School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Role of particle...
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Transcript of School of Cosmic-ray Astrophysics, Erice, July 4, 2004 Thomas K. Gaisser Role of particle...
School of Cosmic-ray Astrophysics, Erice, July 4, 2004
Thomas K. Gaisser
Role of particle interactions in high-energy astrophysics
Uncorrelated fluxesHadronic interactions
Air showers
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
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
School of Cosmic-ray Astrophysics, Erice, July 4, 2004
Thomas K. Gaisser
Basic formulation
Equation for change inEquation for change in particle i in delta distance particle i in delta distance
Primary particles from allPrimary particles from all directions per unit spheredirections per unit sphere
School of Cosmic-ray Astrophysics, Erice, July 4, 2004
Thomas K. Gaisser
Example: production of diffuse in ISM
School of Cosmic-ray Astrophysics, Erice, July 4, 2004
Thomas K. Gaisser
0 2 in diffuse ISM
School of Cosmic-ray Astrophysics, Erice, July 4, 2004
Thomas K. Gaisser
Diffuse galactic spectrum
High-energy spectrum flatter High-energy spectrum flatter than 2.7.than 2.7.Possible contribution from Possible contribution from interactions with source spectrum?interactions with source spectrum?
Cascades in the atmosphere
School of Cosmic-ray Astrophysics, Erice, July 4, 2004
Thomas K. Gaisser
Unstable hadrons: interaction or decay?
• Decay length, +/- : c (cm) – in (g/cm2) d = ccmc
– = d defines critical = 0.018 (g/cm2) / E
• Earth’s atmosphere at X = 100 g/cm2 : ~ 10-4
– this density exceeds critical when E > , – where ~ 115 GeV: E > , interaction > decay
• Around astrophysical acceleration sites– < critical even for very high E
School of Cosmic-ray Astrophysics, Erice, July 4, 2004
Thomas K. Gaisser
Boundary conditions & scaling• Air shower, primary of mass A, energy E0 :
– N(X=0) = A (E- E0 /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
• Fji( Ei,Ej) has no explicit dimension, F F()– = Ei/Ej & ∫…F(Ei,Ej) dEj / Ei ∫…F() d / 2
– Expect scaling violations from mi, QCD ~ GeV
Uncorrelated fluxes in atmosphereExample: flux of nucleonsExample: flux of nucleons ~ constant,~ constant, leading nucleon onlyleading nucleon only
Separate X- and E-dependence; try factorized solution, N(E,X) = f(E) g(X):Separate X- and E-dependence; try factorized solution, N(E,X) = f(E) g(X):
Separation constant Separation constant N N describes attenuation of nucleons in atmospheredescribes attenuation of nucleons in atmosphere
School of Cosmic-ray Astrophysics, Erice, July 4, 2004
Thomas K. Gaisser
Nucleon fluxes in atmosphereEvaluate Evaluate NN::
Flux of nucleons:Flux of nucleons:
K fixed by primary spectrum at X = 0K fixed by primary spectrum at X = 0
Comparison to proton fluxesAccount for p Account for p n n
CAPRICE98 (E. Mocchiutti, thesis)CAPRICE98 (E. Mocchiutti, thesis)
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
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/cmDecay probability per g/cm22
production spectrum:production spectrum:
Note extra power of 1/E for E >> Note extra power of 1/E for E >> = 115 GeV = 115 GeV
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
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
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
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 E1E1 E3E3E2E2
ss1212 = x = x11xx22s = 2mxs = 2mx11xx22EElablab > few GeV > few GeV resolves quarks/gluons in target;resolves quarks/gluons in target;Gluon structure function:Gluon structure function: g(x) ~ (1/xg(x) ~ (1/x22))pp, p ~ 0.2 …. 0.4, p ~ 0.2 …. 0.4
xx22
xx11
11
School of Cosmic-ray Astrophysics, Erice, July 4, 2004
Thomas K. Gaisser
Geometrical model of p-A interactions
T(b) is number ofT(b) is number of target nucleons attarget nucleons at impact parameter bimpact parameter b
is nucleon-nucleon cross sectionis nucleon-nucleon cross section
{…} is probability of{…} is probability of at least one interactionat least one interaction at impact parameter bat impact parameter b
NN is partial cross section for N wounded nucleons is partial cross section for N wounded nucleons
School of Cosmic-ray Astrophysics, Erice, July 4, 2004
Thomas K. Gaisser
Wounded nucleons & inelasticity
Mean number of wounded nucleons:Mean number of wounded nucleons:
pApA ~ A ~ A⅔⅔ , , so <Nw> ~ Aso <Nw> ~ A⅓⅓
ZZNNNN(air) = P(air) = P11 ∫ x∫ x1.71.7 dx dx
+ P+ P22 ∫ x ∫ x1.71.7 log(1/x) dx log(1/x) dx
+ + ½½ P P33 ∫ x ∫ x1.71.7 [log(1/x)] [log(1/x)]2 2 dxdx
≈≈ 0.30.3
School of Cosmic-ray Astrophysics, Erice, July 4, 2004
Thomas K. Gaisser
E1E1 E3E3E2E2
ss1212 = x = x11xx22s = 2mxs = 2mx11xx22EElablab > few GeV > few GeV resolves quarks/gluons in target;resolves quarks/gluons in target;Gluon structure function:Gluon structure function: g(xg(x22) ~ (1/x) ~ (1/x22))pp, p ~ 0.2 …. 0.4, p ~ 0.2 …. 0.4
xx22
xx11
Analogy of pp and p-nucleus physics
• If Atarget = Atarget(E) then – NW would increase with E– Inelasticity ≡ 1 - <x(E)>
would also increase ~ A⅓
• Something like this happens with pp collisions (M. Strikman, R. Engel)
• Amount of scaling violation is uncertain
Model-dependence of Xmax
G. Archbold, P. Sokolsky, et al.,Proc. 28th ICRC, Tsukuba, 2003
HiRes new composition result: transition occurs before ankle
Sybil 2.1 (some screening Sybil 2.1 (some screening of gluons at small x)of gluons at small x)
QGSjet (strong increase of gluonQGSjet (strong increase of gluon multiplicity at small x) multiplicity at small x)
•XXmax max ~ ~ log(E log(E00 / A) with scaling / A) with scaling
•With increase of inelasticity,With increase of inelasticity,•Primary energy is further subdivided:Primary energy is further subdivided:•XXmaxmax ~ ~ log{ E log{ E00 / (A * (1 - <x(E)>) ) } / (A * (1 - <x(E)>) ) }
Example of increasing inelasticity
Effect is limited because energy notEffect is limited because energy not carried by leading nucleon is dividedcarried by leading nucleon is divided among pions, which divide theamong pions, which divide the remaining energy, as in scaling.remaining energy, as in scaling.
Such a large change would haveSuch a large change would have a significant effect on interpretationa significant effect on interpretation
-in terms of composition-in terms of composition-of energy in a ground array-of energy in a ground array
11
001515 1616 1717 1818 1919
Inel
astic
ityIn
elas
ticity