Transcript B Physics Behond CP Violation

B Physics Beyond CP Violation
— Semileptonic B Decays —
Masahiro Morii
Harvard University
KEK Theory Group Seminar
15 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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CKM Matrix

Cabibbo-Kobayashi-Maskawa matrix connects the weak and
mass bases of the quarks
 Vud Vus Vub   d L 
g
  
 
L 
u
c
t

V
V
V
 L L L   cd cs cb   sL W  h.c.
2
V V V  b 
ts
tb   L 
 td

We don’t know the origin of the EW symmetry breaking
 Fermion masses and the CKM matrix are inputs to the SM


We are looking for the Higgs particle at the Tevatron, and at the LHC
in the future
Unlike the fermion masses, the CKM matrix contains more
measurable quantities than the number of degrees of freedom
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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
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?
E
Exclusive: Reconstruct final-state hadrons
 B  pv, B  v, B  wv, B  v, …

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
11
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
12
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
18
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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Next in Theory of Inclusive |Vub|

New calculations of partial BFs are appearing

Aglietti, Ricciardi, Ferrera, hep-ph/0507285, 0509095, 0509271
Andersen, Gardi, hep-ph/0509360

Numerical comparison with BLNP will be done soon


Combine b  uv and b → s without going through the SF
G( B  X u  ) 
Vub
Vts
2
2
 W ( E )
d G( B  X s  )
dE
dE
Weight function

Leibovich, Low, Rothstein, PLB 486:86
Lange, Neubert, Paz, hep-ph/0508178
Lange, hep-ph/0511098

No need to assume functional forms for the Shape Function


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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
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-1
23
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?
24
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)

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
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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.
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dB(B → p)/dq2

Measurements start to
constrain the q2 dependence


Errors on |Vub| dominated
by the FF normalization
15 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

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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
15 November 2005
M. Morii, Harvard
33
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
15 November 2005
B → pv
|Vub|
mX
mX-q2
mX
LQCD
M. Morii, Harvard
LCSR
34
The UT 2004  2005


Dramatic improvement in |Vub|!
sin2b went down slightly  Overlap with |Vub/Vcb| smaller
15 November 2005
M. Morii, Harvard
35
|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 average is
Inclusive
Vub incl.  (4.38  0.33) 103
2.0s off
 UTfit Group finds 2.8s


Not a serious conflict (yet)
We keep watch
 Careful evaluation of theory errors
 Consistency between different methods

15 November 2005
M. Morii, Harvard
36
Summary

Precise determination of |Vub| complements sin2b to test the
(in)completeness of the Standard Model

7.6% 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

15 November 2005
M. Morii, Harvard
37