[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 T z = +1/2 T z = -1/2

NUCLEON T=1/2 T z = +1/2 T z = -1/2 Isospin Conservation J=1/2 B-field Ordinary spin (ang. mom)Iso-spin Without a B-field the nucleon’s spin states J z =±1/2 cannot be distinguished – A B-field breaks the symmetry causing the J z =+1/2 state to have a different energy to the J z = -1/2 state J z = +1/2 J z = -1/2 The analogy between conventional SPIN and ISOSPIN J is conserved Without a EM -field the nucleon’s isospin states T z =±1/2 cannot be distinguished – i.e. same mass The EM -field breaks the symmetry causing the T z =+1/2 state to have a different energy to the T z = -1/2 state. n is slightly heavier than p p n T is conserved

Iso-spin Conservation T=1/2 T z = -1/2 T z =+1/2

Isospin conservation What is the isospin of the pion? Well that’s easy MeV T z =-1 T z =0 T z =+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: T= Thus T is conserved and this reaction could proceed via the S.I. It does. However, take a look at this decay: 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 Take some examples Neutron decay B= Thus this reaction is allowed (1) (2) Anti – proton production. Q = B = This reaction is thus allowed (3) 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 1 st generation2 nd generation3 rd generation Lepton no= +1 e - e  -   -  Lepton no= -1 Lepton numbers are defined according to Example (1) Lμ=Lμ= Pion decay Muon decay Example (2) Le=L μ =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 ~ s) but their lifetimes were typically to s. It is possible to explain this in terms of a new conservation law: the conservation of strangeness.

Conservation of Strangeness Murray Gell-MannKazuhiko 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 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=

Conservation of Strangeness

A synopsis of conservation laws Conservation ofBASIC SYMMETRY-Quant. noInteraction violated in Energy TRANSLATIONS in TIMEnone Momentum TRANSLATIONS in SPACEnone Ang. momentum DIRECTIONS in space J none ParityREFLECTIONS in space  (or P) *Weak interaction Charge conjugation parityParticle - Antiparticle C *Weak interaction ChargeCharge in EM gauge Q none Lepton number (electron) Charge in Weak charge LeLe none Lepton number (muon) Change in Weak charge LL none Lepton number (tauon) Change in Weak charge L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)