Ashra のよる GRB 由来の PeV- TeV τ ニュートリノ観測 コロキ

AshraのよるGRB由来のPeV-­‐TeV  

τニュートリノ観測

廣田誠子

 

@KUHEP  コロキ  

2013.5.27

背景：高エネルギー宇宙線

•  宇宙から来る高エネルギー宇

宙線は熱的には説明がつか

ない。

 

•  そこで、宇宙内には何かしら

の粒子加速機構があると考え

られる。

 

• 

PeV(10

15

_)~EeV(10

18

_{)領域あた}

りを境に、起源が違うと考えら

れる。

 

–  ＜PeV  :  銀河内  

–  ＞PeV:  銀河外  

Figure 1:

All particle cosmic ray flux multiplied by E2 _{observed by ATIC (Ahn et al. 2008), Proton}

(Grigorov et al. 1971), RUNJOB (Apanasenko et al. 2001), Tibet AS- (Chen 2008), KASCADE (Kampert et al. 2004), KASCADE-Grande (Apel et al. 2009), HiRes-I (Abbasi et al. 2009), HiRes-II (Abbasi et al. 2008b), and Auger (Abraham et al. 2010b). LHC energy reach of p p collisions (in the frame of a proton) is indicated for comparison.

radiation? What secondary particles are produced from these interactions? What can we learn about particle interactions at these otherwise inaccessible energies? Here we review recent progress towards answering these questions.

The dominant component of cosmic rays observed on Earth originate in the Galaxy. As shown in Figure 1, the study of this striking non-thermal spectrum requires a large number of instruments to cover over 8 orders of magnitude in energy and 24 in flux. Galactic cosmic rays are likely to originate in supernova remnants (see, e.g., Hillas 2006, for a recent update on the origin of Galactic cosmic rays). A transition from Galactic to extragalactic cosmic rays should occur somewhere between 1 PeV (_{⌘ 10}15_{eV) and 1 EeV (}

⌘ 1018 _eV). Progress on determining this transition relies both on the study of the highest energies reached in Galactic accelerators as well as the search for extragalactic accelerators that produce ultrahigh energy cosmic rays (UHECRs).

We begin with a brief summary of recent observations (Section 2), which reveal a

spec-2 Kotera & Olinto

銀河内起源

銀河外起源

くるぶし

カットオフ

• 

PeV以上の大変に高い高エネルギー宇宙線に関しては、粒子の種類もまだよくわ

からない。

 

–  第一候補は陽子だけど、もっと重いのではないかという疑惑もある  

–  スペクトルの「くるぶし」や「カットオフ」をヒントにモデルが色々…。  

•  銀河外起源に関しては、ガンマ線バーストやブラックホールなどあり、モデルが

色々あるが、まだわからない状態。

 

　

Ashra  計画概要

 

All-­‐sky  Survey  High  ResoluKon  Air  shower  detector

 

高エネルギー粒子による大気シャワーを撮像することで、

 

高エネルギー粒子放出を伴うと想定されるガンマ線バースト等の天

体現象の解明や新しい現象の発見を目指す。

 

可視光、ガンマ線、ニュートリノを同時観測できることが売り。

 

hQp://asrws300.icrr.u-­‐tokyo.ac.jp/sskgrp/

research/Ashra/ippan9.html

←ハワイ島マウナロアの観測

ステーション。　標高

_3300m  

↓他にもハワイ島内に2カ所、

計

_{3カ所の観測所からなる。}  

hQp://www.icrr.u-­‐tokyo.ac.jp/profiles/faculKes/sasaki.html

1m

12組の要素望遠鏡が存在  

各要素望遠鏡の瞳径は

_1m  

全体で全天の

_{80%をカバー！}

Ashra  計画の目的

•  各種高エネルギー粒子放出を伴うと想定される突発

的に発光する天体現象の解明。

 

–  ガンマ線バーストのモデルの検証  

•  標準モデル

(fireballモデル)とプリカーサルモデルの検証比較。  

•  ガンマ線バーストが

EeV領域までハドロンを加速するという仮説の

検証

 

•  可視光領域での測定と高エネルギー粒子の測定を同時に行う事

で、より詳細なモデル検証が出来る事を期待。

 

–  軟ガンマ線リピータ、活動銀河核、超新星etc  

–  新しい現象の発見  

 

いつ、どこで起こるかわからないので、なるべく広

い領域を常に監視する必要がある。

 

検出方法

全天の

77%を常時監視。以下の複数の測定を同時に

行う。

 

–  可視光、X線の測定  

•  常に撮像。

Fermi  衛星、Swi_  衛星などのGEB監視衛星の

アラートを受けて、

衛星のトリガーがかかった時間の

2時

間前からの測定を選択的に保存

。

 

–  超高エネルギー粒子の測定(γ線、ニュートリノ)  

•  超高エネルギー粒子に

よる大気シャワーを大気発光現

象

(チェレンコフ光と蛍光)として撮像

。事象毎の大気シャ

ワーノ全体像を取ることで、超高エネルギー粒子の同定、

エネルギー、到来方向の決定を行う。

 

 

検出１　ガンマ線バーストの観測　

•  ガンマ線バーストを起こし

たと思われる天体そのもの

の測定。

 

•  可視光を捕える  

•  修正ベーカー・ナン光学系  

– 

42度の視野  

–  角度分解能　

~1分角程度

(人の目と同じぐらい)  

• 

2.2m径の球面鏡  

• 

3枚の補正用レンズ  

検出

2　大気発光現象の検出

CMOS

検出

2-­‐1  (集光器)  

50cm

>2.5cm

光電面

蛍光版

 

(Y

₂

SiO

₅

)

40kV

•  集光を担うイメージインテンシ

ファイア

 

•  光電管＋蛍光版  

•  光子を一度電子に変換して、増

幅及び収集。最後に再度蛍光版

で光に戻して

CMOSセンサーへ。  

•  増幅率

 ~90  

• 

QE7.7%  @center  

355nm  

•  蛍光版

decay  Kme  

~110ns  

•  分解能

50um@cencter  

QE

中心からの距離

1光電子の

電荷分布

ペデスタル

γ線バーストモデルの検証：  

高エネルギータウニュートリノ探索

•  測定期間：

_{2008年10月から12月。計197.1時間}  

•  測定対象：

_GRB081203A  

•  測定施設：

 _{Ashra-­‐1、マウナロア観測所より}  

•  標的

_{:  τニュートリノが反応する標的として隣接す}

るマウナケアを想定。

hQp://www.sciencedirect.com/science/arKcle/pii/S0927650512001855#gr2

γ線バーストモデルの検証：  

トリガー

The Astrophysical Journal Letters, 736:L12 (5pp), 2011 July 20 Aita et al.

Horizontal [deg]

-20 -15 -10 -5 0 5 10 15 20

Vertical [deg]

-20 -15 -10 -5 0 5 10 15 20 trajectory of GRB081203A

Figure 1. Boundary (large red circle) between the inside (open circle) and outside (hatched area) of the FOV of the Ashra-1 light collector, which faces Mauna Kea, and the layout of trigger pixel FOVs (blue boxes) for Cherenkov τ shower observation. Repositioned array of the trigger pixel FOVs (upper blue boxes) to check the detection sensitivity with ordinary cosmic-ray air showers at a higher elevation. Firing trigger pixels (thick blue boxes) of an observed image of a cosmic-ray air shower readout along the trigger (points). An extended portion of the trajectory of GRB081203A counterpart (circular arc), the segment of this trajectory used in the ντ search (thick circular arc), the ridge lines of

Mauna Kea (red) and Mauna Loa (green) mountains, the horizon, and Mauna Kea access road are shown.

(A color version of this figure is available in the online journal.)

performance image sensor, providing a high resolution over a

wide FOV. The electron optics use an image pipeline to

trans-port the image from the focal sphere of the reflective mirror

optical system. After the light from the image is split, it is

trans-ported to both a trigger device and high-gain, high-resolution

complementary metal-oxide semiconductor image sensor.

One of the Ashra light collectors built on Mauna Loa has the

geometrical advantages of not only facing Mauna Kea, allowing

it to encompass the large target mass of Mauna Kea in the

obser-vational FOV, but has also an appropriate distance of ∼30 km

from Mauna Kea, yielding good observational efficiency when

imaging air-shower Cherenkov lights which are directional with

respect to the air-shower axis. Using the advanced features, we

performed commissioning search for Cherenkov τ showers for

197.1 hr between October and December of 2008. We served

limited 62 channels of photomultiplier tubes (PMTs) as

trig-ger sensors prepared for the commissioning runs to cover the

view of the surface area of Mauna Kea, maximizing the trigger

efficiency for Cherenkov τ showers from Monte Carlo (MC)

study, as shown in Figure

1

. Adjacent-two logic was adopted

to trigger the fine imaging, by judging discriminated waveform

signals from each pixel of the multi-PMT trigger sensor. During

the search period, ∼2 hr before the trigger of GRB081203A

(Parsons et al.

2008

), GRB counterpart (R.A. 15:32:07.58, decl.

+63:31:14.9) passed behind Mauna Kea, as viewed from the

Ashra-1 observatory. Using the same light collector but

contin-uously taking fine images of split lights just before the trigger

and readout sensors in the image pipeline, we set a limit on the

light curve as a function of time in the region of 300 s bracketing

the Swift trigger time for GRB081203A, including the precursor

and prompt afterglow optical counterpart (Aita et al.

2008b

).

3. ANALYSIS

To investigate the features, selection criteria, detection

effi-ciency, and background rate for the observation of Cherenkov

τ

shower images, we generated ν

τ

MC events with primary

en-ergies of 1 PeV to 100 EeV by 0.5 decade steps, which entered

into the rock of Mauna Kea uniformly and isotropically from a

sufficiently large aperture. We used a geodetic database around

Hawaii island (Mooney et al.

1998

), and surveyed for ourselves

the position of the observatory and the terrain of the mountain

and its surroundings. To study the generation and propagation

of τ ’s in the Earth and in the mountain, we used PYTHIA

(Sj¨ostrand et al.

2001

) to simulate the charged current

interac-tion of ν

τ

’s with nucleons and GEANT4 (Agostinelli et al.

2003

)

for the energy loss due to pair production and bremsstrahlung

in τ propagation. Photonuclear interaction was estimated using

the differential cross section given in Iyer Dutta et al. (

2001

)

and Abramowicz & Levy (

1997

). TAUOLA (Jadach et al.

1993

)

was used for τ decays, and CORSIKA (thinning = 10

−7

_{; Heck}

et al.

1998

) for air showers induced by τ decays. To simulate

the Ashra detector, we took into account the geometry, light

collection area, mirror reflection, corrector lens transmittance,

and the quantum efficiency of the photoelectric tubes, so that

the fine images corresponding to the trigger judgement were

simulated in an event-by-event manner.

∆θ

τ

, the deflection

an-gle of τ with respect to the primary ν

τ

, was estimated to be

significantly less than 1 arcmin at energies above 1 PeV due to

the physical processes occurring in the rock of the Earth and

of the mountain (Y. Asaoka & M. Sasaki 2011, in preparation).

In addition, the reconstructed τ shower axis can point toward

the ν

τ

object within an accuracy of 0.

◦

1 if the resolution of the

image is sufficiently high. Therefore, the Cherenkov τ shower

induced by PeV–EeV ν

τ

is a fine probe into VHE hadron

ac-celerators once an image is obtained with sufficient resolution.

Such images can be obtained with the Ashra detector.

The photometric and trigger sensitivity calibration of the

Ashra light collector was based on a very stable YAP

(YAlO

3

:Ce)-light pulser (Kachanov et al.

1992

) which was

placed at the center of the input window of the photoelectric

lens image tube mounted on the focal sphere of the optical

sys-tem and illuminated it. Non-uniformity in the detector gain due

to the input light position was relatively corrected by

mount-ing a spherical plate uniformly covered with luminous paint on

the input window. To correct for the time variation of the

pho-tometric and trigger sensitivity because of variations in

atmo-spheric optical thickness, which were mainly due to clouds and

hazes during the observation period, we performed careful

cross-calibration to compare the instrumental photoelectric response

with the photometry of standard stars such as BD+75D325 of

B-magnitude 9.2, for which the detected images passed through

the same optical and photoelectric instruments except for the

final trigger-controlled readout device. We estimated the

sys-tematic uncertainty on the basis of our understanding of the

detector sensitivity to be 30% after applying a combination of

the above three complementary calibration procedures.

To validate the detection sensitivity and gain calibration for

the Cherenkov τ shower, we detected and analyzed 140 events

of ordinary cosmic-ray air-shower Cherenkov images for a total

of 44.4 hr in 2008 December using the same instruments used in

the Ashra light collector, but after rearranging the trigger pixel

layout to view the sky field above Mauna Kea (Figure

1

). In

2

•  赤い円がイメージインテン

シファイアで見る事が出来

る範囲

 

•  青いマス目(トリガーピクセ

ル

)がトリガー用PMT(64本)

が見ている領域。１つでも

なるとトリガーがかかる。

 

 

•  黒い線はガンマ線バースト

を発していると思われる天

体の軌跡

 

AshraのよるGRB由来のPeV-­‐TeV  

τニュートリノ観測2

廣田誠子

 

@KUHEP  コロキ  

2013.6.3

宿題

•  ガンマ線バーストの紹介

 

•  ニュートリノのフレーバーの識別の方法

 

•  チェレンコフ大気シャワー

 

ガンマ線バーストの紹介

•  突然γ線を大量に放出する事象。ガンマ線時間にして、

数

m秒~数百秒程度

と短い。

 

•  ガンマ線を

ジェット

として放出。

 

•  全天(裏側も含む)で

1~数個/日  

•  ガンマ線放出後に一週間程度の

可視光や

X線での残

光

を伴う。（ただし遠方のため、弱い

)  

• 

2種類ある  

–  銀河系外(かなり遠い)で平均より少し大きい程度の規模

の超新星爆発に伴って起きると考えられるもの。

 

–  中性子星や天体の合体など起きる。上記のものより小さ

な規模。

 

•  発生メカニズムの詳細は未だ不明  

ガンマ線バーストの紹介

:歴史

• 

1967年。  

–  初観測。エネルギー放出の総量がわからず、規模もあわから

ない、発生個所もわからない、ということで謎な現象として認識

される。

 

• 

1997年  

– 

X線残光を発見。発生源候補となる天体の赤方偏移により距離

を推定。

120億年程度と大変に遠い事が判明。  

–  距離がわかる事でエネルギーの規模が推定。  

•  等法的に放出すると現実的でないほどの大きさになる

 

• 

2001年他  

–  残光の光度曲線野観測から、事象が当方的でない可能性が

示唆

→ジェットを出しているという理解へ  

ガンマ線標準モデルでは、前後方向に衝撃波が出、それ加速により、光学閃光が出ると

予言される。

 

→

高エネルギー粒子とイベントのはじめに起こる光学閃光の両方を同時に捕える

 

Earth-­‐Skimming法

高エネルギーニュートリノを捕まえたい。

 

1.  岩盤中のニュートリノが荷電カレント反応でレ

プトンを生成

 

2.  岩盤中をレンプトンが伝搬  

3.  空気中に突入して、シャワーを起こす  

4.  起こしたシャワーがチェレンコフ光を放出する  

5.  チェレンコフ光を検出器で検出  

τニュートリノの同定方法1

•  基本的には

τニュートリノが入射するところから、最

後にチェレンコフ光を検出するところまでのシミュ

レーションとの比較。

 

 

•  バックグラウンド候補　

 

– 

_{τニュートリノ  (一次宇宙線由来)}  

•  通常の宇宙線から大気中で作られるもの  

•  銀河面方向から来る同じく宇宙線pを親とするもの  

–  高エネルギー

ν

_μ

からのミューオン

 (これは本当は見れたら

嬉しいものだけど、　

ν

_τ

の同定ではバックグラウンド

)

 

•  ポイント

 

– 岩盤中の飛程  (岩盤を突き

抜ける

)  

• 

τの飛程　~17km@  1EeV  

(10

9

_GeV)    

– 山を出た後の崩壊長(全体

が撮像できる領域に収まる

)  

•  大気中での崩壊長は

500m程

度

@1PeV

τニュートリノの同定方法2

where

E

˜

0

!E

˜ (X;E

0

)

with

dE

˜

0

/dX!"

"

(E

˜

0

)

and

E

˜

₀

_(0;E

₀

_)!E

₀

_{. The tau-lepton range is simply}

R

#

$E

0

%!

!

0 &

dX P

$E

₀

,X %.

$8%

For E

0

!10

9

GeV, we find that R

#

!10.8 km in standard

rock (Z!11, A!22) while R

#

!5.0 km in iron. Both values

are in good agreement with those obtained by Monte Carlo

calculations '11(. To compare the tau-lepton ranges, we have

followed the convention in Ref. '11( by requiring the final

tau-lepton energy E

˜ (X;E

0

) to be greater than 50 GeV.

It is to be noted that we obtain R

#

by using the continuous

tau-lepton energy-loss approach, rather than the stochastic

approach adopted in Ref. '11(. In the muon case, the

con-tinuous approach to the muon energy loss is known to

over-estimate the muon range '16(. Such an overover-estimate is not

significant in the tau-lepton case, because of the decay term

in Eq. $7%. In fact, tau-lepton decay term dictates the tau

range in the rock until E

_#

)10

7

_{GeV. Even for E}

#

#10

7

_{GeV, the tau-lepton range is still not entirely}

deter-mined by the tau-lepton energy loss. Hence different

treat-ments on the tau-lepton energy loss do not lead to large

differences in the tau-lepton range, in contrast to the case for

the muon range. Our results for the tau-lepton range up to

10

12

GeV are plotted in Fig. 1. This is an extension of the

result in Ref. '11(, where the tau-lepton range is calculated

only up to 10

9

GeV. Our extension is seen explicitly in the

addition of a charged-current scattering term on the

right-hand side $RHS% of Eq. $5%. This term is necessary because

1/*

_#CC

becomes comparable to 1/

+

d

#

in rock for E

)10

10

_{GeV; whereas one does not need to include the}

con-tribution by the tau-lepton neutral-current scattering, since

such a contribution cannot compete with the last term in Eq.

$5% until E)10

16

_{GeV '11(. We remark that our extended}

results for R

_#

are subject to the uncertainties of the

neutrino-nucleon scattering cross section at high energies. We use the

CTEQ6 parton distribution functions '17( in this work, and

at the high energy $the small x region, namely, for x

$10

"6

_{), we fit these parton distribution functions into the}

form proportional to x

"1.3

as a guide.

Having checked the tau-lepton range, we now proceed to

calculate the tau-lepton flux. It is instructive to begin with

the simple case: the

,

e

e

"

resonant scattering. It is well

known that '9,10(

-

$

,

_e

e

"

_→W

"

_→

,

#

#

"

%!

G

_F2

m

_W4

3

.

•

s

$s"m

_W2

%

2

_%m

W 2

_/

W 2

,

$9%

with s!2m

_e

E

_, e

and 1/

-

•d

-

/dz!3(1"z)

2

_{, where z}

!E

_#

/E

,_e

. We shall focus on only those

,

e

’s for which E

,_e

satisfies the resonance condition, i.e., E

,_e

0E

R

!m

W2

/2m

e

. It

is clear from Eq. $4% that F

#

(E,X) depends only on

F

_,

e

(E

R

,X), because of the narrow peak nature of

,

e

e

"

scat-tering cross section. One also expects that F

#

(E,X) is

sig-nificant only for E around the resonance energy E

_R

. In this

energy region, one may neglect the first term on the RHS of

Eq. $4% in comparison with the second term. In the narrow

width approximation, the last term in Eq. $4% can be recast

into

13

(1"E/E

R

)

2

(

.

/

W

/L

R

m

W

)F

,_e

(E

R

,X), where /

W

is

the width of the W boson while L

R

is the interaction

thick-ness of the resonant

,

_e

e

"

_→W

"

scattering $see Appendix A

for details%. The tau-lepton flux can be readily obtained once

F

,_e

(E

R

,X) is given. We observe that the regeneration term

in Eq. $3% $second term on the RHS% can be neglected as it is

necessarily off the W boson peak. Hence, we easily obtain

F

,_e

(E

R

,X)!exp("X/L

R

)F

,_e

(E

R

,0). Substituting this

expres-sion into Eq. $4%, we obtain

F

_#

$E,X %

F

_, e

$E

R

,0%

!3.3&10

"4

&

"

E

E

R

#

&

"

1"

E

E

R

#

2

&exp

"

"

X

L

R

#

$10%

in the limit X'

+

d

_#

. The prefactor 3.3&10

"4

is obtained by

assuming a standard-rock medium. In water it becomes 1.4

&10

"4

. It is to be noted that E$E

_R

in the above equation.

We shall see later that the contribution to F

#

(E,X) by the W

resonance is negligible compared to that by the

,

_#

-N

scatter-ing.

Let us now turn to the case of tau-lepton production by

,

_#

-N charged-current scattering. The tau-lepton flux can be

calculated from Eqs. $1% and $2% once the incoming

,

#

flux is

given. The

,

_#

flux can be obtained by the following ansatz

'18(:

F

,_#

$E,X %!F

,_#

$E,0%exp

"

"

X

1

_,

$E,X %

#

,

$11%

where 1

,

(E,X)!*

,

(E)/'1"Z

,

(E,X)

(, with the factor

Z

,

(E,X) arising from the regeneration effect of the

,

#

flux.

On the other hand, the tau-lepton flux is given by

5 6 7 8 9 10 11 12 10-3 10-2 10-1 100 101 102 103

Tau lepton decay length Tau lepton range in water Tau lepton range in rock

Ta u le p to n ra n g e (k m ) log(E / GeV)

FIG. 1. The tau-lepton range in rock and in water using Eq. $8% and the tau-lepton decay length d#in km as a function of tau-lepton

energy in GeV.

ENERGY SPECTRUM OF TAU LEPTONS INDUCED BY . . . PHYSICAL REVIEW D 68, 063003 $2003%

063003-3

τニュートリノの同定方法3  

高エネルギー

μニュートリノとの分別

同じ高エネルギーレプトンでも

μとτでエネルギー損失の違いから、飛程に

違いが出てくる。

à

τの方が1桁程度生き残りやすい  

 

1.  エネルギー損失  

 

α： イオン化による損失  (コンスタント)  

β:    制動放射、電子対生成、光子原子核散乱による損失  

tion of F2 is not valid, to values of Q2 where perturbative

QCD is valid. Consequently, a parametrization of F2p

consis-tent with all the data is most useful for our purposes. The

parametrization of F2p used here is the one by Abramowicz,

Levin, Levy and Maor !ALLM" #32$. The ALLM parametri-zation involves two terms: a Pomeron contribution and a Reggeon contribution. Parameters are used to fit all data available from the pre-HERA era as well as H1 and ZEUS data published through 1997. The specific form with param-eters is detailed in the Appendix B.

Equation !3.4" shows the alternative to the BB formula for d%/dy which appears in Appendix A. As an initial compari-son of the two approaches, we show in Fig. 1 the cross sec-tion for real photon-nucleon scattering, as a funcsec-tion of inci-dent photon energy,

%!&N "! lim

Q2→0

4'2(F2

N

Q2 , !3.12"

indicated by the solid line, and the Bezrukov-Bugaev cross section !dashed line". Photon-proton data collected in Ref. #33$ are also shown. Our cross section agrees with the BB

parametrization at energies below E&)104 GeV; however,

the BB cross section increases more quickly with energy. At E&!109 GeV, our cross section is 0.40 mb, while the BB

cross section is 0.58 mb.

For the calculation of the lepton propagation in rock, it is

useful to compare the &A cross section for standard rock

(A!22). Here we include the nuclear shadowing effects. Our results are shown in Fig. 2 with the solid line. The BB cross section is the dashed line. We note that our results are

in agreement with the BB parametrization for&A, namely

%!&A "!A%!&N "#0.75G!x ""0.25$, !3.13"

where x, G(x) and %(&N) appear in Eq. !A11", over a wide

energy. The largest deviation occurs at the lowest photon

energy shown, where the photo-nuclear contribution is least important for charged lepton energy loss.

IV. MUON ENERGY LOSS, SURVIVAL PROBABILITY, AND RANGE

The expected average muon energy loss in traversing a

material of depth *X is characterized by

+

dE/dX

,

, indicated

in Eq. !1.1". The results for the standard bremsstrahlung, pair production and photonuclear !BB" differential cross sections summarized by LKV, and our results of using the ALLM differential cross section are shown in Fig. 3. Our result for

-nuc _{begins to diverge from the standard values at E}

)106 _{GeV, and is a factor of about 1.6 higher at E}

!109 _{GeV. In terms of the total -, the total with ALLM}

contributions is a factor of 1.15 larger than with the BB

photonuclear contribution at E!109 _GeV.

To explore the effect of the slightly larger value of -nuc

for muons, we have evaluated the muon survival probability FIG. 1. The photon-nucleon cross section as a function of

inci-dent photon energy for the BB !dashed line" and ALLM !solid line" parametrizations. Also shown are photon-proton data collected in Ref. #33$.

FIG. 2. The photon-nucleus cross section standard rock (A !22), as a function of incident photon energy E using the ALLM parametrization and Eqs. !3.9" and !3.10" for the shadow factor and conversion to nucleon structure function !solid line". The BB photon-nucleus cross section is shown by a dashed line.

FIG. 3. The - value for muon in standard rock (A!22), includ-ing bremsstrahlung !solid line", pair production !dashed line" and photonuclear !dotted line" interactions.

S. IYER DUTTA, M. H. RENO, I. SARCEVIC, AND D. SECKEL PHYSICAL REVIEW D 63 094020

094020-4

Propagation of muons and taus at high energies

S. Iyer Dutta,

1

M. H. Reno,

2

I. Sarcevic,

1

and D. Seckel

3

1

_{Department of Physics, University of Arizona, Tucson, Arizona 85721}

2

_{Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242}

3

_{Bartol Research Institute, University of Delaware, Newark, Delaware 19716}

!Received 2 January 2001; published 9 April 2001"

The photonuclear contribution to charged lepton energy loss has been reevaluated taking into account DESY

HERA results on real and virtual photon interactions with nucleons. With large Q

2

processes incorporated, the

average muon range in rock for energies of 10

9

GeV is reduced by only 5% compared with the standard

treatment. We have calculated the tau energy loss for energies up to 10

9

GeV taking into consideration the

decay of tau. A Monte Carlo evaluation of tau survival probability and range shows that at energies below

10

7

–10

8

GeV, depending on the material, only tau decays are important. At higher energies the tau energy

losses are significant, reducing the survival probability of the tau. We show that the average range for tau is

shorter than its decay length and reduces to 17 km in water for an incident tau energy of 10

9

GeV, as

compared with its decay length of 49 km at that energy. In iron, the average tau range is 4.7 km for the same

incident energy.

DOI: 10.1103/PhysRevD.63.094020

PACS number!s": 13.60.!r

I. INTRODUCTION

Neutrino telescopes have the potential for detecting

dis-tant sources of high energy neutrinos, for example, from

ac-tive galactic nuclei and gamma ray bursters #1$.

Upward-going muons from muon neutrino conversions to muons via

charged current interactions with nuclei are the main signal

of muon neutrinos #2,3$. In addition, muons as well as

neu-trinos are produced in the atmosphere by cosmic ray

interac-tions with air nuclei. Underground detector measurements of

muon fluxes as a function of zenith angle are one way to

determine the atmospheric muon flux as a function of

en-ergy. At high energies, one expects the muon flux to reflect

the onset of contributions from the production of charm in

the atmosphere #4$. A good understanding of the muon

en-ergy loss at high energies is an essential ingredient to the

analysis of the high energy atmospheric muon flux.

Recent SuperK measurements of atmospheric neutrinos

strongly suggest

%

_&

_→

%

_'

oscillation #5$ with large mixing

angle of sin

2

2(

"0.84 and a neutrino mass squared

differ-ence of 2#10

!3

eV

2

$

)m

2

$6#10

!3

eV

2

#6$. Assuming

%

_&

_→

%

_'

oscillation of extragalactic neutrinos with SuperK

parameters, about half of the muon neutrinos are converted

to tau neutrinos on the way to the Earth. This leads to

com-parable fluxes of ultrahigh energy tau neutrinos and muon

neutrinos at the Earth. Tau energy loss affects tau neutrino

propagation in the Earth, where tau neutrinos interact with

nucleons to produce taus which subsequently decay #7$. An

understanding of tau energy loss at very high energies could

help with the interpretation of long tracks produced by

charged particles in large underground detectors.

Future neutrino telescopes such as AMANDA, NESTOR,

ANTARES and ICECUBE are aimed at detecting high

en-ergy events from extragalactic neutrino sources. The high

energy behavior of muon and tau interactions with water or

rock nuclei has implications for event rates and the eventual

unfolding of their respective parent neutrino flux.

One way to characterize the energy loss of charged

lep-tons is to consider the average lepton energy loss per

dis-tance traveled (X in units of g/cm

2

), which can be expressed

in the form

!

!

dE

dX

"

%

*

&

+

E

!1.1"

where E is the lepton energy,

*

is nearly constant,

deter-mined by the ionization energy loss, and

+

%

,

_i

+

i

is weakly

dependent on energy and due to radiative energy loss

through bremsstrahlung, pair production and photonuclear

scattering. Generically,

+

i

!E"%

N

A

#

_y

_min

y

_max

dy y

d

-i

_{! y,E"}

dy

!1.2"

where y is the fraction of lepton energy loss in the radiative

interaction:

y%

E!E

!

E

!1.3"

for final lepton energy E

!

. The superscript i denotes

brems-strahlung !brem", pair production !pair" and photonuclear

!nuc" processes. Avogadro’s number is N and the atomic

mass number of the target nucleus is A. For rock, typical

values for initial muons of energy .100 GeV are

*

$2.4 MeV/(g cm

!2

_{) and}

₊

_$3#10

!6

_{/(g cm}

!2

_{) #8$.}

At low energies, continuous energy loss by ionization

dominates muon propagation, but at higher energies !above

.10

3

GeV), losses through pair production, bremsstrahlung

and photonuclear interactions dominate. In the case of the

muon, pair production is the most important mechanism, but

for taus, the photonuclear process is at least as important as

pair production. The high energy extrapolation of the

photo-nuclear cross section has the largest theoretical uncertainty in

the contributions to energy loss.

PHYSICAL REVIEW D, VOLUME 63, 094020

0556-2821/2001/63!9"/094020!10"/$20.00

63 094020-1

©2001 The American Physical Society

SEARCH FOR HIGH ENERGY SKIMMING NEUTRINOS ... 351

of energy as E

!_L

_{= E}

_ν

×(1 − y). The variable y limits in:

y

min

= 1/E

ν

max[E

ν

+ E

C

− (E

L

+ E

C

)×e

−xT/ζ

, 0]

y

max

= 1 − E

L

/E

ν

.

The differential cross section depends on energy approximately as dσ

cc

/dy = σ

0

E

ν0.363

as mentioned, where σ

0

= 10

−32

cm

2

and E

ν

= [EeV ]. The last term in (1) expresses

the survival probability of lepton for emerging from the rock to the atmosphere, where:

η = m

L

c

2

ζ/(E

C

ρ · cτ

L

), which contains lepton mass m

L

, its lifetime τ

L

and the density of

standard rock ρ = 2.65 gr·cm

−3

_.

Fig. 1.

Fluxes of emerging leptons

The physiscal process is quite similar for both muon and tauon, except the

de-cay probability being more sensitive for tauon survival. In particular, at energies lower

0.01 EeV tauons decay on a distance less than the radiative length and almost can not

emerge from the rock, while it is not a problem for high energy muons to pass freely few

radiative lengths without decay. The integration (1) gives us a flux of emerging leptons

at a given energy range and under a given solid angle. In Fig. 1 there are shown graphs

of estimated fluxes of muon and tauon in according to (1).

III. THE DETECTION PROBABILITY AND THE RATE OF

DETECTABLE EVENTS

Skimming leptons interact with medium by bremsstrahlung (BS), direct pair

pro-duction (DPP) and photonuclear reaction (PNR) [11]. At energies above 0.001 EeV, in

case of muon the DPP dominates and consists of about 0.47 total contribution, while BS

contribution is roughly 0.33. PNR consists less 0.20 at lower 1.EeV then getting more

significant at energies higher 1. EeV. At high energies above 0.001 EeV PNR dominates for

tauon which consists of 0.80 at 1. EeV while DPP consists of 0.20 and BS is small.

Pho-tonuclear reaction cross section increases with energy and can not be useful for producing

radiation at the medium interfasce.

in standard rock. The survival probability P(E,X) for a muon to survive to a depth X given incident energy E incor-porates the effects of fluctuations due to radiation. In Fig. 4, we show our muon survival probabilities !solid lines" for E

!103–109 GeV, in decades of energy, versus survival depth

X #in kilometers of water equivalent !kmwe"$ for standard

rock (A!22 and %!2.65 g/cm3_{). We have taken E}

min

!1 GeV in the Monte Carlo program. Using the LKV de-faults in our Monte Carlo program yields the dashed lines, which agree with the Lipari-Stanev result in Ref. #17$.

The two sets of survival probabilities translate to average

muon ranges with incident energy E and final energy Emin

!1 GeV. The average range

&

R(E)

'

is defined by

&

R!E"

'

!

!

0 (

dX P!E,X". !4.1"

The average ranges for our calculation are shown in Fig. 5 by the solid lines. The standard LKV ranges that we have cal-culated using the same muon transport Monte Carlo

simula-tion are shown with dashed lines. At E!109 GeV, the two

calculations differ by only 5%. The deviation from the stan-dard calculation increases with energy.

V. TAU ENERGY LOSS, SURVIVAL PROBABILITY, AND RANGE

Essentially the same procedure for calculating muon en-ergy loss can be applied to the tau lepton, with the important modification that the tau has a decay length considerably shorter than the muon decay length. We have evaluated the pair production, bremsstrahlung and ionization energy loss

according to the formulas in Appendix A for tau leptons, and we have evaluated the tau photonuclear differential cross section using the ALLM expression in Eq. !3.4". Figure 6

shows the tau energy loss contributions to ) for standard

rock. In this figure, ) is plotted on a logarithmic scale

be-cause the bremsstrahlung is very suppressed relative to the other contributions, due to the much heavier lepton mass.

The photonuclear contribution to ) dominates above E

*105 _GeV.

In the absence of energy loss, the tau survival probability corresponding to the curves in Fig. 4 are exponentials of the form

P!E,X"!exp

"

" X

+c,%

#

, !5.1"

where+!E/m,is the Lorentz gamma factor, c,!86.93-m

is the tau decay length and % is the material density. The

average range with no energy loss, as defined by Eq. !4.1", is just

FIG. 4. Muon survival probabilities in rock using BB differen-tial cross section for the photonuclear term !dashed line" and the ALLM differential cross section !solid line".

FIG. 5. Average muon range in standard rock !kmwe depth", for incident muon energy E, final muon energy Ef.1 GeV, using the

standard LKV treatment of energy loss, including the BB differen-tial cross section !dashed line" and substituting the ALLM photo-nuclear calculation !solid line".

FIG. 6. The)value for tau in standard rock (A!22), including bremsstrahlung !solid line", pair production !dashed line" and pho-tonuclear !ALLM line" !dotted" interactions.

PROPAGATION OF MUONS AND TAUS AT HIGH ENERGIES PHYSICAL REVIEW D 63 094020

094020-5

βの値：

τ

　　　　　　　　　

_{βの値：  μ}

岩盤から出てくるフラックス

μ  

•  一次宇宙線

_p由来のν

_τ  

– 大気中でつくられたもの  

– 銀河内でつくられたもの

τニュートリノの同定方法4  

ガンマ線バースト由来以外の

τニュートリノ

withpffiffi_s

¼ 1:8 " 103_{GeV, which corresponds to}

an Ep# 1:7 " 106GeV, as s# 2mpEpin our set-ting. Note that up to thispffiffi_s

, the agreement between the two approaches is quite good, ac-cording to Fig. 1. We have used a factorization scale Q2_{¼ ^ss=4 and the one-loop running strong}

coupling constantaswith the valueasðQ2¼ MZ2Þ ¼

0:118, and the mc¼ 1:35 GeV.

An important quantity in the neutrino flux calculation is the average fraction of the injected proton energy being transferred to the tau neu-trino, i.e., the ratio r& E=Ep. The average value of r is given either by the mean

hri ¼ R rdr dE " #dr R dr dE " #dr; ð7Þ or by the value of r at which the distribution dr=dE attains the peak. We have found that both averages of r are very close to each other. Thehri ranges from 5" 10'3to 5" 10'7for Epfrom 103

to 1011_{GeV for the production channel pp!}

c!cc ! Dsþ Y ! msþ Y , using the PQCD approach.

The higher the injected proton energy, the smaller is the fraction of the incident Epthat goes into hadrons.

2.2.2. Via b!bb, t!tt, W)_{and Z})

The production of b!bb and t!tt in pp interactions can be calculated quite reliably by the PQCD ap-proach, similar to the calculation of c!cc. The rele-vant matrix elements, including the ones for W)

and Z)_{, are listed in Appendix A.}

The results are shown in Fig. 2. Let us remark that after taking into account the sources of un-certainties such as values of mc, mb, mt, R, np, etc., we estimate that our calculation of the intrinsic galacticmsflux is reliable within an order of mag-nitude. A few observations can be drawn from the Fig. 2. (i) The production via Dsmesons dominates for E6 109_{GeV, followed by b-hadrons, W}), Z),

Fig. 2. Intrinsic galactic tau neutrino flux calculated via various intermediate states and channels: Ds, b-hadron, W), Z), and t!tt. The

injected proton flux spectrum is also shown.

H. Athar et al. / Astroparticle Physics 18 (2003) 581–592 585

フラックス

 

銀河内でできたもの

For downward going neutrinos produced in the

earth atmosphere, we take l

’ 20 km as an

ex-ample. We use the (prompt) dN

ml

=d

ðlog

10

EÞ given

in [29], whereas for dN

ms

=d

ðlog

10

EÞ, we use our

results obtained in Section 3. For horizontal and

upward going atmospheric neutrinos, l

# 10

3

_–10

4

km. Here, l

osc

$ l, and so the intrinsic

atmos-pheric tau neutrino flux dominates over the

oscil-lated one for E

P 10

3

_{GeV, essentially irrespective}

of the incident direction. We present these results

in Fig. 4, along with the GZK oscillated tau

neu-trino flux briefly mentioned in Section 1. For the

GZK neutrinos, l

P Mpc and dN

ml

=d

ðlog

10

EÞ is

taken from Ref. [10]. From the figure, we note that

the galactic-plane oscillated

m

s

flux dominates over

the intrinsic atmospheric

m

s

flux for E

6 5 % 10

7

GeV, whereas the GZK oscillated tau neutrino

flux dominates for E

P 5 % 10

7

_GeV.

A prospective search for high-energy tau

neutri-nos can be done by appropriately utilizing the

char-acteristic

s lepton range in deep inelastic (charged

current) tau–neutrino–nucleon interactions, in

ad-dition to the attempt of observing the associated

showers. For E close to 6

% 10

6

_{GeV, the}

(anti-electron) neutrino–electron resonant scattering is

also available to the search for (secondary)

high-energy tau neutrinos [30]. The main advantages of

using the latter channel are that the neutrino flavor

in the initial state is least affected by neutrino flavor

oscillations and that this cross section is free from

theoretical uncertainties [31]. The appropriate

uti-lization of the characteristic

s lepton range in both

interaction channels not only helps to identify the

incident neutrino flavor but also helps to bracket

the incident neutrino energy as well, at least in

principle.

For downward going or near horizontal

high-energy tau neutrinos, the deep inelastic neutrino–

nucleon scattering, occurring near or inside the

detector, produces two (hadronic) showers [32].

The first shower is due to a charged-current

neu-trino–nucleon deep inelastic scattering, whereas

the second shower is due to the (hadronic) decay

of the associated

s lepton produced in the first

shower. It might be possible for the proposed large

neutrino telescopes such as IceCube to

con-strain the two showers simultaneously for 10

6

_{6 E=}

GeV

6 10

7

_{, depending on the achievable shower}

separation capabilities [33] (see, also, [1]). Here,

the two showers develop mainly in ice. Using the

same shower separation criteria as given in [33], we

note that the

#(100 m)

3

_{proposed neutrino}

detec-tor, commonly called the megaton detector [34],

may constrain the two showers separated by

P10

m, typically for 5

% 10

5

_{6 E=GeV 6 10}

6

_{. The two}

nearly horizontal showers may also possibly be

contained in a large surface area detector array

such as Pierre Auger, typically for 5

_{% 10}

8

6 E=

GeV

6 10

9

_{[35]. In contrast to previous situations,}

here the two showers develop mainly in air.

Sev-eral different suggestions have recently been made

to measure only one shower, which is due to the

s

lepton decay, typically for 10

8

_{< E=GeV < 10}

10

_,

while the first shower is considered to be mainly

absorbed in the earth [36]. The upward going

high-energy tau neutrinos with E

P 10

4

_{GeV, on the}

other hand, may avoid earth shadowing to a

cer-tain extent because of the characteristic

s lepton

range, unlike the upward going electron and muon

neutrinos, and may appear as a rather small pile

up of

m

l

(l

¼ e, l, and s) with E # 10

3

GeV [37,

38]. However, the empirical determination of

in-cident tau neutrino energy seems rather

challeng-ing here.

Fig. 4. Galactic-plane, horizontal atmospheric and GZK tau neutrino fluxes under the assumption of neutrino flavor oscil-lations.

588 H. Athar et al. / Astroparticle Physics 18 (2003) 581–592

摂動論的

QCDを用いた

数値計算によると

、

1EeV領域では

、

ガンマ

線バースト由来が優勢

for EP 108

GeV. We remark that the major un-certainty for determining the abovemsflux is the

Z-moment ZpDs. In Ref. [7], the authors

calcu-late ZpDsusing two different approaches, which then

give rise to different results for themsflux. The first

approach is based upon next-to-leading order (NLO) perturbative QCD [25], while the second approach rescales the ZpD0given by the PYTHIA

[26] calculation of Thunman, Ingelman, and Gon-dolo (TIG) [27]. In the inset of Fig. 3, we also show our calculated ZpDs in comparison with the one

given by rescaling TGI!s result for ZpD0. We do

not show the ZpDs obtained by NLO

perturbat-ive QCD since it is not explicitly gperturbat-iven in Ref. [7].

4. Effects of oscillations and prospects for observa-tions

In the context of two neutrino flavors,mlandms,

the totalmsflux, dNmtots=dðlog10EÞ, is given by [28]

dNtot

ms=dðlog10EÞ ¼ P dNml=dðlog10EÞ

þ ð1 % PÞ dNms=dðlog10EÞ:

ð12Þ Here P & Pðml! msÞ ¼ sin22h sin2ðl=loscÞ. The

neutrino flavor oscillation length for ml! ms is

losc' ðE=dm2Þ. For 1036 E=GeV 6 1011and with

dm2

' 10%3_eV2_{, we obtain 10}%8_{6 losc=pc6 1. We}

assume maximal flavor mixing betweenmlandms.

For intrinsic neutrinos produced along the galactic-plane, we take dNml=dðlog10EÞ given by

Ingelman and Thunman in Ref. [5] by extra-polating it up to E6 1011_{GeV, whereas for dN}

ms=

dðlog10EÞ, we use our results obtained in Section 2.

For galactic-plane neutrinos, we note that losc( l,

where l' 5 kpc is the typical average distance the intrinsic high-energy muon neutrinos traverse after being produced in our galaxy. Eq. (12) then im-plies that, on the average, half of the muon neu-trino flux will be oscillated into tau neuneu-trino flux, reducing its intrinsic level to one half.

Fig. 3. Intrinsic horizontalmsflux via production and decay of the Dsmeson in the earth atmosphere. For 103_{6 E=GeV 6 10}6_{, the}

results by PR are also shown. In the inset, we compare our calculated ZpDswith the one given by rescaling TIG!s ZpD0. The total intrinsic galactic-plane tau neutrino flux is also shown.

H. Athar et al. / Astroparticle Physics 18 (2003) 581–592 587

フラックス

 

大気中で作られたもの

「マウナケアを

10km以上通過して出てきた事」を保障する事が必要。  

→観測された大気シャワーを作った粒子の到来方向への精度が重要  

 

τニュートリノの同定方法5  

総括と粒子到来方向

Tau Lepton Deflection Angle [deg]

-7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 1 10 Number of Events 0 200 400 600 800 1000 1200 1400 1600 1800

From right to left = 1 PeV τ E =10 PeV τ E PeV 2 =10 τ E PeV 3 =10 τ E GEANT4 (All processes except photonuclear)

Tau Lepton Deflection Angle [deg]

-7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 1 10 Number of Events 0 20 40 60 80 100 120 140

160 From right to left

= 1 PeV τ E =10 PeV τ E PeV 2 =10 τ E PeV 3 =10 τ E ALLM reproduced (Photonuclear only)

Figure 3: The simulation results of deflection angle of τs after propagating 10km of rock. (Left) the GEANT4 results including all the high energy processes except for photonuclear interaction. (Right) the results of photonuclear interaction simulated by handmade simulation. Note that the decay of τs was switched off for the above simulations. The hatched histograms indicate that the τ range is less than 10km.

neutrino energies of 1 PeV and 10 PeV, respectively. Furthermore, none of the simulated events with E

τ

>

13.7 TeV

satisfied the trigger requirements in both of Commissioning and Ashra-1 detector configurations. We conclude that

the deflection angle between decay particles which produce the air shower and parent ν

τ

was less than 1 arcmin for

detectable events.

Finally, the direction of the hadron air shower was evaluated using CORSIKA (ver. 6.900). At the shower

maxi-mum, we compared the direction of the parent particle (charged pion) to that of electrons and positrons which are the

dominant producers of Cherenkov photons. We found that on average the direction of electrons and positrons and the

parent particle of the air shower was coincident within 0.1

◦

_{at 1 PeV. In conclusion, we found that the arrival direction}

of PeV ν

τ

s was preserved within 0.1

◦

including the hadron air-shower generation. The accurate reconstruction of the

arrival direction by means of fine imaging will be a very powerful technique to determine point sources of PeV ν

τ

s.

3.3. Monte Carlo simulation

To investigate the neutrino identification capability and sensitivity, it is vital to develop a detailed Monte Carlo

simulation which simulates all processes from the neutrino interaction to detection of Cherenkov photons produced

by decayed τ air showers. An earlier study mainly based on an analytic approach can be found in Ref.[36]. In our

sim-ulation, the first step is to generate the ν

τ

s from the certain area and solid angle which is large enough compared with

our detector’s detection volume. In this step, τ production due to the charged current interaction of ν

τ

, τ propagation

in the Earth, and the determination of the decay point of τs emerging from the Earth are simulated. These processes

calculate the τ flux emerging from the Earth and subsequent decay in the atmosphere. The flux is calculated for ν

τ

s

whose energies range from 10

15

eV (1 PeV) to 10

20

eV (100 EeV) in steps of 0.5 decades. The simulation code used

in this step is based on the Earth skimming ν

τ

simulation code described in Ref.[37]. The code is further developed to

include the mountain skimming effect. Neutrino and τ interactions are updated from Ref.[37] in part in a relation with

the previous work described in Ref.[38] and are described in the following. The code is hereafter denoted as TauSim.

Considering the direction and energy of τs emerging from the Earth and removing the events with no probability of

detection at this step, the efficiency of the simulation was substantially improved.

For the neutrino-nucleon cross section, we used the calculation [39] based on CTEQ4-DIS parton distribution

functions (PDFs). Inelasticity is considered by fitting its energy dependence shown in Ref. [40] to a quadratic

expression. To estimate the energy losses due to propagation of τs in the Earth, we used the parametrization shown in

Ref. [41] based on Ref. [32]. As the density of the Earth’s crust, we took 2.9 g/cm

3

_{[42] since the main component of}

the Earth’s crust around Hawaii is basalt.

The second step of our simulation deals with τ decay, air-shower generation, and detection in the detector. Four

vectors of secondary particles produced by τ decay were calculated by TAUOLA version 2.4 [35]. The polarity

5

• 

1PeV以上では伝搬するτのずれ

の主な原因は光子原子核散乱

 

• 

1PeV以上ではτは

1分以下の精度

でまっすぐ飛んでくれる。

 

1分以下

• 

τにより作られるシャワーから

のチェレンコフ光の広がりも

1

度程度。

 

(nx,ny) = (0.0, 0.0) [deg]; (X!_,Y!_{) = (0.6, 0.0) [deg];} E = 10 [PeV].

This parameter set corresponds to RP =540 m. The left panel of Figure 6 contains an example of the shower

im-age generated with this parameter set, and it serves as a ”dummy real data” to study reconstruction accuracy. The

right panel of Figure 6 shows the probability density distribution obtained by averaging 106 events generated with

the same parameter set. To generate the shower images, the longitudinal and lateral development of air shower was calculated using Gaisser-Hillas and NKG, respectively. The direction of Cherenkov photon was calculated by

us-ing the parametrization described in Ref. [57], where normalization was adjusted to reproduce the RP dependence

of the detected number of photoelectrons (Npe) obtained with CORSIKA. We confirmed that the RP dependence is

reproduced within ±15% within the RP range we used in this study. In this simulation, fluctuation due to the first

interaction point was taken into account, but air-shower fluctuation due to hadron interaction was not. This effect was

accounted for in Section 3.2 (0.1◦ _{at 1 PeV). Although it is preferable to include hadron air-shower fluctuation using}

CORSIKA, generating a sufficient number of events requires an amount of CPU power unavailable during the writing of this paper. X [deg] -10 -5 0 5 10

Y [deg]

-10 -5 0 5 10 -2 10 -1 10 1 X [deg] -10 -5 0 5 10

Y [deg]

-10 -5 0 5 10 -7 10 -6 10 -5 10 -4 10 -3 10

)=( -0.00, 0.00) deg, (X’,Y’)=( 0.00, 0.00) deg

y ,n x (n : 537.7m p , R 2 10 × >: 4.9 pe Energy: 10PeV, <N

Figure 6: (Left) An example of Cherenkov shower image for event reconstruction (”dummy real data”), (Right) Probability density distribution. Red open circles represents (nx,ny) and green open square represents (X!,Y!). Both images are obtained using the simulated air-showers generated

using Gaisser-Hillas and NKG.

Using the number of photoelectrons in pixel i (Ni

pe) and the photon detection probability at the pixel (pi), the log

likelihood multiplied by −2, which is compatible with chi-square, can be written as follows:

L = −2!

i

Npei log( pi). (1)

Note that the Ni

pe in each pixel was not discretized, as the photoelectric image pipeline distributes the corresponding

charge because of its finite resolution. To estimate errors on the reconstruction parameters, it is necessary to calculate the error matrix for the likelihood function defined above. The error matrix is given as the inverse of the second order

10

発生点

方向

•  集光システムのキャリブレーション

 

–  集光面の場所によりゲインが違う

 

• 

YAP-­‐light  pulse  source  @  <350nmを用いて  

–  タイミング補正

 

•  光量との関係を押さえる

 

•  トリガータイミングとの関係を押さえる  

–  大気の光学的厚さが視野の中でも違ってくる

 

→更に9.2等級の明るさの安定した星を用いて最終的

な系統誤差を見積もった。

 

 

これらのキャリブレーションの結果、集光システムでの

系統誤差は

30%。  

ガンマ線バーストモデルの検証

:  

キャリブレーション

1

YAP-­‐Light  Source