chapter 9: symmetry - university of california,...
TRANSCRIPT
Chapter 9: Symmetry
Rotations
Rotations
5
4
3
Rotations
5
Rotations
51
4.9
Translational and Rotational Symmetry
Light Wave
Quantum Spin
Photon Spin
Massive Spin 1 at Rest
Gauge Symmetry
SU(3) Flavoru
d
s
d
u
s_
_
_
quarks
antiquarks
SU(3) Flavoru
d
s
d
u
s_
_
_du_
ud_
us_
su_
sd_
uu+dd-2ss_ _ _
ds_
uu-dd_ _
quarks
antiquarks
SU(3) Flavoru
d
s
d
u
s_
_
_
quarks
antiquarks
�+
��
K+
K0K�
K0
mesons
⇥0, �
SU(3) Flavoru
d
s
ds_
_
u_
quarks
antiquarks
�+
��
K+
K0K�
K0
mesons
uusuud
udddds
dss
uss
uds⇥0, �
SU(3) Flavoru
d
s
d
u
s_
_
_
quarks
antiquarks
�+
��
K+
K0K�
K0
mesons
�, ⇥0⇥0, �
baryons
�+
p
n
����
�0
4 FlavorssD
0D
sD
–D
0K–!
!
!K
–K
(a)
sD
DD
sD
"# !#
K
(b)
*0
K*"
*!K*0
D 0*D*"
*"
*!
"
*!
"cdcu"cs"
us"ds"
su" sd" ud
"
uc"sc"
dc"
0# $%&J/
uc"sc"
dc"
"cdcu"cs"
!
D!
!
K 0
us"ds"
su" sd"
du"
du"
0D
''()'c
! 0
ud"
K 0*
C
I
Y!!!ccc
"!!cc"
!cc
!!cc
#!!c
"+c"
0c
!$
"0
# !
%!%
0%$
#$
"$
%!!
(b)
"+c
#++c
"0
n p" c
0
(a)
ddcdsc
udc
uscuuc
uuduus
ussdss
udddds
ddd
dssdds
ussuus
uududduds
ssc
uscdscuuc
uccscc
dcc
!!cc
"!!cc"
!cc
#0
c
uuu
#0
"$
#$
# !&,# 0
udc
#!c&
!c,
c#!
!0
c
#0
c
dcc ucc
ddc
uds
ssc
scc
sss
!0
c
mesons baryons
S
QED Potential
Jµ(x)e2
|x� y|Jµ(y)
FourierTransform
Jµ e2
q2Jµ
1/r potential:
QED Potential
Jµ(x)e2
|x� y|Jµ(y)
FourierTransform
elastic scattering amplitude
Jµ e2
q2Jµ
1/r potential:
QED Potential
Jµ(x)e2
|x� y|Jµ(y)
FourierTransform
elastic scattering amplitude
Jµ e2
q2Jµ
1/r potential:
� =e2
4⇥� 1
137
Quantum Corrections
+
coupling is distance dependent
�(10�10 m) � 1137
�(10�17 m) � 1128
�
+ +
Quantum Corrections
gluons contributewith opposite sign
QCD coupling gets stronger at larger distances
gluon
Running Coupling
!"!#
!"!$
!"!%
!"!&
!"'
!"'#
!"'$
SU(3)
SU(2)
U(1)log(Energy)
couplingstrength
longdistance
shortdistance
Electric Fields
Color Fields“Color” Fields
Color Fields“Color” Fields
Flux Tube -> Meson
U(1)
time
+ -
� spin 1, charge 0
spin 1/2 spin 1/2
spin and charge must add up
SU(2)L
time
uL dL
_
W spin 1
spin 1/2 spin 1/2
SU(2) Gauge Bosons
three weak gauge bosons
W+
W 0
W�
u
d
works just like spin: ±12± 1
2= �1, 0, 1
adding SU(2) charges
symmetryuu-dd_ _
SU(2)L Weak Interactions
dL
uL
time
dL
uL
W+
W�
SU(2)L Weak Interactions
uL
dL
time
uL
dL
W+
W�
SU(2)L Weak Interactions
eL
time
eL
W+
W�
L�e L�e
SU(2)L Weak Interactions
eL
time
eL
W+
W�
L�e L�e
Standard Model
SU(2)L Weak Interactions
sL
cL
time
sL
cL
W+
W�
SU(2)L Weak Interactions
time
sL
W+
W�
sL
cL cL
decay
SU(2)L Weak Interactions
bL
tL
time
bL
tL
W+
W�
SU(2)L Weak Interactions
time
bL
W+
W�
bL
tL tL
“on-shell”decay
SU(2)L Weak Interactions
time
W+
W�
Lµ Lµ
L�µ L�µ
SU(2)L Weak Interactions
time
W+
W�
L��L��
L� L�
SU(2)L Weak Interactions
W+W�W+W�
W 0 W� W+
� g � g2
SU(3)c
time
uR uR_
spin 1
spin 1/2 spin 1/2
G
SU(3)c Gauge Bosons
eight gluons
r
gb
g
rb
__
_
three quarks three antiquarks
adding SU(3) charges:
SU(3) Color Interactions
uL
uL
time
dR
dR
G
G
Colors
Color Exchange
Color Gauge Symmetry
Color Gauge Symmetry
Color Exchange
Local Color Symmetry
Local Color Symmetry