Uncertainties beyond 10-100TeV of Gamma ray & CR phenomena : 「QG effects on the detection method etc.」 by T. Kifune

１０－１００ ＴｅＶ 以上の ガンマ線には 通常・従来の検出方法を 適用できない The usual / conventional method of detecting gamma rays can not be applied to gamma rays beyond 10 -100 Tev .

Some comments ………. • Relative Delay time = -5.5 ±10.9 ±10.3 [sec TeV-1] HESS Beijing 2011, Bolmont et al. PKS 2155-304, z=0.116, d = 1.4×109 [ly] = 4.2×1016 [light sec]

M > 2.1×1027 eV = 0.6 Mplanck

• Modified p-E relation

• Systematic errors

emission time within (1-10) second Emission size within 1010-11 cm

2

3

42222

cM

EcmEcP

)10TeV1

E1(c)

Mc

E1(c

dP

dEv 16

2

]c/eV[102.1G2

hcMM 228

PL

Some comments ………. • Relative Delay time = -5.5 ±10.9 ±10.3 [sec TeV-1] HESS Beijing 2011, Bolmont et al. PKS 2155-304, z=0.116, d = 1.4×109 [ly] = 4.2×1016 [light sec]

M > 2.1×1027 eV = 0.6 Mplanck

• Modified p-E relation

• Systematic errors

emission time within (1-10) second Emission size within 1010-11 cm

2

3

42222

cM

EcmEcP

)10TeV1

E1(c)

Mc

E1(c

dP

dEv 16

2

]c/eV[102.1G2

hcMM 228

PL

OPERA Oscillation Project with Emulsion-tRacking Apparatus, CERN CNGS1

d = 7.3×107cm=2.4×10 -3 sec Delay time = 60.7 ±6.9 ±7.4 [nsec] (v –c)/ c = (2.4 ±0.28 ±0.30) ×10 -5

相対論（量子重力理論）の高精度検証

宇宙の構成物の大きさ・質量・密度 長さ：大きさ L

質量 M

原子

惑星 隕石

人間

細菌

分子

銀河

恒星

-30 -20 -10 0 10 20 30

30

-30

0

Log L[m]

Log M[kg]

ブラックホール

電子

コンプトン波長

λ = h/MC

シュワルツシルト半径

R = GM/c2

中性子星

陽子

Planck mass

臨界密度 ρc = 3H02/(8πG)

= 2×10-26[kg/m3]

Log E [eV] 1012 1020 1028 Mc2

Quantum gravity ?

不確定性原理

paticles GUT Super Symmetry cosmos

Ｑｕａｎｔｕｍ Ｇｒａｖｉｔｙ ｅｆｆｅｃｔ ｏｎ ＶＨＥ ｇａｍｍａ ｒａｙ ａｓｔｒｏｐｈｙｓｉｃｓ

1.Propagation 2.Emission 3.Detection

Effect on propagation speed : ● systematic error ??

● higher gamma ray energy ……..

Effects on astrophysical reactions :

yes /no type test/observation

γ + ε (EBL) e++e-

e + ε (EBL) e+ γ

absorption

A : atmospheric nucleus γ + A e++e- + A

e + A e+ γ + A

Inverse Compton

Cascade, Air shower process

Interaction with atmosphere

γ + ε (EBL) e++e- Absorption

Pair creation k0 – ε p+ + p- K0 + ε E+ + E-

Momentum / energy conservation

Energy / momentum of EBL photon

?? term of ξ K2/Mplanck ??

Effect of

ε≄0 for the process to proceed

γ + ε (EBL) e++e- (absorption)

Energy : K0 +ε = E1 + E2 momentum : k0 – ε = p1 + p2 k0 - ε =K0(1+ξK/M)

0.5 - ε p1 = E1 (1-me

2/E12

+ξE1/M)0.5

p2 = E2 (1-me2/E2

2 +ξE2/M)

0.5

Threshold energy, phase volume, …..

ε≄0 for the process to proceed

Relativistic approximation QG modification

γ + ε (EBL) e++e-

M2

EEKm

EE2

K2

2

2

2

1

2

02

e

21

0

K0 - ε + ξK02/(2M)

= p1 + p2 - p1 θ12/2 - p2 θ2

2/2 < p1 + p2 < E1+ E2 – Km

2/(2E1E2) +ξ(E1

2+E12)/(2M)

Perpendicular component

1012 1013 1014 1015 1016

1

0.1

0.01

K0 (eV)

ε0 (

eV

)

ε0 K0 = me2

prohibited

0.001

(1)

(1) (2) (2) (3) (3)

all

M2

EEKm

EE2

K2

2

2

2

1

2

02

e

21

0

M

)a1(a2Km

)a1(aK

14

2

02

e

0

左辺 ＞ 右辺第１項

左辺 ＞ 右辺第２項

右辺第１項 ≈ 右辺第２項

0

1

K

Ea

0

10

0

2

K

EK

K

Ea1

threshold

prohibition /suppression of large K0

characteristic energy “asymmetric parameter “a

characteristic /critical energies

eV10)M

m( 23/1

4

e

c

eV10)Mm(K 133/12ec

eV10eV1

)M(K 142/1*

x

Infra Red

10-100 TeV

1

0.5

K0

a Allowed prohibited

0

me2/ ε0

Q R

(8ε0M)1/ 2

(4ε0M)1/ 2

[case I]

[case II]

P

γ + ε (EBL) e++e-

Inverse Compton

scattering

Energy : E0 + ε = E + K

momentum : p0 - ε = p + k

e + ε (EBL) e+ γ

M

)b1(bEm

)b1(E2

b2

M2

KEEm

EE2

K2

2

02

e

0

222

02

e

0

b=K/E0

1

0.5

E0

b

Allowed

Prohibited

0 (8ε0M)

1/ 2

Q

me2/ (4ε0)

P

R

e + ε (EBL) e+ γ

e + ε (EBL) e+ γ

M

)b1(bEm

)b1(E2

b2

M2

KEEm

EE2

K2

2

02

e

0

222

02

e

0

b=K/E0

Mm

E21

1)

m

E(4K

m

E4E

E4m

E4K

2

e

3

0

2

e

o

2

e

2

0

0

0

2

e

0

IC/synchrotron radiation

1

E0

Q

(8 ε0 M)1/2

Allowed

Prohibited

0

0.5

(me2 M/2 )1/3

me2/(4 ε0)

b

P

R

e + ε (EBL) e+ γ synchrotron radiation

Effects on interaction/process

• Prohibition of reaction

• Suppression

• Asymmetric energy partition

for final particles

(εM)1/2

(me2M)1/3

γ + ε (EBL) e- + e+

M

KAmK4

2

2

e0

0a=E1/K0

A=1/(a(1-a))

AM2Km4

A0

2

e

Asymmetric energy partition

4

e

32

0

m

M2A

M2

K

M4Km4

A0

2

e

Left > 1 st or 2 nd term of right side

1 st ¥ge 2 nd term of right side

3

13

0

2

e

3

0 )10

K(4.0

Mm

KA 2/3

13

0

2

e

3

0 )10

K(9.0

Mm

K2A

From Rene Ong’s talk

e-e+ pair creation bremsstrahlung

momentum : k - ε = p1 + p2

γ + γb (EBL) e++e-

M2

EEKm

EE2

Kq

2

2

2

1

2

02

e

21

0

γ + A e++e- + A

momentum : k = p1 + p2 + Δq

ε Δq k

ε = Δq

Gamma ray proton

1

0.5

K0

a Allowed prohibited

0

me2/ ε0

Q R

(8ε0M)1/ 2

(4ε0M)1/ 2

[case I]

[case II]

P

γ + ε (EBL) e++e-

Asymmetric pairs

Detection altitude

!?

M2

EEEKm

E

Km

EE

)EK(KmK2

2

A

2

2

2

1

2

02

A

A

02

e

21

A00

A0

γ + A e++e- + A

momentum : k = p1 + p2 + pA

The case of all particles are

relativistic

k ε -> Δq

E1 K0 or E2 K0 or EA K0

favored

● Slow development of EAS Penetrating deeper to the bottom of atmosphere ● High altitudes -- sea level ? At least, it is necessary to compare the results at different altitudes

● Proton-like shower……. muon content ? width, concentration …….

Gamma-ray initiated Extensive Air Shower ?

Adding some words onto a slide from Rene Ong’s

Crimea

Not muon poor !?

Time variable Recently detected by Fermi

summary • Extragalactic gamma ray of 1014 – 1015 eV We badly need

clear evidence for quantum gravity effect gamma rays from nearby galaxies CR physics • Suppression of IC, synchrotron radiation for E0 > 10

13 – 1014 eV

SSC model lepton/hadron model.. ..

• Detection method ? Are we driving a right vehicle along the paved road / right road ? toward the destination we are heading for ? • Many other effects ……….. • Prospect for gamma ray astronomy/CR physics will be dramatically changed