「量子重力効果と宇宙背景電磁波放射の「切り口」から想像する Prospect

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
MM 
PL
• Modified p-E relation
hc
 1.2  10 [eV / c ]
2G
28
3
E
P c E m c 
Mc
2
2
2
2
4
2
dE
E
E
v
 c(1 
)  c(1 
 10 )
dP
Mc
1TeV
16
2
• Systematic errors
emission time within (1-10) second
Emission size within 10 10-11 cm
2
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]
OPERA
Oscillation
Apparatus, CERN CNGS1
27Project
M > 2.1×10
eV =with
0.6Emulsion-tRacking
M
planck
-3 sec hc
d = 7.3×10 7cm=2.4×1
0
MM 
 1.2  10
2G
Delay
time
=
60.7
±6.9
±7.4
[nsec]
• Modified p-E relation
-5
(v –c)/ c = (2.4 ±0.28 ±0.30)
×1
0
E
PL
P c E m c 
2
2
2
2
28
2
[eV / c ]
3
4
Mc
2
dE
E
E
v
 c(1 
)  c(1 
 10 )
dP
Mc
1TeV
相対論（量子重力理論）の高精度検証
16
2
• Systematic errors
emission time within (1-10) second
Emission size within 10 10-11 cm
宇宙の構成物の大きさ・質量・密度
長さ：大きさ L
Quantum gravity ?
Log L[m]
30
臨界密度 ρc = 3H02/(8πG)
= 2×10-26[kg/m3]
銀河
恒星
惑星
隕石
中性子星
人間
0
シュワルツシルト半径
細菌
paticles 電子
原子
GUT
Super Symmetry
陽子
コンプトン波長
R = GM/c2
分子
cosmos
λ = h/MC
-30
ブラックホール
Planck mass
不確定性原理
-30
-20
-10
1012
1020
0
1028
10
質量 M
20
Mc2
30
Log M[kg]
Log E [eV]
Effect on propagation speed :
● systematic error ??
● higher gamma ray energy ……..
Effects on astrophysical reactions :
yes /no type test/observation
Ｑｕａｎｔｕｍ Ｇｒａｖｉｔｙ ｅｆｆｅｃｔ ｏｎ
ＶＨＥ ｇａｍｍａ ｒａｙ ａｓｔｒｏｐｈｙｓｉｃｓ
1.Propagation
2.Emission
3.Detection
γ + ε (EBL) 
+
e +e
e + ε (EBL)  e+ γ
absorption
Inverse
Compton
Interaction with atmosphere
γ + A  e++e- + A
e + A  e+ γ + A
A : atmospheric
nucleus
Cascade,
Air shower
process
γ + ε (EBL)  e++ek0 – ε  p+ + pK0 + ε  E+ + E-
Absorption
Pair creation
ε≄0 for the process to proceed
Momentum / energy conservation
Effect of Energy / momentum
of EBL photon
?? term of ξ K2/Mplanck ??
γ + ε (EBL) 
ε≄0
+
e +e (absorption)
for the process to proceed
Energy : K0 +ε = E1 + E2
momentum : k0 – ε = p1 + p2
Relativistic approximation
QG modification
k0 - ε =K0(1+ξK/M)0.5 - ε
p1 = E1 (1-me2/E12 +ξE1/M)0.5
p2 = E2 (1-me2/E22 +ξE2/M)0.5
Threshold energy, phase volume, …..
γ + ε (EBL)  e++ePerpendicular
component
- p2 θ22/2
K0 - ε + ξK02/(2M)
= p1 + p2 - p1 θ12/2
< p1 + p2
< E1+ E2 – Km2/(2E1E2)
2
2
+ξ(E1 +E1 )/(2M)
K
K E E
2 
m 
2E E
2M
2
0
e
1
2
2
2
2
0
1
2
K
K E E
2 
m 
2E E
2M
2
0
2
2
2
0
1
2
e
1
2
(2)
ε0 (eV)
1
(3)
(1) (2) (3)
(1)
0.1
all
prohibited
0.01
ε0 K0 = me2
0.001
1012
1013
1014
K0 (eV)
1015
1016
E
a
K
1
K  2a (1  a )
4 
m 
K a (1  a )
M
2
2
1
0
e
0
0
E
K E
1 a 

K
K
2
0
0
1
0
左辺 ＞ 右辺第１項
threshold
左辺 ＞ 右辺第２項
右辺第１項
≈
右辺第２項
prohibition /suppression
of large K0
characteristic energy
“asymmetric parameter “a
characteristic /critical
energies
4
m
  ( )  10 eV
M
e
2
1/ 3
c
Infra Red
x
K  (m M)  10 eV
2
c
1/ 3
13
e
K  (M)
1/ 2
*
10-100 TeV


 10 eV
1eV
14
γ + ε (EBL) 
+
e +e
(4ε0 M)1/ 2
1
[case I]
P
a
0.5
R
Allowed
Q
prohibited
[case II]
0
me2/ ε0
(8ε0 M)1/ 2
K0
Inverse Compton
e + ε (EBL)  e+ γ
scattering
momentum :
p0 - ε = p + k
Energy : E0 + ε = E + K
K
E E K
2 
m 
2E E
2M
2
2
2
2
0
e
0
b
E  b(1  b)
2 
m 
2E (1  b)
M
2
2
0
e
0
b=K/E0
e + ε (EBL)  e+ γ
1
P
b
0.5
R
Q
Prohibited
Allowed
0
me2/ (4ε0 ) (8ε0 M)1/ 2
E0
IC/synchrotron radiation
e + ε (EBL)  e+ γ
K
E E K
2 
m 
2E E
2M
2
2
2
2
0
e
b=K/E0
0
b
E  b(1  b)
2 
m 
2E (1  b)
M
2
2
0
e
0
4E
4E
K
E 
m  4E
m
0
0
2
e
2
0
e
E
1
K  4( ) 
2E
m
1
mM
o
2
3
0
e
2
e
2
0
e + ε (EBL)  e+ γ
(8 ε0 M)1/2
1
b
0.5
synchrotron radiation
me2/(4 ε0)
Q
R
P
0
Prohibited
Allowed
(me2 M/2 )1/3
E0
Effects on interaction/process
• Prohibition of reaction
• Suppression
(εM)1/2
(me2M)1/3
• Asymmetric energy partition
for final particles
Asymmetric
energy partition
γ + ε (EBL)  e- + e+
a=E1/K0
A=1/(a(1-a))
2
K
4K   Am  
M
2
0
0
e
Left > 1 st or 2 nd term of right side
A
A
m K 
m  K  4M
4
4
2
2
e
e
0
0
2AM
K
2 M
A
2M
m
2
3
0
4
e
1 st ¥ge 2 nd term of right side
3
3
K
K
A
 0.4  (
)
mM
10
0
2
e
0
13
3
2K
K
A
 0.9  (
)
mM
10
0
2
e
0
13
3/ 2
e-e+ pair creation
bremsstrahlung
From Rene Ong’s talk
γ + γb (EBL)  e++e-
momentum :
k - ε = p1 + p2
γ + A  e++e- + A
momentum :
k
= p1 + p2 + Δq
ε  Δq
k
K
K E E
q 
m 
2E E
2M
2
0
e
1
2
2
2
2
0
1
2
ε = Δq
Gamma ray
proton
γ + ε (EBL) 
+
e +e
(4ε0 M)1/ 2
1
[case I]
P
a
0.5
R
Allowed
Q
prohibited
[case II]
0
me2/ ε0
(8ε0 M)1/ 2
K0
Asymmetric
pairs
Detection altitude
!?
γ + A  e++e- + A
momentum :
The case of
all particles are
relativistic
k
= p1 + p2 + pA
K (K  E )
K
K E E E
2K m 
m 
m 
EE
E
2M
0
0
0
A
A
0
e
1
E1  K0
or
E2  K0
or
EA  K0
2
2
favored
2
2
2
2
2
0
1
2
A
A
A
k
ε -> Δq
Gamma-ray initiated Extensive Air Shower ?
● 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 …….
Crimea
Not
muon poor !?
Time variable
Recently detected by Fermi
Adding some words
onto a slide from Rene Ong’s
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 > 1013 – 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
..