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1
Electroweak
interactions of quarks
Benoit Clment,
Universit Joseph Fourier/LPSC Grenoble
HASCO School, Gttingen, July 1527 2012
2
PART 1 : Hadron decay,
history of flavour mixing
PART 2 : Oscillations and
CP Violation
PART 3 : Top quark and
electroweak physics
3
PART 1
Hadron decays
History of flavour mixing
4
Hadron spectroscopy
1950/1960 : lots of hadronic states observed
resonances in inelastic diffusion of nucleons or pions (pp,
p, np,)
Multiplet structure associated with SU(2) group symmetry.
Interpreted as bound
states of strong force
Several particles
 almost same mass
 same spin
 same behavior wrt.
strong interaction
 different electric charge
5
Strange hadrons
A few particles does not fit into this scheme :
Decay time characteristic from weak interaction
Particles stable wrt. strong/EM coupling
Conserved quantum number : strangeness
Name Mass (MeV) Decay Lifetime
1116 N 1.1010s
0, , 1320 3.1010s
+, 1190 N 8.1011s
0 1200 1.1020s (EM)
6
Quark model
GellMann (Nobel 69) and Zweig, 1963 :
hadrons are build from 3 quarks u, d and s.
Strangeness : content in strange quarks
Only weak interaction can induce change of flavour
s Wu or s Zd eg. (++ )
(+0+)
7
Electroweak lagrangian
OK for
leptons
What
happens for
quarks ?
8
SU(2)L and quarks
SU(2)L symetry :
doublets of left handed fermions with Q=1:
and sL or
and dL
singlets for right handed fermions : uR, dR, sR
But both Wud and Wus vertices happen !
Eg. Leptonic pion and kaon decays :
u
d
+
W+
+
u
s
+
W+
K+
9
Flavour mixing
strong interaction eigenstates (mass eigenstates)
may be different from
weak interaction eigenstates
Some mixing of d and s :
=U
universality of weak interaction : conserve the
overall coupling : U +U =1
U is 2x2 rotation matrix , 1 parameter
=cos sin
sin cos is the Cabibbo angle (1963)
10
Back to lagrangian
1 doublet
and 4 singlets uR, dCR, sCR, sCL
Charged currents :
Vertices :
Wud : Wus :
=
2 2
1 5 + + . .
=
2 2
1 5 +
+
2 2
1 5 + + . .
2 2(1 5)
2 2(1 5)
11
Naive estimation of C
From pion and kaon lifetimes
= 2.603 108 = 1.23 10
8
u
d
+
W+
+
u
s
+
W+
K+
gcos
gsin
4
2
2 2
3
BR ~ 100%
4
2
2 2
3
BR ~ 63%
Phase
space Feynman
amplitude
= .
= 0.265= 0.964
12
FCNC troubles
Neutral currents (d and s quark only)
=
2cos
5 +
5
= 3 2sin2 : =
1
2+
2
3sin2 ; =
2
3sin2
= 3 : =
1
2 ; = 0
=
2cos
1 +
2
=
2cos
cos21 + sin2
2 + sin2
1 + cos22
+cossin
2cos
1
2 +
1 2
FCNC inducing term
Introducing mass eigenstates :
13
GIM and charm
Natural solution proposed by Glashow, Iliopoulos,
Maiani in 1970(GIM mechanism)
Add a 4th quark to restore the symmetry : charm
2 SU(2)L doublets + right singlets
,
, uR, dCR, cR, sCR
Then the coupling to the Z becomes :
1 =
2 = 1
2+
2
3sin2
1
25
cossin2cos
1 2 +
1
2 =0 =0
And the FCNC terms cancel out :
14
Top and bottom
Generalization to 6 quarks :
,
,
Complex 3x3 unitary matrix :
Kobayashi & Maskawa in 1973 (Nobel in 2008)
CabibboKobayashiMaskawa or CKM Matrix
=
,
=
Lepton vertex :
2 2(1 5)
W+quqd vertex :
2 2(1 5)
Wquqd vertex :
2 2(1 5)
15
CKM matrix
=
=
0.97428 0.00015 0.2253 0.0007 0.003470.00012+0.00016
0.2252 0.0007 0.973450.00016+0.00015 0.04100.0007
+0.0011
0.008620.00020+0.00026 0.04030.0007
+0.0011 0.9991520.000045+0.000030
First approximation : Diagonal matrix =1 0 00 1 00 0 1
no family change : Wud, Wcs and Wtb vertices
Second approximation : Block matrix = 0 00 0 1
submatrix is almost the Cabibbo matrix
Vud Vcs cosC and Vus Vcd sinC
Top quark only decays to bottom quark
Charm quark mostly decays to strange quark
Bottom and Strange decays are CKM suppressed
16
PART 2
Oscillations and
CP Violation
17
Discrete symmetries
3 discrete symmetries, such as =1
Affects : coordinates, operators, particles fields
= Parity : space coordinates reversal :
= Charge conjugaison : particle to antiparticle transformation (i.e. inversion of all conserved
charges, lepton and baryon numbers)
eg.
+,
, ( )
+( ),( )
( )
= Time : time coordinate reversal :
18
Parity
Weak interaction is not invariant
under parity :
maximum violation of parity
(C.S.Wu experiment on 60Co beta
decay)
Strong and EM interaction are OK.
Parity does not change the nature of particles parity
eigenstates : =
: Intrinsic partity since =1, =1
Under : , vector; , pseudovector
4 potential : , , so : = 1
Strong and EM interaction conserves parity.
19
2 photons, helicity=+1 2 photons, helicity= 1
Parity of the pion
EM decay : 0, conserves parity
Parity eigenstates for photon pair :
Pions can only decay in one of these states
0
e
e+
e+
e
J=0
+ = 1 + 2
2, = 1
= 1 2
2, = 1
Measure angular distribution
of e+e pairs :
+ 1 + cos2 1 cos2
Experimentally : =
20
CP symmetry : pion decay
+ scalar
lefthanded
+
J=0, J3= 0
J=1/2
J3=1/2
J=1/2
J3=+1/2 k
k
+ scalar
+
lefthanded, massless
chirality = helicity
J=0, J3= 0
J=1/2
J3=+1/2
J=1/2
J3=1/2 k
k
 scalar

righthanded
J=0,J3= 0
J=1/2
J3=+1/2
J=1/2
J3=1/2 k
k
C
C
P P
CP
 scalar
righthanded
J=0, J3= 0
J=1/2
J3=1/2
J=1/2
J3=+1/2 k
k 
21
CP symmetry : neutral kaons
Kaons are similar to pions :
same SU(3) octet pseudoscalar mesons
=
and =
K0 (=us) and K0 (=us) are antiparticle of each other
= and =
So: = and =
Then CPeigenstates are :
Does weak currents conserve CP ?
10 =
0 0
2, = 1 2
0 = 0 + 0
2, = 1
22
CP violation in Kaon decays
If CP is conserved by weak interactions then only
10 , ( = 1) and 2
0 , = 1
With a longer lifetime for 20 (more vertices)
Experimentally : 1=0.9x1010s 2=5.2x10
8s
After t>>1 only the longlived components remains but a few 2 pions decays are still observed !
Cronin & Fitch, 1964, Nobel 1980
Conclusion : the long lived component isnt a pure
CP eigenstate : small CP violation !
Physical states : 0 =
10 2
0
1+2,
0 = 1
0 + 20
1+2
= 2.3 103
23
Meson oscillations
Neutral pseudoscalar mesons and (K0, D0, B0, BS)
Propagation/strong interaction Hamiltonian : 0
0 = , 0 = (in rest frame)
Interaction (weak) states propagation states.
Decay is allowed : effective hamiltonian is not hermitian
=
2 with =
+
2 =
hermitian
For eigen states : =1 00 2
=1 00 2
And the time evolution of state 1 is :
1() = 1
1
2 1(0) = 1 0 1 2 = 1
Exponential decay : mass matrix, decay width
24
Interaction eigenstates
In the basis , , the 2 states have the same properties (CPT symmetry) : 11 = 22 0 and 11 = 22 0
If we assume , to be real : 12 = 21 and 12 = 21
Then