Post on 19-Jan-2016
transcript
Bartol Flux Calculation
presented by Giles Barr, Oxford
ICRR-Kashiwa
December 2004
Outline• Neutrino calculation
+Computational considerations
• Results
• Systematic errors (excluding hadron production and primary fluxes which is tomorrow)
• Improvements
Primary cosmic ray
N
N
K
π
π
μ
ν
• 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.
Injection height 80km
Primary cosmic ray
N
N
K
π
π
μ
ν
• Avoid rounding errors when stepping down. Use local Δh during tracking.
• Do not use centre of earth as origin and compute
each step
θ1
Δh
θ2
222 zyx
Shower graphic from ICRC
• L smaller in 3D
Earth’s surface
Earth’s surfaceThreshold 300 MeV
Threshold 1 GeV
Detector
Detector
Detector
80km altitude
80km altitude
No energy threshold
80km altitude
Earth’s surface
SuperKamiokande Collaborationhep-ex/0404034
3D
big
ge
r
>30%
10%-30%
3%-10%
<3%
1D
b
igg
er
3%-10%
10%-30%
3D: Is it important?
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 θcut
of neutrino direction; weight event by apparent detector size.
Bend at20km
Bendα=60o
How big can the detector be ?
Kamioka
Correction if your detector is too big...
Weight problem...• With flat detector, weight by 1/cosθD
– Shortcut in 1D, since θP = θD, generate primaries flat in cosθP, weight by cosθP
• Total weight cosθP/ cosθD = 1.
– In 3D, θP ≠ θD, so must face situation of very large 1/cosθD. Various tricks.
Modified individual weightsWeight zero very close to divergence and weight a bit higher in neighboring regioncos1.00 → 0.10 weight 1/coscos0.10 → 0.01 weight 1/(0.9×coscos0.01 → 0.00 weight 0
‘Binlet’ weightsWeight of each bin 1/cosdetermined at bincentre. With 20 bins, bias is large (~5%), therefore it is done with 80 binlets (bias ~1.5%).
BiasIf the flux is flat within a bin: No bias.Otherwise, bias = fractional difference in flux from centre to edge of binfraction of bin set to weight 0 (0.1)
BiasIf the flux is flat within the bin: No bias.Otherwise bias = 1 fractional difference in flux from centre to edge of bin can be as large as ~15% for bins of cos= 0.1)
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 θZ).
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
Results
dφ
/d ln
(E)
(m
-2s-1
sr-1
)
Give fluxes vs E
Azimuth angle distributionEast-West effect
N E S W N N E S W N
Eν>315 MeVEν>315 MeV
Energy dependence of East-West effect
Flavour ratios
ratios
Down/Horizontal Ratios
Up/Down asymmetry
Some systematics
Cross section changeEffect of artificial increase in total cross section of
15%
AtmosphericDensity
Associative production
• Effect of a 15% reduction in ΛK+ production
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.
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.