[Secs 16.1 Dunlap]

1. Conservation Laws - II [Secs 16.1 Dunlap] [Secs 2.2, 2.3, 16.4, 16.5 Dunlap]

2. 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. Isospin Conservation Tz= +1/2 NUCLEON Tz= -1/2 T=1/2

3. Isospin Conservation The analogy between conventional SPIN and ISOSPIN B-field NUCLEON p Jz= +1/2 Tz= +1/2 n Jz= -1/2 Tz= -1/2 J=1/2 T=1/2 Ordinary spin (ang. mom) Iso-spin 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 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 J is conserved T is conserved

4. Iso-spin Conservation T=1/2 Tz= -1/2 Tz=+1/2

5. Isospin conservation What is the isospin of the pion? Well that’s easy. 140 139 138 137 136 135 134 MeV Tz=-1Tz=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).

6. Isospin Conservation Lets look at some examples: This reaction can proceed through the T=1/2 and T=3/2 channels T= Thus T is conserved and this reaction could proceed via the S.I. It does. However, take a look at this decay: 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 T=

7. 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.

8. Baryon number conservation Take some examples (1) Neutron decay B= Thus this reaction is allowed (2) Anti – proton production. Q = B = This reaction is thus allowed (3) This reaction violates B conservation and is strictly forbidden Q = B =

9. Lepton number conservation L=± 1 L=0 Leptons have L= +1 Anti-Leptons have L= -1 All other types of particle have L=0

10. Lepton number conservation Lepton numbers are defined according to Example (1) Pion decay Lμ= Example (2) Muon decay Le= Lμ=

11. 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.

12. 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.

13. Conservation of Strangeness Consider the reaction that produces K mesons S= 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= S=

14. Conservation of Strangeness

15. A synopsis of conservation laws