M. Cem Güçlü İstanbul Teknik Üniversitesi

M. Cem Güçlü İstanbul Teknik Üniversitesi

RÖLATİVİSTİK AĞIR İYON
ÇARPIŞMALARI
M. Cem Güçlü
İstanbul Teknik Üniversitesi
Fizik Bölümü 9/30/13 IZYEF 2013 1 Elektromanyetik alandan parçacık üretimi
* Lepton-çift üretimi
* Demet ömrü (elektron yakalaması)
* Detektor background
* Non-perturbative ve perturbative yaklaşım
* Saçılma parametreye bağlılık
* Birden fazla lepton çift üretimi
* Kuvvetli EM alanda QED nin test edilmesi
9/30/13
IZYEF 2013
2
Elektromanyetik alandan parçacık üretimi
1.  GİRİŞ
2.  SERBEST ELEKTRON ÇİFT ÜRETİMİ
3.  BAĞLI-SERBEST ELEKTRON ÇİFT ÜRETİMİ
4.  NÜKLEER ÇÖZÜLME ( NUCLEAR DISASSOCIATION) İLE
BİRLİKTE ELEKTRON-POZITRON ÇİFT ÜRETİMİ
5. LASER YARDIMI İLE ION-ION ÇARPIŞMASINDA ELEKTRON
ÇİFT ÜRETİMİ
6. SONUÇ
9/30/13 IZYEF 2013 3 Elektromanyetik alandan parçacık üretimi
Ø Merkezi Çarpışma
QCD (Quantum Chromo Dynamics)
Ø Uzaktan (Peripheral ) Çarpışma
QED (Quantum Electro Dynamics)
b 9/30/13 IZYEF 2013 4 “ The central and peripheral collisions of relativistic heavy ions
may be compared to the case of two potential lovers walking on the
same side of the street, but in opposite directions. If they do not
care, they collide frontally... It could be a good opportunity for the
beginning of strong interactions between them. ...On the other
hand, if they pass far from from each other, they can still exchange
glances ( just electromagnetic interactions!), which can even lead
to their excitation. ...the effects of these peripheral collisions are
sometimes more interesting than violent frontal ones. “
G. Baur and C.A. Bertulani
Physics Reports 163, 299, (1989)
9/30/13
IZYEF 2013
5
Ağır İyonların Çarpışması
E Z1
E b > R1 + R2
9/30/13 IZYEF 2013 Z2
6 Çarpışma Parametreleri :
Critical frequencie s : ωcrit = 2mc 2 = 1.022MeV
Maximum Fourier freq. : ωmax ≈ Δt =
−1
γ  cβ
b
2 2

(mc )
Critical E Field : Ekritik ≈
= 1016V / cm
ec

Zeγ
Maximum E Field : Emaksimum ≈ 2
b
9/30/13 IZYEF 2013 7 
Zeγ
Maximum E Field : Emaksimum ≈ 2
b
Dependence of the electric radial field strengths for a point charge on the Lorentz factor γ 9/30/13 IZYEF 2013 8 Rölativistik Çarpıştırıcılar
ω max ± Emax ± ω max ± Emax ±
(e )
(e )
(µ )
(µ )
ω krit .
Ekrit.
ω krit.
Ekrit .
γ
SPS
RHIC
LHC
9/30/13 200 2×10 4
2.3 ×10
120
1.6
104
1.2x104
7
12
100
107
1.2x107 IZYEF 2013 1.2x103 160
1.2x106
1.6x105
9 QED Lagrangian
LQED =
Lelectron
+ LMaxwell + LInteract
µν
µ
1
ˆ
= Ψ(i∂ − me )Ψ − 4 Fµν F − eΨγ ΨAµ
Ψ
Dirac wave-­‐funcIon of electrons/positrons Aµ
ElectromagneIc vector potenIal Fµν = ∂ µ Aν − ∂ν Aµ
µ
eΨγ ΨAµ
9/30/13
ElectromagneIc field tensor Semiclassical coupling of electrons to the electromagneIc field IZYEF 2013
10
The four-­‐vector potenIal in the rest frame of a charge point Z, centered at the coordinates ( 0, b/2, 0 ) b 
Aµ = ( A0 , A)
A = 0, A0 =
9/30/13 − Ze
(x
2
2
+ ( y − b / 2) + z
IZYEF 2013 2 1/ 2
)
11 Momentum uzayında: 4
A0 (q) = ∫ d x e
iq⋅ x
A0 ( x)
→
∞
− i q ⋅r
b
3 e
= −[2πZe]δ (q0 ) exp(−i q ⊥ ⋅ ) ∫ d r
2 −∞
r
→
→
b 4π
= −(2πZe) δ (q0 ) exp(−i q ⊥ ⋅ ) 2
2 q
→
9/30/13 IZYEF 2013 12 
x⊥

x⊥ʹ′
β
x1
x1ʹ′
Lorentz transform this potenIal to the moving frame: A0ʹ′ = γ ( A0 − β Az ) = γ A0
Azʹ′ = γ ( Az − β A0 ) = −γ β A0


A⊥ʹ′ = A⊥ = 0

 b
δ (q0 + βqz )
2
2
A0ʹ′ = − 8π Zγ 2
exp[−iq⊥ . ]
2
2
2
q z + γ (q x + q y )
2
9/30/13 IZYEF 2013 13 Haraket denklemleri: 1. We construct a semiclassical acIon in terms of a Ime-­‐dependent many electron state Φ (t )
4
S = ∫ d x < Φ(t ) |: L0 ( x) + Lint ( x) :| Φ(t ) >
2. We assume that the iniIal state vector corresponds to a single Slater determinant |0> Lim
Φ(t ) → 0
0 = vacuum state
t →−∞
∑
χ q( + ) χ q( + ) + χ q( − ) χ q( − ) = 1
q
χ q(i ) χ (p j ) = δ q , pδ i , j
9/30/13 IZYEF 2013 Single parIcle and anI-­‐parIcle states 
(+)
ik ⋅ r
(+)
k
σk

(−)
iq ⋅r
(−)
q
σq
χ
=e U
χ
=e U
14 3. We assume the dynamics governing the Ime evoluIon of the states is unitery: Φ(t ) = K (t , − ∞) 0
†
†
where KK = K K = 1
Therefore, the equaIon of moIon can be cast into the form H ( x) K (t , t ʹ′) = i∂ t K (t , t ʹ′)
where
H ( x) = H 0 ( x) + V ( x)
 
H 0 ( x) = −iα ⋅ ∇ + γ 0 m
 
V ( x) = −α ⋅ A( x) + A0 ( x)
9/30/13 IZYEF 2013 15 With the above assumpIons, all orders processes can be obtained. In parIcular, those soluIons which are perturbaIve in potenIal can ve expressed as the series t
K (t , ∞) = K 0 (t ,−∞) + (−i) ∫ dτ K 0 (t ,τ ) V (τ ) K 0 (τ ,−∞)
−∞
t
+ (−i) 2 ∫ dτ
−∞
τ
∫ dτ ʹ′ K (t,τ )V (τ ) K (τ ,τ ʹ′)V (τ ʹ′) K (τ ʹ′,−∞) + ⋅ ⋅ ⋅
0
0
0
−∞
Where in above equaIon, the lowest-­‐order terms is simply K 0 (t , t ʹ′) = exp[− iH 0 (t − t ʹ′)]
9/30/13 IZYEF 2013 16 Energy diagram of the single-­‐par4cle Dirac equa4on and basic atomic processes which occur in ion-­‐atom collisons 9/30/13 IZYEF 2013 17 İkinci mertebe Feynman diyagramı
Ion 1 Foton yayınımı
e+
e−
Ion 2
zaman
Çift üretimi
Foton yayınımı
9/30/13
IZYEF 2013
18
Doğrudan ve değiştokuş diyagramlar : 9/30/13 IZYEF 2013 19 Serbest çift üretimi toplam tesir kesiti:
2
d 3kd 3qd 2 p⊥ ( + )
1
( −)
σ=
A ( k , q : p⊥ ) + A ( k , q : k ⊥ + q⊥ − p⊥ )
∑
8
∫
4π σ qσ k
( 2π )
 
A (k , q :
 
(−)
A (k , q :
(+)
9/30/13 

p⊥ ) = F ( k⊥ −


p⊥ ) = F ( k⊥ −




p⊥ : ω1 ) F ( p⊥ − q⊥ : ω2 ) Tkq ( p⊥ : β )




p⊥ : ω2 ) F ( p⊥ − q⊥ : ω1 ) Tkq ( p⊥ : − β )
IZYEF 2013 20 Haraket eden ağır iyonların momentum uzayında EM alanının skaler kısmı 2
2
4πZγ β

2
2
F(q : ω ) = 2
G
(
q
)
f
(
q
)
Z
2 2 2 E
ω +β γ q
⎛ Ek( + )
⎡ ( s )

Tkq ( p⊥ : β ) = ∑∑ ⎢ E p − ⎜⎜
s σ ⎢
⎝
⎣
p
+
2
Eq( − )
⎤
⎞
k
−
q
⎛
⎞
z
z
⎟ + β ⎜
⎟⎥
⎟
⎝ 2 ⎠⎥⎦
⎠
−1
× uσ( + ) (1 − βα z ) uσ( − ) uσ( s ) (1 + βα z ) uσ( − )
k
9/30/13 p
IZYEF 2013 p
q
21 3
σ T = C∞σ 0 ln ( γ )
9/30/13 IZYEF 2013 22 Serbest elektron-pozitron çift üretimi tesir
kesitleri σ
SPS ,
free − free
γ=10,
∝
2 2
ZT Z P
3
ln (γ )
Au + Au , σ=140 barn
RHIC, γ=100, Au + Au , σ=36 kbarn
LHC, γ=3400, Pb + Pb , σ=227 kbarn
9/30/13 IZYEF 2013 23 İki foton metodu :
1 dσ 1
P(b ) =
=
C∞ λ2C Z12 Z 22 α 4 ln 3 (γ )
2 π b db 2π
a
3
2 2
(a2 + b )
Eşdeğer foton metodu:
2
14 2 2 4 ⎡ λC ⎤
2 ⎛ γ labδ λC ⎞
⎟⎟ + Δ( Z )
P(b ) ≈ 2 Z1 Z 2 α ⎢ ⎥ ln ⎜⎜
9π
⎣ b ⎦
⎝ 2 b ⎠
M. C. Güçlü, Nucl. Phys. A, Vol. 668, 207-217 (2000)
9/30/13 IZYEF 2013 24 9/30/13 IZYEF 2013 25 9/30/13 IZYEF 2013 26 9/30/13 IZYEF 2013 27 Experiments at CERN Super Proton Synchroton SPS 9/30/13 IZYEF 2013 28 S + Au → S + Au + e e
+ −
Energy = 200 A GeV at fixed target frame Measured Cross SecIon for 1-­‐17 MeV /c positron yield σ exp = 85 barns
σ QED = 98 barns
σ QED = 140 barns
with 25% error for 1-­‐17 MeV /c positron For all positron momenta Vane CR at al. Phys. Rev. A 50:2313 (1994). 9/30/13 IZYEF 2013 29 9/30/13 IZYEF 2013 30 Elektron Yakalama (Capture) Olayı Serbest-­‐bağlı çih üreIminde, elektron çarpışan iyonlardan biri tarakndan yakalanır −
+
Z
+
Z
→
(
Z
+
e
)
+
Z
+
e
a
b
a
1
s
b
1 / 2 ,...
ve o iyonun demetden çıkmasını sağlar. 9/30/13 IZYEF 2013 31 Elektromanyetik alandan parçacık üretimi
Bağlı-serbest elektron – pozitron çift üretimi 9/30/13 IZYEF 2013 32 Distorted wave-­‐funcIon for the captured-­‐electron ψ
( −)
⎛
 ⎞

i
= ⎜1 −
α .∇ ⎟uΨnon−r (r )
⎜ 2m
⎟
⎝
⎠
Ψnon−r
9/30/13 1 ⎛ Z
⎜⎜
=
π ⎝ a H
IZYEF 2013 ⎞
⎟⎟
⎠
3/ 2
e
− Zr / aH
33 Positron Wave-­‐FuncIon (+)
ψq
N+ = e
N+
ψ
9/30/13 −π a + / 2
2
'
⎡ i q .r ( + )
' ⎤
= N + ⎢e u σ +ψ ⎥
q
⎣
⎦
Γ(1 + ia+ )
2πa+
= 2πa
e + −1
Ze
a+ =
v+
2
is the distorIon (correcIon term) due to the large charge of the ion. IZYEF 2013 34 SONUÇ This work
RHIC Au+Au at 100 GeV
94.5
LHC Pb+Pb at 2957 GeV
202
Ref.[7]
94.9
225
TABLE I: Bound-­‐free pair producIon cross secIons (in barn) σ BFPP
for selected collision systems and cross secIons as accessible at RHIC and LHC collider faciliIes. 9/30/13 IZYEF 2013 35 FIG. 2: BFPP cross sec4ons for two different systems as func4ons of the nuclear charge Z. 9/30/13 IZYEF 2013 36 FIG. 3: BFPP cross sec4ons for two different systems (Au+Au-­‐dashed line and Pb+Pb-­‐solid line) as func4ons of the . γ
9/30/13 IZYEF 2013 37 FIG. 4: The differen4al cross sec4on as func4on of the transverse momentum of the produced positrons. 9/30/13 IZYEF 2013 38 FIG. 5: The differen4al cross sec4on as func4on of the longitudinal momentum of the produced positrons. 9/30/13 IZYEF 2013 39 FIG. 6: The differen4al cross sec4on as func4on of the energy of the produced positrons . 9/30/13 IZYEF 2013 40 What about experiments at SOLENOIDAL TRACKER ( STAR ) ? RHIC: Relativistic Heavy Ion Collider
Energy =100 GeV/nucleon
Au + Au collisions
Circumference = 2.4 miles
9/30/13 IZYEF 2013 41 Elektromanyetik alandan parçacık üretimi
Nükleer çözülme (disassociation) (Giant Dipole
Resonance) Electron-­‐positron pair produc4on (on the leT) with a mutual Coulomb excita4on (on the right) being mainly giant dipole resonance (GDR). These two processes are independent of each other. 9/30/13 IZYEF 2013 42 Cross Sec.on of electron-­‐positron pairs accompanied by nuclear dissocia.on Giant Dipole Resonance Au + Au → Au + Au + e e
∗
∗
+ −
2
σ = ∫ d b Pe e (b) PXnXn (b) Pno hadronic (b)
+ −
9/30/13 IZYEF 2013 43 No hadronic probability, computed with Woods-­‐Saxon nuclear form factor 1
ρ (b) ∝
1 + exp( b −aR )
9/30/13 IZYEF 2013 44 Probability of mutual Coulomb nuclear excitaIon with breakup as a funcIon of impact parameter S
PXnXn (b) = 2
b
2α 2 Z12 N 2 Z 2
S=
A2 mN ω
= 5.45 ×10 −5 Z12 N 2 Z 2 A2−2 / 3 fm2
G. Baur at al. Nuclear Physics A 729 (2003) 787-­‐808 9/30/13 IZYEF 2013 45 STAR deneyinde kinemaIk sınırlamalar: Rapidity: 1 ⎡ P0 − Pz ⎤
Y = ln ⎢
⎥
2 ⎣ P0 − Pz ⎦
Y ≤ 1.15
Değişmez (invariant) kütle: 2
0
2
z
2 1/ 2
⊥
M = (P − P − P )
140MeV ≤ M e e ≤ 265MeV
+
−
Dik (Transverse) momentum : 2
x
2 1/ 2
y
P⊥ = ( P + P )
P⊥ ≥ 65 MeV
Adams J. At al. Phys. Rev. A 63:031902 (2004) 9/30/13 IZYEF 2013 46 Sonuç: Au + Au → Au + Au + e e
∗
∗
+ −
2
σ = ∫ d b Pe e (b) = 0.32 b
+
−
2
σ = ∫ d b Pe e (b) PXnXn (b) Pno hadronic (b) = 1.52 mb
+
−
σ exp = 1.6 ± 0.2 ( stat ) ± 0.3 ( syst ) (mb)
9/30/13 IZYEF 2013 47 LASER ASSISTED PAIR CREATION IN ION-ION COLLISION nonlinear Bethe-­‐Heitler process Nω + Z → Z + e e
+ −
Carsten Müller lab frame: ħω ≈ 100 eV , E ≈ 10^12 V/cm rest frame: ħ ω ' and E' enhanced by 2γ 9/30/13 IZYEF 2013 48 LASER ASSISTED PAIR CREATION IN ION-ION COLLISION A lepton pair is produced in the Coulomb fields of the heavy-­‐ions ( Z ) with the simultaneous absorpIon of N photons from the background laser field. Nω + Z + Z → Z + Z + e e
+ −
We aim to combine the pair creaIon in ion-­‐ion collisions with the pair creaIon in strong laser fields by invesIgaIng pair creaIon in ion-­‐ion collisions occuring in the presence of an intense laser field. 9/30/13 IZYEF 2013 49 SONUÇ:
1. Yarı-klasik iki foton metodu kullanılarak serbest-serbest ve bağlıserbest elektron-pozitron çift üretimi tesir kesitlerini elde edildi.
2.
Hesaplarımız diğer çalışmalar ve deney sonuçları ile uyum içindedir.
3. Tesir kesit ifadesini pozitronların rapiditileri, dik ve paralel
momentumlarının fonksiyonları cinsinden elde ettik.
4.
Benzer hesapları FAIR enerjileri içinde yapabiliriz.
5.
Bu metod kullanılarak diğer bazı parçacıkların (vektör mezonlar, ağır
leptonlar, Higgs parçacığı, v.b.) üretilme tesir kesitlerini
hesaplayabilirmiyiz?
6.
Laser yardımı ile iyon-iyon çarpışmasından çift üretimi çalışmamız
devam ediyor.
9/30/13 IZYEF 2013 50
REFERENCES: 1)  C.A. Bertulani and G. Baur, Phys. Rep. 163, 299 (1988).
2)  A.J. Baltz, M.J. Rhoades-Brown and J. Weneser, Phys. Rev. A 50, 4842
(1994).
3)  C.A. Bertulani and D. Dolci, Nucl. Phys. A 683, 635(2001).
4)  J. Eichler and W.E. Meyerhof, Relativistic Atomic Collisions
(Academic Press, California, 1995).
5)  H. Meier, Z. Halabuka, K. Hencken, D. Trautmann and G. Baur, Phys.
Rev. A 63, 032713 (2001).
6)  Şengül, M. Y., Güçlü, M. C., and Fritzsche, S., 2009, Phys. Rev. A 80,
042711.
7)  K. Hencken, G. Baur, D. Trautmann, Phys. Rev. C 69, 054902 (2004).
8)  M.C. Güçlü, M.Y. Şengül, Progress in Part. and Nucl. Phys. 59, 383
(2007).
9)  Şengul, M. Y., and Güçlü, M. C., 2011, Phys. Rev. C ,83,014902.
10)  C. Müller, A. B. Voitkiv and N. Grün, Phys. Rev. A 67, 063407 (2003).
9/30/13 IZYEF 2013 51