Mass and Fermion Chirality
Parity Symmetry 鏡射對稱性
Parity Symmetry 鏡射對稱性


r ' r


p'  p
  

L '  r ' p '  L
Polarization of Light
當 x-polarzition 落後 y-polarzition 90°，就會形成Circular Polarized Light
旋向與傳播方向同向稱右手旋 Right-Handed
反向稱左手旋 Left-Handed
Circular Polarized Light
左手旋 Left-Handed
右手旋 Right-Handed
光子有左右手，電子自然也有
靜止時，電子也有角動量，稱為自旋 Spin

角動量 S ，大小固定，無法增加
S 
s ( s  1) 
S z  ms
s
1
2
ms  
1
2
電子的自旋只有兩個態，
自旋向上及自旋向下


運動電子的總角動量就是自旋角動量及軌道角動量的和！
Spin states
Chiral States (Helicity States)


Spin up and down states are defined when the electron is at rest.
When the electron is moving, it is more conveniently written in
terms of left-handed and right-handed states, another base.
在鏡射變換下左右旋會互換
長久以來，大家都認為物理是鏡射對稱 Parity Symmetric.
I do not believe that the Lord is a weak left-hander.
I am ready to bet a very large sum.
Pauli
一直到 1956年
Parity symmetry is violated (broken) in weak interaction.


  



0

  



  




Parity even
0
  

Parity odd
兩個看似不同的粒子，竟然質量及半衰期都相同。


  



0

  

Electrons prefer to fly in the direction opposite to Co spin.
Chien-Shiung Wu
The results are shocking to everybody!
I do not believe that the lord is a weak left-hander.
I am ready to bet a very large sum.
Pauli
Ten days later…… “ Now after the first shock is
over, I began to collect myself again”
“I was to give a lecture at 8:15PM on the “past
and recent history of the neutrino”. At 5:00PM
the mail brought me the three experimental
papers. Now where shall I start? It is good that I
did not make a bet.”
What shocks me is not that “God is just left-handed” but
the fact that in spite of this he exhibits himself as left/right
symmetric when he expresses himself strongly.”
The strong interaction is parity symmetric while the weak
interaction is not.
Nobel in just one year.
In a certain sense, a rather complete theoretical structure has been
shatter ed at its base and we are not sure how the pieces will be
put together!
Rabi
The symmetry is broken. The problem now is how bad.
Rochester Conference 1957
將所有看起來像弱作用的反應匯總
Is weak interaction S or V or T or A?
It turns out all the suspected weak interactions are indeed one
universal interaction and its structure is as simple as possible.
It is V-A.
It’s Feynman again and 3 others.
It is V-A.
It means weak interaction is Chiral.
Left-handed fermions act differently from Right handed Fermions.
They can’t talk to each other and hence mass is impossible.
Fermion Masses require both Left-handed and Right handed Fermions
Fermion Masses are forbidden by weak symmetry!
It’s easier to argue from neutrino helicity.
We found all the neutrinos are all left handed!
There is no right-handed neutrino.
Left Handed
如果微中子是左旋，在這個交點中的電子只能是左旋。

e
W
eL
-
只有左旋粒子才與 W 有交互作用
uL
d
L

cL
tL
sL
bL

e
eL
L
W
-



L
只有左旋粒子才與 W 有交互作用
sL
c
u
dL
W

tbL
W
cs
ud L
ee


W
b
tL
L



W

W
e eL
 L
W+


W
 L

弱交互作用不是 Isospin SU(2) gauge interaction
而是 Left-Handed Isospin SU(2)L gauge interaction
Left-Handed Isospin SU(2)L
L
L
 uL

dL

 uL 
  U  


dL 
 cL

 sL

 cL 
  U   

 sL 
 e

 eL

 e 
  U   

 eL 
W 是 Left-Handed Isospin SU(2)L的規範粒子！
a
U  
c

U U 1
b

d
Left-Handed Isospin SU(2)L自然與 Right-Handed Fermion無關！
R
R
R
u , d , s , c , b , t , e,  ,  u , d , s , c , b , t , e,  ,
singlet
W與右旋粒子無作用！
Weak interaction is Chiral.
Left-handed fermions act differently from Right handed Fermions.
But left-handed fermions and right handed fermions can’t be very
different because …………..
對任一有質量的費米子我一定可以找到一個座標系比它運動得快
本來的左旋費米子就變成右旋費米子！
A Fermion must contain both left-handed part and right-handed part!
除非你永遠無法跑得比它快！
A pure left-handed or a pure right-handed must be massless.
Fermion Masses are forbidden by the chiral weak symmetry!
W
±
光子中有與W 3的成分
W ± 與W 3三者性質相似！
規範波色子必須無質量，但W是很重的！
W ± 會比 γ 重如此之多！
Isospin SU(2)變換必須被破壞！
規範對稱必須被破壞！
所有參加 Chiral 弱作用的費米子根據對稱性都不能有質量
所有參加 Chiral 弱作用的費米子都有質量
規範對稱必須被破壞！
H
H
Symmetry can be broken by ground state.
Vacuum is not simple!
受歡迎，與希格斯場交互作用強的粒子，走起來就會較慢，慣性大！
不受歡迎，交互作用弱的粒子，慣性小，走起來就會較快！
It is Higgs that gives everything its mass!
一個粒子的質量及此粒子與 Higgs粒子的交互作用是同一回事！