1. 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

2. Almost all New Physics Theories generate new sources of CP
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

3. Quark Masses,
Weak Couplings and
CP Violation in
the Standard Model

4. 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
Lquarks = Lkinetic + Lweak int + Lyukawa
CP invariant
CP and symmetry breaking are
closely related !

5. Lyukawa  ∑i,k=1,N [ Yi,k (qiL HC ) UkR + Xi,k (qiL H ) DkR + h.c. ]
QUARK MASSES ARE GENERATED
BY DYNAMICAL SYMMETRY
BREAKING
Charge +2/3
Lyukawa  ∑i,k=1,N [ Yi,k (qiL HC ) UkR
+ Xi,k (qiL H ) DkR + h.c. ]
Charge -1/3
∑i,k=1,N [ mui,k (uiL ukR )
+ mdi,k (diL dkR) + h.c. ]

6. 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´= 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 )

7. N(N-1)/2 angles and (N-1)(N-2) /2 phases
N= angles + 1 phase KM
the phase generates complex couplings i.e. CP violation;
6 masses +3 angles +1 phase = 10 parameters

8. 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 (  )

9. | Vud | Quark masses & Generation Mixing | Vud | = 0.9738(5) -decays
| Vus | = (26)
| Vcd | = 0.224(16)
| Vcs | = 0.970(9)(70)
| Vcb | = (8)
| Vub | = (32)
| Vtb | = 0.99(29)
(0.999)
-decays e- W
down e up
Neutron
Proton
| Vud |
| Vcs | = 0.969(39)(94)(24)
| Vcd | = 0.239(10)(24)(20)

10. The Wolfenstein Parametrization
 ~  ~ 0.3
Sin 12 = 
Sin 23 = A 2
Sin 13 = A 3(-i )

11. 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  

12. From
A. Stocchi
ICHEP 2002

14. sin 2 is measured directly from B J/ Ks
decays at Babar & Belle
(Bd J/ Ks , t) - (Bd J/ Ks , t)
AJ/ Ks =
(Bd J/ Ks , t) + (Bd J/ Ks , t)
AJ/ Ks = sin 2 sin (md t)

15. DIFFERENT LEVELS OF THEORETICAL UNCERTAINTIES (STRONG INTERACTIONS)
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

16. Quantities used in the
Standard UT Analysis

17. Roma, Genova, Torino, Orsay
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
THE CKM
NEW 2004 ANALYSIS IN PREPARATION
New quantities e.g. B -> DK will be included
Upgraded experimental numbers after Bejing

18. PAST and
PRESENT
(the Standard Model)

20. Results for  and  & related quantities
With the constraint fromms
68% and 95% C.L.
 =   =  0.027
[ ] [ ] at 95% C.L.
sin 2  =  sin 2  =  0.036
[ ] [ ]

21. Comparison of sin 2  from direct measurements (Aleph, Opal, Babar, Belle and CDF) and UTA analysis
sin 2 measured =  0.048
sin 2 UTA = ± 0.047
sin 2 UTA = ± 0.066
prediction from Ciuchini et al. (2000)
Very good agreement
no much room for physics beyond the SM !!

22. Theoretical predictions of Sin 2  in the years
exist since '95
experiments

23. Crucial Test of the Standard Model Triangle Sides (Non CP) compared to sin 2  and K
From the sides
only
sin 2 =0.715
 0.050

24. PRESENT: sin 2 from B ->  & 
and (2+) from B -> DK & B -> D(D*) 
FROM UTA

25. ms Probability Density
Without the constraint fromms
ms = (20.6 ± 3.5 ) ps-1
[ ] ps-1 at 95% C.L.
With the constraint fromms
+1.7
ms = ( ) ps-1
[ ] ps-1 at 95% C.L.
-1.5

26. fBs √BBs = 276  38 MeV 14% fBs √BBs = 279  21 MeV 8% 6% 4%
Hadronic parameters
fBs √BBs = 276  38 MeV 14%
lattice
fBs √BBs = 279  21 MeV 8%
UTA 6% 4%
fBd √BBd = 223  33  12 MeV
lattice
fBd √BBd = 217  12 MeV
UTA
BK = 0.86  0.06  0.14
lattice
(+0.13)
BK = 0.69
UTA
(-0.08)

27. Limits on Hadronic Parameters
fBs √BBs

29. PRESENT (the Standard Model)
NEW MEASUREMENTS

30. sin 2 from B ->     B B B   

31. sin 2 from B -> 
could be extracted by measuring

32. sin 2 from B -> 

33. PRESENT &
NEAR FUTURE

34. Factorization (see M. Neubert talk)
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. martinafranca 2001

35. CHARMING PENGUINS GENERATE
LARGE ASYMMETRIES
A =
BR(B) - BR(B)
BR(B) + BR(B)
BR(K+ 0) 
typical A ≈0.2
(factorized 0.03)
BR(K+ -)
Large uncertainties
BR(+-)
From g.m. martinafranca 2001

37. B -> DK (K*)

40. Tree level diagrams, not influenced by new physics

41. B -> D K (K*)
and
(b->u)/(b->c)

42. FUTURE:
FCNC &
CP Violation
beyond
the Standard Model

43. CP beyond the SM (Supersymmetry)
Spin 1/ Quarks
qL , uR , dR
Leptons
lL , eR
Spin SQuarks
QL , UR , DR
SLeptons
LL , ER
Spin Gauge bosons
W , Z ,  , g
Spin 1/ Gauginos
w , z ,  , g
Spin Higgs bosons
H1 , H2
Spin 1/ Higgsinos
H1 , H2

44. 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

45. In the latter case the Squark Mass
Matrix is not diagonal
(m2Q )ij = m2average 1ij + mij ij = mij2 / m2average

46. Model independent analysis: Example B0-B0 mixing
Deviations from the SM ?
Model independent analysis:
Example B0-B0 mixing
(M.Ciuchini et al. hep-ph/ )

47. SM solution Second solution also suggested by BNNS analysis
of B ->K,  
decays SM
solution

48. from MK TYPICAL BOUNDS FROM MK AND K x = m2g / m2q
x = mq = 500 GeV
| Re (122)LL | <  10-2
| Re (122)LR | <  10-3
| Re (12)LL (12)RR | <  10-4
from MK

49. from K x = 1 mq = 500 GeV | Im (122)LL | < 5.8  10-3
| Im (122)LR | <  10-4
| Im (12)LL (12)RR | <  10-4

50. MB and A(B J/  Ks )
MBd = 2 Abs |  Bd | H | Bd  |
B=2
eff
A(B J/  Ks ) = sin 2  sin MBd t
2  = Arg |  Bd | H | Bd  |
eff
B=2
eff
eff
sin 2  =  from exps
BaBar & Belle & others

51. TYPICAL BOUNDS ON THE -COUPLINGS
A, B =LL, LR, RL, RR
1,3 = generation index
ASM = ASM (SM )
 B0 | HeffB=2 | B0  = Re ASM + Im ASM
+ ASUSY Re(13d )AB2 + i ASUSY Im(13d )AB2

52. SERIOUS CONSTRAINTS ON SUSY MODELS
TYPICAL BOUNDS ON THE -COUPLINGS
 B0 | HeffB=2 | 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

53. 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 ) = ± 0.04
BR(B  Xs l+ l-) = (6.1 ± 1.4 ± 1.3)  10-6
The lower bound on B0s mixing ms > 14 ps -1

54. SM Penguins W b s t s s g b s b s s

55. SUSY Penguins W Recent analyses by G. Kane et al., Murayama et al.and
Ciuchini et al. t g b s b s
Also Higgs (h,H,A)
contributions s s s

56. AKs = - CKs cos(mB t) + SKs sin(mBt )
ACP (Bd ->  Ks ) (2002 results)
Observable BaBar Belle Average SM prediction
BR (in 10-6)   ~ 5
SKs  0.64   0.054
CKs _ 0.41  
-2.5
-3.0
-2.1
-0.50
AKs = - CKs cos(mB t) + SKs sin(mBt )
[ACP (Bd ->  K ) do not give significant constraints ]
One may a also consider Bs -> 
(for which there is an upper bound from Tevatron, CDF
BR < )

57. AKs = - CKs cos(mB t) + SKs sin(mBt )
ACP (Bd ->  Ks ) (2003 results)
Observable BaBar Belle Average SM prediction
SKs   0.07
see M. Ciuchini et al. Presented at Moriond 2004 by L. Silvestrini
+0.09
-0.06
-0.11
AKs = - CKs cos(mB t) + SKs sin(mBt )

58. PROGRESS SINCE 1988