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Lepton Pair Production Accompanied by Giant Dipole Resonance at RHIC and LHC. M. C. Güçlü and M. Y. Şengül İstanbul Technical University . Particle production from E M Fields. * Lepton- pair production * Beam Lifetime ( ele c tron capture and nuclear dissociation )

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lepton pair production accompanied by giant dipole resonance at rhic and lhc

Lepton Pair Production Accompanied by Giant Dipole Resonance at RHIC and LHC

M. C. Güçlü and M. Y. Şengül

İstanbul Technical University

Winter Park - Colorado

slide2

Particle production from EMFields

* Lepton-pair production

* Beam Lifetime

(electroncapture and nuclear dissociation)

* Detector background

* Impact parameter dependence

* Test of QED at high fields

31/03/ 2006

slide3

Collisions of Heavy Ions

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slide4

Particle production from EMFields

Large number of free lepton-pair production

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slide5

Particle production from EMFields

Bound-free electron– positron pair production)

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slide6

Particle production from EMFields

Nuclear dissociation (Giant Dipole Resonance)

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slide7

Collision Parameters :

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slide8

QED Lagrangian :

Electromagnetic four vector potential

Electromagnetic field tensor

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slide9

Lepton-Pair Production

Semi Classical Action :

Free Lagrangian :

Interaction Lagrangian :

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slide11

Scalar part of EM Fields in momentum

space of moving heavy ions;

Amplitude Tkq relates the intermediate-photon

lines to the outgoing-fermion lines

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free electron positron pair production
Free electron-positron pair production

SPS , γ=10, Au + Au , σ=140 barn

RHIC, γ=100, Au + Au , σ=36 kbarn

LHC, γ=3400, Pb + Pb , σ=227 kbarn

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electron capture process
Electron Capture Process

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positron wave function
Positron Wave-Function

is the distortion (correction term)

due to the large charge of the ion.

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slide16
Using the positron and the captured electron wave-functions, direct term of the Feynman diagram can be written as:

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having the amplitudes for the direct and crossed diagram the cross section for bfpp is
Having the amplitudes for the direct and crossed diagram, the cross section for BFPP is;

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slide18

Total Cross Section for Bound-Free

Pair Production

Impact parameter dependence probability

for Bound-Free Pair Production

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bound free electron positron pair production
Bound- free electron-positron pair production

RHIC, γ=100, Au + Au , σ=83 barn

LHC, γ=3400, Au + Au , σ=161 barn

Pb + Pb, σ=206 barn

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slide20

FIG.2: BFPP cross sections for two different systems as functions of the

nuclear charge Z [8].

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slide21

FIG.3: BFPP cross sections for two different systems (Au+Au-dashed line and

Pb+Pb-solid line) as functions of the [8].

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slide22

FIG.4:The differential cross section as function of the transverse

momentum of the produced positrons [8].

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slide23

FIG.5: The differential cross section as function of the longitudinal

momentum of the produced positrons [8].

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slide24

FIG.6: The differential cross section as function of the energy of the

produced positrons [8] .

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FIG.7: The differential cross section is shown as function of the rapidity [8].

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slide26

What about experiments

at

SOLENOIDAL TRACKER ( STAR ) ?

RHIC: Relativistic Heavy Ion Collider

Energy =100 GeV/nucleon

Au + Au collisions

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slide27

Cross Section of electron-positron pairs

accompanied by nuclear dissociation

Giant Dipole Resonance

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the total cross section of electron positron pair production with giant dipole resonance
The total cross section of electron-positron pair production with giant dipole resonance

the probability of electron-positron

pair production

the probability of a simultaneous

nuclear excitation as a function of

impact parameter[9].

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slide29

Kinematic restrictions at STAR experiment

Rapidity:

Invariant mass:

Transverse momentum :

Adams J. At al. Phys. Rev. A 63:031902 (2004)

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slide30

Results:

Şengül, M. Y., Güçlü, M. C., and Fritzsche, S., 2009, Phys. Rev. A 80, 042711

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bound free electron positron pair production with giant dipole resonance
BOUND-FREE ELECTRON-POSITRON PAIR PRODUCTION with GIANT DIPOLE RESONANCE

the probability of electron-positron

pair production

the probability of a simultaneous

nuclear excitation as a function of

impact parameter

slide32

INTEGRATED CROSS SECTIONS FOR GOLD-GOLD COLLISIONS AT RHIC ENERGIES AND FOR LEAD-LEAD COLLISIONS AT LHC ENERGIES FOR FREE AND BOUND-FREE PAIR PRODUCTION

slide33

Şengul, M. Y., and Güçlü, M. C., 2011, Phys. Rev. C ,83,014902.

FIG.8: The probability of positron pair production with (a) gold beams at RHIC and

(b) lead beams at the LHC as a function of b with XnXn (dashed line) and 1n1n (dotted line) and

without nuclear excitation [11].

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slide34

FIG.9: The differential cross section as function of energy of the

produced positrons is shown in the graph (a) for RHIC and (b) for LHC.

And the differential cross section is shown as function of the longitudinal

momentum of the produced positrons in the graph (a) for RHIC and (b) for LHC [11].

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slide35

FIG.10: The differential cross section as function of transverse

momentum of the produced positrons is shown in the graph (a) for RHIC

and (b) for LHC. And the differential cross section is shown as function

of the rapidity of the produced positrons in the graph (a) for RHIC and (b) for LHC [11].

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slide36

CONCLUSIONS:

1. We have obtained impact parameter dependence of free-free and bound-free electron-positron pair production cross section by using the semi-classical two photonmethod.

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 and compered with the STAR experiment.

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 ?

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references
REFERENCES:

1) C.A. Bertulani and G. Baur, Phys. Rep. 163, 299 (1988).

2) M.J. Rhoades-Brown, C. Bottcher and M.R. Strayer, Phys. Rev. A 40, 2831 (1989).

3) A.J. Baltz, M.J. Rhoades-Brown and J. Weneser, Phys. Rev. A 50, 4842 (1994).

4) C.A. Bertulani and D. Dolci, Nucl. Phys. A 683, 635(2001).

5) V.B.Berestetskii, E.M. Lifshitz and L.P. Pitaevskii, Relativistic Quantum Field Theory (Pergamon Press, NewYork, 1979).

6) J. Eichler and W.E. Meyerhof, Relativistic Atomic Collisions (Academic Press, California, 1995).

7) H. Meier, Z. Halabuka, K. Hencken, D. Trautmann and G. Baur, Phys. Rev. A 63, 032713 (2001).

8)Şengül, M. Y., Güçlü, M. C., and Fritzsche, S., 2009, Phys. Rev. A 80, 042711.

9) K. Hencken, G. Baur, D. Trautmann, Phys. Rev. C 69, 054902 (2004).

10) M.C. Güçlü, M.Y. Şengül, Progress in Part. and Nucl. Phys. 59, 383 (2007).

11)Şengul, M. Y., and Güçlü, M. C., 2011, Phys. Rev. C ,83,014902.

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