Transcript Leptonic B decays: a rare window to New Physics

Leptonic B decays:
a rare window to New Physics
Paul D. Jackson
Universita’ “La Sapienza” & INFN Rome
2
A sketch of what follows

Motivation of leptonic B studies

Outline experiments/detectors

Techniques/analyses and results

Future outlook and summary
Paul D. Jackson
Leptonic B decays
Motivation and
Theory
4
The Lure of Leptons
d
A simple example illustrates the
full extent of the attraction:
p+
(And, it scales easily to similar
decays starting from a heavy,
pseudoscalar meson...)
m+
W+
u
n
2
2
2
G
m
m
m
F
2
π+
μ+ 
μ+ 
+
+
2
BR π  μ ν  =
1
f π Vud  τ π+


8π

mπ2+ 


Pros
Cons
Relatively free of hadronic uncertainties
(encapsulated in “fX”, the “decay
constant of meson X”)
 Recognizable experimental signature

Paul D. Jackson



Leptonic B decays
Helicity suppression (m2l)
less of a con when new physics can
enhance the rate over the SM
Undetectable final state particle
Measurement of fB
Extract fB through leptonic decays: B+ → l+νl


Cleanest source (1% measurements for π+,K+ )
Heavy B+: low branching ratios to leptons
τ+
W+
B+
ν
2


2
G

m 
+
+
2
2
2
F
BR
(B   ) 
f | V | M  m 1 

B
B
B
SM
ub
2
8p

M 
B

B meson decay constant
CKM mixing
(disfavours M = B, Bs, D)
ντ
τ+
B+
Helicity Suppression
(disfavours l=e, favours l=τ)
Paul D. Jackson
Leptonic B decays
2
6
Beyond the Standard Model
 Sensitive to contributions from physics beyond SM
 In two Higgs doublet model (type II) (W.Hou, Phys. Rev. D. 48, 2342 (1993))
++
W+, H

m
2
BR B   n  BRSM ( B   n )  1  tan 

m


+
+

+
2
B
2
H
+




2
tan is the ratio of vacuum expectation values for two Higgs doublets.
 Provide important constraints on
tan  / m H

 Can enhance or suppress the rate depends on tan and mH 
for example: mH = 140 GeV, tan = 40, give ~1.6 enhancement
Paul D. Jackson
Leptonic B decays
7
B+→τ+ν and the CKM Formalism
BR B+

 τ + ν 
theory
 meas
( Δm )
meas
 f (  , )
d
CKM Fit
Prediction:
(post-ICHEP
update)
post-ICHEP 2006 update
(1.390.44)10-4
The measured branching fraction yields
an independent constraint on the plane.
Likewise, all other measurements
excluding the BF (and fB) can constrain
it using the theory relations.
Paul D. Jackson
Leptonic B decays
The Experimental
Environment
Experiments
BaBar
CDF
Belle
Dzero
I will present results
primarily from BaBar,
making comparisons
to Belle, CLEO-c, and
the Tevatron where/if
appropriate.
CLEO-c
Paul D. Jackson
There are currently
several active
experiments which
produce and study
heavy flavour in large
numbers (and several
others will join the
game soon!).
Leptonic B decays
10
Plan view of SLAC
Linac
PEP-II Storage Rings
SF Bay
BaBar detector
Paul D. Jackson
Leptonic B decays
11
B Factory operations
e+e  (4S )  BB
B B production threshold
Not just a B-factory….similar cross
section for b, c, τ production
Paul D. Jackson
Asymmetric collider operating at
(4S) resonance (Ecms=10.58 GeV)
with 3.1 GeV e+ and 9 GeV eB-mesons in lab have =0.56
 ( BB )  1.1nb   (cc )  1.3nb   ( +  )  0.9nb
Leptonic B decays
12
The BaBar “Collider-Scope”
©
Limited
streamer
Instrumented
Fluxtubes
Return
Electromagnetic Calorimeter
6580 CsI crystals
e+ ID, p0 and  reco
19
layers during
of RPCs
Completed
winter 2006
+
m and KL ID
e+ [3.1 GeV]
Cherenkov Detector
(DIRC)
144 quartz bars
K,p separation
Drift Chamber
40 layers
Tracking + dE/dx
Silicon Vertex
Tracker
e- [9 GeV]
Paul D. Jackson
5 layers of double
sided silicon strips
Leptonic B decays
13
PEP-II Luminosity Performance
Best Performance
PEPII peak Luminosity:
1.2x1034 cm-2 sec-1
Integrated Luminosity:
in 24 hours: 891.2 pb-1
390 fb-1 total
data sample
2000
Doubled again
Integrated Luminosity [fb-1]
1800
Data
“doubled”
2007
~0.55 ab-1
1600
1400
1200
1000
800
2008
~1 ab-1
600
400
200
Paul D. Jackson
Leptonic B decays
Jul-10
Jan-10
Jul-09
Jan-09
Jul-08
Jan-08
Jul-07
Jan-07
Jul-06
Jan-06
Jul-05
Jan-05
0
14
Analysis Techniques I
Beam Kinematics
Mesons produced directly by the beams must satisfy collider-based
kinematic constraints
 Define “Energy-Substituted Mass” (m
ES) and “Energy Difference” (DE)
variables, characterizing such production:

mES =
E    p 

2
beam

2
B
ΔE = mB + pB  Ebeam
2
2

“Single B Beam” or “Tag B” Methods
Takes advantage of anticipated quark/anti-quark system
 Reconstruct one of the two bottom mesons in a well-defined final
state, “tagging” the event as BB.
 Search in the recoiling particles (the “single B beam”) for evidence of
the target rare decay

Paul D. Jackson
Leptonic B decays
15
Analysis Techniques II
Non-resonant Background Rejection
Light quark events typically more “jetty”
 Use a suite of event-shape variables, such
as thrust angles, Fox-Wolfram moments, etc.
s
as selection variables or in a multivariate
(Fisher, NN) approach.

s
b
b
upper sideband
Signalbox(es)/Sideband(s)
middle
sideband
lower sideband
Paul D. Jackson
“Blind”
signalbox
Use discriminating variables in
which signal “peaks” and bkgds are
distributed (or also peak)
 Define signal-rich regions (signal
box) and background-rich regions
(sidebands) as control samples

Leptonic B decays
Analyses:
B0→l+l-(γ)
17
Expectations from Theory
Standard Model
New Physics Models





Photon emission from the initial state
relaxes the helicity suppression
Unlikely to observe SM with current
datasets
Fully reconstructable final state

Supersymmetry: different
models predict different
mechanisms
R-parity violating models allow
for tree-level FCNC, enhancing
the rate at smaller tan.
MSSM models predict ~tan6
enhancement, allowing for up
to 100x enhancement over SM
γ
ℓ+
ℓ-
An example Standard Model diagram
Paul D. Jackson
Leptonic B decays
18
Signal Selection
We search for B0→ℓ+ℓ-γ in a sample of
324106 BB events
Construct B0 candidates from two
leptons (electron or muon) and a photon
leptons and photon required to be well within
the fiducial region of the detector (reduce ISR,
higher-order QED backgrounds)

leptons required to meet at a common vertex,
and 0.3 < mll < 4.9 (4.7) GeV/c2 for electrons
(muons)

Constrain the B candidates to be consistent
with production at the Ύ(4S) using mES and ΔE:

Paul D. Jackson
Fully reconstructing the signal B means that a
“tag B” technique is unnecessary.
BABAR
(MC)
19
Background Rejection
Reject backgrounds from J/ψ, ψ(2S)
decay (leptons) or p0 decay (photon)
electrons
Reject non-resonant e+e-→qq (q=u,d,s,c)
background using signal B kinematics and
event shape information in a Fisher
discriminant
Optimal selection criteria are determined
using Monte Carlo simulations and minimizing
the predicted upper limit (assuming no signal
is observed).
Define a plane in mES and ΔE in which to perform the final signal
extraction: mES > 5.2 GeV/c2 and -0.5 < ΔE < 0.5
εesignal = (6.07±0.14)%
Paul D. Jackson
εμsignal = (4.93±0.12)%
Leptonic B decays
20
Background Estimate
upper sideband
middle
sideband
Determine the mES shape of
backgrounds using the upper+lower
sideband - extrapolate the middle
sideband into the signal box:
lower sideband
electrons
muons
electrons
electrons
exp
bkg
n = 1.28± 0.80
muons
n exp
= 1.40± 0.42
bkg
Paul D. Jackson
Data shown are from the upper+lower sidebands
Leptonic B decays
ALL RESULTS ARE
PRELIMINARY
Results
electrons
21
muons
Systematic Uncertainties
Photon Energy
e
(μ)
1.6% (1.6%)
Particle ID
0.7% (1.3%)
B counting
1.1% (1.1%)
Charged Particle
Reconstruction
0.94% (0.94%)
Total:
2.3% (2.5%)
hep-ex/0607058
We observe 0 (3) events in the signal box in
electron (muon) events. We set frequentist upper limits on
the branching fractions (including systematic uncertainties):
BRB
0
 e e γ  < 0.7  10
+

PRELIMINARY
7
at the 90% C.L.
BRB  μ μ γ  < 3.4  10 at the 90% C.L.
0
Paul D. Jackson
+

7
Leptonic B decays
22
RESULTS ARE
PRELIMINARY
Results
CDF presented their latest result in the search for Bdm+m at
ICHEP '06. Using vertexed muon pairs and a likelihood
discriminant to search for B(s,d)→m+m.
CDF public note 8176
central-central
central-extension
Standard Model Prediction:
BR  Bs  μ + μ -  = 3.4 ± 0.5  10-9
CDF observes 1 (2) events in the Bs (Bd)
channel (consistent with background).
Upper limits are set:
BR(Bsmm) < 1.0×10-7 @ 95% CL
< 8.0×10-8 @ 90% CL
BR(Bdmm) < 3.0×10-8 @ 95% CL
< 2.3×10-8 @ 90% CL
Paul D. Jackson
Currently world's best limits.
Leptonic B decays
Analyses:
B+→µ+ν
B+→l+ν hadronic tagged
Paul D. Jackson
Leptonic B decays
B+→l+ν hadronic tagged
Paul D. Jackson
Leptonic B decays
25
B+→l+ν Inclusive approach
Paul D. Jackson
Leptonic B decays
26
Analyses:
B+→l+νγ
28
B+→l+n (l=e,m)

Presence of photon removes helicity suppression and
hence universality of leptonic branching fractions is
recovered (apart from phase space)



R =1/ΛB , related to the B light cone distribution amplitude
SM BR(B→ln) ~(1-5)x10-6 (Korchemsky, Pirjol and Yan Phys Rev D61, 114510, 2000)
Recent BaBar analysis based on 232M BB pairs



Paul D. Jackson
Identify lepton and signal photon and perform and inclusive
reconstruction (i.e. 4-vector sum) of the other B
Neutrino 4-vector obtained from missing momentum vector
Veto p0 candidates and suppress continuum backgrounds with
event shape variables
Leptonic B decays
29
B+→l+n (l=e,m) results
Br(B→mn) < 5.2x10-6
Extract signal from maximum
likelihood fit to mES and
neutrino E-|p| yields in signal
and sideband regions
Br(B→en) < 5.9x10-6
Br(B→ln) < 5.0x10-6
(combined)
Experimental sensitivity approaching
Standard Model rate
BB MC
Continuum MC
PRELIMINARY
PRELIMINARY
Paul D. Jackson
Leptonic B decays
Analyses:
B+→τ+ν
31
383x106 BB pairs
Analysis Strategy
B- g D(*)0 l- n (l = e, m)
D0 (p0/)
K- p+
K- p+ p0
K- p+ p- p+
K0s p+ p
Choose best tag with P(Vtx)

Apply cuts to suppress bkgd

e+
BB-D(*)0 lνX
(4S)
n
B+
ne
n
B++n, +e+nen
B++n, B-X (X=anything)
Main  decay modes
enn, mnn
pn, pp0n
Multiple neutrinos in the final state lacks experimental constraints


Reconstruct B meson in the event with B→D0lνX.
Compare remainder of event with signature for signal decay.
Techniques pioneered by BaBar!!
Paul D. Jackson
Leptonic B decays
B++n
”by eye”
Event contains a
well-reconstructed
“tag” B, here
decaying into a
semileptonic final
state
Events then
characterized by “Eextra”,
the sum of neutral (and
in cases, charged)
energy left over after all
tag and signal sources
are accounted.
Paul D. Jackson
Tagged signal MC
event, where D0→Kπ
and there is a neutral
pion from D*0 decay.
The tau decays to ππ0
32
Signal B decay is
low multiplicity and
should comprise of
the remaining wellreconstructed
charged particles
BABAR
Leptonic B decays
33
Event Selection

Starting from 383106 BB events, reconstruct tag B in a
semileptonic final state B→D0lνX
D0→K-π+, K-π+π-π+, K-π+π0, K0sπ+πX = γ, π0 from D*0 decay, which we do
not explicitly reconstruct
Require lepton CM momentum
> 0.8 GeV/c
Require that -2.0 < cosθB-D0l < 1.0, where
and we determine the parent B energy
and momentum from the collider energy

Data are from double-tag events,
showing the extra energy distribution.
Tag B reconstruction efficiency:
6.57 ± 0.03stat. ± 0.06syst. 10
We study the tag reconstruction efficiency in “double-tag” events, where
both B mesons are reconstructed as B→D0lνX, and correct based on the
data/MC comparison
Paul D. Jackson
Leptonic B decays
3
34
Eextra variable

Most sensitive signal selection variable
Eextra = Etotal - ΣEtag – ΣEsignal
Use energy from all unassigned clusters and tracks

Background prefers higher values, signal peaks near zero


bump from missing
π0/gamma from tagB
PRELIMINARY
Signal MC
PRELIMINARY
Eextra (GeV)
Paul D. Jackson
Leptonic B decays
Eextra (GeV)
35
Overview of signal selection
We select signal candidates as: τ+→e+νν, μ+νν, π+ν, ρ+ν
Background rejection
constrain the event missing mass and signal candidate momentum
0 candidates or extra neutral pions
 veto events with reconstructed K
L
 reject non-resonant background using a combination of thrust and
minimum invariant mass information (R)

Paul D. Jackson
Leptonic B decays
Double tagging



Reconstruct both B’s as B→D0lnuX tagging mode (several 1k’s events)
Study quantities NK0L, MMiss, D0Mass, in this control sample
Compare data/MC for corrections and syst. Errs




Ratio Ndata/NMC ≈ 1, difference from unity correction factor
The uncertainty in this method → systematic error
Similar comparisons for other quantities like Eextra etc
This method is essential to the analysis
Paul D. Jackson
Leptonic B decays
36
37
Sideband scaling and projection
sideband
The final discriminant is Eextra, sum of all
unused energy from charged and neutral
particles. Final bkgd prediction by scaling
of sideband in data using sideband/signal
ratio from MC.
Bkg. MC is scaled using
data vs. MC bkg.
prediction ratio
scaled to
BR=110-4
Paul D. Jackson
Signal efficiency (relative to the number
of semileptonic tag Bs):
Leptonic B decays
New Results
hep-ex/0608019 (update
to be submitted to PRD)
Mode
Expected
Observed
τ+→e+νν
44.3±5.2
59
τ+→μ+νν
39.8±4.4
43
τ+→π+ν
120.3±10.2
125
τ+→π+π0ν
17.3±3.3
18
All modes
221.7±12.7 245
N s = 23.3 ± 20.2
“Naive”
signal yield
Observe a result
consistent with zero
signal at 1.6σ, so we
set a limit and quote
a central value.
ALL RESULTS ARE
PRELIMINARY
Interpret results with a modified
frequentist technique. A ratio of
likelihoods, includes systematics as
Gaussians convoluted with the
likelihoods
BR (B+  +n )  1.8x10- 4 at the 90% CL
BR B+  τ +ν  = 1.0 ± 0.6stat. ± 0.1syst.104


Calculate the
product fB|Vub|
Paul D. Jackson
f |V | (7.0+ 2.0( stat .)  0.5( syst.))x10 4GeV
B ub
 2.8
39
Hadronic tag: Analysis strategy
n
e-
e,m,p,,a1
Brecoil

e+
1 or 2 n
Breco
p
D*

Tag B reco.
 Clean event
 Get B count for BF
calculation: ns
BR(Bn) = eN
B
Paul D. Jackson
B++n
enn, mnn
pn, pp0n, pppn
2-3 neutrinos in the final
state lacks experimental
constraints
Fully reconstruct the tag side in
hadronic B to D(*) decays and look
in the recoil for signal events.
• Pre-selection
 Sample divided in 5 subsamples
(e,m,p,,a1 (80% BF))
 Removes continuum background
 Used to perform data/MC
comparison
Leptonic B decays
40
B counting
• Fit to mES to determine the total number of B mesons
• Non-peaking component yields on the mES sideband
(mES<5.26GeV)
• Peaking component obtained by subtracting the
extrapolated comb. bkg under peak: nB ~ 6.86 x 105.
PRELIMINARY

Shapes of the non
peaking components
fixed from MC

Continuum fraction
scaled from off-peak
data by the luminosity
ratio
cont.
B0
B+
signal
mES (GeV/c2)
Paul D. Jackson
Leptonic B decays
41
Final selection cuts

Cut on topological and kinematical variables to
reject backgrounds.





Missing momentum direction and magnitude
# of charged tracks
particles momenta
Resonance mass (for the )
Cuts values determined by an iterative procedure
aiming at the best s/√b.
Paul D. Jackson
Leptonic B decays
42
Discriminating Variables
PRELIMINARY
Data
Combinatorial bkg
mnn
total bkg (peaking+comb.)
signal
PRELIMINARY
pn
Paul D. Jackson
PRELIMINARY
n
Leptonic B decays
43
The Eextra variable (again)
PRELIMINARY

enn
As with the SL tags most
discriminating variable is the
(extra) energy in the
calorimeter.

PRELIMINARY
mnn

Defined as sum of the cluster
energies not overlapping
with the tag B.


Paul D. Jackson
Since we don’t expect extra
reconstructed objects for signal
events.
Cut on minimum cluster energy
choosen to remove noise
Data/MC agreement affected by
the choice of the threshold
Leptonic B decays
44
Efficiency evaluation



Determined from signal MC
Efficiency table before the cut on Eextra
Cross feed between channels taken into account to
calculate the total efficiency of each reconstruction
mode
PRELIMINARY
Paul D. Jackson
Leptonic B decays
45
To be completed….




Hadronic tagged analysis not quite completed
but is complimentary to the S.L. tagged
analysis and can be easily combined.
Should provide competitive measurement
and good consistency check within expt.
Expect (hopeful) that both BaBar analysis will
complete updates with our entire data set in
the next few weeks/months.
Stay tuned…..
Paul D. Jackson
Leptonic B decays
Belle Result

Revised for
ICHEP06
PRL 97 251802
(2006)
The final results are deduced by unbinned likelihood fit to the
obtained EECL distributions.
Signal +
background
S : Statistical Significance
Background
Bn
Signal
Observe 17.2 +5.3
events in the
- 4.7
signal region.
Significance decreased to 3.5 
after including systematics
Signal shape : Gaussian + exponential
Background shape : second-order polynomial
+ Gaussian (peaking component)
Paul D. Jackson
Leptonic B decays
46
47
Belle Result

Measured branching fraction;
+0.56
Br B  n   1.79 -0.49

-4
×10

Product of B meson decay constant fB and CKM matrix
element |Vub|
+1.6
fB Vub = 10.1 -1.4

+0.46
-0.51
+1.3
-1.4
-4
×10
GeV

Using |Vub| = (4.39  0.33)×10-3 from HFAG
fB = 0.229
GeV
+0.036 +0.034
-0.031 -0.037
16% = 14%(exp.) + 8%(Vub)
15%
fB = 216  22 MeV
[HPQCD, Phys. Rev. Lett. 95, 212001 (2005) ]
Paul D. Jackson
Leptonic B decays
48
Combined Results
PRELIMINARY

Combining the central values
of recent BaBar and Belle
results.
BF(B+→τ+ν) = 1.36±0.48
(BaBar+Belle combined)


Errors are still large, but….
There have been great
improvements by both
collaborations
Paul D. Jackson
Leptonic B decays
Future prospects and
summary
50
Results in context of BSM
Interpretting the results from B+→τ+ν using the type II 2HDM:
W.S. Hou, Phys.Rev.D.
Brief Report 48 (1993)
2342.
LEP, Direct Search
(excluded at 95%CL)
Predicted SM branching fraction
taken from UTFit prediction.
Paul D. Jackson
Leptonic B decays
The excluded
regions (coloured)
are determined
using the naive
BaBar+Belle
average for
B++n, the LEP
direct search limit
(>79.3 GeV)
51
Physics Reach: Expectations
B++n:
Expect each experiment's branching fraction uncertainty to
go from ~0.65x10-4 to ~0.4x10-4 with the advent of 109 B+
mesons at the B factories (assuming no improvements)
BaBar also has a statistically independent hadronic-tagged analysis
comparable to Belle's, which effectively “doubles” the number of Bs, bringing
the BaBar error down to 0.48 (0.3) with the current (future 109) B+ sample.
BaBar+Belle
(excluded at 95%CL)
109 B
2 BaBar +
1 Belle
analysis
LEP, Direct Search (excluded at 95%CL)
Paul D. Jackson
LEP, Direct Search (excluded at 95%CL)
Leptonic B decays
52
Physics Reach: Future

Br(B n) measurement:
More luminosity help to reduce both stat. and syst. errors.

Some of the syst. errors limited by statistics of the control sample.

|Vub| measurement: < 5% in future is a realistic goal.

fB from theory: ~10% now  5% ?
My assumption
Lum.
DfB(LQCD) = 5%
DB(Bn)
exp
D|Vub|
414 fb-1
36%
7.5%
5 ab-1
10%
5.8%
50 ab-1
3%
4.4%
Br(Bn)/Dmd to cancel fB ?
G.Isidori&P.Paradisi, hep-ph/0605012
Paul D. Jackson
Leptonic B decays
5ab-150ab-1
Concluding remarks
Leptonic decays of heavy mesons are
Experimentally interesting
Critical tests of the Standard Model
Potential gateways to new physics phenomena
Large datasets at many experiments will
Allow further reach in the rarest decays, making
some of them accessible
Allow experimental limitations to be placed on new
physics in time for LHC
Paul D. Jackson
Leptonic B decays
Standard
Model
1ab-1 @ B-factories…
Direct evidence from LHC
Super-flavour factory(?)
New Physics in
The flavour sector
Backup slides and
additional material
All works:
Art listings I
Caravaggio (1571-1610)
“Supper at Emmaus” (1601-1602)
National Gallery, London
“The Incredulity of St. Thomas” (1601-1602)
Neues Palais, Potsdam
“The Inspiration of St. Matthew” (1602)
Contarelli Chapel, San Luigi di Francesi, Roma
“The Calling of St. Matthew” (1599-1600)
Contarelli Chapel, San Luigi di Francesi, Roma
Paul D. Jackson
Leptonic B decays
Art listings II
“The Sacrifice of Isaac” (1601-1602)
Galleria degli Uffizi, Firenze.
“St. Francis in Ecstacy” (1595)
Wadsworth Atheneum. Hartford, Connecticut.
“The Calling of Saints Peter and Andrew” ??
Currently above platform 24 of Rome’s Termini Station.
Paul D. Jackson
Leptonic B decays
Paul D. Jackson
Leptonic B decays
b→s and B→τν
Exploring complimentary regions of phase space
Paul D. Jackson
Leptonic B decays
More BSM effects…..LFV
Courtesy of G. Isidori
Paul D. Jackson
Leptonic B decays
Limit Setting Procedure
(LEP Higgs method, A. L. Read, J. Phys. G28, 2693 (2002) )

Using a likelihood ratio estimator to combine different channels :
L s + b 
Q
Ls + b 
Lb 
nchannels

i 1
nchannels b ni
esi +bi  si + bi  i
e bi
, Lb  
ni !
ni !
i 1
n
si  N B B  BR( B  n )e tag .e i
• Statistical and systematic uncertainties on expected backgrounds are included in
the likelihood definition by convoluting with a Gaussian G(bi,bi), where bi is the
expected background and bi is the uncertainty on background expectation.
L(si + bi )  L(si + bi )  G(bi , bi )
• Branching fraction upper limit calculated by running toy MC for different
branching fraction hypothesis.
• The confidence level (C.L.) for certain signal
hypothesis is computed as:
Paul D. Jackson
Leptonic B decays
C.L.s +b N Qs+b Qobs
C.L.s 

C.L.b
N Qb Qobs
Paul D. Jackson
Leptonic B decays
Courtesy of A. Stocchi
UT fit 2006 vs 2015
Courtesy of M. Ciuchini
Paul D. Jackson
Leptonic B decays
Motivation

B+→l+n (l=e,m)
The purely leptonic decay B+  l+ nl provides a theoretically clean
means of testing a QCD calculation of a simple process:
~

b
W+
B ( B +  l + n) 
n
u

l+
GF2 Vub
8p
2
Calculable in
Lattice QCD
 m 
f B2  B mB ml2 1 

m


2
l
2
B
But these decays are difficult to observe:
Mode
Challenge
SM prediction
Current upper limit (90% C.L.)
B →mn
Helicity suppression
(4±2)  10-7
<6.6 x 10-6 BaBar PRL 92, 221803 ’04
B →n
Multi-n final state
(9±4)  10-5
<2.6 x 10-4 BaBar PRD 73, 057101 ‘06
– The radiation of a photon relieves the helicity suppression, at the cost of
an additional 30-50% theoretical uncertainty (at least for the time being).
Paul D. Jackson
Leptonic B decays
2
Radiative Leptonic Decays

Theoretical predictions: B(B+  l+ n ) ~ (1–4)×10-6
R, a ratio of moments of the spectator quark momentum. A
measurement or even an upper limit on the branching fraction of
B→lνγ would allow us to derive non-trivial constraints on R.
(Korchemsky, Pirjol, Yan, PRD 61 114510, 2000)

Most recent results are from Belle (hep-ex/0408132,
unpublished) using 140 fb-1:
 B( B ene ) < 2.210-5 (90% C.L.)
 B( B mnm ) < 2.310-5 (90% C.L.)
B+→l+n (l=e,m)
Paul D. Jackson
Leptonic B decays
Analysis scheme






B+→l+n (l=e,m)
Inclusive reconstruction: sum up all missing E, p in event
Use 232M BB pairs in on-peak data (+ off-peak, MC)
Blind analysis
 Validate simulation with control samples and sideband fit before
unblinding
Event selection criteria:
 Signal side: lepton, photon energies, angle, cos BY
 Recoil B side: total recoil energy and momentum
 Neutrino reconstruction: missing E – missing |p|
 Miscellaneous: Event shape, p0 veto
 Two-photon rejection: longitudinal momentum, etc.
Iterative cut optimization procedure
Binned ML fit to extract signal count
Paul D. Jackson
Leptonic B decays
Neutrino reconstruction
Detected recoil particles
(CM 3-vectors)
Signal lepton
(select highest CM E)
Signal photon
(select
highest CM E)
Vector sum
Unscaled recoil B
candidate
Vector sum
LP combination
Unscaled recoil B
and LP
Scaled recoil B
candidate
Vector
sum,
flipped
Scaled recoil B
and LP
Scale to
expected
magnitude
(~320 MeV)
Unscaled neutrino
Scaled neutrino
B+→l+n (l=e,m)
Paul D. Jackson
Leptonic B decays
Important selection variables

nuEP En – |scaled pn|



Beam-constrained neutrino energy
= En = Ebeam – ELP
Use scaled momentum for better res
mES calculated for the recoil B candidate


no cuts applied
Recoil DE is not very useful: very poor resolution
p0 veto:

Combine the signal photon candidate with every other
photon candidate in the event and take the invariant
mass combination closest to the p0 mass.
Paul D. Jackson
Leptonic B decays
Recoil B reconstruction


After choosing signal lepton and photon, remaining
particles are assigned to the recoil B candidate
Compute standard kinematic variables for this
inclusively reconstructed B


Unlike a standard exclusive analysis, the loose reconstruction
reduces the power of these variables
MES
Recoil variables:


mES: Still has discriminatory power; useful for fit
DE:
 Computed assuming charged tracks have
pion mass and neutrals are all photons


Paul D. Jackson
5
5.3 GeV
DE
Tried PID in the calculation with little improvement
Resolution is not good
Leptonic B decays
-4
0
2 GeV
Signal MC, valid. sample, all cuts
Final signal extraction – fit I
B3
B1

Too few off-peak events are expected for any reasonable PDF
Divide plane of recoil mES and nuEP into 1 signal and 3 sideband regions


S
Signal extraction fit is a compromise between a cut-and-count and full-blown
ML fit


B2
Exploit the differences in shape between signal, BB background, and continuum
Boundaries between regions optimized using toy-MC fits for best sensitivity
Paul D. Jackson
Leptonic B decays
Final signal extraction - fit II
Scaled region event counts, electron mode, valid. sample
nuEP
mES
Signal
S
sig
sig
21.2
B1
sig
side
B2
side
sig
3.7
3.1
B3
side
side
0.9
Template
shapes
300
250
200
150
(3×10-6)
buln
100
50
0
41.1
15.7
52.2
33.7
300.0
250.0
200.0
150.0
7-mode MC
100.0
50.0
0.0
Gen B
MC
21.0
39.1
82.0
310.5
300.0
250.0
200.0
150.0
100.0
50.0
0.0
Cont
MC*
14.1
67.8
10.5
117.4
300.0
250.0
200.0
150.0
100.0
50.0
0.0
Paul D. Jackson
Leptonic B decays
BFx10