Intro. to elementary particle physics Y. Kwon 11/24/2003
1
Universality of weak interactions?
Do all leptons and quarks carry the same unit of weak charge?– Yes, for leptons and no for quarks
for quarks, the couplings to the weak gauge bosons depend on the quark flavors, due to “quark-mixing” CKM mechanism
W e
eeg
Intro. to elementary particle physics Y. Kwon 11/24/2003
2
Weak decays of quarks
Consider the (semileptonic) weak decay
een
eeus eepn
eeud 1S 0S
20
1
)(
)(
e
e
pen
ne
Assuming universality of weak decays of quarks,
we expect both decays would happen in similar rate, but...
Intro. to elementary particle physics Y. Kwon 11/24/2003
3
Weak decays of quarks (2)
s u
W e
e
dd
dd
p
usg d u
W e
e
ud
n ud
p
udg
)1(20
1
)(
)(2
Og
g
ued
ues
ud
us
e
e
Intro. to elementary particle physics Y. Kwon 11/24/2003
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Weak decays of quarks (3)
So, what are we going to do?Discard the universality of weak interaction?
It was also noticed that the value of the Fermi constant GF deduced from nuclear -decay was slightly less than that obtained from muon decay.
d u
W e
e
ud
n ud
p
udg
2
4
2
2/ 2
2
22
2
F
WW
G
m
g
qm
g
eeM
W e
e
Intro. to elementary particle physics Y. Kwon 11/24/2003
5
Cabibbo theory
Try to keep the universality, but modify the quark doublet structure…
Assume that the charged current (W) couples the “rotated” quark states
where d’, s’ (weak interaction eigenstates) are linear combinations of mass eigenstates d, s
'du
'sc
sd
sd
cc
cc
cossinsincos
''
angle Cabibbo"" angle mixingquark the:c
Intro. to elementary particle physics Y. Kwon 11/24/2003
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Cabibbo theory (2)
What we have done is to change our mind about the charged current: “Cabibbo-favored” vs. “-suppressed”
effective weak coupling for S=0 (duW) is cos c
effective weak coupling for S=1 (suW) is sin c
)1(20
1
cos
sin
)(
)(22
Og
g
ued
ues
c
c
ud
us
e
e
o12 c
Wu
d
Wu
sccos csin
q'q
c
Intro. to elementary particle physics Y. Kwon 11/24/2003
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Cabibbo theory (3)
(Ex) What is the relationship between the weak couplings for muon decay (G=GF) and nuclear -decay (G) ?
d u
W e
e
ud
n ud
p
W e
e
ccos
cGG cos25
25
GeV 10)003.0136.1(
GeV 10)00001.016639.1(
G
G
Intro. to elementary particle physics Y. Kwon 11/24/2003
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Suppression of flavor-changing neutral currents
a very stringent suppression of flavor-changing neutral current reactions
)%08.017.3()(
10)5.1()(0
104.32.1
KBF
KBF
(Ex) Draw the decay diagrams for the above two reactions!
Is it easy to understand this stringent suppression?
Intro. to elementary particle physics Y. Kwon 11/24/2003
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Flavor-changing neutral currents (FCNC)
Neutral-current reactions for (u,d’) quarks
cccc sddsssdduu cossin)()sincos( 22
0S 1S
In this picture, FCNC is perfectly allowed by theory ???
0Z
u
u
0Z
CC sdd sincos'
CC sdd sincos'
Intro. to elementary particle physics Y. Kwon 11/24/2003
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GIM mechanism for FCNC suppression
In 1970, Glashow, Iliopoulos & Maiani (GIM) proposed the introduction of a new quark of Q=+2/3, with label c for ‘charm’.
With this new quark, a second quark doublet is also introduced.
, sincos'
cc sdu
du
cc dsc
sc
sincos'
Then we have additional terms for the neutral current reactions.
Intro. to elementary particle physics Y. Kwon 11/24/2003
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GIM mechanism (2)
cccc
cccc
sddsssddcc
sddsssdduu
cossin)( )cossin(
cossin)( )sincos(22
22
ccssdduu FCNC has disappeared!
0Z
u
u
0Z
CC sdd sincos'
CC sdd sincos'
0Z
c
c
0Z
CC dss sincos'
CC dss sincos'
Intro. to elementary particle physics Y. Kwon 11/24/2003
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GIM mechanism (3)
At the price of a new quark ‘charm’ and another quark doublet, the (experimentally) unwanted FCNC has been removed!
Later, in 1974, the bound state of charmanti-charm was discovered: J/
Indeed, just before this discovery, it had been possible to estimate the mass of the new quark!!
by considering mixing00KK
Intro. to elementary particle physics Y. Kwon 11/24/2003
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Extension of Cabibbo theory to 3 quark generations
Leptons are not involved in the strong interactions Quarks & Leptons do not change its flavor when i
nteracting with neutral gauge bosons– quarks do not change flavor under strong int.
– leptons & quarks do not change flavor when interacting with or Z0
– leptons & quarks change flavor only when interacting with W, and only within its family
LLLb
t
s
c
d
u
'''
W
t b'
W+
Intro. to elementary particle physics Y. Kwon 11/24/2003
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Decays of b quark
Then how does b decay at all?Note: b Wt but m(t) >> m(b)
For quarks,– mass eigenstates weak interaction eigenstates
– flavor mixing through CKM matrix
weak interactioneigenstates
masseigenstates
bsd
bsd
tbtstd
cbcscd
ubusud
VVVVVVVVV
'''
very importantfor CP study
responsible formost b decays
Intro. to elementary particle physics Y. Kwon 11/24/2003
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CKM matrix
tbtstd
cbcscd
ubusud
VVVVVVVVV
CKMV CKM is 3x3 and unitary
– only 3 generations in the SM CKM is almost 1, but not exactly
Vii 1, Vij 0 for i j
)( phase 1 and ),,( parameters real 3
)1.0(
1)1(2/1
)(2/1
23
22
32
CKM
A
O
AiAA
iA
V
How do we determine the CKM matrix elements?
Intro. to elementary particle physics Y. Kwon 11/24/2003
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Expt’l determination of CKM elements
Vud
– from nuclear -decay 0008.09735.0 udV
Vus
– from– results of K+ and K0 decays agree
eeK 0023.02196.0 usV
Vcd
– from charm meson production via neutrino scattering
cd 016.0224.0 cdV
Intro. to elementary particle physics Y. Kwon 11/24/2003
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Vcs
– from semileptonic decay of D meson– unitarity constraint assuming only 3 generations gives a much tighter bound
11122s 1054.1)0( csDe VfeKD
16.004.1 csV
Expt’l determination of CKM elements
Intro. to elementary particle physics Y. Kwon 11/24/2003
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Expt’l determination of CKM elements
Vcb: from and HQETeeDB *0
0019.00402.0 cbV
Intro. to elementary particle physics Y. Kwon 11/24/2003
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Expt’l determination of CKM elements
Vub: from eeB 0
025.0090.0/ cbub VV
Intro. to elementary particle physics Y. Kwon 11/24/2003
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Expt’l determination of CKM elements
Vtb: from t-quark decay, assuming only 3 generations
• at the Tevatron collider at Fermi Lab, top quarks are produced mainly in pairs• Assuming one could obtain a pure sample of tt
b
b
NN
N
WqtBR
WbtBRR
/events taggedevents untagged
/events tagged
CL %90 80.015.099.0 29.099.0 3gen tbVR
(Ref. hep-ex/9707026)
Intro. to elementary particle physics Y. Kwon 11/24/2003
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Vtd and Vts
(1)
(2)
2
*/*
ts
tdK V
V
KBBR
BBRR
Vtd
Vtd
(s) (s)
Expt’l determination of CKM elements