- Email: [email protected]
Charmless two-body decays
ELSEVIER
Proceedings of ICHEP 2002, pp. 574–577 S. Bentvelsen, P. de Jong, J. Koch and E. Laenen (Editors)
1
31st INTERNATIONAL CONFERENCE ON HIGH ENERGY PHYSICS AMSTERDAM
Charmless two-body decays Ascelin Gordon∗ , for the Belle Collaboration School of Physics, University of Melbourne, Victoria 3010 Australia We report the latest results of a study of charmless two-body B meson decays using data recorded by the Belle experiment at KEKB. Branching fractions or upper limits are provided for the complete set of Kπ, ππ and KK final states; the B → ρπ decays with final states ρ0 π + , ρ± π ∓ and ρ0 π 0 ; we also provide a first measurement of the branching fraction of the vector-vector decay B + → ρ+ ρ0 .
1. Introduction This report summarises the latest results from the Belle collaboration on measuring branching fractions and upper limits for B meson decays to charmless two-body modes. These include decays with final states Kπ, ππ, and KK (which we collectively label hh) as well as the pseudo-two-body decays ρπ and ρ+ ρ0 . Through investigating these modes, many of the parameters that describe CP violation can be measured. The hh modes alone contain enough information to measure all angles of the Unitarity Triangle [1]. The ρπ and ρ+ ρ0 decays also provide ways of measuring φ2 [2] and φ3 [3]. Partial-rate and time-dependent asymmetry measurements have been performed using some of the hh modes; the results are reported elsewhere [4,5]. The results presented here are based on data taken with the Belle detector [6] at KEKB [7]. The hh and ρπ results are based on a 29 fb−1 data sample while the ρρ results use a 43 fb−1 data sample. 2. Event Reconstruction B meson candidates are identified using the 2 − p2B and beam constrained mass Mbc = Ebeam the energy difference ∆E = EB − Ebeam . Here, pB and EB are the momentum and energy of a B candidate in the centre-of-mass (CM) frame and Ebeam is the CM beam energy. For charged particle identification (PID), three subsystems of the Belle detector are used. The ∗ email:
[email protected]
c 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0920-5632(02)02234-X
central drift chamber dE/dx measurements are combined with the responses of the aerogel ˇ threshold Cerenkov counters and time-of-flight scintillation counters to form likelihoods Lπ or LK . We distinguish pions from kaons by applying selection requirements on the likelihood ratio LR = Lπ /(Lπ + LK ). A similar likelihood ratio including calorimeter information is used to identify electrons. All charged tracks that originate from the interaction point and are not positively identified as electrons are considered as kaon or pion candidates. Candidate KS0 mesons are reconstructed using pairs of oppositely charged tracks with a displaced vertex as well as a flight direction and invariant mass consistent with a KS0 originating from the interaction point. Neutral pion candidates are selected from γγ pairs by requiring that their invariant mass to be within about 3σ of the nominal π 0 mass. To reduce combinatorial backgrounds, mode-dependent momentum cuts are made on the γ and π 0 momenta. Candidate ρ mesons are reconstructed from pion pairs whose invariant mass is required to be within a mode-dependent window of about 150 MeV either side of the nominal ρ mass. All the modes presented here have large backgrounds from e+ e− → qq continuum events (q = u, d, s, c), which typically exhibit a two-jet-like structure. This background is suppressed by means of a likelihood ratio derived from two variables. One is a Fisher discriminant formed from six modified Fox-Wolfram [8] moments. The coefficients of the Fisher discriminant are determined
2
Charmless two-body decays
by optimizing the separation between the signal and continuum MC events. The other variable is cos θB , where θB is the angle between the B flight direction and the electron beam direction. Probability density functions obtained from the Fisher discriminant and the cos θB distribution are multiplied to form the likelihood functions for signal (Lsig ) and continuum (Lcont ) [9]. A requirement on the likelihood ratio Lsig /(Lsig +Lcont ) is then made which varies from mode to mode. As the ρ+ ρ0 mode suffers from the largest continuum background, additional suppression is achieved by making an initial requirement of | cos θthr | < 0.8 (θthr is the angle between the thrust axis of the candidate tracks and that of the remaining tracks in the event). 3. Signal Yield Extraction Figures 1 to 3 show the ∆E distributions in the Mbc signal region for many of the modes analysed after all the selection criteria have been applied. Signal yields are obtained by performing maximum likelihood fits on the ∆E distributions, each using a signal function and one or more background functions. The signal functions are obtained from the MC and adjusted based on comparisons of B → Dπ decays in data and MC. Different D meson decays are used to obtain the same final state particles as the modes being measured. The solid line in all plots shows the sum of the signal and background components. A Chebyshev polynomial with coefficients determined from the Mbc sideband is used to model the continuum background for all fits. Backgrounds from other B decays vary for the different modes. Below is a detailed description of ∆E fits for the modes analysed. 3.1. B → hh Apart from continuum, the ∆E fits for the hh modes include up to two background components: crossfeeds from other misidentified B → hh decays and backgrounds from multi-body and radiative charmless B decays. For charged particle final states, the signal is modeled with a Gaussian. For modes containing π 0 s, the signal is modeled as the sum of a primary Gaussian and a secondary
575
asymmetric Gaussian. The crossfeed component has the same shape as the signal component but is shifted by 45 MeV. Backgrounds from charmless B decays are modeled by a smoothed MC histogram. For all final states except K + π 0 and π + π 0 , the normalizations of the four components are the only free parameters in the fits. Due to the large overlap of the signal and crossfeed components in the K + π 0 and π + π 0 signals, we perform a simultaneous fit to the K + π 0 and π + π 0 ∆E distributions constraining the crossfeed to the expected values based on the PID fake rates. 3.2. B → ρπ For the ρ0 π + mode there are rare B decays that are expected to contaminate the ∆E distribution. The modes are of the type B 0 → h+ h− , B → ρρ and B → Kππ. These background modes are modeled by smoothed MC histograms. The normalisations of the Kππ and h+ h− components are fixed to their expected yields, which are calculated using efficiencies determined by MC and branching fractions measured by previous Belle analyses [10]. The ρρ component is left to float. For the ρπ modes with a π 0 , the signal component is modeled by a Crystal Ball (CB) function [11]. The parameterization for rare B decays includes one component for the B → Kππ 0 modes [12], one for all the B → ρρ modes and a component for the background from the b → c transition. The normalisation of the B → ρρ component is left to float while the other components are fixed to their expected yields. 3.3. B → ρρ The ∆E fit for the ρ+ ρ0 mode uses the sum of a Gaussian and a CB function to represent the signal. The only background contributions in the fit is from the b → c transition and is modeled by a smoothed histogram with a shape that is obtained from MC. All parameters are fixed except the overall normalisation. 4. Results Table 1 summarizes the results of the ∆E fits, showing the number of events, signal yields, reconstruction efficiencies, statistical significance and branching fractions (BF) or upper limits
3
A. Gordon
Signal _ BB Kππ Cont
0 +
ρπ
30 25
Signal _ BB 0 Kππ Cont
+ -
ρ π
20 15 10 5
-0.2
0
∆E (GeV)
0
0.2
-0.2
-0.1
0
0.1
∆E(GeV)
0.2
Figure 1. The ∆E distribution for the B → ρ0 π + and B 0 → ρ± π ∓ modes. The various backgrounds are shown with different hatchings. Table 1 The signal yields, efficiencies, statistical significance, and branching fractions/upper limits from the ∆E fits for all modes. * See text for description of ρ+ ρ0 efficiency. mode K + π− K + π0 K 0 π+ K 0 π0 π+ π− π+ π0 π0 π0 K +K − ¯0 K +K 0 ¯0 K K ρ0 π + ρ+ π − ρ0 π 0 ρ+ ρ 0
Nsig 218 59 67 20 51 37 13 0+3.2 −0 0+2.0 −0 0+2.9 −0.9 24.3 44.6 -4.4 31
(%) 31 30 20 14 16 32 17 23 13 20 9.6 6.8 8.5 *
S(σ) 16.4 6.4 7.6 2.8 5.4 3.5 2.4 4.4 3.7 4.2
BF/UL[×10−6 ] 22.5 ± 0.19 ± 0.18 13.0+0.25 −0.24 ± 0.13 19.4+0.31 −0.30 ± 0.16 +0.33 8.0−0.31 ± 0.16 5.4 ± 0.12 ± 0.05 +0.23 7.4−0.22 ± 0.09 < 6.4 < 0.9 < 2.0 < 8.2 8.0+2.3+0.7 −2.0−0.7 20.8+6.0+2.8 −6.3−3.1 < 5.3 +5.9+2.5 38.5 ± 10.9−5.4−7.5
(UL) obtained from each fit. The first error in the BF is statistical, the send systematic. The statis tical significance is defined as −2 ln(L0 /Lmax ), where Lmax denotes the likelihood at the nominal signal yield and L0 is the likelihood with the signal yield fixed to zero. The systematic error in the fitting procedure is determined by varying the parameters of the fitting functions within their errors and measuring the change in the signal yield. There is an added complication for the ρ+ ρ0 mode: the final state is a vector-vector system so both longitudinal (H11 ) and transverse (H00 )
polarizations of the ρ meson are possible. For these two polarizations the ρ → ππ daughters have different momentum distributions giving the H00 state a lower reconstruction efficiency of 1.81 ± 0.04% compared to the 3.27 ± 0.05% for the H11 final state. The fraction of events with each polarisation is obtained by performing a simultaneous fit to the background-subtracted ρ+ and ρ0 helicity-angle distributions using MC-determined expectations for the H00 and H11 helicity states. The fit results are H00 = 0.86 ± 0.41, H11 = 0.14 ± 0.23 which indicate that the H00 state dominates, as expected [13]. We estimate the branching fraction error due to the uncertain mixture of helicity states by shifting the ratio of the H00 state to the H11 state by ±1σ, and assign the change in the branching fraction as the third error.
24 + 0
Events/ 33 MeV
22.5 20 17.5 15 12.5 10 7.5 5 2.5 0
Events/18 MeV
Events/16 MeV
576
ρρ
20 16 12 8 4 0 -0.40
-0.20
0.00
∆E (GeV)
0.20
0.40
Figure 2. The ∆E distribution for the B → ρ+ ρ0 candidates. The hatched histogram represents the b → c background component.
5. Conclusion The complete set of hh modes has been investigated with significant signals seen in the Kπ, π + π − and π + π 0 modes. We place upper limits on π 0 π 0 and the KK modes. For the B → ρπ modes, branching fractions B(B + → ρ0 π + ) = −6 (8.0+2.3+0.7 and B(B 0 → ρ± π ∓ ) = −2.0−0.7 ) × 10 +6.0+2.8 −6 (20.8−6.3−3.1 ) × 10 are obtained. No evidence is seen for the mode B 0 → ρ0 π 0 and we pro-
4
Charmless two-body decays
+ 0
Events / 20 MeV
Events / 20 MeV
+ −
Kπ
∆E (GeV)
0 0
Events / 20 MeV
Events / 20 MeV
0 +
∆E (GeV)
+ 0
Events / 20 MeV
Events / 20 MeV
+ −
π0π0
ππ
∆E (GeV)
Events / 40 MeV
∆E (GeV)
Events / 40 MeV
Kπ
∆E (GeV)
ππ
vide an upper limit of 5.3 × 10−6 at 90% confidence level. We also provide a measurement of the first charmless b → u vector-vector mode B + → ρ+ π 0 with a branching fraction B(B + → 6 ρ+ ρ0 ) = (38.5 ± 10.9+5.9+2.5 −5.4−7.5 ) × 10 . REFERENCES
∆E (GeV)
Kπ
∆E (GeV)
Kπ
577
K 0K +
∆E (GeV)
Figure 3. The ∆E distribution for the B → hh modes. The hatched histograms represents the charmless B background component. For the K + π − and K + π 0 distributions, the crossfeed components from π + π − and π + π 0 are shown by dot-dashed curves centered 45 MeV above the signal components.
1. H. Quinn, A. I. Sanda, Eur. Phys. Jour. C 15, 628 (2000). 2. A.E. Snyder and H.R. Quinn, Phys. Rev. D 48, 2139 (1993). 3. I. Bediaga, R.E. Blanco, C. G¨ obel, and R. M´endez-Galain, Phys. Rev. Lett. 81, 4067 (1998). 4. Belle Collaboration, B. C. K. Casey, et al. submitted to PRD ; hep-ex/0207090 5. Belle Collaboration, K.Abe, et al. Phys. Rev. Lett. 89, 071801 (2002). 6. Belle Collaboration, A. Abashian et al., Nucl. Instr. and Meth. A 479, 117 (2002). 7. E .Kikutani ed., KEK Preprint 2001-157 (2001), to appear in Nucl. Instr. and Meth. A. 8. G.C. Fox and S. Wolfram, Phys. Lett. B 41, 1581 (1978). 9. For more details see: Belle Collaboration, A. Gordon et al., Phys. Lett. B 542 183, (2002). 10. Belle Collaboration, A. Garmash et al., Phys. Rev. D 65, 092005 (2002). 11. J.E. Gaiser et al., Phys. Rev. D 34, 711 (1986). 12. Belle Collaboration, K. Abe et al., BELLECONF-0115, submitted as a contribution paper to the 2001 International Europhysics Conference on High Energy Physics (EPSHEP 2001). 13. R. Aleksan et al., Phys. Rev. Lett. 356, 95 (1995).
Proceedings of ICHEP 2002, pp. 574–577 S. Bentvelsen, P. de Jong, J. Koch and E. Laenen (Editors)
1
31st INTERNATIONAL CONFERENCE ON HIGH ENERGY PHYSICS AMSTERDAM
Charmless two-body decays Ascelin Gordon∗ , for the Belle Collaboration School of Physics, University of Melbourne, Victoria 3010 Australia We report the latest results of a study of charmless two-body B meson decays using data recorded by the Belle experiment at KEKB. Branching fractions or upper limits are provided for the complete set of Kπ, ππ and KK final states; the B → ρπ decays with final states ρ0 π + , ρ± π ∓ and ρ0 π 0 ; we also provide a first measurement of the branching fraction of the vector-vector decay B + → ρ+ ρ0 .
1. Introduction This report summarises the latest results from the Belle collaboration on measuring branching fractions and upper limits for B meson decays to charmless two-body modes. These include decays with final states Kπ, ππ, and KK (which we collectively label hh) as well as the pseudo-two-body decays ρπ and ρ+ ρ0 . Through investigating these modes, many of the parameters that describe CP violation can be measured. The hh modes alone contain enough information to measure all angles of the Unitarity Triangle [1]. The ρπ and ρ+ ρ0 decays also provide ways of measuring φ2 [2] and φ3 [3]. Partial-rate and time-dependent asymmetry measurements have been performed using some of the hh modes; the results are reported elsewhere [4,5]. The results presented here are based on data taken with the Belle detector [6] at KEKB [7]. The hh and ρπ results are based on a 29 fb−1 data sample while the ρρ results use a 43 fb−1 data sample. 2. Event Reconstruction B meson candidates are identified using the 2 − p2B and beam constrained mass Mbc = Ebeam the energy difference ∆E = EB − Ebeam . Here, pB and EB are the momentum and energy of a B candidate in the centre-of-mass (CM) frame and Ebeam is the CM beam energy. For charged particle identification (PID), three subsystems of the Belle detector are used. The ∗ email:
[email protected]
c 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0920-5632(02)02234-X
central drift chamber dE/dx measurements are combined with the responses of the aerogel ˇ threshold Cerenkov counters and time-of-flight scintillation counters to form likelihoods Lπ or LK . We distinguish pions from kaons by applying selection requirements on the likelihood ratio LR = Lπ /(Lπ + LK ). A similar likelihood ratio including calorimeter information is used to identify electrons. All charged tracks that originate from the interaction point and are not positively identified as electrons are considered as kaon or pion candidates. Candidate KS0 mesons are reconstructed using pairs of oppositely charged tracks with a displaced vertex as well as a flight direction and invariant mass consistent with a KS0 originating from the interaction point. Neutral pion candidates are selected from γγ pairs by requiring that their invariant mass to be within about 3σ of the nominal π 0 mass. To reduce combinatorial backgrounds, mode-dependent momentum cuts are made on the γ and π 0 momenta. Candidate ρ mesons are reconstructed from pion pairs whose invariant mass is required to be within a mode-dependent window of about 150 MeV either side of the nominal ρ mass. All the modes presented here have large backgrounds from e+ e− → qq continuum events (q = u, d, s, c), which typically exhibit a two-jet-like structure. This background is suppressed by means of a likelihood ratio derived from two variables. One is a Fisher discriminant formed from six modified Fox-Wolfram [8] moments. The coefficients of the Fisher discriminant are determined
2
Charmless two-body decays
by optimizing the separation between the signal and continuum MC events. The other variable is cos θB , where θB is the angle between the B flight direction and the electron beam direction. Probability density functions obtained from the Fisher discriminant and the cos θB distribution are multiplied to form the likelihood functions for signal (Lsig ) and continuum (Lcont ) [9]. A requirement on the likelihood ratio Lsig /(Lsig +Lcont ) is then made which varies from mode to mode. As the ρ+ ρ0 mode suffers from the largest continuum background, additional suppression is achieved by making an initial requirement of | cos θthr | < 0.8 (θthr is the angle between the thrust axis of the candidate tracks and that of the remaining tracks in the event). 3. Signal Yield Extraction Figures 1 to 3 show the ∆E distributions in the Mbc signal region for many of the modes analysed after all the selection criteria have been applied. Signal yields are obtained by performing maximum likelihood fits on the ∆E distributions, each using a signal function and one or more background functions. The signal functions are obtained from the MC and adjusted based on comparisons of B → Dπ decays in data and MC. Different D meson decays are used to obtain the same final state particles as the modes being measured. The solid line in all plots shows the sum of the signal and background components. A Chebyshev polynomial with coefficients determined from the Mbc sideband is used to model the continuum background for all fits. Backgrounds from other B decays vary for the different modes. Below is a detailed description of ∆E fits for the modes analysed. 3.1. B → hh Apart from continuum, the ∆E fits for the hh modes include up to two background components: crossfeeds from other misidentified B → hh decays and backgrounds from multi-body and radiative charmless B decays. For charged particle final states, the signal is modeled with a Gaussian. For modes containing π 0 s, the signal is modeled as the sum of a primary Gaussian and a secondary
575
asymmetric Gaussian. The crossfeed component has the same shape as the signal component but is shifted by 45 MeV. Backgrounds from charmless B decays are modeled by a smoothed MC histogram. For all final states except K + π 0 and π + π 0 , the normalizations of the four components are the only free parameters in the fits. Due to the large overlap of the signal and crossfeed components in the K + π 0 and π + π 0 signals, we perform a simultaneous fit to the K + π 0 and π + π 0 ∆E distributions constraining the crossfeed to the expected values based on the PID fake rates. 3.2. B → ρπ For the ρ0 π + mode there are rare B decays that are expected to contaminate the ∆E distribution. The modes are of the type B 0 → h+ h− , B → ρρ and B → Kππ. These background modes are modeled by smoothed MC histograms. The normalisations of the Kππ and h+ h− components are fixed to their expected yields, which are calculated using efficiencies determined by MC and branching fractions measured by previous Belle analyses [10]. The ρρ component is left to float. For the ρπ modes with a π 0 , the signal component is modeled by a Crystal Ball (CB) function [11]. The parameterization for rare B decays includes one component for the B → Kππ 0 modes [12], one for all the B → ρρ modes and a component for the background from the b → c transition. The normalisation of the B → ρρ component is left to float while the other components are fixed to their expected yields. 3.3. B → ρρ The ∆E fit for the ρ+ ρ0 mode uses the sum of a Gaussian and a CB function to represent the signal. The only background contributions in the fit is from the b → c transition and is modeled by a smoothed histogram with a shape that is obtained from MC. All parameters are fixed except the overall normalisation. 4. Results Table 1 summarizes the results of the ∆E fits, showing the number of events, signal yields, reconstruction efficiencies, statistical significance and branching fractions (BF) or upper limits
3
A. Gordon
Signal _ BB Kππ Cont
0 +
ρπ
30 25
Signal _ BB 0 Kππ Cont
+ -
ρ π
20 15 10 5
-0.2
0
∆E (GeV)
0
0.2
-0.2
-0.1
0
0.1
∆E(GeV)
0.2
Figure 1. The ∆E distribution for the B → ρ0 π + and B 0 → ρ± π ∓ modes. The various backgrounds are shown with different hatchings. Table 1 The signal yields, efficiencies, statistical significance, and branching fractions/upper limits from the ∆E fits for all modes. * See text for description of ρ+ ρ0 efficiency. mode K + π− K + π0 K 0 π+ K 0 π0 π+ π− π+ π0 π0 π0 K +K − ¯0 K +K 0 ¯0 K K ρ0 π + ρ+ π − ρ0 π 0 ρ+ ρ 0
Nsig 218 59 67 20 51 37 13 0+3.2 −0 0+2.0 −0 0+2.9 −0.9 24.3 44.6 -4.4 31
(%) 31 30 20 14 16 32 17 23 13 20 9.6 6.8 8.5 *
S(σ) 16.4 6.4 7.6 2.8 5.4 3.5 2.4 4.4 3.7 4.2
BF/UL[×10−6 ] 22.5 ± 0.19 ± 0.18 13.0+0.25 −0.24 ± 0.13 19.4+0.31 −0.30 ± 0.16 +0.33 8.0−0.31 ± 0.16 5.4 ± 0.12 ± 0.05 +0.23 7.4−0.22 ± 0.09 < 6.4 < 0.9 < 2.0 < 8.2 8.0+2.3+0.7 −2.0−0.7 20.8+6.0+2.8 −6.3−3.1 < 5.3 +5.9+2.5 38.5 ± 10.9−5.4−7.5
(UL) obtained from each fit. The first error in the BF is statistical, the send systematic. The statis tical significance is defined as −2 ln(L0 /Lmax ), where Lmax denotes the likelihood at the nominal signal yield and L0 is the likelihood with the signal yield fixed to zero. The systematic error in the fitting procedure is determined by varying the parameters of the fitting functions within their errors and measuring the change in the signal yield. There is an added complication for the ρ+ ρ0 mode: the final state is a vector-vector system so both longitudinal (H11 ) and transverse (H00 )
polarizations of the ρ meson are possible. For these two polarizations the ρ → ππ daughters have different momentum distributions giving the H00 state a lower reconstruction efficiency of 1.81 ± 0.04% compared to the 3.27 ± 0.05% for the H11 final state. The fraction of events with each polarisation is obtained by performing a simultaneous fit to the background-subtracted ρ+ and ρ0 helicity-angle distributions using MC-determined expectations for the H00 and H11 helicity states. The fit results are H00 = 0.86 ± 0.41, H11 = 0.14 ± 0.23 which indicate that the H00 state dominates, as expected [13]. We estimate the branching fraction error due to the uncertain mixture of helicity states by shifting the ratio of the H00 state to the H11 state by ±1σ, and assign the change in the branching fraction as the third error.
24 + 0
Events/ 33 MeV
22.5 20 17.5 15 12.5 10 7.5 5 2.5 0
Events/18 MeV
Events/16 MeV
576
ρρ
20 16 12 8 4 0 -0.40
-0.20
0.00
∆E (GeV)
0.20
0.40
Figure 2. The ∆E distribution for the B → ρ+ ρ0 candidates. The hatched histogram represents the b → c background component.
5. Conclusion The complete set of hh modes has been investigated with significant signals seen in the Kπ, π + π − and π + π 0 modes. We place upper limits on π 0 π 0 and the KK modes. For the B → ρπ modes, branching fractions B(B + → ρ0 π + ) = −6 (8.0+2.3+0.7 and B(B 0 → ρ± π ∓ ) = −2.0−0.7 ) × 10 +6.0+2.8 −6 (20.8−6.3−3.1 ) × 10 are obtained. No evidence is seen for the mode B 0 → ρ0 π 0 and we pro-
4
Charmless two-body decays
+ 0
Events / 20 MeV
Events / 20 MeV
+ −
Kπ
∆E (GeV)
0 0
Events / 20 MeV
Events / 20 MeV
0 +
∆E (GeV)
+ 0
Events / 20 MeV
Events / 20 MeV
+ −
π0π0
ππ
∆E (GeV)
Events / 40 MeV
∆E (GeV)
Events / 40 MeV
Kπ
∆E (GeV)
ππ
vide an upper limit of 5.3 × 10−6 at 90% confidence level. We also provide a measurement of the first charmless b → u vector-vector mode B + → ρ+ π 0 with a branching fraction B(B + → 6 ρ+ ρ0 ) = (38.5 ± 10.9+5.9+2.5 −5.4−7.5 ) × 10 . REFERENCES
∆E (GeV)
Kπ
∆E (GeV)
Kπ
577
K 0K +
∆E (GeV)
Figure 3. The ∆E distribution for the B → hh modes. The hatched histograms represents the charmless B background component. For the K + π − and K + π 0 distributions, the crossfeed components from π + π − and π + π 0 are shown by dot-dashed curves centered 45 MeV above the signal components.
1. H. Quinn, A. I. Sanda, Eur. Phys. Jour. C 15, 628 (2000). 2. A.E. Snyder and H.R. Quinn, Phys. Rev. D 48, 2139 (1993). 3. I. Bediaga, R.E. Blanco, C. G¨ obel, and R. M´endez-Galain, Phys. Rev. Lett. 81, 4067 (1998). 4. Belle Collaboration, B. C. K. Casey, et al. submitted to PRD ; hep-ex/0207090 5. Belle Collaboration, K.Abe, et al. Phys. Rev. Lett. 89, 071801 (2002). 6. Belle Collaboration, A. Abashian et al., Nucl. Instr. and Meth. A 479, 117 (2002). 7. E .Kikutani ed., KEK Preprint 2001-157 (2001), to appear in Nucl. Instr. and Meth. A. 8. G.C. Fox and S. Wolfram, Phys. Lett. B 41, 1581 (1978). 9. For more details see: Belle Collaboration, A. Gordon et al., Phys. Lett. B 542 183, (2002). 10. Belle Collaboration, A. Garmash et al., Phys. Rev. D 65, 092005 (2002). 11. J.E. Gaiser et al., Phys. Rev. D 34, 711 (1986). 12. Belle Collaboration, K. Abe et al., BELLECONF-0115, submitted as a contribution paper to the 2001 International Europhysics Conference on High Energy Physics (EPSHEP 2001). 13. R. Aleksan et al., Phys. Rev. Lett. 356, 95 (1995).