Cem Güçlü İstanbul Technical University Physics Department
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Transcript of Cem Güçlü İstanbul Technical University Physics Department
September 23, 2008 Erice 2008 1
Cem Güçlüİstanbul Technical University
Physics Department
Production of electron-positron pairs by nuclear dissociation in
heavy ion collisons
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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
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“ The central and peripheral collisions of relativistic heavy ions may be compared to the case of two potential lovers walking on the same sideof 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 ofthese peripheral collisions are sometimes more interesting than violentfrontal ones. “
G. Baur and C.A. Bertulani Physics Reports 163, 299, (1989)
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Collision Parameters :
22: mcsfrequencieCritical crit
bctfreqFourierMaximum 1
max:.
cemcEFieldECritical kritik
22 )(:
2:b
ZeEFieldEMaximum maksimum
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Relativistic Colliders
)(.
max ekrit
)(.
max eEE
krit
)(.
max
krit
)(.
max kritE
E
SPS
RHIC
10
100
100 120 12 1.6
10000 12000 1200 160
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21 RRb
1Z
2Z
Collisions of Heavy Ions
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Dirac wave-function of electrons/positrons
A Electromagnetic vector potential
AAF Electromagnetic field tensor
μμν
μν AFF
LLLL
ΨγΨe)Ψmˆ(iΨ μ41
e
InteractMaxwellelectronQED
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Lepton-Pair ProductionSemi Clasical Action :
)(:|)()(|:)(4
txxtxdS int0 LLFree Lagrangian :
)()()()( xmixx 0L
Interaction Lagrangian :
)()()()( xAxxxL
int
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)2()1( AAA
]2.exp[)()(8)1( 2222
0220 bqiqqq
qqZAyxz
z
)1()1( 0AAz
0)2()1(0)2()1(
yy
xx
AA
AA
Four Vector Potentials of the Colliding Ions :
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ee
time
Ion 1
Ion 2
Emits photon Emits photonPair Production
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Direct and exchange diagrams :
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Total Cross Section
):():():():,():():():():,(
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
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)()(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
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SPS , γ=10, Au + Au , σ=140 barnRHIC, γ=100, Au + Au , σ=36 kbarnLHC, γ=3400, Pb + Pb , σ=227 kbarn
RHIC, γ=100, Au + Au , σ=83 barnLHC, γ=3400, Au + Au , σ=161 barn Pb + Pb, σ=206 barn
Free electron-positron pair production
Bound- free electron-positron pair production
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)()(0
0 qFqbJbqdqdbd
];[]);(21[
];[]);(21[
];[]);(21[];[]);(2
1[
)2(8)(
2121
2
010
222
2
KqkTqQkT
KkTqQkT
KqFqQFKFqQF
QKddkddqdkqF
kqkq
kqkq
zz
k q
Impact Parameter Dependence Cross Sections :
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ca
qaeF
qF
35.1)0()(
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qaT
qa
e
eFqF
)0()(
TF )0()(ln3
0 CT
Ca 35.1
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23
22
1
02
0
00
)(
1)cos(2
)(
ba
ba
dtet
qbtbqdq
ebqJbqdqdbd
T
qaT
bqT
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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)
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( a ) Interaction between the created lepton and anti-lepton( b ) Interaction of the created leptons with the EM fields of heavy ions( c ) Fermion loops only which have exactly two vertices attached to each of the ions are included( d ) Not included
Diagrams which are not included :
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An example of a diagram which is included
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Güçlü M.C. et al, Annals of Physics , 272, 7-48 (1999)
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NN N
bP 0!2ˆ
!2ˆ0!
)]!4/Re(2exp[)( 224
0!2ˆ
!2ˆ0!4Re2 224
0!2ˆ
!2ˆ0)( 22
bP One pair production probability
))(exp(!)()( bP
NbPbP
N
N Poisson distribution
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))(exp(!)()( bP
NbPbP
N
N
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Experiments at
CERN Super Proton Synchroton SPS
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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).
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What about experiments at
SOLENOIDAL TRACKER ( STAR ) ?
RHIC: Relativistic Heavy Ion Collider
Energy =100 GeV/nucleon
Au + Au collisions
Circumference = 2.4 miles
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)()()(2 bPbPbPbd hadronicnoXnXnee
Cross Section of electron-positron pairs
accompanied by nuclear dissociation
Giant Dipole Resonance
eeAuAuAuAu
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Why do we study the reaction ?
eeAuAuAuAu
1. The test of QED at high fields – are there indications that at the available energies more than two photons are involved in an electron-positron pair creation?
2. Is pair production is independent of photonuclear excitation?
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)exp(11)(
aRb
b
No hadronic probability, computed with Woods-Saxon nuclear form factor
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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
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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)
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Results:
mbbPbPbPbd hadronicnoXnXnee 52.1)()()(2
eeAuAuAuAu
bbPbd ee 32.0)(2
)()(3.0)(2.06.1exp mbsyststat
Baur at al. : σ = 1.9 mb
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Adams J. At al. Phys. Rev. A 63:031902 (2004)
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Adams J. At al. Phys. Rev. A 63:031902 (2004)
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FAIR - Facility for Antiproton and Ion Research
Completed in 2016
Cost : 1.2 billion Euro
QEDStrong Fields
Ion -Matter Interactions
Flair @ FAIR: Research Topics with Low-Energy Antiprotons fundamental interactions
- CPT (antihydrogen, HFS, magnetic moment)
- gravitation of antimatter atomic collision studies
- ionization - energy loss
- matter-antimatter collisions anti- protonic atoms
- formation - strong nuclear interaction
and surface effects - trapping anti- protons in nuclei:
short lived bound states?Later perhaps: Low Energy Anti- He
x
I.Mishustin; L. Satarov, HSt; W Greiner;
Cold Nuclear Compression by
Vector Attraction of
p-bars in medium
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CONCLUSIONS:
1. We have obtained impact parameter dependence of lepton-pair production probability by using the semi-classical two photon method.
2. At SPS and RHIC energies, Monte Carlo QED calculations agree well with the experimantal results.
3. Can we use this method to calculate the production of other particles such as mesons, heavy leptons, may be Higgs particles ?
4. Can RHIC be used to test QED? NO… Wait for FAIR…
5. Cross section for bound-free pair production is very large and this will limit the maximum Pb-Pb luminosity at the LHC. Therefore we should understand these QED effects to a high degree of accuracy.
Thank you for your attention.!