PHY 3446 Lecture #7 Monday, Nov. 6, 26 Dr.. Elementary Particle Properties Quantum Numbers trangeness Isospin Gell-Mann-Nishijima Relations Production and Decay of Resonances Monday, Nov. 6, 26 PHY 3446, Fall 26
Announcements LPCC Workshop was very successful Tested the display with random people worked pretty well Follow up: Groups need to discuss within yourselves to prepare for the final push at the upcoming workshop on Dec. 2. 2 nd term exam Monday, Nov. 2 Covers: Ch 4 whatever we finish on Nov. 5 Homework. Reading assignments: 9.6 and 9.7 2. End of chapter problems 9., 9.2 and 9.3 3. Due for these assignments is next Wednesday, Nov. 5 Monday, Nov. 6, 26 PHY 3446, Fall 26 2
Quantum Numbers Baryon Number An additive and conserved quantum number, Baryon number (B) All baryons have B= Anti-baryons? (B=-) Photons, leptons and mesons have B= Lepton Number Quantum number assigned to leptons All leptons carry L= (particles) or L=- (antiparticles) Photons or hadrons carry L= Total lepton number must be conserved Lepton numbers by species must be conserved Monday, Nov. 6, 26 PHY 3446, Fall 26 3
From cosmic ray shower observations K-mesons and Σ and Λ baryons are produced strongly w/ large x-sec But their lifetime typical of weak interactions (~ - sec) Are produced in pairs a K w/ a Σ or a K w/ a Λ Gave an indication of a new quantum number Consider the reaction K and Λ subsequently decay and trangeness π + Λ π + p K + π + π Observations on Λ Always produced w/ K never w/ just a π Produced w/ K + but not w/ K - π π + + p K + π +Λ + + p K + π +Λ p K + Λ + π + p π + π +Λ Monday, Nov. 6, 26 PHY 3446, Fall 26 4
Consider reactions π + + p Σ + + K + and With the subsequent decays and Observations from Σ + Σ + is always produced w/ a K + never w/ just a π + Σ + is also produced w/ a K but w/ an additional π + for charge conservation Observations from Σ Σ is always produced w/ a K + never w/ K - Thus, Observed: π Not observed: trangeness Σ + ( ) + + + + p Σ + π + K + π + p Σ + K n+ π + π + p Σ + K + ( ) K + π π + p Σ + K + + π + p Σ + π + + π Monday, Nov. 6, 26 PHY 3446, Fall 26 5
trangeness Further observation of cross section measurements + The cross section for reactions π + p K + π +Λ and π + p K +Λ w/ GeV/c pion momenta are ~ mb Whereas the total pion-proton scattering cross section is ~ 3mb The interactions are strong interactions Λ at v~.c decays in about.3cm Lifetime of Λ baryon is.3cm τ sec Λ 9 3 cm / s = The short lifetime of these strange particles indicate weak decay Monday, Nov. 6, 26 PHY 3446, Fall 26 6
trangeness trangeness 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 = for all ordinary mesons and baryons as well as photons and leptons For any strong associated-production reaction w/ the initial state =, the total strangeness of particles in the final state should add up to. Monday, Nov. 6, 26 PHY 3446, Fall 26 7
trangeness Based on experimental observations of reactions and w/ an arbitrary choice of (K )=, we obtain (K + )=(K )= and Σ(K )=Σ( Κ )=- (Λ )=(Σ + )=(Σ )=(Σ - )=- Does this work for the following reactions? + π + p K + π +Λ π + p K +Λ K + p Ξ + K For strong production reactions and K p + Ξ + K cascade particles 2 if + + ( Ξ ) = ( Ξ ) = ( ) ( ) K = K = Monday, Nov. 6, 26 PHY 3446, Fall 26 8
More on trangeness Let s look at the reactions again π + p K + Λ This is a strong interaction trangeness must be conserved : + + - How about the decays of the final state particles? π + Λ + p and K π + π These decays are weak interactions so is not conserved : - + and + + A not-really-elegant solution only conserved in trong and EM interactions Unique strangeness quantum numbers cannot be assigned to leptons Leads into the necessity of strange quarks Monday, Nov. 6, 26 PHY 3446, Fall 26 9
Isospin Quantum Number trong 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 ince 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 p = and = Monday, Nov. 6, 26 PHY 3446, Fall 26 n
Isospin Quantum Number 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, π+, π- and π, have almost the same masses X-sec by these particles are almost the same after correcting for EM effects trong force does not distinguish these particles Isospin triplet π + =, Monday, Nov. 6, 26 PHY 3446, Fall 26 π = and π =
Isospin Quantum Number 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 Monday, Nov. 6, 26 PHY 3446, Fall 26 2
Gell-Mann-Nishijima Relation trangeness assignment is based on Gell-Mann- Nishijima relation Electric charge of a hadron can be related to its other quantum numbers Q Y = I + = 3 I + 2 3 2 Where Q: hadron electric charge I 3 : third component of isospin Y=B+, strong hypercharge Quantum numbers of several long lived particles follow this rule B + Monday, Nov. 6, 26 PHY 3446, Fall 26 3
Gell-Mann-Nishijima Relation With the discovery of new flavor quantum numbers, charm and bottom, this relationship was modified to include these new additions (Y=B++C+B) ince 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 Monday, Nov. 6, 26 PHY 3446, Fall 26 4
Quantum numbers for a few hadrons Monday, Nov. 6, 26 PHY 3446, Fall 26 5
Violation of Quantum Numbers 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 Λ π + emi-leptonic decays: both hadrons and leptons are present n Leptonic decays: only leptons are present µ Monday, Nov. 6, 26 PHY 3446, Fall 26 p p+ e + ν e + + e ν ν e µ 6
Hadronic Weak Decays These decays follow selection rules: I 3 =/2 and = QN I 3 QN I 3 Λ Monday, Nov. 6, 26 PHY 3446, Fall 26 - Σ + - QN Κ π + π - I 3 -½ - QN Ξ - Λ π - I 3 -½ - -2 π - - π - p ½ p ½ /2 7 /2 /2 /2
emi-leptonic Weak Decays These decays follow selection rules: I 3 = and = or I 3 = ½ and = QN I 3 n -/2 Monday, Nov. 6, 26 PHY 3446, Fall 26 p /2 e - + ν e QN π - µ ν µ I 3 - QN Κ + π µ + +ν µ I 3 ½ QN I 3 Σ - - - n -/2 e - + ν e 8 /2 /2
ummary of Weak Decays Hadronic weak-decays election rules are I 3 =/2 and = I 3 =3/2 and =2 exists but heavily suppressed emi-leptonic weak-decays Type : trangeness conserving election rules are: =, I 3 = and I = Type 2: trangeness non-conserving election rules are: =, I 3 = ½ and I = ½ or 3/2 I=3/2 and = exist but heavily suppressed Monday, Nov. 6, 26 PHY 3446, Fall 26 9
EM Processes QN I 3 QN I 3 QN I 3 π Monday, Nov. 6, 26 PHY 3446, Fall 26 η Σ - trangeness is conserved but the total isospin is not election rules are: =, I 3 = and I= or γ γ Λ - γ γ γ 2
Quantum Numbers 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 trangeness Numbers Conserved in strong interactions But violated in weak interactions Isospin Quantum Numbers Conserved in strong interactions But violated in weak and EM interactions Monday, Nov. 6, 26 PHY 3446, Fall 26 2