lepton pair production accompanied by giant dipole resonance at rhic and lhc m. c. güçlü and m....
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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
WW2011 Winter Park - Colorado 1
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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
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21 RRb
1Z
2Z
Collisions of Heavy Ions
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Particle production from EM FieldsLarge number of free lepton-pair production
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Particle production from EM Fields
Bound-free electron – positron pair production)
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Nuclear dissociation (Giant Dipole Resonance)
Particle production from EM Fields
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Collision Parameters :
22:
mcsfrequencieCritical crit
b
ctfreqFourierMaximum
1max:.
ce
)mc(E:FieldECritical critic
22
2b
ZeE:FieldEMaximum imummax
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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 :
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Lepton-Pair Production
Semi Classical Action :
)(:|)()(|:)(4
txxtxdS int0 LLFree Lagrangian :
)()()()( xmixx 0L
Interaction Lagrangian :
)()()()( xAxxxL
int
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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
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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;
Amplitude Tkq relates the intermediate-photonlines to the outgoing-fermion lines
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Free electron-positron pair production
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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
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Electron Capture Process
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eZeZZZ bsaba ,...2/11)(
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Positron Wave-Function
')(
q
r.qi)(q ueN
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)1(2/
iaeN a
v
Zea
2
1e
a2N
a2
2
' is the distortion (correction term)due to the large charge of the ion.
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Distorted wave-functionfor the captured-electron
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)(.2
1)( rum
irnon
HaZr
Hrnon e
a
Z /
2/31
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Using the positron and the captured electron wave-functions, direct term of the Feynman diagram can be written as:
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.)(
)1()1();(
);()(.2
12
)(
)()()(
)('
').('3)(.3
)()(
sp
Zss
Z
qb
p s
rqpia
rpirnon
qab
E
uuuuErA
eNrdErAerm
ird
di
S
qPP
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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;
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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
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Bound- free electron-positron pair production
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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
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FIG. 2: BFPP cross sections for two different systems as functions of thenuclear charge Z [8].
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FIG. 3: BFPP cross sections for two different systems (Au+Au-dashed line andPb+Pb-solid line) as functions of the [8].
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FIG. 4: The differential cross section as function of the transverse momentum of the produced positrons [8].
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FIG. 5: The differential cross section as function of the longitudinal momentum of the produced positrons [8].
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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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What about experiments at
SOLENOIDAL TRACKER ( STAR ) ?
RHIC: Relativistic Heavy Ion Collider
Energy =100 GeV/nucleon
Au + Au collisions
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)()()(2 bPbPbPbd hadronicnoXnXnee
Cross Section of electron-positron pairs
accompanied by nuclear dissociation
Giant Dipole Resonance
eeAuAuAuAu
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The total cross section of electron-positron pair production with giant dipole resonance
)()( 22 bPbbPd GDRee
GDR
ee
2)(
b
SbPGDR
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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
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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
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
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
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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
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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.
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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].
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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].
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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 ?
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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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