[Secs 16.1 Dunlap]
Conservation Laws - II
[Secs 2.2, 2.3, 16.4, 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.
NUCLEON
T=1/2
Tz= +1/2
Tz= -1/2
NUCLEON
T=1/2
Tz= +1/2
Tz= -1/2
Isospin Conservation
J=1/2
B-field
Ordinary spin (ang. mom) Iso-spin
12 .NE g B
12 .NE g B
Without a B-field the nucleon’s spin states Jz=±1/2 cannot be distinguished –
A B-field breaks the symmetry causing the Jz =+1/2 state to have a different energy to the Jz = -1/2 state
Jz= +1/2
Jz= -1/2
The analogy between conventional SPIN and ISOSPIN
J is conserved
Without a EM -field the nucleon’s isospin states Tz=±1/2 cannot be distinguished – i.e. same mass
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
p
n
T is conserved
Iso-spin Conservation
T=1/2
Tz= -1/2 Tz=+1/2
Isospin conservationWhat is the isospin of the pion?
Well that’s easy.
140
139
138
137
136
135
134
MeV
0Tz=-1 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 ConservationLets look at some examples:
1 11 1 1
2 21 3 1 3 5
, , ,2 2 2 2 2
p n
T=
Thus T is conserved and this reaction could proceed via the S.I. It does.
However, take a look at this decay:
1 1 1
21
(0,1,2) 2
K
T=
This reaction can proceed through the T=1/2 and T=3/2 channels
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
0 - p e
1 +1 0 0en
Take some examples
Neutron decay
B=
Thus this reaction is allowed
(1)
(2) p p p p p p
+1 +1 +1 +1 +1 -1
+1 +1 +1 +1 +1 -1
Anti – proton production.Q =
B =This reaction is thus allowed
(3) 0
1 +1 0 0
-1 0 +1 0
p n
Q = B =
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
1st generation 2nd generation 3rd generation
Lepton no= +1 e -
e
-
-
Lepton no= -1
e
e
Lepton numbers are defined according to
Example (1)
0 +1 -1
Lμ=
Pion decay
-e e
0 +1 0 -1
+1 0 +1 0
Muon decay
Example (2)
Le=
L μ =
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
0 n K
0 0 -1 +1
Consider the reaction that produces K mesons
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=
weak0 - p
1 0 0
weakK
1 0 0
S=S=
Conservation of Strangeness
0 0
0
0
p K
K
p
A synopsis of conservation lawsConservation 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 Lenone
Lepton number (muon) Change in Weak charge Lnone
Lepton number (tauon) Change in Weak charge Lnone
Baryon number Quark number invarience B none
Isospin ud quark interchange I for non leptonic)+ *EM
Strangeness u (d)s quark interchange S *Weak interaction (S=1)
Charm qc quark interchange c *Weak interaction (c=1)
Bottomness qb quark interchange b *Weak interaction (b=1)
Topness qt quark interchange T *Weak interaction (T=1)
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