wolfgang menges, queen mary semileptonic b decays at babar wolfgang menges queen mary, university of...
TRANSCRIPT
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Semileptonic B Decays at BaBar
Wolfgang MengesQueen Mary, University of London, UK
Teilchenphysik Seminar, Bonn, 4th May 06
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Outline
• Introduction & motivation– CKM Matrix & Unitarity
Triangle– PEP-II and BABAR– Why semileptonic decays?
•Measurements– Inclusive b cl– Exlusive B D*l– Inclusive b ul– Exclusive B l
•Howit all fitstogether
•Outlook / Conclusions
|Vcb|
|Vub|
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
B Decays – a Window on the Quark Sector
•The weak and mass eigenstates of the quarks are not the same•The changes in base are described by unitarity transformations Cabibbo Kobayashi Maskawa (CKM) matrix
The only 3rd generation quark we can study in detail
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
1-c2 c A c
3(-i)
= -c 1- c2/2 A c
2
Ac3(1- -i) -A c
2 1 + O(c
4) [ c= sinc ]CP violation
| Vub| e-i
| Vtd| e-i
|Vub|
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Unitarity Triangle
Unitarity of VCKM
– this is neatly represented by the familiar Unitarity Triangle
– angles can be measured with CPV of B decays– side from semileptonic B decays (|Vcb| and |Vub|)
0ud ub cd cb td tbV V V V V 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
1
td tb
cd cb
V V
V V
†CKM CKM 1V V
ud ub
cd cb
V V
V V
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Unitarity Triangle Fits
Bd mixing: md
Bs mixing:ms / md
J/K0: sin2
bul: |Vub|
D*l: |Vcb|
kaon decays: εK
http://ckmfitter.in2p3.fr
charmless two-body:
interference in
BDK:
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Consistency tests
•Compare measurements in the ()-plane
– If the SM is the whole story,they must all overlap
•The tells us that this is true (status winter 2005)
– But still large enough for New Physics to hide
•Precision of sin2 from B factories dominates determination of
– Must improve the others to get more stringent tests
•Left side of the UT is
– Uncertainty dominated byca. 7% error on |Vub|
ud ub cd cbV V V V
Measurement of |Vub| is complementary to
sin2
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Experiments
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Collides 9 GeV e−
against 3.1 GeV e+
– ECM = 10.58 GeV = mass of (4S)
– Boost = 0.56 allows measurement of B decay times
PEPII Asymmetric B Factory
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
The BaBar Detector
Čerenkov Detector(DIRC)
144 quartz bars11000 PMTs
1.5 T solenoid
ElectroMagnetic Calorimeter
6580 CsI(Tl) crystals
Drift CHamber40 stereo
layers
Instrumented Flux Returniron/RPCs/LSTs
(muon/neutral hadrons)
Silicon Vertex Tracker5 layers, double sided
strips
e+ (3.1 GeV)
e- (9 GeV)
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary Datasets:
Run 1/2: ~80 fb-1
Run 3/4: ~140 fb-1
Run 1-4: ~220 fb-1
Data Taking
Run 5
Run 4
Run 3
Run 2
Run 1
Run 5:
collected: ~100 fb-
1
expected: ~230 fb-1
Peak luminosity 1×1034/cm2/s BB production ~10 Hz
Belle:
collected: ~560 fb-
1
1 fb-1 -> 1.1 x 106 BB
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
KEKB and Belle Detector
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Physics
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Semileptonic B Decays
uX
B
c/u quark turns into one or more hadrons
B → Xlv decays are described by 3 variables
2
2
( ) 1
( ) 50ub
cb
Vb u
b c V
q2 = lepton-neutrino mass squaredq2 = lepton-neutrino mass squared
mX = hadron system massmX = hadron system mass
El = lepton energyEl = lepton energy
b
,c u
W
,cb ubV V
Semileptonic B decays allow measurement of |Vcb| and |Vub| from tree level processes.
Presence of a single hadronic current allows control of theoretical uncertainties.
b clv is background to b ulv:
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
|Vcb |
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
free-quark rate
|Vcb| & the „Atomic Physics“ of B Decays
•Contains b- and c-quark masses, mb and mc
2 related to kinetic energy of b-quark
G2 related to chromomagnetic operator (B/B* mass splitting)
•Darwin term (ρD3) and spin-orbit interaction (ρLS
3) enter at 1/mb3
= 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 (sj , s
k0)
Strategy: Global fit of all parameters measure rate, moments(NB: Several HQE schemes exist; operators and coeff’s are scheme dependent)
Inclusive rate described by Heavy Quark Expansion (HQE) in terms of as(mb) and 1/mb
43
3
2
332
45
2
3322
3
23
52
1)()1(2)),(1(
21),(1)(
1||192
)(
bb
D
b
b
LSDG
pert
b
b
LSDG
pert
EWcbbF
c
mO
mr
m
mrrA
m
mrAr
AVmG
XB
d
z 0
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Inclusive Decays: |Vcb| from b clv
•Fit moments of inclusive distributions: lepton energyhadronic mass
– Determine OPE parameters and |Vcb|
•Measurements from B Factories, CDF, Delphi•We’ll look at an example: Hadronic Mass Moments
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
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
BABARL = 81 fb-1
• Select events with a fully-reconstructed B– Use ca. 1000 decay chains B D(*) + (n) + (mK)– Flavor and momentum of “recoil” B are known
• Find a lepton with E > Ecut in the recoil B– Lepton charge consistent with the B flavor– mmiss consistent with a neutrino
• All remaining particles belong to Xc
– Improve mX with a kinematic fit (require mB2=mB1 and mmiss=0)
– Yields resolution (mX) = 350 MeV
Hadronic Mass Moments
Fully reconstructedB hadrons
lepton
v
X
BABAR PR D69:111103
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Hadronic Mass Moments
• Unmeasured particles measured mX < true mX
– Calibrate using simulation– Depends (weakly) on decay multiplicity and mmiss
– Validate in MC after applying correction– Validate on data using partially reconstructed D *± D 0±, tagged
by the soft ± and lepton
• Calculate 1st-4th mass moments with Ecut = 0.9 … 1.6 GeV
input to HQE fit
BABARValidation:
high mass charm states
Mx2[GeV2/c4]
D,D*
BABAR PRL 93:011803
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
• Calculation by Gambino & Uraltsev
– Kinetic mass scheme to– Eℓ moments
– mX moments
• 8 parameters to determine:
• 8 moments available with several Ecut
– Sufficient degrees of freedom to determineall parameters without external inputs
– Fit quality tells us how well HQE works
Fit Parameters
cbV bm cm 2
2G
3D
3LS( )cB X B
kinetic
chromomagnetic
Darwin
spin-orbit
2(1/ )bmO
3(1/ )bmO
3(1/ )bmO
( )sO
2( )sO
Benson, Bigi, Mannel, Uraltsev, hep-ph/0410080Gambino, Uraltsev, hep-ph/0401063
Benson, Bigi, Uraltsev, hep-ph/0410080
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Results
Global fit in thekinetic scheme
|Vcb| < 2%mb < 1%mc = 5%
Buchmüller, Flächer: hep-ph/0507253
|Vcb| = (41.96
± 0.23 ± 0.35 ± 0.59) 10-3
BRclv = 10.71 ± 0.10 ± 0.08 %
mb = 4.590 ± 0.025
± 0.030
GeV
mc = 1.142 ± 0.037
± 0.045
GeV
μπ2 = 0.401 ±
0.019± 0.035
GeV2
μG2, ρD
3,ρLS3
exp HQE SL
b→sb→clνcombined
Based on:
Babar: • PRD69, 111103 (2004)• PRD69, 111104 (2004)• PRD72, 052004 (2005)• hep-ex/0507001
Belle:• PRL93, 061803 (2004)• hep-ex/0508005
CLEO: • PRD70, 032002 (2004) • PRL87, 251807 (2001)
CDF: PRD71, 051103 (2005)
DELPHI: EPJ C45, 35 (2006)
Use inputs from BaBar, Belle, CLEO, CDF &
DELPHI:
b->clv and b->s
b
s
b
c
Wl
v
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
•Shape of F(w) unknown•Parametrized with 2 (slope at w = 1) and form factor
ratios R1, R2 ~ independent on whA1 expansion a-la Caprini-Lellouch-Neubert
Exclusive |Vcb| and Form Factors
Reconstruct B -> D*+ev as D*+ D0+ with D0 K
G(w) known phase space factorF(w) Form Factor (FF)w = D* boost in B rest frame
BaBar hep-ex/0602023
+0.030
-0.035
•F(1)=1 in heavy quark limit; lattice QCD says: F(1) = 0.919 Hashimoto et al, PRD 66 (2002)
014503
-> measure form factors from multi-dimensional fit to diff rate-> measure |Vcb| with
21222
2
*
,,,,,,coscos
RRqfVddddq
DBdVcb
V
Nucl. Phys. B 530, 153 (1998)
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
B D*l Form Factors and |Vcb|
hep-ex/0602023
Using latest form factors with previous BaBar analysis: PRD71, 051502(2005)
|Vcb| = (37.6±0.3±1.3 ) x 10-3
+1.5-1.3
Reducing FF error: 2.8% -> 0.5% Total sys error: 4.5% -> 3.5%
80 fb-1
80 fb-1Factor 5 improvement of FF uncertainty from previous
CLEO measurement (1996).
1D projections of fit resultR1 = 1.396 ± 0.060 ± 0.035 ± 0.027
R2 = 0.885 ± 0.040 ± 0.022 ± 0.013
2 = 1.145 ± 0.059 ± 0.030 ± 0.035
stat MC sys
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Summary of |Vcb| Results
Excl: |Vcb| = (40.9±1.0exp F(1)) x 10-3 (D*lv)
Incl: |Vcb| = (42.0±0.2exp±0.4HQE±0.6) x 10-3
+1.1-1.3
The new BaBar form factors and |Vcb| result are not included. Work is going
on.
B->D*lv B->Dlv
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
|Vub |
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
How to Measure b → ul
•Need to suppress the large b → clbackground (×50)
• Inclusive: – mu << mc differences in kinematics– Maximum lepton energy 2.64 vs. 2.31 GeV– < 10 % of signal accessible
• How accurately do we know this fraction?
•Exclusive: – Explicit reconstruction of final-state hadrons– B lv, B lv, B lv, B lv, …– Need form factors (FF) to describe hadronization effects– Example: the rate for B lv is
• How accurately do we know the FF ?(for vector mesons 3 FFs)
222 3 2
2 3
( )( )
24F
ub
Gd BV p f q
dq
Form Factor
E
b c
b u
2.64
2.31
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Inclusive b → ulStrategies
Use kinematic cuts to separate bulv from bclv decays:
2q
b c
b u
E
b c
b u
Xm
b cb u
Not to scale!Not to scale!
•smaller acceptance -> theory error increase• OPE breaks down• shape function to resum non-pert. corrections
•measure partial branching fraction B
•get predicted partial rate from theory
Experimental resolution not included!Experimental resolution not included!
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Lepton Endpoint
•Select electrons with 2.0 < El < 2.6 GeV– Push below the charm threshold
Larger signal acceptance Smaller theoretical error
– Accurate subtraction of background is crucial!
– S/B =1/15 for the endpoint El > 2.0 GeV– Measure the partial BF
L(fb-1) E (GeV) (10-4)
BABAR: 80 2.0–2.6 5.72 ± 0.41stat ± 0.65sys
Belle: 27 1.9–2.6 8.47 ± 0.37stat ± 1.53sys
CLEO: 9 2.2–2.6 2.30 ± 0.15stat ± 0.35sys
BABAR
total BF is ~2103
BABAR hep-ex/0602023
MC signalb ulv
Data – bkgd.
Data
MC bkgd.b clv
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
El and q2
• Try to improve signal-to-background
• Use pv = pmiss in addition to pe calculate q2
– Define shmax(El, q2) = the maximum mX squared
• Cutting at shmax < mD
2 removes b clv while keeping most of the signal
– S/B = 1/2 achieved for El > 2.0 GeV and sh
max < 3.5 GeV2
(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 clv
El (GeV)
q2 (G
eV2 )
b ulv
Smaller systematic errors
BABAR
Extract signal normalize bkg
•Measured partial BF
BABAR PRL 95:111801
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
mX and q2
•Must reconstruct all decay products to measure mX or q2
– Use (fully-reconstructed) hadronic B tag
•Suppress b → c lv by vetoing against D (*) decays– Reject events with K– Reject events with B 0 → D *+(→ D0 +)l−v
•Measure the partial BF in regions of (mX, q2)– mX < 1.7 GeV and q2 > 8 GeV2:
(10-4) = 8.7 ± 0.9stat ± 0.9sys (211fb-1)
BABAR hep-ex/0507017
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Theory for b → ul
•Tree level rate must be corrected for QCD• Just like b → cl…, and with similar accuracy
•…until limited experimental acceptance is considered•Poor convergence of HQE in region where b → cl decays
are kinematically forbidden•Non-perturbative Shape Function (SF) must be used to
calculate partial rates
= scale which separates effects from long- and short-distance dynamics
AEW = EW corrections; Apert = pert. corrections (sj , s
k0)
32
2
52
22
32
3
52 12))(1(
21)(1||
1921)(
bb
Gpert
b
Gpertub
bFEWu m
Om
Am
AVmG
AXB
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Light-cone momentum distribution of b quark: f(k+)– Fermi motion of b quark inside B meson– Universal property of the B meson (to leading order);
subleading SFs arise at each order in 1/mb
•Consequences: changes effective mb smears kinematic spectra
•SF cannot be calculated must be measured
Rough features (mean, r.m.s.) are known
k
( )f k
B bM m
Details, especially the tail, are unknown
0
Shape Function – What is it ?
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Extracting the Shape Function
•We can fit inclusive distributions from b → s or b → clv decays with theory prediction
– Must assume a functional form of f (k+)
•Example:
•New calculation connects SF moments with b-quark mass mb and kinetic energy
2 (Neubert, PLB 612:13) – Determined precisely from b → s and b clv decays
• from b → s, and from b c lv– Fit data from BABAR, Belle, CLEO, DELPHI, CDF:
•Use SF together with calculation of triple-diff. decay rate Bosch, Lange, Neubert, Paz (BLNP) to get |Vub|
(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
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
|Vub| from Branching Fraction
Results of different calculations/ HQE parameters using the same partial branching fraction:
For converting a branching fraction into |Vub|the phase space acceptance is needed:
3) |Vub|=(4.82±0.36exp±0.46SF+theo)10-3
2) |Vub|=(4.65±0.34exp ±0.23theo)10-3+0.46–0.38SF
1) |Vub|=(5.00±0.37exp±0.46SF±0.28theo)10-3
4) |Vub|=(4.86±0.36exp±0.22theo)10-
3
Example for mx/q2
1) BLNP: BaBar BXcl moments
mb(SF) = 4.61 ± 0.08 GeV
π2(SF) = 0.15 ± 0.07
GeV2
3) BLL: BaBar BXcl momentsmb(1S) = 4.74 ± 0.06 GeV
2) BLNP: Belle BXs spectrum
mb(SF) = 4.52 ± 0.07 GeV
π2(SF) = 0.27 ± 0.23
GeV2
4) DGE: HFAG averagemb(MS) = 4.20 ± 0.04 GeV
BLL – Bauer, Ligeti, LukeDGE – Anderson, Gardi
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Status of Inclusive |Vub|
|Vub| world average winter 2006
Experimental Error 4.5%
SF parameters (mb,
2)4.1%
Theory Error 4.2%
|Vub| determined to 7.6%
Numbers rescaled by HFAG.SF parameters from hep-ex/0507243,
predicted partial rates from BLNP
BLNP: Shape Function PRD72:073006(2005) 4.45 0.20exp 0.18SF 0.19theo
Andersen-Gardi: DGE JHEP0601:097(2006) 4.41 0.20exp 0.20theo
NEW!
|Vub| [x10-3]:
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Summary
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Exclusive b → ulv
B → lvInclusiveb → ulv q2
lv, lv ?
b → s
ShapeFunction
E
mb
Inclusive b → clv
mXEl
HQE Fit
mX
El
WA
duality
|Vub|
SSFs
FF
LCSR LQCDunquenching
How it all fits togetherExclusive b → clv
|Vcb| B → Dlv
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
Conclusions
• |Vcb| determined with high precision (2%)
Now |Vub| is important!
• Precise determination of |Vub| complements sin2 to test the validity of the Standard Model– 7.6% accuracy achieved so far 5% possible?
• Close collaboration between theory and experiment is importantInclusive |Vub| : – Much exp. and theo. progress in the last 2 yearsExclusive |Vub| : – Significant exp. progress in the last year, but further improvement in B → FF calculations needed (also new calculations for B → lB → lB → l– Accuracy of for exclusive |Vub| in the next few years (?)
• Important to cross-check inclusive vs. exclusive results
Wo
lfg
ang
Men
ges
, Q
uee
n M
ary
The Unitarity Triangle: 2004 2005
•Dramatic improvement in |Vub|
•sin2 went down slightly Overlap with |Vub/Vcb| smaller