B Physics Beyond CP Violation — Semileptonic B Decays —
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Transcript of B Physics Beyond CP Violation — Semileptonic B Decays —
B Physics Beyond CP Violation
— Semileptonic B Decays —
Masahiro Morii
Harvard University
KEK Theory Group Seminar
15 November 2005
15 November 2005 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
|Vub| from exclusive b → uv decays Measurements: (B → v) Theoretical challenge: Form Factors
Summary
15 November 2005 M. Morii, Harvard 3
CKM Matrix Cabibbo-Kobayashi-Maskawa matrix connects the weak and
mass bases of the quarks
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
. .2
ud us ub
cd cs cb
td ts tb
L
L L L L
L
V V V
V V V
V V V
dg
u c t s W h c
b
L
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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
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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?
15 November 2005 M. Morii, Harvard 6
The Unitarity TriangleV†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
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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
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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
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
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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
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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
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)
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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!
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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 hep-ex/0509040Belle PLB 621:28
CLEO PRL 88:231803
BABAR
MC bkgd.b cv
Data
Data – bkgd.
MC signalb uv
cf. Total BF is ~2103
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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
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Measuring mX and q2
Must reconstruct all decay products to measure mX or q2
E was much easier
Select events with a fully-reconstructed B meson 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 (mX) = 350 MeV
4-momentum conservation; equal mB on both sides; mmiss = 0
Fully reconstructedB hadrons
lepton
v
X
BABAR hep-ex/0507017Belle hep-ex/0505088
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Measuring Partial BF Suppress b → cv by vetoing against D(*) decays
Reject events with K Reject events with B0 → D*+(→ D0+)−v
Measure the partial BF in regions of (mX, q2) For example: mX < 1.7 GeV and q2 > 8 GeV2
BABAR hep-ex/0507017Belle hep-ex/0505088
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Partial BF Results
P+ = EX |PX| is a theoretically clean variable Bosch, Lange, Neubert, Paz
PRL 93:221802
Efficiency high Signal vs. background
separation is limited
BABAR hep-ex/0507017Belle hep-ex/0505088
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
Belle
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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
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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 (1/mb) instead of (1/mb
2)
k
( )f k
B bM m
Rough features (mean, r.m.s.) are known
Details, especially the tail, are unknown
0
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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 hep-ex/0507001, 0508004Belle 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*
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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:
New calculation connect the SF moments with the b-quark mass mb and kinetic energy
2 (Neubert, PLB 612:13) Determined precisely from b → sand b cv decays
from b → sand from b cv
Fit data from BABAR, Belle, CLEO, DELPHI, CDF
NB: mb is determined to better than 1%
Determine the SF
(1 )( ) (1 ) ;a a x kf k N x e x
nEnE
nXm
2 2(4.60 0.04)GeV, (0.20 0.04)GeVbm
Buchmüller & Flächerhep-ph/0507253
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Predicting b → u Spectra OPE + SF can predict triple-differential rate
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 → uv by several groups
A triple-diff. rate calculationavailable since Spring 2005 Bosch, Lange, Neubert, Paz, NPB 699:335 Lange, Neubert, Paz, hep-ph/0504071
BABAR and Belle use BLNP toextract |Vub| in the latest results
3
2
( )u
X
d B X
dE dm dq
Lepton-energyspectrum by
BLNP
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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 uv and b → s without going through the SF
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
2
2 ( )( )
( ) ub su
ts
W EV d B X
B X dEdEV
Weight function
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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 4.39 ± 0.25exp ± 0.32SF,theohep-ex/0509040
Belle 27fb-1 E > 1.9 4.82 ± 0.45exp ± 0.31SF,theoPLB 621:28
CLEO 9fb-1 E > 2.2 4.02 ± 0.47exp ± 0.35SF,theoPRL 88:231803
BABAR 80fb-1 E > 2.0, shmax < 3.5 4.06 ± 0.27exp ± 0.36SF,theo
PRL 95:111801
BABAR 211fb-1 mX < 1.7, q2 > 8 4.76 ± 0.34exp ± 0.32SF,theohep-ex/0507017
Belle 253fb-1 mX < 1.7 4.08 ± 0.27exp ± 0.25SF,theohep-ex/0505088
Belle 87fb-1* mX < 1.7, q2 > 8 4.38 ± 0.46exp ± 0.30SF,theoPRL 92:101801
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Status of Inclusive |Vub|
|Vub| determined to 7.6%
The SF parameters can be improved with b → sb cv measurements
What’s the theory error?
|Vub| world average as of Summer 2005
Statistical 2.2%
Expt. syst. 2.5%
b cv model 1.9%
b uv model 2.2%
SF params. 4.7%
Theory4.0
%
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Theory Errors Quark-hadron duality is not considered
b cv and b → sdata fit well with the HQE predictions Weak annihilation 1.9% error
Expected to be <2% of the total rate Measure (B0 Xuv)/(B+ Xuv)
to improve the constraint Reduce the effect by rejecting the high-q2 region
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%
b
u
B
g
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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
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Form Factor Calculations Unquenched LQCD calculations started to appear in 2004
Preliminary B → v FF fromFermilab (hep-lat/0409116) andHPQCD (hep-lat/0408019)
Uncertainties are ~11% Validity of the technique
remains controversial Important to measure
d(B → v)/dq2 as afunction of q2 Compare with differentcalculations
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
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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
15 November 2005 M. Morii, Harvard 29
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 hep-ex/0507003CLEO PRD 68:072003
15 November 2005 M. Morii, Harvard 30
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
15 November 2005 M. Morii, Harvard 31
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
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d(B → )/dq2
Measurements start to constrain the q2 dependence ISGW2 rejected
Partial BF measured to be
q2 range [10−4]
< 16 GeV2 0.89 ± 0.06 ± 0.06
> 16 GeV2 0.40 ± 0.04 ± 0.04
3 2expt FF
3 2expt FF
3 2expt FF
0.540.360.670.460.650.43
(3.27 0.16 ) 10 Ball-Zwicky 16
(4.47 0.30 ) 10 HPQCD 16
(3.78 0.25 ) 10 Fermilab 16
ub
q
V q
q
Errors on |Vub| dominated by the FF normalization
15 November 2005 M. Morii, Harvard 33
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, hep-ph/0509090
15 November 2005 M. Morii, Harvard 34
Exclusive b → uv
How Things Mesh Together
B → vInclusiveb → uv
mX-q2 v, v ?
b → s
ShapeFunction
E
mb
Inclusive b → cv
mXE
HQE Fit
mX
E
WA
duality
|Vub|
SSFs
FF
LCSRLQCD
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The UT 2004 2005
Dramatic improvement in |Vub|!
sin2 went down slightly Overlap with |Vub/Vcb| smaller
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|Vub| vs. the Unitarity Triangle
Fitting everything except for|Vub|, CKMfitter Group finds
Inclusive average is
2.0 off UTfit Group finds 2.8
Not a serious conflict (yet) We keep watch Careful evaluation of theory errors Consistency between different methods
3
CKM
0.250.22(3.56 ) 10ubV
3
incl.(4.38 0.33) 10ubV
Inclusive
Exclusive
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Summary Precise determination of |Vub| complements sin2 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 Rapid progress in inclusive |Vub| in the last 2 years
Improvement in B → form factor is needed
|Vub |