Rare and Semileptonic Decays of
B and K Mesons
Jeffrey D. Richman
University of California, Santa Barbara
BABAR Collaboration
Particles and Nuclei International Conference
Santa Fe, Oct. 27, 2005
Outline

Goals and challenges

KLp0 nn

The “kaon revolution”: KL p+e- n, |Vus|, and the recalibration of
kaon branching fractions

Electroweak penguin/box diagram processes:
BK*g, Brg, BXs g and BK l+l-, BK* l+l-

Semileptonic B decays and the measurement of |Vcb |, |Vub |, mb, mc

[Leptonic B decays: Bsm+m-, B+t + nt]

Perspective and conclusions
Far too many topics to cover... my apologies! Parallel session talks contain many
more details (Bizjak, Godang, Koeneke, Mohapatra,…)
Rare and Semileptonic Decays: Goals
Rare decay: loop/box process
 test SM at 1-loop level
 new (heavy) particles can be
produced in virtual intermediate
states; can compete with SM amps
 search for effects of new physics
b
u , c, t
d
W-
g
s, d
-
d
-
Semileptonic decay: tree diagram
 measure |Vij|
 determine quark masses, QCD
parameters
b, s
WVij
d
n
c, u
d
Common theme: understanding dynamics
-
W-
B b
K
0
t
s
B-
c, u
n
n
Z
d
d W
n
p
d
-
b V f
ub B
u
W-
n
0
• Amplitude factorizes  single
hadronic current
• Form factors/QCD parameters
can sometimes be extracted
from data or be calculated
• Precise rate predictions possible
for some processes
• Methods: HQET, heavy-quark
expansions, lattice QCD,…
Understanding dynamics is an
important goal in itself!
CKM matrix: b and s decays are both suppressed!
(Wolfenstein parametrization)
1 2

V
V
V
1

 ud
us
ub 
2

V

1 2
V
V


1
cs
cb 
2

 cd
V
  A 3 (1 - r - i ) - A 2
V
V
ts
tb 
 td

 0.97 0.23 0.004 

5 highlighted Vij:   -0.23 0.97
0.04


discuss in this talk!
 0.008 -0.04

1


unitarity:
6 triangles, all
with same area
Col(1)  Col(3)*  0
( r , )
VudVub*
VcdVcb*
(0,0)
 (2 )
g (3 )
A 3 ( r - i ) 

2
4
A
+
O
(

)


1

(leaving out phases)
VtdVtb*
VcdVcb*
 (1 )
(1, 0)
B K K K
0
0
S
0
S
0
S
BABAR
KLp0nn
K
0
Vts
s
d
Z
*
td
V
t
W-
n
n
d
n
n
-
K0 V W- W+
ts
s
t
0
p
d
d
Vtd*
d
d
• KL decay directly measures  (height of unitarity triangle)!
VtsVtd*  ( - A 2 )  ( A 3 )  (1 - r + i )
Amp( K L0  p 0nn )  (Vts*Vtd - VtsVtd* )  A2 5
• SM prediction: B( K L0  p 0nn ) SM  (3.0  0.6)  10-11
• Use K+p0 e+ n measurement to compute hadronic current.
B( K  p nn ) SM
 (7.8  1.2)  10
1.30
B( K +  p +nn ) E 787 / E 949  (1.47 +-0.89
)  10-10
+
+
-11
Buras, Schwab, & Uhlig, hep-ph/0405132;
very small theory errors achievable.
E949, PRL 93, 031801 (2004)
Preliminary results on KLp0nn from KEK E391a
1. Measure g position
and energy in CsI
2. Reconstruct decay
vertex assuming
Mgg=M(p0).
• Prelim. result uses 1.14 x
109 KL decays; e=0.73x10-2
• So far, only very small
fraction of data used.
• No events observed in
signal box
B( K L0  p 0nn )  2.86  10-7
• E391a goal
3. Signature:
z(vertex) and pt
Major backgrounds
K L0  p 0p 0
n + X p0 +Y
(90% C.L.)
B( K L0  p 0nn )  1.4  10-9
• Proposal in preparation for
follow-on experiment at
J-PARC
Kpen , |Vus|, and the “kaon revolution”
Vus
W
-
-
Review of Particle Properties, 2002
Vud  0.9734  0.0008
n
s
u
d
d
Vus  0.2196  0.0023
(
1 - Vud + Vus + Vub
2
2
2
  0.0043  0.0019
experiment: BR, tK
2
F
5
K
3
G M
2
K 3 
 Vus  SEW (1 +  K +  SU 2 )C 2  f +2 ( q 2  0)  I K
192p
short distance
radiative corr.
long distance
rad. corrections
SEW  1.022
 Ke  0.0104  0.002
Sirlin, Nucl. Phys.
B196, 83 (1982)
KLen: 1
form factor
I-spin corr.
for K+ decay K+en:1/2 theory: q2=0
exp’t: shape
L
m
 K  0.019  0.003
L
 Ke  0.0006  0.002
+
Cirigliano et al.,
Eur.Phys. J C35, 53 (2004)
Andre, hep-ph/0406006
Leutwyler & Roos,
Z.Phys.25, 91 (1984)
+other work in
progress
Recalibration of KL branching fractions
KTeV measured 6 largest KL modes [PRL 93, 181802-1 (2004)]
• Account for 99.93% of decays; 5 ratios of branching fractions
• 105-106 events/mode; careful treatment of radiation from electrons.
• Measurement of KL semilep form factors (1.7%-4.2% shifts) [hepex/0406003, 0406006]
KL  p  m n
KL  p e n

KL  p p p
0
0
0
K L  p +p -
fit to all new meas.
K L  p +p -p 0
K L  p 0p 0
E. Blucher,
Lepton-Photon 2005
Extraction of |Vus|
E. Blucher, Lepton-Photon 2005
Average of recent results:
• KLOE, KTeV, NA48,
ISTRA+
• correlations taken into
account
Vus f + (0)  0.2173  0.0008
f + (0)  0.961  0.008
Vus  0.2261  0.0021
Vus f + (0)
(
1 - Vud + Vus + Vub
2
2
2
  0.0004  0.0011
Competing method: (K+m+ n [KLOE, hep-ex/0509045] + lattice [MILC,
PRD70, 114501 (2004); Marciano, PRL93, 231803 (2004)]
Vus  0.2223  0.0026
Radiative penguin decays of B mesons
g
b
u , c, t
s, d
W-
d
Observation of BK* g
CLEO II (1993): Loops
in B decays!
Now it’s a physics program!
d
B( B  K *g )
 4  10-5
PRL 71, 674 (1993)
cited >500 times!
M ( K *g )
B(10-6 )
Observation of the bdg decays Br (w g
Belle, 386 M BB
BABAR, 211M BB
hep-ex/0506079
PRL 94, 011801 (2005)
8.2 evts
20.8 evts
Belle
Belle (10-6)
(5.5s signif.)
B +  r +g
 1.8
+ 0.12
0.55+-0.43
0.37 -0.11
B0  r 0g
 0.4
+ 0.09
1.17 +-0.35
0.31- 0.08
B0  wg
 1.0
+ 0.14
0.58+-0.34
0.31-0.10
B ( B  ( r , w )g )

*
B( B  K g )
Vtd
Vts
5.9 evts
BABAR (10-6)
(2.1s signif.)
Mode
Belle
2
(1 - m
(1 - m
Ali, Lunghi, Parkhomenko,
PLB 595, 323 (2004)
2
( r ,w )
2
K*

2 3
B
2 3
/m
0.1  0.1
 2 (1 + R 
/ mB 
  0.85  0.10
Vtd
+0.038 good agreement
 0.200+-0.026
0.025 -0.029
w/global CKM fit
Vts
Inclusive BXs g Decay
• Canonical process for testing the SM at 1 loop level
• Provides powerful constraints on new physics models
• Major effort by theory community to compute QCD and EW
corrections; NLL calculation complete; NNLL calculation forseen
B( B  X sg )  (3.70  0.35 |mc / mb 0.02 |CKM 0.25 |param 0.15 |scale ) 10-4
Hurth, Lunghi, Porod, Nucl. Phys. B 704, 56 (2005); see also Neubert, Eur.Phys. J C40, 165 (2005);
Buras et al., Nucl.Phys. B631, 219 (2002)
+0.30
-4
B( B  X sg )  (3.39 -0.27 )  10 HFAG July 2005
Belle, PRL93, 061803 (2004)
fully incl.
BABAR
K *g
PRD 72, 052004 (2005)
sum of 38 excl.
modes
Eg
Eg
Moments of BXs g Photon Energy Spectrum
(see talk by Karsten Koeneke, Section VI.4)
Used in determination of mb, |Vcb |, and | Vub |
2nd Moment (GeV2)
1st Moment (GeV)
Minimum Eγ (GeV)
hep-ex/0507001
D. Benson, I.I. Bigi and N. Ultrasev
Nucl. Phys. B 710, 371-401 (2005)
Minimum Eγ (GeV)
+lElectroweak penguins BKl+l- and BK*l
+
b
d
g ,Z
u , c, t
W-
n
-
s
+
b
W-
W+
s
u , c, t
d
d
d
• With l+l- pair, can produce both pseudoscalar and vector mesons
• New physics can affect both rate and kinematic distributions.
BABAR hep-ex/0507005 (229M BB)
BK
+ -
B  K*
+ -
Belle prelim. hep-ex/0410006, 0508009
BKl+l- and BK*l+l- : branching fractions
Theory errors
mainly due to
form factors.
B( B  K *
+ -
)WA  (1.18  0.17)  10-6
B( B  K + - )WA  (0.45  0.05)  10-6
(rarest observed B decay)
(10-6 )
pole at low q2
q2
q2
BK*l+l-: Lepton F-B Asymmetry
l
-
l
B
l
+
Belle: lepton A(FB) [raw]
AFB
s
K
q
hep-ex/0508009
*
Lepton angular
distribution in
l+ l- rest frame
386 M BB
SM
NP scenarios
q2
constraints on Wilson coeffs describing short-distance physics
Precision measurement of |Vcb| and the atomic
physics of B mesons
• inclusive semileptonic rate
Observables • inclusive lepton-energy spectrum (moments)
• inclusive recoil hadron mass spectrum (moments)
Heavy-quark expansion theory params: |Vcb|, mb, mc, mp , mG , rD , rLS
GF2 mb5
2
 SL ( B  X cln ) 
V
cb (1 + Aew ) Apert ( r , m )
192p 3
3

kinetic expec.

r D3 + r LS
2
2

 mp - mG + m
value
b
  z0 ( r )  1 2
2mb
kinetic scheme



r  ( mc / mb ) 2 

BABAR, PRL 93, 011803 (2004)
chromomagnetic
expec. value


 - 2(1 - r )



Darwin term
spin-orbit
r D3 + r L3S
2
mG +
r D3
mb
4
mb2


4
+ d ( r ) 3 + O (1/ mb ) 
mb



Benson, Bigi, Mannel & Uraltsev, hep-ph/0410080
Gambino & Uraltsev, Eur.Phys.J. C34, 181 (2004)
Vcb  (41.4  0.4exp  0.4 HQE  0.6 th )  10-3
mp2  (0.45  0.04exp  0.04 HQE  0.01 ) GeV 2
Bc n  (10.61  0.16exp  0.06HQE )%
mG2  (0.27  0.06exp  0.03HQE  0.02 ) GeV 2
mb  (4.61  0.05exp  0.04 HQE  0.02s ) GeV
s
s
r D3  (0.20  0.02exp  0.02 HQE  0.00 ) GeV 3
s
3
mc  (1.18  0.07exp  0.06HQE  0.02s ) GeV r LS
 ( -0.09  0.04exp  0.07 HQE  0.01 ) GeV 3
s
|Vcb| and inclusive parameters from
BXcln and BXs g
Buchmuller and Flacher; hep-ph/0507253
• Fit to moments of inclusive distributions in BXc l n and BXs g
• Experiments: BABAR, Belle, CDF, CLEO, DELPHI
all moments
mp2
Vcb
(GeV2 )
(10-3 )
b  sg
all moments
bc n
bc n
mb (GeV)
Vcb  (41.58  0.45  0.58) 10-3
mb  4.591  0.040 GeV kinetic
mass scheme
mb
-3
)

10
D*ln
<2% Vcb  (41.2  1.0+-1.5
1.7
zero rec.
errors
Measuring |Vub | is hard, but the error is shrinking
Vub
( B  X u n )
 0.1 
 2%
Vcb
( B  X c n )
Lepton spectrum endpoint analysis
BABAR
hep-ex/0509040
Large bc background; suppression cuts
introduce dependence on theory
predictions for kinematic distributions.
Fully reconstructed B recoil analysis
continuum data (off res)
Belle
bc subtraction
bu
p
e-
Xu
Breco
D*
n e+
Brecoil
l
hep-ex/0505088
M (Xu )
q
2
|Vub | inclusive measurements
• Key CKM constraint
Eℓ endpoint
Vub
  r 2 +2
Vcb
• Use mb and QCD
parameters extracted from
inclusive BXc l n and
BXs g spectra.
• Many methods with
uncertainties around 10%.
• Uncertainty from mb has
been reduced to 4.5%.
• With more data, the |Vub|
uncertainties could be
pushed down to 5%-6.5%.
Eℓ vs. q2
mX
mX vs. q2
Vub WAvg  (4.38  0.19  0.27)  10 -3
expt
mb, theory
Measuring |Vub| using Bp l n and lattice QCD
2
q 2  qmin
-
n
q
u
2
q 2  qmax
p+
p+u
-
n
q
B0p+ l- n form-factor predictions
f+(q2) is relevant
form factor for
Bp l n (l=e, m
Fermilab/MILC
HPQCD
restricted q2 range
q
At fixed q2, lepton
momentum spectrum is
exactly known in this
mode, since only one
form factor.
2
HPQCD: hep-lat/0408019
Fermilab/MILC: hep-lat/0409116
Bp l n: branching fraction and q2 distribution
Becher and Hill, hep-ph/0509090
Relatively flat
distribution in spite
of rapidly changing
form factor.
Consequence of p3
factor in decay rate.
HFAG
averages
B( B 0  p + -n )  (1.35  0.08  0.08)  10-4
B( B 0  p + -n | q  16)  (0.40  0.04  0.04)  10-4
-3
Vub (HPQCD; q2  16)  (4.47  0.30+-0.67
0.46 ) 10
-3
Vub (FNAL; q2  16)  (3.78  0.25+-0.65
)

10
0.43
Search for Bsm+m- and B0l+lW-
b
s
t
m-
b
n
m +
W
+WWZ m

+
H
+W +W - Z
t
Highly suppressed in the SM
• B( Bs  m + m - )  (3.5  0.9)  10-9
• Bd suppressed by |Vtd/Vts|2
• No SM signals expected at Tevatron or
at B factories, but can have large
enhancements from new physics.
SM predict.
CDF
D0
0
0
A
m-
m+
b
tan 6 
B( Bs  m m ) 
mA4
+
-
Strong correlation with
neutralino-proton cross
section in mSUGRA!
Beck,Kim,Ko hep-ph/0406033
BABAR
Belle
Bs  m + m - 3.5  10 -9  1.6  10-7  3.0  10-7
Bd  m + m - O (10-11 )  3.9  10-8
 8.3  10-8  1.6  10-7
 6.1  10-8  1.9  10 -7
Bd  e + e - O (10-15 )
Perspective/Conclusions
K Physics
• Early results from 1st dedicated KLp0nn experiment
• KL branching fractions re-measured: 5% to 8% shifts
• |Vus| shift: +3%
• Unitarity of 1st row of CKM matrix looks better; work in progress
on |Vud|
B Physics
• Brg observed; provides interesting constraint on |Vtd|/|Vts|
• Many bsg and bsl+l- modes observed; studies of kinematic
distributions are especially interesting
• |Vcb| measured to 2% via inclusive method; mb well determined
• |Vub| precision now below 10%.
• Keep pushing inclusive vs. exclusive crosscheck!
• Leptonic B decays providing interesting sensitivity to new physics
• B factories will push to 1 ab-1. Many more results to come!
Backup slides
Huge program on B decays to charmless hadronic final states...
see H. Jawahery talk for
hadronic bs decays
(10-6)
Observation of the bdg decays Br (w g
BABAR
Belle
B /10-6
Note: naïve expectation is (B+r+g2 (B0r0g2 (B0wg
BABAR/Belle discrepancy on B0r0g; to be resolved with more data.
B K K K
0
0
S
0
S
0
S
BABAR
BXs g New Physics Sensitivity
• Constraints on Two Higgs doublet models (Type II)
• mH = charged Higgs mass
• tan = ratio of vacuum expectation values of the two doublets
• Hou [PRD48, 2342 (1993)], Gambino & Misiak [Nucl. Phys
B611, 338 (2001)], Neubert [Eur. Phys. J C40, 165 (2005)].
future projections
current BABAR data
mH
(GeV)
90% C.L. allowed
regions (above lines)
combined
B  X sg
B  tn
tan 
2 ab-1 1 ab-1
0.5 ab-1
B  X sg + B  tn
tan 
Search for leptonic B- decays
b
B-
-
Vub W 

n
u
( M Qq
• helicity suppressed
• CKM suppressed (Vub)
• annihilation diagram
• tree-level sensitivity to H-
2
G
m 
2
2
 n )
VqQ f M M  m  1 - 2 
8p
M 

2
F
2
2
Non-relativistic mesons
(2 heavy quarks):
f M2 M  12  (0)
2
Predicted leptonic branching fractions: (|Vub| = 0.0039, fB = 200 MeV)
meson
B (en)
B (mn)
B (tn)
p+
K+
B+
1.2  10 -4
1.2  10-5
1.1  10-11
99.99%
63.5%
4.8  10 -7
1.1  10-4
Search for B-t- n
BABAR, hep-ex 0507069
t reconstruction: a major challenge
• fully reconstruct other B in event
• require lepton (or pion) and no
additional observed energy (2-3n)
e-
B
B
+
rec
t -  e -n en t
Eextra
Belle, hep-ex/0507034
-
e+
te- n nt
e
SM
t -  m -n mnt
Backgrnd
Backgrnd
nt
Expected
signal x10
BABAR (232 M BB)
B(B+t n 1.1  10-4  2.6  10-4 (90% C.L.)
Belle (275 M BB)
 1.8  10-4 (90% C.L.)
Search for Bsm+m- and B0l+lHighly suppressed in the SM
• B( Bs  m + m - )  (3.5  0.9)  10-9
• Bd suppressed by |Vtd/Vts|2
• No SM signals expected at Tevatron or
at B factories, but can have large
enhancements from new physics.
SM predict.
CDF
D0
W-
b
s
t
m
-
n
m +
W
+WWZ m
+
+W +W - Z
BABAR
90% C.L.
Belle
Bs  m + m - 3.5  10 -9  1.6  10-7  3.0  10-7
Bd  m + m - O (10-11 )  3.9  10-8
 8.3  10-8  1.6  10-7
 6.1  10-8  1.9  10 -7
Bd  e + e - O (10-15 )
Bsm+m- and SUSY
b
tan 
B( Bs  m m ) 
mA4
+
-
6
Dermisek, Raby, Roszkowski,
Ruiz de Austri, hep-ph/0507233
H

t
b
0
0
A
m-
m+
Baek, Kim, Ko, hep-ph/0406033
Dark matter cross section s(p) vs. B(Bsm+m-).
Experiment vs. Lattice: DK l n form factor
Measuring |Vub| using Bp l n
BABAR
PRD 72, 051102 (2005)
Projection to 1 ab-1 (data taken to be on
BK fit curve from present measurement).
In the high q2 region alone, we will measure the branching fraction
with an uncertainty of (6-7)% , or (3-3.5)% uncertainty on |Vub |. Lattice
theorists expect to reach 6%, so exclusive/inclusive will be similar.
Precision measurement of |Vcb|: fits to moments of
lepton spectrum and hadron recoil spectrum
BABAR PRL 93:011803 (2004)
mX moments
● = used, ○ = unused
in the nominal fit
BABAR
 2/ndf = 20/15
Eℓ moments
Red line: OPE fit
Yellow band: theory errors