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

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

M. C. Güçlü and M. Y. Şengül

İstanbul Technical University

WW2011 Winter Park - Colorado 1

Işık University 31/03/ 2006 2

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


21 RRb

1Z

2Z

Collisions of Heavy Ions


Particle production from EM FieldsLarge number of free lepton-pair production



Bound-free electron – positron pair production)


Nuclear dissociation (Giant Dipole Resonance)



Collision Parameters :

22:

mcsfrequencieCritical crit

b

ctfreqFourierMaximum

1max:.

ce

)mc(E:FieldECritical critic

22

2b

ZeE:FieldEMaximum imummax


Electromagnetic four vector potential

AAF Electromagnetic field tensor

μμν

μν AFF

LLLL

ΨγΨe)Ψmˆ(iΨ μ41

e

InteractMaxwellelectronQED

)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

QED Lagrangian :


Lepton-Pair Production

Semi Classical Action :

)(:|)()(|:)(4

txxtxdS int0 LLFree Lagrangian :

)()()()( xmixx 0L

Interaction Lagrangian :

)()()()( xAxxxL

int


Total Cross Section for Free Pair Production

):():():():,(

):():():():,(

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


)()(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;

Amplitude Tkq relates the intermediate-photonlines to the outgoing-fermion lines

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

)(ln322 PTfreefree ZZ

Electron Capture Process


eZeZZZ bsaba ,...2/11)(

Positron Wave-Function

')(

q

r.qi)(q ueN


)1(2/

iaeN a

v

Zea

2

1e

a2N

a2

2

' is the distortion (correction term)due to the large charge of the ion.

Distorted wave-functionfor the captured-electron


)(.2

1)( rum

irnon

HaZr

Hrnon e

a

Z /

2/31

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


.)(

)1()1();(

);()(.2

12

)(

)()()(

)('

').('3)(.3

)()(

sp

Zss

Z

qb

p s

rqpia

rpirnon

qab

E

uuuuErA

eNrdErAerm

ird

di

S

qPP

2

0q

)(qba

)()(qab

)(2

2

0q

)(q

)(2

SSbd

Sbd

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



Total Cross Section for Bound-Free Pair Production

BABFPP )ln(

23222 /BFPPBFPP )ba(

a)b(P

Impact parameter dependence probability for Bound-Free 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

)/ln(52 PTfreebound ZZ

FIG. 2: BFPP cross sections for two different systems as functions of thenuclear charge Z [8].


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


FIG. 4: The differential cross section as function of the transverse momentum of the produced positrons [8].


FIG. 5: The differential cross section as function of the longitudinal momentum of the produced positrons [8].


FIG. 6: The differential cross section as function of the energy of the produced positrons [8] .


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



What about experiments at

SOLENOIDAL TRACKER ( STAR ) ?

RHIC: Relativistic Heavy Ion Collider

Energy =100 GeV/nucleon

Au + Au collisions


)()()(2 bPbPbPbd hadronicnoXnXnee

Cross Section of electron-positron pairs

accompanied by nuclear dissociation

Giant Dipole Resonance

eeAuAuAuAu

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

)()( 22 bPbbPd GDRee

GDR

ee

2)(

b

SbPGDR


the probability of electron-positronpair production

the probability of a simultaneousnuclear excitation as a function ofimpact parameter[9].

2/322 )(2

1)(

ba

abP

eeee


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)


Results:

mbbPbPbPbd hadronicnoXnXnee 52.1)()()(2

eeAuAuAuAu

bbPbd ee 32.0)(2

)()(3.0)(2.06.1exp mbsyststat

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

BOUND-FREE ELECTRON-POSITRON PAIR PRODUCTION with GIANT DIPOLE RESONANCE

34

the probability of electron-positronpair production

the probability of a simultaneousnuclear excitation as a function ofimpact parameter

2/322 )(2)(

ba

abP BFPPBFPP

21

b

S)b(P

C

)()(2 )1(

min

bPbPbdb XnnC

b

BFPPGDRBFPP

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

Untagged Tagged TaggedAu+Au at RHIC-FREE

34000 1630 1980

Pb+Pb at LHC-FREE

212000 10200 12400

Au+Au at RHIC-BFPP

94.5 4.5 5.5

Pb+Pb at LHC-BFPP

202 9.7 11.7

32

)b( )mb(nn11 )mb(XnXn


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) andwithout nuclear excitation [11].

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

FIG. 9: The differential cross section as function of energy of theproduced positrons is shown in the graph (a) for RHIC and (b) for LHC.And the differential cross section is shown as function of the longitudinalmomentum of the produced positrons in the graph (a) for RHIC and (b) for LHC [11].


FIG. 10: The differential cross section as function of transversemomentum of the produced positrons is shown in the graph (a) for RHICand (b) for LHC. And the differential cross section is shown as functionof the rapidity of the produced positrons in the graph (a) for RHIC and (b) for LHC [11].



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, 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.


Documents

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