Measurement of angle β with time-dependent CP asymmetry in B0 K+K−K0 decays → E. Di Marco∗ Dipartimento di Fisica, Universit`a di Roma “La Sapienza”, P.le Aldo Moro 2, 00185 Roma, Italy WepresentrecentresultsonCP-violation,andthedeterminationofCKMangleβ,withthedecay B0→K+K−K0, with BABAR and Belle detectors. I. INTRODUCTION isthecenter-of-massenergy,p isthereconstructedmo- B mentumoftheB0 candidate,andE∗ isitsenergycalcu- B In the Standard Model (SM) of particle physics, latedin the e+e− restframe. Forsignaldecays,the mES the phase of the Cabibbo-Kobayashi-Maskawa (CKM) distribution peaks near the B0 mass with a resolutionof quark-mixing matrix [1, 2] is the only source of CP vi- about 2.5 MeV/c2, and the ∆E distribution peaks near 7 olation in the quark sector. Due to the interference be- zerowith a resolutionof10 50 MeV, depending onthe − 0 tween mixing and decay, this phase can be observed in final state. For decays with a K0, K0 momentum is not L L 0 measurements of time-dependent CP asymmetries of B0 measured,but evaluatedby constrainingthe B0 mass to 2 mesons. In the SM, CP asymmetries in b ss¯s decays, thenominalvalue[6]Inthiscaseonly∆E isused,andit n suchasB0 K+K−K0,areexpectedtob→enearlyequal has a resolution of about 3 MeV. The main background a to those ob→served in tree-dominated b ¸cs decays [3]. comes from random combinations of particles produced J However, because in the SM the forme→r are dominated incontinuume+e− →qq¯. Inthe CMframe,theseevents 6 by loop amplitudes, new particles in those loops poten- have a jet-like structure, while B decays have a nearly 2 tiallyintroducenewphysicsatthesameorderastheSM isotropic topology. We parameterize this difference us- process. Within the SM, deviations from the expected ingseveralvariables,providingadditionaldiscrimination 1 v CP asymmetries in B0 K+K−K0 decays depend on betweensignalandbackground. Anothersourceofback- 7 the Dalitz plot position→, but are expected to be small groundcomesfromdecaysofB mesonswhichmimic the 4 and positive [4]. In particular, for the decay B0 φK0 signal. Thisbackgroundistypicallymoredifficulttosup- 0 they are expected to be less than 4%. BABAR e→xtracts press. Thecontributionofthesedecaysisestimatedfrom 1 the time-dependent CP-violation parameters by taking Monte Carlo simulations. 0 7 into account different amplitudes and phases across the For each fully reconstructed B0 meson (BCP), we use 0 B0 and B0 Dalitz plots, while Belle measures it sepa- theremainingparticlesintheeventtoreconstructthede- / rately for B0 φK0 and the rest of K+K−K0 events, cay vertex of the other B meson (Btag) and identify its x → -e negTlhecetianngailnytseersfeprreensceentbeedtwheeerneianrteerbmaesdediatoenst3a4t7es.(535) flthaevoflraqvtoarg.oAf tmheulBtitvaagrimateesotnagigninBgAaBlgARoridtahtma daentdercmlaisnseis- p million BB pairs collected with the BABAR (Belle) de- fies it in one of seven mutually exclusive tagging cate- e tector at the SLAC PEP-II (KEKB) e+e− asymmetric- gories depending on the presence of prompt leptons, one h energy collider. Data are collected on the Υ(4S) res- ormorechargedkaonsandpions[7]. Theperformancesof : v onance, while a fraction of about 10% is collected at this algorithm are measured with a data sample of fully Xi approximatively 40 MeV below the Υ(4S) resonance, reconstructed B0 decays into flavor eigenstates (Bflav): and it is used to study the background arising from B0 D(∗)−π+/ρ+/a+. The effective tagging efficiency ar e+e− qq(q = u,d,s,c) continuum events. The BABAR isQ→ ǫc(1 2wc)21=0.304 0.003forBABAR(similar and B→elle detectors are described in detail elsewhere [5]. for B≡ellPe),cwhe−re ǫc (wc) is the±efficiency (mistag proba- bility)foreventstaggedincategoryc. ForBelle,thetag- ging algorithm returns q and the tag quality r, which tag II. EVENT RECONSTRUCTION varies from r = 0 for no flavor discrimination to r = 1 for unambiguous flavor assignment. Events with r 0.1 ≤ are discarded for the CP-asymmetry measurement, and Events are fully reconstructed combining tracks and neutralclustersinthedetectortoformB0 K+K−K0, the others are sorted into six intervals. The difference withaK0reconstructedasK0 π+π−(B→0 )(BABAR ∆t tCP ttag of the proper decay times of the BCP and Belle) and K0 π0πS0→(B0 ), or(+K−)0 (B0 ) and≡Btag m−esons is calculated from the measured dis- (BABARonly). InorSder→toselectBca(n00d)idatesweLusea(sLe)t tance between the reconstructed decay vertices and the boost(βγ =0.56(0.465)forBABAR(Belle))oftheΥ(4S). of two kinematic variables: the beam-energy-substituted massm = (s/2+p p )2/E2+p2 (M forBelle), The error on ∆t, σ∆t, is also estimated for each event. and theESenerpgy differenic·e B∆E =i E∗B √bsc/2. Here, Events are accepted if the calculated ∆t uncertainty is (E ,p ) is the four-vector of the initiaBl e−+e− system, √s less than 2.5 ps and ∆t <20 ps. The fraction of events i i | | which satisfy these requirements is 95%. The BABAR analysis strategy is to perform a maxi- mumlikelihoodfittothe selectedK+K−K0 eventswith ∗Electronicaddress: [email protected] a likelihood function , which uses as probability den- L 2 sity function (PDF) for each event, (m ,∆E) Z = 4~q p~, where ~q is the momentum of the res- ES r L ≡ P · − · PLow·PDP(mK+K−,cosθH,∆t,qtag)×R(∆t,σ∆t)where onant daughter, and p~ is the momentum of the third n is the yield for each category (i = signal, continuum particle in the resonance frame. We describe the line- i background, and BB backgrounds), and is a ∆t reso- shape for the φ(1020), X (1550), and χ using the rel- 0 c0 R lution function with parameters determined in the B ativistic Breit-Wigner function [8]. For the φ(1020) and flav data sample. is a supplementary PDF used only χ parameters, we use average measurements [6]. For Low c0 P in the fits to the region with mK+K− < 1.1 GeV/c2 dis- the X0(1550)resonance,we useparametersfromthe our cussed below. It depends on the event shape variables analysis of the B+ K+K−K+ decay [8]. The f (980) 0 → and, for B0 only, the missing momentum of the event. resonanceis describedwith the coupled-channel(Flatt´e) (L) ThisPDFaccountsforthe factthatsignaldecayshavea function [8], with the coupling strengths for the KK missingmomentumconsistentwiththereconstructedK0 and ππ channels taken as g = 0.165 0.018 GeV/c2, L π ± direction,while forbackgroundeventsitis moreisotrop- g /g = 4.21 0.33, and the resonance pole mass K π ± ically distributed. We characterize events on the Dalitz m = 0.965 0.010 GeV/c2 [9]. In addition to resonant r plotintermsoftheinvariantK+K− mass,mK+K−,and decays, we i±nclude three non-resonant amplitudes. The the cosine of the helicity angle between the K+ and the existingtheoreticalmodels,whichconsidercontributions K0 in the CM frame of the K+K− system, cosθ . fromcontacttermorhigher-resonancetails[10,11,12]do H IntheBelleapproachthelikelihoodfortheeventselec- notreproduce wellthe features observedin data. There- tion is the same, without . A loose requirement on fore we adopt a phenomenological parameterization [13] DP P the likelihoodratio /( + ) isapplied, and describe the non-resonant terms as an exponential s/b sig sig bkg R ≡L L L andamaximum-likelihoodfittoobserved∆tdistribution decay: is performed to the selected events. ANR =Xcijeiφije−αm2ij ·(1+bNR)·ei(β+δNR) (4) i6=j III. ANALYSIS OF DALITZ PLOT and similarly for ¯ . NR A We compute the CP-asymmetry parameters for com- Accountingfortheexperimentalefficiencyε,theDalitz ponent r from the asymmetries in amplitudes (b ) and r plot PDF for signal events is phases (δ ) given in Eq. (3). The rate asymmetry is r PDP =dΓ·ε(mK+K−,cosθH)·|J(mK+K−)|, (1) ACPr = |A¯¯r|22+−|Ar|22 = 1−+2bbr2, (5) wherethefinaltermistheJacobianofthetransformation |Ar| |Ar| r and β =β+δ is the phase asymmetry. for our choice of Dalitz plot coordinates. effr r The fraction for resonance r is computed The time- and flavor-dependent decay rate over the Dalitz plot is = R dcosθH dmK+K− ·|J|·(|Ar|2+|A¯r|2). (6) dΓ e−|∆t|/τ 2+ ¯2 (2) Fr R dcosθH dmK+K− ·|J|·(|A|2+|A¯|2) ∝ 4τ × h |A| (cid:12)A(cid:12) The sum of the fractions can be larger than one due to + η q (cid:12) 2(cid:12)Im ¯ ∗e−2iβ sin∆m ∆t negative interference in the scalar sector. qCP t2ag ¯2(cid:0)AcAos∆m ∆(cid:1)t , d B0Theafintdto4B99ABAR52dBat0aretsuigrnnasl8c7a9n±d3id6aBte0s(.+−T),h1e3i8so±b1a7r − (cid:16)|A| −(cid:12)(cid:12)A(cid:12)(cid:12) (cid:17) d i am(p00li)tudes, ph±ases and(Lf)ractions are listed in Table I. where η = 1 ( 1) for B0 , B0 (B0 ). τ and Signal weighted distribution for the Dalitz plot projec- ∆m arCePthe life−time and m(+ix−i)ng fr(e0q0)uency(Lo)f the B0 tions in the entire phase space and in a reduced region mesodn,respectively[6]. TheCKMangleβentersthrough mK+K− < 1.1 GeV/c2, where we extract separate CP B0-B0 mixing. Actual worldaverageis β 0.38 [6]. We asymmetry parameters, are shown in Fig. 1. define the amplitude ( ¯) for B0 (B0) d∼ecay as a sum The fit to Belle data returns 840±34 signal B0(+−) A A candidates, after vetoing the φ with the requirement of isobar amplitudes, mK+K− mφ > 15 MeV/c2. | − | ( ¯)= c (1 b )ei(φr±δr) f(f¯) , (3) As a cross-check of the Dalitz model extracted by the A A X r ± r · r fit, we compute angular moments and extract strengths r of the partial waves in mK+K− bins using the B0(+−) where the parameters c and φ are the magnitude and sample. In this approach we only assume that the two r r phase of the amplitude of component r, and we allow lowest partial waves are present. We verified this as- for different isobar coefficients for B0 and B0 decays sumption determining that the higher angular moments through the asymmetry parameters b and δ . Our ( P ) are consistent with zero. In our model, the r r 3−5 model includes the vector meson φ(1020). We include Ph-wavei contribution comes from φ(1020)K0 decays and S also decays into intermediate scalar mesons: f (980), from non-resonant events with K+K0 and K−K0 mass 0 S S X (1550), and χ . The angular distribution is con- dependence. WefindthatthetotalfractionofP-wavein 0 c0 stant for scalar decays, whereas for vector decays is the entire Dalitz plot is f =0.29 0.03(stat). p ± 3 TABLE I: Isobar amplitudes, phases, and fractions from the TABLEII:Time-dependentCP-asymmetriesACP andβeff for fit to BABAR data. The fraction for non-resonant amplitude B0 →K+K−K0 in mK+K− <1.1 GeV/c2 and in the whole is given for the combination of the threecontributions. phase space (BABAR), and C and S for B0 → K+K−K0 in S Decay Amplitudecr Phase φr Fraction Fr (%) mthKe+sKec−on>d1s.y0s3t4emGaetVic/.c2T(hBeeltleh)i.rdTehrerofirrsitneSrroirsissyssttaetmisatticic, φ(1020)K0 0.0098±0.0016 −0.11±0.31 12.9±1.3 effect due tothe CP-contentuncertainty. f0(980)K0 0.528±0.063 −0.33±0.26 22.3±8.9 X0(1550)K0 0.130±0.025 −0.54±0.24 4.1±1.8 Decay CP asymmetry NR (K+K−) 1 (fixed) 0 (fixed) ACP(φK0) −0.18±0.20±0.10 (K+K0) 0.38±0.11 2.01±0.28 91±19 βeff(φK0) 0.06±0.16±0.05 (K−K0) 0.38±0.16 −1.19±0.37 ACP(f0K0) 0.45±0.28±0.10 χc0K0 0.0343±0.0067 1.29±0.41 2.84±0.77 βeff(f0K0) 0.18±0.19±0.04 D+K− 1.18±0.24 – 3.18±0.89 ACP(K+K−K0) −0.034±0.079±0.025 Ds+K− 0.85±0.20 – 1.72±0.65 βeff(K+K−K0) 0.361±0.079±0.037 C(K+K−K0) 0.09±0.10±0.05 S sin(2β )(K+K−K0) 0.68±0.15±0.03+0.21 eff S −0.13 Events / ( 0.095 GeV )Events / ( 0.095 GeV ) 112211220505050500000000 BprAeliBmiAnaRry Events / ( 0.1 )Events / ( 0.1 ) 3456789345678900000000000000 BprAeliBmiAnaRry thereflectionissuppressedfromtheinterferencebetween 5500 2200 CP-evenandCP-odddecaysthatgiverisetoacos(2βeff) 0011 11..55 22 22..55 33 33..55 44 44..55 110000--11 --00..88--00..66--00..44--00..22 --00 00..22 00..44 00..66 00..88 11 term in Eq.3, in addition to the sin(2βeff) terms that mmKK++ KK --((GGeeVV)) ccooss qqHH comefromtheinterferencedecayswithandwithoutmix- ing. In this case we measure an average β and A for Events / ( 0.0028 GeV ) Events / ( 0.0028 GeV ) 12345612345600000000000000 BprAeliBmiAnaRry Events / ( 0.2 )Events / ( 0.2 ) 12345612345600000000000000 BprAeliBmiAnaRry gtdhieoenWncfeeumlmflrKKoe+amK+suK−trhe−e<aKrl1es0os.1tpCohGPfae-stVaehs/esycpmD2a,amcwelie.thtzeryrpelpotathreiasmφheimtgehorlsdyeinrledtdCheuPepceernde--. --1100 --1100 In this region, we fit the CP time-dependent asymme- 11 11..0022 11..0044 11..0066 11..0088 11..11 --11 --00..88--00..66--00..44--00..22 --00 00..22 00..44 00..66 00..88 11 mmKK++ KK --((GGeeVV)) ccooss qqHH tries for the φ(1020) and f0(980) components, while we fix the ones for the low-K+K− tail of the non-resonant FIG. 1: Distributions of the Dalitz plot variables (left) decays to the SM expectation. The Dalitz plot model mK+K− and (right) cosθH for signal events (points) com- is fixed to the one measured in the full phase space and pared with the fit PDF for B0(+−) candidates. Top distri- reported in Table I, with the exception of the φ(1020) butions are for the entire phase space, bottom for a reduced isobar coefficients, which are fitted simultaneously with region mK+K− <1.1 GeV/c2. CP-asymmetryparameters. Inthisreducedregionofthe phase space we find 252 19, 35 9, 195 33 signal ± ± ± events for B0 , B0 and B0 respectively. The re- IV. CP ASYMMETRY (+−) (00) (L) sults on the CP asymmetries are shownin Table II. The sources of systematic uncertainties are briefly described In the Belle “quasi-two-body” approach, the time de- below. pendent decay rate in Eq. 3 is simplified because the in- The significance of the nominal result for β in the terference effects are neglected: eff entire Dalitz plot, compared to the trigonometrical re- e−|∆t|/τ flectionisof4.6σ. ThesignificanceoftheCP-violationis f±(∆t) = (7) 4.5σ. In Fig. 2 the distributions of ∆t for B0-tagged 4τ × and B0-tagged events, and the asymmetry (∆t) = The para[m1e±tersSCsinan(∆dmSdd∆est)cr∓ibCe tchoes(a∆mmoudn∆tt)of]C,P vi- (BNABBA0R−dNatBa0)a/r(eNsBh0o+wnN.BI0n),Ffoigr.b3actkhgeroausynmdmsAuebtrtireasctfeodr olation in decay and in the interference between decay good-tagged (r > 0.5) K+K−K0 events in Belle data S with and without mixing, respectively. The SM expec- are shown. tations for B0 K+K−K0 are S = (2f 1)sin2β, Systematic effects are associated to parameterization → S − +− where f is the CP-even fraction. Using isospin rela- of the signal PDFs, possible fit bias, fixed ∆t resolu- + tions, f has been measured on 357 fb−1 data sample, tion parameters, B0 lifetime, B0-B0 mixing and flavor + and gives f = 0.93 0.09(stat) 0.05(syst) [13]. This tagging parameters. Smaller errors due to beam-spot + ± ± resultisconfirmedbypartialwaveanalysisperformedon position uncertainty, detector alignment, and the boost BABAR data [14]. correction are based on studies done in charmonium de- In the BABAR analysis, the time-dependent fit to the cays. In BABAR analysis, an uncertainty is assigned to Dalitz plot allows to extract β removing the trigono- the resonant and non-resonant line-shapes. We try sev- eff metrical ambiguity β π/2 β . In this analysis eral alternative non-resonant models which omit some eff eff → − 4 Events / ( 2 ps )Events / ( 2 ps )Events / ( 2 ps ) 122312231223505050505050 BprAelBimiAnaRry Events / ( 1.6 ps )Events / ( 1.6 ps )Events / ( 1.6 ps ) 111111686868020202000000000000 BprAelBimiAnaRry φgthioebnud.tiWfftehereetinrhceserheaffroporemeiostmhdieettrteherfmeernineonendc-erferfisotomnaastnhatetsehyrismgthesm-amnaatdsicstaerkere-- 111000 444000 555 222000 ror for φK0 and f (980)K0 CP-asymmetries. In Belle 000---888 ---666 ---444 ---222 000 222 444 666 888 000---888 ---666 ---444 ---222 000 222 444 666 888 0 DDDttt (((pppsss))) DDDttt (((pppsss))) measurement, by far the largest systematic uncertainty AsymmetryAsymmetry 00..5511 AsymmetryAsymmetry 00..5511 ConP-CePvenpafrraamcteiotenrsf+is.associated to the knowledge of the 00 00 --00..55 --00..55 --11--88 --66 --44 --22 00 22 44 66 88 --88 --66 --44 --22 00 22 44 66 88 DDtt ((ppss)) DDtt ((ppss)) V. CONCLUSIONS FIG.2: (top)∆tdistributionsand(bottom)asymmetriesfor We have measured the time-dependent CP- Ban0d(+(−r)igehvte)ntthsefowrh(oleleft)D1a.l0it0z45pl<otmfoKr+BKA−BA<R1d.a0t3a4.5 FGoerV/thc2e asymmetries in B0 → K+K−K0 decays, with a ∆tdistributions,B0-(B0-)taggedsignal-weightedeventsare simultaneous analysis of the Dalitz plot distribu- tion of the intermediate states (BABAR) or with a shownasfilled(open)circles,withthePDFprojectioninsolid blue(dashed red). “quasi-two-body” approach (Belle). The measured value of CP-asymmetries in the entire Dalitz plot is β = 0.361 0.079 0.037, which is consistent with eff ± ± the SM expectations (β 0.38). The trigonometrical 5 ps 1 ambiguity in βeff is remo∼ved at 4.6σ. This is the first w asymmetry / 1.-00..550 aaseuxnnctddrhaBβcmet0ffeeda→s=tuhrfe0e0m.(C188eP9n0±-ta)sKi0ny.m01,p9met±noegt0bruy.ei0n4pβ,amerffroaedms=peeset.c0et.r0iAsv6defol±dyri.t0Bio.T10n6ha→el±lryeφ,0fKo.w0r50ee Ra we do not observe significant deviations from the SM -1 predictions. -7.5 -5 -2.5 0 2.5 5 7.5 D t (ps) In Belle measurement, the measured sin(2βeff) = 0.68 0.15 0.03+0.21 for B0 K+K−K0 decays with FIG. 3: Asymmetry for good-tagged events (r > 0.5) for exclu±sion of±φK0 −ev0e.1n3ts is also→consistentSwith SM pre- B0 → K+K−K0 for Belle data. The solid curve shows the S S dictions. PDF projection for the result of the unbinned maximum- likelihood fit. The dashed curve shows the SM expectation with the measurement of CP-violation parameters for the B0 →J/ψK0 decays. Acknowledgments The author thanks the organizers of the workshop, of the dependencies on K+K0 and K−K0 masses (see and also Fernando Ferroni, Maurizio Pierini, Gianluca Eq. 4). We also study the effect of the uncertainty of Cavoto, and Denis Dujmic, without that I would have the shape parameter α on the CP parameters. The non- not participated to it and that let me to be involved in resonant events contribute to the background under the this fascinating measurement. [1] N.Cabibbo, Phys.Rev. Lett. 10, 531 (1963). 94, 161803 (2005) [2] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, [8] B. Aubert et al. [BABAR Collaboration], Phys. Rev. D 652 (1973). 74, 032003 (2006) [3] K. F. Chen et al. [Belle Collaboration], [9] M. Ablikim et al. [BES Collaboration], Phys. Lett. B arXiv:hep-ex/0608039. 607, 243 (2005) B. Aubert et al. [BABAR Collaboration], [10] H. Y. Cheng and K. 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