Unitarity Triangle Analysis: Past, Present, Future
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Unitarity Triangle Analysis: Past, Present, Future
• INTRODUCTION: quark masses, weak couplings and CP in the Standard Model• Unitary Triangle Analysis: PAST• PRESENT• FUTURE
Dipartimento di Fisica di Roma I Guido Martinelli Cortona May 25th 2005
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C, CP and CPT and their violation arerelated to the foundations of modernphysics (Relativistic quantum mechanics, Locality, Matter-Antimatter properties,Cosmology etc.)
Although in the Standard Model (SM)all ingredients are present, new sourcesof CP beyond the SM are necessary to explain quantitatively the BAU
Almost all New Physics Theoriesgenerate new sources of CP
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Quark Masses,Weak Couplings and
CP Violation in the Standard Model
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Lquarks = Lkinetic + Lweak int + Lyukawa
In the Standard Model the quark mass matrix, from which the CKM Matrix and CP originate, is determined by the Yukawa Lagrangian which couples fermions and Higgs
CP invariant
CP and symmetry breaking are closely related !
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QUARK MASSES ARE GENERATED BY DYNAMICAL SYMMETRY BREAKING
Charge -1/3∑i,k=1,N
[ mui,k (ui
L ukR
)
+ mdi,k (di
L dkR) + h.c. ]
Charge +2/3
Lyukawa ∑i,k=1,N [ Yi,k (qi
L HC ) UkR
+ Xi,k (qiL H ) Dk
R + h.c. ]
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Diagonalization of the Mass Matrix
Up to singular cases, the mass matrix can always be diagonalized by 2 unitary transformations
uiL Uik
L ukL ui
R UikR uk
R
M´= U†L M UR (M´)† = U†
R (M)† UL
Lmass mup (uL uR + uR uL ) + mch(cL cR + cR cL ) +
mtop(tL tR + tR tL )
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N(N-1)/2 angles and (N-1)(N-2) /2 phases
N=3 3 angles + 1 phase KM the phase generates complex couplings i.e. CP violation; 6 masses +3 angles +1 phase = 10 parameters
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CP Violation is natural with three quarkgenerations (Kobayashi-Maskawa)
With three generations all CPphenomena are related to the same
unique parameter ( )
NO Flavour Changing Neutral Currents (FCNC) at Tree Level
(FCNC processes are good candidates for observing NEW PHYSICS)
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Vud Vus Vub
Vcd Vcs Vcb
Vtb Vts Vtb
Quark masses &Generation Mixing
NeutronProton
e
e-
downup
W
| Vud |
| Vud | = 0.9735(8)| Vus | = 0.2196(23)| Vcd | = 0.224(16)| Vcs | = 0.970(9)(70)| Vcb | = 0.0406(8)| Vub | = 0.00363(32)| Vtb | = 0.99(29) (0.999)
-decays
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1 - 1/2 λ2 λ A λ3(ρ - i η)
- λ 1 - 1/2 λ2 A λ2
Aλ3 × (1- ρ - i η)
- A λ2 1
+ O(λ4)
The Wolfenstein Parametrization
λ ~ 0.2 A ~ 0.8 η ~ 0.2 ρ ~ 0.3
Sin 12 = λSin 23 = A λ2
Sin 13 = A λ3(ρ-i η)
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a1
a2
a3
b1
b2
b3
d1
e1
c3
The Bjorken-Jarlskog Unitarity Triangle| Vij | is invariant under
phase rotationsa1 = V11 V12
* = Vud Vus*
a2 = V21 V22* a3
= V31 V32*
a1 + a2 + a3 = 0(b1 + b2 + b3 = 0 etc.)
a1
a2a3
Only the orientation dependson the phase convention
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From A. StocchiICHEP 2002
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sin 2 is measured directly from B J/ Ks
decays at Babar & Belle
(Bd0 J/ Ks , t) - (Bd
0 J/ Ks , t) AJ/ Ks =
(Bd0 J/ Ks , t) + (Bd
0 J/ Ks , t)
AJ/ Ks = sin 2 sin (md t)
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DIFFERENT LEVELS OF THEORETICAL UNCERTAINTIES (STRONG INTERACTIONS)
1) First class quantities, with reduced or negligible
uncertainties
2) Second class quantities, with theoretical errors of O(10%) or less that can be
reliably estimated
3) Third class quantities, for which theoretical predictions are model dependent (BBNS, charming, etc.)
In case of discrepacies we cannot tell whether is new physics orwe must blame the model
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Quantities used in the Standard UT Analysis
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M.Bona, M.Ciuchini, E.Franco,
V.Lubicz, G.Martinelli, F.Parodi,
M.Pierini, P.Roudeau, C.Schiavi,
L.Silvestrini, A.Stocchi
Roma, Genova, Torino, Orsay
THE COLLABORATION
www.utfit.org
www.utfit.org
NEW 2004 ANALYSIS IN PREPARATION
• New quantities e.g. B -> DK will be included
• Upgraded experimental numbers after Bejing THE CKM
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PAST and PRESENT
(the Standard Model)
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With the constraint fromms
ρ = 0.196 0.045 η = 0.347 0.025 [ 0.104 - 0.283] [ 0.296 - 0.386] at 95% C.L.
sin 2 = - 0.21 0.24 sin 2 = 0.726 0.028 [ -0.65 - +0.27] [ 0.670 - 0.780]
Results for ρ and η & related quantitiesResults for ρ and η & related quantities
contours @ 68% and
95% C.L.
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sin 2 measured = 0.726 0.037
Comparison of sin 2 from direct measurements (Aleph, Opal, Babar, Belle and CDF) and UTA analysis
Comparison of sin 2 from direct measurements (Aleph, Opal, Babar, Belle and CDF) and UTA analysis
sin 2 UTA = 0.725 ± 0.043
Very good agreement no much room for physics beyond the SM !!
sin 2 UTA = 0.698 ± 0.066 prediction from Ciuchini et al. (2000)
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Theoretical predictions of Sin 2 in the years
predictions exist since '95
experiments
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Crucial Test of the Standard ModelTriangle Sides (Non CP) compared to
sin 2 and K From the sidesonly sin 2 =0.734 0.043
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PRESENT: sin 2 from B -> & ρρ
and (2+) from B -> DK & B -> D(D*)
FROM UTA
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ms Probability Densityms Probability Density
Without the constraint fromms
ms = (21.2 ± 3.2 ) ps-1
[ 15.4 - 27.8] ps-1 at 95% C.L.
With the constraint fromms
ms = (18.5 ± 1.6) ps-1
[ 15.6 - 23.1] ps-1 at 95% C.L.
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Hadronic parameters Hadronic parameters
fBd √BBd = 223 33 12 MeV
fBd √BBd = 217 12 MeVUTA
BK = 0.86 0.11 lattice
BK = 0.69 0.10 UTA
lattice
fBs √BBs = 276 38 MeV 14%
fBs √BBs = 265 13 MeV 5%lattice
UTA
5%10%
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Limits on Hadronic Parameters
fBs √BBs
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PRESENT(the Standard Model)
NEW MEASUREMENTS
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B
B B
sin 2 from B ->
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sin 2 from B ->
could be extracted by measuring
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sin 2 from B ->
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PRESENT & NEAR FUTURE
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MAIN TOPICS
• Factorization• What really means to test Factorization • B and B K decays and the determination of the CP parameter • Results including non-factorizable contributions • Asymmetries• Conclusions & Outlook
From g.m. qcd@work martinafranca 2001
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CHARMING PENGUINS GENERATELARGE ASYMMETRIES
BR(B) - BR(B) BR(B) + BR(B)
A =
BR(K+ 0)
BR(K+ -)
BR(+-)Large uncertainties
typical A ≈0.2(factorized 0.03)
From g.m. qcd@work martinafranca 2001
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CP VIOLATION IN B DECAYS IN THE SM AND BEYOND
G. Martinelli – University of RomeWith M. Ciuchini, E. Franco, A. Masiero, M. Pierini and L.
Silvestrini
•General ideas about B->M1M2
•B->, K•Supersymmetry in B decays ?•Conclusions
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• BBNS, PQCD & SCET: B decays to light mesons can be consistently computed at NLO in terms of form factors & distribution amplitudes in the MB-> limit
• Is this limit phenomenologically viable?– Expect O(/M)10-20% corrections to
leading factorized amplitudes– Fine unless factorized amplitude suppressed
and/or corrections enhanced
General ideas about B -> M1M2 (I)
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• Corrections to penguins in charmless b->s decays doubly Cabibbo-enhanced w.r.t tree contribution: ( /M)x(1/λ2)>>1 dominant effect! Ciuchini, Franco, G.M., Silvestrini
• Possible physical idea: long-distance contributions in penguin contractions of current-current operators:Charming (c) and GIM (c – u) penguins
CFMS; recently revisited in SCET by Bauer, Pirjol, Rothstein & Stewart
General ideas about B -> M1M2
(II)
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• Our analysis: BR’s Ciuchini, Franco, G.M., Pierini, Silvestrini
• K00 2 too low: “K puzzle”? Fleischer, Mannel; Buras, Fleischer; Buras, Fleischer, Recksiegel, Schwab;
B -> K DECAYS (I)
Channel Fit x 106 Exp x 106
K+0 12.20.6 12.81.1
K+- 18.40.7 18.20.8
K00 8.60.5 11.91.5
K0+ 22.80.9 21.81.4
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• Our analysis: CP asymmetries CFMPS
• Interesting correlations between asymmetries: see plots
B -> K DECAYS (II)
Channel Fit Exp
K+0 -0.060.03
0.000.07
K+- -0.080.03
-0.0950.028
K00 0.030.05 0.030.37
K0+ -0.010.03
0.020.06
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B -> K DECAYS (III)
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Repeat with several fCP final states
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59(16)Using also the DalitzPlot Method
Tree level diagrams, not influenced by new physics
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Only tree level processes
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FUTURE:
FCNC &CP Violation
beyond the Standard Model
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CP beyond the SM (Supersymmetry)
Spin 1/2 Quarks
qL , uR , dR
Leptons
lL , eR
Spin 0 SQuarks
QL , UR , DR
SLeptons
LL , ER
Spin 1 Gauge bosons
W , Z , , g
Spin 1/2 Gauginos
w , z , , g
Spin 0 Higgs bosons
H1 , H2
Spin 1/2 Higgsinos
H1 , H2
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In general the mixing mass matrix of the SQuarks (SMM) is not diagonal in flavour space analogously to the quark caseWe may either Diagonalize the SMM
z , , g
QjLqj
L
FCNC
or Rotate by the same matrices the SUSY partners of the u- and d- like quarks(Qj
L )´ = UijL Qj
L UjLUi
L dkL
g
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In the latter case the Squark MassMatrix is not diagonal
(m2Q )ij = m2
average 1ij + mij2 ij = mij
2 /
m2average
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Deviations from the SM ? Model independent analysis: Example B0-B0 mixing(M.Ciuchini et al. hep-ph/0307195)
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SM solution
Second solutionalso suggestedby BNNS analysisof B ->K, decays
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TYPICAL BOUNDS FROM MK AND K
x = m2g / m2
q
x = 1 mq = 500 GeV
| Re (122)LL | < 3.9 10-2
| Re (122)LR | < 2.5 10-3
| Re (12)LL (12)RR | < 8.7 10-4
from MK
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from K
x = 1 mq = 500 GeV
| Im (122)LL | < 5.8 10-3
| Im (122)LR | < 3.7 10-4
| Im (12)LL (12)RR | < 1.3 10-4
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MB and A(B J/ Ks )
MBd = 2 Abs | Bd | H | Bd |
eff
B=2
A(B J/ Ks ) = sin 2 sin MBd t
2 = Arg | Bd | H | Bd |
eff
eff eff
B=2
sin 2 = 0.726 0.037 from exps BaBar & Belle & others
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TYPICAL BOUNDS ON THE -COUPLINGS
B0 | HeffB=2 | B0 = Re ASM + Im ASM
+ ASUSY Re(13d )AB
2 + i ASUSY Im(13d )AB
2
A, B =LL, LR, RL, RR
1,3 = generation index
ASM = ASM (SM )
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TYPICAL BOUNDS ON THE -COUPLINGS B0 | Heff
B=2 | B0 = Re ASM + Im ASM
+ ASUSY Re(13d )AB
2 + i ASUSY Im(13d )AB
2
Typical bounds: Re,Im(13
d )AB 1 5 10-2
Note: in this game SM is not determinedby the UTA From Kaon mixing: Re,Im(12
d )AB 1 10-4
SERIOUS CONSTRAINTS ON SUSY MODELS
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CP Violation beyond the Standard Model
Strongly constrained for b d transitions,Much less for b s :
BR(B Xs ) = (3.29 ± 0.34) 10-4
ACP (B Xs ) = -0.02 ± 0.04
BR(B Xs l+ l-) = (6.1 ± 1.4 ± 1.3) 10-6
The lower bound on B0s mixing ms > 14 ps -1
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b
b s
s
sg
Wb s
s
s
t
SM Penguins
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SUSY Penguins
b
b s
s
sg
Wb s
s
s
t Recent analysesby G. Kane et al.,Murayama et al.andCiuchini et al.
Also Higgs (h,H,A)contributions
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AKs = - CKs cos(mB t) + SKs sin(mBt )
ACP (Bd -> Ks ) (2002 results)Observable BaBar Belle Average SM prediction
BR (in 10-6) 8.1+3.1 0.8 8.7
+3.8 1.5 8.7 +2.5
~ 5
SKs -0.19+0.520.09 -0.730.64
0.09 -0.390.41
+0.7340.054
CKs _
0.560.41 0.12 0.560.43 -0.08
-2.5 -3.0 -2.1
-0.50
One may a also consider Bs -> (for which there is an upper bound from Tevatron, CDF BR < 2.6 10 - 6)
[ACP (Bd -> K ) do not give significant constraints ]
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AKs = - CKs cos(mB t) + SKs sin(mBt )
ACP (Bd -> Ks ) (2003 results)Observable BaBar Belle Average SM prediction
SKs +0.47 0.34+0.08 -0.96 0.50 +0.730.07
see M. Ciuchini et al. Presented at Moriond 2004 by L. Silvestrini
-0.06 -0.11
+0.09
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WHY RARE DECAYS ?Rare decays are a manifestation of broken(accidental) symmetries e.g. of physics beyond the Standard Model
Proton decay baryon and lepton number conservation
-> e + lepton flavor numberi -> k
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RARE DECAYS WHICH ARE ALLOWEDIN THE STANDARD MODEL
FCNC: qi -> qk +
qi -> qk + l+ l
-
qi -> qk +
these decays occur onlyvia loops because of GIMand are suppressed by CKM
THUS THEY ARE SENSITIVE TO NEW PHYSICS
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Why we like K ? For the same reason as AJ/ Ks
:
1) Dominated by short distance dynamics(hard GIM suppression, calculable in pert. theory ) 2) Negligible hadronic uncertainties (matrix element known)
O(G2F ) Z and W penguin/box s d diagrams
SMDiagrams
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Heff =G2F / (2√2 s2
W )[ Vtd Vts* Xt + Vcd Vcs
* Xc ]
( s (1 - 5 ) d) ( (1 - 5 ) )
NLO QCD corrections to Xt,c and O(G3F m4
t) contributions known
the hadronic matrix element ‹ | s (1 - 5 ) d | K›is known with very high accuracy from Kl3 decays
sensitive to Vtd Vts* and expected large CP
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A(s d ) O(λ5
m2t ) + i O(λ5
m2t ) CKM suppressed
O(λ m2c ) + i O(λ 5
m2c )
O(λ 2
QCD ) GIM
CP conserving: error of O(10%) due to NNLOcorrections in the charm contribution and CKM uncertainties BR(K+)SM = (7.2 2.0) 10-11
BR(K+)EXP = (15.7+17.5- 8.2 ) 10-
11- 2 events observed by E787 - central value about 2 the value of the SM- E949 10-20 events in 2 years
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K+ -> +
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CP ViolatingKL 0
O(λ5 m2
t ) + i O(λ m2t )
O(λ m2c ) + i O(λ 5
m2c )
O(λ 2
QCD )
BR(K+)SM = 4.30 10-10 (mt (mt )/170GeV)2.3
(Im(Vts* Vtd )/ λ5
)2 = (2.8 1.0) 10-11
dominated by thetop quark contribution-> short distances (or new physics)
theoretical error ˜ 2 %
Using (KL 0 ) < (K+ + ) One gets BR(KL 0 ) < 1.8 10-9 (90% C.L.) 2 order of magnitude larger than the SM expectations
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Unitarity Triangle Analysis: Past, Present, Future
CONCLUSION:
Why there must be a conclusion?
experiments and theory continue
Dipartimento di Fisica di Roma I Guido Martinelli Cortona May 25th 2005