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Erratum to “Charming-penguin enhanced B decays” [Nucl. Phys. B 512 (1998) 3]
ELSEVIER
Nuclear Physics B 531 (1998) 656-660
E~mum
Erratum to "Charming-penguin enhanced B decays" [ Nucl. Phys. B 512 (1998) 3 ] * M. Ciuchini, R. Contino, E. Franco, G. Martinelli, L. Silvestrini Received 27 April 1998; accepted 15 May 1998
We have found an error in our calculation of the ABLOPR heavy-light form factor f+, which shows up whenever the light meson is not a pion. Therefore many channels containing this form factor, and consequently the values of the fitted parameters, are modified. However appreciable changes occur only for B ~ K J / ~ and coloursuppressed channels in Table 2. In particular, the correct ABLOPR does not fail in reproducing B ---, K*J/~, even if the X 2 of the global fit of sc and 8~ increases. On the other hand, some of the ABLOPR predictions in Table 1 for the vector sector, which were previously very large, no more exceed the experimental bounds. Apart from these considerations, the main conclusions of our analysis do not change. For completeness we give updated tables of BRs obtained using the correct ABLOPR form factor f ÷ .
Acknowledgements We thank J. Charles and O. P~ne for pointing out the differences between their calculations of BR(B ~ KJ/q~) and our predictions using ABLOPR form factors.
* PII of original article: S0550-3213(97)00768-2. 0550-3213/98/$ - see frontmatter (~) 1998 Published by Elsevier Science B.V. All rights reserved. PH S0550-32 13(98)00405-2
657
M. Ciuchini et a l . / N u c l e a r Physics B 531 (1998) 656-660
Table 1 Predictions for yet unmeasured BR's. The channels above the horizontal line are those enhanced by charming penguins. In square brackets, the BR's obtained without charming penguins are shown. BR(B + ---* wK+), BR(B + ---* w¢r+), BR(B + ---* ~7~K+ ) and BR(B,/ ~ r f K ° ) , for which preliminary measurements exist ( ( .1.~._0.6~+°'74- 0.3) × 10 -5, ( 1.1+°6-0.54- 0.2) × 10 - 5 , (7.1+25-2.14- 0.9) × 10 - 5 and (5.3+2"8_2.24- 1.2) x 10 -5 respectively), have been given in this table since they have not been used in the fit of ~L and 6L Channel
QCDSR-CV QCDSR-BV B R × l0 5 B R x l0 5
Lattice-CV QM-CV B R x l0 5 B R x l0 5
Ba "--* r f K 0
2.45 [0.191
1.97-3.55 [0.12-0.67
2.49 [0.101 2.39 [0.19] 4.69 [0.66]
*
Ba ~ r/IK *°
0.75 [0.01]
0.30-2.41 10.00-0.10
1.41 [0.001 0.47 I0.011 1.69 [0.011
< 9.9
Bd --* ~TK°
0.07 [0.01 I
0.01-0.26 ]0.00-0.02
0.07 I0.001 0.06 10.01 ] 0.11 [0.011
-
Bd ---, rtK *~
0.04 [0.02]
0.01-0.22 10.01-0.06
0.05 [0.01 ] 0.03 [0.02]
Bd -'* oak n
0.73 [0.041
0.13-1.70 [0.03-0.38
0.80 [0.021 0.70 ]0.06] 0.45 [0.061
-
Bd ~
1.85 [0.11]
1.01-3.26 10.08-0.58
2.76 [0.121 1.43 [ 0.08 ] 5.41 [0.531
< 3.8 < 4.2
t o K *°
ABLOPR-CV Experiment B R x 105 B R × l0 5
0.11
[0.061
< 3.3
1.48 [0.111
0.68-2.29 I0.10-0.75
1.77 [0.08] 0.92 [0.12] 1.50 [0.201
Bd ~
(bK *°
3.27 [0.09]
1.90-6.73 [0.07-0.62]
5.08 [0.111 1.65 [0.051 9.75 [0.42]
< 2.2
B,I ~
zr° K ~
0.65 [0.041
0.49-0.95 [0.01-0.26]
0.68 [0.031 0.64 [0.031 1.01 [0.14]
< 4.1 < 2.0
Bd~dpK
°
0.40 I0.031
0.29-0.60 I0.01-0.131
0.61 [0.02] 0.26 [0.03
0.73 [0.101
¢ r - K *+ 3.13 [0.17]
2.05-5.07 [ 0.05-1.01 ]
3.47 [0.11] 3.16 [0.16
2.95 [0.451
< 6.7
0.63 [0.021
0.21-0.67 [0.00-0.11 ]
1.19 [0.02] 0.53 [0.02
0.97 10.091
< 3.3
p - K *+ 2.21 [0.12]
1.44-3.57 [0.03-0.72]
4.15 [0.131 1.75 [0.09
7.86 [1.191
Bd --* p°KO
0.44 [0.03]
0.07-1.63 10.00-0.091
0.81 10.011 0.35 I0.03
0.96 [0.041
B,I ~
p°K*°
1.01 [0.01]
0.50-2.45 10.01-0.131
1.86 10.02] 0.60 [0.01
4.81 [0.191
< 46
B + ~ r/IK +
2.31 [0.201
2.05-3.14 10.11-0.921
2.36 [0.101 2.27 [0.20
3.94 [0.62]
*
B + ~ r f K *+
4.14 [0.04]
1.45-11.22 I0.00-0.57] 4.82 ]0.021 4.18 I0.03
7.93 [0.08]
< 29
B + ~ rlK +
0.12 [0.021
0.02-0.46 [0.00-0.081
B + ~ rlK *+
0.27 10.041 0.04-1.19 [0.01-0.221
0.29 [0.03] 0.25 [0.04
0.63 [0.121
< 24
B + ~ o~K+
0.60 [0.021
0.06-1.39 [0.00-0.661
0.65 I0.041 0.60 [0.03
0.21 10.231
*
B + -'* toK *+
1.50 [0.08]
0.84-2.48 [0.03-1.121
2.24 [0.161 1.20 [0.06
2.82 11.121
< 11
B + --~ ~bK+
1.54 [0.12]
0.70-2.38 [0.10-0.78 I
1.84 [0.091 0.96 [0.13
1.56 [0.211
< 0.53
10.0 10.441
<4.1
B,! ---* ¢r°K *° Bd ~
Bd "4 p - K + Bd ~
0.13 I0.01] 0.11
[0.01
< 3.0
0.27 10.05]
B + --* ~bK*+
3.35 [0.09]
1.96-6.90 [0.08-0.64
5.21 [o.111 1.70 10.06
B + --~ Ir°K +
0.94 [0.18]
0.67-1.03 [0.09-0.74
0.86 [0.101 0.95 I0.181 0.88 I0.401
< 1.6
B + ~ ~'°K*+
1.70 [0.14]
1.15-2.42 [0.06-0.71
1.81 [0.091 1.71 I0.131 1.56 I0.331
< 8.0
B + ~ 7r+K *° 0.92 [0.13]
0.73-1.15 [0.08-0.37
1.29 [0.071 0.62 I0.121 1.61 ]0.371
< 3.9
B + --~ p + / d )
2.67 [0.00]
0.88-7.28 [0.00-0.36
3.05 I0.001 2.62 I0.00] 4.56 I0.00]
< 6.4
B + ---* p + K *°
2.21 [0.091
1.42-4.01 [ 0.06-0.38
3.82 10.091 1.34 I0.071 10.1 I0.991
-
B+ ~
p°K+
0.39 [0.061
0.18-0.61 [0.00-0.21
0.61 [0.03] 0.35 ]0.06] 0.48 [0.10]
< 1.4
B+ ~
p°K*+
1.26 10.15]
0.81-1.62 [0.06-0.63
2.18 [0.141 1.00 [0.I11 4.25 I 1.051
< 90
658
M. Ciuchini et a l . / N u c l e a r Physics B 531 (1998) 656-660
Table I - - continued Channel
QCDSR-CV QCDSR-BV BR x 105 BR x 10 -s
Lattice-CV BR × 105
QM-CV BR x 105
ABLOPR-CV Experiment BR × 105 BR x 105
Bd--~ cr+¢r -
0.99 [0.631
0.39-2.63 [0.15-1.55] 0.71 [0.39]
Bd---* q'r°'rr°
0,04
0.01-0.12 [0.01-0.11] 0.004 I0.002] 0.06 [0.05] 0.01 [0.02
0.95 10.60] 2.36 [1.68
< 1.5 < 0.93
Bd --~ pOq'r°
0.08 [0.11]
0.00-0.21 [0.02-0.21] 0.01 [0.07]
0.12 [0.13] 0.05 [0.10
< 1.8
Ba ~ p + ~ -
2.67 [1.71]
1.02-7.51 [0.45--4.15] 1.93 [1.07]
2.55 [1,631 6.24 [4.43
< 8.8
Bd ~ ~ + p -
0.59 [0.38]
0.22-1.75 [0.11-0.91] 0.66 [0.37]
0.46 [0.30] 1.90 [1.35
Bd ~
pOpO
0.16 [0.18]
0.00-0.58 [0.04-0.46] 0.02 [0.18]
0.21 [0.19] 0.30 [0.59
< 28
Bd -'-+ p + p -
1.81 [1.16]
0.69-5.10 [0.31-2.82] 2.19 [1.22]
1.37 [0.88] 16.5 [11.7
< 220
Ba ~
o ~ "°
0.06 [0.01]
0.03-0.42 [0.00-0,29] 0.08 [0.005]
0.06 [0.021 0.07 [0.01
Bd ~
o~p °
0.10 [0.01]
0.05-1.22 [0.01-0.73] 0.14 10.01]
0.08 [0.01] 0.34 [0.03
< 3.4
Bd ---) q~Tr0
0.00 [0.00]
0.00-0.01 [0.00-0.011 0.00 [0.00]
0.00 [0.001 0.00 [0.0(3
< 0.65
Bd --' ~ o
0,48 [0.36]
0.04-2.14 [0.01-2.91] 0.21 [0.22]
0.44 [0.33] 0.97 [0.93]
< 2.2
B + --* 7"r+Tr°
0,53
0.16-1.18
0.51
1.16
< 2.0
0.36
B + --, p+Tr°
1,12
0.30-2.62
0.80
1.05
2.73
< 7.7
B + --* cr+p °
0.52
0.19-1.08
0.47
0.47
1.16
<5.8
1.08
0.73
8.02
B + _~ p+pO
0.94
0.23-2.11
B + ~ ~oqr+
0.84 [0.50]
0.38-2.35 [0.08-1.04] 0.94 [0.45]
< 100
0.70 [0.45] 1.82 [1.09]
4r
B + --* o~p+
1.81 [0.941
0.8O-5.57 [0.19-3.40] 2.44 [1.04]
1.36 [0.72] 13.4 [7.61]
B + ---, ~b~-+
0.00 [0.00]
0.00-0.02 [0.00-0.021 0.00 [0.00[
0.00 110.001 0.00 [0.00]
< 0.56
B+ --* ~'+~7'
1.09 [0.761
0.01-3.33 [0.13-3.361 0.87 [0.581
0.97 [0.651 3.34 [2.78]
<4.5
Bd ---* c r ° J / ~
2,27
2.06-2.36
1.82
2.70
1.48
<6
Bd ~
pOj/qt
4.44
4.04-4.63
5.05
3.61
5.22
< 25
B + ___+p + j / q t
9,22
8.39-9.62
10.48
7.49
10.8
< 77
Bd ~
K°[( °
0,09 [0.01]
0.05-0.56 [0.00-0.41] 0.09 [0.005]
0.08 [0.01l 0.13 [0.03]
< 1.7
B,l ~
K+K -
0,00 [0.00]
0.00-0.50 [0.00-0.50] 0.00 I0.00]
0.00 [0.001 0.00 [0.00]
< 1.7
0.05-0.58 [0.00-0.43] 0.09 [0.0051
0.08 [0.011 0.14 [0.03]
<2.1
B + ~ K+/~ ~ 0,09 I0.011
Table 2 Predictions for emission-dominated decay channels for which only experimental upper bounds exist Channel
B,t Ba Bd Bd Bd Bj
~ 7r°D ° --~ 7r°D *°
--~ pO/)o --'* pO[).o - ~ w/) I) ~ w D *°
Bd ~ r/ID ° Bd ~
r i l l ) *°
QCDSR-CV BR × 105
Lattice-CV B R x 105
QM-CV B R x 105
ABLOPR-CV B R × 105
17 28 8 32 8 32 8 12
11 19 10 40 10 40 5 8
17 35 10 28 9 27 8 14
13 23 10 71 10 70 9 14
Exp. upper bound B R x 105 < < < < < < < <
33 55 55 117 57 120 33 50
M. Ciuchini et al./Nuclear Physics B 531 (1998) 6561660
"~
659
>
t-N
~ ~
~
-
-
~
~
00¢'I
1
~~. Ul~ 0 ~ 0
0 0
:°i
0~0~
~ ~
P~ OC
~" Cq O~ "~ "~
~
N
-
~ m
--
~
~
0
~×
l
H~
~ ~
'~.'~.~ ~ ~
~
~
~
T T T T T T T T T T T T T T T T T T T T -~
.~
~ +
"~ +
~3
660
M. Ciuchini et aL /Nuclear Physics B 531 (1998) 656-660
Table 4 BR's for several values of the CKM parameters cos S and ~r and different choices of the Wilson coefficients. The results are given for QCDSR and ABLOPR only. Results with LQCD and QM are very similar to those obtained with QCDSR. In square brackets we give the results obtained without charming penguins cos8
o-
BR( B+ ---+ K°~'+) BR(Bd ---* K+Tr-) BR(B,I --*~+~r-) BR × 105 B R × 105 B R × 105 9 a +Ll+°2 4-0.2 -'--o.9-o~2
Experiment
15 • +°'5+°A -i).4-o.1 4-0.1
~TL
~L
< 1.5
QCDSR-CV LO ,u.=5 GeV
-0.7 0.38 +0.7 -0.7 0.38 +0.7 -0.7 0.38 +0.7
0.48 0.48 0.48 0.36 0.36 0.36 0.24 0.24 0.24
1.49 1.62 1.68 1.36 1.49 1.54 1.23 1.37 1.42
10.181 10.19] [0.201 [0.19] [0.191 [0.201 [0.191 [0.191 10.191
1.61 1.60 1.59 1.62 1.61 1.61 1.63 1.62 1.62
10.48] 10.19] [0.11l [0.40] ]0.191 ]0.121 [0.331 [0.19] [0.14]
2.09 1.59 1.49 1.30 0.99 0.94 0.69 0.52 0.51
I0.931 I1.10[ [1.151 [0.501 [0.631 [0.67] [0.211 [0.30] [0.321
-0.26 1.73 -0.29 0.38 -0.30 0.06 -0.25 1.71 -0.28 0.32 -0.29 0.004 -0.24 1.62 -0.27 0.18 -0.27 -0.10
QCDSR-CV NLO /z = 5 GeV
-0.7 0.38 +0.7 -0.7 0.38 +0.7 -0.7 0.38 +0.7
0.48 0.48 0.48 0.36 0.36 0.36 0.24 0.24 0.24
1.43 1.75 1.85 1.30 1.62 1.71 1.22 1.50 1.57
[0.531 [0.561 [0.571 10.53] [0.561 [0.561 10.541 10.55] 10.56]
1.62 1.58 1.57 1.63 1.60 1.59 1.63 1.61 1.60
[0.971 [0.491 [0.351 10.85] [0.49] 10.39] 10.75] 10.51] [0.44]
2.24 1.71 1.64 1.30 1.04 1.02 0.47 0.53 0.54
[0.96] [I.261 [1.34] [0.51] [0.731 [0.80] [0.20] ]0.35] [0.401
-0.34 -0.28 -0.26 -0.32. -0.25 -0.24 -0.25 -0.22 -0.21
1.43 0.25 -0.08 1.25 0.15 -0.16 0.65 -0.4 -0.31
ABLOPR-CV - 0 . 7 0.48 LO 0.38 0.48 /z = 5 GeV +0.7 0.48 - 0 . 7 0.36 0.38 0.36 +0.7 0.36 - 0 . 7 0.24 0.38 0.24 +0.7 0.24
2.30 2.30 2.30 2.12 2.24 2.25 1.86 1.98 1.99
[0.52] [0.541 10.551 [0.521 ]0.541 [0.551 [0.521 [0.54] [0.541
1.50 1.50 1.50 1.53 1.51 1.51 1.58 1.56 1.56
[1.25] [0.51] [0.29] [1.04] [0.49] 10.321 I0.86] 10.49] [0.381
4.29 3.47 3.74 2.75 2.36 2.25 1.38 1.21 1.17
I2.451 [2.92] 13.05] [1.331 ll.681 [1.78] [0.55] [0.781 10.851
0.53 -0.25 0.31 0.60 0.25 0.16 0.55 0.24 0.16
-0.10 0.90 -0.44 0.04 -0.60 -0.99 0.01 -0.59 -0.95
ABLOPR-CV - 0 . 7 0.48 NLO 0.38 0.48 /z= 5 GeV +0.7 0.48 - 0 . 7 0.36 0.38 0.36 +0.7 0.36 - 0 . 7 0.24 0.38 0.24 +0.7 0.24
2.19 2.30 2.30 1.92 2.20 2.30 1.65 1.94 2.03
11.42] [1.491 [1.521 11.431 [1.491 I 1.50] I 1.44] 11.48] ]1.491
1.52 1.50 1.50 1.57 1.52 1.50 1.60 1.56 1.55
[2.491 [1.261 [0.89[ 12.191 [1.27] [0.991 [1.921 [1.31] [1.121
5.13 3.78 3.60 3.07 2.53 2.43 1.52 1.26 1.23
12.51] 13.28] 13.511 [1.341 [1.921 12.091 [0.53] [0.92] [1.04]
0.92 -0.19 -0.12 0.87 -0.24 -0.20 0.79 0.20 -0.16
-0.85 0.25 -0.49 -0.86 0.64 0.32 -0.89 0.60 0.30
Nuclear Physics B 531 (1998) 656-660
E~mum
Erratum to "Charming-penguin enhanced B decays" [ Nucl. Phys. B 512 (1998) 3 ] * M. Ciuchini, R. Contino, E. Franco, G. Martinelli, L. Silvestrini Received 27 April 1998; accepted 15 May 1998
We have found an error in our calculation of the ABLOPR heavy-light form factor f+, which shows up whenever the light meson is not a pion. Therefore many channels containing this form factor, and consequently the values of the fitted parameters, are modified. However appreciable changes occur only for B ~ K J / ~ and coloursuppressed channels in Table 2. In particular, the correct ABLOPR does not fail in reproducing B ---, K*J/~, even if the X 2 of the global fit of sc and 8~ increases. On the other hand, some of the ABLOPR predictions in Table 1 for the vector sector, which were previously very large, no more exceed the experimental bounds. Apart from these considerations, the main conclusions of our analysis do not change. For completeness we give updated tables of BRs obtained using the correct ABLOPR form factor f ÷ .
Acknowledgements We thank J. Charles and O. P~ne for pointing out the differences between their calculations of BR(B ~ KJ/q~) and our predictions using ABLOPR form factors.
* PII of original article: S0550-3213(97)00768-2. 0550-3213/98/$ - see frontmatter (~) 1998 Published by Elsevier Science B.V. All rights reserved. PH S0550-32 13(98)00405-2
657
M. Ciuchini et a l . / N u c l e a r Physics B 531 (1998) 656-660
Table 1 Predictions for yet unmeasured BR's. The channels above the horizontal line are those enhanced by charming penguins. In square brackets, the BR's obtained without charming penguins are shown. BR(B + ---* wK+), BR(B + ---* w¢r+), BR(B + ---* ~7~K+ ) and BR(B,/ ~ r f K ° ) , for which preliminary measurements exist ( ( .1.~._0.6~+°'74- 0.3) × 10 -5, ( 1.1+°6-0.54- 0.2) × 10 - 5 , (7.1+25-2.14- 0.9) × 10 - 5 and (5.3+2"8_2.24- 1.2) x 10 -5 respectively), have been given in this table since they have not been used in the fit of ~L and 6L Channel
QCDSR-CV QCDSR-BV B R × l0 5 B R x l0 5
Lattice-CV QM-CV B R x l0 5 B R x l0 5
Ba "--* r f K 0
2.45 [0.191
1.97-3.55 [0.12-0.67
2.49 [0.101 2.39 [0.19] 4.69 [0.66]
*
Ba ~ r/IK *°
0.75 [0.01]
0.30-2.41 10.00-0.10
1.41 [0.001 0.47 I0.011 1.69 [0.011
< 9.9
Bd --* ~TK°
0.07 [0.01 I
0.01-0.26 ]0.00-0.02
0.07 I0.001 0.06 10.01 ] 0.11 [0.011
-
Bd ---, rtK *~
0.04 [0.02]
0.01-0.22 10.01-0.06
0.05 [0.01 ] 0.03 [0.02]
Bd -'* oak n
0.73 [0.041
0.13-1.70 [0.03-0.38
0.80 [0.021 0.70 ]0.06] 0.45 [0.061
-
Bd ~
1.85 [0.11]
1.01-3.26 10.08-0.58
2.76 [0.121 1.43 [ 0.08 ] 5.41 [0.531
< 3.8 < 4.2
t o K *°
ABLOPR-CV Experiment B R x 105 B R × l0 5
0.11
[0.061
< 3.3
1.48 [0.111
0.68-2.29 I0.10-0.75
1.77 [0.08] 0.92 [0.12] 1.50 [0.201
Bd ~
(bK *°
3.27 [0.09]
1.90-6.73 [0.07-0.62]
5.08 [0.111 1.65 [0.051 9.75 [0.42]
< 2.2
B,I ~
zr° K ~
0.65 [0.041
0.49-0.95 [0.01-0.26]
0.68 [0.031 0.64 [0.031 1.01 [0.14]
< 4.1 < 2.0
Bd~dpK
°
0.40 I0.031
0.29-0.60 I0.01-0.131
0.61 [0.02] 0.26 [0.03
0.73 [0.101
¢ r - K *+ 3.13 [0.17]
2.05-5.07 [ 0.05-1.01 ]
3.47 [0.11] 3.16 [0.16
2.95 [0.451
< 6.7
0.63 [0.021
0.21-0.67 [0.00-0.11 ]
1.19 [0.02] 0.53 [0.02
0.97 10.091
< 3.3
p - K *+ 2.21 [0.12]
1.44-3.57 [0.03-0.72]
4.15 [0.131 1.75 [0.09
7.86 [1.191
Bd --* p°KO
0.44 [0.03]
0.07-1.63 10.00-0.091
0.81 10.011 0.35 I0.03
0.96 [0.041
B,I ~
p°K*°
1.01 [0.01]
0.50-2.45 10.01-0.131
1.86 10.02] 0.60 [0.01
4.81 [0.191
< 46
B + ~ r/IK +
2.31 [0.201
2.05-3.14 10.11-0.921
2.36 [0.101 2.27 [0.20
3.94 [0.62]
*
B + ~ r f K *+
4.14 [0.04]
1.45-11.22 I0.00-0.57] 4.82 ]0.021 4.18 I0.03
7.93 [0.08]
< 29
B + ~ rlK +
0.12 [0.021
0.02-0.46 [0.00-0.081
B + ~ rlK *+
0.27 10.041 0.04-1.19 [0.01-0.221
0.29 [0.03] 0.25 [0.04
0.63 [0.121
< 24
B + ~ o~K+
0.60 [0.021
0.06-1.39 [0.00-0.661
0.65 I0.041 0.60 [0.03
0.21 10.231
*
B + -'* toK *+
1.50 [0.08]
0.84-2.48 [0.03-1.121
2.24 [0.161 1.20 [0.06
2.82 11.121
< 11
B + --~ ~bK+
1.54 [0.12]
0.70-2.38 [0.10-0.78 I
1.84 [0.091 0.96 [0.13
1.56 [0.211
< 0.53
10.0 10.441
<4.1
B,! ---* ¢r°K *° Bd ~
Bd "4 p - K + Bd ~
0.13 I0.01] 0.11
[0.01
< 3.0
0.27 10.05]
B + --* ~bK*+
3.35 [0.09]
1.96-6.90 [0.08-0.64
5.21 [o.111 1.70 10.06
B + --~ Ir°K +
0.94 [0.18]
0.67-1.03 [0.09-0.74
0.86 [0.101 0.95 I0.181 0.88 I0.401
< 1.6
B + ~ ~'°K*+
1.70 [0.14]
1.15-2.42 [0.06-0.71
1.81 [0.091 1.71 I0.131 1.56 I0.331
< 8.0
B + ~ 7r+K *° 0.92 [0.13]
0.73-1.15 [0.08-0.37
1.29 [0.071 0.62 I0.121 1.61 ]0.371
< 3.9
B + --~ p + / d )
2.67 [0.00]
0.88-7.28 [0.00-0.36
3.05 I0.001 2.62 I0.00] 4.56 I0.00]
< 6.4
B + ---* p + K *°
2.21 [0.091
1.42-4.01 [ 0.06-0.38
3.82 10.091 1.34 I0.071 10.1 I0.991
-
B+ ~
p°K+
0.39 [0.061
0.18-0.61 [0.00-0.21
0.61 [0.03] 0.35 ]0.06] 0.48 [0.10]
< 1.4
B+ ~
p°K*+
1.26 10.15]
0.81-1.62 [0.06-0.63
2.18 [0.141 1.00 [0.I11 4.25 I 1.051
< 90
658
M. Ciuchini et a l . / N u c l e a r Physics B 531 (1998) 656-660
Table I - - continued Channel
QCDSR-CV QCDSR-BV BR x 105 BR x 10 -s
Lattice-CV BR × 105
QM-CV BR x 105
ABLOPR-CV Experiment BR × 105 BR x 105
Bd--~ cr+¢r -
0.99 [0.631
0.39-2.63 [0.15-1.55] 0.71 [0.39]
Bd---* q'r°'rr°
0,04
0.01-0.12 [0.01-0.11] 0.004 I0.002] 0.06 [0.05] 0.01 [0.02
0.95 10.60] 2.36 [1.68
< 1.5 < 0.93
Bd --~ pOq'r°
0.08 [0.11]
0.00-0.21 [0.02-0.21] 0.01 [0.07]
0.12 [0.13] 0.05 [0.10
< 1.8
Ba ~ p + ~ -
2.67 [1.71]
1.02-7.51 [0.45--4.15] 1.93 [1.07]
2.55 [1,631 6.24 [4.43
< 8.8
Bd ~ ~ + p -
0.59 [0.38]
0.22-1.75 [0.11-0.91] 0.66 [0.37]
0.46 [0.30] 1.90 [1.35
Bd ~
pOpO
0.16 [0.18]
0.00-0.58 [0.04-0.46] 0.02 [0.18]
0.21 [0.19] 0.30 [0.59
< 28
Bd -'-+ p + p -
1.81 [1.16]
0.69-5.10 [0.31-2.82] 2.19 [1.22]
1.37 [0.88] 16.5 [11.7
< 220
Ba ~
o ~ "°
0.06 [0.01]
0.03-0.42 [0.00-0,29] 0.08 [0.005]
0.06 [0.021 0.07 [0.01
Bd ~
o~p °
0.10 [0.01]
0.05-1.22 [0.01-0.73] 0.14 10.01]
0.08 [0.01] 0.34 [0.03
< 3.4
Bd ---) q~Tr0
0.00 [0.00]
0.00-0.01 [0.00-0.011 0.00 [0.00]
0.00 [0.001 0.00 [0.0(3
< 0.65
Bd --' ~ o
0,48 [0.36]
0.04-2.14 [0.01-2.91] 0.21 [0.22]
0.44 [0.33] 0.97 [0.93]
< 2.2
B + --* 7"r+Tr°
0,53
0.16-1.18
0.51
1.16
< 2.0
0.36
B + --, p+Tr°
1,12
0.30-2.62
0.80
1.05
2.73
< 7.7
B + --* cr+p °
0.52
0.19-1.08
0.47
0.47
1.16
<5.8
1.08
0.73
8.02
B + _~ p+pO
0.94
0.23-2.11
B + ~ ~oqr+
0.84 [0.50]
0.38-2.35 [0.08-1.04] 0.94 [0.45]
< 100
0.70 [0.45] 1.82 [1.09]
4r
B + --* o~p+
1.81 [0.941
0.8O-5.57 [0.19-3.40] 2.44 [1.04]
1.36 [0.72] 13.4 [7.61]
B + ---, ~b~-+
0.00 [0.00]
0.00-0.02 [0.00-0.021 0.00 [0.00[
0.00 110.001 0.00 [0.00]
< 0.56
B+ --* ~'+~7'
1.09 [0.761
0.01-3.33 [0.13-3.361 0.87 [0.581
0.97 [0.651 3.34 [2.78]
<4.5
Bd ---* c r ° J / ~
2,27
2.06-2.36
1.82
2.70
1.48
<6
Bd ~
pOj/qt
4.44
4.04-4.63
5.05
3.61
5.22
< 25
B + ___+p + j / q t
9,22
8.39-9.62
10.48
7.49
10.8
< 77
Bd ~
K°[( °
0,09 [0.01]
0.05-0.56 [0.00-0.41] 0.09 [0.005]
0.08 [0.01l 0.13 [0.03]
< 1.7
B,l ~
K+K -
0,00 [0.00]
0.00-0.50 [0.00-0.50] 0.00 I0.00]
0.00 [0.001 0.00 [0.00]
< 1.7
0.05-0.58 [0.00-0.43] 0.09 [0.0051
0.08 [0.011 0.14 [0.03]
<2.1
B + ~ K+/~ ~ 0,09 I0.011
Table 2 Predictions for emission-dominated decay channels for which only experimental upper bounds exist Channel
B,t Ba Bd Bd Bd Bj
~ 7r°D ° --~ 7r°D *°
--~ pO/)o --'* pO[).o - ~ w/) I) ~ w D *°
Bd ~ r/ID ° Bd ~
r i l l ) *°
QCDSR-CV BR × 105
Lattice-CV B R x 105
QM-CV B R x 105
ABLOPR-CV B R × 105
17 28 8 32 8 32 8 12
11 19 10 40 10 40 5 8
17 35 10 28 9 27 8 14
13 23 10 71 10 70 9 14
Exp. upper bound B R x 105 < < < < < < < <
33 55 55 117 57 120 33 50
M. Ciuchini et al./Nuclear Physics B 531 (1998) 6561660
"~
659
>
t-N
~ ~
~
-
-
~
~
00¢'I
1
~~. Ul~ 0 ~ 0
0 0
:°i
0~0~
~ ~
P~ OC
~" Cq O~ "~ "~
~
N
-
~ m
--
~
~
0
~×
l
H~
~ ~
'~.'~.~ ~ ~
~
~
~
T T T T T T T T T T T T T T T T T T T T -~
.~
~ +
"~ +
~3
660
M. Ciuchini et aL /Nuclear Physics B 531 (1998) 656-660
Table 4 BR's for several values of the CKM parameters cos S and ~r and different choices of the Wilson coefficients. The results are given for QCDSR and ABLOPR only. Results with LQCD and QM are very similar to those obtained with QCDSR. In square brackets we give the results obtained without charming penguins cos8
o-
BR( B+ ---+ K°~'+) BR(Bd ---* K+Tr-) BR(B,I --*~+~r-) BR × 105 B R × 105 B R × 105 9 a +Ll+°2 4-0.2 -'--o.9-o~2
Experiment
15 • +°'5+°A -i).4-o.1 4-0.1
~TL
~L
< 1.5
QCDSR-CV LO ,u.=5 GeV
-0.7 0.38 +0.7 -0.7 0.38 +0.7 -0.7 0.38 +0.7
0.48 0.48 0.48 0.36 0.36 0.36 0.24 0.24 0.24
1.49 1.62 1.68 1.36 1.49 1.54 1.23 1.37 1.42
10.181 10.19] [0.201 [0.19] [0.191 [0.201 [0.191 [0.191 10.191
1.61 1.60 1.59 1.62 1.61 1.61 1.63 1.62 1.62
10.48] 10.19] [0.11l [0.40] ]0.191 ]0.121 [0.331 [0.19] [0.14]
2.09 1.59 1.49 1.30 0.99 0.94 0.69 0.52 0.51
I0.931 I1.10[ [1.151 [0.501 [0.631 [0.67] [0.211 [0.30] [0.321
-0.26 1.73 -0.29 0.38 -0.30 0.06 -0.25 1.71 -0.28 0.32 -0.29 0.004 -0.24 1.62 -0.27 0.18 -0.27 -0.10
QCDSR-CV NLO /z = 5 GeV
-0.7 0.38 +0.7 -0.7 0.38 +0.7 -0.7 0.38 +0.7
0.48 0.48 0.48 0.36 0.36 0.36 0.24 0.24 0.24
1.43 1.75 1.85 1.30 1.62 1.71 1.22 1.50 1.57
[0.531 [0.561 [0.571 10.53] [0.561 [0.561 10.541 10.55] 10.56]
1.62 1.58 1.57 1.63 1.60 1.59 1.63 1.61 1.60
[0.971 [0.491 [0.351 10.85] [0.49] 10.39] 10.75] 10.51] [0.44]
2.24 1.71 1.64 1.30 1.04 1.02 0.47 0.53 0.54
[0.96] [I.261 [1.34] [0.51] [0.731 [0.80] [0.20] ]0.35] [0.401
-0.34 -0.28 -0.26 -0.32. -0.25 -0.24 -0.25 -0.22 -0.21
1.43 0.25 -0.08 1.25 0.15 -0.16 0.65 -0.4 -0.31
ABLOPR-CV - 0 . 7 0.48 LO 0.38 0.48 /z = 5 GeV +0.7 0.48 - 0 . 7 0.36 0.38 0.36 +0.7 0.36 - 0 . 7 0.24 0.38 0.24 +0.7 0.24
2.30 2.30 2.30 2.12 2.24 2.25 1.86 1.98 1.99
[0.52] [0.541 10.551 [0.521 ]0.541 [0.551 [0.521 [0.54] [0.541
1.50 1.50 1.50 1.53 1.51 1.51 1.58 1.56 1.56
[1.25] [0.51] [0.29] [1.04] [0.49] 10.321 I0.86] 10.49] [0.381
4.29 3.47 3.74 2.75 2.36 2.25 1.38 1.21 1.17
I2.451 [2.92] 13.05] [1.331 ll.681 [1.78] [0.55] [0.781 10.851
0.53 -0.25 0.31 0.60 0.25 0.16 0.55 0.24 0.16
-0.10 0.90 -0.44 0.04 -0.60 -0.99 0.01 -0.59 -0.95
ABLOPR-CV - 0 . 7 0.48 NLO 0.38 0.48 /z= 5 GeV +0.7 0.48 - 0 . 7 0.36 0.38 0.36 +0.7 0.36 - 0 . 7 0.24 0.38 0.24 +0.7 0.24
2.19 2.30 2.30 1.92 2.20 2.30 1.65 1.94 2.03
11.42] [1.491 [1.521 11.431 [1.491 I 1.50] I 1.44] 11.48] ]1.491
1.52 1.50 1.50 1.57 1.52 1.50 1.60 1.56 1.55
[2.491 [1.261 [0.89[ 12.191 [1.27] [0.991 [1.921 [1.31] [1.121
5.13 3.78 3.60 3.07 2.53 2.43 1.52 1.26 1.23
12.51] 13.28] 13.511 [1.341 [1.921 12.091 [0.53] [0.92] [1.04]
0.92 -0.19 -0.12 0.87 -0.24 -0.20 0.79 0.20 -0.16
-0.85 0.25 -0.49 -0.86 0.64 0.32 -0.89 0.60 0.30