Determination of Vcb A

1
Determination of Vcb (?A)
Vcb is determined in semileptonic B-decays to
charm Two methods 1) Exclusive Decays
(Based on Heavy Quark Symmetry/ Heavy
Quark Effective Theory (HQET)) 2) Inclusive
Decays (Based on Operator Product Expansion
(OPE) Heavy Quark Effective Theory (HQET))
2
H(Qq) with mQ gtgt mq gt
Radius of H RH 1/?QCD Compton wave length
?Q 1/mQ ltlt RH gt q can only resolve
distances gtgt ?Q gt q blind to flavor
(mass) and spin orientation of Q gt Q is a
static color-electric source Analogy to
H-atom Flavor symmetry
Spin symmetry
?e independent of nucleus mass
Hyperfine levels nearly degenerated Only
total nuclear charge matters
Nuclear spin decouples for me/mN?8 Consider
elastic scattering B(v) ?B(v') induced by
current vv' q does not realize the
current acting on Q(b) v?v' q interacts
with a moving color source gt
Form Factor suppression m b ?8 FF
?(vv') dimensionless function (Isgur-Wise
function) w vv' Lorentz boost
connecting initial and final state
3
In the heavy quark limit
Only one universal FF Isgur-Wise function
We do not know ?(w) but we know the
normalisation
Theoretical uncertainty on Form Factor Phase
Space Experimental BG
4
Y(4S) Good resolution in w
Kinematic constraints to suppress BG
e.g. cos?B,Dl - Efficiency
drops for w?1 (Why?) LEP - Lower
resolution in w - BG suppression
more difficult e.g. hemisphere
and vertex separation to
identify extra tracks from Bsig
Constant efficiency in w (Why?)
Important source of BG D !
5
Exclusive Semileptonic B?Dl? Decays Vcb F(1)
Measure the spectrum
Factor out the FF part
W
And extrapolate to the point of zero recoil
From Theory
Fit for it
6
Exclusive Semileptonic B?Dl ? Decays Vcb
We need now the FF at zero recoil
As a result
Exercise What is the CL corresponding to ??21 ?
Expected future improvement from Lattice QCD
Vcb.F(1) 0.0367 ? 0.0013 (S1.7)
F(1) 0.913 0.030-0.035 (Lattice QCD)
Vcbexcl 0.04020.021-0.018
7
Determination of Vcb Inclusive Decays
W
Quark Level Decay
l
Taking into account non-perturbative strong
interaction (OPE HQET)
Mean value of the heavy-quark kinetic energy
Mean value of the chromomagnetic interaction
Not a physical quantity ?Theoretical Estimates
or see later on
8
Determination of Vcb Inclusive Decays
h X ?h l- ? Y
l?X ? ee-
? ?(4S) ? B sig B tag
? l- ?X or Breco
BF ? (dG/dEl ) dEl 98 b ? c 2 b ? u
?(B0)1.543 0.013 ps ?(B)1.653 0.014 ps
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Determination of Vcb Inclusive Decays
Energy contributed by the light degrees of
freedom ?QCD
Eliminate the b-quark mass using
Problem Theoretical uncertainty on the
extraction of Vcb depends on Idea
Differential decay rates have different
sensitivities to these
parameters in different phase space regions
Assign different phase space regions
different weights
However Too high moments will
lead to (local) duality
violations Duality One-to-one translation
from
parton to hadron world
10
Determination of Vcb Moment measurements
ltmX2-mD2gt
CLEO mX,s?
lt(mX2-mD2)2gt
CLEO E l
ltmX2-mD2gt
CLEO B?Xs?ltEygt
Vcbincl 0.0420 ? 0.006exp ?0.0008theo
11
Determination of Vcb Summary
12
Determination Vub
Extraction from semileptonic B-decays Two
methods 1) Exclusive Decays ( Y(4S) )
(In contrast to Vcb extraction much
more model dependence) 2) Inclusive Decays (
LEP, Y(4S) ) (Extraction based on OPE/HQET)
13
Determination of Vub Exclusive Determination
In contrast to B?D() transitions No Heavy Quark
Symmetry leading to Form Factor Normalisation
Form Factor from Model calculations Quark
Models Symmetry relating Heavy-to-Light
transitions B?h and D?h (CLEO-c) Light
Cone Sum Rules (LCSR) Lattice QCD
.... Eventually, the mode B?p l ? is the
prefered mode from the theoretical point of view.
See Lectures of D. Melikhov A. Kronfeld
14
Determination of Vub Exclusive Determination
Signal Crossfeed Downfeed b ? c l ?
15
CLEO 2003
Determination of Vub Exclusive Determination

Detector hermeticity Neutrino Reconstruction
??q2 and El gt1.0 GeV (?), gt1.5 GeV(?)
whitesignal, redcrossfeed, yellowdownfeed,
greencontinuum, blackb?cl?
16
Determination of Vub Exclusive Determination
.16 .53 ?.17 ?.39
.39 ?.56
Vubexcl (3.35 ? 0.20? 0.50) 10 3
17
Determination of Vub Inclusive Decays
Good Total rate predicted with 5 theo.
error Bad Need to suppress BG from b?c l ?
(B/S 50) gt Less statistics (not
a real problem) gt Theoretical error
enhanced
The original method Lepton endpoint spectrum
Systematic error BG from Measures
?BF What is the fraction fu of events
in the measured phase space region? 10
Years ago Use models to extrapolate
to the full BF.
18
Determination of Vub Inclusive Decays
1) Shape function What does it mean?
Fermi-Motion of the b-quark inside the
B-meson. 2) Can we measure it? Yes, in B?Xs
? measuring the spectrum dG/dE? However
Shape Function in B?Xu l ? and B?Xs ? only
the same up to O(1/mb) corrections.
Bauer,Luke, Mannel (2002) Leibovich, Ligeti,
Wise (2002) up to 15 for (El gt 2.2
GeV) Neubert not more few (2002)
Pictures provided by Z. Ligeti
Difference
CLEO
19
Determination of Vub Inclusive Decays
Kinematic limit B?Xc l ?
Exercise What would you do to pin them down?
Strategies 1) El Shape Function from
B?Xs? 2) MX (Shape Function vary ?, ?1) 3) If
possible, reject low q2 values However
Annihilation diagrams (Reduce shape function
might
become important! dependence)


20
Determination of Vub Inclusive Decays
Enormous statistics available at the
B-factories New experimental methods can be
realised!
e.g. BaBar Full reconstruction of one B small
efficiency but quite clean
Lepton plgt1.0 GeV/c S/B 2.5
21
Determination of Vub Inclusive Decays
Enriched sample charm BG in signal region
(mXlt1.5 GeV) fixed using mXgt1.5 GeV
Belle Alternative method using D l ? tags
CLEO Hermeticity of the detector !
22
Determination of Vub Inclusive Decays
My Average (4.12 ? 0.13 ? 0.42) ? 103 Does
not take into account subleading shape function
effects and annihilation diagrams Error
inflated (4.12 ? 0.13 ? 0.60) ? 103
23
Determination of Vub Summary
Error not inflated
68 CL region
Input for the CKM fit LL(Incl.)
L(Excl.) if Incl. Excl. independent In other
words log L log L(Incl.) log L(Excl.) ?2
?2(Incl.) ?2(Excl.)