Rare hadronic B-meson decays allow us to study CP violation. The class of B
decays final states containing two vector mesons provides a rich set of angular
correlation observables to study. This article reviews some of the recent
experimental results from the BaBar and Belle collaborations.Comment: International Conference on Flavor Physics, Chung-Li, Taiwan, 3rd-8th
  October 200

Bevan, A. J.

English

arXiv

Rare hadronic B-meson decays allow us to study CP violation. The class of B-decays final states containing two vector mesons provides a rich set of angular correlation observables to study. This article reviews some of the recent experimental results from the BABAR and Belle collaborations

Bevan, A.J.

UNT Digital Library

Work supported in part by Department of Energy contract DE-AC02-76SF00515Rare hadronic B decays.Adrian BevanDepartment of PhysicsQueen Mary, University of London, Mile End Road, E1 2NS, UK.e-mail: bevan@slac.stanford.eduPresented at the International Conference on Flavor Physics,Chung-Li, Taiwan, 3rd − 8th October 2005.Rare hadronic B-meson decays allow us to study CP violation. The class of B-decays final states containingtwo vector mesons provides a rich set of angular correlation observables to study. This article reviews someof the recent experimental results from the BABAR and Belle collaborations.1 IntroductionThe study of rare hadronic B-meson decays with branching fractions O(10−6) enable us to probe a wide rangeof phenomena. Such decays can be used to probe our understanding of the CKM [1] description of quarkmixing and CP violation (CPV ) in the Standard Model of Particle Physics (SM) by measuring all three ofthe Unitarity Triangle angles α, β and γ, as well as charge asymmetries in direct CPV Δb = 1 transitions.CPV was ﬁrst seen in the decay of neutral kaons [2]. The ﬁrst observation of CPV in B-meson decay was themeasurement of a non-zero value of sin 2β by the B-factories [3]. The measurements of the Unitarity Triangleangles and time-dependent CP observables (S and C) in hadronic B-meson decays are discussed elsewhere [4].The phenomenon of direct CPV was experimentally established in the study of neutral kaon decay to two pionﬁnal states, through the measurement of a non zero value of the ratio ′/ = (1.67 ± 0.26) × 10−3 [5, 6]. Incontrast to the kaon system, where the direct CPV parameter ′ is O(few× 10−6), one can accommodate largedirect CPV in B-meson decay. For a B-meson decays to a ﬁnal state f , the direct CP asymmetry is deﬁned asACP = (N −N)/(N + N), (1)where N (N) is the number of B (B) decays to f (f). In order for a decay to be direct CP violating (ACP = 0),one requires that there are at least two interfering amplitudes Ai with both non-zero weak (φ) and strong phase(δ) diﬀerences whereACP ∝∑i,j;i=jAiAj sin(φi − φj) sin(δi − δj). (2)The values of the strong phases of amplitudes are a priori unknown. As a result, there is a limited amount ofinformation that one can extract from a measured CP asymmetry in a single decay channel.There are still questions remaining on the subject of the hierarchy and values of the branching fractions ofa number of rare hadronic B-meson decays. The B-factories, the BABAR experiment at SLAC [7] and the Belleexperiment at KEK [8], continue to improve measurements of such decays with the aim of providing theoristswith more accurate data to test calculations. There has recently been signiﬁcant progress on the experimentalstudy of B → hh (h = π,K) ﬁnal states, where the BABAR experiment has accounted for the eﬀects of ﬁnalstate radiation in B meson decays to π+π−, K+π−, and K+K− [9, 10]. The recent observation of B0 → a+1 π−might lead to additional constraints on the value of the Unitarity Triangle angle α [11].B-meson decays to two vector particles (V ) are particularly interesting. In addition to the CP violatingobservables, S, C, and ACP , one has a number of angular correlation observables to measure and comparewith predictions. Any deviations from theoretical expectations indicate either a deﬁciency in our currentSLAC-PUB-11888June 2006Invited Talk presented at 3rd International Conference On Flavor Physics (ICFP 2005),10/3/2005-10/8/2005, Chungli, TaiwanStanford Linear Accelerator Center,  Stanford, CA 94025understanding of these decays, or a tantalizing hint of possible new physics eﬀects. There has been considerableactivity in the study these B → V V decays recently.The remaining sections of these proceedings discuss experimental techniques, results on searches for directCP violation, branching fractions for the B-meson decays to h+h− and a+1 π−, and studies of B → V V decays.There is a summary of results at the end of the article. Charge conjugation is implied throughout theseproceedings.2 Experimental techniquesSignal candidates are identiﬁed using two kinematic variables mES and ΔE. The energy diﬀerence ΔE is deﬁnedas the diﬀerence between the energy of the B candidate and the beam energy,√s/2, in the center of mass (CM)frame. The beam-energy substituted mass, mES, is deﬁned asmES =√(s/2 + pi · pB)2/E2i − p2B , (3)where√s is the total energy of both beams (10.58GeV), the B momentum pB and four-momentum of theinitial state (Ei,pi) are deﬁned in the laboratory frame.Continuum e+e− → qq (q = u, d, s, c) events are the dominant background to rare hadronic B-decays. Todiscriminate signal from the continuum background one uses the fact that ﬁnal state particles in B events tendto be spherically distributed, whereas continuum events are more jet-like. Event shape variables are combinedinto a single variable with the purpose of discriminating between signal and continuum background events (Forexample, see Refs. [12] and [13].). All of the results discussed here are obtained using an extended unbinnedmaximum-likelihood ﬁt to the data.3 Results3.1 Direct CP violation searchesB0-meson decays to the K+π− and K−π+ ﬁnal states are self tagging in that the charge of the kaon in theﬁnal state determines the ﬂavor of the decaying B-meson: B0 → K−π+, and B0 → K+π−. The B-factorieshave measured a signiﬁcantly non-zero ACP in these decays. The results reported areACP Kπ = −0.113± 0.022(stat)± 0.08(syst), (Belle)ACP Kπ = −0.133± 0.030(stat)± 0.09(syst), (BABAR)using 386×106, and 227×106 BB pairs, respectively [14, 15]. On averaging the results one obtains ACP =−0.115± 0.018 [16]. This average includes results from the CDF and CLEO experiments, however the BABARand Belle results dominate the average. This constitutes an observation of direct CPV in B-meson decay, whichis the second type of CPV observed in B decays. Figure 1 shows the mES distributions of B0 → K−π+, andB0 → K+π− from the BABAR data.There is considerable activity in searching for other possible indications of direct CPV at the B-factories.So far, there has been no additional observations of this eﬀect to date. The best evidence obtained for directCPV in other B decays is in the channel B0 → π+π−. More statistics are required to establish CPV in thisdecay. The Belle data give a 4.0σ evidence for direct CPV [12]. The BABAR data do not yet show any evidencefor direct CPV [13]. The measurements areCππ = −0.56± 0.12(stat)± 0.06(syst), (Belle)Cππ = −0.09± 0.15(stat)± 0.04(syst), (BABAR)using 275×106, and 232×106 BB pairs, respectively.Another promising decay channel that provides evidence for direct CPV is B+ → ρ0K+. The Belle dataare consistent with a 3.9σ evidence for direct CPV , whereas currently the BABAR data shows no indication of2)2 (GeV/cESm5.2 5.22 5.24 5.26 5.28 5.32200400 a))2 (GeV/cESm5.2 5.22 5.24 5.26 5.28 5.3Asymmetry-0.100.1Events / 2.5 MeV/cAsymmetryb)Figure 1: Distributions of (a) mES B0 → K−π+, and B0 → K+π− from the BABAR data, and (b) ACP takenfrom Ref. [14]. The solid histogram is for K+π− and the dashed histogram is for K−π+. The region below theB mass is dominated by continuum background. The Belle data exhibit similar properties [15].an asymmetry [17]. The measured asymmetries areACP ρ0K+ = 0.30± 0.11(stat)± 0.02(syst)+11−4 (model), (Belle)ACP ρ0K+ = 0.32± 0.13(stat)± 0.06(syst)+8−5(model), (BABAR)using 386×106, and 226×106 BB pairs, respectively. Again, more data are required in order to establish directCPV in this mode.3.2 Branching fractions of B → hh decaysThe decay of B mesons to ππ, and Kπ ﬁnal states are of general interest to the ﬁeld of B physics. The B0 →π+π− branching fraction is an input to the ππ isospin analysis, and measurement of α [18], and measurementsof the decays to Kπ are inputs to help elucidate the so-called Kπ puzzle [19].The BABAR collaboration have recently updated these measurements with 232×10−6 B pairs [9]. In thisanalysis, BABAR take into account the possible eﬀects of ﬁnal state radiation (FSR) [10]. Taking FSR intoaccount has ramiﬁcations on the extraction of the signal yield, as well as the quoted signal eﬃciency that isused in calculating branching fractions. The results obtained are:B(B0 → K+π−) = (19.2± 0.6(stat)± 0.6(syst))× 10−6,B(B0 → π+π−) = (5.5± 0.4(stat)± 0.3(syst))× 10−6,B(B0 → K+K−) < 0.4× 10−6(90%C.L.).The Kπ (ππ) branching fractions reported are 7% (17%) higher than previous measurements from the B-factories [20]. This highlights the signiﬁcance of further understanding and treatment of FSR in rare hadronicB-decays.3.3 Observation of the decay B0 → a±1 π∓Some time ago it was suggested that one could measure the Unitarity Triangle angle α using the non-CPeigenstate decay B0 → a±1 π∓ [21]. BABAR has recently observed the decay B0 → a±1 π∓, and Belle have3conﬁrmed this observation [22]. The measured branching fraction for this decay isB(B0 → a±1 π∓) = (33.2± 3.8(stat)± 3.0(syst))× 10−6, (BABAR)B(B0 → a±1 π∓) = (48.6± 4.1(stat)± 3.9(syst))× 10−6, (Belle)using 218×106, and 275×106 BB pairs, respectively. One can expect the B-factories to investigate the prospectsof such a time-dependent CP analysis in the coming years. An isospin analysis of B → a1π decays would beexperimentally challenging. The use of SU(3) to measure α with B → a1π decays has recently been proposed [11]as an alternative. This approach requires experimental knowledge of the decays B → a1K, B → K1(1270)πand B → K1(1400)π. BABAR recently performed a search for the related decay B0 → a±1 ρ∓ [23] using 110×106BB pairs. The result of this search was an upper limit of < 61× 10−6 (90%C.L.).3.4 Dynamics of B-meson decays to two vector particlesThe B-factories have performed studies of the angular correlations of several types of B → V V decay: B → ρρ,B → Kρ, B → Kω, and B → Kφ [24, 25]. Figure 2 shows a schematic of the topology of a B → V V decay,where each vector particle decays to a two body ﬁnal state. where θi (i=1,2) is the helicity angle of the vectorθ 2θ 1V122431Vφ  Figure 2: The decay of a B-meson to via two vector mesons, V1 and V2, to a four particle ﬁnal state.particle deﬁned as the angle between the daughter momentum in the vector particle rest frame and the ﬂightdirection of the B0 in this frame. The angle φ is the angle between the decay planes of the vector mesons. Mostof the decays studied have limited statistics and focus on extracting the fraction of longitudinally polarizedevents (fL) from the data after integrating over φ. The angular distribution used for these decays isd2ΓΓd cos θ1d cos θ2=94(fL cos2 θ1 cos2 θ2 +14(1 − fL) sin2 θ1 sin2 θ2), (4)A full angular analysis is performed for B-meson decays to φK∗ [25, 26]. Early calculations of fL predicted thelongitudinal polarization would dominate in B → V V decays [27]. Figure 3 shows the measured values of fLobtained from experiment. There is a pattern to the underlying physics processes which needs to be understoodin the measured values of fL. The tree dominated decays of B mesons to ρρ, Kω and Kρ are consistent withthe naive expectation that: fL ∼ O(1−m2V /m2b). However the loop dominated modes (Kφ and K+ρ−) havelower values of fL than expected. It is possible that improvements in calculations of fL for the loop dominatedmodes could resolve this issue. Possible new physics contributions modifying these observables have also beendiscussed [28]. There remains work to be done in this area, both on the experimental and theoretical side. TheB-factories need to perform as many diﬀerent measurements in as many diﬀerent B → V V decay modes aspossible. One can also measure CP -violating, T -odd triple product asymmetries in B → V V decays [29].4ρ+ρ−ρ+ρ0K∗+ρ0ωρ+K∗0ρ+φK∗0φK∗+Polarizations of Charmless DecaysLongitudinal Polarization Fraction (fL) 0.2 0.4  1.0  1.2 0.6  0.8PDG2004BABARBelleCLEONew Avg.HFAGJULY 15th 2005CDFFigure 3: The measured values of fL in B → V V decays [16].4 SummaryThe B-factories have established direct CP violation in B0 → K±π∓ decays in recent years. Tantalizing hintsof direct CPV are starting to emerge in other modes. As the B-factories continue to accumulate data we shouldsee direct CPV being established in more decay modes.In summary, the study of rare hadronic B-meson decays has provided a rich harvest of information sincethe B-factories started taking data. There is still a wide range of physics that we can learn from using thesedecays. The recent observation of B0 → a±1 π∓ raises the possibility that the B-factories might be able to addanother mode to the list of those providing measurements of the Unitarity Triangle angle α. Experimental andtheoretical work is required to understand the pattern of measured fL in B → V V decays.5 AcknowledgmentsThis work is supported in part by the UK’s Particle Physics and Astronomy Research Council, and the U.S.Department of Energy under contract number DE-AC02-76SF00515.References[1] N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963);M. Kobayashi and T. Maskawa, Prog. Th. Phys. 49, 652 (1973).[2] J. Christenson et al., Phys. Rev. Lett. 13, 138 (1964).[3] BABAR Collaboration, Phys. Rev. Lett. 87 091801 (2001), Belle Collaboration, Phys. Rev. Lett. 87 091802(2001).[4] See the contributions of M. Hazumi and S. Ganzur at this conference;A. Bevan, Modern Physics Letters A, Vol. 21, No. 4 305-317 (2006).[5] NA48 Collaboration, R. Batley et al., Phys. Lett. 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Rare Hadronic B Decays

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Rare hadronic B decays

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