January 6, 2011 Belle time-integrated φ (γ) measurements 3 1 1 0 2 n a J Yasuyuki Horii 5 (Belle Collaboration) ] x Department of Physics, Tohoku University e - 6-3, Aramaki Aza-Aoba, Aoba-ku, Sendai, Miyagi 980-8578, Japan p e h JSPS Research Fellow [ 1 v 8 7 8 0 . 1 We report recent results by the Belle collaboration on the determina- 0 tion of the CP-violating angle φ (γ) using time-integrated methods. 1 3 1 : v i X r a Proceedings of CKM2010, the 6th International Workshop on the CKM Unitarity Triangle, University of Warwick, UK, 6-10 September 2010 1 Introduction Precise measurements of the parameters of the standard model are fundamentally important and may reveal new physics. The Cabibbo-Kobayashi-Maskawa (CKM) matrix [1, 2] consists of weak-interaction parameters for the quark sector, and the phase φ (also known as γ) is defined by the elements of the CKM matrix as φ ≡ 3 3 arg(−V V ∗/V V ∗). This phase is less accurately measured than the two other ud ub cd cb angles φ (β) and φ (α) of the unitarity triangle.∗ 1 2 In the usual quark phase convention where large complex phases appear only in V and V [3], the measurement of φ is equivalent to the extraction of the phase ub td 3 of V relative to the phases of other CKM matrix elements except for V . Figure 1 ub td shows the diagrams for B− → D¯0K− (b → u) and B− → D0K− (b → c) decays.† By analyzing the interfering processes produced when D¯0 and D0 decay to the same final states, we extract φ as well as relevant dynamical parameters. We define the 3 magnitude of the ratio of amplitudes r = |A(B− → D¯0K−)/A(B− → D0K−)| and B thestrong phasedifference δ = δ(B− → D¯0K−)−δ(B− → D0K−), which arecrucial B parameters needed in the extraction of φ . In this report, we show recent results by 3 the Belle collaboration on the determination of φ . 3 b u s D¯0 K− W− c¯ W− u¯ B− s b c K− B− D0 u¯ u¯ u¯ u¯ Figure 1: Diagrams for the B− → D¯0K− and B− → D0K− decays. 2 Result for B− → D(∗)K−, D → K π+π− S One of most promising ways of measuring φ uses the decay B− → DK−, D → 3 K π+π− [4, 5], where D indicates D¯0 or D0. The method is based on the fact that S the amplitudes for B± can be expressed by M = f(m2,m2)+r e±iφ3+iδBf(m2,m2), (1) ± ± ∓ B ∓ ± where m2 are defined as Dalitz plot variables m2 ≡ m2 , and f(m2,m2) is the ± ± KSπ± + − amplitude of the D¯0 → K π+π− decay. By applying a fit on m2, φ is extracted with S ± 3 ∗ The angles φ1 and φ2 are defined as φ1 ≡ arg(−VcdVcb∗/VtdVtb∗) and φ2 ≡ arg(−VtdVtb∗/VudVub∗). † Charge conjugate modes are implicitly included unless otherwise stated. 1 r and δ . The decay B− → D∗K− can also be used by reconstructing D∗ from Dπ0 B B or Dγ, for which the parameters r∗ and δ∗ are introduced. B B The result [6] is based on a data sample that contains 6.6×108 BB¯ pairs. The amplitude f(m2,m2) is obtained by a large sample of D¯0 → K π+π− decays pro- + − S duced in continuum e+e− annihilation, where the isobar model is assumed with Breit- Wigner functions for resonances. The background fractions are determined depend- ing on ∆E ≡ E − E , M ≡ E2 −|p~ |2, and event-shape variables for B beam bc q beam B suppressing the e+e− → qq¯(q = u,d,s,c) background, where E (p~ ) and E are B B beam defined in the e+e− center-of-mass frame as the energy (the momentum) of the recon- structed B candidates and the beam energy, respectively. Using obtained amplitude f(m2,m2) and background fractions, the fit on m2 is performed with the parameters + − ± x = r cos(±φ +δ ) and y = r sin(±φ +δ ), where we take r separately for ± ± 3 B ± ± 3 B B B± as r . The results are shown in Figure 2 for B− → DK− and B− → D∗K−. ± The separations with respect to the charges of B± indicate an evidence of the CP violation. From the results of the fits, we measure φ = 78.4◦ +10.8◦(stat)±3.6◦(syst)±8.9◦(model) (2) 3 −11.6◦ as well as r = 0.161 +0.040 ± 0.011 +0.050, r∗ = 0.196 +0.073 ± 0.013 +0.062, δ = B −0.038 −0.010 B −0.072 −0.012 B 137.4◦ +13.0◦ ±4.0◦±22.9◦, and δ∗ = 341.7◦ +18.6◦ ±3.2◦±22.9◦. The model error is −15.7◦ B −20.9◦ duetotheuncertainty indetermining f(m2,m2). Notethatitispossible toeliminate + − this uncertainty using constraints obtained by analyzing ψ(3770) → D0D¯0 [7]. y 0.4 B–→DK– y 0.4 B→[Dp 0]D*K B→[Dg] K with Dd =1800 D* 0.2 0.2 B+→D*K+ 0 0 -0.2 -0.2 B+→DK+ B–→D*K– -0.4 -0.4 -0.4 -0.2 0 0.2 0.4 -0.4 -0.2 0 0.2 0.4 x x Figure 2: Results of the fits for B− → DK− (left) and B− → D∗K− (right) samples, where the contours indicate 1, 2, and 3 (left) and1 (right) standard-deviation regions. 2 3 Result for B− → DK−, D → K+π− The effect of CP violation can be enhanced, if the final state of the D decay following to the B− → DK− is chosen so that the interfering amplitudes have comparable magnitudes [8]. The decay D → K+π− is a particularly useful mode; the usual observables are the partial rate R and the CP-asymmetry A defined as DK DK B(B− → [K+π−] K−)+B(B+ → [K−π+] K+) D D R ≡ DK B(B− → [K−π+] K−)+B(B+ → [K+π−] K+) D D = r2 +r2 +2r r cos(δ +δ )cosφ , (3) B D B D B D 3 B(B− → [K+π−] K−)−B(B+ → [K−π+] K+) D D A ≡ DK B(B− → [K+π−] K−)+B(B+ → [K−π+] K+) D D = 2r r sin(δ +δ )sinφ /R , (4) B D B D 3 DK where [f] indicates that the state f originates from a D meson, r = |A(D0 → D D K+π−)/A(D0 → K−π+)|, and δ = δ(D0 → K−π+) − δ(D0 → K+π−). For the D parameters r and δ , external experimental inputs can be used [9]. D D In this report, we show a preliminary result based on a data sample that contains 7.7×108 BB¯ pairs (the full data sample collected by Belle at Υ(4S) resonance). The decay B− → Dπ− is also analyzed similarly as a reference mode. For the largest background from the continuum process e+e− → qq¯, we apply the new method of the discrimination based on NeuroBayes neural network [10]. The inputs are a Fisher discriminant of modified Super-Fox-Wolfram moments, cosine of the decay angle of D → K+π−, vertexseparationbetween thereconstructedB andtheremainingtracks, and seven other variables. The signal is extracted by a two-dimensional fit on ∆E and NeuroBayes output (NB), where we simultaneously fit for DK−, DK+, Dπ−, and Dπ+, as shown in Figure 3. As a result, we obtain R = [1.62±0.42(stat) +0.16(syst)]×10−2, (5) DK −0.19 A = −0.39±0.26(stat) +0.06(syst), (6) DK −0.04 R = [3.28±0.37(stat) +0.22(syst)]×10−3, (7) Dπ −0.23 A = −0.04±0.11(stat) +0.01(syst), (8) Dπ −0.02 where the first evidence of the suppressed DK signal is obtained with a significance 3.8σ including systematic error. Our study will make a significant contribution to a model-independent extraction of φ by combining relevant observables, e.g., the 3 partial rates and the CP-asymmetries for D → CP eigenstates [11]. 4 Conclusion In conclusion, recent results on the decays B− → D(∗)K− followed by D → K π+π− S andD → K+π− arereported. BytheDalitz-plotanalysisforD → K π+π−, thevalue S 3 3300 3300 4400 4400 3355 3355 2255 2255 VV VV VV 3300 VV 3300 MeMe 2200 MeMe 2200 MeMe 2255 MeMe 2255 Events / 10 Events / 10 11115500 Events / 10 Events / 10 11115500 Events / 10 Events / 10 111212550000 Events / 10 Events / 10 111212550000 55 55 55 55 00 00 00 00 --00..11 00 00..11 00..22 00..33 --00..11 00 00..11 00..22 00..33 --00..11 00 00..11 00..22 00..33 --00..11 00 00..11 00..22 00..33 DDEE ((GGeeVV)) DDEE ((GGeeVV)) DD EE ((GGeeVV)) DD EE ((GGeeVV)) 4400 4400 3355 3355 6600 6600 3300 3300 5500 5500 Events / 0.04Events / 0.04 121222555500 Events / 0.04Events / 0.04 121222555500 Events / 0.04Events / 0.04 234234000000 Events / 0.04Events / 0.04 234234000000 1100 1100 55 55 1100 1100 00 00 00 00 --00..55 00 00..55 11 --00..55 00 00..55 11 --00..55 00 00..55 11 --00..55 00 00..55 11 NNBB NNBB NNBB NNBB Figure 3: The distributions of ∆E for NB > 0.5 (top) and NB for |∆E| < 40 MeV (bottom) on the suppressed modes DK−, DK+, Dπ−, and Dπ+ from left to right. The components are thicker long-dashed red (DK), thinner long-dashed magenta (Dπ), dash-dotted green (BB¯ background), and dashed blue (qq¯background). of φ is measured to be φ = 78.4◦ +10.8◦(stat)±3.6◦(syst)±8.9◦(model). For D → 3 3 −11.6◦ K+π−, preliminary results on the partial rate R and the CP-asymmetry A are DK DK reported, where the first evidence of the signal is obtained with a significance 3.8σ. References [1] N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963). [2] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973). [3] L. Wolfenstein, Phys. Rev. Lett. 51, 1945 (1983). [4] A. Giri, Yu. Grossman, A. Soffer, and J. Zupan, Phys. Rev. D 68, 054018 (2003). [5] A. Bondar, Proceedings of BINP Special Analysis Meeting on Dalitz Analysis, 2002 (unpublished). [6] A. Poluektov et al. (Belle Collaboration), Phys. Rev. D 81, 112002 (2010). [7] A. Bondar, A. Poluektov, Eur. Phys. J. C 55, 51 (2008). [8] D. Atwood, I. Dunietz, and A. Soni, Phys. Rev. Lett. 78, 3257 (1997); Phys. Rev. D 63, 036005 (2001). [9] HFAG, online update at http://www.slac.stanford.edu/xorg/hfag/charm. [10] M. Feindt, U. Kerzel, Nucl. Instrum. Methods Phys. Res., Sect. A 559, 190 (2006). [11] M. Gronau and D. Wyler, Phys. Lett. B 265, 172 (1991). 4