On the Characteristics of the Neutrino Events in (Ultra-)High Energy

Astrophysics Experiments from the view point of Energy Estimation

Akeo Misaki

Research Institute

For Science and engineering, Waseda University, Tokyo, Japan

Invitation to a point in dispute

• The Fundamental parameters in (Ultra-)High Energy Astrophysics are:

1.Reliable Estimation of the Energies of the Neutrino Events2. Reliable Estimation of the Incident Direction of the Neutrino

Events

To invite the participants to a point dispute, let us start from CONCLUSION, not INTRODUCTION.

Conclusion 1

1. Muon Neutrino Events: Inevitably Partially Contained Events

One could not even estimate the energies of the muons from muon neutrino events (! ?)

2. Electron Neutrino Events: Usually, Fully Contained Events. Inevitably, Partially Contained Events in Ultra-High Energies (LPM shower)

Conclusion 2

• COMPUTER NUMERICAL EXPERIMENTS

• should be carried out simultaneously together with the REAL XPERIMENTS CONCERNED, not in the usual sense of Monte Carlo Simulation.

Range Fluctuation of (Ultra)-High Energy Muons

• The Muon Range with Definite Energy is governed by the stochastic characters of the direct electron pair production, remsstrahlung and nuclear interaction which are also the origins of the accompanied electron showers.

Range Fluctuation of (Ultra-) High Energy Muon

The Image of (Ultra-)High Energy Muon

• Muons from Muon Neutrino Events should be recognized as an aggregate of electron cascade showers with different starting points and different primary energies.

• “Electron clouds” are twined around such the muon.

• Namely, the muon could not be imaged as “Single or Naked Muon “

Is the Muon Itself the Dominant Source for the Cherenkov Light ?

• For the question, it enough to examine the track lengths concerned, because the Cherenkov light production is proportional to the corresponding track length.

• Ratio= track lengths of electrons from the accompanied showers/(track lengths of electrons from the accompanied showers + track length of the muon )

The transition curves for the integral of the track lengths from the muon as whole

Cherenkov Light from the Mother Muon and Her Daughters Electron Shower

• Accompanied electron showers are produced fr

om the direct electron pair production, beremsstrahlung and nuclear interaction due to muon.

• These electron showers are exactly simulated in one-dimensional treatment .

• The electron segments in the simulated electron showers produced corresponding Cherenkov light

The Exactly Simulated Energy Losses of a Muon with 100 TeVas the Function of the traversed depth

The Exactly Simulated Energy losses of a Muon with 1 PeV as the function of the traveresed distance

Five Examples of Transition Curves for the Cherrenkov Light

Cherenkov Photon Number Distribution at 1000m

Cherenkov Light vs. Muon Energy

EμCherenkov Light(t) N=N+1

Eμ

Random sampling of Eμ from Eμ

－ (γ+1) dEμ

N N≦ max

N=1

Yes

No

A production Spectrum for MuonNμ(Eμ)dEμ E∝ μ

－ (γ+1) dEμ

For given γ

Energy Estimation of Muon for given Ch

erenkov Light 　　 1

Energy Estimation of Muon for Given Cherenkov Light 2

The LPM showers as Partially Contained Events

• The Characteristics of the LPM showers:

• [1] The Average behavior of the LPM showers is quite different from that of BH (Bethe-Heitler) Showers ( Konishi,Misaki and Fujimaki, Nuovo Cimento,(1978))

• [2] TheIndividual Behavior of the LPM shower is quite different from that of the Averaged LPM shower ( Konishi,Adachi,Takahashi and Misaki, J.Phys.G, (1991))

•

Nuovo Cimento 48A, 509 (1978)

The first prediction on the characteristics of the LPM shower

LPM LPM

BHBH

E0/Em=103 E0/Em=103

The first prediction on the multi-peak structure of the LPM shower.

E0=1017 eV Emin=109 eV

The same LPM shower with different threshold energies.

Eth=109 eV

Eth=1012 eV

Eth=1014 eV

Multi-peak threshold

The LPM shower with deep crevasse.

E0=1017 eV

Em=109 eV

The first description on the average behavior of the LPM shower in water.

Fractional dissipated energies of the LPM shower in water.

4848 cu = 1700 meters

LPM shower electron number E0=10^15 eV LPM shower in Water

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

0 5 10 15 20 25 30 35 40 45 50

depth ( m )

No.

of e

lect

ron

1系列2系列3系列4系列5系列6系列7系列8系列9系列10系列

Emin=109eVEprim=1015 eV

LPM shower track length E0=10^15 eVtrack lenghts of LPM shower in Water

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

0 5 10 15 20 25 30 35 40 45 50

depth ( m )

trac

k le

ngth

( m

) 1系列2系列3系列4系列5系列6系列7系列8系列9系列10系列

Emin=109eVEprim=1015 eV

LPM shower electron number E0=10^18 eV

LPM shower in Water

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

0 20 40 60 80 100 120 140 160 180 200

depth ( m )

No.

of

elec

tron

1系列2系列3系列4系列5系列6系列7系列8系列9系列10系列

Emin=1012eVEprim=1018 eV

LPM shower track length E0=10^18 eVtrack lenghts of LPM shower in Water

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

0 20 40 60 80 100 120 140 160 180 200

depth ( m )

trac

k le

ngth

( m

) 1系列2系列3系列4系列5系列6系列7系列8系列9系列10系列

Eprim=1018 eV Emin=1012eV

LPM shower electron number E0=10^21 eV LPM shower in Water

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

0 100 200 300 400 500 600 700 800 900 1000

depth ( m )

No.

of

elec

tron

1系列2系列3系列4系列5系列6系列7系列8系列9系列10系列

Emin=1015eVEprim=1021 eV

LPM shower track length E0=10^21 eVtrack lenghts of LPM shower in Water

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

0 100 200 300 400 500 600 700 800 900 1000

depth ( m )

trac

k le

ngth

( m

) 1系列2系列3系列4系列5系列6系列7系列8系列9系列10系列

Emin=1015eVEprim=1021 eV

Final Conclusion

• At the early stage of the REAL XPERIMENTS, COMPUTER NUMRERICAL XPERIMENT should be being carried out with parallel them, collaborating with them closely.

• In the presence of the Computer numerical experiment, one need not the transformation from the Cherenkov light to the Muon Energy