Results from Belle on sin 2φ1

PROCEEDINGS SUPPLEMENTS ELSEVIER

Nuclear

Physics

B (Proc.

Suppl.)

99B (2001)

148-156

Results from Belle on sin 24, Y. Sakai” a High Energy

Research

Organization

(KEK),

Tsukuba,

Japan

A measurement of the Cl’ violation parameter sin241 at the KEKB asymmetric e+e- collider is reported. A data sample of 6.2 fb-’ recorded at the T(45) resonance with the Belle detector is used. In this analysis, we select B” meson decay modes to the JI+Ks, @‘KS, xclKs and J/$KL CP eigenstates. The flavor of the other B meson is identified using high and medium momentum leptons, K’, or a slow pion. The proper-time difference between the two B mesons are obtained from the vertices measured with a silicon vertex detector, and sin241 is obtained from a fit to the proper-time difference distribution. The current preliminary result is sin 241 = 0.45t0,$(stat) ‘t:Xi(sys).

1.

INTRODUCTION

The main goal of the Belle experiment

Since its first observation system[l], major

CP violation

in the neutral

has remained

unsolved issues in our understanding

particle

physics.

The

B-meson

Kaon

one of the

system

of the provides

opportunities to observe indirect- and direct-CP violations, and also CP (and CPT) violations in the BOB0 mixing matrix.

In the Standard

as proposed by Kobayashi violation is the consequence the quark mixing

(CKM)

Model,

and Maskawa[2], CP of complex phases in matrix,

sure these unitarity

CP

angles triangle

violation

T(4S)

together

and confirm

or discover

resonance,

the

is to mea-

with the sides of the the SM scheme for

new physics.

interference

At the

between

the

amplitudes for two different ways that a neutral B meson can decay into a CP eigenstate f,

f)

A(B” + dependent

and A(B” + B” + CP asymmetry

R(B” + AcP(A~)

=

R(B” +

f; f;

f),

gives a time-

At) - R(B”

-+

At) + R(B”

+

f; f;

At) At)

= qcp sin 2r$cp sin(AmAt), ({;

;;

g)

(I)

where the nontrivial complex phases are conventionally assigned to the furthest off-diagonal elements &, and Vtd. Sanda and Carter pointed out that rather large CP violating asymmetries could appear in certain decay modes of the B mesons [3].

As is well known,

matrix complex

the unitarity

gives the following triangle numbers

VtdVt; + Vcdv;

&,

of the KM

relation

for the

and Vtd:

is the CP

eigenvalue

between

states

=

and At

the proper

time

(2) triangle

are de-

f,

of

Am is the

the two B” mass eigen-

tl - t2, where for the

decays

tl

and t2 are

of B -+

f

and

the other B, respectively. The angle 4cp is the phase difference between the two interfering amplitudes,

which

of the unitarity

is directly triangle.

related

to the angles

If the J/$Ks

or other

decay modes that arise from b + CESor ci?d transitions are chosen as the CP eigenstate equal to 41. At the T(4S),

+ vudV;b = 0.

The three angles of this unitarity fined as:

where qcp

mass difference

(4)

by Eq.

(4) vanishes

f, $cp is

the asymmetry

in the time integrated

this is the motivation for the asymmetric energies in the B factories.

given rate; beam

Experimentally, the CP violation is observed as an asymmetry in the distribution of the proper time difference of two B decays produced in pair by the decay of T(4S), one to the CP eigenstate 0920-5632/01/$ - see front matter 0 2001 Elsevier Science B.V. All rights reserved. PII SO920-5632(01)01373-l

I! SakaiINuclear

Physics B (Proc. Suppl.) 99B (2001) 148-156

and another to any final state whose flavor is identified. Leptons and K* play an essential role in the flavor tagging, and hence the detector is required to have good capabilities for identifying leptons and K*. 2. KEKB

AND

BELLE

EXPERIMENT

KEKB[4] is an asymmetric e+e- collider that is 3 km in circumference and consists of 8 GeV e- and 3.5 GeV e+ storage rings and an injection linear accelerator. KEKB has one interaction point where the e+ and e- beams collide with a finite crossing angle of 22 mrad. The collider has been operated with peak beam currents 700 mA(e+) and 500 mA(e-) with a peak luminosity of 2.04~10~~/crn~/sec. Due to the energy asymmetry, the T’(4S) and its daughter B mesons are produced at ,@y =0.425 in the laboratory frame. The average distance between the two decay vertices of the B mesons is approximately 200 pm. The Belle detector[5] is a general purpose large solid angle magnetic spectrometer surrounding the interaction point. Charged particle tracking is done by the central drift chamber (CDC)[6], which is a smallcell cylindrical drift chamber consisting of 50 layers of anode wires, 18 of which have wires that are oriented at small angles to provide three-dimensional reconstruction of charged particle trajectories. The CDC is operated with a He(50%)+CsHs(50%) mixture to ensure a good momentum resolution, especially for low momentum particles. The vertex measurement is done by a silicon vertex detector (SVD)[7]. It consists of three layers of double-sided silicon strip detectors (DSSD) arranged in barrel and covers 86% of solid angle. The three layers are at radii of 3.0,4.5 and 6.0 cm, respectively. The strip pitch is 25 pm for r4 and 84 pm for z strips. The impact parameter resolutions are measured as functions of momentum p (GeV/c) to be o,,=21@69/(ppsin3/28) pm and a,=41@48/(pflsin ‘I2 0) pm, where t3is the polar angle with respect to the beam axis. The beampipe is a double-wall beryllium cylinder of 2.3 cm radius and 1 mm thick.

149

The electromagnetic calorimetry is provided by a CsI(T1) crystal calorimeter (ECL)[8] that consists of 8736 crystal blocks of 16.1 radiation lengths (Xe) thick. namely Charged particle identification, r&/K* separation, is done with three detectors; energy loss (dE/dz) measurement in the CDC, time-of-flight counters (TOF) [lo] and aerogel Cherenkov counters (ACC)[9]. The CDC provides a resolution of cr(dE/&c)= 6.0%(7.8%) The TOF for Bhabha and p-pairs (pions). consists of 128 plastic scintillators viewed by fine-mesh photomultipliers on both ends. The time resolution is 95 psec (rms), which provides n&/K& separation up to 1.2 GeV. The ACC consists of 1188 aerogel blocks with refractive indices between 1.01 and 1.03 depending on the polar angle. Fine-mesh photomultipliers are also used for them. Using these information, P(K/r) = L(K)/(L(K) + L(T)), a likelihood for a particle to be K* is calculated. The K* efficiency is about 90% and the rr fake rate is 6% with P(K/r) > 0.6. Electron identification is based on a combination of dE/dx measurements in the CDC, the response of the ACC, and the position, shape and total energy (i.e. E/p) of its associated CsI shower. The electron identification efficiency is is more than 90% for pl,,b > 1.0 GeV and the hadron misidentification probability is below 0.5%. All the detectors mentioned above are inside the 1.7 m radius superconducting solenoid. The outermost detector is for the measurement of p* and consists of 14 layers of and KL (KLM)[ll], iron (4.7 cm thick) absorbers alternating with resistive plate counters @PC). The overall muon identification efficiency is greater than 90% for plab > 1 GeV tracks detected in the inner tracker. The corresponding pion misidentification probability is less than 2%. The total integrated luminosity of 6.8 fb-l has been accumulated during the first running period between Oct. 1999 and July 2000; 6.2 fb-l and 0.6 fb-’ are on the T(4S) and off-resonance, respectively. The results presented in this article are based on these data.

150

3. RECONSTRUCTION EIGENSTATES

Y. Sakai/Ndear

OF

B”

Physics B (Proc. Suppl.) 99B (2001) 148-156

+

CP

We use the following decay modes for the measurement of sin 241. 1. B” -+ J/$Ks; KS + T+T-, r”ro 2. B” -+ @‘KS; $’ + e+e-, p+p-, J/$m+n3. B” + xc1K.s xc1 + Jhr B” + J/tin0 5. B” + J/$KL Among the above, l-3 are CP are CP = +l states. 4.

Yield: 4609. f

= -1

126.

and 4-5

3.1. Reconstruction of charmonia In all of above modes, the J/lc, is reconstructed using decays into lepton (electron or muon) pairs. We use oppositely charged track pairs where at least one track is positively identified as a lepton and the other is identified as a lepton with a looser condition for B” + J/$Ks(Ks + T+T-) case. For other modes, tight criteria are required for both leptons in order to reduce the background. We require -0.06(-0.15) < M(f?.f?) - MJ,G < 0.036GeV/c2 for muon (electron) pairs. In the electron channel, we partially correct for final state radiation or real bremsstrahlung in the inner parts of the detector by including every photon detected within 0.05 radians of the original electron direction in the e+e- invariant mass calculation. We require the J/$ momentum in the CMS to be below 2 GeV, which is consistent with the kinematics of the two-body decay. Fig.1 shows the invariant mass distributions for J/ll, + p+pand J/$ -+ e+e- after the selection. For $’ --+ e+L-, we require -0.06(-0.15) < M(l+t-) - M+i < 0.036GeV/c2 for muon (electron) pairs. For +’ + J/$vr+r, T+Kpairs with an invariant mass greater than 400 MeV/c2 are selected. Then, the mass difference, me+e-,+,- me+e-, is required to be between 0.58 MeV/c2 and 0.60 MeV/c”. The xc1 + J/+-y candidates are also selected by the mass difference me+e-.-, - me+e- . Photons consistent with x0 decays are removed. 3.2. Reconstruction of B” + (cF)Ks(r”) Reconstructed charmonium candidates are combined with KS or no candidates. The KS +

Dilepton mass (GeVk’)

Figure 1. The invariant mass distributions for J/$ -+ p+p- (upper) and J/$ + e+e- (lower).

7r+n- candidates are reconstructed from oppositely charged track pairs with an invariant mass between 482 and 514 MeV/c2. The KS + 7roro decay mode is also used for the JI+Ks mode. We determine the KS decay point to minimize the sum of the x2 values for the two 7r” masses while varying the decay point along the KS momentum direction from the I.P. We require the invariant mass of two x0’s between 470 and 520 MeV/c2. We calculate the energy difference, AE and the beam constrained mass, Mb. The energy difference is defined as AE = Echarmonium + EKs (+ Ebeam where Ej is a measured energy of particle j in the CMS and Ebeclm is the CMS beam energy. The beam constrained mass is defined as, Mb = dw, where ps is the B candidate momentum in the CMS. The scatter plot of Mb and AE for the J/$Ks case is shown in Figure 2 together with the projections onto each axis. Candidate B mesons are selected by requiring k3.50 box cuts for Mb and AE as shown in Figure 2. As a result we obtain 70 B” + J/+Ks candidates.

IT Sakai/Nuclear

Physics B (Proc. Suppl.) 99B (2001) 148-156

Table 1 Summary of number of signal candidates, pected background, end tagged events.

3.3. Background Estimation iFrom Figure 2 we expect some background events in the signal box. We calculate the expected number of background events by multiplying the number of observed events in the sideband by the ratio of the number of MC events in the signal box and the number of MC events in the sideband. We average events in two sidebands; the i&, sideband -0.08 < A&, < -0.02 GeV and the AE sideband 0.1 < lAE[ < 0.25GeV. The numbers of events in the signal region and the estimated background levels are summarized in Table 1.

Decay mode

0.00 AE

0.u)

5.200

(GeV)

5.250

5.300

ex-

signal

background

tagged events

70 4

3.4 0.3

40 4

5 8 5 10 102 204

0.2 0.6 0.75 1 48 54.25

2 3 3 4 42 98

B” -+ JIWs KS -+ T+TKS -+ r”ro B” + qb’Ks $’ -+ e+e$’ + J/@r+n-B” + xc1 KS B” -+ J/@r’ B” -+ J/$KL Total

$J;,-I%~~ -i&O

151

1. Nearby KLM hits within 5” opening angles (KLM cluster) are combined. The KLM cluster must have at least 1 hit if it is accompanied by an ECL cluster (> 0.16 GeV) within 15” opening angle, or at least 2 hits otherwise.

Mb (Gev/cZ)

2. The direction of KLM clusters is calculated. For ECL-associated KLM clusters, we use the ECL cluster direction as the direction of the KLM cluster. Otherwise, a center of a KLM cluster is defined as its direction.

5.200

5.250

Mb (Gev/G)

Figure 2. Scatter plot of AE versus Mb. The box represents the signal region. The upper left figure is the AE projection with Ii&, - M T,$ (
3.4. B” -+ J/$KL reconstruction KL candidates are selected with the following algorithm.

5.300

3. The KLM cluster lated position of KLM first layer around the KLM

is removed if the extrapoany charged track at the lies within the 15” cone cluster direction.

Then, we impose the following criteria for selecting the B” -+ J/$KL candidates. The KL cluster must be inside a cone with 45” opening angle with respect to the expected direction calculated in the laboratory frame assuming a two-body decay of B” -+ J/$ + KL from Y(4S). No charged track that has more than half of the expected momentum exists within a cone of 15” opening angle in the laboratory frame.

I! Sakai/Nuclear Physics B (Proc. Suppl.) 99B (2001) 148-156

152 3. 1.42

5 p;,+

The B meson’s CMS momentum, p;3, is calculated from the KLM cluster direction and twobody decay kinematics. We extract the J/T,LJKL signal yield by fitting the p> distribution of the data to an expected distribution which is obtained using Monte Carlo. Both the signal and the J/GKLT background shapes are parameterized in terms of the reversed Crystal Ball function[l2] which gives tails toward the higher side instead of normal cases where the tails are toward the lower side. The J/$Khr background includes both the resonance K* -+ KLT and non-resonant KLT modes. The combined background of all other sources is parameterized by a 4th order polynomial. We add the two background categories and only its magnitude becomes a free parameter in the fit. For the signal, the magnitude, width, and mean of the crystal ball function are free parameters. Figure 3 shows the pf3 distribution with the fit result. The background contribution coming from B” + J/+K*O(KLT~) is shown separately because it might have its own CP asymmetry. The fraction of this contribution is given by analyzing the Monte Carlo event sample. Among 102 events in the signal region, 0.2 5 p> 2 0.45, we obtain a background of 48 events. 4. VERTEX

data

5 2.0 GeV/c.

RECONSTRUCTION

The proper time difference, At, is given by At N Az/cPr, where ,& is the Lorentz boost factor due to the asymmetric beam energy (& = 0.425 at KEKB) and AZ is the distance between the decay vertices of the two B mesons along the boost axis. The vertices for the CP side are reconstructed using leptons from J/lc, and requiring that they come from the interaction point profile (IP profile) smeared with the finite B flight length in the r-4 plane. We use only leptons with at least one layer having associated SVD hits both in z and r-4, and with two or more z hits in total. The IP profile is calculated offline for every accelerator fill using hadronic events. The typical size of the IP profile is lOOpurnin 2, 5pm in y and 3000pm in z. The resolution estimated with MC is typically

Figure 3. The p;3 distribution with the fit result. The upper solid line is the sum of signal and background. The total background (lower solid line) is divided into the J/$Kao(K~ro) contribution (above the dotted line) and those coming from all other sources (below the dotted line).

40pm.

For the tag-side, among all the charged tracks remaining after the Bcp reconstruction, we use tracks with SVD hits (the same condition as the one used for the CP side) with an impact parameter (from the IP center) less than lmm in r-4 plane, and less than 2mm (from the Bcp vertex) in z. Tracks are also removed if they form a KS. The remaining tracks and an IP constraint are used to reconstruct the tag-side vertex. If the vertex reduced x2 is sufhciently small, we take this vertex. Otherwise we remove the track that gives the largest contribution to the x2 of the vertex and do the vertex reconstruction again. However, we keep the lepton used for tagging and remove the track with the second worst x2. The vertex resolution is dominated by secondary tracks from charmed mesons and estimated to be - 85pm by MC.

Y Sakai/Nuclear

Physics B (Proc. Suppl.) 99B (2001) 148-156

4.1. Resolution Function The resolution function Rsig (At) is parameterized by the sum of two Gaussians: R+(At)

=

(1 - ftail)G(p~t,g~t;At)

+

.ftailG(&$y

aeil,til At)

(4)

where fta;l is the fraction of the tail part, and CAt and &$l are the proper-time difference resolutions for the main part and the tail part, respectively. Pat and /.&,“il are the mean value shifts of the proper-time difference which are determined by the Monte Carlo. fta;l is determined to be 0.08 f 0.06 from the lifetime analysis of the B + D*!+Y sample using the same resolution function. The proper-time difference resolution (Tat (and (skim) is calculated event-by-event from the error matrices of the vertex fits of the CP- and tag-side. It also includes the effect of the approximation At = AZ/C& with fixed @y, and effect due to the charm daughters. These effects are determined by the Monte Carlo. Fig 4 shows the At,,, - Atgen distribution for the MC signal events and the resolution function described above, where At,,, and Atgen are the reconstructed and true proper-time differences, respectively. The distribution is well-represented by the resolution function. 4.2. B lifetime measurements Using a subset(5.1 fb-‘) of data, the lifetimes of B mesons have been measured with the above mentioned resolution function. The combined result for the B” lifetime from B” -+ D*-@v, D*-TT+, D-T+, and J/$K*O decay modes is 780 = 1.50 f O.O5(stat) f O.O7(sys) ps. For B* mesons, using the B+ + D*Ol+v, D*‘r+, and J/$K+ decay modes, rB+ = 1.70 Z!ZO.OG(stat) f O.ll(sys) ps. These are consistent with the PDG values[l3] and verify the validity of our vertex reconstruction and resolution function. 5. FLAVOR

TAGGING

To measure CP asymmetry, the flavor of the other B-meson has to be determined. We use either the sign of primary lepton in semi-leptonic B”-decay, the Kaon charge which signatures a

-6

4

-2

0

2

4

6

Figure 4. The At,,, - At,,, distribution for the MC signal events. A fit with the resolution function is superimposed.

cascade decay b + c -+ s, or the sign of slow pion from D*% + r*D decays. These are well known, clear, and simple methods. We assign the B-flavor for the tag-side B-meson using the following criteria for tag-side particles with a priority from 1 to 4. 1. High-p Lepton: Take the sign of the highest momentum lepton if piepton > 1.1 GeV/c. An electron has higher priority than a muon. Kaon: Find charged kaons and take the sign of their total charge(QK). Medium-p Lepton: Take the sign.of lepton with p& ton > 0.6 GeV/c if p&,ton+pkiss > 2 GeVb, where pkiss is the missing momentum, computed assuming the B” to be at rest in the CMS. Slow pion: Take the opposite sign of slow pion which satisfies p* < 0.2 GeV/c and cost& > -0.06 + 8.7p* - 17.9p*2, where Bthr is the angle between the slow pion and the thrust calculated using all tag-side particles except the slow pion. The efficiency and wrong tag fraction are obtained using (semi)exclusively reconstructed B --+

I! Sakai/Nuclear Physics B (Proc. Suppl.) 99B (2001) 148-156

154

DC*)& events from a 5.1 fb-’ subset of the data. Taking into account the wrong-tag fraction w, the time evolution of the opposite flavor (OF) and same flavor (SF) neutral B-meson pair is given as poF(At)

m

1 + (1 - 2w) cos(AmdAt),

psF(At)

o(

1 - (1 - 2w) cos(AmdAt).

The wrong-tag fraction determines the oscillation amplitude of the OF-SF asymmetry, A 7n22

=°F-SF OF-i-SF

*

= (1 - 2w) cos(AmdAt).

7.

1

4

Proper

s decoy

5

7

B

time

10

0

(PS>

We fit the time evolution of the OF and SF events simultaneously and obtain the wrong-tag fraction. We use the decay modes: B” -+ D’-e+v, D*- + D07r- (DO -+ K+7r-, K+7r-7r”, and K+T+T-T-); and B” --+ D-e+u, D- + KT-T-. We obtain the wrong-tag fraction together with the mixing parameter Am, by fitting the AZ distribution of the SF and OF events. Figure 5 shows the OF-SF asymmetries as s function of At for tagged D*Fefv and Dre*v events together with the fit results. We obtain Am, = 0.488 f O.O26(stat) ps-‘,

(5)

which is consistent with the value obtained from the dilepton sample, Amd = 0.456fO.O08(stat)f O.O3O(sys) ps-1 [14]. The tagging performance is summarized in Table 2. The number of events after tagging is also listed in Table 1. We obtain the total effective tagging efficiency is 21.8 & 5.7 %.

Figure 5. Asymmetry as a function of the proper decay time difference, (top) for D*e, (bottom) for Dfe.

Table 2 Summary of the tagging efficiencies (ctag), wrongtag fractions (wtag), and effective tagging efficiencies (eeff = etas(l - 2~)~).

6. CP FITTING We perform a maximum likelihood fit to the observed proper time distributions to extract sin2&. The probability density function (PDF) is given by P*(At)

fs&‘&(At)

(6)

where * denotes if the tagged flavor is fl. and background PDF are given by

Signal

P&(At)

= f&&(At)

= c,e -‘*t”Tql

+ (1-

f (1 - 2C.q)

ncp sin 241 sin(AmAt)]

mode High e Kaon Med. ! Slow 7r Total

etog(%) 14.2 & 2.1 27.9 f 4.2 2.9 f 1.5 7.0 f 3.5 52.0 f 6.0

Wtog(%) 7.1 & 4.5 19.9 f 7.0 29.2 f 15 34.1 f 15

P&(At) = frbkgCbe-lAtl/7bkg (7)

sin(AmAt)]

(1 f

Eeff @o)

10.5 f 10.1 f 0.5 i 0.7 f 21.8 f

2.7 4.9 0.5 0.7 5.7

a&

+ (1 - fTbkg)6(At)

(8)

Y Sakai/Nuclear

Physics B (Proc. Suppl.) 99B (2001) 148-156

Here c, and cb are normalization factors and Wj is the wrong tag fraction for tagging category j. f TBG is the fraction of the background component with the effective lifetime r&g and a&g is the background asymmetry which is taken to be zero except for the B + J/+KL mode. The above PDF’s are convolved with the resolution functions R+ and Rb,+ for signal and background, respectively. The fit is done with rB and Amd fixed at their PDG values(l31. 6.1. Preliminary results From the fit to the 98 tagged events in all the decay modes mentioned above, we obtain a preliminary result of sin241 to be 0.45f~$~(stat) ‘~:$(sgs). We estimate the systematic error by repeating the fit by changing the parameters with the amount of uncertainties. The sources and amounts of systematic errors are summarized in Table 3. Figure 6 shows the At distribution of data and the fit result. In the figure, the sign of At is reversed if the tagged flavor multiplied by the CP eigenvalue of the event is

98

-15

-10

-5

Events :

0

At

5

Table 3 Summary of the systematic errors of sin 241 measurement . Source Wrong Tag fraction Resolution function Background resol. function Background fraction/shape Errors on rB and Am, I.P. profile Total

15 PS

a+ 0.050 0.026 0.029 0.029 0.005 0.004 0.070

u-0.066 -0.025 -0.042 -0.032 -0.006 -0.000 -0.088

We also perform the fit to CP=-1 state (52 events) and CP=+l state (46 events) decay modes separately. Obtained sin241 values are 0.81+;:;4, and -0.61_,,,, +‘.s’ for CP=-1 and +l states, respectively. We check for any possible fit bias by applying the same fit to the non-CP eigenstate mode B” -+ J/$K*‘(K*’ -+ K+r-) and B* decay modes (J/$K*, Do&). We obtain the fit results -O.O94?g:~~~ (J/$K*O), 0.215+g:i$ (J/$K*), and -0.096f0.174 (Don*), which are consistent with zero. 7.

10

155

CONCLUSION

We have measured the CP violation parameter, sin241 = 0.45+~:~~(stat) +~:~~(sys) with a data sample of 6.2 fb-1 collected at T(4S) resonance with the Belle detector at the KEKB asymmetric e+e- collider. The flavor tagging and the fit to the proper time evolution have been demonstrated by the measurements of the mixing parameter, Arnd = 0.456fO.O08(stat) fO.fX?O(sys) ps-l, and B lifetimes, 7~0 = 1.5O(stat) f 0.05 f O.O’l(sys) ps and rB+ = 1.70 f O.OG(stat) 3.~ O.ll(sys) ps. REFERENCES

Figure 6. At distribution of sum of all tagged events. The fit curves are also drawn. The lower curve shows background.

1. 2. 3.

J.H.Christenson et al., Phys Rev. Lett. 13, 138 (1964). M.Kobayashi and T.Maskawa, Prog. Theo. Phys. 49, 652 (1973). A.Carter and A.I.Sanda, Phys. Rev. Lett.

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Physics B (Proc. Supp1.j 99B (2001) 148-156

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