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Erice 1
Lepton pair production at RHIC and LHC energies
Cem Güçlüİstanbul Technical University
Physics Department
September 20, 2012
September 20, 2012 Erice 2
Particle production from EM Fields
* Lepton-pair production
* Beam Lifetime (electron capture)
* Detector background
* Non-perturbative and perturbative approach
* Impact parameter dependence
* Multi-pair production
* Test of QED at high fields
Erice 3September 20, 2012
Particle production from EM Fields1. INTRODUCTION
2. FREE LEPTON PAIR PRODUCTION
3. BOUND FREE LEPTON PAIR PRODUCTION
4. ELECTRON-POSITRON PAIR PRODUCTION WITH NUCLEAR DISASSOCIATION
5. LASER ASSISTED PAIR CREATION IN ION-ION COLLISION
6. CONCLUSION
Erice 4
Central Collision QCD (Quantum Chromo Dynamics)
Peripheral Collision QED (Quantum Electro Dynamics)
b
September 20, 2012
Particle production from EM Fields
September 20, 2012 Erice 5
21 RRb
1Z
2Z
Collisions of Heavy Ions
E
E
September 20, 2012 Erice 6
Collision Parameters :
MeVmcsfrequencieCritical crit 022.12: 2
bctfreqFourierMaximum
1max:.
cmVce
mcEFieldECritical kritik /10)(: 1622
2:b
ZeEFieldEMaximum maksimum
Erice 7
2:b
ZeEFieldEMaximum maksimum
Dependence of the electric radial field strengths for a point chargeon the Lorentz factor γ
September 20, 2012
September 20, 2012 Erice 8
Relativistic Colliders
200 100 120 12 1.6
104
1.2x104 1.2x103 160
107 1.2x107 1.2x106 1.6x105
)(.
max ekrit
)(.
max eEE
krit
)(.
max
krit
)(.
max kritE
E
SPS
RHIC
LHC
4102
7103.2
September 20, 2012 Erice 9
Dirac wave-function of electrons/positrons
A Electromagnetic vector potential
AAF Electromagnetic field tensor
μμν
μν AFF
LLLL
ΨγΨe)Ψmˆ(iΨ μ41
e
InteractMaxwellelectronQED
QED Lagrangian
μAΨγΨe μSemiclassical coupling of electrons to the electromagnetic field
Erice 10September 20, 2012
The four-vector potential in the rest frame of a charge point Z, centered at the coordinates ( 0, b/2, 0 )
2/12220)2/(
,0zbyx
ZeAA
),( 0 AAA
b
İn momentum space:
20
30
04
0
4)2
exp()()2(
)2
exp()(]2[
)()(
qbqiqZe
rerdbqiqZe
xAexdqA
rqi
xiq
September 20, 2012 11Erice
Erice 12September 20, 2012
x
1x
x
1x
Lorentz transform this potential to the moving frame:
0
)()(
00
000
AA
AAAAAAAA
zz
z
]2
.exp[)(
)(8 2222022
0bqi
qqqqqZA
yxz
z
Erice 13September 20, 2012
Equation of motion:
1. We construct a semiclassical action in terms of a time-dependent many electron state )(t
)(:|)()(|:)(4
txxtxdS int0 LL2. We assume that the initial state vector corresponds to a single Slater determinant |0>
0)(
tLimt
statevacuum0
jipqj
pi
q
qqqq
q
,,)()(
)()()()( 1
)()(
)()(
q
k
Ue
Uerqi
q
rkik
Single particle and anti-particle states
Erice 14September 20, 2012
3. We assume the dynamics governing the time evolution of the states is unitery:
10),()( KKKKwheretKt ††
Therefore, the equation of motion can be cast into the form
)()()(
)(
)()()(
),(),()(
0
00
0
xAxAxV
mixH
xVxHxHwhere
ttKittKxH t
Erice 15September 20, 2012
With the above assumptions, all orders processes can be obtained. In particular, thosesolutions which are perturbative in potential can ve expressed as the series
),()(),()(),()(
),()(),()(),(),(
0002
000
KVKVtKddi
KVtKditKtK
t
t
Where in above equation, the lowest-order terms is simply
)(exp),( 00 ttiHttK
Erice 16
Energy diagram of the single-particle Dirac equation and basic atomic processes which occur in ion-atom collisons
September 20, 2012
September 20, 2012 Erice 17
ee
time
Ion 1
Ion 2
Emits photon Emits photonPair Production
Second-order Feynman diagram
September 20, 2012 Erice 18
Direct and exchange diagrams :
September 20, 2012 Erice 19
Total Cross Section of free pair production
):():():():,():():():():,(
12)(
21)(
pTqpFpkFpqkA
pTqpFpkFpqkA
kq
kq
3 3 22( ) ( )
8
1 , : , :4 2
p k q pq k
d kd qd p A k q A k q
September 20, 2012 Erice 20
)()(4):( 222222
22qfqG
qZqF ZE
)()()()(
1)()()(
)1()1(
22):(
qppk
p
uuuu
qkEEEpT
zs
z
s
zzqkspkq
Scalar part of EM Fields in momentum space of moving heavy ions
Erice 21September 20, 2012
)(ln30 CT
Free electron-positron pair production
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SPS , γ=10, Au + Au , σ=140 barn
RHIC, γ=100, Au + Au , σ=36 kbarn
LHC, γ=3400, Pb + Pb , σ=227 kbarn
)(ln322 PTfreefree ZZ
Erice 23September 20, 2012
23
22
3422
21
2
)()(ln2
121)(
ba
aZZCdbd
bbP C
)(2ln914)( 2
242
2212 Z
bbZZbP ClabC
Two Photon Method :
Equivalent Photon Method:
M. C. Güçlü, Nucl. Phys. A, Vol. 668, 207-217 (2000)
Erice 24September 20, 2012
Erice 25September 20, 2012
Erice 26September 20, 2012
In the bound-free pair-production, theelectron is captured by one of thecolliding ions
and leads to the loss of the (oneelectron) ion from the beam.
eZeZZZ bsaba ,...2/11)(
Electron Capture Process
27EriceSeptember 20, 2012
September 20, 2012 Erice 28
Particle production from EM FieldsBound-free electron – positron pair production)
Distorted wave-functionfor the captured-electron
)(.2
1)( rumi
rnon
HaZr
Hrnon e
aZ /
2/31
September 20, 2012 29Erice
Positron Wave-Function
')(
q
r.qi)(q ueN
September 20, 2012 30Erice
)1(2/
iaeN a
v
Zea2
1ea2N a2
2
' is the distortion (correction term)due to the large charge of the ion.
RESULTS
This work Ref.[7]RHIC Au+Au at 100 GeV 94.5 94.9LHC Pb+Pb at 2957 GeV 202 225
TABLE I: Bound-free pair production cross sections (in barn) for selected collision systems and cross sections as accessible at RHIC and LHC collider facilities.
BFPP
September 20, 2012 31Erice
FIG. 2: BFPP cross sections for two different systems as functions of thenuclear charge Z.
September 20, 2012 32Erice
FIG. 3: BFPP cross sections for two different systems (Au+Au-dashed line andPb+Pb-solid line) as functions of the .
September 20, 2012 33Erice
FIG. 4: The differential cross section as function of the transverse momentum of the produced positrons.
September 20, 2012 34Erice
FIG. 5: The differential cross section as function of the longitudinal momentum of the produced positrons.
September 20, 2012 35Erice
FIG. 6: The differential cross section as function of the energy of the produced positrons .
September 20, 2012 36Erice
Erice 37September 20, 2012
Experiments atCERN Super Proton Synchroton SPS
Erice 38September 20, 2012
eeAuSAuSEnergy = 200 A GeV at fixed target frame
Measured Cross Section for 1-17 MeV /c positron yield
barns85exp with 25% error
barnsQED 98 for 1-17 MeV /c positron
barnsQED 140 For all positron momenta
Vane CR at al. Phys. Rev. A 50:2313 (1994).
Erice 39September 20, 2012
Erice 40September 20, 2012
What about experiments at SOLENOIDAL TRACKER ( STAR ) ?
RHIC: Relativistic Heavy Ion Collider
Energy =100 GeV/nucleon
Au + Au collisions
Circumference = 2.4 miles
September 20, 2012 Erice 41
Nuclear disassociation (Giant Dipole Resonance)
Particle production from EM Fields
Electron-positron pair production (on the left) with a mutual Coulomb excitation (on theright) being mainly giant dipole resonance (GDR). These two processes are independentof each other.
Erice 42September 20, 2012
)()()(2 bPbPbPbd hadronicnoXnXnee
Cross Section of electron-positron pairs
accompanied by nuclear dissociation
Giant Dipole Resonance
eeAuAuAuAu
Erice 43September 20, 2012
)exp(11)(
aRb
b
No hadronic probability, computed with Woods-Saxon nuclear form factor
Erice 44September 20, 2012
2)(bSbPXnXn
23/2222
21
5
2
222
12
1045.5
2
fmAZNZ
mAZNZS
N
Probability of mutual Coulomb nuclear excitation with breakupas a function of impact parameter
G. Baur at al. Nuclear Physics A 729 (2003) 787-808
Erice 45September 20, 2012
z
z
PPPPY
0
0ln21
2/12220 )( PzPPM
2/122 )( yx PP P
Rapidity:
Invariant mass:
Transverse momentum :
15.1Y
MeVMMeV ee 265140
MeVP 65
Kinematic restrictions at STAR experiment
Adams J. At al. Phys. Rev. A 63:031902 (2004)
Erice 46September 20, 2012
Results:
mbbPbPbPbd hadronicnoXnXnee 52.1)()()(2
eeAuAuAuAu
bbPbd ee 32.0)(2
)()(3.0)(2.06.1exp mbsyststat
Erice 47September 20, 2012
LASER ASSISTED PAIR CREATION IN ION-ION COLLISION
eeZZN
nonlinear Bethe-Heitler process
lab frame: ħω ≈ 100 eV , E ≈ 10^12 V/cm
rest frame: ħ ω ' and E' enhanced by 2γ
Carsten Müller
Erice 48September 20, 2012
LASER ASSISTED PAIR CREATION IN ION-ION COLLISION
eeZZZZN
We aim to combine the pair creation in ion-ion collisions with the pair creation in strong laser fields by investigating pair creation in ion-ion collisions occuring in the presence of an intense laser field.
A lepton pair is produced in the Coulomb fields of the heavy-ions ( Z ) with the simultaneous absorption of N photons from the background laser field.
September 20, 2012 Erice 49
FAIR - Facility for Antiproton and Ion Research
Completed in 2018
Cost : 1.2 billion Euro
QEDStrong FieldsIon -Matter Interactions
September 20, 2012 Erice 50
CONCLUSIONS:1. We have obtained free-free and bound-free electron-positron pair production cross section by using the semi-classical two photon method.
2. Our calculations agree well with the other calculations shown at references.
3. We have also obtained cross sections as a function of rapidity, transverse momentum and longitudinal momentum of produced positrons.
4. We can repeat the similar calculation for the FAIR energies.
5. Can we use this method to calculate the production of other particles such as mesons, heavy leptons, may be Higgs particles ?
6. Laser assisted pair creation in ion-ion collisons
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).
September 20, 2012 Erice 51