1 PHYS 3446 Wednesday, Nov. 13, 2013 Dr. Jae Yu 1. Elementary Particle Properties Quantum Numbers Strangeness Isospin Gell-Mann-Nishijima Relations Production and Decay of Resonances Wednesday, Nov. 13, 2013

Announcements Dr. Farbin will be at UTA between 11am – 4pm Friday for research discussions –Please send an ahead with an estimated time for your to stop by Wednesday, Nov. 13,

3 Baryon Number –An additive and conserved quantum number, Baryon number (B), assigned to baryons –All baryons have B=1; How about anti-baryons? –Anti-baryons have B=-1; How about leptons and mesons? –Photons, leptons and mesons have B=0 Lepton Number –Quantum number assigned to leptons –All leptons carry L =1 (particles) or L =-1 (antiparticles) –Photons or hadrons carry L =0 –Total lepton number must be conserved –Lepton numbers by species must be conserved Quantum Numbers Wednesday, Nov. 13, 2013

4 From cosmic ray shower observations –K-mesons and  Λ0 Λ0 baryons are produced strongly w/ large x-sec But their lifetime is typical of weak interactions (~ sec) Are produced in pairs – a K w/ a  or a K w/ a Λ0Λ0 –Gave an indication of a new quantum number Strangeness Wednesday, Nov. 13, 2013

Kaon Properties and Quark Compositions Wednesday, Nov. 13,

6 From cosmic ray shower observations –K-mesons and  Λ0 Λ0 baryons are produced strongly w/ large x-sec But their lifetime is typical of weak interactions (~ sec) Are produced in pairs – a K w/ a  or a K w/ a Λ0Λ0 –Gave an indication of a new quantum number Consider the reaction –K0 –K0 and Λ0 Λ0 subsequently decay – and Observations on Λ0Λ0 – Always produced w/ K0 K0 never w/ just a 00 – Produced w/ K+ K+ but not w/ K-K- Strangeness Wednesday, Nov. 13, 2013

Λ properties and quark compositions Wednesday, Nov. 13,

8 Consider reactions and –With the subsequent decays and Observations from ++ – + + is always produced w/ a K+ K+ never w/ just a ++ – + + is also produced w/ a K0 K0 but w/ an additional + + for charge conservation Observations from  –   is always produced w/ a K+ K+ never w/ K-K- Thus, –Observed: –Not observed: Strangeness Wednesday, Nov. 13, 2013

 Properties and Quark Compositions Wednesday, Nov. 13,

10 – Λ0 Λ0 at v~0.1c decays in about 0.3cm Lifetime of Λ0 Λ0 baryon is The short lifetime of these strange particles indicate a weak decay Further observation of cross section measurements –The cross section for reactions and w/ 1GeV/c pion momenta are ~ 1mb Whereas the total pion-proton scattering cross section is ~ 30mb The interactions are strong interactions Strangeness Wednesday, Nov. 13, 2013

11 The strangeness quantum number –Murray Gell-Mann and Abraham Pais proposed a new additive quantum number that are carried by these particles – Conserved in strong interactions –Violated in weak decays –S=0 for all ordinary mesons and baryons as well as photons and leptons –For any strong associated-production reaction w/ the initial state S=0, the total strangeness of particles in the final state should add up to 0. Strangeness Wednesday, Nov. 13, 2013

12 Based on experimental observations of reactions and w/ an arbitrary choice of S(K 0 )=1, we obtain –S(K + )=S(K 0 )=1 and  K  )=   )=-1 –S( Λ 0 )=S    S(  0 )=S(  - )=-1 –Does this work for the following reactions? – – For strong production reactions and – cascade particles if Strangeness Wednesday, Nov. 13, 2013

Ξ properties and quark compositions Wednesday, Nov. 13,

14 Let’s look at the reactions again –This is a strong interaction Strangeness must be conserved S:  +1 How about the decays of the final state particles? – and –These decays are weak interactions so S is not conserved –S:  and +1  A not-really-elegant solution – – only conserved in Strong and EM interactions  Unique strangeness quantum numbers cannot be assigned to leptons Leads into the necessity of strange quarks More on Strangeness Wednesday, Nov. 13, 2013

15 Strong force does not depend on the charge of the particle –Nuclear properties of protons and neutrons are very similar –From the studies of mirror nuclei, the strengths of p-p, p-n and n-n strong interactions are essentially the same –If corrected by EM interactions, the x-sec between n-n and p-p are the same Since strong force is much stronger than any other forces, we could imagine a new quantum number that applies to all particles –Protons and neutrons are two orthogonal mass eigenstates of the same particle like spin up and down states Isospin Quantum Number Wednesday, Nov. 13, 2013

16 Protons and neutrons are degenerate in mass because of some symmetry of the strong force –Isospin symmetry  Under the strong force these two particles appear identical –Presence of Electromagnetic or Weak forces breaks this symmetry, distinguishing p from n Isospin works just like spins –Protons and neutrons have isospin ½  Isospin doublet –Three pions,  +, - - and  0, have almost the same masses –X-sec by these particles are almost the same after correcting for EM effects –Strong force does not distinguish these particles  Isospin triplet Isospin Quantum Number Wednesday, Nov. 13, 2013

17 This QN is found to be conserved in strong interactions But not conserved in EM or Weak interactions Third component of the isospin QN is assigned to be positive for the particles with larger electric charge Isospin is not a space-time symmetry Cannot be assigned uniquely to leptons and photons since they are not involved in strong interactions –There is something called weak-isospin for weak interactions Isospin Quantum Number Wednesday, Nov. 13, 2013

18 Strangeness assignment is based on Gell-Mann- Nishijima relation –Electric charge of a hadron can be related to its other quantum numbers –Where Q: hadron electric charge I 3 : third component of isospin Y=B+S, strong hypercharge –Quantum numbers of several long lived particles follow this rule Gell-Mann-Nishijima Relation Wednesday, Nov. 13, 2013

19 With the discovery of new flavor quantum numbers, charm and bottom, this relationship was modified to include these new additions (Y=B+S+C+B) –Since the charge and the isospin are conserved in strong interactions, the strong hypercharge, Y, is also conserved in strong interactions This relationship holds in all strong interactions Gell-Mann-Nishijima Relation Wednesday, Nov. 13, 2013

20 Quantum numbers for a few hadrons Wednesday, Nov. 13, 2013

21 The QN we learned are conserved in strong interactions are but many of them are violated in EM or weak interactions Three types of weak interactions –Hadronic decays: Only hadrons in the final state –Semi-leptonic decays: both hadrons and leptons are present –Leptonic decays: only leptons are present Violation of Quantum Numbers Wednesday, Nov. 13, 2013

22 QN Λ 0  -- p I3I3 0½ S 00 These decays follow selection rules: | Δ I 3 |=1/2 and | Δ S|=1 Hadronic Weak Decays QN  +  00 p I3I3 10½ S00 QN  0  ++ -- I3I3 - ½1 S100 QN  -  Λ0Λ0 -- I3I3 - ½0 S-20 ΔΔ 1/

Wednesday, Nov. 13, QNnn p e - +  e I3I3 -1/21/2 S00 These decays follow selection rules: | Δ I 3 |=1 and | Δ S|=0 or | Δ I 3 |= ½ and | Δ S|=1 Semi-leptonic Weak Decays QN  -     I3I3 S0 QN  +  00     I3I3 ½0 S10 QN  -  n e - +  e I3I3 -1/2 S0 ΔΔ /2 1 1

24 Hadronic weak-decays –Selection rules are | Δ I 3 |=1/2 and | Δ S|=1 –| Δ I 3 |=3/2 and | Δ S|=2 exists but heavily suppressed Semi-leptonic weak-decays –Type 1: Strangeness conserving Selection rules are: | Δ S|=0, | Δ I 3 |=1 and | Δ I |=1 –Type 2: Strangeness non-conserving Selection rules are: | Δ S|=1, | Δ I 3 |= ½ and | Δ I |= ½ or 3/2 Δ I =3/2 and | Δ S|=1 exist but heavily suppressed Summary of Weak Decays Wednesday, Nov. 13, 2013

25 EM Processes QN  0   I3I3 0 S0 QN  0   I3I3 0 S0 QN  0  ΛΛ  I3I3 00 S ΔΔ Strangeness is conserved but the total isospin is not –Selection rules are: | Δ S|=0, | Δ I 3 |=0 and Δ I = 1or 0 Wednesday, Nov. 13, 2013

26 Baryon Number –An additive and conserved quantum number, Baryon number (B) –This number is conserved in general but not absolute Lepton Number –Quantum number assigned to leptons –Lepton numbers by species and the total lepton numbers must be conserved Strangeness Numbers –Conserved in strong interactions –But violated in weak interactions Isospin Quantum Numbers –Conserved in strong interactions –But violated in weak and EM interactions Quantum Numbers Wednesday, Nov. 13, 2013