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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 Bejing
2004
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C, CP and CPT and their violation are related to
the foundations of modern physics (Relativistic
quantum mechanics, Locality, Matter-Antimatter
properties, Cosmology etc.)
Although in the Standard Model (SM) all
ingredients are present, new sources of CP
beyond the SM are necessary to explain
quantitatively the BAU
Almost all New Physics Theories generate new
sources of CP
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Quark Masses, Weak Couplings and CP Violation
in the Standard Model
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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
Lquarks Lkinetic Lweak int Lyukawa
CP invariant
CP and symmetry breaking are closely related !
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QUARK MASSES ARE GENERATED BY DYNAMICAL
SYMMETRY BREAKING
Charge 2/3
Lyukawa ? ?i,k1,N Yi,k (qiL HC ) UkR
Xi,k (qiL H
) DkR h.c.
Charge -1/3
?i,k1,N mui,k (uiL ukR ) mdi,k
(diL dkR) 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
? UikL ukL uiR ? UikR ukR M UL
M UR (M) UR (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
N3 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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NO Flavour Changing Neutral Currents (FCNC) at
Tree Level (FCNC processes are good candidates
for observing NEW PHYSICS)
CP Violation is natural with three
quark generations (Kobayashi-Maskawa)
With three generations all CP phenomena are
related to the same unique parameter ( ? )
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Quark masses Generation Mixing
Vud 0.9738(5) Vus 0.2200(26) Vcd
0.224(16) Vcs 0.970(9)(70) Vcb
0.0406(8) Vub 0.00363(32) Vtb
0.99(29) (0.999)
e-
?-decays
W
?e
down
up
Neutron
Proton
Vud
Vcd 0.239(10)(24)(20)
Vcs 0.969(39)(94)(24)
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cij Cos ?ij sij Sin ?ij cij 0
sij 0 0 ? ? ? 2 ? s12 Sin
?c for small angles sij Vij
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The Wolfenstein Parametrization
O(?4)
? 0.2 A 0.8 ? 0.2 ? 0.3
Sin ?12 ? Sin ?23 A ?2 Sin ?13 A ?3(?-i ?)
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The Bjorken-Jarlskog Unitarity Triangle
Vij is invariant under phase rotations
a1
b1
a1 V11 V12 Vud Vus a2 V21 V22 a3
V31 V32
d1
a2
b2
e1
a1 a2 a3 0 (b1 b2 b3 0 etc.)
a3
b3
c3
?
a3
a2
Only the orientation depends on the phase
convention
a1
?
?
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From A. Stocchi ICHEP 2002
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sin 2? is measured directly from B J/?
Ks decays at Babar Belle
?(Bd0 J/? Ks , t) - ?(Bd0 J/? Ks , t)
AJ/? Ks
?(Bd0 J/? Ks , t) ?(Bd0 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 or we must blame the model
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Quantities used in the Standard UT Analysis
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• NEW 2004 ANALYSIS IN PREPARATION
• New quantities e.g. B -gt DK will be included
• Upgraded experimental numbers after Bejing

www.utfit.org
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PAST and PRESENT (the Standard Model)
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Results for ? and ? related quantities
With the constraint from?ms
contours _at_ 68 and 95 C.L.
? 0.174 ? 0.048 ? 0.344 ? 0.027
0.085 - 0.265 0.288 - 0.397
at 95 C.L.
sin 2 ? - 0.14 ? 0.25 sin
2 ? 0.697 ? 0.036 -0.62 - 0.33
0.636 - 0.779
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Comparison of sin 2 ? from direct measurements
(Aleph, Opal, Babar, Belle and CDF) and UTA
analysis
sin 2 ?measured 0.739 ? 0.048
sin 2 ?UTA 0.685 0.047
sin 2 ?UTA 0.698 0.066 prediction from
Ciuchini et al. (2000)
Very good agreement no much room for physics
beyond the SM !!
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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 sides only sin 2 ?0.715 ?
0.050
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• PRESENT sin 2? from B -gt ?? ??
• and (2??) from B -gt DK B -gt D(D) ?

FROM UTA
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?ms Probability Density
Without the constraint from?ms
?ms (20.6 3.5 ) ps-1 14.2 - 28.1 ps-1 at
95 C.L.
With the constraint from?ms
1.7
?ms (18.3 ) ps-1 15.6 - 22.2 ps-1 at
95 C.L.
-1.5
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Hadronic parameters
fBs vBBs 276 ? 38 MeV 14
lattice
fBs vBBs 279 ? 21 MeV 8
UTA
6
4
fBd vBBd 223 ? 33 ? 12 MeV
lattice
fBd vBBd 217 ? 12 MeV
UTA
BK 0.86 ? 0.06 ? 0.14
lattice
(0.13)
BK 0.69
UTA
(-0.08)
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Limits on Hadronic Parameters
fBs vBBs
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PRESENT (the Standard Model) NEW MEASUREMENTS
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sin 2? from B -gt ??
?
?
?
B
B
B
?
?
?
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sin 2? from B -gt ??

• could be extracted by measuring

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sin 2? from B -gt ??
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PRESENT NEAR FUTURE
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MAIN TOPICS

• Factorization (see M. Neubert talk)
• 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_at_work martinafranca 2001
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CHARMING PENGUINS GENERATE LARGE ASYMMETRIES
BR(B) - BR(B) BR(B) BR(B)
A
BR(K ?0)
?
typical A 0.2 (factorized 0.03)
BR(K ?-)
Large uncertainties
BR(??-)
From g.m. qcd_at_work martinafranca 2001
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B -gt DK (K)
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Tree level diagrams, not influenced by new physics
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B -gt D K (K) and ?(b-gtu)/?(b-gtc)
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FUTURE FCNC CP Violation beyond the
Standard Model
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CP beyond the SM (Supersymmetry)
Spin 0 SQuarks QL , UR
, DR SLeptons
LL , ER
Spin 1/2 Quarks qL ,
uR , dR Leptons
lL , eR
Spin 1/2 Gauginos w , z ,
? , g
Spin 1 Gauge bosons 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 case We may either
Diagonalize the SMM
z , ? , g
FCNC
QjL
qjL
Rotate by the same matrices the SUSY partners of
the u- and d- like quarks (QjL ) UijL QjL
or
g
UjL
UiL
dkL
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In the latter case the Squark Mass Matrix is not
diagonal
(m2Q )ij m2average 1ij ?mij2 ?ij ?mij2
/ 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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Second solution also suggested by BNNS
analysis of B -gtK?, ? ? decays
SM solution
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TYPICAL BOUNDS FROM ?MK AND ?K x
m2g / m2q x 1 mq 500 GeV
Re (?122)LL lt 3.9 ? 10-2 Re
(?122)LR lt 2.5 ? 10-3 Re (?12)LL
(?12)RR lt 8.7 ? 10-4
from ?MK
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from ?K x 1 mq 500 GeV
Im (?122)LL lt 5.8 ? 10-3 Im
(?122)LR lt 3.7 ? 10-4 Im (?12)LL
(?12)RR lt 1.3 ? 10-4
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?MB and A(B J/ ? Ks )
?MBd 2 Abs ? Bd H Bd ?
?B2
eff
A(B J/ ? Ks ) sin 2 ? sin ?MBd
t 2 ? Arg ? Bd H Bd ?
eff
?B2
eff
eff
sin 2 ? 0.734 ? 0.054 from exps BaBar
Belle others
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TYPICAL BOUNDS ON THE ?-COUPLINGS
A, B LL, LR, RL, RR 1,3 generation index
ASM ASM (?SM )
? B0 Heff?B2 B0 ? Re ASM Im ASM
ASUSY Re(?13d )AB2 i ASUSY Im(?13d )AB2
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TYPICAL BOUNDS ON THE ?-COUPLINGS
? B0 Heff?B2 B0 ? Re ASM Im ASM
ASUSY Re(?13d )AB2 i ASUSY Im(?13d )AB2
Typical bounds Re,Im(?13d )AB ? 1? 5
?10-2 Note in this game ?SM is not
determined by the UTA From Kaon mixing
Re,Im(?12d )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 gt 14 ps -1
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SM Penguins
W
b
s
t
s
s
g
b
s
b
s
s
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SUSY Penguins
W
b
s
Recent analyses by G. Kane et al., Murayama et
al.and Ciuchini et al.
t
g
b
s
b
Also Higgs (h,H,A) contributions
s
s
s
s
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ACP (Bd -gt ? Ks ) (2002 results) Observable
BaBar Belle
Average SM prediction BR (in 10-6)
8.13.1? 0.8 8.73.8 ? 1.5 8.7 2.5
5 S?Ks
-0.190.52?0.09 -0.73?0.64 ?0.09 -0.39?0.41
0.734?0.054 C?Ks _
0.56?0.41 ?0.12 0.56?0.43 -0.08
-2.1
-2.5
-3.0
-0.50

• A?Ks - C?Ks cos(?mB t) S?Ks sin(?mBt )

ACP (Bd -gt ? K ) do not give significant
constraints
One may a also consider Bs -gt ?? (for which
there is an upper bound from Tevatron, CDF BR lt
2.6 10 - 6)
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ACP (Bd -gt ? Ks ) (2003 results) Observable
BaBar Belle
Average SM prediction S?Ks 0.47 ?
0.340.08 -0.96 ? 0.50
0.73?0.07 see
M. Ciuchini et al. Presented at Moriond 2004 by
L. Silvestrini
0.09
-0.11
-0.06

• A?Ks - C?Ks cos(?mB t) S?Ks sin(?mBt )

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PROGRESS SINCE 1988
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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 ? -gt e ?

lepton flavor
number ?i -gt ?k
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RARE DECAYS WHICH ARE ALLOWED IN THE STANDARD
MODEL
FCNC qi -gt qk ? ? qi -gt qk
l l- qi -gt qk ?
these decays occur only via loops because of
GIM and 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
SM Diagrams
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Heff G2F ?/ (2v2? s2W ) Vtd Vts Xt Vcd
Vcs Xc ? ( s ?? (1 -
?5 ) d) ( ? ?? (1 - ?5 ) ? )

? NLO QCD corrections to Xt,c and O(G3F m4t)
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(?5 m2t ) i O(?5 m2t )
CKM suppressed O(? m2c ) i O(? 5 m2c ) O(?
?2QCD ) GIM
CP conserving error of O(10) due to
NNLO corrections in the charm contribution and
CKM uncertainties BR(K)SM (7.2 ? 2.0) ?
10-11
BR(K)EXP (15.717.5- 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 -gt ? ??
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CP Violating KL ? ?0 ? ? O(?5 m2t ) i O(?
m2t ) O(? m2c ) i O(? 5 m2c ) O(? ?2QCD )
dominated by the top quark contribution -gt short
distances (or new physics)
theoretical error 2
BR(K)SM 4.30 ? 10-10 (mt (mt )/170GeV)2.3 ?
(Im(Vts Vtd )/ ?5 )2 (2.8 ? 1.0) ? 10-11
Using ?(KL ? ?0 ??) lt ?(K ? ? ??) One gets
BR(KL ? ?0 ??) lt 1.8 ? 10-9 (90 C.L.) 2 order
of magnitude larger than the SM expectations
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