aa r X i v : . [ h e p - e x ] J u l Measurements of the CKM angle φ /β at the B Factories
Himansu Sahoo on behalf of the Belle and BaBar Collaborations
Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu,Hawaii, 96848, USA, [email protected]
Abstract
In this proceeding, we report the recent measurements of the CKMangle φ /β using large data samples collected by the Belle and BaBarexperiments. The experiments have collected more than 1 billion BB pairs of data sample at the Υ(4 S ) resonance using the facilities of theasymmetric-energy e + e − colliders KEKB and PEP-II.PRESENTED AT The Ninth International Conference onFlavor Physics and CP Violation(FPCP 2011)Maale Hachamisha, Israel, May 23–27, 2011
Introduction
In the standard model (SM), CP violation in B meson decays originates from anirreducible complex phase in the 3 × V ud V ∗ ub + V cd V ∗ cb + V td V ∗ tb = 0, which can be represented by a triangle in the complex plane, knownas the Unitarity Triangle (UT). The main objective of the B -factories is to test theSM picture of the origin of CP violation by measuring the angles (denoted by φ , φ and φ ) ∗ and sides of the UT using different B decays. In this paper, we report therecent measurements concerning the angle φ ( ≡ π − arg( V ∗ tb V td /V ∗ cb V cd )). The measurements discussed in this paper have been obtained by the Belle and BaBarexperiments, located at the KEKB and PEP-II asymmetry-energy e + e − B factories.The accelerators operate at the Υ(4 S ) resonance, which is produced with a Lorentzboost of 0.43 at KEKB (3.5 on 8.0 GeV) [2] and 0.56 at PEP-II (3.1 on 9.0 GeV) [3].The KEKB accelerator of the B factory in Japan achieved the current world recordwith a peak luminosity of 2 . × cm − s − . Both the experiments have alreadystopped data dating. BaBar stopped operation in April 2008 and collected morethan 430 fb − of data at Υ(4 S ) resonance. Belle stopped operation in June 2010 andcollected more than 710 fb − of data. After a decade of successful operation, the B factories have a data sample of nearly 1200 × BB pairs. The Belle and BaBardetectors are described in detail elsewhere [4, 5]. φ /β Measurements of time-dependent CP asymmetries in B meson decays that proceedvia the dominant CKM favored b → ccs tree amplitude, such as B → J/ψK , haveprovided a precise measurement of the angle φ , thus providing a crucial test of themechanism of CP violation in the SM. For such decays the interference between thetree amplitude and the amplitude from B − B mixing is dominated by the singlephase φ . Other decay modes, which allow the measurements of φ are b → ccd transitions like B → J/ψπ , B → D ( ∗ )+ D ( ∗ ) − , B → D + D − . These modes aredominated by tree diagram, but loop may contribute. We can also measure φ frompure penguin decays like φK S , f K S , K + K − K , K S π , η ′ K S and ωK S . In thesedecays sensitivity to new physics (NP) increases.The sin 2 φ measurement from the B factories is one of the main constraints inthe global fit by CKM fitter Collaboration. Recently CKM fitter reported a tension ∗ BaBar uses an alternative notation β , α and γ corresponding to φ , φ and φ . ∼ . σ ) between the measurement of B ( B → τ ν ) and the value predicted from otherobservables excluding this measurement. So further measurements of sin 2 φ will helpto clarify this tension. In the B meson system, the CP violating asymmetry lies in the time-dependent decayrates of the B and B decays to a common CP -eigenstate ( f CP ). The asymmetrycan be written as: A CP ( t ) = Γ[ B ( t ) → f CP ] − Γ[ B ( t ) → f CP ]Γ[ B ( t ) → f CP ] + Γ[ B ( t ) → f CP ]= S sin(∆ m d t ) + A cos(∆ m d t )where S = 2 Im λ | λ | + 1 A = | λ | − | λ | + 1 . (1)Here Γ( B ( B ) → f CP ) is the decay rate of a B ( B ) meson decays to f CP at a propertime t after the production, ∆ m d is the mass difference between the two neutral B mass eigenstates, λ is a complex parameter depending on the B − B mixing as wellas the decay amplitudes of the B meson decays to the CP eigenstate. The parameter S is the measure of mixing-induced CP violation, whereas A is the measure of direct CP violation † .In the B factories, in order to measure the time-dependent CP violation param-eters, we fully reconstruct one neutral B meson into a CP eigenstate. From theremaining particles in the event, the vertex of the other B meson is reconstructedand its flavor is identified. In the decay chain Υ(4 S ) → B B → f CP f tag , where oneof the B mesons decays at time t CP to a CP eigenstate f CP , which is our signal mode,and the other decays at time t tag to a final state f tag that distinguishes between B and B , the decay rate has a time dependence given by [6] P (∆ t ) = e −| ∆ t | /τ B τ B (cid:26) q · h S sin(∆ m d ∆ t ) + A cos(∆ m d ∆ t ) i(cid:27) . (2)Here τ B is the neutral B lifetime, ∆ t = t CP − t tag , and the b -flavor charge q equals+1 ( −
1) when the tagging B meson is identified as B ( B ). Since the B and B areapproximately at rest in the Υ(4 S ) center-of-mass system, ∆ t can be determined fromthe displacement in z between the f CP and f tag decay vertices: ∆ t ≃ ∆ z/ ( βγc ), where c is the speed of light. The vertex position of the f CP decay is reconstructed usingcharged tracks (for example, lepton tracks from J/ψ in B → J/ψK S decays) and † Note that BaBar uses the convention C = −A . f tag decay from well-reconstructed tracks that are not assigned to f CP [7].The ∆ z is approximately 200 µ m in Belle and 250 µ m in BaBar. We also considerthe effect of detector resolution and mis-identification of the flavor [8]. Finally, the CP violation parameters are obtained from an unbinned maximum likelihood fit tothe ∆ t distribution. b → ccs Decay Modes
The b → ccs decays are known as the golden modes for CP violation measurements.They have clean experimental signatures: many accessible modes with relatively largebranching fractions O (10 − ), low experimental background levels and high recon-struction efficiencies. These modes are dominated by a color-suppressed b → ccs tree diagram and the dominant penguin diagram has the same weak phase. The CP violation comes from the V td element in the mixing box diagram, which contains thephase. For f CP final states resulting from a b → ccs transition, the SM predicts S = − ξ CP sin 2 φ and A = 0, where ξ CP is known as the CP eigenvalue and havevalues +1( −
1) for CP -even ( CP -odd) final states. The asymmetry is given as A CP = ξ CP sin(2 φ ) sin(∆ m ∆ t ) . (3)We can verify this experimentally by measuring the number of B ( B ) decays to CP eigenstate. Because of the high experimental precision and low theoretical uncertaintythese modes provide a reference point in the SM. A non-zero value of A or anymeasurement of sin 2 φ that has a significant deviation indicates an evidence for NP.Belle recently reported new measurements with its full data sample (772 × BB pairs) using the modes B → J/ψK , B → ψ ′ K S and B → χ c K S . The J/ψ candidates are reconstructed from their decays to e + e − and µ + µ − , with the K S re-constructed from π + π − . The ψ ′ candidates are reconstructed from e + e − , µ + µ − as wellas J/ψπ + π − decays. The χ c is reconstructed from its decays to J/ψγ . Belle reportednearly 15600 CP -odd signal events with a purity of 96% and nearly 10000 CP -evensignal events with a purity of 63%. Belle observed CP violation in all charmoniummodes and the results are summarized in Table 1.Figure 1 shows the background-subtracted ∆ t distributions for good-tagged eventsonly (all charmonium modes are combined). We define the raw asymmetry in each∆ t bin as ( N + − N − ) / ( N + + N − ), where N + ( N − ) is the number of observed can-didates with q = +1 ( − φ = 0 . ± . ± . , A = 0 . ± . ± . . (4)3ecay Mode S A B → J/ψK S . ± . − . ± . B → J/ψK L − . ± .
047 0 . ± . B → ψ ′ K S . ± .
079 0 . ± . B → χ c K S . ± . − . ± . CP -violating parameters measured by Belle with golden modes usinga data sample of 772 × BB pairs (the errors are statistical only). Belle observed CP violation in all charmonium modes. t (ps) ∆ f ξ --6 -4 -2 0 2 4 6 E n t r i es / . p s ∆ f ξ --6 -4 -2 0 2 4 6 A sy mm e t r y -1-0.8-0.6-0.4-0.200.20.40.60.81 Figure 1: The left plot shows the ∆ t distribution for q = +1 (red) and q = − B → J/ψK , B → ψ ′ K S , B → χ c K S , B → η c K S and B → J/ψK ∗ . Using a data sample of 465 × BB pairs, BaBarreported nearly 8400 CP -odd signal events with a purity of 93% and nearly 5800 CP -even signal events with a purity of 56%. Combing all charmonium modes BaBarmeasured sin 2 φ = 0 . ± . ± .
012 and C = 0 . ± . ± .
016 [11].Combining the measurements from Belle and BaBar, the new world average cal-culated by the Heavy Flavor Averaging Group (HFAG) is [12]sin 2 φ ( b → ccs ) = 0 . ± . , A ( b → ccs ) = − . ± . . (5)Figure 2 summarizes the results of sin 2 φ for b → ccs decays from Belle and BaBar.The measurements of the two experiments agree very well within the statistical un-certainties. The experimental uncertainty on sin 2 φ is reduced to 3% and thus servesas a firm reference point for the SM. The value of A is consistent with zero. The newresults will definitely provide a better constraint on the allowed region in the CKMfitter. The measurement of sin 2 φ leaves a two-fold ambiguity in the value of φ .Both Belle and BaBar measured the sign of cos 2 β to be positive at 98 .
3% and 86%4onfidence levels, respectively. This favors the smaller value of φ solution. The newmeasurements give the value [12] φ ( β ) = (21 . ± . ◦ , (6)which is the most precise measurement with < ◦ error. sin(2 β ) ≡ sin(2 φ ) H F A G B eau t y BaBar
PRD 79 (2009) 072009 ± ± BaBar χ c0 K S PRD 80 (2009) 112001 ± ± ± BaBar J/ ψ (hadronic) K S PRD 69 (2004) 052001 ± ± Belle
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PRELIMINARY β ≡ φ ρ – η – -0.2 0 0.2 0.4 0.6 0.8 1-0.200.20.40.60.81 β ≡ φ = ( . ± . )˚ β ≡ φ = ( . ± . )˚ D I S F AV O UR E D BY J / ψ K * , D * D * K S & D h HF AGHF AG
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Figure 2: The left plot shows the comparison between the Belle and BaBar measure-ments of sin 2 φ with b → ccs decays and constraints on φ on the ( ρ, η ) plane isshown in the right plot. The hatched area is excluded corresponding to the negativecos(2 φ ) solution. b → ccd Decay Modes
The B → J/ψπ decay takes place through a b → ccd transition. The dominant treediagram is Cabibbo-suppressed. However, there is a penguin diagram of the sameorder that has a different weak phase. So, small deviation in sin 2 φ from goldenmodes is expected in the SM. The BaBar result provides an evidence of CP violationat 4 σ level [13], while the value for Belle result is 2 . σ [14]. The decay B → D ∗ + D ∗− also goes through the b → ccd transition. This mode requires an angular analysis toseparate CP -even and CP -odd events. Belle reports a statistical significance of 3 . σ for direct CP violation in the B → D + D − mode [15]. b → sqq Decay Modes
An alternative way to measure the angle φ is to measure the time-dependent CP asymmetries in charmless hadronic final states. These are b → s penguin dominateddecays. Any non-SM particles, like Higgs or SUSY particles can enter the loop.So, these are sensitive to NP. The value of S is expected to be sin 2 φ for a purepenguin amplitude, but can be different if there is an extra CP phase from NP. As a5onsequence, an effective sin 2 φ value is measured. Significant deviation from sin 2 φ in golden modes would indicate NP. The deviations have been estimated in severaltheoretical models and are expected to be positive. These estimates are mode andmodel dependent.Belle and BaBar have recently performed time-dependent Dalitz analyses in the B → K + K − K S [16] final state using 657 × BB [17] and 465 × BB pairs,respectively. This gives directly the value of φ (we do not need to worry about thetwo-fold ambiguity here). The results are consistent with the SM expectation from b → ccs decays. The sin 2 φ eff1 in various b → s penguin modes is summarized in Fig. 3.The results are consistent between Belle and BaBar and also consistent with the SMexpectation within the statistical uncertainties. It is fair to say that we need moredata to see a sensitivity comparable with theoretical uncertainties. sin(2 β eff ) ≡ sin(2 φ e1ff ) H F A G B eau t y H F A G B eau t y H F A G B eau t y H F A G B eau t y H F A G B eau t y H F A G B eau t y H F A G B eau t y H F A G B eau t y H F A G B eau t y H F A G B eau t y H F A G B eau t y H F A G B eau t y H F A G B eau t y H F A G B eau t y b → ccs φ K η ′ K K S K S K S π K ρ K S ω K S f K S f K S f X K S π π K S φ π K S π + π - K S NR K + K - K -2 -1 0 1 2 World Average ± BaBar ± ± Belle +-00..0199
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Figure 3: The summary of effective sin 2 φ measurements in b → s penguin decaymodes. In this review, we have presented the recent measurements of the CKM angle φ /β by Belle and BaBar. Thanks to the excellent performance of the two B factories,which collected large data sample at the Υ(4 S ) resonance; the angle φ has beenmeasured with < ◦ precision. The CP violating parameters in b → ccs decays are themost precise measurements and provides a reference point for new physics searches.The time-dependent CP asymmetry in penguin dominated decays is consistent withstandard model expectations within the uncertainties of the measurement.6 CKNOWLEDGEMENTS
I would like to thank my Belle colleagues for their valuable help in providinginformation regarding the measurements of φ . I am also thankful to the conferenceorganizers for their invitation to present this review. References [1] N. Cabibbo, Phys. Rev. Lett. , 531 (1963); M. Kobayashi and T. Maskawa,Prog. Theor. Phys. , 652 (1973).[2] S. Kurokawa and E. Kikutani, Nucl. Instrum. Methods Phys. Res., Sect. A ,1 (2003), and other papers included in this volume.[3] PEP-II Conceptual Design Report, SLAC-PUB-0418 (1993).[4] A. Abashian et al. , Nucl. Instrum. Methods Phys. Res., Sect. A , 117 (2002).[5] B. Aubert et al. , Nucl. Instrum. Methods Phys. Res., Sect. A , 1 (2002).[6] A. B. Carter and A. I. Sanda, Phys. Rev. D , 1567 (1981); I. I. Bigi andA. I. Sanda, Nucl. Phys. B , 85 (1981).[7] H. Tajima et al. , Nucl. Instrum. Methods Phys. Res., Sect. A , 370 (2004).[8] H. Kakuno et al. , Nucl. Instrum. Methods Phys. Res., Sect. A , 516 (2004).[9] K.-F. Chen et al. (Belle Collaboration), Phys. Rev. Lett. , 031802 (2007).[10] H. Sahoo et al. (Belle Collaboration), Phys. Rev. D , 091103 (2008).[11] B. Aubert et al. (BaBar Collaboration), Phys. Rev. D et al. (BaBar Collaboration), Phys. Rev. Lett. , 021801 (2008).[14] S. E. Lee et al. (Belle Collaboration), Phys. Rev. D , 071101 (2008).[15] S. Fratina et al. (Belle Collaboration), Phys. Rev. Lett. , 221802 (2007).[16] Y. Nakahama et al. (Belle Collaboration), Phys. Rev. D , 073011 (2010).[17] B. Aubert et al.et al.