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

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001515 1616 1717 1818 1919

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