1. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Role of particle interactions in high-energy astrophysics Uncorrelated fluxes Hadronic interactions Air showers

2. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Particle interactions for cosmic rays Atmosphere –Nuclear targets –Nuclear projectiles –Forward region –High energy –“Minimum bias” –Limited guidance from accelerator data Astrophysics –Astrophysical uncertainties are more severe

3. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Particle production: two scenarios 1.Inject beam of particles – follow secondary cascades in target – Earth or stellar atmosphere 2.Inject particles from cosmic accelerators – diffuse in low-density gas – occasional interactions

4. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Basic formulation Equation for change in particle i in delta distance particle i in delta distance Primary particles from all directions per unit sphere directions per unit sphere

5. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Example: production of diffuse  in ISM

6. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser  0  2  in diffuse ISM

7. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Diffuse galactic  spectrum High-energy spectrum flatter than 2.7. than 2.7. Possible contribution from interactions with source spectrum? interactions with source spectrum?

8. Cascades in the atmosphere

9. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Unstable hadrons: interaction or decay? Decay length,  +/- :  c   (cm) –in (g/cm 2 )  d  =  c       c  m   c  –  = d  defines  critical = 0.018 (   g/cm 2 ) / E  Earth’s atmosphere at X = 100 g/cm 2 :  ~ 10 -4 – this density exceeds  critical when E  >  , –where   ~ 115 GeV: E  >  , interaction > decay Around astrophysical acceleration sites –  <  critical even for very high E 

10. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Boundary conditions & scaling Air shower, primary of mass A, energy E 0 : –N(X=0) = A  (E- E 0 /A) for nucleons –N(X=0) = 0 for all other particles Uncorrelated flux from power-law spectrum: –N(X=0) =  p (E) = K E -(  +1) – ~ 1.7 E -2.7 ( cm -2 s -1 sr -1 GeV -1 ), top of atmosphere F ji ( E i,E j ) has no explicit dimension, F  F(  ) –  = E i /E j & ∫…F(E i,E j ) dE j / E i  ∫…F(  ) d  /  2 – Expect scaling violations from m i,  QCD ~ GeV

11. Uncorrelated fluxes in atmosphere Example: flux of nucleons ~ constant, ~ constant, leading nucleon only leading nucleon only Separate X- and E-dependence; try factorized solution, N(E,X) = f(E) g(X): Separation constant  N describes attenuation of nucleons in atmosphere

12. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Nucleon fluxes in atmosphere Evaluate  N : Flux of nucleons: K fixed by primary spectrum at X = 0

13. Comparison to proton fluxes Account for p  n CAPRICE98 (E. Mocchiutti, thesis)

14. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Primary spectrum of nucleons Plot shows –5 groups of nuclei – plotted as nucleons – Heavy line is E -2.7 fit to protons

15. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser  ±   ± in the atmosphere Production spectrum of Production spectrum of  ± : at high energy: Decay probability per g/cm 2  production spectrum: Note extra power of 1/E for E >>   = 115 GeV

16. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Comparison to measured  flux High-energy analysis – o.k. for E  > TeV Low-energy: – dashed line neglects  decay and energy loss – solid line includes an analytic approximation of deday and energy loss by muons

17. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Uncertainties for uncorrelated spectra p  K +  gives dominant contribution to atmospheric neutrino flux for E > 100 GeV p  charm gives dominant contribution to neutrino flux for E > 10 or 100 or ? TeV –Important as background for diffuse astrophysical neutrino flux because of harder spectrum

18. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Calculations of air showers Cascade programs –Corsika: full air-shower simulation is the standard –Hybrid calculations: CASC (R. Engel, T. Stanev et al.) uses libraries of presimulated showers at lower energy to construct a higher-energy event SENECA (H-J. Drescher et al.) solves CR transport Eq. numerically in intermediate region Event generators plugged into cascade codes: –DPMjet, QGSjet, SIBYLL, VENUS, Nexus

19. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Hadronic interactions at UHE Scaling assumption for fast secondaries is equivalent to assuming distribution of final state radiation from leading di-quark is independent of beam energy At higher energy more complex interactions may be important E1E3 E2 s 12 = x 1 x 2 s = 2mx 1 x 2 E lab > few GeV resolves quarks/gluons in target; resolves quarks/gluons in target; Gluon structure function: g(x) ~ (1/x 2 ) p, p ~ 0.2 …. 0.4 g(x) ~ (1/x 2 ) p, p ~ 0.2 …. 0.4 x2x2x2x2 x1x1x1x11

20. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Geometrical model of p-A interactions T(b) is number of target nucleons at target nucleons at impact parameter b impact parameter b  is nucleon-nucleon cross section  is nucleon-nucleon cross section {…} is probability of at least one interaction at least one interaction at impact parameter b at impact parameter b  N is partial cross section for N wounded nucleons  N is partial cross section for N wounded nucleons

21. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Wounded nucleons & inelasticity Mean number of wounded nucleons:  pA ~ A ⅔, so ~ A ⅓ Z NN (air) = P 1 ∫ x 1.7 dx + P 2 ∫ x 1.7 log(1/x) dx + P 2 ∫ x 1.7 log(1/x) dx + ½ P 3 ∫ x 1.7 [log(1/x)] 2 dx + ½ P 3 ∫ x 1.7 [log(1/x)] 2 dx ≈ 0.3 ≈ 0.3

22. School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser E1E3 E2 s 12 = x 1 x 2 s = 2mx 1 x 2 E lab > few GeV resolves quarks/gluons in target; resolves quarks/gluons in target; Gluon structure function: g(x 2 ) ~ (1/x 2 ) p, p ~ 0.2 …. 0.4 g(x 2 ) ~ (1/x 2 ) p, p ~ 0.2 …. 0.4 x2x2x2x2 x1x1x1x1 Analogy of pp and p-nucleus physics If A target = A target (E) then –N W would increase with E –Inelasticity ≡ 1 - would also increase ~ A ⅓ Something like this happens with pp collisions (M. Strikman, R. Engel) Amount of scaling violation is uncertain

23. Model-dependence of X max G. Archbold, P. Sokolsky, et al., Proc. 28 th ICRC, Tsukuba, 2003 HiRes new composition result: transition occurs before ankle Sybil 2.1 (some screening of gluons at small x) of gluons at small x) QGSjet (strong increase of gluon multiplicity at small x) multiplicity at small x) X max ~ log(E 0 / A) with scalingX max ~ log(E 0 / A) with scaling With increase of inelasticity,With increase of inelasticity, Primary energy is further subdivided:Primary energy is further subdivided: X max ~  log{ E 0 / (A * (1 - ) ) }X max ~  log{ E 0 / (A * (1 - ) ) }

24. Example of increasing inelasticity Effect is limited because energy not carried by leading nucleon is divided carried by leading nucleon is divided among pions, which divide the among pions, which divide the remaining energy, as in scaling. remaining energy, as in scaling. Such a large change would have a significant effect on interpretation a significant effect on interpretation -in terms of composition -of energy in a ground array 10 1516 17 1819 Inelasticity