Post on 21-Dec-2015
Inclusive B Decays - Spectra, Moments and
CKM Matrix Elements
Presented by Daniel Cronin-Hennessy
(CLEO Collaboration)
Feb 24, 2004
Outline
Motivation and discussion of moments Overview of CESR/CLEO
Moments Measurements and |Vcb| E spectrum in inclusive decays B Xs
MX2 spectrum in inclusive decays B Xc l
El spectrum in inclusive decays B Xc l
Extraction of |Vub| More from E spectrum and lepton energy endpoint (|Vub|)
Summary
Motivation
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cbcscd
ubusud
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' CKM matrix relates quark mass eigenstates to weak eigenstates
Fundamental Standard Model parameters. Must be measured.
Describes math of CP Violation.
May not describe observed matter- antimatter asymmetry.
OverviewCKM matrix relates quark mass eigenstates to weak eigenstates
Fundamental Standard Model parameters. Must be measured.
Describes math of CP Violation.
May not describe observed matter- antimatter asymmetry.
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Motivation
c
u
d
b c d u
b
W
b c Decay
• Still need QCD corrections• Perturbative
Hard gluon (Short distance)
s
• Non-Perturbative Soft gluon (Long distance) , 1 & 2
B D e
W
e
]D
c
B[b
Just right?
W
b c
u
d]
]DB[
B D
Very difficult
Not always 3-body
Gluons in final state.
Quark Motion
Rate of decay modifiedby motion of quark in B meson. b quark lives longer. ~p2/E2 ~ (.5/5)2
Challenges:
Quark Hidden
We know MB well. mb not so well.
Semileptonic Rate
3
522
192
||)()(
bqbF
bs
mVGqlbBRqlb
GoalRate of semileptonic decay of beauty quark CKM element(s)
HQET+OPE allows any inclusive observable to be written as a double expansion in powers of s and 1/MB:
HQET
O(1/M) energy of light degrees of freedom (MB ~ mb + )
O(1/M2)1 -momentum squared of b quark
2 hyperfine splitting (known from B/B* and D/D* M)
O(1/M3) ~(.5 GeV)3 from dimensional considerations
sl = |Vcb|2 (A(s,,os2)+B(s)/MB+ C1/MB
2+…)
1 combined with the sl measurements better |Vcb|2
)1
()(),(32
22
12
22
MO
ME
MD
MC
MBAObservable sss
Semileptonic Decay Width
sl (B Meson Semileptonic Decay Width) – Calculated from B meson branching fraction and lifetime
measurements (CLEO, CDF, BaBar, Belle …)– It is the first approximation to the b quarks decay width
)]/1(474.7185.3946.0648.11[192
||)3689.0()( 3
22
21
2
2
3
522
BBBBB
BcbFcs MO
MMMM
MVGlXB
Free quarkdecay width
b quark motion –increased b lifetime
M hyperfine splitting
)]/1(2
9
21[
192
||)( 3
22
21
3
522
Bbb
bubFus MOradiative
mm
mVGlXB
Observables
B Xs : 1st and 2nd moments of Photon energy
B Xc : 1st and 2nd moments of hadronic recoil mass
B Xc : lepton energy moments
Moments dxxfxMomentth )(0 0
How much is there? (area)
dxxfdxxfx
Momentnd)()(
22
How wide is it? (width)
dxxfdxxfx
Momentst)()(
11
Where is it? (mean)
b s Moments
)
1(
94
33
12
3313))(175.1954.01()(620.0385.01
2 47
222
34321
3212
02
0M
OCMM
C
MMM
mE
BBDBB
ss
B
ssb
)
1(
12
3
12
32))(05412.005083.0()(01024.000815.0
12 4321
3212
02
02
122
MO
MMMMMEE
BBB
ss
B
ss
BB
u, c, t
b s Moments
)
1(
94
33
12
3313))(175.1954.01()(620.0385.01
2 47
222
34321
3212
02
0M
OCMM
C
MMM
ME
BBDBB
ss
B
ssB
)
1(
12
3
12
32))(05412.005083.0()(01024.000815.0
12 4321
3212
02
02
122
MO
MMMMMEE
BBB
ss
B
ss
BB
u, c, t
b s Moments
)
1(
94
33
12
3313))(175.1954.01()(620.0385.01
2 47
222
34321
3212
02
0M
OCMM
C
MMM
ME
BBDBB
ss
B
ssB
)
1(
12
3
12
32))(05412.005083.0()(01024.000815.0
12 4321
3212
02
02
122
MO
MMMMMEE
BBB
ss
B
ss
BB
radiative tail
u, c, t
Hadronic Mass Moments
)( 22
MM DX
Monte Carlo model shown
Measure moments of recoil mass
D and D* well measured
Need to determine contribution to moments from high mass components
Details of resonances not included in parton level calculation
2
B D
B D*
B D** B D
B Xc
Strategy
At least two inclusive measurements needed in addition to the B branching fraction and B lifetime in order to extract Vcb.
Measure: 1st and 2nd moments of Photon energy (b s) 1st and 2nd moments of hadronic recoil mass (B Xc ) lepton energy moments (B Xc )
Many measurements are needed to verifyConvergence of ExpressionsQuark-Hadron Duality
LEPP
Cornell Electron-positron Storage Ring
~ ¾ km circumference
e+e- collisions
Ebeam: 1.5-5.6 GeV
Most data collected near (4S) resonance.
Operating Energies 2/3 data collected ON (4S)
e+e- (4S) BB ( ~ 1.0 nb) e+e- qq ( ~ 3.0 nb)
1/3 data collected OFF 60 MeV below Resonance Continuum only Almost perfect qq background sample
(4S)
CLEO
Photons: XtalCal (res=1.8%)
Electrons: XtalCal, Tracking
Muons: MuCh, Tracking
p K e : ToF+DeDx
HadronicMass Moments Want from B Xc but can not
use hadronic daughters
Reconstruct mass with B, , and four-vectors
)cos(2222 BBBBX PPEEMMM
EEMMM BBX 2~ 222
2XM
Xsmall unknown
Xc
Lepton: Select events with very high lepton momentum (1.5 GeV) above lower momentum secondaries (eg D decays)
Neutrino: Use all observed energy-momentum to calculate neutrino 4-vector fakes arise from non-interacting neutrals (Klong, secondary neutrinos, neutrons)
– Fit spectrum with• B D • B D*• B
XH(various models for XH)
– Find moments of true MX
2 spectrum
Hadronic Mass Moments
0.0620.0230.251)( 22 MM DX
163.0048.0576.0)(222 MM XX
PRL 87 251808, 2001
Hadronic Mass Moments
• If we believed the second moment expansion, we could get Vcb from this
• Use first moments from b s and hadronic b cinstead...
Photon Energy Moments Always require high
energy photon 2.0 < E < 2.7 GeV |cos | < 0.7
Naïve strategy: Measure E spectrum for ON and OFF resonance and subtract
But, must suppress huge continuum background![veto is not enough] and
Three attacks: Shape analysis Pseudoreconstruction Leptons
Hadronic Mass and Photon Energy
011.0032.0346.2 E
0020.00066.00226.022 EE
GeV
GeV 2
0.0620.0230.251)( 22 MM DX
163.0048.0576.0)(222 MM XX
GeV 2
GeV 4
CLEO
PRL 87 251807, 2001
Vcb
In MS scheme, at order 1/MB3
and s2o
= 0.35 + 0.07 + 0.10 GeV1= -.236 + 0.071 + 0.078 GeV2
|Vcb|=(4.04 + 0.09 + 0.05 + 0.08) 10-2
sl, 1 Theory
Lepton Energy Moments in B X l
Muons Electrons
5.1
7.1
0
dEdEd
dEdEd
Rl
l
sl
ll
sl
5.1
5.1
1
dEdEd
dEdEdE
Rl
l
sl
ll
sll
Unfolded Lepton Energy Spectrum
for leptons from B X l
R0 = 0.6187+0.0014 +0.0016
R1 = 1.7810+0.0007+0.0009 GeV
CLEOMeasure lepton energy
From energy spectrum:
PR D67 072001, 2003
Consistency Among
Observables and ellipse extracted from 1st moment
of B Xs photon energy spectrum and 1st moment of hadronic mass2 distribution(B Xc l). We use the HQET equations in MS scheme at order 1/MB
3 and s2 o.
Expressions: A. Falk, M. Luke, M. Savage, Z. Ligeti, A. Manohar, M. Wise, C. Bauer
The red and black curves are derived from the new CLEO results for B X l lepton energy moments. Expressions: M.Gremm, A. Kapustin, Z. Ligeti and M.
Wise, I. Stewart and I. Bigi, N.Uraltsev, A. Vainshtein
Gray band represents total uncertainty for the 2nd moment of photon energy spectrum.
CLEO
Consistency Among
Experiments
CLEO • BABAR Preliminary• CLEO
OPE (Falk, Luke), 1 free param.
OPE (Falk, Luke), 1 using CLEOs photon energy moment.
Interpretation of Data
• BABAR Preliminary• CLEO
OPE (Falk, Luke), 1 free param.
OPE (Falk, Luke), 1 using CLEOs photon energy moment.
Expect average hadronic mass to increase with lowering lepton momentum cut
Increase observed much larger than expected
Suspects
Heavy Quark Expansion
BaBar measurement(s)
CLEO measurement(s)
Repeat BaBar’s measurement (underway)Suspect photon energy moments
Did we miss a contribution at low photon energy?Need to have missed a strange quark state with high mass. Baryon (our Neural Networks were never informed of this possibility)
Mechanism for baryon production in B decay
Internal W Emission External W Emission
Di-quark popping providing a mechanism for baryon production in B semileptonic decays will also allow for the same in B radiative decays.
Limits on Baryon Production (External W Emission)
Br(BXs <3.8 x 10-5 90% CL(E>2.0 GeV , Xs containingBaryons )PR D68:011102, 2003
SemileptonicCase
RadiativeCase
Br(Bpe-X)< 5.9 x 10-4 90% CLPR D68:012004, 2003Strong Limit but not enough.
Recent Moments Results
Current standing from CLEO and BaBar. (Extrapolates well to DELPHI measurement)
Good agreement between analyses.
Tolerable agreement with theory.
Global Analysis: hep-ph/0210027 Bauer,Ligeti,Luke &
Manohar
|Vcb|=(4.08+0.09) 10-2
PR D67:054012, 2003
|Vub| from Lepton Endpoint (using b s )
|Vub| from b u– We measure the endpoint
yield– Large extrapolation to obtain |
Vub|
– High E cut leads to theoretical difficulties (we probe the part of spectrum most influenced by fermi momentum)
GOAL: Use b s to understand Fermi momentum and apply to b ufor improved measurement of |Vub|
Kagan-Neubert DeFazio-Neubert
Convolute with light cone shape function.
b s (parton level)
B Xs (hadron level)
B lightquark shape function, SAME (to lowest order in QCD/mb) for b s B Xs and b u l B Xu l.
b u l (parton level)
B Xu l (hadron level)
Fraction of b uspectrum above 2.2 is
0.13 ± 0.03
Method for partial inclusion of subleading corrections: Neubert
•Published
•With subleading corrections
Subleading corrections large C. Bauer, M. Luke, T. Mannel A. Leibovich, Z. Ligeti, M. Wise M.B. Voloshin
|Vub| from Lepton Endpoint (using b s )
|Vub| = (4.08 + 0.34 + 0.44 + 0.16 + 0.24)10-3
The 1st two errors are from experiment and 2nd from theory
PRL 88 231803 2002
CLEO
Summary Vcb: Bound state corrections to the semileptonic width, predicted
by HQET and measured by a number moments analyses have permitted the extraction of Vcb to a level of a few %.
The precision has a minimal impact on constrains but we can view as stringest test of HQE methods used for Vub.
Many new measurements now available (some overlapping) Recent measurements of hadronic mass moments with lower
cut on lepton momentum. More inclusive. Hints at trend that may be incompatible with theory but experimental and theoretical uncertainties are still large.
CLEO: Soon to publish lepton moments at lower lepton energy cut.
Enough data available for a global fit (with correlations properly accounted for). Need more input from theory on best method of including theory uncertainties.
Summary Vub: Important to reduce uncertainties for test of standard model
The photon energy spectrum in b s provides a
quantitative model for the bound state effects in b u l This approach has not yet reached its full potential We
expect improved measurements from B factories (in progress at CLEO).
Current work is to improve shape extraction particulalry at low photon energy
The method does require additional theoretical refinements. Can theory calculate differences in the b light quark
processes or provide reliable estimate of this difference.
Improved Photon Energy Spectrum
Original analysis optimized for Br Measurement.Motivation for improving spectrum particularly in the low photon energy region.
Backgrounds are numerous in low energy region. 0 electrons (with no track matching) anti-neutrons KLong
-More efficient 0/ veto -CC simulation of non-photon showers constrained by data
Calorimeter Lateral Shape
Improved Photon Energy Spectrum
Repeat entire analysis without a cut on the Calorimeter cluster shape.
MC does not model data well either dueto incorrect simulation of shower shape or wrong Klong and anti-neutron rates.
Improved Photon Energy Spectrum
Require enriched anti-neutron sample
Select events with L baryon if no anti-proton found look at “photons” in the event. The antineutron calorimeter responseis extracted from this sample.
B X l with Neutrino Reconstruction Neutrino four-momentum inferred from hermeticity of detector.
Maximum likelihood fit over full three dimensional decay distribution
Contributions from B Xc l(D,D*,D**and NR) and B Xu l
|Vub| =(4.05 + 0.18 + 0.58 + 0.25 + 0.21 + 0.56) 10-3
stat syst b->c b->u theory model model
Coswl q2 MX2
MX2<2.25 GeV2 Q2>11 GeV2
CLEO CONF 02-09ICHP02 ABS933
Preliminary
MX2<2.25 GeV2
Q2>11 GeV2
Inclusive B Decays
• CLEO II&IIV
37 M hadronic 9.7 M BB Pairs 3.8 M B Xc
34 k B Xu
7 k B Xs
• Observables
E EE 2
2XM )(
222
MM XX ELepton
Fraction Branching
Consistency Across Schemes- 1S Mass v.
MS and ellipse extracted from 1st moment of B Xs photon energy spectrum and 1st moment of hadronic mass2 distribution (B Xc l). We use the HQET equations in 1S scheme at order 1/MB
3 and s2 o.
1S Expressions(recent): C. Bauer, M. Trott (hep-ph/0205039) C. Bauer, A. Manohar, Z.Ligeti and M. Luke private communication
In 1S mass scheme, at order 1/MB
3
and s2o
|Vcb|=(4.05+0.09+0.04+0.10) 10-2
(recall MS: |Vcb|=(4.04+0.09+0.05+0.08) 10-2)
BaBar at ICHEP
• BABAR Preliminary• CLEO
OPE (Falk, Luke), 1 free param.
OPE (Falk, Luke), 1 using CLEOs photon energy moment.
DELPHI
0.0 0.4
0.534
)( 22
MM DX
Lepton Cut (GeV)
Inclusive?CLEO moments analysis reduce background withcuts on variables of interest (but no explicit mass cut on mass moments)
semileptonic: e.g. leptons from charm decay radiative: eg: photons from 0 decay model dependence of course but even more fundamental concerns
Assumption that the average value of observable is the same at the hadron and quark level relies on a truly inclusive analysis. Must lower cuts in all analyses.
BaBar (and later CLEO) measures mass moments with various lepton momentum cuts. Lower lepton momentum correlates with higher mass hadronic state. Moments expected to increase but how much?
Preliminary results indicate larger increases than expected if one uses the HQET parameter () derived from photon energy spectrum.
Moment CLEO DELPHI(prelim)
BABAR(prelim)
<m2H - m2
D> 0.251±0.023±0.062 (El>1.5GeV) 0.534±0.041±0.074 Later<(m2
H- <m2H>)2
>.576±0.048±0.163 (El > 1.5GeV) 1.23±0.16±0.15
<(m2H- <m2
H>)3
>2.97±0.67±0.48
<E 2.3460.032 0.011
(E E)2 0.02260.00660.0020
<E 1.7810+0.0007+0.0009 (El > 1.5 GeV)
1.3830.012 0.009
(E E)2 0.192 0.005 0.010
(E E)3 0.029 0.0050.005
R0 0.6187+0.0014 +0.0016 (El > 1.5 GeV)
Global Analysis: hep-ph/0210027 Bauer,Ligeti,Luke &
Manohar
Overview
VVVVVVVVV
tbtstd
cbcscd
ubusud
Unitarity
0*** VVVVVV tbtdcbcdubudVV tbtd
*
VV cbcd*
VV ubud*
Algebra
0,0
1,0
||
||
VV
cb
ub
CP
Moments Summary
CLEO has measured six moments, two each from 1) the photon energy distribution in B Xs
2) the hadronic mass2 distribution in B Xc l
3) most recently the lepton energy spectrum in B Xc l
The allowed values for HQET parameters and 1 are in agreement for all measurements.
|Vcb| extracted at the level of 3%