Lepton Pair Production Accompanied by Giant Dipole Resonance at RHIC and LHC M. C. Güçlü and M. Y. Şengül İstanbul Technical University WW2011Winter Park - Colorado 1

Işık University31/03/ Particle production from EM Fields * Lepton-pair production * Beam Lifetime (electron capture and nuclear dissociation) * Detector background * Impact parameter dependence * Test of QED at high fields

WW2011Winter Park - Colorado3 Collisions of Heavy Ions

WW2011Winter Park - Colorado4 Particle production from EM Fields Large number of free lepton-pair production

WW2011Winter Park - Colorado5 Particle production from EM Fields Bound-free electron – positron pair production)

WW2011Winter Park - Colorado6 Nuclear dissociation (Giant Dipole Resonance) Particle production from EM Fields

WW2011Winter Park - Colorado7 Collision Parameters :

WW2011Winter Park - Colorado8 Electromagnetic four vector potential Electromagnetic field tensor QED Lagrangian :

WW2011Winter Park - Colorado9 Lepton-Pair Production Semi Classical Action : Free Lagrangian : Interaction Lagrangian :

WW2011Winter Park - Colorado10 Total Cross Section for Free Pair Production

WW2011Winter Park - Colorado11 Scalar part of EM Fields in momentum space of moving heavy ions; Amplitude T kq relates the intermediate-photon lines to the outgoing-fermion lines

Free electron-positron pair production WW2011Winter Park - Colorado12 SPS, γ=10, Au + Au, σ=140 barn RHIC, γ=100, Au + Au, σ=36 kbarn LHC, γ=3400, Pb + Pb, σ=227 kbarn

Electron Capture Process WW2011Winter Park - Colorado13

Positron Wave-Function WW2011Winter Park - Colorado14 is the distortion (correction term) due to the large charge of the ion.

Distorted wave-function for the captured-electron WW2011Winter Park - Colorado15

Using the positron and the captured electron wave-functions, direct term of the Feynman diagram can be written as: WW2011Winter Park - Colorado16

Having the amplitudes for the direct and crossed diagram, the cross section for BFPP is; WW2011Winter Park - Colorado17

WW2011Winter Park - Colorado18 Total Cross Section for Bound-Free Pair Production Impact parameter dependence probability for Bound-Free Pair Production

Bound- free electron-positron pair production WW2011Winter Park - Colorado19 RHIC, γ=100, Au + Au, σ=83 barn LHC, γ=3400, Au + Au, σ=161 barn Pb + Pb, σ=206 barn

FIG. 2: BFPP cross sections for two different systems as functions of the nuclear charge Z [8]. WW2011Winter Park - Colorado20

FIG. 3: BFPP cross sections for two different systems (Au+Au-dashed line and Pb+Pb-solid line) as functions of the [8]. WW2011Winter Park - Colorado21

FIG. 4: The differential cross section as function of the transverse momentum of the produced positrons [8]. WW2011Winter Park - Colorado 22

FIG. 5: The differential cross section as function of the longitudinal momentum of the produced positrons [8]. WW2011Winter Park - Colorado 23

FIG. 6: The differential cross section as function of the energy of the produced positrons [8]. WW2011Winter Park - Colorado 24

FIG. 7: The differential cross section is shown as function of the rapidity [8]. WW2011Winter Park - Colorado 25

WW2011Winter Park - Colorado26 What about experiments at SOLENOIDAL TRACKER ( STAR ) ? RHIC: Relativistic Heavy Ion Collider Energy =100 GeV/nucleon Au + Au collisions

WW2011Winter Park - Colorado27 Cross Section of electron-positron pairs accompanied by nuclear dissociation Giant Dipole Resonance

The total cross section of electron-positron pair production with giant dipole resonance WW2011Winter Park - Colorado28 the probability of electron-positron pair production the probability of a simultaneous nuclear excitation as a function of impact parameter[9].

WW2011Winter Park - Colorado29 Rapidity: Invariant mass: Transverse momentum : Kinematic restrictions at STAR experiment Adams J. At al. Phys. Rev. A 63: (2004)

WW2011Winter Park - Colorado30 Results: Şengül, M. Y., Güçlü, M. C., and Fritzsche, S., 2009, Phys. Rev. A 80,

BOUND-FREE ELECTRON-POSITRON PAIR PRODUCTION with GIANT DIPOLE RESONANCE 34 the probability of electron-positron pair production the probability of a simultaneous nuclear excitation as a function of impact parameter

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 UntaggedTagged Au+Au at RHIC- FREE Pb+Pb at LHC- FREE Au+Au at RHIC- BFPP Pb+Pb at LHC- BFPP

WW2011Winter Park - Colorado33 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]. Şengul, M. Y., and Güçlü, M. C., 2011, Phys. Rev. C,83,

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]. WW2011Winter Park - Colorado34

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]. WW2011Winter Park - Colorado35

WW2011Winter Park - Colorado 36 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 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 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 ?

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, (2001). 8) Şengül, M. Y., Güçlü, M. C., and Fritzsche, S., 2009, Phys. Rev. A 80, ) K. Hencken, G. Baur, D. Trautmann, Phys. Rev. C 69, (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, WW2011Winter Park - Colorado37