B Physics Behond CP Violation
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Transcript B Physics Behond CP Violation
B Physics Beyond CP Violation
— Semileptonic B Decays —
Masahiro Morii
Harvard University
University of Pennsylvania High Energy Physics Seminar
17 January 2006
Outline
Introduction: Why semileptonic B decays?
CKM matrix — Unitarity Triangle — CP violation
|Vub| vs. sin2b
|Vub| from inclusive b → uv decays
Measurements: lepton energy, hadron mass, lepton-neutrino mass
Theoretical challenge: Shape Function
|Vub| from exclusive b → uv decays
Measurements: G(B → pv)
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
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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
33 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 33 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 cv 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
bc
bu
How accurately do we know this fraction?
Exclusive: Reconstruct final-state hadrons
B pv, B v, B wv, B v, …
E
2.31
2.64
Example: the rate for B pv 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 → Xv
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!
bc
bc
bu
bu
E
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bu
q2
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bc
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 cv
Data – bkgd.
(10-4)
5.72 ± 0.41stat ±
0.65sys
8.47 ± 0.37
1.53sys
MC signal
b uv
±
stat 3
cf. Total BF is ~210
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 uv
15
10
5
b cv
0.5
1
1.5
2
2.5
Cutting at shmax < mD2 removes b cv
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 → cv 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
92 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
Cannot be calculated by theory
Leading term is O(1/mb) instead
of O(1/mb2)
f (k )
0
We must determine the Shape Function
from experimental data
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k
M B mb
20
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
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Partial BF/bin (10-3)
Predict
partial BFs in
b → uv
Sum of exclusive
K*
BABAR
Exclusive Xs + measurement. Photon
energy determined from the Xs mass
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Extracting the Shape Function
Data are not (yet) precise enough to extract the SF from scratch
We must assume a few plausible functional forms
Example: f (k ) N (1 x) a e(1 a ) x ; x
k
First two moments of the SF are connected with the b-quark
mass mb and kinetic energy p2 (Neubert, PLB 612:13)
Can be determined from b → s and/or b cv decays
En from b → s,
E n and m Xn from b cv
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%
We’ve got the Shape Function
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Predicting b → u Spectra
Soft Collinear Effective Theory is
d 3 G( B X u )
used to predict the triple-differential rate:
2
A triple-diff. rate calculation
available since Spring 2005
Bosch, Lange, Neubert, Paz, NPB 699:335
Lange, Neubert, Paz, hep-ph/0504071
We use BLNP to extract |Vub|
Developed since 2001 by Bauer,
Fleming, Luke, Pirjol, Stewart
dE dmX dq
Lepton-energy
spectrum by
BLNP
New calculations are appearing
Aglietti, Ricciardi, Ferrera, hep-ph/0507285, 0509095, 0509271
Andersen, Gardi, hep-ph/0509360
Numerical comparison with BLNP will be done soon
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Avoiding the Shape Function
Possible to combine b uv and b → s so that the SF cancels
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 cv
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)
BABARAdjusted
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
25
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 cv model 1.9%
b uv model 2.2%
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SF params.
4.7%
Theory
4.0%
The SF parameters can be
improved with b → s,
b cv measurements
What’s the theory error?
26
Theory Errors
Quark-hadron duality is not considered
b cv 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 Xuv)/G(B+ Xuv)
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 → pv
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 → pv
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 → pv 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 → pv)/dq2 as a ISGW2
function of q2
Compare with different
calculations
f+(q2) and f0(q2)
q2 (GeV2)
Measure dG(B → pv)/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 ) 104
8.4% precision
B(B0 → pv) [10-4]
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Untagged B → p
BABAR PRD 72:051102
CLEO PRD 68:072003
Missing 4-momentum = neutrino
Reconstruct B → pv and calculate mB and DE = EB – Ebeam/2
BABAR
data
MC signal
signal with
wrong p
b uv
b cv
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 pv 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 uv
b cv
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
17 January 2006
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
0.46 FF
0.65
3
2
(3.78
0.25
)
10
Fermilab
q
16
expt
FF
0.43
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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
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How Things Mesh Together
b → s
Inclusive b → cv
E
E
SSFs
Shape
Function
HQE Fit
mb
Exclusive b → uv
E
Inclusive
b → uv
wv, v ?
FF
duality
WA
17 January 2006
B → pv
|Vub|
q2
mX
mX
LCSR
M. Morii, Harvard
LQCD
unquenching
36
The UT 2004 2005
Dramatic improvement in |Vub|!
sin2b went down slightly Overlap with |Vub/Vcb| smaller
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37
|Vub| vs. the Unitarity Triangle
Fitting everything except for
|Vub|, CKMfitter Group finds
Exclusive
3
Vub CKM (3.560.25
)
10
0.22
Inclusive
Inclusive average is
Vub incl. (4.38 0.33) 103
2.0s off
UTfit Group finds 2.8s
Not a serious conflict (yet)
Careful evaluation of theory errors
Consistency between different calculations
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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
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