3. Resonance Region and Isospin Or: Hints of Hadron Substructure - PowerPoint PPT Presentation

PHYS 6610: Graduate Nuclear and Particle Physics I H. W. Grießhammer INS Institute for Nuclear Studies The George Washington University Institute for Nuclear Studies Spring 2018 II. Phenomena 3. Resonance Region and Isospin Or: Hints of Hadron Substructure References: [PRSZR 2.4, 6.2, 7.1/4; HG 6.8, 14.2, 8.4-7; Per 3.12; HM 2.6/7; PDG 48] PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University II.3.0

(a) The Resonance Region d 2 σ d Ω d E ′ with E ′ 1 p ( e , e ′ ) X inelastic inclusive: E < unconstrained. 1 + E M ( 1 − cos θ ) ep → e ′ X at fixed θ 1 Virtual probe with wave length λ ∼ Q 2 . = ⇒ � Dissipate energy & momentum into small volume ∼ λ 3 . [Tho] Q 2 � ( 0 . 3GeV ) 2 � r − 2 N : Response of whole nucleon: (a) Excite resonances = ⇒ elastic process with bump: W 2 =( p + q ) 2 resonance as global excitation of nucleon. inv. mass (b) Knock out constituents (virtual particle cloud) = ⇒ inelastic process, also via resonance. ∝ Q − 6 γ π + resonance e.g. [HG 6.18] p n Importance of elastic decreases. PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University II.3.1

(b) Nucleon Resonances [PRSZR 7.1] PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University II.3.2

More Resonances: Different Probes – Same Pattern W 2 = ( p + q ) 2 : inv. mass 2 of fragments First Resonance Region: One narrow, isolated bump around Q ≈ [ 0 . 3 ... 0 . 6 ] GeV ⇔ W ≈ 1 . 2GeV also in π + p , π 0 p , π − p , π − n (etc.) The ∆ ( 1232 ) : ∆ ++ , ∆ + , ∆ 0 , ∆ − Width Γ ≈ 100MeV (FWHM) ⇒ τ = 1 Γ ≈ 2 3 × 10 − 23 s = Second Resonance Region: Q ∼ [ 0 . 5 ... 1 ] GeV ( W ∼ [ 1 . 5 ... 2 ] GeV ) ep → e ′ X at fixed θ Two isolated slightly broader bumps in π − p , π + n , γ p in π + p , π − n but nothing (see next slide) [PRSZR 7.1; data 1968] PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University II.3.3

Resonances in π N → π N Scattering & γ N → X Photo-Absorption Not all bumps in all channels, but some pattern! π N → π N elastic γ p → X photo-absorption (inelastic) [Weise: “Quarks, Hadrons,. . . ”, Les Houches Lecture 1996] PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University II.3.4

Some Baryon Resonances Identified by the Particle Data Group What is the guiding principle/underlying symmetry? PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University II.3.5

(c) Isospin in Nuclear Physics Heisenberg 1932 [PRSZR] isotriplet I = 1 [HG] isodoublet I = 1 2 PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University II.3.6

(d) Isospin in Particle Physics a a a EV to I 3 nucleon � EV to I 3 EV to I 3 � pion     | π + � | ∆ ++ � + 3 + 1 | p � ∆ ( 1232 ) iso- + 1 iso-doublet 2 2 iso-triplet + )  | π 0 �  | ∆ + � + 1 I ( J P ) = 1 2 ( 1 − 1   | n � quadruplet 0     2 2 2 I ( J P ) = 1 ( 1 − ) + )   | π − � | ∆ 0 � − 1 I ( J P ) = 3 2 ( 3 − 1   2 2 | ∆ − � − 3 m π ± − m π 0 M p − M n m π ± + m π 0 ≈ 1 . 7 × 10 − 2 2 ≈ 0 . 7 × 10 − 3 M p + M n [HG] Q = I 3 + B Relation between charge, baryon number, isospin: 2 � Postulate: Strong Interactions are approximately isospin-independent: [ I , H strong ] ≈ 0 . Mass difference from electromagnetism & small explicit breaking: ε ( H em + H expl ) with ε ∼ 10 − 2 . PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University II.3.7

(e) Iso-Multiplets Predict Cross Section Ratios Postulate: Isospin Multiplets have common origin. = ⇒ Combine like spin. � I tot = � I N ⊗ 1 π + 1 N ⊗ � I π = ⇒ | IM � = ( IM | I N m n , I π m π ) | I N m N �⊗| I π m π � ∑ m N m π � �� � Clebsch-Gordan with M = m N + m π , | I N − I π | ≤ I ≤ I N + I π like spinology. ⇒ � I ′ M ′ |M strong | IM � = δ II ′ δ MM ′ M 2 I + 1 ( E ) : reduced ME is function of E only, labelled by I . = = ⇒ Just 2 independent functions M 2 ( E ) , M 4 ( E ) characterise 8 π N processes: 6 direct/elastic reactions: N π ± 0 → N π ± 0 & 2 charge-exchange reactions p π 0 ↔ n π + , p π − ↔ n π 0 I = 3 I = 1 π triplet N doublet 2 2 Clebsch-Gordan coefficient | I N = 1 M = 3 1 − 1 − 3 1 − 1 2 ;m N � | I π = 1;m π � 2 2 2 2 2 2 ( IM | I N m n , I π m π ) + 1 π + + 1 p 1 2 � � π + − 1 1 2 + 1 n 2 3 3 � � + 1 π 0 2 1 − p 0 2 3 3 � � − 1 2 1 π 0 n 0 2 3 3 � � + 1 1 2 π − − 1 − p 2 3 3 − 1 π − − 1 n 1 2 PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University II.3.8

Compare to Data PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University II.3.9

Baryon Resonances, Again: I ( J P ) Assignment Nucleon Resonances: I = 1 ∆ Resonances: I = 3 2 2 PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University II.3.10

(f) Isospin-Invariant Interactions (g) Photons and Isospin (h) The Fundamental Doublet PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University II.3.11

Next: 4. Deep Inleastic Scattering and Partons Familiarise yourself with: [HM 9; PRSZR 7.2, 8.1/4-5; HG 6.8-10] PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University II.3.12