april 23, 2008 workshop on “high energy photon collisions at the lhc 1 cem güçlü İstanbul...
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April 23, 2008 Workshop on “High energy photon collisions at the LHC 1
Cem Güçlü
İstanbul Technical UniversityPhysics Department
Physics of
Ultra-Peripheral Nuclear Collisions
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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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
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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Collision Parameters :
22:
mcsfrequencieCritical crit
b
ctfreqFourierMaximum
1max:.
ce
mcEFieldECritical kritik
22 )(:
2:
b
ZeEFieldEMaximum maksimum
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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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
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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21 RRb
1Z
2Z
Collisions of Heavy Ions
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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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
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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Lepton-Pair Production
Semi Clasical Action :
)(:|)()(|:)(4
txxtxdS int0 LLFree Lagrangian :
)()()()( xmixx 0L
Interaction Lagrangian :
)()()()( xAxxxL
int
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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)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 :
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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e
e
time
Ion 1
Ion 2
Emits photon Emits photonPair Production
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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Direct and exchange diagrams :
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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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
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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)()(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
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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SPS , γ=10, Au + Au , σ=140 barnRHIC, γ=100, Au + Au , σ=36 kbarnLHC, γ=3400, Au + Au , 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
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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)()(
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 :
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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ca
qaeF
qF
35.1)0()(
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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qaT
qa
e
eFqF
)0()(
TF )0(
)(ln30 CT
Ca 35.1
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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23
22
1
02
0
00
)(
1
)cos(2
)(
ba
ba
dtet
qbtbqdq
ebqJbqdqdb
d
T
qaT
bqT
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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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)
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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April 23, 2008 Workshop on “High energy photon collisions at the LHC
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April 23, 2008 Workshop on “High energy photon collisions at the LHC
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b C C Ctoplam A B AB
2 2
3 22
28ln
27A Bb Z Z
m
2 2
2 22
28ln
9A BC
A A
Z Zf Z
m
2 2
2 22
28ln
9A BC
B B
Z Zf Z
m
2 2
22
56ln
9A BC
AB A B
Z Zf Z f Z
m
Born Approximation with Coulomb Corrections
R.N.Lee at al, Phys. Rev. A 64, 032106 (2001)
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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April 23, 2008 Workshop on “High energy photon collisions at the LHC
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April 23, 2008 Workshop on “High energy photon collisions at the LHC
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April 23, 2008 Workshop on “High energy photon collisions at the LHC
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4.0
''
''
0
1.0
0
kd z
dkd z
kd z
dkd z
m
2.0
''
''
0
0
kd
dkd
kd
dkd
m
Small momentum approximation
mk z mk
M.C. Güçlü at al. Phys. Rev. A 72 022724 (2005).
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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Experiments at
CERN Super Proton Synchroton SPS
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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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).
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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April 23, 2008 Workshop on “High energy photon collisions at the LHC
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April 23, 2008 Workshop on “High energy photon collisions at the LHC
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April 23, 2008 Workshop on “High energy photon collisions at the LHC
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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
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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)()()(2 bPbPbPbd hadronicnoXnXnee
Cross Section of electron-positron pairs
accompanied by nuclear dissociation
Giant Dipole Resonance
eeAuAuAuAu
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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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?
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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)exp(1
1)(
aRb
b
No hadronic probability, computed with Woods-Saxon nuclear form factor
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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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
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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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)
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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
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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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 2015
Cost : 1.2 billion Euro
QEDStrong Fields
Ion -Matter Interactions
April 23, 2008 Workshop on “High energy photon collisions at the LHC
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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?
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.