Stato di Vub e Vcb
Concezio Bozzi
INFN Ferrara
Babar Italia, Trieste 14 Aprile 2005
Sommario
• Decadimenti semileptonici inclusivi
– con charm (Vcb)
– senza charm (Vub)
• Decadimenti semileptonici esclusivi
– pln, rln (nuovi risultati, Moriond&CKM05)
– D*ln
• NB: ho attinto a piene mani da materiale
presentato (da altri ma anche da me!) a
CKM2005
Misure inclusive
Inclusive Decays – the Big Picture
Semileptonic B Decays & HQE
3




r D3  r LS
2
2




p   G 
mb




pert
z
(
r
)
1

A
(
r
,

)
1

3
 0

2


2
m
b
2
5




G F mb


2


 ( B  X c n ) 
| Vcb | 1  AEW  


3
192 p


3
3
r

r


LS
 G2  D
free-quark rate
3

 1 
mb
rD
pert
4
  (1  A5 (r ,  )) 2(1  r )
 d(r ) 3  O 4  
2


m
mb
b
 mb  

= scale which separates effects from long- and short-distance dynamics


r = mc/mb; z0(r), d(r): phase space factors; AEW = EW corrections; Apert = pert. corrections (asj , askb0)

contains b- and c-quark masses, mb and mc

p2 related to kinetic energy of b-quark

G2 related to chromomagnetic operator: B / B* mass splitting

Darwin term (ρD3) and spin-orbit interaction (ρLS3) enter at 1/mb3
No 1/mb term!
Several HQE schemes exist; op’s and coeff’s are scheme dependent
Inclusive bcℓν

Measure electron momentum spectrum and mass of
hadronic system in SL decay

Determine moments to allow comparison with partonlevel calculations (duality assumed)

Calculations exist for the following:
Lepton energy spectrum
Eln
El  E 0
Gambino & Uraltsev
(hep-ph/0401063, 0403166)
3
  B  Eln d  f n ( E0 , mb , mc ,  G2 , p2 , r D3 , r LS
)
E0
Mass of hadronic system
M xn

El  E 0
3
  B  M Xn d  f nx ( E0 , mb , mc ,  G2 , p2 , r D3 , r LS
)
E0
Fit for HQE parameters and |Vcb|
BABAR PRL 93:011803
Fit Results
mX moments
● = used, ○ = unused
in the nominal fit
BABAR
c 2/ndf = 20/15
Eℓ moments
Red line: OPE fit
Yellow band: theory errors
BABAR PRL 93:011803
Fit Results
precision on
|Vcb| = 2%
precision on
mb = 1.5%
Vcb  (41.4  0.4exp  0.4HQE  0.6 th ) 10 3
Bc n  (10.61  0.16exp  0.06HQE )%
mb  (4.61  0.05exp  0.04 HQE  0.02as ) GeV
mc  (1.18  0.07 exp  0.06HQE  0.02as ) GeV
p2  (0.45  0.04exp  0.04HQE  0.01a ) GeV 2
s
G2  (0.27  0.06exp  0.03HQE  0.02a ) GeV 2
s
r D3  (0.20  0.02exp  0.02HQE  0.00a ) GeV 3
s
3
r LS
 (0.09  0.04exp  0.07 HQE  0.01a ) GeV 3
Uncalculated
corrections to 
kinetic mass scheme
with μ=1 GeV
Fitted values
consistent with
external knowledge
c 2/ndf = 20/15
s


Impressive agreement between data and theory
≈ identical results obtained in another renorm. scheme:
Bauer, Ligeti, Luke, Manohar, Trott in hep-ph/0408002
Inclusive |Vcb| status

BaBar result compared with previous measurements:

Agrees with value coming from exclusive BD* ℓ ν
3
V

(41.4

1.0

1.8
)

10
decays (from HFAG): cb
expt
theo
Inclusive bu

Limiting factor in CKM precision tests; known much
less well than |Vcb|

CKM suppressed – therefore harder to measure

Challenge for experiment and theory
Starting point: HQE

Just like bcℓν…, and with similar accuracy


G F2 mb5
 p2   G2
2
pert
( B  X u n )  1  AEW 
| Vub |  1  A3 (  ) 1 
3
192 p
2mb2





 1 
 G2
pert
  (1  A5 (  )) 2 2  O 3 
mb

 mb 
= scale which separates effects from long- and short-distance dynamics
AEW = EW corrections; Apert = pert. corrections (asj , askb0)

…until limited expt’l acceptance is considered

Poor convergence of OPE in region where bcℓν
decays are kinematically forbidden

Non-perturbative Shape Function must be used to
calculate partial rates
Theory input
• Reference (ICHEP04, HFAG) results based on triple differential
decay rate (Ee, mX, q2) computed to O(as, mb-2) over the entire
phase space by de Fazio and Neubert (DFN, JHEP 06:17 (1999))
• Use as input the shape function parameters determined by a fit
(hep-ex/0407052) to the Belle b→sg spectrum:
Λ = 0.66 GeV, λ1 = -0.40 GeV2 + covariance
δΛ ~ δmb ≈ 80 MeV
Eg spectrum
in
b → sg
•
f(k+)
Acceptance in
b → uℓv
q2 vs mX analysis: take acceptances from Bauer, Ligeti and Luke
(BLL, hep-ph/0111387), OPE calculation in a region of the phase space
where SF effects are small.
Inclusive Vub measurements with BaBar
method
S/B
0.050.2
•High statistics
•Duality valid for
tight Ee cuts?
•Bkg subtraction
4.40 ± 0.24exp ± 0.35theo
~0.5
•High statistics
•Lower syst. on
shape functions
•Bkg subtraction
4.99 ± 0.48exp ± 0.29theo
~1.7
•Low background
•High resolution
•Low statistics
•Shape func. syst.
5.22 ± 0.43exp ± 0.33theo
~2
•Low background
•Very small syst.
on SF param.
•Small statistics
5.18 ± 0.57exp ± 0.34theo
Untagged
Electron spectrum endpoint
Ee>2.0GeV
Total rate using DeFazio-Neubert
Untagged
Ee vs q2 and neutrino reconstruction
Ee>2.0GeV and sh<3.5 GeV2/c4
Total rate using DeFazio-Neubert
Breco Tags
mX analysis (1-D)
mX<1.55 GeV/c2
Total rate using DeFazio-Neubert
Breco Tags
mX vs q2 analysis
mX<1.7 GeV/c2 and q2 >8.0 GeV2/c4
Vub using Bauer et al.
Partial Tags
Vub(x10-3)
Pros&Cons
•Very small bkg
Currentexclusive
Vub errors:
10-15%
•~no cut on kinem ( B( B  p l n )  (1.22  0.26) 10
120
Breco Tags
•Small statistics
Total
experimental syst @250-500
ifb: 3-6%
Total rate using Form Factors calc.
0
 
4
)
Vub measurements
A different theory approach
• Bosch, Lange, Neubert and
Paz (BLNP)
Nucl. Phys. B 699, 335 (2004)
• Acceptances computed in
BLNP using SF parameters
from
– Belle b→sg
hep-ex/0407052
– BaBar b→cℓn moments
(hadronic and leptonic)
hep-ex/0404017
• Proper translation into shape
function scheme of BLNP
hep-ph/0412241
Courtesy of Henning Flächer
Results with BLNP and
BaBar b→cℓn moments
Using mb = 4.63±0.08 GeV and μπ2 = 0.15±0.07 GeV2 (SF scheme) with
correlation coefficient -0.4.
Errors are: expt ± SF ± theory
expt ± (SF+theory)
Method
Endpoint
q2-Ee
∆B × 104
5.31±0.59
4.46±0.93
q2-mx
8.96±2.04
Average
|Vub| (BLNP)
SF params from bcℓν
3.93 ± 0.34 ± 0.38 ± 0.18
(8.7 ± 9.7 ± 4.6)%
3.89 ± 0.40 ± 0.45 ± 0.21
(10.3 ±11.5 ± 5.4)%
4.45 ± 0.49 ± 0.40 ± 0.22
(11.1 ± 9.0 ± 4.9)%
|Vub| (BLNP)
(Belle SF)
|Vub| ICHEP
(DFN, Belle SF)
4.55
4.40 ± 0.24 ± 0.35
( ± 6.4 ± 8.6) %
4.53
4.99 ± 0.48 ± 0.29
( ± 9.6 ± 5.8) %
5.00
5.18 ± 0.57 ± 0.34
( ±11.0 ± 6.5) %
4.07 ± 0.51
b→cℓn moments: significant change in inclusive |Vub| values
BLNP: increased sensitivity to SF
4.61 ± 0.46
Misure di Vub esclusive
Exclusive B  Xuln Decays
Breco Tags
p
Y(4S)
n
l-
Xu = p+, p0, r+, r0, w, h, h’, a00, a0+
low bkg, low stat.: 27p,… (ICHEP’04)
Semilep.Tags
Balance between
efficiency and purity
Untagged
High statistics, high
hackground (b  cln)
3 new
pln
results
▪ Goal : Measure Branching Fractions and |Vub|
▪ Need FF predictions to describe QCD effects
03/16/05

New unquenched LQCD calculations
(HPQCD’04, FNAL’04)

Try to measure q2 dependence of FF
with data
Jochen Dingfelder – CKM Workshop 2005
Semileptonic Tag Analyses

Reconstruct B  D(*)ln and study semileptonic recoil
 use both D and D* tags  sizable BF
 Tagging efficiency measured with “Double Tags” (two D(*)ln)
D(*)ln
decays
Correct sl. decay  |cosqBY| < 1
( tag side: cosqBY, signal side: cosqB,pl )
03/16/05
cos2fB < 1 for signal, bkg flat
Jochen Dingfelder – CKM Workshop 2005
p0ln with SL Tag : Signal Extraction
 Cut-and-count analysis in cosqB,pl and mD
82 fb-1
 Signal region: -1.1 < cosqBpl < 1.0
 Subtract mD sidebands
 remove cominatoric background
 Subtract other background using MC
normalized in -10 < cosqBpl < -1.5
45 p0
03/16/05
Jochen Dingfelder – CKM Workshop 2005
p+ln with SL Tag : Signal Extraction
Extract signal yields by binned c2 fit to cos2fB in 3 bins of q2:
Fit parameters = signal and background normalizations
26 p+
21 p+
14 p+
211 fb-1
Mainly B0B0 bkg
≈ 30% rln X-feed
03/16/05
Jochen Dingfelder – CKM Workshop 2005
p+ln with SL Tag : Branching Fractions and q2
 SL tag analyses statistically limited.
 Yields not yet large enough to discriminate between FF models.
03/16/05
Jochen Dingfelder – CKM Workshop 2005
Untagged B  pln and B  rln
 Neutrino Reconstruction: Reconstruct n from full event
& ensure good reco. quality
 Cut on missing mass: |M2miss / 2Emiss| < 0.4 GeV
 Harsh suppression of b  cln bkg
(kinem. cuts, mainly for rln)
e+e-  qq bkg (topological cuts)
 Max-LH fit of signal and background in DE, mES, and q2
 Fit all 4 signal modes simultaneously (p+, p0, r+, r0)
 Use isospin relations to reduce number of signal parameters:
 (B0  p-l+n) = 2  (B+  p0l+n)
 (B0  r-l+n) = 2  (B+  r0l+n)
03/16/05
Jochen Dingfelder – CKM Workshop 2005
Untagged pln: Fitted DE and mES
76 fb-1
427 p, 147 p0
03/16/05
Jochen Dingfelder – CKM Workshop 2005
5 bins for pln
3 bins for rln
Untagged pln: Fitted DE and mES
76 fb-1
101 r, 104 r0
03/16/05
Jochen Dingfelder – CKM Workshop 2005
5 bins for pln
3 bins for rln
Measured q2 Distributions and Form Factors
pln
 Recent LQCD and LCSR calculations agree well with data
 ISGW2 shows marginal agreement for pln
 Errors for rln still too large to study 3 form factors.
03/16/05
Jochen Dingfelder – CKM Workshop 2005
rln
Systematic Uncertainties (Untagged)
 Better statistical precision than previous measurements
 Syst. error dominated by n reconstruction. Will decrease with improved
track/neutral reconstruction.
 Results less dependent on theoretical predictions (own FF measurement)
03/16/05
Jochen Dingfelder – CKM Workshop 2005
Overview: Branching Fraction Measurements
pln
rln
Testing isospin symmetry:
Measure p+ln, p0ln separately (untagged)
03/16/05
Jochen Dingfelder – CKM Workshop 2005
Extraction of |Vub|
 Measurement in bins of q2 allows extraction of |Vub| for various q2 regimes
and FF calculations :
LCSR q2 <15 GeV2, LQCD q2 > 15 GeV2
extrapolation to whole q2 range
or
Quote LQCD2 as
representative
03/16/05
Jochen Dingfelder – CKM Workshop 2005
Misure di Vcb esclusive
Ultimate solution: combined measurement of form factors and Vcb!
(work in progress in Trieste)
Other ideas?
• D*0ln (little/undermanned efforts)
• Yet another measurement of D*+ln
– D* partial reconstruction
– On the recoil of a fully reconstructed hadronic decay
Run1-4
Conclusioni
• Mole impressionante di risultati sperimentali e teorici
• Collaborazione virtuosa tra le due comunità
• Effetto complessivo:
– Vcb inclusivo: ~1.5%
• Accordo impressionante teoria-esperimenti!
– Vub inclusivo: 10% → 5% ?
• Aggiornare misure con tutta la statistica disponibile
• Ampio consenso teorico sulla validità delle relazioni
b→cℓν  b→sg  b→uℓν
• Un po’ meno sulle incertezze relative
– Vub esclusivo:
• Occorre più statistica e migliorare le sistematiche sperimentali
• calcolo dei fattori di forma non ancora pienamente maturo
– Vcb esclusivo: 4% → ?
• Nuove misure (Dln) per limitare incertezze teoriche e per risolvere
l’accordo marginale tra le misure esistenti (D*ln)