP-odd and CP-even signal components are shown by the red dot-dashed and orange dashed lines respectively, the S-wave component is given by the green dashed line and the blue dotted line shows the background contribution. The contributions of the interference terms are negligible in these projections and are not shown.
atic uncertainties due to the choice o f pT intervals are estim ated by repeating the fit, varyin g these intervals. T h e biggest deviations observed in the fit results were taken to represent the system atic uncertainties.
B a c k g r o u n d a n g le s m o d e l, choice o f m a ss sid e b a n d s : the param eters o f the Legendre polyn om ial functions given in equation ( 5.4) are adjusted to give the best fit to the angular distributions for events in the B
0
mass sidebands. T o test the sensitivity o f the fit results to the choice o f sideband regions, the fit is repeated w ith altern ative choices for the excluded signal mass regions: |m (B0
) — 5.366| > 0.085 G eV and |m (B0
) — 5.366| > 0.160 G eV (instead o f |m (B0
) — 5.366| > 0.110 G eV ).T h e differences in the fit results are assigned as system atic uncertainties.
Bd
c o n trib u tio n : the contam ination from Bd ^ J / ^ K0
* events m is-reconstructed as B0
^ J / ^ $ is accounted for in the final fit. Studies are perform ed to evaluate the effect o f the uncertainties in the Bd ^ J / ^ K0
* fraction, and the shapes o f the mass and transversity angles distribution. In the M C events the angular distribution o f the Bd ^ J / ^ K0
* decay is m odelled using param eters taken from ref. [32] . T h e uncertainties o f these param eters are taken into account in the estim ation o f system atic
J H E P 0 8 (2 0 1 6 )1 4 7
uncertainty. A fte r applying the B ° signal selection cuts, the angular distributions are fitted using Legendre polyn om ial functions. T h e uncertainties o f this fit are in
cluded in the system atic tests. T h e im pact o f all these uncertainties is found to have a negligible effect on the B ° fit results. T h e contribution o f B d ^ events as well as their interference w ith Bd ^ J / 0 K °* events is not included in the fit and is instead assigned as a system atic uncertainty. T o evaluate this uncertainty, the M C background events are m odelled using both the P -w a ve B d ^ J / 0 K 0* and S-wave B d ^ J / ^ K n decays and their interference, using the input param eters taken from ref. [32] . T h e B ° fit using this input was com pared to the default fit, and differences are included in table 7.
• A b c o n trib u tio n : the contam ination from A d ^ J / ^ p K - events m is-reconstructed as B ° ^ J / ^ 0 is accounted for in the final fit. Studies are perform ed to evaluate the effect o f the uncertainties in the A b ^ J / ^ p K - fraction /a6 , and the shapes o f the mass, transversity angles, and lifetim e distributions. A d d itio n a l studies are perform ed to determ ine the effect o f the uncertainties in the A d ^ J / ^ A * branching ratios used to reweight the generated M C . These are uncertainties are included in table 7.
• F it m o d e l v a ria tio n s: to estim ate the system atic uncertainties due to the fit m odel, variations o f the m odel are tested in pseudo-experiments. A set o f ^2500 pseudo
experim ents is generated for each variation considered, and fitted w ith the default m odel. T h e system atic error quoted for each effect is the difference between the mean shift o f the fitted value o f each param eter from its input value for the pseudo
experim ents altered for each source o f system atic uncertainty. In the first variation tested, the signal mass is generated using the fitted B ° mass convolved w ith a Gaus
sian function using the measured per-candidate mass errors. In another test, the background mass is generated from an exponential function w ith the addition o f a first-degree polyn om ial function instead o f an exponential function plus a constant term . T h e tim e resolution m odel was varied by using tw o different scale factors to generate the lifetim e uncertainty, instead o f the single scale factor used in the default m odel. T h e non-negligible uncertainties derived from these tests are included in the system atic uncertainties shown in table 7. T o determ ine the possible systematics effects o f m is-m odelling o f the background events by the fitted background m odel, as seen in the low mass side-band region (5.150-5.210 G e V ) o f figure 7, left, alternative mass selection cuts are used w ith the default fit m odel. T h e effect o f these changes on the fit results are found to be negligible.
• D e fa u lt fit m o d e l: due to its com plexity, the fit m odel is less sensitive to some nuisance param eters. Th is lim ited sensitivity could p oten tia lly lead to a bias in the measured physics param eters, even when the m odel p erfectly describes the fitted data. T o estim ate the system atic uncertainty due to the choice o f default fit m odel, a set o f pseudo-experim ents were conducted using the default m odel in both the generation and fit. T h e system atic uncertainties are determ ined from the mean o f
