6. Scattering and Decay of Particles Or: How Long to Count - 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 I. Tools 6. Scattering and Decay of Particles Or: How Long to Count References: [HH; HG 10.1-2, 5.7/12; PRSZR 4; HM 4.3, 2.10, 4.4; PDG 47, 47.5, 48] PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University I.6.0

Garbage-In – Garbage-Out PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University I.5.1

(c) Scattering for Theorists target has length d typical target density for liquid/solid: 1 particle Ångstrom ≈ 1 × 10 30 m − 3 for gas: 6 × 10 23 particles ≈ 1 × pressure 4 × 10 26 m − 3 × pressure 22litres � = 1mol 1bar [ bar ] PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University I.5.2

(f) Resonances in Quantum Mechanics Classical Mechanics: resonance frequencies reveal properties of materials. Electrodynamics: Lorentz-Drude model, resonance fluorescence Quantum Mechanics: interference = ⇒ resonance even when no bound states. [HG] PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University I.5.3

Describe Resonance as Creation & Decay of Unstable Particle σ ( 1 + 2 → BC ... ) ∝ |M ( 1 + 2 → A ∗ → BC ... ) | 2 Model as Nonrelativistic Breit-Wigner: Collision with total cm-energy E cm , relative momentum � k cm , spins S 1 , S 2 . = ⇒ Produces resonance at E 0 , total decay width Γ total , spin J . ⇒ Decays into A ∗ → BC ... (final state fully specified). = multiplicity of resonance � �� � B 1 + 2 → A ∗ out Γ 2 B BC ... total / 4 2 J + 1 4 π σ ( 1 + 2 → A ∗ → BC ... ) = in ( E cm − E 0 ) 2 + Γ 2 ( 2 S 1 + 1 )( 2 S 2 + 1 ) � k cm | 2 total / 4 | � �� � � �� � flux factor for in-multiplicities Lorentzian/Breit-Wigner Γ total : decay width into any final state: “Full Width at Half-Maximum” FWHM Γ A ∗ → BC ... = B BC ... × Γ total : partial decay width into specific final state BC ... out B BC ... = 1 Γ total = Γ BC ... , ∑ ∑ all finals all finals Branching Ratios: B BC ... : percentage of resonances decaying into specific final state BC ... out B in = B 1 + 2 by detailed balance: “probability” to produce A ∗ by colliding 1 + 2 . PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University I.5.4

Be Wary of Breit-Wigner Parametrisations in Hadron Physics! Must account for energy constraints (thresholds) in decay! = ⇒ energy-dependent width Γ BW ( s ) √ s Γ elastic BW ( s ) Relativistic Breit-Wigner parametrisation : M res = BW + i √ s Γ total s − M 2 BW ( s ) often used but not unique BUT Breit-Wigner parametrisations work only for narrow, well-separated resonances! → HW Problems: – M = M res + M background : split is arbitrary! Where does background start/end? – Resonances overlap = ⇒ interference! = ⇒ Only positions s R and residues Γ residue ( s R ) of poles in scattering amplitude are unique! √ s R � = M BW − i Γ BW : 2 Breit-Wigner mass is not pole position! More in PHYS 6710: Nuclear & Particle Physics II PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University I.5.5

Next: 7. Electron Scattering Familiarise yourself with: [HM 4, 6.1/3-6/9/11/13, 8] PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2018 H. W. Grießhammer, INS, George Washington University I.6.6