P u b l i s h e d f o r SISSA b y S p r i n g e r R e c e i v e d : May 25, 2016 A c c e p t e d : June 6, 2016 P u b l i s h e d : Ju n e 14, 2016
Measurement of the relative width difference of the B 0- B 0 system with the ATLAS detector
T h e A T LA S collaboration
E -m ail: a t l a s . p u b l i c a t i o n s @ c e r n . c h
Ab s t r a c t: This paper presents the measurement o f the relative w idth difference A r ^ / r ^
o f the B ° - B 0 system using the data collected by the A T L A S experim ent at the LH C in pp collisions at yfs = 7 T eV and yfs = 8 T eV and corresponding to an integrated lum inosity o f 25.2 fb - 1 . T he value o f A r d/ r d is obtained by com paring the decay-tim e distributions o f B ° ^ J / ^ K s and B ° ^ J / ^ K *°(892) decays. T he result is A r d/ r d = ( —0 .1 ± 1 .1 (stat.) ± 0.9 (syst.)) x 10- 2 . Currently, this is the m ost precise single measurement o f A r d/ r d. It agrees with the Standard M odel prediction and the measurements by other experiments.
Ke y w o r d s: B physics, H adron-H adron scattering (experim ents)
ArXi y ePr i n t: 1605.07485
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Contents
1 In trod u ction 1
2 M easu rem en t m e th o d 2
3 T h e A T L A S d etector 5
4 D a ta sam ple and event selection 6
5 P rop er decay length o f the B ° m eson 8
6 P ro d u ctio n a sy m m etry o f the B ° m eson 11
7 R a tio o f efficiencies 13
8 Fit o f A r d 15
9 S ystem atic uncertainties 16
10 R esu lts 19
11 C onclusions 19
T h e A T L A S collaboration 22
1 I n t r o d u c t i o n
T he w idth difference A r q, where q = d ,s , is one o f the parameters describing the time evolution o f the B 0-B 0 system. It is defined as A r q = — T^1, where and are the decay widths o f the light and heavy B q states, respectively. T he relative value o f A r d/ r d is predicted in the Standard M odel (SM ) [1]:
A r d/ r d (SM ) = (0.42 ± 0.08) x 10- 2 .
Here r d is the total w idth o f the B 0 meson defined as r d = 1 (r ^ + r H).
Measurements o f A r ^ have been perform ed by the BaBar [2] , Belle [3], and L H C b [4]
collaborations. T he current world average value [5] is:
A r d/ r d (W orld average) = (0.1 ± 1.0) x 10- 2 .
The current experim ental uncertainty in A r ^ is to o large to perform a stringent test o f the SM prediction. In addition, independent measurements o f other quantities d o not constrain
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the value o f A r d. It has been shown [6] that a relatively large variation o f A r d due to a possible new physics contribution would not contradict other existing SM tests. Therefore, an experim ental measurement o f A r ^ with im proved precision and its com parison to the SM prediction can provide an independent test o f the underlying theory [7] , com plem entary to other searches for new physics.
This paper presents the measurement o f A r ^ by the A T L A S experim ent using Run 1 data collected in pp collisions at yfs = 7 T e V in 2011 and at yfs = 8 T e V in 2012. T he total integrated lum inosity used in this analysis is 4 .9 fb -1 collected in 2011 and 2 0 .3 fb -1 co l
lected in 2012. T he value o f A r d/ r d is obtained by com paring the decay tim e distributions o f B 0 ^ J / ^ Ks and B ° ^ J / ^ K *°(892) decays.
2 M e a s u r e m e n t m e t h o d
The tim e evolution o f the neutral B ° -B ° system is described by the Schrodinger equation with H am iltonian M q:
d B ° (t) dt B ° (t )
Mq
B 0(t) B ° (t )
Mq
mq
( m i2)* mq ( r l 2)* r (2.1)
T he non-diagonal elements o f Mq result from the transition B ° o B ° m ediated by b ox diagrams and depend on the parameters o f the C K M quark m ixing m atrix. Due to these non-diagonal elements, the B q0 meson propagates as a m ixture o f tw o physical mass eigen
states BL and B ^ :
|BqL) = p|Bq°) + q O°) |BqH) = p| B q °)- q|B°°). (2.2)
Here p and q are com plex numbers satisfying |q|2 + |p|2 = 1. BL and BH have distinct the following relations hold:
masses mL, mH and widths rL , rH . Assum ing that r l 2 ^ m12
A m q = mH — mL = 2 1 m l21, (2.3)
A r q = rL — rH = 2|r12| cos(^12), (2.4)
1 L H
m q = 2 (m q + m ^ ’ (2.5)
rq = 2 ( r L + r H ), (2.6)
^ 2 = arg f n^1/2> 1 . (2.7)
T he sign convention adopted in eqs. ( 2.3) and ( 2.4) ensures that the values o f A m q and A r q are positive in the Standard M odel.
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The decay rates o f the B p and Bp1 mesons to a given final state f may be different.
Therefore, the tim e dependence o f the decay rate B ° ^ f is sensitive to f . T he tim e- dependent decay rate r ( B ° ( t ) ^ f ) is [8]:
r ( B ° ( t ) ^ f ) « e- r q * cosh A r q - + ACp c o s (A m q t) + A Ar sinh + Amp sin (A m q t) (2.8) Here t is the proper decay tim e o f the B ° meson. T he parameters AjCp, A A r and Amp depend on the final state f . T he abbreviations “dir” and “ m ix” stand for “direct” and
“ m ixing” . B y definition:
A P | 2 + |Aa p|2 + |Agpx |2 = 1. (2.9) Assum ing that the C P -violating phase ¢^2 is small, which is experim entally confirm ed for b oth the B ° and B ° mesons [9] , the tim e-dependent decay rate r ( B ° ( t ) ^ f ) is:
r ( B ° ( t ) ^ f ) « e- r q * cosh — A pp c o s (A m qt) + A A r sinh — A p p sin (A m qt) (2.10) T he parameters A p p , A A r and A g p are theoretically well defined for flavour-specific final states and C P eigenstates [8] . For a flavour-specific final state f fs, such that only the decay B ° ^ f fs is allowed while A f = ( f fs|B°) = 0, the parameters are:
ACp = 1, A Ar = 0, Appx = 0. (2.11)
For a flavour-specific final state f fs, such that A f = ( / fs|B°) = 0, i.e. only the decay B ° ^ f fs is allowed, the parameters are:
ACp = —1, A A r = 0, A g p = 0. (2.12)
For the B ° decay to the CP eigenstate J / p K S the parameters are:
ACp = 0, A A r = cos(2P ), A ^ p = — sin(2P). (2.13)
Here P is the angle o f the unitarity triangle o f the C K M matrix:
P = a r g ( — . (2.14)
V Vtd Vtb /
If the initial flavour o f the B ° meson is not tagged, the decay rates given by eqs. ( 2.8) and (2.10) are added together. In this case, the produ ction asym m etry A P o f the B ° meson in pp collisions should be taken into account. This asym m etry is defined as:
a ( B ° ) — a ( B ° )
A P = - 7 - ^ --- , (2.15)
P a ( B ° ) + a ( B ° ) , ( )
where a denotes the produ ction cross-section o f the corresponding particle. A lthough b quarks are predom inantly produced in bb pairs, which result in an equal number o f b and b quarks, the presence o f a valence u quark in pp collisions leads to a small excess o f B +
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mesons (quark content bu) over B - mesons (bu) [10, 11]. Similarly, there is an excess of B °(b d ) mesons over B °(b d ) mesons due to the presence o f a valence d quark. T he larger number o f B mesons than B mesons is com pensated for by the excess o f b baryons over their corresponding anti-particles. In each case the excess is expected to be o f the order o f 1%. Only the L H C b experim ent has measured A p in pp collisions so far [12] . Their result is not directly applicable to the conditions o f the A T L A S experim ent because o f the different ranges o f pseudorapidities n and transverse m om enta pT o f the detected B mesons.
Therefore, a dedicated measurement o f A p is necessary. This measurement is presented in section 6 .
Taking into account the produ ction asym m etry A P and using eqs. ( 2.8) and (2.10) , the untagged tim e-dependent decay rate r [t, f ] to a final state f is:
r [t, f] = a ( B ° ) r ( B ° ( t ) ^ f ) + a ( B ° ) r ( B ° ( t ) ^ f ) ( 2.16)
oc e r<q* A r t A r t
cosh — rq- + A P ACp c o s (A m q t) + A ap sinh — + A p Amp sin (A m q t)
The w idth difference A r q can be extracted from the decay tim e distribution o f the decay B ° ( B ° ) ^ f using eqs. (2.11) - (2.16) . Such a measurement em ploying a single final state f , although possible, would give p o o r precision for A r q. This is because A r q ^ r q and therefore the term e -Pq* dom inates the decay tim e distribution. A more promising m ethod [2] consists in obtaining A r q from the ratio o f the decay tim e distributions o f two different decay m odes o f B q, one o f them being a CP eigenstate and the other a flavour- specific state. Using this ratio eliminates the dom inant factor e -Pq* and leads to improved precision for A r q.
The measurement o f A r d presented in this paper em ploys the ratio o f the C P eigenstate J / p K S and the flavour-specific states J /p K * ° (8 9 2 ) and J /p K * ° (8 9 2 ). T he J / p K * ° and J / p K * ° states are added together and are denoted by J / p K * ° throughout this paper, unless otherwise specified.
The decay rate r [t, J / p K S] is obtained from eqs. ( 2.13) - ( 2.16) :
r [t, J / p K S] a e Pd* cosh A r d t + cos(2P ) sinh A ^ — A P sin(2P) sin (A m dt) (2.17)
The expression for r [t , J /p K * ° ] is obtained from eqs. (2.11) , ( 2.12) , and (2.16) by summing over the J / p K * ° and J / p K * ° final states:
r [ t , J / p K * ° ] a e- r d * cosh A T " . (2.18)
If the detection efficiencies o f K *° and K * ° are different, the term proportional to A p in eq. (2.16) also contributes to eq. ( 2.18) . This contribution is multiplied by the relative difference in the detection efficiencies o f K * ° and K *° mesons. B oth o f these factors are o f the order o f 10- 2 , which is shown in section 6 . Therefore, the contribution o f the term proportional to A p is o f the order o f 10-4 and is neglected. A nother contribution to eq. ( 2.18) com ing from C P violation in m ixing is experim entally constrained to be less than 0.1% and is also neglected in this analysis.
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The world average values o f r d, A m d and P are [5] :
1 / r d = (1.520 ± 0.004) x 10-12 s, (2.19) A m d = (0.510 ± 0.003) x 1012 s- 1 , (2.20)
sin2P = 0.682 ± 0.019. (2.21)
Their uncertainties produce a negligible im pact on the measured value o f A r d.
In this analysis, the proper decay length o f the B 0 meson, LBrop = ct, is used in place o f the proper decay tim e t. T he procedure to measure LBrop is described in section 5. The decay rates r[LB rop, J / p K S] and r[LB rop, J /p K * ° ] expressed as functions o f LBrop are:
r [L £ ro p ,J /^ K s ] = / G(LBrop — ct, J / ^ K s ) r [ t , J /^ K s ]d t , ( 2.22) J°
r[LBrop, J /^ K * ° ] = G(LBrop — ct, j / ^ k * ° ) r [ t , J /^ K * ° ]d t . (2.23)
°
Here G(LBrop — ct, J / p K S) and G(LBrop — ct, J / p K * ° ) are the LBrop detector resolution functions for the B ° ^ J / p K s and B ° ^ J / p K * ° channels, respectively. These functions are discussed in section 5.
The w idth difference A r d is obtained from the fit to the ratio R(LBrop) o f the distri
butions o f the number o f reconstructed B ° ^ J / p K S and B ° ^ J / p K * ° candidates as a function o f LBrop. T he expected form o f R(LBrop) is obtained using eqs. ( 2.22) and ( 2.23) . The details o f the fitting procedure are given in section 8 . M any experim ental system atic uncertainties cancel in the ratio o f the LBrop distributions, which improves the precision o f the A r d measurement. This is an im portant advantage o f the m ethod used in this analysis.
A similar m ethod is used by the L H C b C ollaboration [4] , except that the value o f A r d is obtained from the difference o f the partial decay widths o f the B ° ^ J / p K s and B ° ^ J / p K * ° decay m odes and the production asym m etry A P (B ° ) is not taken into account.
The J / 0 meson is reconstructed using the decay J / p ^ ^ + ^ - , which exploits a clean selection o f J / p mesons and a highly efficient online trigger. T he trigger efficiencies in the tw o B ° decay channels are equal, apart from minor effects related to differences in the decay kinematics, as only the properties o f the J / p meson are used to trigger the events.
The K S and K *° mesons are reconstructed using the K S ^ n + n - and K * ° ^ K + n - (K * ° ^ K - n + ) decay m odes. T he details o f this reconstruction are given in section 4 .
3 T h e A T L A S d e t e c t o r
The A T L A S experim ent [13] uses a general-purpose detector consisting o f an inner tracker, a calorim eter and a muon spectrom eter. A brief outline o f the com ponents that are most relevant for this analysis is given below.
The A T L A S experim ent uses a right-handed coordinate system with its origin at the nominal interaction point (IP ) in the centre o f the detector and the z-axis along the beam pipe. T he x-axis points from the IP to the centre o f the LH C ring, and the y-axis points upward. T he inner detector (ID ) surrounds the interaction point; it includes a silicon pixel
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detector (P ixel), a silicon m icrostrip detector (S C T ) and a transition radiation tracker (T R T ). T he ID is immersed in an axial 2 T m agnetic field. T he ID covers the pseudorapidity range |n| < 2.5. T he pseudorapidity is defined in terms o f the polar angle d as n =
— ln ta n (0 /2 ). T he ID is enclosed by a calorim eter system containing electrom agnetic and hadronic sections. T h e calorim eter is surrounded by a large muon spectrom eter (M S) in an air-core toroidal magnet system. T he MS contains a com bination o f m onitored drift tubes (M D T s) and cathode strip chambers (C SC s), designed to provide precise position measurements in the bending plane in the range |n| < 2.7. In addition, resistive plate chambers (R P C s) and thin gap chambers (T G C s) with a coarse position resolution but a fast response tim e are used primarily to trigger muons in the ranges |n| < 1.05 and 1.05 <
|n| < 2.4, respectively. R P C s and T G C s are also used to provide position measurements in the non-bending plane and to im prove the pattern recognition and track reconstruction.
M om entum measurements in the MS are based on track segments form ed in at least two o f the three stations o f the M D T s and the CSCs.
The A T L A S trigger system had three levels during R un 1: the hardware-based Level-1 trigger and the two-stage H igh Level Trigger (H L T ), which com prises the Level-2 trigger and the Event Filter. A t Level-1, the m uon trigger searched for patterns o f hits satisfying dif
ferent transverse m om entum thresholds using the R P C s and T G C s. T he region-of-interest around these Level-1 hit patterns then served as a seed for the HLT m uon reconstruction, in which dedicated algorithms were used to incorporate inform ation from b oth the MS and the ID, achieving a position and m om entum resolution close to that provided by the offline m uon reconstruction.
4 D a t a s a m p l e a n d e v e n t s e l e c t i o n
This analysis uses the full sample o f pp collision data collected by the A T L A S detector in 2011 at a/s = 7 T eV and in 2012 at a/s = 8 TeV. A fter applying strict data quality criteria the integrated lum inosity is 4.9 fb -1 for the 2011 sample and 20.3 fb -1 for the 2012 sample.
A set o f dim uon trigger chains designed to select J / p ^ ^ - decays is used [14, 15].
It includes numerous triggers with different m uon pT thresholds and additional topological and invariant mass requirements. A n y dependence o f the triggers on the proper decay time cancels to a g o o d approxim ation in the ratio R(LBrop) introduced in section 2 because both the B ° ^ J / p K S and B ° ^ J / p K * ° decays are selected with the same set o f triggers.
For a given event, the prim ary vertex (P V ) o f the pp collision producing the B ° meson is determ ined using good-qu ality tracks reconstructed in the ID. T he average transverse position o f the pp collisions (the beam spot) is used in this determ ination as a constraint.
The beam spot is m onitored continuously and is reconstructed at regular intervals using several thousand interactions collected from many events. T he size o f the beam spot for the 2012 data is 15 ^m in the plane transverse to the beam direction. Due to the high LH C luminosity, each event containing a B ° meson is accom panied by a large number o f pile-up interactions, which occu r at various z positions along the beam line. These background interactions produce several P V candidates. T he selection o f the primary vertex corresponding to the B ° production point is described in section 5.
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The J / 0 candidates are reconstructed from pairs o f oppositely charged muons with Pt > 2.5 G eV and |n| < 2.4. Their ID tracks are fitted to a com m on vertex. T he x 2 o f the vertex fit must satisfy %2( J / ^ ) / N D F < 16, where N D F stands for the number o f degrees o f freedom and is equal to one in this case. T he mass o f the J / 0 candidate is required to be between 2.86 and 3.34 G eV.
The K S candidates are reconstructed from pairs o f oppositely charged particle tracks not used in the prim ary or pile-up vertex reconstruction. Each track is required to have at least one hit in either o f the tw o silicon detectors. T he transverse m om enta o f the tracks must be greater than 400 M eV and have |n| < 2.5. T h e pairs are fitted to a com m on vertex and kept if the x 2( K S)/N D F < 15 (N D F = 1), and the projection o f the distance between the J / 0 and K S vertices along the K S m om entum in the transverse plane is less than 44 cm . T he ratio o f this projection to its uncertainty must be greater than 2. T w o additional requirements are related to the point o f closest approach o f the K S trajectory to the J / 0 vertex in the x y plane. T he distance between this point and the position o f the J / 0 decay vertex in the x y plane is required to be less than 2 mm. T he difference in the z coordinates o f these tw o points must be less than 10 mm. These requirements help to reduce the com binatorial background. T he mass o f the K S candidate is required to be between 450 and 550 M eV.
The B ° ^ J / ^ ( p + p - ) Ks(n + n - ) candidates are constructed by refitting the four tracks o f the J / 0 and K S candidates. T he muon tracks are constrained to intersect in a secondary vertex and their invariant mass is constrained to the nominal J / 0 mass [5].
T he tw o pions from the Ks decay are constrained to originate from a tertiary vertex and their invariant mass is constrained to the nominal mass o f the Ks meson [5] . T h e com bined m om entum o f the refitted Ks decay tracks is required to point to the dim uon vertex. T he fit has N D F = 6. T he quality o f the cascade vertex fit is ensured by the requirement x 2(B ° ) — X 2( J / ^ ) < 25. Finally, the transverse m om entum o f the B ° is required to exceed 10 G eV.
For the selection o f B ° ^ J / 0 K *° candidates, a J / 0 candidate and tw o additional oppositely charged particles are com bined together. One particle is assigned the mass o f the charged kaon and the other the mass o f the charged pion. T he transverse m om entum o f the kaon is required to exceed 800 M eV and the transverse m om entum o f the pion must be greater than 400 M eV. B oth tracks must have |n| < 2.5. A vertex fit o f the four selected tracks is perform ed where the invariant mass o f the tw o m uon tracks is constrained to the nominal J / 0 mass. All four tracks are constrained to originate from the same vertex. T he fit has N D F = 6. T he quality o f the vertex fit is ensured by the requirement X 2( B ° ) — %2( J / ^ ) < 16. T he invariant mass o f the K n system is required to be between 850 and 950 M eV . This range is slightly shifted with respect to the world average value o f the K *° mass (895.81 ± 0.18 M eV ) [5] to provide a better suppression o f reflections from the B s ^ J / ^ 0 decay. T he transverse m om entum o f the K n pair is required to exceed 2 G eV and the transverse m om entum o f the B ° candidate is required to be greater than 10 G eV.
Particle identification o f charged hadrons is not used in this analysis. Therefore, each pair o f tracks is tested again with the assignments o f the kaon and pion swapped. If both assignments satisfy the above selection criteria, the com bination with the smaller deviation from the nominal K * ° mass is chosen. Section 6 gives more details about the number o f
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such events. In this analysis the final states J / p K * ° and J / p K * ° are not distinguished and the definition o f the B ° proper decay length discussed in section 5 is not sensitive to the assignment o f masses. Therefore, the m isidentification between pion and kaon has a limited im pact on the result o f this analysis.
None o f the presented selection criteria for the J / p K S and J / p K * ° final states are applied relative to the prim ary interaction point, thus avoiding a bias in the decay time distribution o f the B ° candidates. Different groups o f particles from the same event can be included in the J / p K S and J / p K * ° samples. In such cases, the additional candidates contribute to the com binatorial background and d o not im pact the signal yields.
For the measurement o f A r d , the ratio R(LBrop) built from the number o f the recon
structed B ° ^ J / p K S and B ° ^ J / p K * ° decays is used. In this ratio the dependence o f the reconstruction efficiencies o f the tw o final states on LBrop should be taken into ac
count. A large part o f this dependence, together with the associated uncertainties, cancels in R(LBrop) because the number o f final particles in b oth decay m odes is the same and the procedure to measure LBrop described in section 5 is similar in the tw o cases. Having similar selection criteria in the tw o channels also minimises the decay-tim e bias. Thus, the correction to the ratio R(LBrop) is expected to be small. Still, it cannot be eliminated com pletely because the hadronic tracks in the B ° ^ J / p K S decay originate in a displaced Ks ^ n + n - vertex, whereas all four tracks in the B ° ^ J / p K * ° decay originate in a single vertex. This difference between the tw o channels is the main source o f the exper
imental bias in the ratio R(LBrop), which can be evaluated only with M onte Carlo (M C ) simulation. Using simulated events, the ratio o f efficiencies to reconstruct B ° ^ J / p K S and B ° ^ J / p K * ° decays, R eff(LBrop), is obtained as a function o f LBrop.
T he M onte Carlo samples are produced by simulating the produ ction and decays o f B ° mesons using PYTHIA 6 .1 [16] for the 7 T eV M C samples and with PYTHIA 8 .1 [17] for the 8 T eV M C samples. In b oth cases, the underlying event, parton shower and hadronisation in the PYTHIA simulation are tuned with A T L A S data [18]. In all cases, the events are filtered at generator level by requiring tw o muons with |n| < 2.5 and transverse mom enta exceeding 2.5 G eV for the 7 T eV samples and 3.5 G eV for the 8 T eV samples. T he events are passed through a full simulation o f the detector using the A T L A S simulation [19] based on Geant4 [20, 21] and processed with the same reconstruction algorithms as used for the data. All samples are produced w ith M onte Carlo configurations adjusted to properly account for different conditions during the tw o years o f data-taking.
5 P r o p e r d e c a y l e n g t h o f t h e B 0 m e s o n
T he procedure adopted in this analysis to measure the proper decay length o f the B ° meson is explicitly designed to use the same input inform ation for b oth the B ° ^ J / p K S and B ° ^ J / p K * ° channels. T he aim o f this approach is to reduce the experim ental bias in the ratio R(LBrop). T he origin o f the B ° meson coincides with the prim ary vertex o f the pp collision. T he tracks from the B ° candidate are excluded in the measurement o f the P V position. T he position o f the B ° decay is determ ined by the J / p vertex, which is obtained
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Bin number 1 2 3 4 5 6 7 8 9 10 Lower edge [mm] —0.3 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 3.0 U pper edge [mm] 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 3.0 6.0
T able 1. Definition of the pr o p„ bins.
from the vertex fit o f the tw o muons. T he residual im pact o f the additional particles from the B 0 decays is evaluated using M C simulation and is found to be small.
The proper decay length o f the B 0 meson, BBrop, is determ ined in the x y plane o f the detector because o f the better precision com pared to the measurement in three dimensions, strengthened by the small transverse size o f the beam spot. A further advantage o f mea
suring BBrop in the x y plane is the reduced dependence on pile-up interactions. T he P V corresponding to the B 0 produ ction point is selected from all reconstructed P V s as follows.
For each P V candidate, the point o f closest approach o f the B 0 trajectory to the P V in the x y plane is determ ined and the difference 5z o f the z coordinates o f these tw o points is measured. T he candidate with the minimum absolute value o f 5z is selected as the B 0 pro
duction vertex. As with any other procedure o f P V selection, this m ethod is not ideal and occasionally a w rong P V is selected due to the resolution for the B 0 m om entum direction.
However, any selected P V should be close enough to the true B 0 produ ction vertex because numerically 5z ~ O (1 m m ) and b oth vertices are located on the beam line, which has a slope o f about 10-3 in b oth the x z and y z planes. T he transverse size o f the beam spot is about 15
^m in b oth the x and y directions. Therefore, the distance between the true vertex and the selected vertex in the x y plane is expected to be much less than the precision o f the decay length measurement, which is about 100 ^m . Thus, the measurement o f LBrop perform ed in the x y plane is not affected by a wrong selection o f the P V in a small fraction o f events.
For each reconstructed B 0 ^ J / 0 Ks or B 0 ^ J / 0 K *° candidate, LBrop is measured using the projection o f the B 0 decay length along the B 0 m om entum in the plane transverse to the beam axis:
_B ( x J/^ — x PV )pB + (y J/^ — y PV)pB
“ T B )
LBop = ' ---U l B # ---™ B .. (5.1)
Here x J/^ , y J /^ are the coordinates o f the J / 0 vertex; x PV, y PV are the coordinates o f the prim ary vertex; pB ,pB are the x and y com ponents o f the m om entum o f the B 0 meson and m Bo = 5279.61 M eV is its mass [5] . T he resolution o f LBrop is obtained from simulation and is parameterised by a double Gaussian function. It is found to be similar for the two decay m odes due to the applied procedure for the LBrop measurement. T he uncertainty in this resolution is propagated into the system atic uncertainty o f the A r d measurement as discussed in section 9 . T o obtain the proper decay length distribution, the range o f LBrop between —0.3 and 6 mm is divided into ten bins defined in table 1. T he selected bin size is much larger than the expected LBrop resolution, which is about 34 ^m . In each bin o f LBrop, the number o f B 0 ^ J / ^ Ks and B 0 ^ J / 0 K *0 decays are extracted from a binned log-likelihood fit to the corresponding mass distributions.
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In this fit, the mass distributions are m odelled by a sum o f functions describing the signal and background com ponents. For the B 0 ^ J / 0 K *0 channel, the signal function f j/'^k is defined as the sum o f tw o Gaussian functions. T he Gaussian functions are constrained to have the same mean. T he background function / J / ^K is defined using an exponential function with a second-order polynom ial as the exponent. T he fit is first applied to the total sample to determine the mean and standard deviations o f the two Gaussian functions and their relative fractions. For the fit in each LBrop bin, all parameters describing the signal, except the norm alisation o f / Js J/K , are fixed to the values obtained in the fit o f the total sample. It was verified in this analysis that fixing the parameters of the signal does not produce any bias in the result. T he parameters o f / J / ^K remain free.
T he signal function for the B 0 ^ J / ^ K s channel / J / ^Ks is defined as the sum o f tw o Gaussian functions. T he background is m odelled by the sum o f tw o functions:
/ j / PKs = /b + /Ba. T he com binatorial background function / is defined using an e x p o nential function with a second-order polynom ial as the exponent. T he second function, / B ° , accounts for the contribution from B°? ^ J /-0 K S decays and is defined as the sum o f tw o Gaussian functions. T he B°? ^ J /-0 K S contribution is visible in the mass distribution as a shoulder in the signal peak. Its fraction relative to the B 0 ^ J /-0 K S signal is ~ 1%.
T he signal Gaussian functions are constrained to have the same mean. T he relative frac
tions and standard deviations o f the B ° background Gaussian functions are parameterised to be the same as those o f the signal Gaussian functions. T he B ° background Gaussian functions are also constrained to have the same mean. T he mean o f the B ° background Gaussian functions is shifted relative to the mean o f the signal Gaussian functions by the difference between the nominal masses o f the B0 and B 0 mesons (87.34 M eV ) [5] . The fit is first applied to the total sample to determ ine the mean and standard deviations o f the signal Gaussian functions and their relative fractions. For the fit in each L^rop bin, all parameters describing the signal, except the norm alisation o f / J / ^K s, are fixed to the values obtained in the fit o f the total sample. It was verified in this analysis that fixing the parameters o f the signal does not produce any bias in the result. T he parameters o f / ^ are also fixed, except for the normalisation. All parameters o f /£ remain free.
T he separation o f the B 0 ^ J /-0 K S and B ° ^ J /-0 K S contributions is im portant for the A r d measurement because the mean lifetimes o f the B 0 and B ° mesons decaying to this C P eigenstate are different. On the contrary, the separation o f B 0 ^ J / 0 K *0 and B ° ^ J / 0 K *0 decays is not necessary because the lifetimes o f the B 0 and B ° mesons decaying to this final state are equal to within 1% [5, 9] . Thus, the small (~ 1 % ) contribution o f the B ° ^ J / 0 K *0 decay does not have an im pact on the A r ^ measurement.
T he fit ranges o f the J / ^ K S and J / 0 K *0 mass distributions are selected such that the background under the B 0 signal is sm ooth. T he mass distribution m ( J / ^ K S) contains a contribution from partially reconstructed B ^ J / ^ K Sn decays. This contribution has a threshold at m ( J / ^ K S) ~ 5130 M eV . For this reason, the fit range 5160 < m ( J / ^ K S) <
5600 M eV is selected. T he corresponding contribution o f B ^ J / 0 K *0n decays is smaller.
Therefore, the lower limit o f the fit range o f m ( J / 0 K * 0) is selected at 5000 M eV . The im pact o f the selection o f the fit range on the value o f A r d is included in the system atic uncertainty.
J H E P 0 6 ( 2 0 1 6 ) 0 8 1
F igu re 1. The invariant mass distributions for (a) B 0 ^ J /p K S candidates and (b) B 0 ^ J /p K * 0 candidates for the 2012 data sample for 0.0 < LBrop < 0.3 mm. The full line shows the result of the fit to the function described in the text. The dashed line shows the combinatorial background contribution. The filled area in figure (a) shows the peaking background contribution from the B ° ^ J / p K S decay. The lower frame of each figure shows the difference between each data point and the fit at that point divided by the statistical uncertainty of the data point.
T he total number o f signal B ° ^ J /p K S decays obtained from the fit is 28170 ± 250 in the 2011 data set and 110 830 ± 520 in the 2012 data set. For B ° ^ J / p K * ° decays the corresponding numbers are 129 200 ± 900 in the 2011 data set and 555 800 ± 1900 in the 2012 data set. Figure 1 shows the fitted mass distribution o f B ° ^ J / p K S candidates and B ° ^ J / p K * ° candidates for 0.0 < < 0.3 mm.
T he ratio o f the numbers o f B ° candidates in the tw o channels com puted in each bin i gives the experim ental ratio R j,uncor defined as:
= w.j /p k ) (5 2)
N i( J / p K * ° ) ' ( )
Here N ( J / p K S ) and N J / p K * ° ) are the numbers o f events in a given bin i. This ratio has to be corrected by the ratio o f the reconstruction efficiencies in the tw o channels as discussed in section 7.
6 P r o d u c t io n a s y m m e t r y o f th e B 0 m e s o n
T he produ ction asym m etry A p o f the B ° meson can be obtained from the tim e-dependent charge asym m etry o f the flavour-specific B ° ^ J / p K * ° decay. If the initial flavour o f the B ° meson is not determ ined, it follows from eqs. ( 2.11) , (2.12) , and ( 2.16) that the tim e-dependent rate o f the decay B ° ^ J / p K * ° is equal to:
r [t, J / ^ K *0] a e rdt cosh — rd - + A P c o s (A m dt) , (6.1)
J H E P 0 6 ( 2 0 1 6 ) 0 8 1
while the tim e-dependent rate o f the decay B 0 ^ J / 0 K *0 is equal to:
r [t, J / 0 K *0] a e- r d * cosh — A P c o s (A m dt) , (6.2)
C P violation in m ixing is predicted to be small in the SM and is om itted from these expressions.
T he terms proportional to A p in eqs. (6.1) and (6.2) reflect the oscillating com ponent o f the B 0 ^ J / 0 K *0 decay. T he corresponding charge asym m etry due to B 0 oscillations in bin i o f LBrop, A i,osc, is defined as:
/ L T (/0 00 G (L £ o p — ct, J / ^ K * 0)(r\t, J / ^ K * 0] — r [t, J /^ K * ° ] ) d t ) dLBrop
A i,OSC = T max ( “ ) . (6A )
& in ( / 00 G(LBrop — ct, J / ^ K *0)( r [ t , J / ^ K *0] + r [t, J / ^ K *0])d t) dLBrop
i
Here G (L ^ rop — ct, J / 0 K *0) is the detector resolution o f LBrop for the B 0 ^ J / 0 K *0 channel. T he values o f the lower and upper edges o f bin i, L™in and L “ ax, are given in table 1. Using eqs. ( 6.1) and ( 6.2) , A j,osc can be presented as:
/pmm ( /0 ° G (L B op — ct, J / 0 K *0)e - r d * co s(A m d t)d t) d L BTOp
A i,oSC = A P 2 max f ~ \ . (6A )
/ Llin ( / 0° G(LBrop — ct, J / ^ K * 0)e - r d* cosh ^ d t ) dL gop
In addition to B 0 oscillations, the asym m etry in the number o f J / ^ K * 0 and J / ^ K * 0 events is also caused by a detector-related asym m etry A det due to differences in the recon
struction o f positive and negative particles. T he main source o f A det is the difference in the interaction cross-section o f charged kaons with the detector material, which for m om enta below 1 0 G e V is significantly larger for negative kaons [5] . Therefore, the observed number o f K * 0 ^ K + n - decays is larger than that o f K *0 ^ K - n + , resulting in a positive value o f the detector asym m etry A det. This effect is independent o f the B 0 decay time.
The values o f A j,osc and A det are diluted by misidentification o f the kaon and pion in the B 0 ^ J / 0 K *0 decay. T he observed number o f J / 0 K *0 events, N ( J / 0 K *0), includes genuine B 0 ^ J / 0 K *0 and some B 0 ^ J / 0 K *0 decays. T he latter decay contributes because o f a wrong assignment o f the kaon and pion masses to the tw o reconstructed charged particles, so that the decay K * 0 ^ K + n - is identified as a K * 0 ^ K - n + . The mistag fraction W quantifies this w rong contribution to the J / 0 K *0 sample. It is defined as the fraction o f true B 0 ^ J / 0 K *0 decays in N ( J / 0 K *0). T he mistag fraction does not depend on the B 0 decay tim e and is determ ined in simulation. T he obtained value is:
W = 0.12 ± 0.02. (6.5)
T he uncertainty o f W is system atic. It takes into account possible variations o f the M C simulation which describes B 0 production and decay. T he simulation confirms that the mistag fraction is the same for B 0 ^ J / 0 K *0 and B 0 ^ J / 0 K *0 decays within the statistical uncertainty o f 0.4% determ ined by the number o f M C events. T he system atic uncertainty o f the difference o f the mistag fraction o f the B 0 ^ J / 0 K *0 and B 0 ^ J / 0 K *0
J H E P 0 6 ( 2 0 1 6 ) 0 8 1
decays cancels to large extent. Therefore, the same value o f W applies to candidates classified as J / ^ K *0.
Using the above inform ation, the expected charge asym m etry in bin i o f LBrop, A gexp, can be expressed as:
A i,exp = (A det + A i,osc) ( 1 — 2 W ) . (6 .6) Here the factor 1 — 2 W takes into account the contribution o f w rongly identified B 0 decays, which is the same for both A det and A i,osc. T he second-order terms proportional to A detA P are o f the order o f 10-4 and are neglected in this expression.
T he observed charge asymmetry, A i,obs, is defined as:
_ N i(J / ^ K *0) — N i(J / ip K *0) N i(J / ^ K *0) + N i(J / ^ K *0) '
A i,obs = , 7 ,-, , , Ts*0\ , r t i i „m . (6A )
Figure 2 shows the asym m etry A obs as a function o f LBrop for the 2011 and 2012 samples com bined together. T he result o f the fit to eq. ( 6.6) is superim posed. T he asym m etry A P is obtained from a x 2 minimisation:
2r 4 4 1 (A i,obs — A i,exp)2 „x
X [A det, A P] 2--- . (6A )
i=2 Gi
The free parameters in the fit are Adet and A p. T he values ai are the statistical uncertainties o f A i obs. T he fit has a x 2 o f 6.50 per seven degrees o f freedom . T he first bin o f LBrop corresponds to a negative decay length due to the detector resolution. It is not included in this sum as it is affected more than the other data points by system atic uncertainties.
Ignoring it has a negligible im pact on the uncertainty o f this measurement. T he fit yields the following values for the asymmetries:
Adet = (+ 1 .3 3 ± 0.24 ± 0.30) x 10- 2 . (6.9) A p = (+ 0 .2 5 ± 0.48 ± 0.05) x 10- 2 . (6.10) In these values the first uncertainty o f AP and Adet is statistical and the second is due to the uncertainties in the mistag fraction and in the deviations o f |q/p| from unity [5] (see eq. ( 2.2) ). T he system atic uncertainty o f A det also contains a contribution from the possible difference between the mistag fractions o f the B 0 ^ J / 0 K *0 and B 0 ^ J / ^ K *0 decays.
T he value o f Adet is consistent with results from simulation o f interactions in the detector.
This measurement o f the B 0 produ ction asym m etry A p for P t ( B 0) > 10 G eV and |n(B0)| <
2.5 is consistent with zero. It is also consistent with the L H C b result A P = ( —0.36 ± 0.76 ± 0.28) x 10-2 [12] obtained for 4 < pT ( B 0) < 30 G eV and 2.5 < n (B 0) < 4.0. T he measured value o f A P given in eq. ( 6.10) is used for the extraction o f the w idth difference A r d.
7 R a t i o o f e f f i c i e n c i e s
in each LBrop bin i. It is defined as
T he ratio R i,uncor given by eq. ( 5.2) is corrected by the ratio o f efficiencies R i,eff com puted
R _ £ i(B ° ^ J / j,K s ) ( 7 1 )
i,eff e i ( B 0 ^ J / ^ K *0) . ( . )
J H E P 0 6 ( 2 0 1 6 ) 0 8 1
F igu re 2. Observed charge asymmetry A obs in B 0 ^ J /p K * ° decays measured as a function of the proper decay length of the B 0 meson (LBrop). The line shows the asymmetry A exp obtained from fitting eq. (6.6) to the data. The first point corresponding to negative proper decay length is not used in the fit. The error bands correspond to the combination of uncertainties obtained by the fit for the production asymmetry A P and the detector asymmetry A det.
Here £ i(B ° ^ J / p K S) and £ i(B ° ^ J / p K * ° ) are the efficiencies to reconstruct B ° ^ J / p K S and B ° ^ J / p K * ° decays, respectively, in bin i. This ratio is determined using M C simulation. T o obtain reliable values for this efficiency ratio, the kinematic properties o f the simulated B ° meson and the accom panying particles must be consistent with those in data. T he com parison o f several such properties, which can produce a sizeable im pact on R i,eff, reveal some differences between data and simulation. T hose differences are corrected for by an appropriate re-weighting o f the simulated events.
The properties taken into account include the transverse m om entum and pseudorapid
ity o f the B ° meson and the average number o f pile-up events. T he ratio o f the distributions o f each specified variable in data and in simulation defines the corresponding weight. The resulting weight applied to the M C events is defined as the product o f these three weights.
The norm alisation o f R yeff after the re-weighting procedure is arbitrary since only the deviation o f R yeff from their average value can im pact the measurement o f A r d . This deviation is found to not exceed 5% for proper decay lengths up to 2 mm. Such a stability o f R yeff is a consequence o f the chosen measurement procedure. This stability helps to reduce the system atic uncertainty o f A r d due to the uncertainty o f the R yeff value.
J H E P 0 6 ( 2 0 1 6 ) 0 8 1
8 F i t o f A r d
T he obtained values o f R i;eff are used to correct the observed ratio R i)Uncor given by eq. ( 5.2) . T he resulting ratio R i)Cor is defined as:
D _ R i,unCor fo
R i,cor — D • (8 .1)
R i,eff
This ratio is shown in figure 3 . It is used to obtain A r d/ r d by the following procedure.
For each LBrop bin i defined in table 1, the expected numbers o f events in the J / 0 Ks and J / 0 K *0 channels are com puted as:
., ąmax
N i [ A r d / r d, J / ^ K s ] — C 1 I r[L B rop,J/^K s]dL B rop, (8.2) j ąmin
., ąmax
N i[ A r d/ r d, J / ^ K * 0] — C W * r [L B r o p ,J /^ K * 0]d+Brop. (8.3) Jl mini
T he integration limits L “ in and L {max for each bin i are given by the lower and upper bin edges in table 1. C i and C 2 are arbitrary norm alisation coefficients. T he expressions for r[LB rop, J / 0 Ks] and r[LB rop, J / ^ K * 0] are given by eqs. ( 2.22) and (2.23) , respectively.
T he sensitivity to A r d com es from r[LB rop, J / ^ K S] (see eq. (2.17) ) while r[LB rop, J / ^ K * 0]
provides the normalisation, which helps to reduce the system atic uncertainties.
T he expected ratio o f the decay rates in the tw o channels in each LBrop bin is:
R A T 1 [A r d / r d V / W O ]
R *’e x p [ A r j/r d ] — N ,[ A r d /r d , j/ ^k *0]. (8 4 ) The relative w idth difference A r ^ / r ^ is obtained from a x 2 minimisation:
x 2[ A r d/ r d] — V (R j’cor - R i,ex2p [ A r d /r d ] ) 2 . (8.5) j .
i=2 j
The values j j are the statistical uncertainties o f R i)Cor. In the sum, the first bin o f LBrop is not included as it corresponds to a negative decay length.
The free parameters in this m inimisation are the overall norm alisation and A r ^ /r ^ . All other parameters describing the B 0 meson are fixed to their world average values. T he fit is perform ed separately for the 2011 and 2012 samples because the system atic uncertainties for the tw o data samples are different. T he result o f the fit is shown in figure 3 . T he x 2 o f the fit is 4.34 (N D F — 7) in the 2011 data set and 2.81 (N D F — 7) in the 2012 data set.
The fit yields
A r d/ r d — ( - 2 . 8 ± 2.2 (stat.) ± 1.5 (M C stat.)) x 10-2 (2011), (8.6) A r d/ r d — (+ 0 .8 ± 1.3 (stat.) ± 0.5 (M C stat.)) x 10-2 (2012). (8.7)
Here the uncertainties due to the data and M C statistics are given separately. T he sys
tem atic uncertainties are discussed in section 9 .
J H E P 0 6 ( 2 0 1 6 ) 0 8 1
F igu re 3. Efficiency-corrected ratio of the observed decay length distributions, R cor(LBrop) for (a)
a/ s = 7TeV and (b) a/s = 8TeV data sets. The normalisation of the two data sets is arbitrary.
The full line shows the fit of R cor(LBrop) to R ^ p given by eq. (8.4) . The error bands correspond to uncertainties in A r d/ r d determined by the fit.
9 S y s t e m a t ic u n c e r ta in tie s
The relative B 0 w idth difference is extracted from the ratio o f the L^rop distributions in the tw o B 0 decay modes, which are obtained using a similar procedure, the same type o f inform ation and in the same prod u ction environm ent. Therefore, the im pact o f many system atic uncertainties, such as the trigger selection, decay-tim e resolution or B 0 produc
tion properties, is negligible. However, some differences between the B 0 ^ J / 0 Ks and B 0 ^ J / 0 K *° channels cannot be eliminated and the inaccuracy o f their simulation results in system atic uncertainties, which are estim ated in this section.
The mean proper decay length o f the Ks meson is 26.8 mm. Since the p t o f the Ks meson can be high, some K s mesons decay outside the inner detector and are lost. The probability o f losing a Ks meson is higher for large B 0 decay tim e due to the reduction o f the fiducial volum e o f the Ks decay. Thus, the displaced vertex o f the Ks decay and the absence o f such a vertex in the K * 0 ^ K + n - decay results in a decay-tim e dependence o f R eff defined in eq. ( 7.1) . A pplying the correction given by eq. ( 8.1) to R uncor takes into account this dependence.
The test o f the simulated Ks reconstruction is perform ed by com paring the distribution o f the Ks decay length and the Ks pseudorapidity in data and simulation. This dedicated study shows that there is a residual difference between data and M C simulation in the distributions o f the laboratory decay length o f reconstructed Ks mesons projected along the Ks m om entum in the transverse plane, L xy( Ks). It is caused by the remaining difference between the Ks m om entum distributions in data and M C simulation. A fter applying an additional weight to the M onte Carlo events to correct for this difference a change in the value o f A r d/ r d o f 5 ( A r d/ r d) = -0 .2 1 x 10-2 is obtained for the 2011 data set and 5 ( A r d/ r d) = - 0 .1 6 x 10-2 for the 2012 data set. This difference is taken as the system atic uncertainty due to m odelling o f the L xy( K ) dependence o f the K reconstruction.
J H E P 0 6 ( 2 0 1 6 ) 0 8 1
The same procedure is applied for the pseudorapidity distribution o f the K s meson, n (K S). T he system atic uncertainty due to m odelling o f the |n(KS)| dependence o f the K s reconstruction is estim ated by re-weighting the M C events to make the |n(KS)| distribution the same as in data. T he observed changes are 5 ( A r d/ r d) = + 0 .1 4 x 10-2 for the 2011 data set and 5 ( A r d/ r d) = —0.01 x 10-2 for the 2012 data set.
The system atic uncertainty due to the choices made in the m odel used to fit the mass distributions can be estim ated by considering different variations o f the fit m odel. The range over which the B 0 ^ J / ^ K s and B 0 ^ J / 0 K *0 mass fits are applied is varied and the measurement o f A r d/ r d is repeated for each variation. T he system atic uncertainty is estim ated by taking the difference between the values o f A r d/ r d obtained from the default fit and each o f the varied fits. Variations 5 ( A r d/ r d) = —0.47 x 10-2 and —0.30 x 10-2 are obtained for the 2011 data set in the J / ^ K S and J / 0 K *0 channels, respectively. The changes for the 2012 data set are 5 ( A r d/ r d) = —0.59 x 10-2 and —0.15 x 10-2 in the J / ^ K S and J / 0 K *0 channels, respectively. These values are included as the system atic uncertainty from this source.
Additionally, the background function is changed from an exponential to a fourth- order polynom ial and the system atic uncertainty due to the choice o f background function is estim ated from the difference between the value o f A r d/ r d from the default fit and the value from the fit using the polynom ial background function. A change ^ A r ^ / r ^ ) =
—0.16 x 10-2 is obtained for the 2011 data set. T he change for the 2012 data set is ć ( A r d/ r d) = + 0 .0 9 x 10- 2 .
In the fit o f the number o f B 0 ^ J / ^ Ks decays the contribution from the B ° ^ J / ^ K S is a free param eter o f the fit. As a system atic uncertainty cross-check, the ratio o f the yields o f these tw o decays is fixed to be the same as that measured by the LH C b C ollaboration [22]. T he resulting change in the A r d/ r d value is 5 ( A r d/ r d) = —0.11 x 10-2 for the 2011 data set and 5 ( A r d/ r d) = + 0 .0 8 x 10-2 for the 2012 data set and is included as an additional source o f system atic uncertainty.
T he system atic uncertainty due to the resolution o f LBrop is also considered. The average decay length resolution is 35 ^m for B ° ^ J / ^ K S and 33 ^m for B 0 ^ J / 0 K *0.
In this analysis, separate resolution functions are used for the tw o channels. T o test the sensitivity to the resolution, the measurement o f A r d/ r d is repeated by using the resolution o f J / 0 K *0 for b oth channels. A change in the value o f A r d/ r d o f 5 ( A r d/ r d) = —0.29 x 10-2 is obtained and is used as the system atic uncertainty from this source. It is found to be the same for the 2011 and 2012 data sets.
A toy M C sample is em ployed to identify any possible bias in the fitting procedure. In this toy M C sample, the expected number o f J / ^ K S and J / 0 K *0 candidates in each bin o f LBrop is determ ined according to the analytic functions given by eqs. ( 2.17) and ( 2.18) , respectively, and a value o f A r d/ r d = 0.42 x 10-2 corresponding to the SM expectation [1].
Using these expected numbers o f candidates as the mean values, the number o f candidates in b oth channels is random ly generated in each LBrop bin with an uncertainty corresponding to that obtained in data. T he ratio o f the obtained distributions is then fitted using the m ethod described in section 8. T he procedure is repeated 10 000 times giving a bias in the mean fitted value 5 ( A r d/ r d) = + 0 .0 7 x 10- 2 . This value is used as the system atic
J H E P 0 6 ( 2 0 1 6 ) 0 8 1
Source <5(Ard/ r d), 2011 <5(Ard/ r d), 2012
K S decay length 0.21 x 10-2 0.16 x 10-2
K S pseudorapidity 0.14 x 10-2 0.01 x 10- 2
B ° ^ J / ^ K S mass range 0.47 x 10-2 0.59 x 10-2 B ° ^ J / 0 K *° mass range 0.30 x 10-2 0.15 x 10- 2 Background description 0.16 x 10-2 0.09 x 10-2 B ° ^ J / ^ K S contribution 0.11 x 10-2 0.08 x 10- 2
resolution 0.29 x 10-2 0.29 x 10-2
Fit bias (T oy M C ) 0.07 x 10-2 0.07 x 10- 2 B ° production asym m etry 0.01 x 10-2 0.01 x 10-2
M C sample 1.54 x 10-2 0.45 x 10-2
Total uncertainty 1.69 x 10-2 0.84 x 10" 2
T able 2. Sources of systematic uncertainty in the A r d/ r d measurement and their values for the 2011 and 2012 data sets.
uncertainty due to the fitting procedure and it is taken to be the same for the 2011 and 2012 data sets.
The im pact o f the uncertainty o f the B ° production asym m etry is ^ A r ^ / r ^ ) = 0.01 x 10-2 for both the 2011 and 2012 data sets.
The system atic uncertainty from the number o f events in the M C samples corresponds to an uncertainty o f 5 ( A r d/ r d) = 1.54 x 10-2 for the 2011 data set and 5 ( A r d/ r d) = 0.45 x 10-2 for the 2012 data set.
Table 2 gives a summary o f the estimated system atic uncertainties. All o f the quantified system atic uncertainties are symmetrized.
In addition to the estim ate o f the system atic uncertainty, several cross-checks are per
form ed. Some o f the selection cuts described in section 6 are m odified and the corresponding changes in the A r d/ r d value are assessed. In particular, the transverse m om enta o f the charged pions from the Ks decay and the charged pion from the K * ° decay are required to be greater than 500 M eV , rather than 400 M eV . A lso, the transverse m om entum o f the charged kaon from the K *° is required to be greater than 1 G eV , rather than 800 M eV . A d ditionally, the transverse m om entum o f the B ° meson is required to be less than 60 G eV.
In all cases, the change o f the measured value o f A r d is consistent with fluctuations due to the reduced number o f events.
Furthermore, a number o f consistency checks related to the description o f the exper
imental conditions in simulation are perform ed. M ost notably, the M C description o f the spread o f the z position o f the prim ary vertex, the angular distributions o f the B ° decay products, and the trigger rates are studied in detail. In all cases, the residual differences between data and M C simulation do not im pact the measured value o f A r d.
J H E P 0 6 ( 2 0 1 6 ) 0 8 1
1 0 R e s u l t s
Using the measurements o f A r d/ r d given in eqs. ( 8.6) and (8.7) and the study o f system atic uncertainties presented in section 9 , the following measurements are obtained:
A r d/ r d = ( —2.8 ± 2.2 (stat.) ± 1.7 (syst.)) x 10-2 (2011), A r d/ r d = (+ 0 .8 ± 1.3 (stat.) ± 0.8 (syst.)) x 10-2 (2012).
In the com bination o f these measurements, the correlations o f different sources o f system atic uncertainty between the tw o years are taken into account. T he system atic uncertainties due to the background description and the size o f the M C samples are assumed to be uncorrelated. All other sources o f system atic uncertainty are taken to be fully correlated.
The com bination is done using the x 2 m ethod. T he x 2 function includes the correlation terms o f the different com ponents o f the uncertainty as specified above. T he com bined result for the data collected by the A T L A S experim ent in Run 1 is:
A r d/ r d = ( —0.1 ± 1.1 (stat.) ± 0.9 (syst.)) x 10- 2 .
It is currently the m ost precise single measurement o f this quantity. It agrees well with the SM prediction [1] and is consistent with other measurements o f this quantity [2- 4] . It also agrees with the indirect measurement by the D 0 C ollaboration [23] .
11 C o n c l u s i o n s
The measurement o f the relative w idth difference A r ^ / r ^ o f the B 0- B 0 system is perform ed using the data collected by the A T L A S experim ent at the LH C in pp collisions at a/s = 7 T e V and yfs = 8 T e V and corresponding to an integrated lum inosity o f 25.2 f b - 1 . The value o f A r d/ r d is obtained by com paring the decay tim e distributions o f B 0 ^ J / ^ K S and B 0 ^ J / 0 K *0(892) decays. T he result is
A r d/ r d = ( —0.1 ± 1.1 (stat.) ± 0.9 (syst.)) x 10- 2 .
Currently, this is the most precise single measurement o f A r d/ r d. It agrees with the Standard M odel prediction and the measurements by other experiments.
The produ ction asym m etry o f the B 0 meson with p x ( B 0) > 1 0 G e V and |n(B0)| < 2.5 is found to be
A p ( B 0) = (+ 0 .2 5 ± 0.48 ± 0.05) x 10- 2 .
The value o f A p ( B 0) is consistent w ith the measurement o f the L H C b C ollaboration per
form ed in the 2.5 < n (B 0) < 4.0 and 4 < pT ( B 0) < 30 G eV range.
A c k n o w l e d g m e n t s
W e thank C E R N for the very successful operation o f the LH C, as well as the support staff from our institutions w ithout whom A T L A S could not be operated efficiently.
J H E P 0 6 ( 2 0 1 6 ) 0 8 1
W e acknowledge the support o f A N P C y T , Argentina; YerPhI, Arm enia; A R C , A us
tralia; B M W F W and F W F , Austria; A N A S, Azerbaijan; SSTC, Belarus; C N P q and FAPESP, Brazil; N SERC, N R C and CFI, Canada; C E R N ; C O N IC Y T , Chile; C A S, M O S T and NSFC, China; C O L C IE N C IA S , Colom bia; M S M T C R , M P O C R and V SC CR, Czech R epublic; D N R F and D N SR C , Denmark; IN 2P3-C N R S, C E A -D S M /IR F U , France;
GN SF, Georgia; B M B F , H G F, and M P G , Germany; G SR T, Greece; R G C , H ong K ong SA R , China; ISF, I-C O R E and B enoziyo Center, Israel; INFN, Italy; M E X T and JSPS, Japan; C N R ST , M orocco; F O M and N W O , Netherlands; R C N , Norway; M N iS W and NCN, Poland; F C T , Portugal; M N E /IF A , Rom ania; M ES o f Russia and N R C KI, Russian Fed
eration; JINR; M E ST D , Serbia; M SSR, Slovakia; A R R S and M IZS, Slovenia; D S T /N R F , South Africa; M IN E C O , Spain; SRC and W allenberg Foundation, Sweden; SERI, SNSF and Cantons o f Bern and Geneva, Switzerland; M O S T , Taiwan; T A E K , Turkey; STFC, United K ingdom ; D O E and NSF, United States o f Am erica. In addition, individual groups and members have received support from B C K D F , the Canada Council, C A N A R IE , C R C , C om pute Canada, F Q R N T , and the O ntario Innovation Trust, Canada; E P L A N E T , E R C , F P 7, H orizon 2020 and Marie Sklodowska-Curie Actions, European Union; Investissements d ’Avenir L abex and Idex, A N R , R egion Auvergne and Fondation Partager le Savoir, France;
D F G and A vH Foundation, Germany; Herakleitos, Thales and Aristeia program m es co financed by E U -E SF and the Greek N SRF; BSF, G IF and Minerva, Israel; B R F , Norway;
Generalitat de Catalunya, Generalitat Valenciana, Spain; the R oyal Society and Lever- hulme Trust, United K ingdom .
The crucial com puting support from all W L C G partners is acknowledged gratefully, in particular from C E R N and the A T L A S Tier-1 facilities at T R IU M F (C anada), N D G F (Denmark, Norway, Sweden), C C -IN 2P3 (France), K I T /G r id K A (G erm any), IN F N -C N A F (Italy), N L -T 1 (Netherlands), P IC (Spain), A S G C (Taiw an), R A L (U .K .) and BNL (U .S .A .) and in the Tier-2 facilities worldwide.
O p en A ccess. This article is distributed under the terms o f the Creative Com m ons A ttribution License ( C C -B Y 4.0) , which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
R e f e r e n c e s
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