Inferring neutrino cross sections above 1019 eV

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Inferring neutrino cross sections above 1019 eV

• Workshop on Exotic Physics with Neutrino
  Telescopes
• Uppsala, Sweden, September 20-22, 2006

based on SPR, A. Irimia and T. J. Weiler, Phys.
Rev. D73 083003, 2006
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Why ultrahigh energy neutrinos?

• Neutrinos point back to their cosmic sources
• Above GZK energy ( 5 x 1019 eV), they may be the
  only propagating primaries
• Neutrinos are little affected by the ambient
  matter carry information about the central
  engine
• Neutrinos carry a quantum number that cosmic rays
  and photons do not have flavor
• Travel over cosmic distances allows studies of
  their fundamental properties stability,
  pseudo-Dirac mass patterns
• Extreme energies allow studies of neutrino cross
  sections beyond the reach of terrestrial
  accelerators

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?-N cross section extrapolations to low-x
K. Kutak and J. Kwiecinski, Eur. Phys. J.
C29521, 2003
E. M. Henley and J. Jalilian-Marian, Phys. Rev.
D73094004, 2006
L. A. Anchordoqui, A. M. Cooper-Sarkar, D. Hooper
and S. Sarkar, Phys. Rev. D74043008, 2004
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?-N cross section new physics thresholds
Black Hole production
p-brane production
J. L. Feng and A. D. Shapere, Phys. Rev. Lett.
88021303, 2002
L. A. Anchordoqui, J. L. Feng and H. Goldberg,
Phys. Lett. B535302, 2002
EW instanton effects
Exchange of KK modes
F. Bezrukov et al., Phys. Rev. D68036005,
2003 and Phys. Lett. B57475, 2003

• Ringwald,
• Phys. Lett. B555227, 2003

M. Kachelriess and M. Plümacher, Phys. Rev.
D62103006, 2000
T. Han and D. Hooper, Phys. Lett. B58221, 2004
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?-N cross section bounds
HERA experiments in the lab E 52 TeV ? 2
10-34 cm2
Using RICE data
I. Kravchenko et al., Phys Rev. D73082002, 2006
V. Barger, P. Huber and D. Marfatia,
hep-ph/0606311
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Fluorescence detectors

• Two types of events
• Neutrino-induced Horizontal Air-Showers (HAS)
• NC 20 energy transfer and 44 smaller cross
  section only CC ?e
• Neutrino-induced Upgoing Air-Showers (UAS) ?
  decay 64 hadrons (2/3 E? into shower), 18
  electrons (1/3 E? into shower), 18 muons
• Two types of experiments
• Ground-based HiRes, Auger
• Space-based EUSO, OWL

UAS
??
?
?e
HAS
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Inference of the ?-N cross section at UHE

• Ratio HAS/UAS
• HAS atmosphere is a low density medium Rate / ?
• UAS Earth opaque for E? gt PeV ? only
  Earth-skimming neutrinos
• ?? ! ? process / 1/?
• More complicated dependence due to the ? ! shower
  process in the atmosphere

A. Kusenko and T. J. Weiler, Phys. Rev. Lett.
88161101, 2002
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Improvements

• Inclusion of energy dependences of the ? energy
  losses in the Earth and of the ? lifetime in the
  atmosphere (for UAS)
• Inelasticity of ?? ? ? ltygt0.2 (for UAS)
• Distinction between ? propagation in rock and
  water (for UAS)

SPR, A. Irimia and T. J. Weiler, Phys. Rev. D73
083003, 2006
9
Improvements

• Constraints from shower development and
  identification
• Minimum projected length of the shower track
  lmin
• Minimum column density beyond the point of shower
  initiation (for the shower to develop in
  brightness) dmin
• Maximum column density (after which shower
  particles are below threshold for excitation of
  N2 molecules) dmax
• Too-thin altitude beyond which the signal becomes
  imperceptible zthin

SPR, A. Irimia and T. J. Weiler, Phys. Rev. D73
083003, 2006
10

• For EUSO, each pixel is a map of km2
  lmin 5, 10 km
• dmin 300-400 g/cm2
• dmax 1200-1500 g/cm2
• zthin 3 h 24 km
• ?(z) ?0 e-z/h

Flys Eye 320 EeV event
D. J. Bird et al., Astrophys. J. 441144, 1995
SPR, A. Irimia and T. J. Weiler, Phys. Rev. D73
083003, 2006
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Improvements

• Corrections from Earth curvature (for UAS)
• ? (1020 eV) 4900 km REarth 6371 km
• Curvature-corrected altitude is increased
• Curvature-corrected angle with respect to horizon
  is increased
• Overall effect ? overestimate the air density for
  shower development

SPR, A. Irimia and T. J. Weiler, Phys. Rev. D73
083003, 2006
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Improvements

• Effects of a cloud layer
• Simplified model infinitely thin layer with
  infinite optical depth
• The constraints depend on whether the detector is
  space-based or ground-based straightforward
  implementation for UAS?G and HAS?S
• Critical altitude for UAS below which
• clouds obscure detector
• for UAS?G
• clouds have no effect
• for UAS?S

SPR, A. Irimia and T. J. Weiler, Phys. Rev. D73
083003, 2006
13
Cloudless case
lmin 10 km
lmin 5 km
ocean
Eth 1019 eV
land
Eth 5 1019 eV
ocean
land
SPR, A. Irimia and T. J. Weiler, Phys. Rev. D73
083003, 2006
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Cloudy case
lmin 5 km zcloud 2 km
ground-based
space-based
ocean
Eth 1019 eV
land
Eth 5 1019 eV
ocean
land
SPR, A. Irimia and T. J. Weiler, Phys. Rev. D73
083003, 2006
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Other dependences for space detectors
Eth 1019 eV
Eth 5 1019 eV
lmin 5 km ocean E? 1020 eV
dotted without Earth-curvature dashed with
Earth-curvature thick zcloud 4 km thin
zcloud 12 km
Dependence of Acc on cloud altitude
(dmax, dmin, lmin) solid (0 g/cm2, 105
g/cm2, 0 km) dashed (300 g/cm2, 1500 g/cm2, 5
km) dotted (300 g/cm2, 1500 g/cm2, 10
km) dash-dotted (400 g/cm2, 1200 g/cm2, 10 km)
Dependence of Acc on dmin, dmax , lmin
SPR, A. Irimia and T. J. Weiler, Phys. Rev. D73
083003, 2006
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Prospects
25600 km2
EUSO FOV 170000 km2
L. A. Anchordoqui, A. M. Cooper-Sarkar, D. Hooper
and S. Sarkar, Phys. Rev. D74043008, 2004
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Conclusions

• Comparison of HAS and UAS rates in neutrino
  observatories may allow us to infer a
  neutrino-nucleon cross section different from the
  commonly used extrapolation at ultra high
  energies
• We have presented a mostly analytic and detailed
  extension of Kusenko and Weilers idea for
  ground- and space-based detectors
• Included in the calculation are the dependences
  of the acceptances on the initial neutrino
  energy, trigger threshold, composition of the
  Earth, several shower parameters, cloud layers of
  arbitrary altitude and Earths curvature effects
• Our calculation is valid for the energy range
  1018-1021 eV
• We can establish the no-lose theorem
  acceptances are robust regardless of the cross
  section value
• Odds we assume
• to know the flavor ratio at the detector
• a small NC/CC ratio
• inelasticities as in the SM