Dilepton production

1
Dilepton production

• Presentation for FYS4530
• Atle Jorstad Qviller

2
What is a dilepton?

• A dilepton is a particle-antiparticle pair of
  same-flavour leptons.
• Only electron-type dileptons are of interest here

3
Why look at dileptons?

• aem is small (1/137)
• as 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

4
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.

5
Nucleon structure

• Nucleons are composite objects
• They consist of partons valence quarks, virtual
  sea quarks and gluons.
• The partons carry a fraction of the nucleons
  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)

6
Quark momentum distributions

• Quark distribution function
• 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

7
Momentum distributions
8
DigressionParton 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 ?

9
Hard scattering/parton collision
10
Hard scattering

• The xs 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.

11
Hard scattering

• Gluon fusion is a strong process.
• Drell-Yan processes are electroweak.
• There are lots of other possible cases.

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General cross section for hard processes

• Results from chapter 4
• 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.

13
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! ?

14
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

15
Dileptons from Drell-Yan

• The result of a Drell-Yan process is ee-,µµ- or
  tt-,a dilepton.

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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 dont care about Z exchange here.

17
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.
• Taus decay very fast, mostly into jets and also
  leptonneutrino. We dont care about them.

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Dilepton kinematics

• Momentum C and invariant mass M
• Feynman x

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Parton momentum fractions
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Cross sections
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Glauber model

• Baryon thickness function
• Probability of finding baryon in A at (ba,za)
• Probability for baryon collision for nuclei A,B

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Glauber model

• Probability of n baryon baryon collisions

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Glauber Drell Yan

• For spherical nuclei colliding head on
• Scales as A to the 4/3

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Dileptons from the QGP

• Considering a Nb0 QGP
• Quark phase space density
• Quark spatial density
• Number of dileptons produced in dtd3x

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Dileptons from the QGP

• The cross section sigma comes from QED
• Remember threefold color degeneracy for the quark
  pair (and other degeneracies).

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Dileptons from the QGP

• For a QGP with Boltzmann statistics

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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

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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

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Dileptons from hadrons and resonances

• Dileptons are produced in reactions like
• pp- ?µµ
• Assume pion gas for simplicity
• Also from decay of hadron resonances
• ?,F,?, J/?

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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

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Dileptons from hadrons and resonances

• This process is NOT fundamental.
• Use this cross section in previous showed
  formula
• Where F
• Width and mass of rho meson

32
Dileptons from hadrons and resonances

• Resonances originate from nucleus-nucleus
  collision or from collisions in the hadron gas
• J/psi at 3.1 GeV is massive and therefore arises
  mostly from hard scattering.

33
Charm production

• Charm quarks are made in reactions like
• qqbar?g?ccbar
• gg?ccbar
• This state can from charmonium or fragment
  directly into a DD- pair.
• Look at figure 14.7

34
Dileptons from charm decay

• Charmonium can decay directly into a dilepton
• ccbar?µµ-
• A pair of D mesons can further decay into a
  dilepton
• These dileptons have approximately exponential
  distribution with a low temperature.

35
Total spectrum

• We must have dilepton yield from the QGP of large
  enough magnitude.
• M less than 1 GeV Resonance decays from ?,F,?
  dominate. Difficult to see QGP signal
• Continuum (not resonances) over 1.5 GeV Hadron
  interactions and charm decay not important.

36
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 e sT4
• The energy density goes as the 4th power of the
  temperature.

37
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.