Cem Güçlü İstanbul Technical University Physics Department

September 23, 2008 Erice 2008 1

Cem Güçlüİstanbul Technical University

Physics Department

Production of electron-positron pairs by nuclear dissociation in

heavy ion collisons


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


“ 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)


Collision Parameters :

22: mcsfrequencieCritical crit

bctfreqFourierMaximum 1

max:.

cemcEFieldECritical kritik

22 )(:

2:b

ZeEFieldEMaximum maksimum


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


21 RRb

1Z

2Z

Collisions of Heavy Ions


Dirac wave-function of electrons/positrons

A Electromagnetic vector potential

AAF Electromagnetic field tensor

μμν

μν AFF

LLLL

ΨγΨe)Ψmˆ(iΨ μ41

e

InteractMaxwellelectronQED


Lepton-Pair ProductionSemi Clasical Action :

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

txxtxdS int0 LLFree Lagrangian :

)()()()( xmixx 0L

Interaction Lagrangian :

)()()()( xAxxxL

int


)2()1( AAA

]2.exp[)()(8)1( 2222

0220 bqiqqq

qqZAyxz

z

)1()1( 0AAz

0)2()1(0)2()1(

yy

xx

AA

AA

Four Vector Potentials of the Colliding Ions :


ee

time

Ion 1

Ion 2

Emits photon Emits photonPair Production


Direct and exchange diagrams :


Total Cross Section

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

12)(

21)(

pTqpFpkFpqkA

pTqpFpkFpqkA

kq

kq

3 3 22( ) ( )

8

1 , : , :4 2

p k q pq k

d kd qd p A k q A k q


)()(4):( 222222

22qfqG

qZqF 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


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


)()(0

0 qFqbJbqdqdbd

];[]);(21[

];[]);(21[

];[]);(21[];[]);(2

1[

)2(8)(

2121

2

010

222

2

KqkTqQkT

KkTqQkT

KqFqQFKFqQF

QKddkddqdkqF

kqkq

kqkq

zz

k q

Impact Parameter Dependence Cross Sections :


ca

qaeF

qF

35.1)0()(


qaT

qa

e

eFqF

)0()(

TF )0()(ln3

0 CT

Ca 35.1


23

22

1

02

0

00

)(

1)cos(2

)(

ba

ba

dtet

qbtbqdq

ebqJbqdqdbd

T

qaT

bqT


23

22

3422

21

2

)()(ln2

121)(

ba

aZZCdbd

bbP C

)(2ln914)( 2

242

2212 Z

bbZZbP ClabC

Two Photon Method :

Equivalent Photon Method:

M. C. Güçlü, Nucl. Phys. A, Vol. 668, 207-217 (2000)



( 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 :


An example of a diagram which is included


Güçlü M.C. et al, Annals of Physics , 272, 7-48 (1999)


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(!)()( bP

NbPbP

N

N Poisson distribution


))(exp(!)()( bP

NbPbP

N

N


Experiments at

CERN Super Proton Synchroton SPS


eeAuSAuSEnergy = 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).


What about experiments at

SOLENOIDAL TRACKER ( STAR ) ?

RHIC: Relativistic Heavy Ion Collider

Energy =100 GeV/nucleon

Au + Au collisions

Circumference = 2.4 miles


)()()(2 bPbPbPbd hadronicnoXnXnee

Cross Section of electron-positron pairs

accompanied by nuclear dissociation

Giant Dipole Resonance

eeAuAuAuAu


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?


)exp(11)(

aRb

b

No hadronic probability, computed with Woods-Saxon nuclear form factor


2)(bSbPXnXn

23/2222

21

5

2

222

12

1045.5

2

fmAZNZ

mAZNZS

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


z

z

PPPPY

0

0ln21

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

Baur at al. : σ = 1.9 mb






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 antiprotons 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


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.!

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Cem Güçlü İstanbul Technical University Physics Department