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B Physics Beyond CP Violation
— Semileptonic B Decays —
Masahiro Morii
Harvard University
University of Illinois Urbana-Champaign HETEP Seminar
3 April 2006
3 April 2006 M. Morii, Harvard 2
Outline Introduction: Why semileptonic B decays?
CKM matrix — Unitarity Triangle — CP violation |Vub| vs. sin2
|Vub| from inclusive b → uv decays Measurements: lepton energy, hadron mass, lepton-neutrino mass Theoretical challenge: Shape Function Latest from BABAR – Avoiding the Shape Function
|Vub| from exclusive b → uv decays Measurements: (B → v) Theoretical challenge: Form Factors
Summary
3 April 2006 M. Morii, Harvard 3
Mass and the Generations Fermions come in three generations
They differ only by the masses The Standard Model has no explanation
for the mass spectrum The masses come from the interaction
with the Higgs field ... whose nature is unknown We are looking for the Higgs particle at
the Tevatron, and at the LHC in the future
310
410
510
610
710
810
910
1010
1110
Part
icle
mas
s (e
V/c
2 )
1210
e
u
c
t
d
s
b
Q = 1 0 +2/3 1/3
The origin of mass is one of the most urgent questions in particle physics today
3 April 2006 M. Morii, Harvard 4
If there were no masses Nothing would distinguish u from c from t
We could make a mixture of the wavefunctions and pretend it represents a physical particle
Suppose W connects u ↔ d, c ↔ s, t ↔ b
That’s a poor choice of basis vectors
u u
c c
t t
M
d d
s s
b b
N M and N are arbitrary33 unitary matrices
1 1 1
u u d d d
c c s s s
t t b b b
M M M N V
Weak interactions between u, c, t, and d, s, b are “mixed” by matrix V
3 April 2006 M. Morii, Harvard 5
Turn the masses back on Masses uniquely define the u, c, t, and d, s, b states
We don’t know what creates masses We don’t know how the eigenstates are chosen M and N are arbitrary
V is an arbitrary 33 unitary matrix
The Standard Model does not predict V ... for the same reason it does not predict the particle masses
ud us ub
cd cs cb
td ts tb
Wu d V V V d
c s V V V s
t b V V V b
V
Cabibbo-Kobayashi-Maskawa matrix or CKM for short
3 April 2006 M. Morii, Harvard 6
Structure of the CKM matrix The CKM matrix looks like this
It’s not completely diagonal Off-diagonal components are small
Transition across generations isallowed but suppressed
The “hierarchy” can be best expressed in theWolfenstein parameterization:
One irreducible complex phase CP violation The only source of CP violation in the minimal Standard Model
0.974 0.226 0.004
0.226 0.973 0.042
0.008 0.042 0.999
V
0.974 0.226 0.004
0.226 0.973 0.042
0.008 0.042 0.999
V
3212
2 2 41
32
2
1
1 ( )
1
( )
(1 )
A i
i AA
A
V O
Vub
3 April 2006 M. Morii, Harvard 7
CP violation and New Physics
The CKM mechanism fails to explain the amount of matter-antimatter imbalance in the Universe ... by several orders of magnitude
New Physics beyond the SM is expected at 1-10 TeV scale e.g. to keep the Higgs mass < 1 TeV/c2
Almost all theories of New Physics introduce new sources of CP violation (e.g. 43 of them in supersymmetry)
Precision studies of the CKM matrix may uncover them
New sources of CP violation almost certainly existNew sources of CP violation almost certainly exist
Are there additional (non-CKM) sources of CP violation?
3 April 2006 M. Morii, Harvard 8
The Unitarity Triangle V†V = 1 gives us
Measurements of angles and sides constrain the apex (, )
* * *
* * *
* * *
0
0
0
ud us cd cs td ts
ud ub cd cb td tb
us ub cs cb ts tb
V V V V V V
V V V V V V
V V V V V V
This one has the 3 terms in the same
order of magnitude
A triangle on the complex plane
1
td tb
cd cb
V V
V V
ud ub
cd cb
V V
V V
0
*ud ubV V
*td tbV V
*cd cbV V
*
*
*
*
*
*
arg
arg
arg
td tb
ud ub
cd cb
td tb
ud ub
cd cb
V V
V V
V V
V V
V V
V V
3 April 2006 M. Morii, Harvard 9
Consistency Test Compare the measurements (contours) on the (, ) plane
If the SM is the whole story,they must all overlap
The tells us this is trueas of summer 2004 Still large enough for New
Physics to hide Precision of sin2 outstripped
the other measurements Must improve the others to
make more stringent test
3 April 2006 M. Morii, Harvard 10
Next Step: |Vub|
Zoom in to see the overlap of “the other” contours It’s obvious: we must make
the green ring thinner Left side of the Triangle is
Uncertainty dominated by15% on |Vub|
ud ub cd cbV V V V
Measurement of |Vub| is complementary to sin2
Goal: Accurate determination of both |Vub| and sin2
3 April 2006 M. Morii, Harvard 11
Measuring |Vub|
Best probe: semileptonic b u decay
The problem: b cv decay
How can we suppress 50× larger background?
25
2
2( )
192 ubF
b
Gb mVu
b
u
ubV
2
2
( ) 1
( ) 50ub
cb
Vb u
b c V
Tree level
decoupled from hadronic effects
3 April 2006 M. Morii, Harvard 12
Detecting b → u Inclusive: Use mu << mc difference in kinematics
Maximum lepton energy 2.64 vs. 2.31 GeV First observations (CLEO, ARGUS, 1990)
used this technique Only 6% of signal accessible
How accurately do we know this fraction?
Exclusive: Reconstruct final-state hadrons B v, B v, B v, B v, … Example: the rate for B v is
How accurately do we know the FFs?
E
b c
b u
222 3 2
2 3
( )( )
24F
ub
Gd BV p f q
dq
Form Factor(3 FFs for vector mesons)
2.64
2.31
3 April 2006 M. Morii, Harvard 13
There are 3 independent variables in B → Xv
Signal events have smaller mX Larger E and q2
Inclusive b → u
2q
b c
b u
uX
B
u quark turns into 1 or more hardons
q2 = lepton-neutrino mass squaredq2 = lepton-neutrino mass squared
mX = hadron system massmX = hadron system mass
E = lepton energyE = lepton energy
E
b c
b u
Xm
b cb u
Not to scale!Not to scale!
3 April 2006 M. Morii, Harvard 14
Lepton Endpoint Select electrons in 2.0 < E < 2.6 GeV
Push below the charm threshold Larger signal acceptance Smaller theoretical error
Accurate subtraction of backgroundis crucial!
Measure the partial BF
E (GeV) (10-4)
BABAR 80fb-1 2.0–2.6 5.72 ± 0.41stat ± 0.65sys
Belle 27fb-1 1.9–2.6 8.47 ± 0.37stat ± 1.53sys
CLEO 9fb-1 2.2–2.6 2.30 ± 0.15stat ± 0.35sys
BABAR PRD 73:012006Belle PLB 621:28
CLEO PRL 88:231803
BABAR
MC bkgd.b cv
Data
Data – bkgd.
MC signalb uv
cf. Total BF is ~2103
3 April 2006 M. Morii, Harvard 15
E vs. q2
Use pv = pmiss in addition to pe Calculate q2
Define shmax = the maximum mX squared
Cutting at shmax < mD
2 removes b cv while keeping most of the signal
S/B = 1/2 achieved for E > 2.0 GeV and sh
max < 3.5 GeV2
cf. ~1/15 for the endpoint E > 2.0 GeV
Measured partial BF
BABAR PRL 95:111801
BABAR (10-4)
BABAR 80fb-1 3.54 ± 0.33stat ± 0.34sys
0.5 1 1.5 2 2.5
5
10
15
20
25
b cv
E (GeV)
q2 (G
eV2 )
b uv
Small systematic errors
3 April 2006 M. Morii, Harvard 16
Measuring mX and q2
Must reconstruct all decay products to measure mX or q2
Select events with a fully-reconstructed B meson Rest of the event contains one “recoil” B
Flavor and momentum known
Find a lepton in the recoil B Neutrino = missing momentum
Make sure mmiss ~ 0
All left-over particles belong to X We can now calculate mX and q2
Suppress b → cv by vetoing against D(*) decays Reject events with K Reject events with B0 → D*+(→ D0+)−v
BABAR hep-ex/0507017Belle PRL 95:241801
Fully reconstructedB hadrons
lepton
v
X
3 April 2006 M. Morii, Harvard 17
Measuring Partial BF Measure the partial BF in regions of (mX, q2)
BABAR hep-ex/0507017Belle PRL 95:241801
Phase Space (10-4)
BABAR 211fb-1 mX < 1.7, q2 > 8 8.7 ± 0.9stat ± 0.9sys
Belle 253fb-1
mX < 1.7 12.4 ± 1.1stat ± 1.0sys
mX < 1.7, q2 > 8 8.4 ± 0.8stat ± 1.0sys
P+ < 0.66 11.0 ± 1.0stat ± 1.6sys
Large thanks tothe high efficiency of the mX cut
For example:mX < 1.7 GeV and
q2 > 8 GeV2
3 April 2006 M. Morii, Harvard 18
B
uX
b
u
ubVB
uX
Theoretical Issues Tree level rate must be corrected for QCD Operator Product Expansion gives
us the inclusive rate Expansion in s(mb) (perturbative)
and 1/mb (non-perturbative)
Main uncertainty (5%) from mb5 2.5% on |Vub|
But we need the accessible fraction (e.g., Eℓ > 2 GeV) of the rate
2
15
22
2
3( )
22
91
19F u
b
b b su
G
m
V mB X
O
known to (s2) Suppressed by 1/mb
2
3 April 2006 M. Morii, Harvard 19
Shape Function OPE doesn’t work everywhere in the phase space
OK once integrated Doesn’t converge, e.g., near the E end point
Resumming turns non-perturb. terms into a Shape Function b quark Fermi motion parallel
to the u quark velocity Cannot be calculated by theory Leading term is (1/mb) instead
of (1/mb2) k
( )f k
B bM m 0We must determine the Shape Function
from experimental data
3 April 2006 M. Morii, Harvard 20
b → s Decays Measure: Same SF affects (to the first order) b → s decays
Measure E
spectrum inb → s
Extract f(k+) Predict
partial BFs inb → uv
BABAR PRD 72:052004, hep-ex/0507001Belle hep-ex/0407052
CLEO hep-ex/0402009
Inclusive
Sum of exclusive BABAR
Part
ial B
F/bi
n (1
0-3)
Inclusive measurement. Photon energy in the Y(4S) rest frame
Exclusive Xs + measurement. Photon energy determined from the Xs mass
K*
3 April 2006 M. Morii, Harvard 21
Predicting b → u Spectra Fit the b → s spectrum to extract the SF
Must assume functional forms, e.g. Additional information from b cv decays
E and mX moments b-quark mass and kinetic energy
NB: mb is determined to better than 1%
First two moments of the SF Plug in the SF into the b uv
spectrum calculations Bosch, Lange, Neubert, Paz, NPB 699:335 Lange, Neubert, Paz, PRD 72:073006
Ready to extract |Vub|
(1 )( ) (1 ) ;a a xf k N x e x k
2 2(4.60 0.04)GeV, (0.20 0.04)GeVbm Buchmüller & Flächerhep-ph/0507253
Lepton-energyspectrum by
BLNP
3 April 2006 M. Morii, Harvard 22
Turning into |Vub|
Using BLNP + the SF parameters from b → sb cv
Adjusted to mb = (4.60 0.04) GeV, 2 = (0.20 0.04) GeV2
Theory errors from Lange, Neubert, Paz, hep-ph/0504071 Last Belle result(*) used a simulated annealing technique
Phase Space |Vub| (10-3) Reference
BABAR 80fb-1 E > 2.0 4.41 ± 0.29exp ± 0.31SF,theoPRD 73:012006
Belle 27fb-1 E > 1.9 4.82 ± 0.45exp ± 0.30SF,theoPLB 621:28
CLEO 9fb-1 E > 2.2 4.09 ± 0.48exp ± 0.36SF,theoPRL 88:231803
BABAR 80fb-1 E > 2.0, shmax < 3.5 4.10 ± 0.27exp ± 0.36SF,theo
PRL 95:111801
BABAR 211fb-1 mX < 1.7, q2 > 8 4.75 ± 0.35exp ± 0.32SF,theohep-ex/0507017
Belle 253fb-1 mX < 1.7 4.06 ± 0.27exp ± 0.24SF,theoPRL 95:241801
Belle 87fb-1* mX < 1.7, q2 > 8 4.37 ± 0.46exp ± 0.29SF,theoPRL 92:101801
3 April 2006 M. Morii, Harvard 23
Inclusive |Vub| as of 2005
|Vub| determined to 7.4%
The SF parameters can be improved with b → sb cv measurements
What’s the theory error?
|Vub| world average, Winter 2006
Statistical 2.2%
Expt. syst. 2.7%
b cv model 1.9%
b uv model 2.1%
SF params. 4.1%
Theory4.2
%
3 April 2006 M. Morii, Harvard 24
Theory Errors Subleading Shape Function 3.8% error
Higher order non-perturbative corrections Cannot be constrained with b → s
Weak annihilation 1.9% error Measure (B0 Xuv)/(B+ Xuv) or(D0 Xv)/(Ds Xv) to improve the constraint Also: study q2 spectrum near endpoint (CLEO hep-ex/0601027)
Reduce the effect by rejecting the high-q2 region Quark-hadron duality is believed to be negligible
b cv and b → sdata fit well with the HQE predictions
Ultimate error on inclusive |Vub| may be ~5%
b
u
B
g
3 April 2006 M. Morii, Harvard 25
Avoiding the Shape Function Possible to combine b uv and b → s so that the SF cancels
Leibovich, Low, Rothstein, PLB 486:86 Lange, Neubert, Paz, JHEP 0510:084, Lange, JHEP 0601:104
No need to assume functional forms for the Shape Function Need b → s spectrum in the B rest frame
Only one measurement (BABAR PRD 72:052004) available Cannot take advantage of precise b cv data
How well does this work? Only one way to find out…
2
2 ( )( )
( ) ub su
ts
W EV d B X
B X dEdEV
Weight function
3 April 2006 M. Morii, Harvard 26
SF-Free |Vub| Measurement
BABAR applied LLR (PLB 486:86) to 80 fb-1 data (B Xuv) with varying mX cut
d(B Xs)/dE from PRD 72:052004
With mX < 1.67 GeV
SF error Statistical error
Also measured mX < 2.5 GeV Almost (96%) fully inclusive No SF necessary
Attractive new approaches with increasing statistics
mX cut (GeV)1.67
3(4.43 0.38 0.25 0.29) 10ubV
stat. syst. theory
3(3.84 0.70 0.30 0.10) 10ubV Theory error ±2.6%
BABAR hep-ex/0601046
Theory error
Expt. error
3 April 2006 M. Morii, Harvard 27
Exclusive B → Measure specific final states, e.g., B → v
Can achieve good signal-to-background ratio Branching fractions in (10-4) Statistics limited
Need Form Factors to extract |Vub|
f+(q2) has been calculated using Lattice QCD (q2 > 15 GeV2)
Existing calculations are “quenched” ~15% uncertainty Light Cone Sum Rules (q2 < 14 GeV2)
Assumes local quark-hadron duality ~10% uncertainty ... and other approaches
22 223
2 3
( )
24( )F
ub
Gd BV f
dqqp
One FF for B → vwith massless lepton
3 April 2006 M. Morii, Harvard 28
Form Factor Calculations Unquenched LQCD calculations started to appear in 2004
Fermilab (hep-lat/0409116) andHPQCD (hep-lat/0601021)
Uncertainties are ~11%
f +(q
2 ) a
nd f 0(
q2 )
q2 (GeV2)
Measure d(B → v)/dq2 as a function of q2
Compare with differentcalculations
LCSR*FermilabHPQCDISGW2
*Ball-Zwicky PRD71:014015
3 April 2006 M. Morii, Harvard 29
Measuring B → Measurements differ in
what you do with the “other” B
Total BF is
8.4% precision
(B0 → v) [10-4]
Technique Efficiency
Purity
Untagged High
Low
Low
High
Tagged by B D(*)v
Tagged by B hadrons
4stat syst(1.35 0.08 0.08 ) 10
3 April 2006 M. Morii, Harvard 30
Untagged B → Missing 4-momentum = neutrino Reconstruct B → v and calculate mB and E = EB – Ebeam/2
BABAR
BABAR
data
MC signalsignal withwrong
b uvb cvother bkg.
BABAR PRD 72:051102CLEO PRD 68:072003
3 April 2006 M. Morii, Harvard 31
D(*)-tagged B → Reconstruct one B and look for B v in the recoil
Tag with either B D(*)v or B hadrons Semileptonic (B D(*)v) tags are
efficient but less pure Two neutrinos in the event
Event kinematics determined assumingknown mB and mv
vv
D
soft
cos2B 1 for signaldata
MC signalMC background
BABAR hep-ex/0506064, 0506065Belle hep-ex/0508018
3 April 2006 M. Morii, Harvard 32
Hadronic-tagged B → Hadronic tags have high purity, but low efficiency
Event kinematics is known by a 2-C fit Use mB and mmiss distributions to
extract the signal yield
or Kv
D
soft
0B 0B
data
MC signal
b uvb cvother bkg.
BABAR hep-ex/0507085
3 April 2006 M. Morii, Harvard 33
d(B → )/dq2
Measurements start to constrain the q2 dependence ISGW2 rejected
Partial BF measured to be
q2 range [10−4]
< 16 GeV2 0.94 ± 0.06 ± 0.06
> 16 GeV2 0.39 ± 0.04 ± 0.04
3 2expt
3 2expt
3 2ex
FF
p
FF
FFt
0.550.370.630.430.650.43
(3.36 0.15 ) 10 Ball-Zwicky 16
(4.20 0.29 ) 10 HPQCD 16
(3.75 0.26 ) 10 Fermilab 16
ub
q
V q
q
Errors on |Vub| dominated by the FF normalization
HFAG 2006Winter
3 April 2006 M. Morii, Harvard 34
Future of B → Form factor normalization dominates the error on |Vub|
Experimental error will soon reach 5% Significant efforts in both LQCD and LCSR needed
Spread among the calculations still large Reducing errors below 10% will be a challenge
Combination of LQCD/LCSR with the measured q2 spectrum and dispersive bounds may improve the precision Fukunaga, Onogi, PRD 71:034506 Arnesen, Grinstein, Rothstein, Stewart
PRL 95:071802 Ball, Zwicky, PLB 625:225 Becher, Hill, PLB 633:61-69
3 April 2006 M. Morii, Harvard 35
Exclusive b → uv
How Things Mesh Together
B → vInclusiveb → uv q2
v, v ?
b → s
ShapeFunction
E
mb
Inclusive b → cv
mXE
HQE Fit
mX
E
WA
duality
|Vub|
SSFs
FF
LCSR LQCDunquenching
3 April 2006 M. Morii, Harvard 36
The UT 2004 2005
Dramatic improvement in |Vub|!
sin2 went down slightly Overlap with |Vub/Vcb| smaller
3 April 2006 M. Morii, Harvard 37
Summary Precise determination of |Vub| complements sin2 to test the
(in)completeness of the Standard Model 7.4% accuracy achieved so far 5% possible?
Close collaboration between theory and experiment is crucial Rapid progress in inclusive |Vub| in the last 2 years
Improvement in B → form factor is needed
|Vub |