Combination of measurements from BaBar γ 1 Denis Derkach 2 INFN, Sezione di Bologna, I-40127 Bologna, ITALY 3 and 4 LAL, Orsay, F-91898, FRANCE 5 3 On behalf of the BABAR collaboration 1 6 0 2 n 7 Proceedings of CKM 2012, the 7thInternational Workshop on the CKM Unitarity a Triangle, University of Cincinnati, USA, 28 September - 2 October 2012 J 8 5 Abstract 1 9 ] 10 We present the combination of the CKM angle γ measurements performed by x e 11 the BABAR experiment at the PEP-II e+e− collider at SLAC National Labora- p- 12 tory. The analysis◦ supersedes previous results obtained by collaboration and e 13 gives γ = (cid:16)69+−1167(cid:17) modulo 180◦. The results are inconsistent with the absence h [ 14 of CP violation at a significance of 5.9 standard deviations. 1 v 1 Introduction 3 15 8 2 The Cabibbo-Kobayashi-Maskawa (CKM) [1] angle γ is one of the least precisely 3 16 1. 17 known parameters of the unitarity triangle. 0 18 Several methods have been proposed to extract γ. Those using charged B me- 3 son decays into D(∗)K(∗) final states have no penguin contribution, which gives an 19 1 : 20 important difference from most of other direct measurements of the angles. These v processes are theoretically clean provided that hadronic unknowns are determined i 21 X from experiment. The b → cus and b → ucs tree amplitudes are used to construct 22 r a 23 the observables that depend on their relative weak phase γ, on the magnitude ratio r ≡ |A(b → ucs)/A(b → cus)| and on the relative strong phase δ between the two 24 B B amplitudes. 25 The various methods can be classified by the neutral D decay final state that is 26 reconstructed [2]. The three main approaches employed by the B factory experiments 27 are: 28 • the Dalitz plot (DP) or Giri-Grossman-Soffer-Zupan (GGSZ) method, based on 29 3-body, self-conjugate final states, such as K0ππ [3]; 30 S • the Gronau-London-Wyler (GLW) method, based on decays to CP eigenstates, 31 such as K+K− and K0π0 [4]; 32 S 1 • theAtwood-Dunitz-Soni(ADS)method, basedonD decays todoubly-Cabibbo- 33 suppressed final states, such as D0 → Kπ [5]. 34 The BABAR collaboration that analyzes data recorded at the asymmetric e+e− col- 35 lider PEP-II at SLAC national laboratory, have produced several important results in 36 the field. These results can be combined into a single number using all available infor- 37 mation including the experimental information, which was not previously published 38 by BABAR. In the following, we show the results of the combination of GGSZ [6], 39 GLW [7, 8, 9], and ADS [10, 11] analyses, performed by BABAR. These analyses are 40 based on474 millions BB pairsat most. Results fromBelle andLHCbwere presented 41 at this conference too. A more complete discussion of analysis can be seen at [12]. 42 2 Combination Method 43 Real part (%) Imaginary part (%) z− 8.1±2.3±0.7 4.4±3.4±0.5 z −9.3±2.2±0.3 −1.7±4.6±0.4 + z∗ −7.0±3.6±1.1 −10.6±5.4±2.0 − z∗ 10.3±2.9±0.8 −1.4±8.3±2.5 + zs− 13.3±8.1±2.6 13.9±8.8±3.6 z −9.8±6.9±1.2 11.0±11.0±6.1 s+ Table 1: CP-violating complex parameters z(±∗) = x(±∗) + iy±(∗) and zs± = xs± + iys± obtained from the combination of GGSZ, GLW, and ADS measurements. The first error is statistical (corresponding from −2∆lnL = 1), the second is the experimental systematic uncertainty including the systematic uncertainty associated to the GGSZ decay amplitude models. We combine all the GGSZ, GLW, and ADS observables (34 in total) to extract 44 γ in two different stages. First, we extract the best-fit values for the CP-violating 45 quantities in terms of the GGSZ analysis observables given as 46 z(±∗) = rB(∗±)ei(δB(∗)±γ) (1) and 47 zs± = κrs±ei(δs±γ), (2) for B± → D(∗)K± and B± → DK∗± decays, respectively. The hadronic parameter κ 48 is defined as 49 A (p)A (p)eiδ(p)dp κeiδs ≡ R c u , (3) A2(p)dp A2(p)dp qR c R u 2 where A (p) and A (p) are the magnitudes of the b → cus and b → ucs amplitudes 50 c u as a function of the B± → DK0π± phase space position p, and δ(p) is their relative 51 S strong phase. This coherence factor, with 0 < κ < 1 in the most general case and 52 ± ∗± κ = 1 for two-body B decays, accounts for the interference between B → DK and 53 other B± → DK0π± decays, as a consequence of the K∗± natural width [17]. In our 54 S analysis κ has been fixed to 0.9 [6], and a systematic uncertainty has been assigned 55 varyingitsvalueby±0.1. Thustheparameterδ isaneffectivestrong-phasedifference 56 s averaged over the phase space. Parameter 68.3% C.L. 95.5% C.L. γ (◦) 69+17 [41,102] −16 r (%) 9.2+1.3 [6.0,12.6] B −1.2 r∗ (%) 10.6+1.9 [3.0,14.7] B −3.6 κr (%) 14.3+4.8 [3.3,25.1] s −4.9 δ (◦) 105+16 [72,139] B −17 δ∗ (◦) −66+21 [−132,−26] B −31 ◦ δ ( ) 101±43 [32,166] s Table 2: 68.3% and 95.5% 1-dimensional C.L. regions, equivalent to one- and two- (∗) (∗) standard-deviation intervals, for γ, δ , δ , r , and κr , including all sources of B s B s uncertainty, obtained from the combination of GGSZ, GLW and ADS measurements. (∗) ◦ The results for γ, δ and δ are given modulo a 180 phase. B s 57 L L 1 L C 1 B– fi DK– C C 1 1 - B– fi D*K– 1 - 0.8 1 - 0.8 B– fi DK*– 0.8 Combined 0.6 0.6 0.6 0.4 1s 0.4 1s 0.4 1s 0.2 0.2 0.2 2s 2s 2s 0 0 0 -150-100 -50 0 50 100 150 0 0.1 0.2 0.3 0.4 0.5 -150-100 -50 0 50 100 150 g (deg) r(*),k r d (*),d (deg) B s B s (∗) Figure 1: (color online). Combined 1 − C.L. as a function of γ (left), r , and κr B s (∗) (middle), and δ , δ (right), including statistical and systematic uncertainties, for B s ± ± ± ∗ ± ± ∗± B → DK , B → D K , and B → DK decays. The combination of all the B decay channels is also shown for γ. The dashed (dotted) horizontal line corresponds to the one- (two-) standard-deviation C.L.. 3 CL 1 CL 1 CL 1 1s 1 - 0.8 GGSZ 1 - 1 - 2s 0.8 GGSZ+GLW 10-2 0.6 Combination 0.6 3s 0.4 1s 0.4 1s 10-4 4s 0.2 0.2 2s 2s 0 0.1 0.2 0.3 0.4 0.5 00 0.1 0.2 0.3 0.4 0.5 10-6 -150-100 -50 0 50 100 150 rB r*B g (deg) ∗ Figure2: (coloronline). Comparisonof1−C.L.asafunctionofr (left), r (middle), B B and γ (right) for all B decay channels combined with the GGSZ-only method only, the combination with the GLW measurements, and the global combination, including statistical and systematic uncertainties. The horizontal lines represent the one-, two-, three- and four-standard-deviation C.L.. The combination also profits from external inputs for the D hadronic parameters: 58 amplitudes ratio r , strong phase δ , and coherence factor k . These are taken 59 D D D from PDG [15] and CLEO-c [16] results. All external observables are assumed to be 60 uncorrelated with the rest of the input observables, while we take into account the 61 correlation measured by CLEO-c. 62 z(∗) z 63 The best-fit values of ± and s± are obtained by maximizing a combined like- lihood function constructed as the product of partial likelihood P.D.F.s for GGSZ, 64 65 GLW, and ADS measurements. For the decays B± → DC∗P−[DCP−π0]K±, B± → 66 DC∗P+[DCP−γ]K±, and B± → DCP−K∗±, measurement without the D → KS0φ chan- nel, which is common in GGSZ and GLW analyses is not available. The impact is 67 estimated by increasing the uncertainties quoted in Refs. [8, 9] by 10% while keeping 68 the central values unchanged. This is done in accordance to the study performed in 69 ± ± 70 the B → DCP−K analysis [7]. The results for the combined CP-violating parame- z(∗) z 71 ters ± and s± are summarized in Table 1. In a second step, we transform the measurements from Table 1 into the physically 72 relevant quantities γ and the set of hadronic parameters u ≡ (r ,r∗,κr ,δ ,δ∗,δ ). 73 B B s B B s We adopt a frequentist procedure [15] to obtain one-dimensional confidence intervals 74 of well defined C.L. that takes into account non-Gaussian effects due to the non- 75 linearity of the relations between the observables and physical quantities. Figure 1 76 (∗) (∗) illustrates 1−C.L. as a function of γ, r , κr , δ , and δ , for each of the three B 77 B s B s decay channels separately and, in the case of γ, their combination. From these dis- 78 tributions we extract one- and two-standard-deviation intervals as the sets of values 79 for which 1−C.L. is greater than 31.73% and 4.55%, respectively, as summarized in 80 Table 2. To assess the impact of the GLW and ADS observables in the determination 81 4 (∗) ofγ, we compare1−C.L.asa functionof r andγ forall B decay channels combined 82 B using the GGSZ method alone, the combination with the GLW measurements, and 83 the global combination, as shown in Fig. 2. While the constraints on r are clearly 84 B ∗ improved at one- and two-standard-deviation level, and to a lesser extent on r , their 85 B best (central) values move towards slightly lower values. Since the uncertainty on γ 86 (∗) scales roughly as 1/r , the constraints on γ at 68.3% and 95.4% C.L. do not improve 87 B compared to the GGSZ-only results, in spite of the tighter constraints on the com- 88 bined measurements shown in Table 1. However, adding GLW and ADS information 89 reduces the confidence intervals for smaller 1 − C.L., as a consequence of the more 90 (∗) Gaussian behavior when the significance of excluding r = 0 increases. 91 B The significance of direct CP violation is obtained by evaluating 1 − C.L. for 92 the most probable CP conserving point, i.e., the set of hadronic parameters u with 93 γ = 0. Including statistical and systematic uncertainties, we obtain 1 − C.L. = 94 3.4× 10−7, 2.5 × 10−3, and 3.6 × 10−2, corresponding to 5.1, 3.0, and 2.1 standard 95 ± ± ± ∗ ± ± ∗± deviations, for B → DK , B → D K , and B → DK decays, respectively. 96 For the combination of the three decay modes we obtain 1 − C.L. = 3.1 × 10−9, 97 corresponding to 5.9 standard deviations. 98 3 Conclusions 99 We determine γ = (69+17)◦ (modulo 180◦), where the total uncertainty is dominated 100 −16 by the statistical component, with the experimental and amplitude model systematic 101 ◦ uncertainties amounting to ±4 . 102 The combined significance of γ 6= 0 is 1−C.L. = 3.1×10−9, corresponding to 5.9 103 standard deviations, meaning observation of direct CP violation in the measurement 104 of γ. 105 References 106 [1] N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963); M. Kobayashi and T. Maskawa, 107 Prog. Th. 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