Transcript B Physics Behond CP Violation

B Physics Beyond CP Violation
— Semileptonic B Decays —
Masahiro Morii
Harvard University
University of Illinois Urbana-Champaign HETEP Seminar
3 April 2006
Outline

Introduction: Why semileptonic B decays?
CKM matrix — Unitarity Triangle — CP violation
 |Vub| vs. sin2b


|Vub| from inclusive b → uv decays
Measurements: lepton energy, hadron mass, lepton-neutrino mass
 Theoretical challenge: Shape Function
 Latest from BABAR – Avoiding the Shape Function



|Vub| from exclusive b → uv decays

Measurements: G(B → pv)

Theoretical challenge: Form Factors
Summary
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Particle mass (eV/c2)
Mass and the Generations
10
12
10
11
10
10
10
9
10
8
10
7
 Fermions
t

c

b
 The
u
6
10
5
10
4
10
3
They differ only by the masses
 The Standard Model has no explanation
for the mass spectrum

s
10
come in three generations
d
e
Q = 1
3 April 2006

0
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

The origin of mass is one of the most urgent
questions in particle physics today
+2/3 1/3
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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
u 
u 
 
 
c M c
 
 
 t  
 t 
 Suppose
u 
 
1
c M
 
 t 

 d 
d 
 
 
s N s
 
 
 b  
 b 
M and N are arbitrary
33 unitary matrices
W connects u ↔ d, c ↔ s, t ↔ b
u 
 
1
c  M
 
 t  
 d 
 
1
s M N
 
 b  
d 
d 
 
 
s V s
 
 
 b 
 b 
Weak interactions
between u, c, t, and
d, s, b are “mixed”
by matrix V
That’s a poor choice of basis vectors
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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 33 unitary matrix

u 
 d  V ud
  W
  
c   V s  V cd
 
  
 t 
 b   V td
V us
V cs
V ts
Cabibbo-Kobayashi-Maskawa matrix
 The

V ub   d 
 
V cb
s
 
V tb   b 
or CKM for short
Standard Model does not predict V
... for the same reason it does not predict the particle masses
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Structure of the CKM matrix
CKM matrix looks like this 
 0.974

 It’s not completely diagonal
V  0.226

 Off-diagonal components are small
 0.008
 Transition across generations is
allowed but suppressed
 The
0.226
0.973
0.042
0.004 

0.042

0.999 
 The
“hierarchy” can be best expressed in the
Wolfenstein parameterization:
2

1  12 

V 

 A  3 (1    i )

 One


3
1  12 
 A
A  (   i ) 

2
4
A

O
(

)


1

2
2
irreducible complex phase  CP violation
Vub
The only source of CP violation in the minimal Standard Model
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CP violation and New Physics
Are there additional (non-CKM) sources of CP violation?
 The
CKM mechanism fails to explain the amount of matterantimatter 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)

New sources of CP violation almost certainly exist

Precision studies of the CKM matrix may uncover them
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The Unitarity Triangle
 V†V
= 1 gives us
V ud V us  V cd V cs  V td V ts  0
*
V ud V
*
ub
*
 V cd V
*
cb
*
 V td V
*
tb
This one has the 3
terms in the same
order of magnitude
0
V usV ub  V csV cb  V tsV tb  0
*
*

A triangle on the
complex plane
V td V
*
V ud V
V cd V


ub

cb
Vud V
*
ub
0

*
V td V tb

V cd V

tb

cb
b

*
V cd V cb
1
 V td V tb* 
  arg  
* 
V
V
ud ub 

 V cd V cb* 
b  arg  
* 
V
V
td tb 

 V ud V ub* 
  arg  
* 
V
V
cd cb 

Measurements of angles and sides constrain the apex (, )
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Consistency Test

Compare the measurements (contours) on the (, ) plane


The
tells us this is true
as of summer 2004


If the SM is the whole story,
they must all overlap
Still large enough for New
Physics to hide
Precision of sin2b outstripped
the other measurements

Must improve the others to
make more stringent test
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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


V ud V ub V cd V cb

Uncertainty dominated by
15% on |Vub|
Measurement of |Vub| is
complementary to sin2b
Goal: Accurate determination of both |Vub| and sin2b
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Measuring |Vub|

Best probe: semileptonic b  u decay


decoupled from
hadronic effects
b
2
V ub
Tree level
G (b  u  ) 
u


GF
192p
2
V ub
2
5
mb
The problem: b  cv decay
G (b  u  )
G (b  c  )


V ub
V cb
2
2

1
50
How can we suppress 50× larger background?
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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



b c
b u
How accurately do we know this fraction?
Exclusive: Reconstruct final-state hadrons
 B  pv, B  v, B  wv, B  v, …

E
2.31
2.64
Example: the rate for B  pv is
d G(B  p  )
dq

3 April 2006
2
2

GF
24 p
3
V ub
2
3
2
2
pp f  ( q )
Form Factor
(3 FFs for vector mesons)
How accurately do we know the FFs?
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Inclusive b → u

There are 3 independent variables in B → Xv

B
q2 = lepton-neutrino mass squared
Xu
u quark turns into
1 or more hardons

E = lepton energy
mX = hadron system mass
Signal events have smaller mX  Larger E and q2
Not to scale!
b c
b c
b c
b u
b u
E
3 April 2006
b u
q
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mX
13
BABAR PRD 73:012006
Belle PLB 621:28
CLEO PRL 88:231803
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 background
is crucial!
 Measure the partial BF
BABAR

E
(GeV)
BABAR 80fb-1
2.0–2.6
Belle 27fb-1
1.9–2.6
CLEO 9fb-1
2.2–2.6
3 April 2006
DB
Data
MC bkgd.
b  cv
Data – bkgd.
(10-4)
5.72 ± 0.41stat ±
0.65sys
8.47 ± 0.37
1.53sys
MC signal
b  uv
±
stat 3
cf. Total BF is ~210
2.30M.
± Morii,
0.15stat
±
Harvard
14
BABAR PRL 95:111801
E vs. q2
q2 (GeV2)

Use pv = pmiss in addition to pe  Calculate q2

25
Define shmax = the maximum mX squared

20
b  uv
15

10
5
b  cv
0.5
1
1.5
2
2.5
Cutting at shmax < mD2 removes b  cv
while keeping most of the signal
S/B = 1/2 achieved for E > 2.0 GeV and
shmax < 3.5 GeV2

cf. ~1/15 for the endpoint E > 2.0 GeV
E (GeV)

Measured partial BF
DB (10-4)
BABAR 80fb-1
3 April 2006
BABAR
3.54 ± 0.33stat ±
0.34
sys
Small
systematic
errors
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Measuring mX and


Rest of the event contains one “recoil” B

Fully reconstructed
B  hadrons
Neutrino = missing momentum

Make sure mmiss ~ 0
v
All left-over particles belong to X


Flavor and momentum known
Find a lepton in the recoil B


2
q
Must reconstruct all decay products to measure mX or q2
Select events with a fully-reconstructed B meson


BABAR hep-ex/0507017
Belle PRL 95:241801
We can now calculate mX and q2
lepton
Suppress b → cv by vetoing against D(*) decays
X
Reject events with K
 Reject events with B0 → D*+(→ D0p+)−v

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Measuring Partial BF

BABAR hep-ex/0507017
Belle PRL 95:241801
Measure the partial BF in regions of (mX, q2)
For example:
mX < 1.7 GeV and
q2 > 8 GeV2
BABAR 211fb-1
Phase Space
DB (10-4)
mX < 1.7, q2 >
8
8.7 ± 0.9stat ± 0.9sys
mX < 1.7
Belle
3 April 2006
253fb-1
mX < 1.7, q2 >
8
12.4 ± 1.1stat ±
1.0sys
Large DB thanks to
the high efficiency of
the mX cut
8.4 ± 0.8stat ± 1.0sys
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Theoretical Issues



Tree level rate must be corrected for QCD
Operator Product Expansion gives
b
us the inclusive rate
B
 Expansion in s(mb) (perturbative)

V ub
and 1/mb (non-perturbative)
G(B  X u  ) 
2
mb 
  s  9  2  1
1

O




3
2
19 2 p
2 mb
 p 

2
G F Vub
5
known to O(s2)


u



Xu
Suppressed by 1/mb2
Main uncertainty (5%) from mb5  2.5% on |Vub|
But we need the accessible fraction (e.g., Eℓ > 2 GeV) of the rate
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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 O(1/mb) instead
of O(1/mb2)

f (k )
k
0
We must determine the Shape Function
from experimental data
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  M
B
 mb
19
BABAR PRD 72:052004, hep-ex/0507001
Belle hep-ex/0407052
CLEO hep-ex/0402009
b → s Decays
Measure: Same SF affects (to the first order) b → s decays
Measure E
spectrum in
b → s
Extract f(k+)
Inclusive
Inclusive  measurement. Photon
energy in the Y(4S) rest frame
3 April 2006
Partial BF/bin (10-3)

Predict
partial BFs in
b → uv
Sum of exclusive
K*
BABAR
Exclusive Xs +  measurement. Photon
energy determined from the Xs mass
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Predicting b → u Spectra

Fit the b → s spectrum to extract the SF


Must assume functional forms, e.g.
(1  a ) x
;
x  k 
E and mX moments  b-quark mass and kinetic energy
m b  (4.60  0.04) G eV ,

 p  (0.20  0.04) G eV
2
Plug in the SF into the b  uv
spectrum calculations


2
Buchmüller & Flächer
hep-ph/0507253
NB: mb is determined to better than 1%
 First two moments of the SF

a
Additional information from b  cv decays


f ( k  )  N (1  x ) e
Lepton-energy
spectrum by
BLNP
Bosch, Lange, Neubert, Paz, NPB 699:335
Lange, Neubert, Paz, PRD 72:073006
Ready to extract |Vub|
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Turning DB into |Vub|

Using BLNP + the SF parameters from b → s, b  cv
Phase Space
|Vub| (10-3)
Reference
BABAR 80fb-1
E > 2.0
4.41 ± 0.29exp ± PRD 73:012006
0.31SF,theo
Belle 27fb-1
E > 1.9
4.82 ± 0.45exp ±
0.30SF,theo
CLEO 9fb-1
E > 2.2
4.09 ± 0.48exp ± PRL 88:231803
0.36SF,theo
BABAR 80fb-1
E > 2.0, shmax <
3.5
4.10 ± 0.27exp ± PRL 95:111801
0.36SF,theo
PLB 621:28
2
hep-ex/0507017
(4.60
GeV, p2 =4.75
(0.20
 0.04)
BABARAdjusted
211fb-1 tommXb <= 1.7,
q2>0.04)
8
± 0.35
exp ±GeV
0.32SF,theo
 Theory errors from Lange, Neubert, Paz, hep-ph/0504071
m(X*)<used
1.7 a simulated annealing
4.06 ±technique
0.27exp ± PRL 95:241801
 Last Belle
result
-1
Belle 253fb
0.24SF,theo
3 April 2006
-1
22
mX < 1.7, q2 > 8M. Morii, Harvard 4.37 ± 0.46exp ± PRL 92:101801
Inclusive |Vub| as of 2005
|Vub| world average, Winter 2006

|Vub| determined to 7.4%
Statistical
2.2%
Expt. syst.
2.7%
b  cv model 1.9%
b  uv model 2.1%
3 April 2006
M. Morii, Harvard
SF params.
4.1%
Theory
4.2%

The SF parameters can be
improved with b → s,
b  cv measurements

What’s the theory error?
23
Theory Errors

Subleading Shape Function  3.8% error
Higher order non-perturbative corrections
 Cannot be constrained with b → s


Weak annihilation  1.9% error

B


u
Measure G(B0  Xuv)/G(B+  Xuv) or
G(D0  Xv)/G(Ds  Xv) to improve the constraint


b

g
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  cv and b → s data fit well with the HQE predictions

Ultimate error on inclusive |Vub| may be ~5%
3 April 2006
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Avoiding the Shape Function

Possible to combine b  uv and b → s so that the SF cancels
G(B  X u  ) 


V ub
V ts
2
2
 W ( E )
d G ( B  X s )
dE 
dE 
Weight function

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  cv data


How well does this work? Only one way to find out…
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BABAR hep-ex/0601046
SF-Free |Vub| Measurement


BABAR applied LLR (PLB 486:86) to 80 fb-1 data

G(B  Xuv) with varying mX cut

dG(B  Xs)/dE from PRD 72:052004
With mX < 1.67 GeV
V u b  (4.43  0.38  0.25  0.29)  10
stat.


Expt. error
syst. theory
SF error  Statistical error
Also measured mX < 2.5 GeV

1.67
Almost (96%) fully inclusive  No SF necessary
V u b  (3 .8 4  0 .7 0  0 .3 0  0 .1 0 )  1 0

Theory error
3
3
mX cut (GeV)
Theory error ±2.6%
Attractive new approaches with increasing statistics
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Exclusive B → p

Measure specific final states, e.g., B → pv
Can achieve good signal-to-background ratio
 Branching fractions in O(10-4)  Statistics limited


Need Form Factors to extract |Vub|
d G(B  p  )
dq
 f+(q2)

2
2

GF
24 p
3
V ub
2
3
2
pp f  ( q )
2
One FF for B → pv
with massless lepton
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
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Form Factor Calculations

Unquenched LQCD calculations started to appear in 2004
Fermilab (hep-lat/0409116) and
HPQCD (hep-lat/0601021)
 Uncertainties are ~11%
LCSR*
Fermilab
HPQCD
ISGW2
f+(q2) and f0(q2)

q2 (GeV2)

Measure dG(B → pv)/dq2
as a function of q2

*Ball-Zwicky PRD71:014015
3 April 2006
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Compare with different
calculations
28
Measuring B → p

Measurements differ in
what you do with the
“other” B
Technique
Efficiency Purity
Untagged
Tagged by B  D(*)v
Tagged by B  hadrons

High

Low
Low

High
Total BF is
(1 .3 5  0 .0 8 stat  0 .0 8 syst )  1 0

8.4% precision
B(B0 → pv) [10-4]
3 April 2006
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4
Untagged B → p


BABAR PRD 72:051102
CLEO PRD 68:072003
Missing 4-momentum = neutrino
Reconstruct B → pv and calculate mB and DE = EB – Ebeam/2
BABAR
data
MC signal
signal with
wrong p
b  uv
b  cv
BABAR
other bkg.
3 April 2006
M. Morii, Harvard
30
BABAR hep-ex/0506064, 0506065
Belle hep-ex/0508018
D(*)-tagged B → p

Reconstruct one B and look for B  pv in the recoil


Semileptonic (B 
efficient but less pure
D(*)v)


Tag with either B  D(*)v or B  hadrons
tags are
Two neutrinos in the event
Event kinematics determined assuming
known mB and mv
soft p
p
D

v
v

cos2fB  1 for signal
data
MC signal
MC background
3 April 2006
M. Morii, Harvard
31
BABAR hep-ex/0507085
Hadronic-tagged B → p

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

B p
0




B p
0


soft p
p
D

v
p or K
data
MC signal
b  uv
b  cv
other bkg.
3 April 2006
M. Morii, Harvard
32
dB(B → p)/dq2

Measurements start to
constrain the q2 dependence


Errors on |Vub| dominated
V ub
by the FF normalization
3 April 2006
ISGW2 rejected
Partial BF measured to be
q2 range
DB [10−4]
< 16
GeV2
0.94 ± 0.06 ± 0.06
> 16
GeV2
HFAG 2006
0.39 ± 0.04
± Winter
0.04
 (3.36  0.15 expt  0.55 FF )  10  3
 0.37


 0.63
3
  (4.20  0.29 expt  0.43 FF )  10

 0.65
3
(3.75

0.26
)

10
ex p t  0.43 FF


M. Morii, Harvard
B all-Zw icky q  16
2
H P Q C D q  16
2
Ferm ilab q  16
2
33
Future of B → p

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
34
How Things Mesh Together
b → s
Inclusive b → cv
E
E
SSFs
Shape
Function
HQE Fit
mb
Exclusive b → uv
E
Inclusive
b → uv
wv, v ?
FF
duality
WA
3 April 2006
B → pv
|Vub|
q2
mX
mX
LCSR
M. Morii, Harvard
LQCD
unquenching
35
The UT 2004  2005


Dramatic improvement in |Vub|!
sin2b went down slightly  Overlap with |Vub/Vcb| smaller
3 April 2006
M. Morii, Harvard
36
Summary

Precise determination of |Vub| complements sin2b to test the
(in)completeness of the Standard Model

7.4% accuracy achieved so far  5% possible?
b

Close collaboration between theory and experiment is crucial
Rapid progress in inclusive |Vub| in the last 2 years
 Improvement in B → p form factor is needed

3 April 2006
M. Morii, Harvard
37