High Energy Cosmic Ray Interactions

Transcription

1 Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft High Energy Cosmic Ray Interactions (Lecture 1: Basics) Ralph Engel Karlsruhe Institute of Technology (KIT)

2 Outline Lecture 1 Basics, low-energy interactions Energies, projectile and target particles Cross sections Particle production threshold: resonances Hadronic interactions of gamma-rays Lecture 2 Intermediate energy physics Intermediate energy range: two-string models String fragmentation Rapidity, Feynman scaling Inclusive fluxes, spectrum weighted moments Lecture 3 Highest energies, air shower phenomenology Minijets, multiple interactions, scaling violation Model predictions, uncertainties Elongation rate theorem Outlook: accelerator measurements 2

3 Examples of cosmic ray interactions Centaurus A M31 Source Interstellar medium (1 proton/cm 3 ) Intergalactic medium ( -6 proton/cm 3 ) Earth s atmosphere (7x 20 protons/cm 3 ) Air shower 3

4 Radiation fields 400 ph/cm 3 CMB: Penzias & Wilson (1965) E γ ev Smaller interaction probability compensated by larger density URB IR visible x-rays γ-rays In source regions: much higher densities power-law spectra 4

5 Four-momentum kinematics Calculation with four-momenta (c=1) p =(E, p) p 1 p 2 = E 1 E 2 p 1 p 2 p 2 = E 2 p 2 = m 2 Resonance production p 2 p 1 Energy-momentum conservation p 3 p 1 + p 2 = p 3 Mass of produced resonance p 2 3 = m 2 3 =(p 1 + p 2 ) 2 =(E 1 + E 2 ) 2 ( p 1 + p 2 ) 2 = p p 1 p 2 + p 2 2 = m m E 1 E 2 2 p 1 p 2 5

6 Laboratory and center-of-mass system Mass of produced resonance p 2 3 = m 2 3 =(p 1 + p 2 ) 2 =(E 1 + E 2 ) 2 ( p 1 + p 2 ) 2 = p p 1 p 2 + p 2 2 = m m E 1 E 2 2 p 1 p 2 Lab system: p 1 =(E 1, p 1 ) p 2 =(m 2, 0) m 2 3 = 2m 2 E 1 + m m 2 2 Center-of-mass system (CMS, *): p 1 = p 2 m 2 3 =(E 1 + E 2) 2 CMS energy: E cm = s = E 1 + E 2 6

7 Interaction of protons with photons of CMB photon Δ + resonance (1.232 GeV) proton, neutron proton (0.938 GeV) π 0, π + Energy threshold not sharp E γ,max 3 3 ev E p,min = m 2 m2 p E γ,max (1 cosθ) 5 19 ev In proton rest frame: E γ,lab 300 MeV Decay branching ratio proton:neutron = 2:1 Mean proton energy loss 20% Decay isotropic up to spin effects 7

8 Equivalent c.m. energy s pp (GeV) ) 1.5 sec -1 sr -1 ev ATIC PROTON RUNJOB 3 4 KASCADE (QGSJET 01) KASCADE (SIBYLL 2.1) KASCADE-Grande (prel.) Akeno 5 HiRes-MIA HiRes I HiRes II AGASA Auger J(E) (m Scaled flux E HERA (!-p) RHIC (p-p) Tevatron (p-p) LHC (p-p) Energy (ev/particle)

9 Cross section Defined as beam target σ = 1 Φ dn int dt (Units: 1 barn = -28 m 2 1 mb = -27 cm 2 ) Flux of particles on single target Φ = dn beam da dt Interaction rate per unit time Fundamental Lorentz-invariant quantity, can be measured at accelerators ``Master equation for interaction rates dn int dtdv = ρ target σφ 9

10 Compilation of total cross sections 2 2 "!! p (p) p K p Σ p π p Particle Data Group (COMPETE Collab. PRD65, 2002) Total cross section (mb) ! γp Similar behaviour for different projectile/target combinations -3 3! γγ s GeV CMS energy (GeV)

11 Simulation concepts: energy ranges "!p (mb) (Heck et al., 1998) H1 ZEUS γ p X E! (GeV) Resonances (fireball) Scaling region (longitudinal phase space) Minijet region (scaling violation)??? 11

12 Example: Low-energy interaction model SOPHIA Description of proton/neutron interaction with background photons, Greisen-Zatsepin-Kuzmin effect SOPHIA (Mücke et al. Comp. Phys. Commun.124, 2000) 12

13 Diagrams implemented in SOPHIA p/n n/p Direct pion production Resonance production (s channel) γ π ± p/n γ Δ + decay products (distribution depends only on spin etc. of resonance and that of products) p/n p/n p/n Multiparticle production Elastic scattering γ String model γ ρ, ω, ϕ,... 13

14 Direct pion production Possible interpretation: p fluctuates from time to time to n and π + p n π + p n π + fluctuation materialized time photon (from CMB or other background field) Heisenberg uncertainty relation E t 1 Energy threshold very low: E cm,min = m π + m p 1.07 GeV (Δ + resonance: GeV) 14

15 Superposition of resonances Baryon resonances and their physical parameters implemented in SOPHIA (see text). Superscripts + and 0 in the parameters refer to pγ and nγ excitations, respectively. The maximum cross section, σ max = 4m 2 N M2 σ 0 /(M 2 m 2 N )2, is also given for reference Resonance M Γ 3 b + γ σ + 0 σ + max 3 b 0 γ σ 0 0 σ 0 max (1232) N(1440) N(1520) N(1535) N(1650) N(1675) N(1680) (1700) (1905) (1950) Breit-Wigner resonance cross section σ bw (s; M, Γ, J ) = s 4πb γ (2J + 1)sΓ 2 (s m 2 N )2 (s M 2 ) 2 + sγ 2 15

16 Multiparticle production: vector meson dominance Photon is considered as superposition of ``bare photon and hadronic fluctuation Vi = ρ, ω, ϕ,... γ = γ bare + P had i V i P had Cross section for hadronic interaction ~1/300 smaller than for pi-p interactions p/n p/n p/n Multiparticle production Elastic scattering ρ, ω, ϕ,... γ ρ, ω, ϕ,... γ ρ, ω, ϕ,... 16

17 Lifetime of fluctuations Consider photon with momentum k k Vi = ρ, ω, ϕ,... Heisenberg uncertainty relation E t 1 Length scale (duration) of hadronic interaction t int < 1fm 5GeV 1 t 1 E = 1 k 2 + m 2 V k = 1 k( 1 + mv 2 /k2 1) 2k m 2 V Fluctuation long-lived for k > 3 GeV t 2k m 2 V > t int 17

18 Putting all together: description of total cross section total cross section (µbarn) 00 0 total direct multi-pion diffraction resonances γ p X SOPHIA PDG: 9 resonances, decay channels, angular distributions Regge parametrization at higher energy Direct contribution: fit to difference to data photon lab. energy! (GeV) Many measurements available, still approximations necessary SOPHIA (Mücke et al. CPC124, 2000) 18

19 Comparison with measured partial cross sections SOPHIA 1.4 "p # p $ 0 "p # p $ + $ %! (µbarn) SOPHIA 1.4 "p # n $ + "p # p $ + $ % $ E lab (GeV)! (µbarn) E lab (GeV) 19

20 Comparison with measured partial cross sections! (µbarn) SOPHIA 1.4 "p # p $ 0 "p # p $ + $ % Resonance region SOPHIA 1.4 "p # n $ + "p # p $ + $ % $ E lab (GeV)! (µbarn) 0 Continuum region (multiparticle production) E lab (GeV) 20