[Secs 16.1 Dunlap] Conservation Laws - II [Secs 2.2, 2.3, 16.4, 16.5 Dunlap]
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[Secs 16.1 Dunlap]Conservation Laws - II[Secs 2.2, 2.3, 16.4, 16.5 Dunlap]
Isospin ConservationISO-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.NUCLEONT=1/2Tz= +1/2Tz= -1/2
NUCLEONT=1/2Tz= +1/2Tz= -1/2Isospin ConservationJ=1/2B-fieldOrdinary spin (ang. mom)Iso-spinWithout a B-field the nucleons 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 stateJz= +1/2Jz= -1/2The analogy between conventional SPIN and ISOSPINJ is conservedWithout a EM -field the nucleons isospin states Tz=1/2 cannot be distinguished i.e. same massThe 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 ppnT is conserved
Iso-spin ConservationT=1/2Tz= -1/2 Tz=+1/2
Isospin conservationWhat is the isospin of the pion?Well thats easy.140139138137136135134MeVTz=-1 Tz=0 Tz=+1Clearly the pion is a T=1 particle state. The reason that the states are higher in energy is that the EM force between 2 quarks decreases binding energy (anti-binding).
Isospin ConservationLets 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 channelsThis 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 conservationB= B=0Baryon no is +1 for BaryonsBaryon no is -1 for Anti-Baryons (i.e. anti-protons)Baryon no is strictly conserved.
Baryon number conservationTake some examplesNeutron decayB=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 conservationL= 1L=0Leptons have L= +1Anti-Leptons have L= -1All other types of particle have L=0
Lepton number conservationLepton numbers are defined according toExample (1) L= Pion decayMuon decayExample (2) Le=L =
1st generation2nd generation3rd generationLepton no= +1e -e - -Lepton no= -1
Conservation of StrangenessIn 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 StrangenessMurray Gell-MannKazuhiko NishijimaIn 1953 two physicists, one in the USA and one in Japan, simultaneously understood the reason why the 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 StrangenessConsider the reaction that produces K mesonsStrangeness 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=S=
Conservation of Strangeness
A synopsis of conservation laws
Conservation of BASIC SYMMETRY-Quant. noInteraction violated inEnergyTRANSLATIONS in TIMEnone MomentumTRANSLATIONS in SPACEnoneAng. momentumDIRECTIONS in spaceJnoneParityREFLECTIONS in space (or P)*Weak interactionCharge conjugation parityParticle - AntiparticleC*Weak interactionChargeCharge in EM gaugeQnoneLepton number (electron)Charge in Weak chargeLenoneLepton number (muon)Change in Weak chargeLnoneLepton number (tauon)Change in Weak chargeLnoneBaryon numberQuark number invarienceBnoneIsospin ud quark interchangeIfor non leptonic)+ *EMStrangenessu (d)s quark interchangeS*Weak interaction (S=1)Charmqc quark interchangec*Weak interaction (c=1)Bottomnessqb quark interchangeb*Weak interaction (b=1)Topnessqt quark interchangeT*Weak interaction (T=1)