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.