Bartol Flux Calculation

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Bartol Flux Calculation

• presented by Giles Barr, Oxford
• ICRR-Kashiwa
• December 2004

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Outline

• Neutrino calculation
• Computational considerations
• Results
• Systematic errors (excluding hadron production
  and primary fluxes which is tomorrow)
• Improvements

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Injection height 80km

• Track forward.
• When first neutrino hits detector, perform cutoff
  calculation i.e. track back.
• Forward stepping equal steps except
• smaller near Earth surface or when near end of
  range.
• large steps for high energy muons
• Backward stepping adaptive step sizes depending
  on the amount of bending and the distance from
  the earth.

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• Avoid rounding errors when stepping down. Use
  local ?h during tracking.
• Do not use centre of earth as origin and compute
• each step

?1
?2
?h
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Shower graphic from ICRC
80km altitude
Detector
Earths surface
No energy threshold
80km altitude
Detector
Threshold 300 MeV
Earths surface
80km altitude
Detector
Earths surface
Threshold 1 GeV

• L smaller in 3D

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3D Is it important?
3D bigger gt30
3D bigger 10-30
3D bigger 3-10
lt3
1D bigger 3-10
1D bigger 10-30
SuperKamiokande Collaboration hep-ex/0404034
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Detector shape

• Main technique
• Use flat detector on surface of Earth.
• Extend to make MC calculation more efficient, but
  do not want to extend in vertical direction as
  3-D effect is very sensitive in that direction
  (P.Lipari). ? Flat.
• Second technique
• Spherical detector neutrino hits detector if
  direction is within ?cut of neutrino direction
  weight event by apparent detector size.

Bend at 20km
Bend a60o
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How big can the detector be ?
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Kamioka
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Correction if your detector is too big...
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Weight problem...

• With flat detector, weight by 1/cos?D
• Shortcut in 1D, since ?P ?D, generate primaries
  flat in cos?P, weight by cos?P
• Total weight cos?P/ cos?D 1.
• In 3D, ?P ? ?D, so must face situation of very
  large 1/cos?D. Various tricks.

Modified individual weights Weight zero very
close to divergence and weight a bit higher in
neighboring region cosq1.00 ? 0.10 weight
1/cosq cosq0.10 ? 0.01 weight
1/(0.9cosq) cosq0.01 ? 0.00 weight 0
Binlet weights Weight of each bin 1/cosq
determined at bin centre. With 20 bins, bias is
large (5), therefore it is done with 80
binlets (bias 1.5).
Bias If the flux is flat within a bin No
bias. Otherwise, bias 1 rg r fractional
difference in flux from centre to edge of
bin g fraction of bin set to weight 0 (0.1)
Bias If the flux is flat within the bin No
bias. Otherwise bias 1 r/3 r fractional
difference in flux from centre to edge of
bin (r can be as large as 15 for bins of Dcosq
0.1)
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A little history...

• Before full 3D was tuned to be fast enough DST
  method.
• Based on idea of trigger in experiment
• Rough calculation done first
• Neutrinos which went near detector got repeat
  full treatment.
• Speed up by reusing rough calculation at lots of
  points on Earth (always same ?Z).

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A bit more on technique...

• Plug and play modules of code
• Hadron production module
• Target (different versions)
• Simple test generators
• Used Honda_int for tests
• Decay generator
• Atmospheric model

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Results
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df/d ln(E) (m-2s-1sr-1)
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Give fluxes vs E
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Azimuth angle distributionEast-West effect
N
E
S
W
N
N
E
S
W
N
E?gt315 MeV
E?gt315 MeV
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Energy dependence of East-West effect
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Flavour ratios
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Down/Horizontal Ratios
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Up/Down asymmetry
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Some systematics
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Cross section change
Effect of artificial increase in total cross
section of 15
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AtmosphericDensity
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Associative production

• Effect of a 15 reduction in ?K production

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Effects not considered

• Later talk on hadron model and primary fluxes
• Effect of mountain at Kamioka. (effects of
  altitude variation around the earth are in, but
  no local Kamioka map).
• Solar wind Assume it can be lumped in with flux
  uncertainty.
• Charm production.
• Neutral kaon regeneration.
• Polarisation in 3 body decays.

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Summary

• Considered here all systematic errors except
  hadron production and fluxes (next talk).
• Most of them are small.
• 3D effects are not large, but increase in program
  complexity is large.
• Cross checks between calculations.
• Improvements
• Mountain needed ?
• Use more information from muon fluxes.

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