implications of the recent results on cp violation and rare decay searches in the b and k meson...
DESCRIPTION
CP Violation in the Standard Model Local SU(2) invariance of L SM with doublets ( iL, l iL ), (u iL, d iL ), i=1..3 gives rise to charged weak currents Mass terms: require scalar doublet ( 1, 2 ) Spontaneous symmetry breaking leads to 3x3 quark mass matrices Unitary rotation from mass to flavour eigenstates via Modifies L SM for charged weak currents: Kobayashi- Maskawa 1973 CKM MatrixTRANSCRIPT
Implications of the Recent Results on CP Implications of the Recent Results on CP Violation and Rare Decay SearchesViolation and Rare Decay Searches
in the B and K Meson Systemsin the B and K Meson Systems
Jan Stark on behalf of Andreas HöckerLPNHE-Paris and Laboratoire de l”Acélérateur Linéaire-Orsay
France
Status of the CKM ParadigmStatus of the CKM Paradigm
Workshop WIN 2002
Christchurch, New ZealandJanuary 21-26, 2002
Quark Mass Mixing in the
Standard Model
The Unitarity Triangle
Constraining the CKM Matrix
statistical framework
standard constraints
charmless B decays
…and conclusion
Newest B and K Physics Results
OutlineOutline
CP Violation in the Standard Model Local SU(2) invariance of LSM with doublets (iL, liL), (uiL, diL), i=1..3
gives rise to charged weak currents
Mass terms: require scalar doublet (1, 2)
Spontaneous symmetry breaking leads to 3x3 quark mass matrices
Unitary rotation from mass to flavour eigenstates via
Modifies LSM for charged weak currents:
LRRLf ffffm
2g v
M u(d)u(d)
)m,m,diag(mUMU τ)t(b,μ)c(s,e)u(d,e)u(d,e)u(d, e)u(d,
d
UUV uCKM
Kobayashi-Maskawa 1973
Id)V(V CKMCKM
CKM MatrixCKM Matrix
1Ai1AA2/1
iA2/1V
23
22
32
CKM
Wolfenstein parametrization (expansion in ~ 0.2):
tbtstd
cbcscd
ubusud
CKM
VVVVVVVVV
V Complex matrix described by 4 independent real parameters
phase
ηλA 62J
0VVVV Im ** kjikijJ CP Violation:
SMin CPV no 0η
The Cabibbo-Kobayashi-Maskawa Matrix
(phase invariant!)Jarlskog 1985
The Unitarity Triangle(s)
γi22
cbcd
ubudu eηρ
VVVV
R
βi22
cbcd
tbtdt eη)ρ(1
VVVV
R
βγπα , argVγ *ub
0VVVV
VVVV
VVVV
cbcd
tbtd
cbcd
cbcd
cbcd
ubud
0VVVV
VVVV
VVVV
cscd
tstd
cscd
cscd
cscd
usud
B sector: K sector:
0λA λA 1
λA λA
3
3
3
3
Large CPV expected in the B system
0,0 0,1
RtRu
η,ρ
ρ
η
Constraining the Unitarity Triangle
Wolfenstein parameters:
and , A,
plane - and
:level 5% the At
:level 1% the At
|V||V|
06.083.0A/VA
V
0018.02205.0sinV
V
tdub
2cb
cb
cusus
What is the value of in our world ?
J/2
J
The Quest for CP Violation in the B System
ATLAS
BTEBTEVV
CLEO 3BBAABBARAR
Belle
2005 (???)
199919992000
2006
2001
Primary GoalPrimary GoalObtain precision measurements
in the domain of the charged weak interactions for testing the CKM sector of the Standard Model, andprobing the origin of the
CP violation phenomenon
CP Violation in InterferenceCP Violation in Interference
DecayMixing
B0 K0–
J/
d
b–
c–
c
s
d–W W
t
t–W
i2e~
Time-dependent CP Observable:
CP violation arises from interference between decays with and without mixing
t)sin( S t)cos(Δ C dfdf CPCP mm
)f(t)ob(BPr)f(t)Bob(Pr1λ CP0
CP0
fCP
0B
0B
CPfCP
mixing
decay
0t
tCPfA
CPfACP
CPCPCP
f
fff A
Apqηλ
CP eigenvalue i2e
amplitude ratio
2f
2f
f |λ|1|λ|1
CCP
CP
CP
2f
ff |λ|1
λ Im 2S
CP
CP
CP
cosine term sine term)sin(2α S π π B,B efff00 CP
2βsin S J/ψ B,B CPf0S
00 K
)f (t)Γ(B )f (t)BΓ()f (t)Γ(B )f (t)BΓ( (t)A
CP0CP0
CP0CP0fCP
0.79 0.10World average
sin2
sin2 per experiment: sin2eff (BABAR):
BABAR hep-ex/0110062
(submitted to PRD)
S+– = 0.03 ± 0.56
C+– = –0.25 ± 0.48
stat. and syst. errors aver-aged and symmetrized
Status: Lepton-Photon 2001
Rare B Decays and Rare B Decays and CP Violation in DecayCP Violation in Decay
f)Prob(B)fBProb(1/AA ff
φsin θsin AA)fBΓ(f)Γ(B)fBΓ(f)Γ(BA 21CP
Time-independent CP observable:
CPV in decay (“direct CPV”) arises from: Interference between various contributions to the decay amplitude
CP violation in decay amplitude
requires 2 decay amplitudes A1 and A2
Strong phase difference
Weak phase difference
For neutral modes, direct CP violation competes with other types of CP violation
partial decay rate asymmetry
1A Re
Im φ φ
θ
2A
CPVdirect no 0 Δθor 0 Δφ
fB fB
Teλ P A γi2Kπ
Also: CP-averaged BFs together with direct CPV can beused to obtain non-trivial constraints on CP angle
Fleischer, Mannel (98)Gronau, Rosner, London (94, 98)Neubert, Rosner (98)Buras, Fleischer (98)Beneke, Buchalla, Neubert, Sachrajda (01)Ciuchini et al. (01)
Theoretical analysis deals with:
SU(3) breaking Rescattering (FSI) W Annihilation EW penguins
B K and the Determination of Contributions from interfering tree and penguin amplitudes
Potential for significant direct CP asymmetries
Experimental tests: overall consistency of BF and direct CPV predictions
000
0
0
0
πKBπKBπKBππB
KKBπKBππB
0
0
0
%)90 (9.12.12.17
5.03.45.24.1
6.14.1
4.23.3
9.51.5
6.40.4
4.13.1
0.37.2
6.14
6.12.18
6.11
%)90(7.12
%)90 (5.2
3.16.17.167.00.11.4
2.12.8
0.22.18
0.18.10
8.07.5
1.37.2
3.30.3
1.29.1
0.28.1
%)90 (7.23.19
4.06.55.16.0
4.32.3
3.20.2
5.27.2
2.79.5
9.18.1
7.58.4
6.18.1
5.33.3
0.16
7.13
3.16
%)90(4.13
CLEO9.1 fb – 1
BABAR20.7 fb–1
BELLE10.5 fb – 1)10(BF 6
47.130.1
89.086.0
37.17
44.4
66.266.2
60.251.2
70.167.1
73.10
41.17
13.12
WorldAverage
B / K Branching Fractions, Summary
Compatibility among experiments. Most rare 2-body modes discovered!
Status: Lepton-Photon 2001
18.021.0)π(KA18.000.0)π(KA10.019.0)π(KA
0SCP
0CP
CP
BABAR
43.034.0
0SCP
22.020.0
0CP
19.017.0CP
10.0)π(KA
06.0)π(KA
04.0)π(KA
BABAR hep-ex/0105061
BELLE hep-ex/0106095BELLE
K
0K
πK0S
CLEO
BABAR
BELLE
24.018.0)π(KA23.029.0)π(KA16.004.0)π(KA
0SCP
0CP
CP
CLEO PRL 85 (2000) 525CLEO
Direct CP Asymmetries in K modes
Compatibility among experiments. No significant deviation from zero
Rare Kaon DecaysRare Kaon Decays
Rare Kaon Decays: K+ +–
2
τμ,e,ttd* tsNLcd* cs
422us
02 xXVVXVV
θsin 2π VνeπKB α νν π K BW
Semileptonic FCNC transition governed mainly by td coupling:
E787 (BNL-68713) hep-ex/0111091
Two decays detected so far at BNL (E787), yielding:
B(K+ +) = (1.57 +1.75 –0.82)10 –10
Theory:
Experiment:
Theoretical uncertainty domin. by charm exchange in box, in particular, mc
Consequences for the Consequences for the CKM Picture ? CKM Picture ?
http://www.slac.stanford.edu/~laplace/ckmfitter.html
Present Constraints
Parameter Observable Measurement Accuracy of constraint
Theoretical Uncertainties Quality
|Vud|
|Vus|
nuclear decayK+(0) +(0) e ~1% -
A |Vcb|Excl. B D*l Incl. b lXc
~5%FD*(1)
Model
2 + 2 |Vub|Excl. B0 ()l
Incl. b lXu
~17% ModelModel
(1–)–1 K CPV (K0) ~20% BK, cc, fK
’/K Direct CPV (K0) ? B6, B8 ?
(1–)2 + 2 md Mixing (Bd) 15% fBd, Bd
fBd2Bd ms Mixing (Bs) Lower limit
, sin2 CPV (bccs) 13% - , sin2 CPV (b uud) >100% Strong phases ?
, b uud,uus ? Strong Phases ?
(1–)2 + 2 |Vtd| K+ + ~50% charm loop ()
How can we Deal with Dominant Theoretical Uncertainties
Definition of the Fit Problem:
²(ymod) = – 2 ln L(ymod) (ymod = , A, , , ..., yQCD)
L(ymod) = Lexp(xexp – xtheo(ymod)) Ltheo(yQCD)
The experimental likelihood can be assumed to be Gaussian
Two main ways of approaching the theoretical likelihood:
Theoretical uncertainties arise from “Educated guesswork” (Hadronic Models, quenched approx., SU(3)-break., ...)
Critical piece of information from mind of physicistsCritical piece of information from mind of physicists
“Uniform likelihoods: ranges”
Frequentist Bayesian
“Probabilities”
If CL(SM) good
Obtain limits on New Physics parameters
If CL(SM) bad
Hint for New Physics: stop working and buy ticket to
Stockholm
Frequentist CKM Analysis using Rfit:
Three main analysis steps:
Test New PhysicsMetrologyProbing the SM
2
χχ
2 dχ)F(χCL(SM)2
modymin;2
Define: ymod = {a; µ} = {, , yQCD, ...}
Set Confidence Levels in {a} space, irrespective of the µ values:
Fit with respect to {µ} CL(a) = maxµ { CL(a, µ) }
Calculate confidence level: ²(a) = ²min; µ (a) – ²min;ymod
CL(a) = Prob(²min(a), Ndof)
Eval. global minimum: ²min;ymod
(ymod-opt)
“Fake” perfect agreement: xexp-opt = xtheo(ymod-opt)
generate xexp using Lexp
Re-perform many fits:
²min-toy(ymod-opt) F(²min-toy)
the package
Höcker, Lacker, Laplace, Le Diberder EPJ C21 (2001) 225, [hep-ph/0104062]
errorsrelevant less with parametersother Nierste) & (Herrlich 0.53 1.38 ) 2000 (Lattice 0.13 0.06 0.87 B) 2000 Lattice ( 0.05 0.03 1.16
) 2000 Lattice (GeV 0.028) 0.028 (0.230 Bf
2000)PDG (CDF/D0, GeV 5)(166 )(
rescaled)not 2001,Summer (WA, 0.102 0.793 sin22001) SLD, LEP, (CDF, Spectrum plitude Amm
) 2001 SLD, LEP, CDF, Belle, (BABAR, ps 0.008)(0.489 m
) 2000PDG ( 100.017)(2.271
(CLEO) lysisMoment Ana /Incl.Excl. 100.9) 1.3 (40.4 V
)Excl.(CLEOIncl.(LEP) 100.55)0.243.49 ( V
(OPAL) 0.058 0.969 V
)( :production dimuon 0.014 0.224 V
K 0.0025 0.2200 V
decay-nuclear neutron 0.00089 0.97394 V
cc
K
dB
s
1-d
3-K
3-cb
3-ub
cs
cd
us
ud
d
MSm
XXW
DISN
t
c
CLEO lepton-endpointmeasurement usingbs not yet included
Fit Inputs (Status: LP 2001)
B(K+ +) and charmless B decays not yet included
3-3Bs
1
cb
3-
3-cb
10)),1/M0.8(
exp):,0.9(1.0(40.4(CLEO) analysismoment |:V|
102) 2(41 :CLEO
102.0)0.5(40.7 :LEP
inclusive : |V|
semi-lep(B) quite safeB->D* at zero recoilmore vulnerable (1/mc)
)ph/9907270hep Bigi, I.I.(
08.089.0)0()Book Physics (
042.0913.0)0(
DB
DB
FBABAR
F
Status of |Vcb|
Bigi, N. Uraltsev: “A Vademecum on Quark-Hadron Duality”
hep-ex/0106346
CLEO
Belle
|Vcb| exclusive:LEP, CLEO, Belle
22
2
121
22
1ln2
21
212
211
1
AAs
AA
A
CL
A
AAmL
AErfcErfc
AErfcA
A
At present, we do not use the likelihood ratio. A rigorous proof that it provides a proper CL, for the present data set, must be given by means of a realistic Monte Carlo simulation.
CERN CKM Workshop (February’02)
Treatment of ms:
Lepton-Photon’01
Lepton-Photon’01
Probing the SM
Confidence Level of Standard Model: CL(SM) = 70%
²min;ymod = 2.3
Metrology (I)
LP’01 constraints
not including sin2
The standard constraints
5% CL bounds
Theoretical uncertainties
Metrology (I)
Compatible with sin2WA
Note: 4-fold ambiguity for
sin2
Metrology (I)
Zoom:
Metrology (I)LP’01 constraints including sin2Amplitude method
for ms limitLikelihood
ratio for ms
Metrology (II)
One-dimensional constraints:
Status: LP’01
Metrology (II)
One-dimensional constraint on sin2:
SM constraint without sin2
Differences among statistical approaches matter !
Metrology (III)
Constraints in the sin2 - sin2 plane:
LP’01 constraints not including sin2
Be aware of ambiguities !
Metrology (IV)
Constraints in the sin2 - plane:
Metrology (V)
Constraints from B(K+ +) [BNL-E787]:
At present dominated by experimental errors.
However: theoretical uncertainties will become important for constraints in the - plane
Metrology (VI)
Selected numerical results
Parameter 95% CL region
0.2221 ± 0.0041
A 0.763 – 0.905
0.07 – 0.37
0.26 – 0.49
J (2.2 – 3.7) 105
sin2 – 0.90 – 0.51
sin2 0.59 – 0.88
75º – 122º
18.1º – 30.8º
37º – 80º
mt (95 – 405) GeV/c2
Observable 95% CL region
BR(KL0) (1.6 – 4.4) 1011
BR(K++) (4.8 – 9.4) 1011
BR(B++) (5.6 – 23.8) 105
BR(B++) (2.2 – 9.4) 107
improves to 46º – 77º when using likelihood ratio for ms
Charmless B Decays Charmless B Decays
into two Pseudoscalarsinto two Pseudoscalars
HERE: FITS TO BBNS
BBNS: QCD FACTORISATION APPROACH:M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda
"QCD Factorization in B -> pK, pp Decays and Extraction of Wolfenstein Parameters", Nucl.Phys.B606 (2001) 245
PERTURBATIVE QCD APPROACH Y. -Y. Keum, H-n. Li and A.I. Sanda
“Penguin enhancement and B ->pK decays in perturbative QCD", hep-ph/0004173
M. Ciuchini, E. Franco, G. Martinelli, M. Pierini and L. Silvestrini,
“Charming Penguins strike back", Phys.Lett. B515 (2001) 33; “Two body B
Decays, Factorization and QCD / mB corrections”, hep-ph/0110022 S. J. Brodsky and S. Gardner,
“Evading the CKM Hierarchy”, hep-ph/0108121
F1F2
Endpoint Singularities ?
W Annihilation ?
b ( c c ) d ?
Sudakov ?
?
b W c d ?
C R I T I C I S M
W E A K N E S S E S ?
…and many more papers !
We follow…
ijji
jjii
udubF
eff
udbuO
udbuO
OCOCVVGH
21
21
21
21
24
552
551
2211*
From Naive Factorization…
b uu u
du
u
buu
ud
W
W
–
–
–
–
–
–
to the QCD Factorization Approach (BBNS, …)Color transparency:
energy release large qq pair in emitted meson is collinear soft gluons do not interact with small color dipole non-factorizable contributions calculable in pQCD
No problem for: mb However: mb finite (QCD/mb) corrections occur
B M1
M2
Non-perturbative physics:formation of M2 and B M1
Vertex corrections and penguinsHard spectator interactions
0ππB
Tree, strong and EW penguin Wilson coefficients are calculatedStrong phases are calculated and found to be small in general
direct CP asymmetries are smallthis is not in agreement with pQCD approach by Li, Keum, Sanda
Annihilation diagrams are not rigorously calculated but estimatedassumed to be small
Soft physics contribution in the spectator interaction is parametrizedassumed to be small
…in CKMfitter
Full BBNS calculation is implemented in CkmFitter Wilson Coefficients are calculated in each fit step incl. scale dependence Theoretical uncertainties are scanned within given ranges
Implementation of BBNS Model…
Fit to BR’s and ACP’s Within BBNS
BBNS5% CL
32%
90%
Compared to standard CKM fit Theoretical
uncertainties:
ms, mc, B, RK
Renorm. scale Gegenbauer mom.:a1(K), a2(K), a2()
F(B), fB
XH, XA
²min;ymod = 2.0
Prediction of BR’s for Unobserved Modes
Example: B0 00
Note: theoretical prediction uses BR of B+ +0 which is not known with sufficient accuracy at present !
Confidence Level
Branching Fraction
Large values of B0 00 correspond to 180º
γsin 0.181.06 )KBR(π)πBR(K
)τ(B)τ(B R 2
00
Fleischer-Mannel, Neubert-Rosner & BBNS
FM bound:
NR bound + additional theoretical input: 0.140.71 )KBR(π)πBR(K R 0
0*
0.034)(0.223BBNS)(SU(3),R )KBR(π )πBR(π 2
fftanθR ε T/P a) th0
0
π
Kcth3/2
small phases strong :FA(BBNS) b)Outlook to Summer 2002
Constraints if no penguins are present:
Sin2a = 0.31 4 ambiguities:
/2 – +
3/2 –
CL
0 1 2-1
0
-1
1
Time-Dependent CP Asymmetry in B+–
Use BABAR result: S = 0.03 +/– 0.56
& BBNS(Theoretical errors small compared to experiment)ππππ
iγππππ
iγ2iβ
ππ
2ππ
ππππ
/TPe/TPeeλ
λ12ImλS
constraint: sin2 & sin2
constraint: sin2 constraint: sin2
Global CKM fit gives consistent picture of Standard Model (CKMfitter) sin2 is competitive with the other (theoretically limited) constraints
consistency: BABAR Belle ?
ms : constraint on UT angle crucially depends on stat. interpretationfortunately: expect measurement from TEVATRON soon
More statistics needed for rare K decays
Need more constraints on CKM phase:
Charmless B decays and CP violation: best fits (in BBNS) around 80º
Other approaches intended to be implemented into CKMfittercollaboration with theorists much appreciated: please contact us !
Further discussion of theoretical uncertainties needed
ConclusionsConclusions
Summer ’02: (sin2) < 0.06 for 200 fb–1
http://www.slac.stanford.edu/~laplace/ckmfitter.html
More statistics to come from B-factories: interesting times ahead