Hiroyuki Sagawa KEK OHO 1-1, Tsukuba, Ibaraki, Japan In the neutral B meson system, it is possible to measure the CKM angle α using the decay mode b uud in the presence of penguin pollution. Here the recent status of C violation in B π + π and B ρπ decays and the prospects are presented. 1 Introduction In 1973, Kobayashi and Maskawa (KM) proposed a model where CP violation is accommodated as an irreducible complex phase in the quark mixing matrix [1]. Recent measurements of the CP-violating asymmetry parameter sin 2β by the Belle and BaBar Collaborations established CP violation in the neutral B meson [2]. Measurements of other CP-violating asymmetry parameters provide important tests of the KM model. Any mode with a contribution from b uud is a possible source of measurement of the Cabibbo-Kobayashi-Maskawa (CKM) angle α (= φ 2 ) [3]. Here the status of CP violation in B π + π and B ρπ decays [4] and the prospects are presented. 2 B π + π decays The KM model predicts CP-violating asymmetries in the time-dependent rates for B and B decays to a common CP eigenstate, f CP. In the decay chain Υ (4S) B B f CP f tag,in which one of the B mesons decays at time t CP to f CP and the other decays at time t tag to a final state f tag that distinguishes between B and B,theB π + π decay rate has a time-dependence given by P q ππ ( t) =e t /τ B 4τ B [1 + q {S ππ sin( m d t) C ππ cos( m d t)}], (1) where τ B is the B lifetime, m d is the mass difference between the two B mass eigenstates, t = t CP t tag,andtheb-flavor charge q =+( 1) when the tagging B meson is a B (B ). The CP-violating asymmetry parameters S ππ and C ππ (= A ππ ) [5] defined in Eq. (1) are expressed as C ππ = (1 λ ππ 2 )/(1 + λ ππ 2 )ands ππ = 2Imλ ππ /(1 + λ ππ 2 ), where λ ππ is a complex parameter that depends on both B -B mixing and the amplitudes for B and B decay to π + π. If the decay proceeded only via a b u tree amplitude, S ππ =sin2α and C ππ =. In general, S ππ is given by 1 Cππ 2 sin 2α eff Here α eff α depends on the magnitudes and relative 49
weak and strong phases of the tree and penguin amplitudes. With significant contributions from gluonic b d penguin amplitudes, S ππ may not be equal to sin 2α and direct CP violation, C ππ, may occur. B candidates are reconstructed using two variables, the energy difference E E cms Ecms beam B and the beam-energy constrained mass M bc (Ebeam cms )2 (p cms B ) 2 [6], where Ebeam cms is the cms beam energy, and EB cms and p cms B are the cms energy and momentum of the B candidate. Charged tracks in B h + h candidates are identified as charged pions or kaons. Here h and h represent a π or K. The Belle Collaboration uses the likelihood ratio for a particle to be a K ± meson, which is the combined information from the Aerogel Cherenkov counter and CDC de/dx. The BaBar Collaboration uses the Cherenkov angle measurement θ c from a detector of internally reflected Cherenkov light. The probability density function (PDF) from the difference between measured and expected values of θ c is used in the extended likelihood function for the fit to extract yields and CP parameters. The qq continuum (q = u, d, s, c) background is suppressed by the event topology. The Belle Collaboration forms signal and background likelihood functions L S and L BG from a Fisher discriminant using six modified Fox-Wolfram moments [7] and the cms B flight direction. The continuum background is reduced by imposing requirements on the likelihood ratio LR = L S /(L S + L BG ). The BaBar Collaboration uses the angle θ S between the sphericity axis of the B candidate and the sphericity axis of the remaining particles in the cms frame, and cut on cos θ S. The shapes of Fisher discriminant F [8] for signal and background events are included as PDFs in the maximum likelihood fit. Leptons, kaons, and charged pions that are not associated with the reconstructed B candidate are used to identify the flavor of the accompanying B meson. The time difference t is obtained from the measured distance between the z positions along the beam direction of the Bππ and Btag decay vertices and the boost factor βγ of the e + e system. Fig. 1 and Fig. 2 show E distributions for events enhanced in signal π + π and K π ± decays from the Belle Collaboration [9] and the BaBar Collaboration [1], respectively. They obtained the following results based on 85 1 6 and 88 1 6 BB pairs, respectively: C ππ =.77 ±.27 ±.8, S ππ = 1.23 ±.41.7 +.8 (Belle), C ππ =.3 ±.25 ±.4, S ππ =.2 ±.34 ±.5 (BaBar). The first and the second errors are statistical and systematic errors, respectively. The average values of C ππ and S ππ are C ππ =.49 ±.19 and S ππ =.47 ±.26 [11]. In Fig. 3 and Fig. 4, the t distributions are shown from the Belle result [9] and the BaBar result [1], respectively. Fig. 5 shows the two-dimensional confidence regions in the A ππ vs. S ππ. The case that CP symmetry is conserved, A ππ = S ππ =, is ruled out at the 99.93% confidence level (C.L.), and the 95.5% C.L. region of A ππ and S ππ gives 78 φ 2 152 from the Belle result [9]. Fig. 6 shows the pqcd prediction [12] and other predictions. As described in [12], the pqcd approach predicts large direct CP asymmetry (16 3%), while QCDF approach predicts 6 ± 12% [13]. Other interpretations for the current results can be found in ref. [14]. Using isospin relations [15], we constrain θ (=α eff α ). From the central values of the recent world average values of the branching ratios of B π + π, B + π + π and the 9% 5
Events/2 MeV 8 7 6 5 4 3 2 1 Total Kπ (a) π + π Three body qq -.2.2.4 E (GeV) Events/2 MeV 18 16 14 12 1 8 6 4 2 (b) -.2.2.4 E (GeV) Figure 1: E distributions for (a) π + π and (b) K + π candidates with LR >.825 from the Belle Collaboration. The sum of the signal and background functions is shown as a solid curve. The hatched area represents the π + π component, the dashed curve represents the K + π component, the dotted curve represents qq background, and the dot-dashed curve represents the charmless three-body B decay background. Events / 1 MeV 2 15 1 (a) Events / 1 MeV 8 6 4 (b) 5 2 -.1.1 GeV E -.1.1 GeV E Figure 2: E distributions for events enhanced in signal (a) π + π and (b) K π ± candidates from the BaBar Collaboration. Solid curves represent projections of the maximum likelihood fit, dashed curves represent qq and ππ Kπ cross-feed background. 51
Figure 3: The raw, unweighted t distributions for π + π candidates with LR >.825 from the Belle Collaboration: candidates tagged as (a) B -tag and (b) B -tag; (c) π + π yields after background subtraction; (d) the CP asymmetry for π + π. In Figs. (a) through (c), the solid curves show the results of the unbinned maximum likelihood fit to the t distributions of the whole π + π candidates. In Fig. (d), the dashed (dotted) curve is the contribution from the cosine (sine) term. 2 (a) B tags Events / 1 ps 2 (b) B tags A ππ / 2 ps.5 -.5 (c) -5-2.5 2.5 5 t (ps) Figure 4: Distributions of t for events enhanced in signal ππ decays from the BaBar Collaboration: candidates tagged as (a) B -or(b)b -tag, and (c) the time-dependent asymmetry. Solid (dashed) curves represent projections of the maximum likelihood fit (the sum of qq and Kπ backgrounds). 52
A ππ 2 1.5 1 Belle 78fb -1 Babar 88M BB Belle 1σ Babar 1σ Belle 2σ Babar 2σ Belle 3σ Babar 3σ Belle 4σ Babar 4σ.5 -.5 Physical boundary -1-2 -1.5-1 -.5.5 1 S ππ Feldman & Cousins confidence interval Figure 5: Confidence regions for A ππ and S ππ from the Belle and BaBar results. 1 CKM f i t t e r SU(2) + SU(3) [5% CL] SU(2) [5% CL] 2 1.5 Belle: A=.77 +.28, S= 1.23 +.42 BaBar: A=.3 +.25, S=.2 +.34.5 QCD FA (BBNS) P + from K π + 2σ 1.955.997 C ππ 1σ A ππ.5.68.5.45.3.23 φ 1 = 24. o φ ο =15 R +.7 2 =.23 c.5 41 o < δ < 32 o ο φ 2 =1 φ = 6 ο 2.18 -.5 Belle BABAR combined [2σ] 1 2 1.5 1.5.5 1 Sππ -1-1 -.5.5 1 S ππ Figure 6: The left plot is A ππ vs. S ππ for various values of φ 2 in the pqcd method. Dark areas are allowed regions in the pqcd method for different φ 2 values. The right plot is the predictions for C ππ (= A ππ )ands ππ for several analysis steps with experimental and theoretical constraints. 53
C.L. upper limit on the B π π branching ratio [11] together with C ππ, the upper limit on θ is 54. 3 B ρπ π + π π decays The CKM angle α can be measured in the presence of penguin contributions using a full Dalitz plot analysis of the final state. In order to extract α cleanly, data with large statistics are required. Following a quasi-two-body approach, the analysis is restricted to the two regions of the π ± π h ± Dalitz plot (h = π or K) that are dominated by ρ ± h. The decay rate is given by f ρ± h q ( t) =(1± A ρh CP ) e t /τ B 4τ B [1 + q {(S ρh ± S ρh )sin( m d t) (C ρh ± C ρh )cos( m d t)}], (2) where t = t ρh t tag as the time interval between the decay of B ρh and that of the other B meson. One finds the relations S ρπ ± S ρπ = 1 (C ρπ ± C ρπ ) 2 sin(2α ± eff ± δ), where 2α± eff = arg[(q/p)(a ± ρπ/a ρπ)], δ =arg[a ρπ/a + ρπ], arg[q/p] istheb -B mixing phase, and A + ρπ(a + ρπ) and A ρπ(a ρπ) are the transition amplitudes of the processes B (B ) ρ + π and B (B ) ρ π +, respectively. The angles α eff ± are equal to α if contributions from penguin amplitudes are absent. The results on direct CP violation can be expressed as A + = N(B ρπ ρ + π ) N(B ρπ ρ π + ) N(B ρπ ρ + π )+N(B ρπ ρ π + ), A + = N(B ρπ ρ π + ) N(Bρπ ρ + π ) N(B ρπ ρ π + )+N(Bρπ ρ + π ). (3) With 89 1 6 BB pairs [16], the BaBar Collaboration measured the asymmetry parameters: A ρπ CP =.18 ±.8 ±.3, C ρπ =+.36 ±.18 ±.4, S ρπ =+.19 ±.24 ±.3, C ρπ = +.28 ±.19 ±.4, S ρπ =+.15 ±.25 ±.3, A + =.62.28 +.24 A + =.11.17 +.16 The raw time-dependent asymmetry dominated by kaons and leptons is shown in Fig. 7. 4 Prospects Table 1 shows the expected errors on asymmetry parameters in B π + π and ρ ± π decays. Fig. 8 shows the prospects of α α eff in B ππ decays [14]. Only a luminosity of around 1 ab 1 allows to separate the solutions. The detailed interpretation for B π + π and ρπ can be found in [17]. 5 Summary The Belle and BaBar Collaborations obtain the CP-violating asymmetries in B decays: π + π A ππ =.77 ±.27 ±.8, S ππ = 1.23 ±.41.7 +.8 (Belle), A ππ =.3 ±.25 ±.4, S ππ =.2 ±.34 ±.5 (BaBar). 54
Figure 7: Time distributions for events enhanced in the ρπ signal tagged as (a) B -tag and (b) B -tag, and (c) time-dependent asymmetry between B -tag and B -tag [16]. The solid (dashed) curve is a likelihood projection of the fit result (the sum of B- and continuum-background contributions). parameters 14 fb 1 4 fb 1 3ab 1 3 ab 1 A ππ.21.13.5.2 S ππ.31.19.7.3 A ρπ CP.7.4.2.8 C ρπ.14.9.3.13 S ρπ.18.11.4.14 Table 1: The errors on asymmetry parameters in B π + π and ρ ± π decays at several luminosities (L), assuming statistical and systematic errors are proportional to 1/ L and 1/ 4 L, respectively. 55
1.2 1 CKM f i t t e r 87 fb 1 1 2 fb 5 fb 1 1 fb 1 Confidence level.8.6.4.2-8 -6-4 -2 2 4 6 8 α α eff (deg) Figure 8: α α eff at several luminosities ( 87 fb 1, 5 fb 1,2ab 1, and 1 ab 1 ). The asymmetry parameters in B ρπ decays are obtained by the BaBar Collaboration: A ρπ CP =.18 ±.8 ±.3, C ρπ =+.36 ±.18 ±.4, S ρπ =+.19 ±.24 ±.3, C ρπ = +.28 ±.19 ±.4, S ρπ =+.15 ±.25 ±.3. References [1] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973). [2] Belle Collaboration, K. Abe et al., Phys. Rev. D 66, 7112 (22); BaBar Collaboration, BAubertet al., Phys. Rev. Lett. 89, 2182 (22). [3] φ 1 (= β) arg[ V cd Vcb/V td Vtb] andφ 2 (= α) arg[ V td Vtb/V ud Vub]. [4] The inclusion of the charge conjugate mode decay is implied unless otherwise stated. [5] C ππ = A ππ. The BaBar Collaboration uses C ππ and the Belle Collaboration uses A ππ. [6] The BaBar Collaboration uses the beam-energy substituted mass m ES = (s/2+p i p B ) 2 /E 2 i p 2 B, where s is the total cms energy, and the B momentum p B and the four-momentum of the initial state (E i, p i ) are defined in the laboratory frame. [7] The Fox-Wolfram moments were introduced in G.C. Fox and S. Wolfram, Phys. Rev. Lett. 41, 1581 (1978). The Fisher discriminant used by the Belle Collaboration is described in Phys. Lett. B 511, 151 (21) and Phys. Rev. D 66, 922 (22). [8] F =.53.6 i p i +1.27 i p i cos(θ i ) 2,wherep i is the momentum of particle i and θi is the angle between its momentum and the B thrust axis in the cms frame. The sum is over all particles in the event excluding those of the B candidate. 56
[9] Belle Collaboration, K. Abe et al., Phys. Rev. D 68, 121 (23). [1] BaBar Collaboration, B. Aubert et al., Phys. Rev. Lett. 89, 28182 (22). [11] Heavy Flavor Averaging Group, http://www.slac.stanford.edu/xorg/hfag. For rare Decays, Pre Winter 23 in http://www.slac.stanford.edu/xorg/hfag/rare/index.html. [12] Y.-Y. Keum and A.I. Sanda, Phys. Rev. D 67, 549 (23); private communication with Y.-Y. Keum. [13] M. Beneke, G. Buchalla, M. Neubert, and C.T. Sachrajda, Nucl. Phys. B66, 245 (21). [14] The CKMfitter site on the web: http://ckmfitter.in2p3.fr/. [15] M. Gronau, D. London, N. Sinha, R. Sinha, Phys. Lett. B 514, 315 (21). [16] BaBar Collaboration, B. Aubert et al., hep-ex/363, submitted to Phys. Rev. Lett. [17] H. Lacker, these proceedings. 57
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