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Two Topics in Rare B Decays
Nuclear Physics B (Proc. Suppl.) 163 (2007) 117–120 www.elsevierphysics.com
Two Topics in Rare B Decays T. E. Browdera a
University of Hawaii at Manoa, 2505 Correa Road, Honolulu, HI, 96822
I discuss two important topics in rare B decay where there has been great progress in recent times: the observation of B → ργ, which establishes the existence of b → d transitions, and evidence for B → τ ν reported by Belle.
1. Observation of b → d transitions. The process b → dγ proceeds through the Feynman diagrams shown in Figure 1. The radiative penguin is dominant; the annihilation diagram is expected to be small and is only present in charged B decays. In the summer of 2005, Belle reported the observation of the flavor-changing neutral current process b → dγ using a sample of 386 × 106 B meson pairs[1]. The combined distributions in the data are shown in Figure 2. The large continuum background is suppressed using event shape variables and tagging information. More continuum rejection is obtained by using the vertex displacement, Δz, which is the difference in the z-position between the signal vertex and tagging vertex[1]. This is effective because most continuum background in b → dγ has zero lifetime. Background from B → K ∗ γ, which has a branching fraction approximately twenty times larger, is rejected using particle identification and a veto on M (Kπ). The residual background is determined using the B → K ∗ γ signals in data and the measured misidentification rates. Belle measured branching fractions for the ex¯ 0 → ρ0 γ and B ¯0 → clusive modes B − → ρ− γ, B ωγ. Assuming that these three modes are related by isospin, from a combined fit Belle finds an excess of 36.9 events with B(B → (ρ, ω)γ) = +0.34+0.10 ) × 10−6 and a significance of 5.1σ (1.32−0.31−0.09 including systematics. The central values of the branching fractions 0920-5632/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2006.11.001
(a) loop diagram γ
t b
(b) annihilation diagram γ b d
d
Vtb
W
Vtd*
u
Vub
W
Vud*
u
Figure 1. The Feynman diagrams for the decay b → dγ.
reported by Belle deviate from the isospin expectation. However, the statistics are very low (the central values of the yields are (8.5, 20.7, 5.7) events for B − → ρ− γ, B 0 → ρ0 γ, B 0 → ωγ modes, respectively). A toy MC shows that the deviation from the isospin expectation is at the 2σ level (probability of 4.9%). With more data, I suspect that this effect will disappear. Within the SM framework the measurement of exclusive b → dγ transitions can be combined with the measurement of B → K ∗ γ decay modes and SU (3) symmetry to determine the ratio of CKM matrix elements |Vtd /Vts | to be +0.026+0.018 0.199−0.025−0.015 .
Here the first error is experimental and the second is theoretical. There are corrections due to form factors, SU(3) breaking effects, and, for the B − decay, inclusion of an annihilation diagram, which are included in the theoretical uncertainty. This result on |Vtd /Vts | from b → dγ can be compared to the precise measurements of Bs −
118
T.E. Browder / Nuclear Physics B (Proc. Suppl.) 163 (2007) 117–120
Figure 2. The ΔE and beam constrained distributions for all B → ργ and B → ωγ candidates. ¯s mixing that have been recently published by B the Tevatron experiments. The Tevatron mixing results give significantly more precise constraints on |Vtd /Vts | as shown in Figure 3. However, it is important to compare the two results; b → dγ is a loop process while Bs mixing involves a box diagram. If new physics is present, the two results may not agree.
from inclusive b → sγ may be handled with high momentum particle identification and the use of the B reconstruction technique. Modes involving b → d transitions are expected to have significant direct CP violating asymmetries in the Standard Model. Mixing induced CP ¯ 0 is expected violation in B 0 → ρ0 γ or B 0 → K 0 K to be negligible due to a subtle cancellation; the ¯d phase of Vtd is opposite to the phase of Bd -B mixing. This cancellation could be spoiled by new physics contributions. However, measurements of this type of asymmetry will require Super B factory levels of luminosity (10 − 50 ab−1 )[2]. 2. Evidence for B → τ ν from Belle The best upper limit on B → τ ν is from BaBar: B(B − → τ ν) < 2.6 × 10−4 [4]. In 2006 Belle announced the first evidence for the existence of B → τ ν[5]. This mode is the first example of a B decay, which in the standard model, proceeds via the W-annihilation process as shown in Figure 4. If new physics is present then the decay can also be mediated by a charged Higgs, which would replace the virtual charged W[6]. Most of the sensitivity to the B + → τ + ν decay is obtained from 1-prong τ decay modes. Thus the experimental signature is a single charged track and missing energy (carried away by three neutrinos).
b Figure 3. A comparison from the UTFIT group of the constraints from Tevatron results on Bs mixing and the Belle result on b → dγ.
The Belle result was confirmed by BaBar after the Capri workshop. In their preliminary result BaBar obtained a similar inclusive branching fraction and a signal with higher significance for the mode B + → ρ+ γ. With much more luminosity, measurements of the inclusive process b → dγ may be possible. ¯ backgrounds including the background Large B B
B
−
W −
u
−
τ
−
−
ντ
Figure 4. The Feynman diagram for the decay B → τ ν in the standard model. The solution is the use of fully reconstructed B tags, which becomes feasible with very large integrated luminosities since the tagging efficiency is ∼ 0.137%. One of the B mesons is fully reconstructed in a hadronic decay mode, we then
119
search for a τ candidate consistent with τ → exνν, τ → μνν, τ → π − ν, τ → π − π 0 ν and τ → 3πν. These modes cover 81% of τ decays. The charged B tag sample contains about 680,000 tags. The signal is then extracted from the extra calorimeter energy (EECL ) distribution, where the decay products of the tag and the measurable decay products of the τ candidate have been removed from consideration. The signal peaks at zero extra energy while the background tends to have a phase-space like shape. Both distributions have long tails to higher EECL . The tails in the EECL distribution arise from beam background and electronic noise. The shapes of the signal and background are taken from Monte Carlo simulation, which includes an accurate model of these effects that is obtained from random trigger data runs. A calibration signal is available from B − → D∗0 − ν events opposite fully reconstructed tags. The branching fraction and normalization of the EECL distribution in data can be compared to MC simulation. The agreement is very good[5]. The result was obtained using 414 fb− 1 of data, ¯ pairs. A sigwhich corresponds to 449 × 106 B B +5.3 events is found (17.2 nal with 24.1+7.6 −6.6 −4.7 events in the nominal ECL signal window). Including systematics, the signal has a significance of 3.5 standard deviations. The corresponding branching fraction is +0.56+0.46 ) × 10−4 B(B − → τ − ν¯τ ) = (1.79−0.49−0.51
The first error is statistical while the second is systematic. The dominant experimental systematic arises from uncertainty in the background shape. In the τ → π − π 0 ν and 3-prong tau channels, a small background that peaks at zero extra calorimeter energy is present. This is taken into account (see Figure 5) and a conservative systematic error is assigned. The branching fraction is given by a known kinematic factor times the product of |Vub |fB . If we take |Vub | = (4.39 ± 0.33) × 10−3 , the Belle measurement implies that fB = 229+36+34 −31−37 MeV.
Events / 0.1 GeV
T.E. Browder / Nuclear Physics B (Proc. Suppl.) 163 (2007) 117–120
50
40
30
20
10
0 0
0.5
1
EECL (GeV)
Figure 5. The extra calorimeter energy distribution in Belle data. The curve shows the fit. The dotted contribution is the signal. This is the first direct measurement of fB , which enters into many other results related to the weak interaction. The Belle result can also be compared to a recent unquenced lattice calculation from the HPQCD group, which gives fB = 216 ± 22 MeV[7]. If fB is taken from lattice QCD calculations, then the Belle result can be used to obtain constraints on the charged Higgs mass as a function of tan β. The Higgs constraint is quite powerful for large values of tan β; it is more restrictive than constraints from direct searches at LEP and the Tevatron as shown in Figure 6. This is the first example of a rare B decay with large missing energy, a mode in this class. Extrapolations from this result indicate that the necessary sensitivity to a rare B mode with the same daunting experimental signature, a single track and a missing energy, can be achieved at a Super B factory[2],[3]. Of particular interest in the future are modes of the type B → Kν ν¯ and B → K ∗ ν ν¯. This type of mode probably cannot be studied at LHCb or other hadronic collider experiments. Further dramatic experimental breakthroughs for these two classes of decay modes will require
120
T.E. Browder / Nuclear Physics B (Proc. Suppl.) 163 (2007) 117–120
7. A. Gray et al. (HPQCD collaboration), Phys. Rev. Lett. 95, 212001 (2005).
300
BB (95 .5%
2
H± Mass (GeV/c )
C.L .
)
250
447 ×1 6 0
200
Be
lle
150
100
Tevatron Run I Excluded (95% C.L.)
LEP Excluded (95% C.L.)
50 0
20
40
60
80
100
tan β Figure 6. The constraints on charged Higgs mass as a function of tan β obtained from the Belle result on B → τ ν. Results from direct searches at LEP and the Tevatron are also showed. The white regions are allowed by the Belle result. Super B factory class luminosity. 3. Acknowledgements I thank the organizers of the Capri Workshop, especially Giulia Ricciardi for her patience and organizational skill. REFERENCES 1. D. Mohapatra et al. (Belle collaboration), Phys. Rev. Lett. 96, 221601 (2006). 2. K. Abe et al., KEK report 04-4, hepex/0406071. 3. The Discovery Potential of a Super B Factory, SLAC-R-709, edited by J.L Hewett and D. G. Hitlin. 4. B. Aubert et al. (BaBar collaboration), Phys. Rev. D 73, 057101 (2006). 5. K. Ikado et al. (Belle collaboration), hepex/0604018, submitted to Phys. Rev. Lett. 6. W. S. Hou, Phys. Rev. D 48, 2342 (1993).
Two Topics in Rare B Decays T. E. Browdera a
University of Hawaii at Manoa, 2505 Correa Road, Honolulu, HI, 96822
I discuss two important topics in rare B decay where there has been great progress in recent times: the observation of B → ργ, which establishes the existence of b → d transitions, and evidence for B → τ ν reported by Belle.
1. Observation of b → d transitions. The process b → dγ proceeds through the Feynman diagrams shown in Figure 1. The radiative penguin is dominant; the annihilation diagram is expected to be small and is only present in charged B decays. In the summer of 2005, Belle reported the observation of the flavor-changing neutral current process b → dγ using a sample of 386 × 106 B meson pairs[1]. The combined distributions in the data are shown in Figure 2. The large continuum background is suppressed using event shape variables and tagging information. More continuum rejection is obtained by using the vertex displacement, Δz, which is the difference in the z-position between the signal vertex and tagging vertex[1]. This is effective because most continuum background in b → dγ has zero lifetime. Background from B → K ∗ γ, which has a branching fraction approximately twenty times larger, is rejected using particle identification and a veto on M (Kπ). The residual background is determined using the B → K ∗ γ signals in data and the measured misidentification rates. Belle measured branching fractions for the ex¯ 0 → ρ0 γ and B ¯0 → clusive modes B − → ρ− γ, B ωγ. Assuming that these three modes are related by isospin, from a combined fit Belle finds an excess of 36.9 events with B(B → (ρ, ω)γ) = +0.34+0.10 ) × 10−6 and a significance of 5.1σ (1.32−0.31−0.09 including systematics. The central values of the branching fractions 0920-5632/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2006.11.001
(a) loop diagram γ
t b
(b) annihilation diagram γ b d
d
Vtb
W
Vtd*
u
Vub
W
Vud*
u
Figure 1. The Feynman diagrams for the decay b → dγ.
reported by Belle deviate from the isospin expectation. However, the statistics are very low (the central values of the yields are (8.5, 20.7, 5.7) events for B − → ρ− γ, B 0 → ρ0 γ, B 0 → ωγ modes, respectively). A toy MC shows that the deviation from the isospin expectation is at the 2σ level (probability of 4.9%). With more data, I suspect that this effect will disappear. Within the SM framework the measurement of exclusive b → dγ transitions can be combined with the measurement of B → K ∗ γ decay modes and SU (3) symmetry to determine the ratio of CKM matrix elements |Vtd /Vts | to be +0.026+0.018 0.199−0.025−0.015 .
Here the first error is experimental and the second is theoretical. There are corrections due to form factors, SU(3) breaking effects, and, for the B − decay, inclusion of an annihilation diagram, which are included in the theoretical uncertainty. This result on |Vtd /Vts | from b → dγ can be compared to the precise measurements of Bs −
118
T.E. Browder / Nuclear Physics B (Proc. Suppl.) 163 (2007) 117–120
Figure 2. The ΔE and beam constrained distributions for all B → ργ and B → ωγ candidates. ¯s mixing that have been recently published by B the Tevatron experiments. The Tevatron mixing results give significantly more precise constraints on |Vtd /Vts | as shown in Figure 3. However, it is important to compare the two results; b → dγ is a loop process while Bs mixing involves a box diagram. If new physics is present, the two results may not agree.
from inclusive b → sγ may be handled with high momentum particle identification and the use of the B reconstruction technique. Modes involving b → d transitions are expected to have significant direct CP violating asymmetries in the Standard Model. Mixing induced CP ¯ 0 is expected violation in B 0 → ρ0 γ or B 0 → K 0 K to be negligible due to a subtle cancellation; the ¯d phase of Vtd is opposite to the phase of Bd -B mixing. This cancellation could be spoiled by new physics contributions. However, measurements of this type of asymmetry will require Super B factory levels of luminosity (10 − 50 ab−1 )[2]. 2. Evidence for B → τ ν from Belle The best upper limit on B → τ ν is from BaBar: B(B − → τ ν) < 2.6 × 10−4 [4]. In 2006 Belle announced the first evidence for the existence of B → τ ν[5]. This mode is the first example of a B decay, which in the standard model, proceeds via the W-annihilation process as shown in Figure 4. If new physics is present then the decay can also be mediated by a charged Higgs, which would replace the virtual charged W[6]. Most of the sensitivity to the B + → τ + ν decay is obtained from 1-prong τ decay modes. Thus the experimental signature is a single charged track and missing energy (carried away by three neutrinos).
b Figure 3. A comparison from the UTFIT group of the constraints from Tevatron results on Bs mixing and the Belle result on b → dγ.
The Belle result was confirmed by BaBar after the Capri workshop. In their preliminary result BaBar obtained a similar inclusive branching fraction and a signal with higher significance for the mode B + → ρ+ γ. With much more luminosity, measurements of the inclusive process b → dγ may be possible. ¯ backgrounds including the background Large B B
B
−
W −
u
−
τ
−
−
ντ
Figure 4. The Feynman diagram for the decay B → τ ν in the standard model. The solution is the use of fully reconstructed B tags, which becomes feasible with very large integrated luminosities since the tagging efficiency is ∼ 0.137%. One of the B mesons is fully reconstructed in a hadronic decay mode, we then
119
search for a τ candidate consistent with τ → exνν, τ → μνν, τ → π − ν, τ → π − π 0 ν and τ → 3πν. These modes cover 81% of τ decays. The charged B tag sample contains about 680,000 tags. The signal is then extracted from the extra calorimeter energy (EECL ) distribution, where the decay products of the tag and the measurable decay products of the τ candidate have been removed from consideration. The signal peaks at zero extra energy while the background tends to have a phase-space like shape. Both distributions have long tails to higher EECL . The tails in the EECL distribution arise from beam background and electronic noise. The shapes of the signal and background are taken from Monte Carlo simulation, which includes an accurate model of these effects that is obtained from random trigger data runs. A calibration signal is available from B − → D∗0 − ν events opposite fully reconstructed tags. The branching fraction and normalization of the EECL distribution in data can be compared to MC simulation. The agreement is very good[5]. The result was obtained using 414 fb− 1 of data, ¯ pairs. A sigwhich corresponds to 449 × 106 B B +5.3 events is found (17.2 nal with 24.1+7.6 −6.6 −4.7 events in the nominal ECL signal window). Including systematics, the signal has a significance of 3.5 standard deviations. The corresponding branching fraction is +0.56+0.46 ) × 10−4 B(B − → τ − ν¯τ ) = (1.79−0.49−0.51
The first error is statistical while the second is systematic. The dominant experimental systematic arises from uncertainty in the background shape. In the τ → π − π 0 ν and 3-prong tau channels, a small background that peaks at zero extra calorimeter energy is present. This is taken into account (see Figure 5) and a conservative systematic error is assigned. The branching fraction is given by a known kinematic factor times the product of |Vub |fB . If we take |Vub | = (4.39 ± 0.33) × 10−3 , the Belle measurement implies that fB = 229+36+34 −31−37 MeV.
Events / 0.1 GeV
T.E. Browder / Nuclear Physics B (Proc. Suppl.) 163 (2007) 117–120
50
40
30
20
10
0 0
0.5
1
EECL (GeV)
Figure 5. The extra calorimeter energy distribution in Belle data. The curve shows the fit. The dotted contribution is the signal. This is the first direct measurement of fB , which enters into many other results related to the weak interaction. The Belle result can also be compared to a recent unquenced lattice calculation from the HPQCD group, which gives fB = 216 ± 22 MeV[7]. If fB is taken from lattice QCD calculations, then the Belle result can be used to obtain constraints on the charged Higgs mass as a function of tan β. The Higgs constraint is quite powerful for large values of tan β; it is more restrictive than constraints from direct searches at LEP and the Tevatron as shown in Figure 6. This is the first example of a rare B decay with large missing energy, a mode in this class. Extrapolations from this result indicate that the necessary sensitivity to a rare B mode with the same daunting experimental signature, a single track and a missing energy, can be achieved at a Super B factory[2],[3]. Of particular interest in the future are modes of the type B → Kν ν¯ and B → K ∗ ν ν¯. This type of mode probably cannot be studied at LHCb or other hadronic collider experiments. Further dramatic experimental breakthroughs for these two classes of decay modes will require
120
T.E. Browder / Nuclear Physics B (Proc. Suppl.) 163 (2007) 117–120
7. A. Gray et al. (HPQCD collaboration), Phys. Rev. Lett. 95, 212001 (2005).
300
BB (95 .5%
2
H± Mass (GeV/c )
C.L .
)
250
447 ×1 6 0
200
Be
lle
150
100
Tevatron Run I Excluded (95% C.L.)
LEP Excluded (95% C.L.)
50 0
20
40
60
80
100
tan β Figure 6. The constraints on charged Higgs mass as a function of tan β obtained from the Belle result on B → τ ν. Results from direct searches at LEP and the Tevatron are also showed. The white regions are allowed by the Belle result. Super B factory class luminosity. 3. Acknowledgements I thank the organizers of the Capri Workshop, especially Giulia Ricciardi for her patience and organizational skill. REFERENCES 1. D. Mohapatra et al. (Belle collaboration), Phys. Rev. Lett. 96, 221601 (2006). 2. K. Abe et al., KEK report 04-4, hepex/0406071. 3. The Discovery Potential of a Super B Factory, SLAC-R-709, edited by J.L Hewett and D. G. Hitlin. 4. B. Aubert et al. (BaBar collaboration), Phys. Rev. D 73, 057101 (2006). 5. K. Ikado et al. (Belle collaboration), hepex/0604018, submitted to Phys. Rev. Lett. 6. W. S. Hou, Phys. Rev. D 48, 2342 (1993).