Results on the CKM Parameter β(ϕ1) from the BaBar and Belle Experiments

Nuclear Physics B (Proc. Suppl.) 142 (2005) 287–292 www.elsevierphysics.com

Results on the CKM Parameter β (φ1) from the BABAR and Belle Experiments S. Tosia a

Universit`a and INFN Genova, I-16146 Genova, Italy

This report presents a review of recent results for the determination of the parameter β (φ1 ) of the CabibboKobayashi-Maskawa matrix through the measurement of time-dependent CP asymmetries in B-meson decays by the BABAR and Belle experiments. 0

1. Introduction

decayed as B 0 (B ) is

In the Standard Model (SM) with three fermion generations, CP violation arises from a single complex phase in the Cabibbo-KobayashiMaskawa (CKM) matrix [1], which describes the mixing between quarks. The unitarity of the CKM matrix implies several relations between its elements, for instance ∗ Vud Vub + Vcd Vcb∗ + Vtd Vtb∗ = 0, which can be represented as a triangle (Unitarity Triangle) in the complex plane. The B-factory experiments, BABAR and Belle, aim to test the CP-violation pattern of the SM by over-constraining the Unitarity Triangle with redundant measurements of its angles and sides. Inconsistencies would signal New Physics (NP) effects. This report presents results for the determination of the angle β (also named φ1 ) 
Vcd Vcb∗ , (1) β = arg − Vtd Vtb∗

e−|t|/τB0 [1 ± S sin(∆md t) ∓ C cos(∆md t)] , 4τB 0

obtained by the BABAR and Belle experiments from studies of neutral B-meson samples produced in Υ(4S) decays. 0 The typical events analyzed contain a B 0B pair, which is produced in a coherent L = 1 state by the Υ(4S), where one of the two B 0 mesons [2] decays into a CP eigenstate of interest, fCP , ac0 cessible to both B 0 and B , and the other to a final state which allows the identification of its b flavor at the decay time (“tagging”). The B decay rate f+ (f− ) when the companion B meson 0920-5632/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2005.01.050

(2)

where τB 0 is the B 0 lifetime, ∆md is the mass difference between the two neutral B-meson mass eigenstates and t is the difference between the proper decay times of the two B mesons. The coefficients S and C are given by S=

2Imλ , 1 + |λ|2

C=

1 − |λ|2 , 1 + |λ|2

(3)

where λ [3] is a complex parameter depending on 0 the B 0B oscillation amplitude and the B 0 and 0 B decay amplitudes to fCP . A time-dependent asymmetry observable can be defined as the ratio between the difference and the sum of f+ and f− : aCP (t) = S sin(∆md t) − C cos(∆md t). Here, the first term is due to the interference between direct B decay and decay after a flavor change. The second term can arise from the interference between decay amplitudes with different weak and strong phases. To a good approximation, in the SM, S equals −ηCP sin 2β, where ηCP is the CP eigenvalue of the final state fCP , and C  0 (that is |λ|  1), for decays dominated by a single weak phase. 2. The BABAR and Belle Experiments The BABAR and Belle experiments record the e+ e− collisions supplied by the accelerators PEPII at SLAC and KEKB at KEK, respectively. The

3. sin 2β Measurement with b → ccs Decays The experimentally and theoretically most favoured system for the measurement of sin 2β is represented by B decays to a charmonium state and a kaon, such as B 0 → J/ψ KS0 , which proceed through the quark-level process b → ccs, dominated by a W -boson mediated tree diagram. BABAR and Belle reconstructed the CP eigenstates ηc KS0 , J/ψ KS0 , χc1 KS0 and ψ(2S)KS0 , all having ηCP = −1, and J/ψ KL0 , which has ηCP = +1. In addition, the decay channel J/ψ K ∗0 , with K ∗0 → KS0 π 0 , was also considered; this is an admixture of CP-even and CP-odd components which are separated by means of an angular analysis. From a fit to the time-dependent CP-asymmetry distributions (Figures 1 and 2), BABAR [6], based on an integrated luminosity of 81 fb−1 , and Belle [7], based on 140 fb−1 , measured sin 2β = 0.741 ± 0.067 ± 0.033 [8] and 0.733 ± 0.057 ± 0.028, respectively. The two results are in good agreement with each other and with SM expectations. Including them, the world average for sin 2β is 0.736 ± 0.049. Also, both experiments found no significant deviation from 1 for the |λ| parameter, again in agreement with the SM. Figure 3 shows the implications for the Unitarity Triangle derived using the sin 2β measurements, compared with indirect constraints. 4. sin 2β Measurement with b → ccd Decays The B decays proceeding through b → ccd are expected to measure the same CP violating phase

Raw Asymmetry

a)

0

B tags −0

100

B tags

0 0.5

b)

0

Entries / 1 ps

-0.5

Raw Asymmetry

extraordinary performances of the two machines provided very large data samples. The results presented here are based on about 80 or 110 fb−1 of data taken at the Υ(4S) peak in the case of BABAR, and 140 fb−1 for Belle. In both cases, the energies of the two beams are asymmetric, resulting in a boost to the Υ(4S) resonance produced, making the decay-time separation between the two B-meson decays obtainable from the decay-vertex separation. The BABAR and Belle detectors are described in detail in Refs. [4] and [5], respectively.

Entries / 0.6 ps

S. Tosi / Nuclear Physics B (Proc. Suppl.) 142 (2005) 287–292

c)

0

B tags −0

100

B tags

0 0.5

d)

0

-0.5

-5

0

5

∆t (ps)

Figure 1. BABAR data for the b → ccs modes. a) 0 ∆t distribution for B 0 and B tags, b) raw time asymmetry, for the ηCP = −1 sample. c) and d): the same as above for ηCP = +1.

(cc)KS(ξf=−1)

0.5

Raw Asymmetry

288

0 -0.5 J/ψKL(ξf=+1)

0.5 0 -0.5

-8

-6

-4

-2

0

∆t(ps)

2

4

6

8

Figure 2. Belle data for the b → ccs modes. Top (bottom): raw time asymmetry for the ηCP = −1 (ηCP = +1) sample.

as the b → ccs modes. However, they may exhibit deviations due to possible contributions from penguin diagrams carrying a weak phase different from the tree diagram and not suppressed with

S. Tosi / Nuclear Physics B (Proc. Suppl.) 142 (2005) 287–292

tudes for D∗+ D− and D∗− D+ , at the tree level one expects S+− = S−+ = − sin 2β. BABAR measured S+− = −0.82 ± 0.75 ± 0.14 and S−+ = −0.24 ± 0.69 ± 0.12 [13], consistent with the expectation. In all cases, measurements of the C observable yielded values consistent with 0.

1.5 excluded area has CL < 0.05

∆md

1

sin 2β

∆ms & ∆md 0.5

η

B → ρρ

α

εK

γ

0

289

β

|Vub/Vcb|

5. Determination of the cos 2β Sign -0.5

εK -1

CKM

fitter Winter 2004

B → ρρ

-1.5 -1

-0.5

0

0.5

1

1.5

2

ρ

Figure 3. Implications on the Unitarity Triangle from the sin 2β measurements and indirect constraints [9].

respect to it. Both BABAR and Belle studied the J/ψ π 0 decay channel. In this case, sin 2β was measured to be −0.05 ± 0.49 ± 0.16 by BABAR with 81 fb−1 [10], −1 [11]. and 0.72+0.37 −0.42 ± 0.08 by Belle with 140 fb These average to 0.40 ± 0.33, consistent with the b → ccs result within the errors. BABAR also studied D(∗)+ D(∗)− decay channels, using a sample of 81 fb−1 . The two-vector final state D∗+ D∗− has both CP-even and CPodd components. An angular analysis was performed to determine its CP content. The CPodd fraction was found to be very small, 0.063 ± 0.055 ± 0.009. The S observable was measured to be SD∗ D∗ = 0.05 ± 0.29 ± 0.10, leading to a value for sin 2β about 2.5 standard deviations from the b → ccs result, possibly indicating penguin-diagram contributions in the process [12]. In the case of D∗+ D− and D∗− D+ , which are not CP eigenstates, a somewhat different formalism for the time-dependent asymmetry has to be used and two S observables, S+− and S−+ , are present. Assuming equal ampli-

The measurement of sin 2β yields the angle β up to a four-fold ambiguity. Using 81 fb−1 , BABAR performed a study for the determination of the sign of cos 2β with B 0 → J/ψ K ∗0 , K ∗0 → KS0 π 0 decays [14], which allows a reduction of the ambiguity on β. The final state considered has both CP-even and CP-odd components. Because of the interference between them, a cos 2β term arises in the time-dependent asymmetry in the observables cos(δ|| − δ⊥ ) cos 2β and cos(δ⊥ − δ0 ) cos 2β, where δ0 , δ|| , δ⊥ are the strong phases of the angular decay amplitudes, A0 , A|| , A⊥ , in the transversity basis [15]. By studying B 0 → J/ψ K ∗0 and B + → J/ψ K ∗+ decays, with K ∗0 → K + π − and K ∗+ → KS0 π + or K ∗+ → K + π 0 , the strong-phase differences δ|| − δ0 and δ⊥ − δ0 were measured to be 2.729 ± 0.101 ± 0.052 and 0.184 ± 0.070 ± 0.046, respectively. These are determined only up to a two-fold ambiguity. The two sets of parameters [(δ|| − δ0 ), (δ⊥ − δ0 )] (referred to as “solution I” in the following) and [−(δ|| − δ0 ), π − (δ⊥ − δ0 )] (“solution II”) are mathematically equivalent. This ambiguity makes the determination of the cos 2β sign not unique. Nonetheless, more information can be added to resolve the ambiguity. In fact, a broad Kπ S-wave is known to lie in the K ∗ region [16] and a corresponding amplitude has to be taken into account in addition to the three P wave amplitudes above, thus introducing a new relative phase, γ = δS −δ0 . According to Wigner’s causality principle [17], the phase of a resonance rotates clockwise with increasing mass. In the K ∗ region, the Kπ S-wave phase moves slowly, while the Kπ P -wave phase moves fast; the phase γ must then rotate clockwise in the K ∗ region. Figure 4 shows γ as a function of the Kπ invariant mass after fixing δ|| − δ0 and δ⊥ − δ0 to solution

290

S. Tosi / Nuclear Physics B (Proc. Suppl.) 142 (2005) 287–292

1.2 1 0.8 0.6 0.4 0.2 0 0.8

0.9

1

1.1

1.2

1.3

1.4

1.5 2

mKπ (GeV/c )

Figure 4. The phase γ as a function of the Kπ invariant mass: open (full) points are obtained using solution I (solution II) values for the strong phases (see text); open diamonds show LASS data for the 1/2 isospin component in K − π scattering [16], shifted by a global offset of π.

By assigning the strong phases to the solution II values, sin 2β and cos 2β were derived from a fit to the time- and angular-dependent asymmetry: sin 2β = −0.10 ± 0.57 ± 0.14, cos 2β = 3.32+0.76 −0.96 ± 0.27. Constraining sin 2β to the world average, one gets cos 2β = 2.72+0.50 −0.79 ±0.27. Assuming that sin 2β and cos  2β come from the same angle, then cos 2β = ± 1 − sin2 2β. It was estimated that the negative cos 2β solution can be excluded at the 89% C.L.. 6. Results with b → s Penguin-Dominated Modes These modes offer a good opportunity to search for effects from physics beyond the SM. In fact, in the SM, b → s gluonic-penguin-diagram-

35 30 25 20 15 10 5 0

35 30 25 20 15 10 5 0

Events / 2 ps

1.4

(a)

15

a)

10 5 0 15

b)

10 5 Asymmetry

1.6

(b)

0.8 0.6 0.4 0.2 -0 -0.2 -0.4 -0.6 (c) -0.8 -10 -8 -6

0 1 0.5 0 -0.5 -1

c)

15

d)

10 5 0 15

e)

10 5

-4

-2

0

2

4

6

8 10 ∆t (ps)

Asymmetry

1.8

Events / 1 ps

2

dominated modes are expected to give a sin 2β value (sin 2βeff in the following) equal to that of b → ccs modes (sin 2βccs ), if the subdominant amplitudes with a different weak phase are neglected [18]. Large discrepancies would be a clear indication of NP. BABAR and Belle studied B 0 decays to η  KS0 [19, 20], φKS0 [21,20], as well as the three-body B 0 → K + K − KS0 decay, after removing K + K − pairs consistent with being from a φ-meson decay [22,20]. In addition, BABAR also studied the φKL0 [21], f0 (980)KS0 [23] and KS0 π 0 [24] decay channels. The expected dominant contributions in the B 0 decays to these final states are from a b → sss penguin diagram in the case of φK 0 and K + K − KS0 , as well as f0 (980)KS0 , if one assumes the ss-component dominance in the f0 (980) meson [25], from a b → dds penguin diagram in the case of KS0 π 0 , and from both b → dds and b → sss penguin diagrams in the case of η  KS0 . Figures 5 and 6 show BABAR and Belle data, respectively, for the η  KS0 and φK 0 decay channels. In the η  KS0 sample, BABAR and Belle measured sin 2βeff (η  KS0 ) = 0.02 ± 0.34 ± 0.03 and

Asymmetry

γ / π = (δS– δ0) / π

I- and solution II-values in turn: the expected behaviour for γ is only observed for solution II. Also, BABAR data in the solution II case compare remarkably well with the high-statistics LASSexperiment data on K − π scattering [16].

0 1 0.5 0 -0.5 -1

-6

f)

-4

-2

0 ∆t [ps]

2

4

6

Figure 5. Left: BABAR results for η  KS0 ; a): ∆t distribution for B 0 tags, b): ∆t distribution for 0 B tags, c) raw time asymmetry. Right: BABAR results for φKS0 (φKL0 ); a) (d): ∆t distribution for 0 B 0 tags, b) (e): ∆t distribution for B tags, c) (f) raw time asymmetry.

S. Tosi / Nuclear Physics B (Proc. Suppl.) 142 (2005) 287–292

1

f) B → η’K s 0

0

1

0.5

Raw Asymmetry

Raw Asymmetry

0

0

-0.5

1

0

0.5

0

-1

b) B → φK s

0.0 < r ≤ 0.5 g)

0.5

-0.5

1

0

-0.5

-0.5

0

∆t (ps)

2.5

5

7.5

c)

0.5

0

-1 0.5 < r ≤ 1.0 -7.5 -5 -2.5

0.0 < r ≤ 0.5

-1

-1 -7.5

0.5 < r ≤ 1.0 -5

-2.5

0

∆t (ps)

2.5

5

7.5

Figure 6. Left (right): Belle results for η  KS0 (φKS0 ); raw time asymmetry for low-quality tags (top) and higher-quality tags (bottom). The dashed lines indicate the SM expectation.

0.43 ± 0.27 ± 0.05, with 81 fb−1 and 140 fb−1 , respectively: the average points to a value somewhat smaller than sin 2βccs . Using the φKS0 and φKL0 samples, BABAR measured sin 2βeff (φK) = 0.47 ± 0.34+0.08 −0.06 , with −1 0 108 fb , while, using the φKS sample, Belle obtained sin 2βeff (φK) = −0.96 ± 0.50+0.09 −0.11 , with 140 fb−1 . The two results are not in good agreement and in particular Belle’s result is about 3.5 standard deviations from sin 2βccs . In the case of K + K − KS0 , an isospin analysis was performed to determine the CP content of the final state. By studying both B 0 → K + K − KS0 and B + → K + KS0 KS0 , the CP-even fraction of K + K − KS0 was found to be very close to 1: 0.98 ± 0.15 ± 0.04 (BABAR [22]) and 1.03 ± 0.15 ± 0.05 (Belle [26]). The value of sin 2βeff (K + K − KS0 ) was measured to be 0.57 ± 0.26 ± 0.04+0.17 −0.00 and by B A B A R using 113 fb−1 , 0.51 ± 0.26 ± 0.05+0.18 −0.00 and Belle using 140 fb−1 , respectively. Here, the last error is due to the uncertainty in the CP content of the final state. The study of B 0 → f0 (980)KS0 was performed by reconstructing the f0 (980) → π + π − decay mode and restrincting the analysis to the region of the KS0 π + π − Dalitz plot dominated by the f0 (980): the B 0 → f0 (980)KS0 decay was observed for the first time and the sin 2βeff (f0 KS0 ) value was measured to be 1.62+0.56 −0.51 ± 0.10 using

291

111 fb−1 of data. In the KS0 π 0 final state, no charged track is present at the B 0 decay vertex; in order to perform a time-dependent CP-asymmetry measurement, the B decay point was determined from the intersection of the KS0 trajectory with the interaction region by constraining the B vertex to the interaction point in the plane transverse to the beam direction. The value of sin 2βeff (π 0 KS0 ) −1 of was found to be 0.48+0.38 −0.47 ± 0.11 using 113 fb data. Measurements of the C observable yielded no significant deviation from 0 in all the above cases. With a similar vertexing technique as for KS0 π 0 , BABAR also performed a study of the timedependent CP asymmetry in the B 0 → K ∗0 γ → KS0 π 0 γ process [27]. In the limit of a massless s-quark, the photon from this decay is completely polarized, with opposite helicities for B 0 0 and B . This does not hold true, however, in many NP scenarios. A time-dependent CP asymmetry can be defined for the process as aCP (t) = S sin(∆md t) − C cos(∆md t). SM expectations for S and C are S ∼ 2ms sin 2β/mb ∼ 0.05, where ms and mb are the s- and b-quark masses, respectively, and |C| < 1%. Using 113 fb−1 , BABAR measured S = −0.25 ± 0.63 ± 0.14 and C = −0.56 ± 0.32 ± 0.09, hence with no significant deviation from the SM. Figure 7 shows a summary of sin 2β measurements from penguin-dominated modes. These have large errors and, in general, no big discrepancy with the b → ccs results is apparent, with the noticeable exception of the Belle result for the φKS0 decay channel [29]. More data are awaited to help clarifying the situation. 7. Conclusions Thanks to the analysis of the largest B-meson data samples ever collected, the BABAR and Belle experiments firmly established CP violation in the B-meson system. The sin 2β value is already measured to good precision using b → ccs modes and is found to be consistent with the CKM mechanism for CP violation. In addition, an extensive program is being carried out aimed at identifying possible disagreements with the SM in a num-

292

Charmonium Modes

S. Tosi / Nuclear Physics B (Proc. Suppl.) 142 (2005) 287–292

OPAL 98 + 1.8

3.2 – 2.0 ± 0.5

ALEPH 00 + 0.82

0.84 – 1.04 ± 0.16

CDF+ 00 0.41 0.79 – 0.44

BABAR 02

0.741 ± 0.067 ± 0.034

Belle 03

0.733 ± 0.057 ± 0.028

Average (charmonium) 0

BABAR 04 + 0.08

φK

0.736 ± 0.049

Belle 03

0.47 ± 0.34 – 0.06

+ 0.09

, 0

η KS

–0.96 ± 0.5 – 0.11

BABAR 03

0.02 ± 0.34 ± 0.03

Belle 03

0.43 ± 0.27 ± 0.05

0

f0KS 0

0

0

KKKS

π KS

BABAR 04 + 0.51

1.62 – 0.56 ± 0.1

BABAR 04 + 0.38

0.48 – 0.47 ± 0.11

BABAR 04 + 0.17 0.56 ± 0.25 – 0.04

Belle 03

+ 0.19

0.51 ± 0.26 – 0.05

Average (s penguin)

H F AG

0.42 ± 0.12

Winter 2004

Average (All) 0.69 ± 0.045

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

– η f × Sf

Figure 7. Summary of results on sin 2β [28].

ber of other processes. These studies will benefit from the additional data samples being accumulated and analyzed. REFERENCES 1. N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963); M. Kobayashi and T. Maskawa, Prog. Th. Phys. 49, 652 (1973). 2. Throughout the paper, charge conjugation is implied when not explicitely stated. 3. See, for example, L. Wolfenstein, Phys. Rev. D 66, 010001 (2002). 4. BABAR Collaboration, B. Aubert et. al, Nucl. Instr. and Methods A479, 1 (2002). 5. Belle Collaboration, A. Abashian et. al, Nucl. Instr. and Methods A479, 117 (2002). 6. BABAR Collaboration, B. Aubert et. al, Phys. Rev. Lett. 89, 201802 (2002). 7. Belle Collaboration, K. Abe et. al, BELLECONF-0353 (2003). 8. Everywhere in the paper, where two errors are quoted for a measurement, the first is statistical and the second is systematic. 9. http://www.slac.stanford.edu/xorg/ckmfitter. 10. BABAR Collaboration, B. Aubert et. al, Phys.

Rev. Lett. 91, 061802 (2003). 11. Belle Collaboration, K. Abe et. al, BELLECONF-0342 (2003). 12. BABAR Collaboration, B. Aubert et. al, Phys. Rev. Lett. 91, 131801 (2003). 13. BABAR Collaboration, B. Aubert et. al, Phys. Rev. Lett. 90, 221801 (2003). 14. BABAR Collaboration, B. Aubert et. al, SLAC-PUB-10515 (2004). 15. S.T’Jampens, Thesis, Universit´e Paris XI (2002). 16. LASS Collaboration, D. Aston et. al, Nucl. Phys. B296, 493 (1988). 17. E.P. Wigner, Phys. Rev. 98, 145-147 (1955). 18. Y. Grossman et. al, Phys. Rev. D 68, 015004 (2003); M. Gronau et. al, Phys. Lett. B579, 331-339 (2004). 19. BABAR Collaboration, B. Aubert et. al, Phys. Rev. Lett. 91, 161801 (2003). 20. Belle Collaboration, K. Abe et. al, Phys. Rev. Lett. 91, 261602 (2003). 21. BABAR Collaboration, B. Aubert et. al, SLAC-PUB-10382 (2003). 22. BABAR Collaboration, B. Aubert et. al, SLAC-PUB-10462 (2004). 23. BABAR Collaboration, B. Aubert et. al, SLAC-PUB-10498 (2004). 24. BABAR Collaboration, B. Aubert et. al, SLAC-PUB-10363 (2004). 25. A.V. Anisovich et. al, hep-ph/0011191 (2000). 26. Belle Collaboration, K. Abe et. al, Phys. Rev. D 69, 012001 (2004). 27. BABAR Collaboration, B. Aubert et. al, SLAC-PUB-10468 (2004). 28. http://www.slac.stanford.edu/xorg/hfag. 29. A preliminary update for sin 2βeff (φK) was reported by Belle after the BEACH 2004 Conference, using both the φKS0 and the φKL0 decay channels, with about 250 fb−1 of data: sin 2βeff (φK) = +0.06 ± 0.33 ± 0.09. This value is in better agreement with the BABAR measurement, and about 2.2 standard deviations from sin 2βccs . See, for instance: Y. Sakai, talk given at the 32nd International Conference on High Energy Physics, Beijing (China), August 16-22, 2004.