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Recent Developments in Beauty and Charm Physics
Achille Stocchi
(LAL-Orsay/IN2P3-CNRS And Université de Paris Sud
P11) stocchi_at_lal.in2p3.fr
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Plan of the lectures
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Historical introduction to the CKM matrix and CP
Violation
The Standard Model in the fermion sector the
CKM matrix and the CP violation. The unitarity
Triangle
30
1h30
Measurements related to CKM parameters and CP
violation
Extraction of the Unitarity triangle parameters
30
What next and New Physics from B physics.
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1
Historical introduction
to the
CKM matrix and CP Violation
4
To show where I start from
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Fundamental role of strange particles in the
development of flavour physics. I use them to
introduce flavour physics
1950 The concept of flavour strangeness
discovery
1955 Parity Violation in weak decay
1963 DS1 vs DS0 Cabibbo theory
1960 K0-K0 mixing
1964 KL ? pp CP violation in weak decays
1970 KL? mm FCNC / GIM mechanism
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The Strangeness the begin of a new eranot
ended yet

• 1947 discovery of new particles (on cosmic
  rays)
• K (500 MeV) L (1100 MeV)

• Why are these particles strange ?
• They are produced (always in pair) as copiously
  as the as the p
• Their lifetime is 10-10 s !

Production through strong interaction
Decay through weak interaction

• There should be a reason to inhibit the decay
  through strong interactions..
• ? Introduction of a new quantum number
• Conserved in strong interaction processes
• Not conserved on weak interaction processes

Pais intuition (1952)
The strangeness
(additive quantum number)
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Details create a new quantum number,
strangeness which is conserved by the
production process (pair production) however,
the decay must violate strangeness if only
weak force is strangeness violating then it
is responsible for the decay process hence
(relatively) long lifetime

• Observations
• High production cross-section
• Long lifetime
• Conclusion
• must always be produced in pairs!

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qc the Cabibbo angle
Cabibbo Theory
The quarks d e s involved in weak processes are
rotated  by an angle
Couplings u d GFcosqc
u s GF sinqc
nm
DS1
m
Purely leptonic decays (e.g. muon decay) do
not contain the Cabibbo factor
cosqcor sinqc
W
u
d, s
1.2 10-8 s
(0.63)
(1)
2.6 10-8 s
8.5
e
ne
W
GF2 sin2qc K- ? p0 e- ne
s
u
u
u
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But the theory predicts flavour changing neutral
transition sd
1970 Glashow, Iliopoulos et Maiani (GIM)
proposed the introduction of a fourth quark the
quark c (of charge 2/3)
Term added to the neutral coupling
The neutral current does not change flavour
absence of FCNC
- A strangeness changing neutral current would
produce contributions larger by several order
of magnitude to for instance KL?mm
?
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Absence of FCNC. The neutral current changing the
strangness (DS1) not observed
e
coupling su
e
coupling sd
?e
e-
Z0
W
u
u
u
u
K?? e e-
K??0 e- ?e
More formally. If we write the weak charged
current
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The interaction comes from a gauge group. From
the previous page it seems to be clear that for
the weak interactions the group is the weak
isospin. s - are the matrices which
increase(decrease) of one unity the weak isospin.
But to form an algebra we also need s3
FCNC
Absence of FCNC
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(No Transcript)
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More on The GIM Mechanism
In 1969-70 Glashow, Iliopoulos, and Maiani (GIM)
proposed a solution to the to the K0 m m- rate
puzzle.
The branching fraction for K0 m m- was
expected to be small as the first order diagram
is forbidden (no allowed W coupling).
nm
m
m-
m
K0 forbidden
K allowed
W
??0
not a Z0
u
s
d
s
The 2nd order diagram (box) was calculated
was found to give a rate higher than the
experimental measurement! with only u quark
there is a ultraviolet divergence
with amplitude µ sinqccosqc
GIM proposed that a 4th quark existed and its
coupling to the s and d quark was s scosq
- dsinq The new quark would produce a second
box diagram amplitude µ -sinqccosqc
These two diagrams cancel out the divergence
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It remains a non zero contribution (which is
infrared divergent) for momentum lower than the
mc, which does not cancel out. The amount of
cancellation depends on the mass of the new
quark
For mcmu It would be
A quark mass of 1.5GeV is necessary to get good
agreement with the experimental data. First
evidence for Charm quark! and the fact that mc
is such that was not yet observed
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neutron decay
Strange particles
Predictions !
Charm sector
The charm discovery in 1974 and the verification
of these predictions have been a tremendous
triumph of this picture and these predictions
have been verified c?d are
Cabibbo suppressed wrt c? s transitions
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1977 b quark Discovery
9.5-10.5 GeV The series of ?
Excess larger than the experimental resolution
? presence of more than one resonance
Today.. more comments later on
B-factories
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The CKM matrix
CP Violation
With 6 quarks REAL Cabibbo matrix COMPLEX
CKM (Cabibbo, Kobayashi,Maskawa)
cicosqi et sisinqi .qi are the three
rotation angle instead of the single qc. The
phase d introduces the possibility of the CP
violation
Parametrization
We will discuss it in great details later
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Le puzzle t-q
In fact the  strange  particles have been also
fundamental for pointing out for the first time
the fact that the parity is not conserved in the
weak interaction

• t ? ? ? ?- (J0, P1)
• q ? ? ?0 (J0, P-1)
• The parity of t and of q are different
• If tqK

Experimentally The mass and the lifetime of la t
and q are identical.
?Parity Violation in weak interaction
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Neutral Kaons

• Known
• K0 can decay to pp-
• Hypothesized
• K0 has a distinct anti-particle K0
• Claims
• K0 (K0) is a particle mixture with two distinct
  lifetimes
• Each lifetime has its own set of decay modes
• No more than 50 of K0 (K0) will decay to pp-

In terms of quarks us vs. us
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CP Violation in the Kaon sector - 1964
def hh1

• K0 and K0 are not CP eigenstates, but

System with 2 p (p0 p0 , p p- )
P(pp)1 C(-1)lS P(-1)l
?CP(-1)2l1
p p- p0
System with 3 p si lL0 C1
P(-1)3(-1)l-1 ?CP -1
l
L
Prod Decay
t
If CP is conserved
Long lifetime because of the reduced space phase
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If KL ?2? there is CP violation. Level of CP
violation is
signal
KL
p
p
p0
2-body decay the two p are back-to-back
cosq1
q
q
p-
cos q 1
cos q ? 1
p-
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2
The Standard Model
in the
fermion sector
CKM matrix and CP Violation. The Unitarity
Triangle
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Flavour Physics in the Standard Model (SM) in the
quark sector
10 free parameters
half of the Standard Model
6 quarks masses
4 CKM parameters
In the Standard Model, charged weak interactions
among quarks are codified in a 3 X 3 unitarity
matrix the CKM Matrix.
The existence of this matrix conveys the fact
that the quarks which participate to weak
processes are a linear combination of mass
eigenstates
The fermion sector is poorly constrained by SM
Higgs Mechanism
mass hierarchy and CKM parameters
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The Standard Model is based on the following
gauge symmetry
SU(2)L ? U(1)Y
Idem for the other families
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Short digression on the mass
?R SU(2) singlet ?L SU(2) doublet
The mass terms are not gauge invariant under
SU(2)L ? U(1)Y
?R (I0,Y-2) leptoniR (I0,Y-2/3) quark
dR (I0,Y4/3) quark uR
Adding a doublet
?L (I1,Y-1) leptoniL (I1,Y1/3) quark
dL (I1,Y1/3) quark uL
h (I1/2,Y1)
Yukawa interaction
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The SM quantum numbers are I3 and Y ? The
gauge interactions are
Flavour blind
In this basis the Yukawa interactions has the
following form
With
To be manifestly invariant under SU(2)
complex
Two matrices are needed to give a mass term to
the u-type and d-type quarks
.
We made the choice of having the Mass
Interaction diagonal
.
.
SSBSpontaneous Symmetry Breaking
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To have mass matrices diagonal and real, we have
defined
The mass eigenstates are
In this basis the Lagrangian for the gauge
interaction is
Unitary matrix
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SUMMARY
h (I1/2,Y1)
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I cannot play the same game with all four
fields but only with 3 over 4
(2n-1) irreducible phases
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If V complex
CPT
T is an anti-linear operator
T(V)V T violated ? CP violated
CP Violation 3 families
Original idea in M.Kobayashi and T.Maskawa,
Prog Theor. Phys 49, 652 (1973) 3 family flavour
mixing in quark sector needed for CP violation.
Note the date 1973 even before the discovery of
the charm quark !
We can also simply say, that the CP
transformation rules imply that each combinations
of fields and derivatives that appear in a
Lagrangian transform under CP to its
hermitian conjugate. The coefficient
(mass/coupling), if there are complex, transform
in their complex conjugate
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Product of three rotation matrix (3 angles 1
phase with 3families)
There are 36 possibilities (3?2)perm. ?
3d0 ? 2 d?1
Standard Parametrization
? c13 c23 1
Now experimentally s13 and s23 are of order
10-3 and 10-2
With an excellent accuracy
Consequently, with an excellent accuracy four
independent parameters are given as
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The expected B meson lifetime
Surprise the B meson lifetime
Both MAC and MARK-II were detectors at PEP, a 30
GeV ee- collider at SLAC (Stanford)
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Mark-II paper
Surprise Vcb is very small!
MAC paper
Vcb 0.04
Vus 0.22
t(B)1.6ps ct 450mm L2mm
This fact is also very important and allow to
perform B physics, since the B mesons can be
identified (their lifetime measured)
Lgb ct
gb5
not measurable !
t(B)0.05ps ct 15mm L75mm
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b?u versus b ? c
CLEO collaboration at CESR (Cornell)?sM?(4S)
From a sample of 42.2K BB events (40.6/pb)
Vub ltlt Vcb ltlt Vus
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L. Wolfenstein, Phys. Rev. Lett. 51 (1983) 1945.

Parametrization of the Kobayashi-Maskawa Matrix

Lincoln Wolfenstein Department of
Physics, Carnegie-Mellon University, Pittsburgh,
Pennsylvania 15213 Received 22 August 1983
The quark mixing matrix (Kobayashi-Maskawa
matrix) is expanded in powers of a small
parameter ? equal to sin?c0.22. The term of
order ?2 is determined from the recently measured
B lifetime. Two remaining parameters, including
the CP-non conservation effects, enter only the
term of order ?3 and are poorly constrained. A
significant reduction in the limit on e'/e
possible in an ongoing experiment would tightly
constrain the CP-non conservation parameter and
could rule out the hypothesis that the only
source of CP non conservation is the
Kobayashi-Maskawa mechanism.
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d
s
u
??????
c
t
?md
?ms
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We observe that
Approximate Parametrization
Diagonal elements 1
Vus , Vcd 0.2
Each element of the CKM matrix is expanded as a
power series in the small parameter lVus0.22
Vcb , Vts 4? 10-2
Vub , Vtd 4 ? 10-3
u
c
t
1
?
??
??
same 1-2 2-3 1-3 familiy
d
s
b
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Wolfenstein parametrization 4 parameters l
,A, r, h
The CKM Matrix
d
s
b
u
1-l2/2
l
c
-l
1-l2/2
h complex, responsible of CP violation in SM
The b-Physics plays a very important
role in the determination of those
parameters
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To have a CKM matrix expressed with Wolfenstein
parameters valid up to l6
We define
the corrections to Vus are at l7
to Vcb are at l8
In particular
Which we will see will allow a generalization of
the unitarity triangle in r and h plane
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The Unitarity Triangle
The CKM is unitary
The non-diagonal elements of the matrix products
correspond to 6 triangle equations
Remember that
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1
42
Each of the angles of the unitarity triangle is
the relative phase of two adjacent sides (a
part for possible extra p and minus sign)
a b g p
The reason of making the arg of the ratio of two
legs is simple
So the relative phase
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APPENDIX Part I
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1974 c quark Discovery J/?
m(J/?)lt2 m(D0)
c
c
Seen as a resonance m3.1 GeV
G10-100KeV
D
u
J/?
u

• Brookhaven (p on Be target)

D
c
c
e m
c
c
hadrons
c
e- m-
c
G70 KeV
ee- final state
G(ee)5 KeV G(mm)5 KeV
SLAC (ee-)
3.10
3.12
3.14
The decay through strong interaction is so
suppressed that the electromagnetic interaction
becomes important
hadronic final state
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There is a HUGE difference between K0?pp and K0 ?
ppp in phasespace (600x!).
The huge difference is because mK0 3mp 75
MeV/c2
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APPENDIX Part II 1) CKM mechanism in the lepton
sector and for the neutral currents (Z0)
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If a similar procedure is applied to the lepton
sector
Since the neutrino are (were) massless the matrix
which change the basis from int-gt mass is in
principle arbitary We can always choose
Now the neutrino have a mass, it exists a similar
matrix in the lepton sector with
mixing a CP violation
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Facultatif
For the Z0
The neutral currents stay universal, in the mass
basis we do not need extra parameters for their
complete description
n
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2) UT area and condition for CP violation (formal)
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The area of the UT
The standard representation of the CKM matrix is
However, many representations are possible. What
are the invariants under re-phasing?

• Simplest Uai Vai2 is independent of quark
  re-phasing
• Next simplest Quartets Qaibj Vai Vbj Vaj
  Vbi with a?b and i?j
• Each quark phase appears with and without
• VV1 Unitarity triangle Vud Vcd Vus Vcs
  Vub Vcb 0
• Multiply the equation by Vus Vcs and take the
  imaginary part
• Im (Vus Vcs Vud Vcd) - Im (Vus Vcs Vub Vcb)
• J Im Qudcs - Im Qubcs
• The imaginary part of each Quartet combination is
  the same (up to a sign)
• In fact it is equal to 2x the surface of the
  unitarity triangle
• Area ½ VcdVcb h hVudVubsin
  arg(-VudVcbVubVcb)
• 1/2 Im(VudVcbVubVcb))
• ImVai Vbj Vaj Vbi J ?eabg eijk where J
  is the universal Jarlskog invariant
• Amount of CP Violation is proportional to J

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The Amount of CP Violation
Using Standard Parametrization of CKM
(eg. JIm(Vus Vcb Vub Vcs) )
(The maximal value J might have 1/(6v3) 0.1)
J/2
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CP Violation at the Lagrangian level
Accept that (or verify) the most general CP
transformation which leave the lagrangian
invariant is
In order to have LM to be invariant under CP, the
M matrices should satisfy the following relations

in this form, these conditions are of little use.
A way of doing is

• The existence of charged current contrains uL,dL
  to trasform in the same way under CP while the
  absence of right charged current allow uR,dR
• to tranform differentely under CP

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Substracting these two equations
If one evaluates the traces of both sides, they
vanish identically and no constraints is
obtained. In order to obtain no trivial contrain,
we have to multiply the previous equation a odd
number of times
Taking the traces one obtain
For n1, and n2 the previous equations are
automatically satified for harbitrary hermitian H
matrices (it is the same as the counting of the
physical phase of the CKM matrix). For n3 or
larger the previous eq. provides non trivial
contraints on the H matrix. It can be shown that
for n3 it implies
CP violation vanish in the limit where any two
quarks of the same charge become degenerate. But
it does not necessarily vanish in the limit
where one quark is massless (mu0) or even
in the chiral limit (mumd0) CP violation
vanish if the triangle has area equal to 0