January 11, 2011 Determination of γ from B K π decays and related modes ∗ → 1 1 0 2 n a J Eugenia Maria Teresa Irene Puccio1 0 1 Department of Physics ] x University of Warwick, Coventry, CV4 7AL, UK e - p e h [ 1 v 9 We present the status of recent results from the BABAR and Belle ex- 2 periments onthemeasurement oftheangleγ fromtheDalitzplotanalyses 8 1 of B0 K0π+π− and B0 K+π−π0. . → S → 1 0 1 1 : v i X r PROCEEDINGS OF a CKM2010, the 6th International Workshop on the CKM Unitarity Triangle University of Warwick, UK, September 6–10, 2010 1Speaker on behalf of the BABAR Collaboration 1 Introduction ∗ At tree level, B K π decays are sensitive to γ through the relation → A(K∗−π+)+√2A K∗0π0 e−2iγ , (1) ∝ A(K∗+π−)+√2A(cid:16)(K∗0π0)(cid:17) where A and A are the decay amplitude and its charge conjugate respectively. To measure γ, three-body decays have an advantage over quasi-two body decays since ∗ B K π can interfere through the same final state in B Kππ. By measur- → → ing the interference pattern in the Dalitz plot, it is possible to determine not only magnitudes of the amplitudes as in the two body decays but also the relative phases between the amplitudes. The cleanest method to determine γ from Kππ Dalitz plots involves the charmless decays B0 K+π−π0 and B0 K0π+π− [1, 2]. The method involves forming isospin triangles→from K∗π intermed→iateSmodes in B0 K+π−π0 and B0 K0π+π−. By using isospin decomposition, the QCD pengui→n contribu- → S ∗ tions in B K π decays are cancelled and the resultant amplitude is as follows: → 3A = A(B0 K∗+π−)+√2A(B0 K∗0π0), (2) 3/2 → → with an equivalent amplitude for the charge-conjugate state, A . In the absence of 3/2 electroweak penguins(EWP), A carries a weak phase γ so that in this limit 3/2 1 A 3/2 γ = Φ = arg . (3) 3/2 −2 A3/2! The phase Φ can be determined by measuring the following quantities: 3/2 phase ∆φ, between B0 K∗+π− and B0 K∗−π+ in B0 K0π+π−. • → → → S phase φ, between B0 K∗+π− and B0 K∗0π0 in B0 K+π−π0; • → → → its charge conjugate equivalent in B0 K−π+π0; • → This method to extract γ is similar to the Snyder-Quinn method used to obtain α from B0 π+π−π0 [3]. B ρπ amplitudes, measured from the three body decay of B0 →π+π−π0, are used i→n this method to provide an SU(3) correction for EWP → contributions, necessary to obtain a constraint for γ. 2 Experimental Results: ∆φ TheB0 K0π+π− Dalitzplotprovidesthephasedifference∆φbetweenB0 K∗+π− and B0 →→ KS∗−π+measured from ∆φK∗π = φK∗−π+ −φK∗+π− To obtain ∆φ,→the K∗π 1 7700 22)V/c)V/c 6600 GeGe 5500 Events/(0.0005 Events/(0.0005 1234123400000000 Norm.Residuals5--02442.272 5.274 5.276 5.278 5.28 5.282 5.284 5.286 m (GeV/c2) ES Figure1: ResultantDalitzplotdistribution(left)andprojectionplotsform (center, ES BABAR results) [4] and ∆E (right, Belle result) [5]. Experiment ∆φ(K∗+π−) BABAR Soln. 1 (58.3 32.7 4.6 8.1)◦ BABAR Soln. 2 (176.6± 28.8± 4.6± 8.1)◦ Belle Soln. 1 ( 0.±7 24 ±11 ±18)◦ 23 Belle Soln. 1 (−14.6 ±19 ±11 ±18)◦ 20 ± ± ± Table 1: Summary of the results for ∆φ(K∗+π−) from time-dependent Dalitz plot analyses of B0 K0π+π−. The uncertainties quoted are statistical, systematic and → S model-dependent respectively. phases need to be measured relative to each other, taking into account also the addi- tional phase of 2β. The relative phases are determined at the interference regions − around the edges of the Dalitz plot. However the overlap region of resonances is small and the effect on event density small, making it crucial to understand backgrounds and efficiencies in the interference regions. The main background contribution in this Dalitz plot is found to come from continuum events and those are mostly rejected by a Neural Network. The remaining background contribution are B meson decays to charm final states, shown as bands in the resultant Dalitz plot distribution in Fig- ure 1. Projection plots for signal and background of discriminating variables, m ES taken from the BABAR result of 383 million BB events [4] and ∆E from the Belle result of 657 million BB events [5], are also shown in Figure 1. The results of the likelihood scans for ∆φ are shown in Figure 2 and summarised in Table 1. Two fit solutions are found corresponding to the interference between K∗0(1430)and the non- 2 resonant component. These two solutions give different results for the values of ∆φ. There is some disagreement between theBABAR and Belle results. The experimentally measured values of ∆φ shown in Table 1 include the B0B0 mixing phase and this has to be removed before the values can be used in the extraction of γ. 2 Figure 2: Likelihood scans of ∆φ from Dalitz plot analyses of B0 K0π+π−. The left likelihood distribution is taken from the BABAR results [4], the→centSre and right distributions are from Belle [5] and represent the scans of the two different solutions. 3 Experimental Results: φ and φ The other two parameters required to determine γ are φ and its charge conju- gate, φ. These are the relative phases between B0 K∗+π− and B0 K∗0π0 and B0 K∗−π+ and B0 K∗0π0 respectively: → → → → φ = φK∗0π0 −φK∗+π− φ = φK∗0π0 −φK∗−π+ (4) BothoftheserelativephasesaredeterminedfromDalitzplotanalysisofB0 K+π−π0 anditschargeconjugate. PreliminaryresultsareavailablefromthefullBAB→ARdataset of 454 million BB events [7]. Expanding Eq. 3, Φ is obtained fromthe combination 3/2 ofthephasesφandφandsubtractingthephase∆φobtainedfromthetime-dependent Dalitz plot analysis of B0 K0π+π−. → S 4 Issues with interpretation The choice of the phase convention isimportant when combining the results since fail- ◦ ure to take the convention into account can result in a 180 shift in relative phase [8]. The amplitude is proportional to the cosine of a helicity angle between the final states particles in a three-body decay. The helicity convention defines an ordering of par- ticles in the SU(2) decomposition that can introduce a sign flip in Eq. 2. Therefore relative phases between vector amplitudes need to be interpreted with respect to a given helicity convention. Another issue with the interpretation of the results is that whereas QCD penguin contributions cancel in the sum of AK∗π so that Eq. 2 is QCD penguin free, EW penguin contributions still need to be accounted for. SU(3) decomposition of operators gives a good approximation to A = Teiγ P A (ρ+iη) 1+r +C 1 r , (5) 3/2 EWP 3/2 3/2 3/2 − ∝ − (cid:16) (cid:17) (cid:16) (cid:17) 3 Decay model BF ( 10−6) A CP × B+ ρ0π+ 8.3+1.2 0.18+0.09 B+ → ρ+π0 10.9−+11.3.4 0.02 −00.1.171 B+ → K+K∗0 0.68 −01..519 ± → ± − B+ K0K0π+ < 0.51 → S S − Table 2: Current experimental results for BF and A for two body and quasi-two CP ∗ body ρπ and K K decays as taken from HFAG Winter 2010 [9]. where T and P are the tree and EW penguin contributions respectively. C in EWP Eq. 5 depends only on EW physics and is well known to a theoretical error below 1% with C = 0.27. The quantity r is the ratio of hadronic matrix elements and is 3/2 − measured from [2, 6]: Aρ+π0 −Aρ0π+ −√2[AK∗+K0 −AK+K∗0] r = (cid:20) (cid:21) . (6) 3/2 Aρ+π0 +Aρ0π+ Current experimental results for these quantities are shown in Table 2. B ρπ ∗ → decays have well known BFs and A , however amplitudes for KK decays are small CP but the relative phases are unknown. The strategy used is to separate the ratio ∗ into well-measured components, add the KK ratio as a systematic uncertainty and account for m /Λ 30% of SU(3) breaking. Preliminary results for r and s QCD 3/2 ≈ subsequently for the EW penguin to tree amplitude ratio are [7] Re(r ) = 0.21 0.13(stat.) 0.77(syst.) 0.06(theo.), (7) 3/2 ± ± ± Im(r ) = 1.45 0.35(stat.) 0.77(syst.) 0.44(theo.), (8) 3/2 ± ± ± ± Re(P /T) = 0.21 0.13(stat.) 0.29(syst.) 0.16(theo.), (9) EWP − ± ± ± Im(P /T) = 0.54 0.05(stat.) 0.29(syst.) 0.04(theo.). (10) EWP ± − ± ± ± The systematic uncertainty is the dominant source of error in this measurement and can only be eliminated by measuring the relative phases for K∗+K0 and K+K∗0. 5 Conclusion BABAR results for K+π−π0 are in process of being finalised and results should soon be combined to form the CKM constraint. The angle γ can also be measured by ∗ looking at the phase difference from ρK and K π. Tree to QCD penguin ratio is ∗ expected to be larger in ρK than in K π giving a potentially better sensitivity to γ. This method is also quite promising for future experiments. A Super B factory can 4 expect results with uncertainties a factor 15 smaller than BABAR’s. LHCb could ∼ also have potential for these measurements and additionally study the constraint in the B decays [10]. s ACKNOWLEDGEMENTS I am grateful to the organisers and participants of CKM 2010 for this opportunity to present and discuss these results. I would like to also thank my colleagues on BABAR and Belle who have made these measurements possible. In particular I would like to thank Tim Gershon, Thomas Latham, Mathew Graham and Andrew Wagner for their help and support in preparing this presentation. References [1] M. Ciuchini, M. Pierini and L. Silvestrini, Phys. Rev. D 74 (2006) 051301 [2] M. Gronau, D. Pirjol, A. Soni and J. Zupan, Phys. Rev. D 75, 014002 (2007) Phys. Rev. D 77, 057504 (2008) [Addendum-ibid. D 78, 017505 (2008)] M. Gronau, D. Pirjol and J. Zupan, Phys. Rev. D 81, 094011 (2010) [3] A. E. Snyder and H. R. Quinn, Phys. Rev. D 48, 2139 (1993). [4] B. Aubert et al. [BABAR Collaboration], Phys. Rev. D 80, 112001 (2009) [5] J. Dalseno et al. [Belle Collaboration], Phys. Rev. D 79, 072004 (2009) [6] M. Antonelli et al., Phys. Rept. 494, 197 (2010), pp. 276–280 [7] A. Wagner, PhD Thesis, SLAC-R-942 (2010). [8] M. Gronau, D. Pirjol and J. L. Rosner, Phys. Rev. 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