Transcript B Physics Behond CP Violation

B Physics Beyond CP Violation
— Semileptonic B Decays —
Masahiro Morii
Harvard University
Duke University High Energy Physics Seminar
9 November 2005
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



|Vub| from exclusive b → uv decays

Measurements: G(B → pv)

Theoretical challenge: Form Factors
Summary
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Mass and the Generations
1012
1011
Particle mass (eV/c2)
1010
10
9
10
8
come in three generations
They differ only by the masses
 The Standard Model has no explanation
for the mass spectrum


c

b
s
107
u d
106
105
 Fermions
t
e
10 4

0
9 November 2005
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
103
Q = 1
 The
+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 
 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 
u  
 d 
d 
d 
 c   M 1  c   M 1  s   M 1N  s   V  s 
 
 
 
 
 
 t 
 t  
 b 
 b 
 b 
 Suppose

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  Vud
 c  
W   V  s   V
 
   cd
 t 
 b  Vtd
Vus Vub   d 
Vcs Vcb   s 
Vts Vtb   b 
Cabibbo-Kobayashi-Maskawa matrix
 The

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
 0.974 0.226 0.004 
 It’s not completely diagonal
V   0.226 0.973 0.042 
 Off-diagonal components are small
 0.008 0.042 0.999 
 The
CKM matrix looks like this 

Transition across generations is
allowed but suppressed
 The
“hierarchy” can be best expressed in the
Wolfenstein parameterization:
 1  12  2


V 

1  12  2
 A 3 (1    i )  A 2

 One

A 3 (   i ) 

4
A 2

O
(

)


1

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
VudVus*  VcdVcs*  VtdVts*  0
This one has the 3
terms in the same
order of magnitude
V V  VcdV  V V  0
*
ud ub
*
cb
*
td tb
VusVub*  VcsVcb*  VtsVtb*  0
A triangle on the
complex plane

VudVub
VcdVcb
VudVub*
0



td tb

cd cb
VV
V V
VtdVtb*

b

VcdVcb*
1
 VtdVtb* 
  arg  
* 
V
V
 ud ub 
 VcdVcb* 
b  arg  
* 
V
V
 td tb 
 VudVub* 
  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
VudVub VcdVcb

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
Vub
Tree level
u

GF2
2
5
G(b  u  ) 
V
m
ub
b
192p 2

The problem: b  cv decay
2
G(b  u  ) Vub
1


2
G(b  c  ) Vcb
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
GF2
d G( B  p  )
2
3
2 2

Vub pp f  (q )
2
3
dq
24p

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
Xu
u quark turns into
1 or more hardons

E = lepton energy
q2 = lepton-neutrino mass squared
mX = hadron system mass
Signal events have smaller mX  Larger E and q2
Not to scale!
bc
bc
bu
bu
E
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bu
q2
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bc
mX
13
BABAR hep-ex/0509040
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
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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
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BABAR
3.54 ± 0.33stat ±
0.34
sys
Small
systematic
errors
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Measuring mX and

2
q
Must reconstruct all decay products to measure mX or q2


BABAR hep-ex/0507017
Belle hep-ex/0505088
E was much easier
Select events with a fully-reconstructed B meson
Fully reconstructed
B  hadrons
Use ~1000 hadronic decay chains
 Rest of the event contains one “recoil” B



Flavor and momentum known
Find a lepton in the recoil-B
Lepton charge consistent with the B flavor
 mmiss consistent with a neutrino


All left-over particles belong to X
 Use a kinematic fit  s(mX) = 350 MeV

v
lepton
X
4-momentum conservation; equal mB on both sides; mmiss = 0
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Measuring Partial BF

BABAR hep-ex/0507017
Belle hep-ex/0505088
Suppress b → cv by vetoing against D(*) decays
Reject events with K
 Reject events with B0 → D*+(→ D0p+)−v


Measure the partial BF in regions of (mX, q2)

For example: mX < 1.7 GeV and q2 > 8 GeV2
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Partial BF Results
BABAR 211fb-1
Phase Space
DB (10-4)
mX < 1.7, q2 >
8
8.7 ± 0.9stat ± 0.9sys
mX < 1.7
12.4 ± 1.1stat ±
1.0sys
BABAR hep-ex/0507017
Belle hep-ex/0505088
Large DB thanks to
the high efficiency of
the mX cut
mX < 1.7, q2 >
8.4 ± 0.8stat ± 1.0sys
Belle
 P+ = EX  |PX| is a 8theoretically clean variable
253fb-1

Bosch, Lange, Neubert,
Paz
P+ < 0.66
PRL 93:221802
11.0 ±Belle
1.0stat ±
1.6sys
Efficiency high
 Signal vs. background
separation is limited

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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)

Vub
and 1/mb (non-perturbative)
2
GF2 Vub mb5
G( B  X u  ) 
192p 3

 s
1

O


p

u
 92  1


2
2mb

known to O(s2)





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
 leading term is O(1/mb) instead of O(1/mb2)

Rough features (mean,
r.m.s.) are known
Details, especially the
tail, are unknown
f (k )
0
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  M B  mb
k
20
BABAR hep-ex/0507001, 0508004
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
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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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Extracting the Shape Function

We can fit the b → s spectrum with theory prediction

Must assume a functional form of f(k+)


Example: f (k )  N (1  x) a e(1 a ) x ; x 
k

New calculation connect the SF moments with the b-quark
mass mb and kinetic energy p2 (Neubert, PLB 612:13)
 Determined precisely from b → s and b  cv decays


En from b → s,
E n and m Xn from b  cv
Fit data from BABAR, Belle, CLEO, DELPHI, CDF
mb  (4.60  0.04)GeV, p2  (0.20  0.04)GeV2

Buchmüller & Flächer
hep-ph/0507253
NB: mb is determined to better than 1%
 Determine the SF
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Predicting b → u Spectra
d 3 G( B  X u  )
 OPE + SF can predict triple-differential rate
dE dmX dq 2
 Unreliable where OPE converges poorly


... that is where the signal is
Soft Collinear Effective Theory offers the right tool
Developed since 2001 by Bauer, Fleming, Luke, Pirjol, Stewart
 Applied to b → uv by several groups


A triple-diff. rate calculation
available since Spring 2005



Bosch, Lange, Neubert, Paz, NPB 699:335
Lange, Neubert, Paz, hep-ph/0504071
Lepton-energy
spectrum by
BLNP
BABAR and Belle use BLNP to
extract |Vub| in the latest results
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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
4.39 ± 0.25exp ± hep-ex/0509040
0.32SF,theo
Belle 27fb-1
E > 1.9
4.82 ± 0.45exp ±
0.31SF,theo
CLEO 9fb-1
E > 2.2
4.02 ± 0.47exp ± PRL 88:231803
0.35SF,theo
BABAR 80fb-1
E > 2.0, shmax <
3.5
4.06 ± 0.27exp ± PRL 95:111801
0.36SF,theo
PLB 621:28
2
hep-ex/0507017
(4.60
GeV, p2 =4.76
(0.20
 0.04)
BABARAdjusted
211fb-1 tommXb <= 1.7,
q2>0.04)
8
± 0.34
exp ±GeV
0.32SF,theo
 Theory errors from Lange, Neubert, Paz, hep-ph/0504071
m(X*)<used
1.7 a simulated annealing
4.08 ±technique
0.27exp ± hep-ex/0505088
 Last Belle
result
-1
Belle 253fb
0.25SF,theo
9 November 2005
-1
24
mX < 1.7, q2 > 8M. Morii, Harvard 4.38 ± 0.46exp ± PRL 92:101801
Status of Inclusive |Vub|
|Vub| world average as of Summer 2005

|Vub| determined to 7.6%
Statistical
2.2%
Expt. syst.
2.5%
b  cv model 1.9%
b  uv model 2.2%
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SF params.
4.7%
Theory
4.0%

The SF parameters can be
improved with b → s,
b  cv measurements

What’s the theory error?
25
Theory Errors

Quark-hadron duality is not considered
 b  cv and b → s data fit well with the HQE predictions

Weak annihilation  1.9% error
b
Expected to be <2% of the total rate
B
 Measure G(B0  Xuv)/G(B+  Xuv)
u
to improve the constraint
 Reduce the effect by rejecting the high-q2 region





g
Subleading Shape Function  3.5% error
Higher order non-perturbative corrections
 Cannot be constrained with b → s


Ultimate error on inclusive |Vub| may be ~5%
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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|
GF2
d G( B  p  )
2
3
2 2

Vub pp f  (q )
2
3
dq
24p
 f+(q2)

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
Preliminary B → pv FF from
Fermilab (hep-lat/0409116) and
HPQCD (hep-lat/0408019)
 Uncertainties are ~11%

Validity of the technique
LCSR*
remains controversial Fermilab

Important to measure HPQCD
dG(B → pv)/dq2 as a ISGW2
function of q2
 Compare with different
calculations
f+(q2) and f0(q2)

q2 (GeV2)

Measure dG(B → pv)/dq2
as a function of q2

Compare with different
calculations
*Ball-Zwicky PRD71:014015
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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
(1.35  0.08stat  0.08syst ) 104


8.4% precision
B(B0 → pv) [10-4]
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Untagged B → p


BABAR hep-ex/0507003
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.
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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
9 November 2005
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 0  p  
B  p 0 
soft p
p
D

v
p or K
data
MC signal
b  uv
b  cv
other bkg.
9 November 2005
M. Morii, Harvard
32
dB(B → p)/dq2

Measurements start to
constrain the q2 dependence


Errors on |Vub| dominated
by the FF normalization
9 November 2005
Vub
ISGW2 rejected
Partial BF measured to be
q2 range
DB [10−4]
< 16
GeV2
0.89 ± 0.06 ± 0.06
> 16
0.40 ± 0.04 ± 0.04
GeV2
3
2
(3.27  0.16expt 0.54
)

10
Ball-Zwicky
q
 16
0.36 FF

3
2
 (4.47  0.30expt 0.67
)

10
HPQCD
q
 16
FF
0.46

0.65
3
2
(3.78

0.25
)

10
Fermilab
q
 16
expt 0.43 FF

M. Morii, Harvard
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, hep-ph/0509090
9 November 2005
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
9 November 2005
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
9 November 2005
M. Morii, Harvard
36
|Vub| vs. the Unitarity Triangle

Fitting everything except for
|Vub|, CKMfitter Group finds
Exclusive
3
Vub CKM  (3.560.25
)

10
0.22

Inclusive
Inclusive average is
Vub incl.  (4.38  0.33) 103
2.0s off
 UTfit Group finds 2.8s


Not a serious conflict (yet)
Careful evaluation of theory errors
 Consistency between different calculations

9 November 2005
M. Morii, Harvard
37
Summary

Precise determination of |Vub| complements sin2b to test the
(in)completeness of the Standard Model
7.6% accuracy achieved so far  5% possible?
 Close collaboration between theory and experiment is crucial

 BABAR
and Belle will
pursue increasingly
precise measurements
over the next few years
b  Will the SM hold up?
B physics continues to offer exciting potential for discovering
(or constraining) New Physics beyond the Standard Model
9 November 2005
M. Morii, Harvard
38