september 23, 2008 erice 2008 1 cem güçlü İstanbul technical university physics department...
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September 23, 2008 Erice 2008 1
Cem Güçlü
İstanbul Technical UniversityPhysics Department
Production of electron-positron pairs by nuclear dissociation in
heavy ion collisons
September 23, 2008 Erice 2008 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
September 23, 2008 Erice 2008 3
“ 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)
September 23, 2008 Erice 2008 4
Collision Parameters :
22:
mcsfrequencieCritical crit
b
ctfreqFourierMaximum
1max:.
ce
mcEFieldECritical kritik
22 )(:
2:
b
ZeEFieldEMaximum maksimum
September 23, 2008 Erice 2008 5
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
September 23, 2008 Erice 2008 7
Dirac wave-function of electrons/positrons
A Electromagnetic vector potential
AAF Electromagnetic field tensor
μμν
μν AFF
LLLL
ΨγΨe)Ψmˆ(iΨ μ41
e
InteractMaxwellelectronQED
September 23, 2008 Erice 2008 8
Lepton-Pair Production
Semi Clasical Action :
)(:|)()(|:)(4
txxtxdS int0 LLFree Lagrangian :
)()()()( xmixx 0L
Interaction Lagrangian :
)()()()( xAxxxL
int
September 23, 2008 Erice 2008 9
)2()1( AAA
]2.exp[
)()(
8)1( 22220220 b
qiqqq
qqZA
yxz
z
)1()1( 0AAz
0)2()1(
0)2()1(
yy
xx
AA
AA
Four Vector Potentials of the Colliding Ions :
September 23, 2008 Erice 2008 12
Total Cross Section
):():():():,(
):():():():,(
12)(
21)(
pTqpFpkFpqkA
pTqpFpkFpqkA
kq
kq
3 3 22( ) ( )
8
1, : , :
4 2p k q p
q k
d kd qd pA k q A k q
September 23, 2008 Erice 2008 13
)()(4
):( 222222
22
qfqGq
ZqF 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
September 23, 2008 Erice 2008 14
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
September 23, 2008 Erice 2008 15
)()(
0
0 qFqbJbqdqdbd
];[]);(21
[
];[]);(21
[
];[]);(21[];[]);(
21[
)2(8)(
2121
2
0
10
222
2
KqkTqQkT
KkTqQkT
KqFqQFKFqQF
QKddkddqdkqF
kqkq
kqkq
zz
k q
Impact Parameter Dependence Cross Sections :
September 23, 2008 Erice 2008 18
23
22
1
02
0
00
)(
1
)cos(2
)(
ba
ba
dtet
qbtbqdq
ebqJbqdqdb
d
T
qaT
bqT
September 23, 2008 Erice 2008 19
23
22
3422
21
2
)(
)(ln21
21
)(
ba
aZZC
db
d
bbP C
)(2
ln914
)( 22
422
212 Z
bbZZbP ClabC
Two Photon Method :
Equivalent Photon Method:
M. C. Güçlü, Nucl. Phys. A, Vol. 668, 207-217 (2000)
September 23, 2008 Erice 2008 21
( 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 :
September 23, 2008 Erice 2008 24
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(!)(
)( bPNbP
bPN
N Poisson distribution
September 23, 2008 Erice 2008 27
eeAuSAuS
Energy = 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).
September 23, 2008 Erice 2008 28
What about experiments at
SOLENOIDAL TRACKER ( STAR ) ?
RHIC: Relativistic Heavy Ion Collider
Energy =100 GeV/nucleon
Au + Au collisions
Circumference = 2.4 miles
September 23, 2008 Erice 2008 29
)()()(2 bPbPbPbd hadronicnoXnXnee
Cross Section of electron-positron pairs
accompanied by nuclear dissociation
Giant Dipole Resonance
eeAuAuAuAu
September 23, 2008 Erice 2008 30
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?
September 23, 2008 Erice 2008 31
)exp(1
1)(
aRb
b
No hadronic probability, computed with Woods-Saxon nuclear form factor
September 23, 2008 Erice 2008 32
2)(
b
SbPXnXn
23/2222
21
5
2
222
12
1045.5
2
fmAZNZ
mA
ZNZS
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
September 23, 2008 Erice 2008 33
z
z
PP
PPY
0
0ln2
1
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)
September 23, 2008 Erice 2008 34
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
September 23, 2008 Erice 2008 37
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
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
September 23, 2008 Erice 2008 39
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.!