Conservation Laws - II
[Secs
[Secs 2.2,
2.3,16.1
16.4, Dunlap]
16.5 Dunlap]
Isospin Conservation
ISO-SPIN in strong interaction:
It originates from the observation that the
NUCLEON can be considered as being the
same particle in 2-states – (i) isospin up =
proton
.
(ii) isospin down = neutron.
Tz= +1/2
NUCLEON
Tz= -1/2
T=1/2
Isospin Conservation
The analogy between conventional SPIN and ISOSPIN
B-field
E   12 g N .B
NUCLEON
p
Jz= +1/2
E   12 g N .B
Tz= +1/2
n
Jz= -1/2
J=1/2
Ordinary spin (ang. mom)
Tz= -1/2
T=1/2
Iso-spin
Without a B-field the nucleon’s spin
states Jz=±1/2 cannot be
distinguished –
Without a EM -field the nucleon’s
isospin states Tz=±1/2 cannot be
distinguished – i.e. same mass
A B-field breaks the symmetry
causing the Jz =+1/2 state to have
a different energy to the Jz = -1/2
state
The EM -field breaks the symmetry
causing the Tz =+1/2 state to have
a different energy to the Tz = -1/2
state. n is slightly heavier than p
J is conserved
T is conserved
Iso-spin Conservation
T=1/2
Tz= -1/2
Tz=+1/2
Isospin conservation
What is the isospin of the pion?
Well that’s easy.
140
139
138




137
136
135

134
MeV
Tz=-1
0
Tz=0
Tz=+1
Clearly the pion is a T=1 particle state. The reason that the π
± states are higher in energy is that the EM force between 2
quarks decreases binding energy (anti-binding).
Isospin Conservation
Lets look at some examples:
   p  n    
T=
1
1 
2
1 3
 , 
2 2
1
11
2
1 3 5
 , , 
2 2 2
This reaction can
proceed through
the T=1/2 and
T=3/2 channels
Thus T is conserved and this reaction could proceed via the S.I. It does.
However, take a look at this decay:
T=
K    
1
1  1
2
1
  (0,1,2)
2
This reaction cannot
proceed by any T
channels and is
absolutely forbidden via
the S.I. However the
reaction does occur –
but not by the S.I
Baryon number conservation
B=±
B=0
Baryon no is +1 for Baryons
Baryon no is -1 for Anti-Baryons (i.e. anti-protons)
Baryon no is strictly conserved.
Baryon number conservation
Take some examples
n
(1)
B=
0
 p
1

 e  e
-
+1
0
Neutron decay
0
Thus this reaction is allowed
(2)
p  p  p  p  p  p
Q = +1
B = +1
+1
+1
+1
+1
-1
+1
+1
+1
+1
-1
Anti – proton
production.
This reaction is thus allowed
(3)
p    n  0
0 0
Q = 1 +1
B = -1 0
+1 0
This reaction violates B
conservation and is
strictly forbidden
Lepton number conservation
L=±
1
L=0
Leptons have L= +1
Anti-Leptons have L= -1
All other types of particle have L=0
Lepton number conservation
Lepton numbers are defined according to
1st generation
2nd generation
3rd generation
e-






Lepton no= +1
e
Lepton no= -1
e
e

Example (1)
Lμ=

0

+1
   e-
Example (2)


Pion decay
-1
   e
Le=
0
+1
0
-1
Lμ=
+1
0
+1
0
Muon decay
Conservation of Strangeness
In the early 1950s physicists discovered in proton-neutron
collisions some Baryons and Mesons that behaved “strangely”
– They had much too long lifetimes! We are talking about
mesons called Kaons (K-mesons) and Baryons called
Hyperons such as 0 and 0. Since such particles were
produced in large quantities in proton-neutron collisions they
had to be classified as strongly interacting particles [i.e
Hadronic matter]. If they were hadronic particles, though, they
should decay very quickly into pions (within the time it takes
for a nucleon to emit a pion ~ 10-23s) but their lifetimes were
typically 10-8 to 10-11s. It is possible to explain this in terms
of a new conservation law: the conservation of strangeness.
Conservation of Strangeness
Murray Gell-Mann
Kazuhiko Nishijima
In 1953 two physicists, one in the USA and one in Japan,
simultaneously understood the reason why the Λ and K
particles were living so long – i.e. why they were decaying
through the WEAK interaction and NOT THE STRONG.
These were Murray Gell-Mann and Kazuhiko Nismijima.
They saw that the explanation lay in a new conservation law
- the conservation of strangeness.
Conservation of Strangeness
Consider the reaction that produces K mesons

 n

0
 K
S= 0
0
-1
+1
Strangeness S is conserved if we assign the 0 a strangeness
quantum no of –1, and the K+ a strangeness quantum no of +1.
The 0 and K are left to decay on its own - not by the
strangeness conserving strong interaction – but by the WEAK
interaction

S= 1
0

 p  
0
0
weak
-
K
S= 1
weak

   
0
0
Conservation of Strangeness
  p K

0
0
K      
0

  p 
0


A synopsis of conservation laws
Conservation of
BASIC SYMMETRY-
Quant. no
Interaction violated in
Energy
TRANSLATIONS in TIME
none
Momentum
TRANSLATIONS in SPACE
none
Ang. momentum
DIRECTIONS in space
J
none
Parity
REFLECTIONS in space
 (or P)
*Weak interaction
Charge conjugation parity
Particle - Antiparticle
C
*Weak interaction
Charge
Charge in EM gauge
Q
none
Lepton number (electron)
Charge in Weak charge
Le
none
Lepton number (muon)
Change in Weak charge
L
none
Lepton number (tauon)
Change in Weak charge
L
none
Baryon number
Quark number invarience
B
none
Isospin
ud quark interchange
I
for non leptonic)+ *EM
Strangeness
u (d)s quark interchange
S
*Weak interaction (S=1)
Charm
qc quark interchange
c
*Weak interaction (c=1)
Bottomness
qb quark interchange
b
*Weak interaction (b=1)
Topness
qt quark interchange
T
*Weak interaction (T=1)