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Dilepton production
Presentation for FYS4530
Atle Jorstad Qviller
What is a dilepton?
• A dilepton is a particle-antiparticle pair of
same-flavour leptons.
• Only electron-type dileptons are of interest
here
Why look at dileptons?
• αem is small (1/137)
• αs is large
• Dileptons have no color charge, interact weakly
with the nuclear medium and escape easily.
Quarks are confined and can not escape.
Composite hadrons and quarks are strongly
attentuated by gluonic bremsstrahlung.
• We can therefore extract information directly
from the reaction zone by looking at dileptons
Sources of dileptons
•
•
•
•
•
Dileptons from Drell-Yan processes
Dileptons from the QGP
Dileptons from hadron gas/resonances
Dileptons from decay of charmed particles
To detect the QGP by dilepton production
requires understanding and subtracting
away a lot of background from other
processes.
Nucleon structure
• Nucleons are composite objects
• They consist of partons: valence quarks, virtual
sea quarks and gluons.
• The partons carry a fraction of the nucleon’s
momentum determined by structure functions.
Gluons carry about 50%.
• A ”hard” parton collision has a high momentum
transfer, and is treatable in pQCD (or QED)
Quark momentum distributions
• Quark distribution function
q f ( x)   c , s  Ga / A ( xa , aT )daT
A
xq ( x, Q)  A 0 x
a
•
•
•
•
a
Aa1
(1  x)
Aa 2
a
P ( x)
A are ”constants” depending on Q2
a is the flavour
P is a smooth function
We must note that q and qbar distributions
are very different
Momentum distributions
Digression:Parton ”tyrrany”
• These momentum distributions are a
headache for particle physicists
• They limit the effective fraction of the
beam energy used for particle production.
• Tevatron (beam energy ~2 TeV) is mostly
seeing collisions with CM energy a couple
of hundred GeV.
• This is not a problem in heavy ion physics

Hard scattering/parton collision
Hard scattering
• The x’s are the momentum fraction carried by
the fusing partons.
• 1-x is carried away by the other constituents.
These fragment into a cloud of mostly low
momentum pions.
• Worried about the lack of anti-valence quarks at
pp/heavy ion collisions? Remember antiquarks
in the sea of virtual pairs!
• Hard scattering can be strong or electroweak
processes.
Hard scattering
• Gluon fusion is a strong process.
• Drell-Yan processes are electroweak.
• There are lots of other possible cases.
General cross section for hard
processes
• Results from chapter 4:
Ec | ABCX   ab  dxb dbT dxa daT Gb / B ( xb , bT )Ga / A ( xa , aT )r
d
Ec
(ba  CX ' )
3
dC
3
• R is a kinematical factor close to 1
• Gb is probability for finding parton b with
momentum fraction x and transverse momentum
fraction bt inside nucleon B. Ga similar.
Scattering formula details
• The last part of the formula is the cross
section for generating two final states C
and X from the fusion of two partons a and
b
• For hadronic final states this is not
possible to calculate, as it is not a
pertubative problem
• For leptonic endstates it is possible! 
Digression: Fragmentation
• For hadron end states: We add a
fragmentation function G times a
fundamentally calculable matrix element to
our cross section. It represents the
probability of parton c to fragment into final
state C
d 3
Ec 3 | ABCX   ab  dxb dbT dxa daT Gb / B ( xb , bT )Ga / A ( xa , aT )r
dc
d 3
 dxc dcT Gc / C ( xC , CT ) Ec dc3 |bacd
Dileptons from Drell-Yan
• The result of a Drell-Yan process is e+e-,μ+μ- or
τ+τ-,a dilepton.
Drell-Yan process
• The virtual vector boson decays into a pair of
fermions.
• Cross section is exactly calculable in
electroweak theory (in FYS 4560/4170 you learn
this)
• Z interference is only significant at high
momentum transfer (over 50-60 GeV).
• Most of our procesess have a lot less momentum
transfer. We don’t care about Z exchange here.
Drell-Yan process
• We have no fragmentation function as
leptons are fundamental.
• Electons and muon pairs are very easy to
detect, as they will somewhat
anticorrelated in angle and give signal in
EM calorimeter/muon chambers.
• Tau’s decay very fast, mostly into jets and
also lepton+neutrino. We don’t care about
them.
Dilepton kinematics
• Momentum C and
invariant mass M

C l l

M 2  C 2  (l   l  ) 2
• Feynman x
CZ
xF 
s /2
Parton momentum fractions:
2
x1, 2
1
4M
2

xF 
 xF
2
s
x1  x2  xF
x1 x2 s  M
2
Cross sections
ef 2 q
d 
1

 ( M ) N f ( )
2
dM dxF sN c
e
2
B
f
( x1 )q
A
f
( x2 )  q
B
f
( x1 )q A f ( x2 )
xF  4 M 2 / s
2

ef 2 B
A
B
d 2
1

 ( M ) N f ( ) q f ( x1 )q f ( x2 )  q f ( x1 )q A f ( x2 )
dx1dx2 N c
e

ef 2 B
A
B
d 2
1 8 2
A


(
)
xq
(
x
)
x
q
(
x
)

x
q
(
x
)
xq
f
f
f
f ( x)
Nf
3
dMdy N c 3N c M
e


Glauber model
• Baryon thickness function
 t (b)db  1
• Probability of finding baryon in A at (ba,za)

A
(bA , z A )dbA dz A  1
• Probability for baryon collision for nuclei A,B
P  T (b) in    A (bA , z A )dbA dz A  B (bB , z B )dbB dz B t (b  bA  bB ) in
Glauber model
• Probability of n
baryon baryon
collisions
 AB 
n
AB  n
T (b) in  1  T (b) in 
P(n, b)  
n 
d in
AB
AB
  n 1 P(n, b)  1  1  T (b) in 
db
AB
Glauber + Drell Yan
• For spherical nuclei colliding head on
3
DY
4 / 3 d

A
2
dMdy 4r0
dMdy
dN l l 
• Scales as A to the 4/3
NN
Dileptons from the QGP
• Considering a Nb=0 QGP
• Quark phase space
density:
• Quark spatial density:
• Number of dileptons
produced in dtd3x:
dN l l 
dtd 3 x
 N c N s  f 1
2
Nf
2
d 3 xd 3 p1
dN q  g q
f ( E1 )
3
(2 )
dN q
d 3 p1
 gq 
f ( E1 )
3
3
d x
(2 )
d 3 p1d 3 p2
f ( E1 ) f ( E2 ) ( M )v12
2 
6
e
(2 )
ef
Dileptons from the QGP
• The cross section sigma comes from QED
• Remember threefold color degeneracy for the
quark pair (and other degeneracies).
2
4mq  12
mq  ml
mq  ml
4ml 12
4  2
 (M ) 
(1 
) (1  2 ) (1  2
4
)
2
2
2
4
3 M
M
M
M
M
2
2
2
2
2
Dileptons from the QGP
• For a QGP with
Boltzmann statistics
dN l l 
2
 N c N s  f 1
2
4
dM d x
dN l l 
2
2
dM dM T d x
 (M ) 2
M
M (1 
)TMK1 ( )
2
4
2
e 2(2 )
M
T
ef
 N c N s  f 1
2
4
Nf
f (E)  e
E
T
2
Nf
4mq
2
 (M ) 2
MT
M (1 
)K0 (
)
2
4
2
e 4(2 )
M
T
ef
2
4mq
2
Dileptons from a QGP with Bjorken
hydrodynamics
• In the Bjorken model, the contracted slabs of
nuclear matter pass straight through each
other.
• They set up an excited color field between
them
• Temperature evolves as:
0
T ( )  T0 ( )

1
3
Dileptons from a QGP with Bjorken
hydrodynamics
• We make simplifications for the Bessel function
and neglect quark masses
• The reseult: Dileptons arising from qqbar
annihilation in the QGP:
dN l l 
dMdy
~

5
3
2
2
a  RA T0
2 2
2
3
7

T0 2 f ( M / Tc )  ( TM  TM ) 
e c 0 
1  ( )
Tc f ( M / T0 )


M  M / T0 M
e
f ( )
T0
T0
Dileptons from hadrons and
resonances
• Dileptons are produced in reactions like:
π+π- →μ+μ
• Assume pion gas for simplicity
• Also from decay of hadron resonances:
ρ,Φ,ω, J/ψ
Dileptons from hadrons and
resonances
• Pion annihilation is very similar to q-qbar
annihilation in the QGP
• Different degeneracies and cross section
• Nc → 1
• Nf → 1
• mq → mpi
• ef →e
• T0 →Ti
• Tc →Tf
Dileptons from hadrons and
resonances
• This process is NOT
fundamental.
• Use this cross section
in previous showed
formula:
4m 12
4ml  12
2ml
4  2
2
 ' (M ) 
(
1

)
(
1

)
(
1

)
|
F
(
m
)
|


3 M2
M2
M2
M2
2
• Where F:
• Width and mass of
rho meson
| F (m ) |2 
m
4
( M 2  m )   2 m
2
2
Dileptons from hadrons and
resonances
• Resonances originate from nucleusnucleus collision or from collisions in the
hadron gas
• J/psi at 3.1 GeV is massive and therefore
arises mostly from hard scattering.
Charm production
• Charm quarks are made in reactions like:
q+qbar→g*→c+cbar
g+g→c+cbar
• This state can from charmonium or
fragment directly into a D+D- pair.
• Look at figure 14.7
Dileptons from charm decay
• Charmonium can decay directly into a
dilepton
c+cbar→μ+μ• A pair of D mesons can further decay into
a dilepton
• These dileptons have approximately
exponential distribution with a ”low”
temperature.
Total spectrum
• We must have dilepton yield from the QGP
of large enough magnitude.
• M less than 1 GeV: Resonance decays
from ρ,Φ,ω dominate. Difficult to see QGP
signal
• Continuum (not resonances) over 1.5
GeV: Hadron interactions and charm
decay not important.
Total spectrum
• Drell-Yan is dominant at higher
temperatures.
• Look at figure 14.8
• The QGP is visible in the dilepton
spectrum if it is hot enough, but we do not
know. Drell-Yan will mask it if too cold.
• Stefan-Boltzmann: ε = σT4
• The energy density goes as the 4th power
of the temperature.
Conclusion
• Dileptons are not a very clean signature of the
QGP due to massive pollution from lots of
sources, but still useful as a supplement and for
extracting information directly from the collision
zone.
• The plasma temperature is crucial.
• The plasma temperature is linked directly to the
energy density through Stefan-Boltzmann.
• Different energy densities will have a big impact
on dilepton production.