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Precise Determination of |Vcb|, |Vub|, and the b-quark mass from
inclusive B decays
• |Vcb| at the ~1% level - The new BABAR result as an example•Towards a ~5% measurement of |Vub| - what can we lean from bcl and bs•bs and its senitivity to „new physics“- how tight are the constraints really?
• |Vcb| at the ~1% level - The new BABAR result as an example•Towards a ~5% measurement of |Vub| - what can we lean from bcl and bs•bs and its senitivity to „new physics“- how tight are the constraints really?DESY TUESDAY SEMINAR
21/09/2004
Oliver Buchmüller CERN
2 Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
CP Violation in the Standard Model(SM)
CKM Matrix
Unitarität
The elements of the CKM matrix
are the only source of CP violationin the SM
The area of the triangle is proportionalto the CP violation in the SM
Measurements of the angles and sides of the triangleMeasurements of the angles and sides of the trianglerepresent a fundamental test of the SM!represent a fundamental test of the SM!
N(q)/N(anti-q) ~ 10N(q)/N(anti-q) ~ 10-20-20
much to small!much to small!
The expected size of CP violation in the SM is much too small The expected size of CP violation in the SM is much too small to explain N(q)/N(anti-q)~10to explain N(q)/N(anti-q)~10-9-9
3 Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
The sides of the triangleThe sides of the triangle
ikjkijVV δ=*
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
tbtstd
cbcscd
ubusud
CKM
VVV
VVV
VVV
V
0*** =++ tbtdcbcdubud VVVVVV
01*
*
*
*
=++cbcd
tbtd
cbcd
ubud
VVVV
VVVV
|Vub/Vcb| describes a circle in the (,) plane
A measurement of a length of a triangle is as good as a measurement of A measurement of a length of a triangle is as good as a measurement of an angle!an angle!
4 Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
The Trinagle Today
sin2sin2 has become a has become aprecision measurement precision measurement
and is now the best know and is now the best know quantity of the triangle!quantity of the triangle!
If we want to sufficiently over constrain the triangle we need to improveIf we want to sufficiently over constrain the triangle we need to improvethe other measurements as well!the other measurements as well!
|Vcb| and |Vub|
5 Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
|Vcb| und |Vub| from semilleptonic B decays
Why semileptonic B decyas?
BXl mit l=e,bcl
No „colour activity“between
W l and c quark
b
cW
1. For |Vxb| we need to have a bx transition (trivial)2. Need a precise theoretical framework to translate the measurements on “meson level” into “quark level” (not trivial)
semileptonic decays are theoretical semileptonic decays are theoretical necessity! necessity!
6 Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
The Inclusive ApproachThe Inclusive ApproachThe advantage of being inclusive! QCD«mb : inclusive decays admit systematic expansion in QCD/mb Non-pert corrections are generally small and can be controlled
Hadronization probability =1, approximately insensitive to details of meson structure as QCD«mb (at least far from perturbative
singularities)
02
2
dqdqdE
d
l
Γ can be expressed as double series in s s and and QCD/mb
(OPE) with parton model as leading term No 1/mb
correction!
7 Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
The Heavy Quark Expansion (HQE)The Heavy Quark Expansion (HQE)
•Short-distance physics encoded in coefficients of operator products(to some order in s). Calculable!
•Long-distance physics encoded in exp. values of products of quark operators (to some order in 1/mb). NOT calculable! Must be determined empirically.
Need to get access to the not very well know HQE parameters!Need to get access to the not very well know HQE parameters!
8 Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Access to the HQE ParameterThe HQE not only predicts the inclusive decay rates but also inclusive
differential decay distributions for semileptonic decays (e.g. moments of the lepton energy spectrum).
Measure (a lot) moments of inclusive kinematic distributions
Extract HQE parameters (e.g. mb) from a fit to all moments
Compare predicted inclusive decay rate with its measurement Γsl = Γsl (B, BRsl)
|Vcb|
9 Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Pioneering Work
M1(Mx) M2(Mx) M3(Mx)
M1(E) M2(E) M3(E)
mb,kin(GeV= 4.58 +0.06fit+0.05sys
GeVmc,kin(GeV= 1.15 +0.09fit+0.08sys
GeV
2 (GeV= 0.41 +0.04fit+0.04sys GeV2
D3 (GeV= 0.05 +0.02fit+0.01sys
GeV3
Input constraints: mb= 4.57 0.10 GeV mc= 1.05 0.30 GeV
DELPHI CLEO
Multi parameter fits to moments but sensitivity was limited …
10
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
The B Factory BABAR and PEPII
LINAC
BABAR
SLD
11
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
BABAR AND PEPII
9 GeV
3.1 GeV
e+e- 4s(10.58 GeV) BB (96%, 4% non-BB)
4s(10.58 GeV)
BB production threshold
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
A Tough Race
RUNI
RUNII
RUNIII
RUNIV
Competition is important:Both B factories perform very well (15/06/2004) BABAR 227 fb-1
BELLE 275 fb-1 500 fb-1
Better than expectedand gives hope for the future.
(ca. 550 Mio BB events)
BABAR results of this talk are based on 82 fb-1
ca. 90 Mio BB events
13
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Semileptonic B Events: Access to Vcb and Vub
A theoretical necessity …A theoretical necessity …
Vcb
b c
W
(Vub)
“Tree Level”“Detector Level”
No color interaction between W and c-quark
“CKM Matrix”
… … but an experimental challenge!but an experimental challenge!
DD**
ll
ee--
ee++
BBrecoreco
BBrecoilrecoil
XXcc
νν
Need to fully reconstruct the Need to fully reconstruct the semileptonic B Event in ordersemileptonic B Event in order to get access to the kinematicto get access to the kinematic
information of the signal B decayinformation of the signal B decay“Neutrino Reconstruction”
14
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Kinematic of Semileptonic B Events
Reco. B:4 measured quantities
X-System4 gemessene
Größen(e.g. Mx )
Lepton3 measured quantities(e.g. El)
Energy and Momentum ConservationEnergy and Momentum Conservation
Ebreco + EX + El + E - EPEPII = 0
Pbreco + PX + Pl + P - PPEPII = 0
4 Constraints
+ Mass Constraint+ Mass Constraint
M(Breco)=M(X,l,)
+ 1 Constraint
Neutrino3 unmeasured quantities
5 Constarints – 3 unmeasured quantities =
2 times overconstraint System„2C kinematic fit“
Use fulll reconstructed B sample:„Tag“ B is full reconstructed and
the signal B is identified via the lepton.
Pe-Pe+
Incomming momentum of the two beams are well measured
(EPEPII ,PPEPII) bekannt!
full reconstruction of the entire semileptonic event (especially Mx und El)
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
1. Fully reconstructed hadronic B-decay2. Semileptonic decay of other B
o Identify Lepton (e or )o reaming tracks and neutral objects define the X-System
3. Mx determined by 2C kinematic fit
4. Sideband subtraction of the combinatoral B background
.
Hadron Moments <Mxn>
,e
,e
(*)D
K
2/350)( cMeVMx ≈σ
signalbackgroundK
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 mES[GeV/c2]
225020001750150012501000750500250
0
Eve
nts
/ 1.8
MeV
/c2
SLBrecBBABAR Y(4S)
24 recBs
ES pm −=
7114 signal events,2102 combinatoral bg.
Out of 90 Mio BB events!
HX
high mass final states
Mx2[GeV2/c4]
16
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Lepton Moments <ELn>
BABAR
eesigsig
ee--
ee++
BBtagtag
BBsigsig
νν
eetagtag
“e+e-” unlike sign
“e±e” like sign
“double lepton tag”
Subtract irreducible bg. and unfoldthe number of primary electrons from the
two samples (“ARGUS method”).
Select events withtwo identified electrons:
e+e- and e±e
Unfolded primary electron spectrum for BXl
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
<Mx> (ELCUT) and
<EL>(ELCUT)
Measure moments over a large rage in phase space
as function of a cut in the lepton energy
A cut in the lepton energy will restrict the phase space for high mass states production (D**, D*).
Thus <Mx> (ELCUT) and <EL>(EL
CUT) will probethe underlying “decay dynamic” of BXcl events.
Mx
Mx
High mass states
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
<Mx> (ELCUT) and
<EL>(ELCUT)
)( eXBBr c→ ( )2ee EE − ( )3ee EE −eE
Incr
ease
of t
he m
ean
Decrease of truncated BR
BABAR BABAR BABAR BABAR
EcutEcut EcutEcut
Phys.Rev.D69:111103,2004
Phys.Rev.D69:111104,2004
Reduction of high mass final states
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
HQE Fit
=/)( 00 EM l )( eXBBr c→B/= 3322
DLSGcb mm ),,,,,,( 0E)( eXBBr c→ lΓf
2|| cbV
),( 0EEeXBBr lc >→ i-th central El moment for El>E0:
i-th Mx moment and El>E0 :
|Vcb| „master“ formula : : l
0f3322DLSGcb mm ),,,,,,( 0E
)4..1()(
)3..1()(
0
0
==
==
iEM
iEMXi
il l
ifX
if
3322DLSGcb mm ),,,,,,( 0E3322DLSGcb mm ),,,,,,( 0E
Use dedicated HQE for every measured observable:Γclv (BR, lifetime)Hadron Mass Moments <Mx
n>(Ecut)Lepton Energy Moments <El
n>(Ecut)(Fit parameters are in red)
i-th E moment and E>E0 : l
0f3322DLSGcb mm ),,,,,,( 0E From BXs
Extract the HQE parameter mb,mc,2,G
2, D3, LS
3 and |Vcb| as well as BRclv from a simultaneous fit to all moment measurements (27+1*).
Experimental and theoretical errors and their correlations are all accounted for in the fit.* Only external input to the fit is:
B lifetime B+B0 =1.6080012 ps
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Combined Fit to Ee and Mx
Moments =/)( 00 EM l )( eXBBr c→
B/= 3322DLSGcb mm ),,,,,,( 0E)( eXBBr c→ l
Γf2|| cbV
),( 0EEeXBBr lc >→ i-th central El moment for El>E0:
i-th Mx moment and El>E0 :
|Vcb| „master“ formula : : l
0f3322DLSGcb mm ),,,,,,( 0E
)4..1()(
)3..1()(
0
0
==
==
iEM
iEMXi
il l
ifX
if
3322DLSGcb mm ),,,,,,( 0E3322DLSGcb mm ),,,,,,( 0E
Calculations taken from Gambino and Uraltsev, hep/ph 0401063
xf1xf2
xf3 xf4
SLBf ×l0
l1f
l2f
l3f
high correlationbetweenmeasurements : this fit uses solid points only
)20ndof(0.152 ==χ
21
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Fit Results
Strong correlation between mb and mc:
mb(1 GeV) – mc(1 GeV) = (3.44±0.03exp±0.02HQE±0.01αs
) GeVkine
tic
mas
s sc
hem
e
GeVGeVm
GeVGeVm
eXBBr
V
c
b
c
cb s
)02.006.007.018.1()1(
)02.004.005.061.4()1(
)%06.016.061.10()(
10)6.02.04.04.04.41(||
s
s
SL
HQEexp
HQEexp
HQEexp
3HQEexp
±±±=±±±=
±±=→×±±±±= −
Γ
Phys. Rev. Lett.93:011803,2004hep-ex/0404017
BABAR BABAR
χ2=1 ellipses
2D projections of the fit result:
BABAR
22
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
|Vcb| and BR(BXl)
But comparison is not on “equal footing”because the input (e.g. B lifetime and BR ) as well as the theoretical error assumption
are not the same job of HFAG
A better comparison is the total semileptonic BR.
The from the HQE Fit extracted BRis roughly 30% more accurate than
the HFAG average.sets roughly the scale of improvement
23
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
b-quark and c-quark mass
Conversion from kinetic mass scheme to MS scheme with hep-ph/9708372, hep-ph/0302262
See also report from CKM WS hep-ph/0304132
mc(mc) = 1.33 ± 0.10 GeVmb(mb) = 4.22 ± 0.06 GeV BABAR
24
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
New Moment Measurements
ICHEP04 has surprised us with a lot more moment measurementsfrom various collaborations:
BABAR:•hep-ex/0403031 (Phys.Rev.D69,2004) Hadron Moments from semileptonic B decays•hep-ex/0403030 (Phys.Rev.D69,2004) Lepton Moments from semileptonic B decays
BELLE:•hep-ex/0408139 (preliminary) Hadron Moments from semileptonic B decays•hep-ex/0409015 (preliminary) Lepton Moments from semileptonic B decays•hep-ex/0403004 (Phys.Rev.Lett.93,2004) Photon Energy Moments from BBXXss decays decays
CDF:•http://www-cdf.fnal.gov/physics/new/bottom/040428.blessed-bhadr-moments/ Hadron Moments from semileptonic B decays
CLEO:•hep-ex/0403052 (Phys.Rev.D70:,2004) Hadron Moments from semileptonic B decays•hep-ex/0403053 (Phys.Rev.D70:,2004) Lepton Moments from semileptonic B decays•hep-ex/0108032 (Phys.Rev.Lett.87,2001) Photon Energy Moments from BBXXss decays decays DELPHI:•hep-ex/0210046 Hadron Moments from semileptonic B decays•hep-ex/0210046 Lepton Moments from semileptonic B decays
More than 100 single moment measurements! perfect playground for consistency tests …
25
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Include Additional Moments in the HQE Fit
BABAR moments only All Momentsχ2/NDF 0.75 0.55|Vcb|x10-3 41.390.59(0.62) 41.380.45(0.62) mb [GeV] 4.6110.067 4.6100.053mc [GeV] 1.180.09 1.170.08BRclv [%] 10.610.17 10.640.14
Very consistent results and the inclusion of the additionalVery consistent results and the inclusion of the additionalmoments leads to significant improvements of the extractedmoments leads to significant improvements of the extracted
fit parameters (e.g. mfit parameters (e.g. mbb ~25%) ~25%)
Include all moment measurements in the fit that are givenwith a full covariance matrix.
Use the extracted HQE parameters as base for the theoretical predictions!
26
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Comparison: Hadron Moments
Y-a
xis:
HQ
E p
red
icti
on
- M
easu
rem
en
t
Best fit
Total Error
Exp. Error
Very good agreement!
Also the moments notincluded in the fit agree
well with the HQE predictionbased on the fit results!
27
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Comparison: Lepton Moments
Y-a
xis:
HQ
E p
red
icti
on
- M
easu
rem
en
t
Very good agreementfor lepton momentsfrom BABAR, BELLE
and DELPHI.
Under investigation.Under investigation. Need to properly take into
account common systematics, all correlations, etc …
but looks like a ~3σ difference
Keep in mined that the moments are highly correlate.Typical between the two extreme values is ~50%
Best fit
Total Error
Exp. Error
But the results from CLEO fit not too well …
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Comparison with other (independent) determinations
In hep-ph/0408002 Bauer et al. have carried out an independent |Vcb|determination based on calculations in the 1s scheme (and other schemes).
mb, mc
Leading orderdefined in different schemes
(2, G
2)
1,2
O(1/mb2)
&
(D3, LS
3)
1,2O(1/mb
3)
& Gremm,Kapustin
A simultaneous fit to all data yields: (hep-ph/0408002 - 1s scheme)
|Vcb|=41.90.6(fit)0.1(B) x10-3
mb1s =4.680.4(fit) GeV
1 =-0.230.06(fit) GeV2
(our results - kinetic scheme) |Vcb|=41.40.5(fit) [0.6(theo)] x10-3
mbkin =4.610.5(fit) GeV
2
=0.400.04(fit) GeV2
Comparison:
2 = -1 + O(s) -1 + 0.17 GeV2
translate mb into MS: mb(mb) — —
|Vcb|: 41.9 vs.. 41.4 [x10-
3] 0.4 vs. 0.4 [GeV2] 4.19 vs. 4.22 [GeV]
Leading HQE parameters are consistent but |Vcb| differs by 1.2% - - too much?
29
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Inclusive |Vcb|
• Moment measurements from various experiments as well as improved theoretical calculations in the HQE framework allow the extraction of the O(1/mb
3) parameters without any external constraints. Example BABAR analysis:
GeVGeVm
GeVGeVm
eXBBr
V
c
b
c
cb s
)02.006.007.018.1()1(
)02.004.005.061.4()1(
)%06.016.061.10()(
10)6.02.04.04.04.41(||
s
s
SL
HQEexp
HQEexp
HQEexp
3HQEexp
±±±=±±±=
±±=→×±±±±= −
Γ Phys. Rev. Lett,2004hep-ex/0404017
Orhep-ph/0408002
1S scheme Bauer et al.
The determination of |Vcb| from inclusively defined moments of semileptonic kinematic distributions has entered the phase of a
precision measurement.
Still a few outstanding issues:•Consistency of CLEO lepton moments•Compatibility of extracted |Vcb| values (inconsistently applied QED corrections?!)•Uncertainty of calculations for the non-integer moment <Mx> and <Mx3>
>2% measurement of |Vcb| + extraction of all HQE parameters to O(1/mb
3)
But the general picture looks very encouraging ….
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Unitarity Triangle and |Vcb|
What have we learned … 5% vs. 2%What have we learned … 5% vs. 2%
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
|Vub| today… and its (current) limitations
|Vub| has crossed the ~10% error barrier!Already quite an accomplishment but we
want more (target ~5% error)
Error Budget|Vub| |Vub| [0.09(exp) 0.1(SF) 0.05(HQE)]
10% - experimental error:With increasing statistic BABAR and BELLE will be able to significantly improve this error!
10% - “shape function” error:Limited knowledge of the shape function leads to the largest theoretical uncertainty. Currently the shape function parameter are obtained from the BELLE photon energy spectrum from bs
5% - “HQE” error:OPE based translation of the measured Brulv
into |vub|. The limiting factor is the uncertainty of the b quark mass!
Need to work hard on the extractionNeed to work hard on the extractionof the shape function parameter and of the shape function parameter and
a better determination of ma better determination of mbb
32
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Photon Energy SpectrumBesides “new physics” the radiative penguin decay bs probes also very important SM quantities such as the b-quark mass and the “Fermi motion”.
s
b
bs
<E> mb
<(E-<E>)2 > Fermi Motion (
2)
Heavy Quark Limit mb
8
<E> =mb/2 and <(E-<E>)2 >= 2/12
Probes directly mb while bcl is most sensitive to mb-mc
Gives access to the shape function (b quark distribution function) for the heavy to light quark transition
Complementary information to semileptonic decays
33
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
The experimental challenge
Schnitt
bsBR ~ 10-4
BBudsc
Before all cuts After almost all selection cuts
The very difficult background situation requires a lower cut on the photon energy to measure relevant quantities like BRbs or the moments of the spectrum.
How far can we go down …?
34
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
The Measured Spectrum BELLE 2004 CLEO 2001
E>1.8 GeV
E>2.0 GeV
Ecut=1.8 GeV: BELLE
<E> =2.292 0.043 GeV<E
2> - <E>2 =0.0305 0.0100 GeV2
Ecut=2.0 GeV: CLEO
<E> =2.346 0.034 GeV<E
2> - <E>2 =0.0226 0.0070 GeV2
35
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Shape Function ParameterThe shape function from bs and bul are related and it is possible
to use the photon energy spectrum to extract the shape function parametervalid for bul decays (Caveat: 1/mb corrections)
HFAG: Use the BELLE photon energy spectrum to determinethe shape function (hep-ex/0407052)
Fit true underlying photon spectrum via a Monte Carlo simulation to the measured
spectrum (similar to an unfolding)
36
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
HQE Prediction for <E> and <(E-<E>)2 >
New HQE calculation from Benson, Bigi and Uraltsevin the kinetic scheme [O(1/mb
3); O()] (soon to be published)(soon to be published)
Comparable to those for clv moments.
l0f
3322DLSGcb mm ),,,,,,( 0E i-th E moment and E>E0 :
Caveat: For tight cutoffs the expansion scale QMB-2E
cut(“hardness”) becomes to small for a reliable 1/Q expansion Bias in the leading HQE parameters mb am
2
Benson et al provide alsopredictions for the bias effect
as a function of the cutoffExpected bias at 2E
cut=2.0 GeV:δmb 40 MeV ; δ
2 0.1 GeV2
In the following consider both scenarios:1. HQE prediction only2. HQE prediction & bias correction
37
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Consistency between bs and b clUse extracted HQE parameters from the clv moment fit to predict the moments of the photon energy spectrum.
“HQE only” “bias corrected HQE”Moment measurements agree wellwith HQE prediction obtained from
the clv moment fit. Evidence that bias correction is
needed for moments above E>1.8 GeV
But we can do more …Use the shape function parameter
which ft the BELLE spectrum to obtainthe moments as a function of the cut.
(Test: agrees nicely at E=1.8 GeV with the
direct measurement from BELLE)
Remarkable agreement withHQE prediction
Strong evidence, especially from the second moment, that bias corrections are needed above above E>1.8 GeV.
38
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
What can we learn from this?
1. The HQE parameter extracted from b cl events are the same as the one obtained from b s events (e.g. mb
from clv=mbfrom s)
We can use the enormous potential of our clv momentmeasurements to predict the moments of the photon energy
spectrum and to extract the shape function parameter from it!… very important for |Vub|
2. There is compelling evidence that for E>1.8 GeV the HQE prediction have to be bias corrected
(as claimed in hep-ph/0308165)We need more moment measurements as a function of E to
to established this bias effect … but the current evidence is already strong.
39
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Moment Predictions
Ecut=1.8 GeV:
<E> =2.312 0.024 GeV<E
2> - <E>2 =0.0329 0.0026 GeV2
Ecut=2.0 GeV:
<E> =2.341 0.025 GeV<E
2> - <E>2 =0.0222 0.0024 GeV2
Ecut=1.8 GeV: BELLE
<E> =2.292 0.043 GeV<E
2> - <E>2 =0.0305 0.0100 GeV2
Ecut=2.0 GeV: CLEO
<E> =2.346 0.034 GeV<E
2> - <E>2 =0.0226 0.0070 GeV2
Experimental ResultsPredictions for the HQE fitbased on cl moments
The HQE fit results would constrain the moments of the photonenergy spectrum by a factor ~2 better than the current experimental
measurements. Using this information for the extractionof the shape function parameters will significantly improve
the theoretical uncertainties on Vub!
|Vub| |Vub| [0.09(exp) 0.05(SF) 0.04(HQE)]
|Vub| |Vub| [0.09(exp) 0.1(SF) 0.05(HQE)]Getting much closer to a 5% theoretical error
40
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Unitarity Triangle - The Future?!
Vcb ~ 1% and Vub ~5%(theo) 5% (exp)Vcb ~ 1% and Vub ~5%(theo) 5% (exp)
41
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
bs: very sensitive to “new physics”
b
s
“New physics” can contribute in the loop …
…and would lead to an increase of BR(bs)
Tight constraints on “new physics parameter” which are especially important for the search at the LHC/LC.
42
Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
BR(BXs) TodaySlide from the ICHEP04 Plenary Talk of Ahmed Ali (DESY). BRHFAG=3.540.3
BRSM =3.700.3
However, a new paper (hep-ph/0408179)from M. Neubert claims that
perturbative uncertainties have beenunderestimated in the theoretical
calculations of BRSM:
BRSM0.6
100% increase of the uncertaintyfor the SM prediction!
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Potential Impact on “New Physics” Constraints
tan
BR(bs)MH
ICHEP2004
BR(bs)
BR
(b
s)
Since the bs decay is very sensitiveto certain contributions from „new physics“
a significant incraese of thetheoretical uncertainties would softena lot of rather tight (indirect) limits on
„new physics“ processes (e.g. 2HDM).
For illustrative purpose only - the TYPEII Two Higgs Doublet Model
0.65
200
Neubert - hep/ph 0408179
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
How can we validate the prediction?
hep-ph/0408179
According to hep-ph/0408179, also the prediction of the first moment of the photon energy spectrum <E>must suffer from large perturbative uncertainties:
<E> ~0.06 GeV (mb~ 120 MeV)
The prediction from hep-ph/0408179 are compatible with the data (E=[1.6,2.0]) but the HQE prediction in the kinetic scheme from Bigi et al. describe the data over the entire
cut range much better than the claimed <E> ~0.06 GeV (mb~ 120 MeV).
Evidence that perturbative (and non-perturbative) uncertainties are under control?
In any case, the multitude of moment measurements represent a tool to scrutinize the prediction power of the theory important for bs and its sensitivity to new physics.
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
TodayToday2007?2007?
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
BACKUP - UT Fits
----------------------------------------------------------Vcb_err : 0 ( 0.2% ) | 2% | 5%----------------------------------------------------------===> Lmax (flat Likelihood)----------------------------------------------------------rho_bar : 0.21 +- 0.05eta_bar : 0.35 +- 0.02----------------------------------------------------------===> L*e^{-1/2}----------------------------------------------------------rho_bar : 0.22 +- 0.12 | 0.22 +- 0.12 | 0.21 +- 0.14eta_bar : 0.34 +- 0.05 | 0.34 +- 0.06 | 0.35 +- 0.07----------------------------------------------------------===> L*e^{-2}----------------------------------------------------------rho_bar : 0.21 +- 0.17 | 0.20 +- 0.18 | 0.19 +- 0.20eta_bar : 0.35 +- 0.08 | 0.35 +- 0.08 | 0.36 +- 0.11
---------------------------------------
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Backup - RESULTS
mb(mb) = 4.22 ± 0.06 GeV mc(mc) = 1.33 ± 0.10 GeV
Conversion from kinetic mass scheme to MS scheme with hep-ph/9708372, hep-ph/0302262
See also report from CKM WS hep-ph/0304132
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Backup
Lepton Moment Measurement
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Selecting B X e Decays Based on events with one high energetic electron
p* > 1.4 GeV/c , J/-veto „tag electron“ , originates predominantly from semileptonic B-decays
Look for oppositely charged electrons :
J/
Backgrounds (MC)Signal (MC)
pe[GeV/c]pe[GeV/c]
+−→ eeJ tag/ψpe[GeV/c]
B‘s at rest :
no angularcorrelation between e+ & e cut
e+ & e „back-to- back“
1.0
0.5
0.0
-0.5
-1.00 0.5 1.0 1.5 2.0 2.5
„ARGUS-Method“
−tage cX +e
e
e
Y
BcX
+e e
B −tage
cX
e
B
0 0.5 1.0 1.5 2.0 2.5
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Raw Spectra & Backgrounds
Sizable contribution of „upper Vertex“ processes : dominant source of syst. uncertainties at low energies
e
sce
eY
DDBBXe
+
+− →←tag
e
ce
eY
KDDBBXe
+
− →← (*)(*)tag
e
ce
e
XBBXe+
+− →←tag
e
ce
e
XBBXe+
+− →←tag
%28≈BrBr
%25≈BrBr
XeB →mostly
mostlyYeXB C →→
Ele
ctro
ns
/ 50
MeV
/c
meetag±
±± eetag
14.47 −=∫ fbdtL
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Inclusive e Spectrum Correction for electron efficiency e and B0B0
mixing
Bremsstrahlung corrections full detector simulation checked appropriate modeling
of detector material Compare Ee distribution of
ee ee events in datawith simulation
Partial branching fraction :
⎥⎦
⎤⎢⎣
⎡−
−−−
=±±±→
dp
dN
f
f
dp
dN
f
f
dp
dNeeee
cute
exb
)21()21(
111
00
00
00
00
χ
χ
χ
χ
εεν m
=>
=>→ →
tagacc
eexbe N
GeVENGeVEXeBBr
εγν ν )6.0(
)6.0),(( )%23.006.036.10( sysstat
)(eXB c→
Consistent with previous result ( Phys. Rev. D 67, 031101)
cut- cos of acceptance
))4((
parameter mixing
e,e
000
000
tag±=
→=
=
mθε
χ
cut
BBsYBrf
BB
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Inclusive e Spectrum : Moments
Subtraction of contribution from BXu e decays Br(BXu e from BABAR-measurement ( this talk)
Correction for QED-radiative effects PHOTOS
Moments estimated from histogram small corrections due to finite binning and boost into B-
restframe
Results (Ee > Ecut) : )( eXBBr c→ eE ( )2ee EE − ( )3ee EE −
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Backup
Hadron Moment Measurements
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Mxn Analysis : Event
Selection Fully reconstructed hadronic B-decay
Semileptonic decay of other B lepton with : missing energy Emis & momentum pmis
completeness of XH : Emis pmis
Mx determined by 2C kinematic fit energy conservation, p2
miss = 0
HX
,e
,e
(*)D
K
2/350)( cMeVMx ≈σ
signalbackgroundK
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 mES[GeV/c2]
225020001750150012501000750500250
0
Eve
nts
/ 1.8
MeV
/c2
high mass final states
Mx2[GeV2/c4]
SLBrecBBABAR Y(4S)
24 recBs
ES pm −=
0)( >× lBb QQSL
7114 signal events,2102 combinatoral bg.
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Determination of Mxn
(n=1,2,3,4)
Measured Mxn differs from true Mx
n
For each interval in Mxn, full detector
simulation delivers Mxn and Mx
n calibration curve which is applied to
data event-by-event weak dependence on decay model validated on data with decays function of multiplicity and
Event selection efficiency depends on decay mode
influence on Mxn determined with MC,
systematic error estimated by variationof individual exclusive decay modes
missmiss pEr
−
)high()low( nx
nx MM ≠
→ lDB *
0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 pmin[GeV/c]
4.5
4.4
4.3
4.2
4.1
4.0
Mx2
[G
eV2 /
c4 ]~
calibration (D,D*, D**,D(*) mix)
verification withexcl. modes
D
*D
.Resnon−
**D
3 4 5 6 7 8 9 10 11 12 Mx
2 [GeV2/c4]
1211109876543
Mx2
[G
eV2 /
c4 ]
~
~
182 −=∫ fbdtL
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Hadron Moments: <Mx> and <Mx3>
Bauer et al. 1s scheme (hep-ph/0408002) Our results - kinetic scheme
<Mx> <Mx2>
<Mx3> <Mx4>
Not in the fitNot in the fit Not in the fitNot in the fit
Not in the fitNot in the fit
Not in the fitNot in the fit
While the lepton energy moments lead to very similar results, especiallythe non-integer hadron mass moments <Mx> and <Mx3> are different …
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Scale Dependence of the Kinetic SchemeCheck scale dependence on the level of the physical observables (moments)
that are supposed to be scale independent!
Valuable input fromPaolo Gambino and Nikolai Uraltsev
Vary the scale dependent HQE parameters simultaneously between =[0.5-1.5] GeV. However, to maintain the
physical meaning of the c quark mass =[0.8-1.2] GeV is a more appropriated choice for a reasonable scale variation.
Red Band:Propagated theoretical uncertainty from the extracted HQE parameters
in the BABAR analysis.
Yellow Band:10% variation of the O(1/mb
2) and O(1/mb
3) contribution. This variation corresponds to an
0.1x10-3 uncertainty in |Vcb|
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Scale Dependence of the Kinetic Scheme
The observed scale dependence of the predicted moments in the kinetic scheme is very small and even for the large scale variation of =[0.5-1.5] GeV (default =1GeV), the observed
moment shifts are already covered by an uncertainty of the O(1/mb2)
and O(1/mb3) contributions of 10%.
Such an uncertainty would manifest itself in an error on |Vcb | of 0.1x10-3.
Following the suggestion for the theoretical error evaluation in hep-ph/0401063, the final theoretical errors of the BABAR
analysis on |Vcb| and the extracted HQE parameters fully cover the small effect of the observed scale dependence:
Example: |Vcb| (theo-BABAR) =0.7x10-3
to be compared with |Vcb| (scale) <0.1x10-3
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
BSG MOMENT PREDICTION
I------------------- Eg=1.8 EG 2.31394725 0.0183035162 VEG 0.0329645342 0.0026 RHO 0.759208181 I------------------- Eg=2.0 EG 2.34259823 0.0190865906 VEG 0.0222734452 0.0024 RHO 0.694841549
CLV + BSG BELLE + BSG CLEO + BSG BABAR
I------------------- Eg=1.8 EG 2.31247747 0.0243168435 VEG 0.0328578215 0.0026 RHO 0.845508417 I------------------- Eg=2.0 EG 2.34107022 0.0253493739 VEG 0.0221826394 0.0024 RHO 0.795027137
CLV + BSG BELLE
Ecut=1.8 GeV: BELLE
<E> =2.292 0.043 GeV<E
2> - <E>2 =0.0305 0.010 GeV2
Ecut=2.0 GeV: CLEO
<E> =2.346 0.034 GeV<E
2> - <E>2 =0.0226 0.007 GeV2
Experimental Results
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
Yet another “triangle” to be tested …
bbss, X, Xssllll
BR ~10BR ~10-4-4
mmbb
bbululBR ~10BR ~10-3-3
VVub ub
bbclclBR ~10BR ~10-1-1
VVcbcb,,
mmbb, ,
“shape function”
HQE link established? HQE link not y
et esta
blished
bbss: : Large potential for new physics but still the issue of the rather high photon energy cutoff.
bbXXssll: ll: “Flag ship analysis” forfuture b exp. (LHCB, BTEV,1035-36)
Theoretical uncertainties on Xsll will dependent on the
knowledge of the b quark massand its fermi motion in B meson.
VubVub//Vcb: Vcb: The largest uncertainty is dueto the imperfect knowledge of the b quark
mass and its fermi motion (Vub).
We need Theory and Experiment to not onlyWe need Theory and Experiment to not only establish establish the the missing linksmissing links in the “HQE triangle” but also to check its in the “HQE triangle” but also to check its consistencyconsistency! !
The measurement of the moments is one step in this direction …
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Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004
The three requirements from Andrei Sacharow (1967):1. Baryon number violation2. C und CP violation3. Abkehr vom thermodynamischen Gleichgewicht
Somewhere here
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