Phenomenology of Cosmic Ray Air Showers

1
Phenomenology of Cosmic Ray Air Showers
María Teresa Dova UNLP, Argentina Faro, Portugal
- January 2005
2
The Extensive Air Showers

• Hadronic processes
• Low-pT jet physics
• beyond collider energies
• SIBYLL vs QGSJET
• Electromagnetic
• processes
• - The electromagnetic
• component
• - The muon component

Anchordoqui, MTD, Mariazzi, McCauley, Paul,
Reucroft, Swain Annals of Physics (2004)
3
Hadronic Processes
For SOFT processes the rates and properties are
dominated by non-perturbative QCD effects
SEMIHARD interactions lead to the MINIJET
phenomenon, i.e., jets with transverse energy
(ETpT) much smaller than the total
center-of-mass energy. Perturbative QCD.
4
Factorisation in QCD precision predictions
Steeply rising gluon density xg ? x 0.4, which
dominates the quark density at low x, in
agreement with HERA results.
Courtesy of Max Klein
xg (x,Q2) ? x DH DH 0.3 - 0.4
Primary protons with E 1011 GeV yield partons
with x10-7.
5

• The high energy minijet cross section is
  determined by the small-x
• behavior of the parton distributions.
• Leading contribution of the diferential cross
  section for gg scattering.

Unitarization eikonal approximation
6
QGSJET
SIBYLL
taken as the Fourier transform of the proton
electric form factor
7
and more

• In QGSJET the minimum virtuality characterizing
  a
• hard scattering process is 1.5 GeV2.
• SIBYLL 2.1 uses the cutoff parametrization
• Particle production String fragmentation models
• Generalization to hadron-nucleus scattering
• Gribov-Glauber
• 
  
  

with pT0 2.5 GeV
8
Implications for EAS
Inelasticity

QGSJET
SIBYLL
Anchordoqui, MTD, Epele, Sciutto PRD 59,094003
(1999)
9
SIBYLL
QGSJET


Knapp, Heck, Sciutto, MTD, Risse Astrop. Phys. 19
(2003)77
10
EAS
Evolution dominated by electromagnetic processes.
11
The electromagnetic component

• The generation of the em component (growth
  phase) is driven by
• electron bremsstrahlung
• pair production

• Relevant quantities
• Probability for an electron of energy E to
  radiate a photon of energy kyE ,
• Probability for a photon to produce a pair ee-
  in which one of the particles (e-) has energy
  Exk.
• Determined by the properties of the air and the
  cross sections of the two processes.

12
The total probability for bremsstralung radiation
is logarithmically divergent. This infrared
divergence is eliminated by the interference of
bremsstrahlung amplitudes from nearby scattering
centers.
LPM effect
LPM suppression of the cross section.
E1019eV, q600
Effective increase of the m.f.p of e and g.

• g primaries
• E gt ELPM 1019eV
• Shift in the Xmax.
• Larger fluctuations.

13
Geomagnetic cooling gs convert into ee- pairs,
which in turn emit synchrotron photons.
Gamma-ray primaries

• LPM effect
• Significant above 1019.0eV
• Geomagnetic field effect
• Significant above 1019.5eV

.

• Large directional and geographical dependence
  of shower observables.

Courtesy of Kenji Shinosaki
14
Electron lateral distribution function
The transverse development in electromagnetic
cascades scales with the Molière radius
NKG formula
The age parameter snkg characterizes the stage
of the shower development
15
Generalization of NKG formula for the em portion
of baryon-induced showers
1010GeV proton (rgt100 m)
s 3 (1 2 b/ t) -1
b takes into account the deviations from snkg
MTD, Epele, Mariazzi Astropart. Physics 18, 351
(2003)
16
The muon component

• m from the decay of cooled (Ep 1 TeV) charged
  p.
• Number of m at ground number of e. No muonic
  cascade!
• m has a much smaller cross section for radiation
  and pair
• production than the electron.
• Smaller multiple scattering suffered by muons
  leads to earlier
• arrival times for muons than em component.

• 1011GeV vertical proton
• Nee- /Nmm- varies from 17 (200 m from the
  core) to 1 (2000 m).
• Average m energy at ground 1 GeV
• 1011GeV proton, q 750
• Nee- /Nmm- is 400 times smaller than for a
  vertical shower.
• Average m energy at ground for horizontal
  showers 100 GeV

17
Muon lateral distribution function

• Greisen ( inspired by NKG parametrization)

• Vernov et al ( semi-analytical form)

• Shower age-dependence in the muon structure
  function
• Lateral growth determined by the direction of
  emission of the parent particles

G 2 s(t)

Vernov
MTD, Epele, Mariazzi, Astropart. Phys. 18, 351
(2003)
18
Muon lateral distribution
Vernov-like with s(t) and r(t)
19
LDF for inclined showers ( qlt700)

• Azimuthal asymmetry due to
• Development of the lateral distribution in the
  atmosphere.
• Attenuation of particles traveling longer path
  in the atmosphere.

20
VERTICAL SHOWERS
Shower parameters of the LDF r(r,t) s (t)
longitudinal shower
development r 0 (t)
transverse shower development
MTD, Epele, Mariazzi Astropart. Phys. 18, 351
(2003)
INCLINED SHOWERS
Evaluation of s (attenuation effect) and r0
(spread of the shower), at slant depth t,
with t t secq (1a tagq cosz)

r(r,t(z,q))
21
r z distributions of electrons 1019 eV proton
shower - 600
z
z
z
z
z
z
22
r z distributions of muons 1019 eV proton
shower - 600
z
z
z
z
z
z
23
Conclusions

• The chief uncertainty in shower modeling arises
• from lack of definitive knowledge of hadronic
• interactions.
• Pierre Auger Observatory
• - New arsenal of hybrid data.
• - Studies of particle physics well beyond
  collider
• energies.