1# CKM Unitarity angles a (f 2 ) and g (f 3 ) (Recent results from the B factories.) Hassan Jawahery Univ. of Maryland Lepton-Photon Symposium Fermi National Accelerator Laboratory August 12, 2003 Outline • Introduction & definitions • Experimental observables related to a and g • Experimental results, some discussion of implications for SM & constraints on a and g
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CKM Unitarity angles a (f and g (f · B‡Kp: (K+ p-, K0 p+, K0 p0,..) CKM suppressed Penguins (gluonic & E.W) can also lead to the same decays: W t b d,s u u g Main source of info
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1#
CKM Unitarity anglesa (f2) and g (f3)
(Recent results from the B factories.)
Hassan JawaheryUniv. of Maryland
Lepton-Photon SymposiumFermi National Accelerator Laboratory
August 12, 2003
Outline• Introduction & definitions• Experimental observables related to a and g• Experimental results, some discussion of
implications for SM & constraints on a and g
2#
||VVcdcb
VtdVub*
**tdtbcdcbVVVV**udubcdcbVVVV
0VVVVVV *tbtd
*cbcd
*ubud
=++
( )
( ) ˜˜˜
¯
ˆ
ÁÁÁ
Ë
Ê
---
--
--
ª
11
2/1
2/1
23
22
32
lhrl
lll
hrlll
AiA
A
iA
VCKM
The Unitarity Test
CPDefinitions
)arg(
)arg(
)arg(
*
*
*
*
*
*
cdcb
cdub
tdtb
cdcb
udub
tdtb
VV
VV
VV
VV
VV
VV
-=
-=
-=
g
b
a
Both involve Vub
f1=b f2=a f3=g
3#
Constraints from the CKM fit |Vub|, |Vcb|, eK, Dmd , Dms
oo
o
o
o
o
8037
12277
5.264.19
<<
<<
<<
g
a
b
At 95% C.L.
ÿ Unitarity Tests : Search for deviation from SM
ÿUsing direct measurements of angles check: a + g + b=p
ÿ Check if B Decays are consistent with the range of angles from theCKM fit?
Indirect infoon angles
A. Hoeoecker et al, Eur. Phys. Jour.
C21 (2001) 225, [hep-ph/0104062]
4#
b uu
sd ,
W
B‡p p: (p+ p-, p+ p0, p0 p0 )
B‡rp, B‡ r r, a1p,….
Tree diagrams are not alone:
b uu
sd ,
W
B‡Kp: (K+ p- , K0 p+ , K0 p0 , ..) CKM suppressed
Penguins (gluonic & E.W) can alsolead to the same decays:
W
t
b sd ,
u
u
g
Main source of info on a and g: Decays involving b‡u transitions
Data indicate gluonic penguins arelarge & complicate extraction of a
I- Charmless B Decays
Interference of T & P results in Direct CPviolation & sensitivity to g
Direct CP asymmetrysensitive to sin(2b+g) arg(Vub)=g
Same finalstate via B0
mixing & b‡u
6#
Experimental Observables
With Tree and Penguins both in action:
ãä |T
P|cpA
|T
P|ãä |
T
P|Br
)iä|P|eiã(|T|eA)iä|P|eiã(|T|eA
sinsin2
2coscos21
-=
++µ
+--=+-=
To constrain g requires estimates of:
| Ppp/Tpp| & relative strong phase d
ÿBranching fractions for various non-charm B decays
ÿTime Integrated (Direct) CP asymmerties
)fÂÃf)ÂÃ
f)ÂÃ)fÂÃAcp
Æ(+Æ(
Æ(-Æ(=
7#
More observables: Time – Dependent CP Asymmetries
)==== ahl a 2sin(&02**
**
SCeVVVV
VVVV i
udubtdtb
udubtdtb
With Tree alone
2
2
1
1
||
||
l
l
+
-=fC
21
2
||
)Im(
ll
+=fS
ÿ Time evolution of tagged B0 decays, e.g. in the case of B0 Æ p+p-
)]tmcos(C)tmsin(S1[4
e)t(f dfdf
)/t(
DDDD±t
=DtD-
± m
CPV due to mixing and decay interference
Direct CPV in Decay)(
)(
p
q0
0
fBA
fBA
Æ
Æ=l
iãeiäe|T
P|1
iãeiäe|T
P|1
2ieë-+
+= a
With Penguin and TreeS=sin2aeff
Da=aeff –a
C ≠ 0
Belle: Af = - Cf (BaBar)
8#
A few comments on the already established pattern fromcharmless 2-body decays
Connected via Isospin symmetry(Gronau &London) (Isospin engineering)
( ) ( )00 ∂∂∂∂~ ++-- Æ=Æ BABA
( )-+Æ ∂∂~
2
10BA
( )-+Æ ∂∂2
10BA
( )000 ∂∂ÆBA
( )000 ∂∂~
ÆBA∂∂kDa
With Tree alone,expect:
%5ªÆB
Æ
pppKB
4ªÆB
Æ
pppKB
Measurements:
ËPenguins are significant players
P’ & use SU(3)connections to estimate P
(P’ & T’)
(P’)
(P & T)(P & T)
(T)
(P’ & T’)(P’ & T’)
Control rescattering effects
Constructing these triangles is amajor goal of the experiments
9#
Goals and Issues on the Measurement Side
ÿThe reality (Considering the presences of large Penguin effects)
ÿNo single measurement is expected to lead to determination of a & g
ÿNeed info from many decay modes and the emerging pattern & connectionsvia symmetries, [isospin, SU(3) ], and eventually more predictive theories[perhaps QCD factorization or perturbative QCD- when verified ] to constrainvarious components of the problem.
ÿSearch for CP violation: Direct (C≠ 0) & Indirect (S≠0) deviating from(sin2b): [i.e. indirect CPV outside of mixing phase.]
ÿMeasure/Constrain a & g using many different modes and exploit theredundancy to resolve the ambiguities.
Keep finding the pieces of the charmless puzzle a & gThe job description Eventually
10#
Experiments and Data
Belle at KEK-B Machine140 fb-1 on U(4s) (158 fb-1 total)
152x106 B B events
BaBar at SLAC PEP-II Machine113 fb-1 on U(4s) ( 126 fb-1 total)
124x106 B B events
CLEO at the CESR Machine – Some results on Br & direct Asymmetries.
The pioneer of the field and the first source of information on B decays,
Including observation of charmless decays. [~13 fb-1 on peak]
Asymmetric e+e- B Factories:Physics coverage : Bd & Bu Decays
The B physics reach of hadronmachines & current status coveredby Kevin Pitts . Next Talk
The focus of this talk
11#
Analysis Issues for Rare B Charmless decays
-Looking for modes with Br~10-6 to 10-5
-Continuum qq(bar) background at 103 larger than the signal BKG Suppression using event shape & topology, kinematics, particle ID,..
Kinematic variables:
DE=Ebeam-EB
provides separationof KK, Kp, pp decays
22Bbeam pEMes -=
Signal Monte Carlo
p+p-
Other info into analysis:
ÿ Dt=Dz/<cgb>
ÿFlavor tag of other side
ÿParticle ID, event shape,..
12#
The road to a: Measurement of CPV in B‡p+ p-
p+p-
Kp
BaBar: 81 fb-1 Belle 78 fb-1
p+p- Kp
Isolation of Signals
~200 B‡p+ p-
Per experiment
Kp
p+p-
13#
Time Dependent CPV in B‡p+ p-
(BaBar)
Asy
mm
etry
E
vent
s/1p
s
(Belle)
5-5 0
5-5 0
B0 tag
B0 tag
Fits to: )]tmcos(C)tmsin(S1[4
e)t(f dfdf
)/t(
DDDD±t
=DtD-
± m
81 fb-1 78 fb-1
04.025.030.0
05.034.002.0
±±-=
±±=
pp
pp
C
S
)(08.027.077.0
41.023.1 08.007.0
pppp
pp
AC
S
-±±-=
±-= +-
Dt(ps) Dt(ps)
14#
New Results:BaBar Update of CPV measurementswith full data sample (Run 1+2+3): 113 fb-1 on Peak data
013.0041.0107.0
05.019.019.0
03.022.040.0
±±-=
±±-=
±±-=
p
pp
pp
KA
C
S
4.105.12
5.373.873
0.249.265
±=
±=
±=
KK
K
N
N
N
p
pp
ÿReprocessed Run1+2 (82 fb-1 )
ÿAdded Run 3 ((31 fb-1 )
New CPV Results
Run1+2(reprocessed)
S=-0.252±0.27 C=-0.166 ±0.22
Run 3
S=-0.67±0.35 C=-0.33 ±0.34
B0 tag
B0 tag
15#
Summary of CPV in B‡p+ p-:
Current world average (with BaBar new results)
S=-0.58±0.20 C=-0.38 ±0.16
Too early to claim observation of CPV in B‡p+ p- :Direct (in decay) or Indirect(mixing & decay)
Belle’s update with their full data set awaited
S & C not enough to measure a:
Need Da=aeff – a, which requires the otherpieces of the isospin analysis.
What about g: Current errors are still toolarge to allow for simultaneous extraction of g &ratio of (b‡c) and (b‡u) amplitudes (rdk) andthe strong phase. Need many fold more data.(dg~20 may be possible with 500 fb-1)
With assumptions on (rdk): mild limits can beextracted. e.g M. Gronau (hep-ph/0306308): g>72o at1 sigma level.
35#
Reaching sin(2b+g)
via
(b‡u(cd) & b‡c(ud) interference
(& B0 mixing)
B0‡D(*+) p-
Method and observables first suggested by Sachs,Dunietz
36#
B0‡D(*+)p- Modes
c0B
d
b ud
*D-
p+
()
Dominant diagramb ‡ c transition
d
bc
d
p+0Bu
*D-()Suppressed diagramb ‡ u transition
0B
b
d
*||)( udcbi VVeADBA 2
10 dp µÆ -+ gdp i
ubcdi eVVeADBA ||||)( *
20 2µÆ -+
)}sin()cos(1{),(
)}sin()cos(1{),(|0
|0
tmStmCNetDBP
tmStmCNetDBP
ddt
ddt
DD-DD=DÆ
DD+DD±=DÆD|G-±
D|G-±
mm
mm
mp
p
Time evolution:
)±++
=± dgb2sin(1
22r
rS
22111rCr-=+ª
02.0)(
)(0
0
ªÆ
Æ=
+-
+-
pp
DBA
DBAr Small asymmetry expected
37#
BaBar
II - Fully reconstructed
B0‡D(*+)p- Decays
Lepton tags kaons tags
()()0000tagtagtagtagBBCPBBNNNN-=+A
Belle Fully reconstructed B0‡D(*+)p- Decays
)±±±=-+
)±±±=++
)±±±=-+
)±±±=++
ndgb
ndgb
ndgb
ndgb
pp
pp
pp
pp
lDr
lDr
lDr
lDr
DD
DD
DD
DD
*(036.0013.0056.0022.0)2sin(2
*(036.0013.0059.0094.0)2sin(2
*(036.0016.0056.0033.0)2sin(2
*(036.0016.0059.0092.0)2sin(2
**
**
**
I- Partially reconstructed B0‡D*+p- Decays: (number of events)
Summary & Conclusionsÿ Major progress made in probing the charmless sector of B decays for
information on unitarity angles a & g:ÿ New updated measurements of CPV in B‡ p+p- still show no
significant evidence for CP violation in this mode.ÿ Observation of B‡p0 p0 – a missing component of Tree/Penguin disentanglement plan.ÿ CPV studies in B‡rp shows hints of direct CP violation.ÿ The decay B‡rr is now measured and looks promising for CPV
studies and constraining a. Indications that penguins are smaller.ÿ Indication of direct CPV in B‡K-p+ (WA: Belle, BaBar, CLEO) No indication for large direct CP yet.ÿ The emerging constraints on the angles from the pattern of data are
consistent with the favored range from the CKM picture in theStandard Model.
ÿ Penguin free modes (B‡DK & D*p) are beginning to contribute toconstraints on CKM parameters & many new B‡DK modes identified.
ÿ Much more data & major progress in theoretical understanding ofhadronic B decays needed to complete the picture and conclusivelyperform the CKM unitarity test.