Signatures of Quark-Gluon-Plasma/1Dilepton production

In the QGP a quark may interact with an antiquark to form a virtual photon which decays into a lepton-antilepton pair.

The lepton-antilepton pair is also called a dilepton.

This is characterized by its invariant mass

M2 = (ml+ + ml

-)2

Dilepton 4-momentum: P = pl+ + pl-

Dilepton transverse momentum pT

After a lepton pair is produced, the two leptons must traverse the collision region. However, their mean free path is quite large, since they interact through the electromagnetic interaction, and the lepton-charged particle cross section is of the order of

= the lepton-charged particle c.m. energy

= the fine structure constant

Production rate and momentum distributions of the lepton pair depend on the quark and antiquark momentum distributions in the QGP

We take the cross section of the quark-antiquark into two leptons as:

This can be shown by perturbative QED through the use of Feynman diagrams (see Wong, Exercise 14.2 for full details)

Assume quark and antiquark distribution in the form exp(-E/T)

eq =quark charge

If the temperature T drops down as a function of time as

The lepton pairs produced during the time interval from the proper time t0 to the critical time tc (time at which the temperature drops below the critical temperature) will be

ef= charge of quark with flavor f

H(z) is a function related to the Bessel function

Neglecting the quark mass and the lepton mass, the dilepton distribution in invariant mass and rapidity is approximated by

where the dominant invariant mass dependence is contained in the factor exp(-M/T0).If the dilepton invariant mass

distribution is parametrized as

then the dilepton temperature is nearly the same as the quark initial temperature.

This means that if one could measure the dilepton spectrum coming from quarks, one could extract the quark initial temperature!

f(z)=1+4/z+8/z2+16/z3

NICE, BUT…

other processes contribute…

Drell-Yann processes

Dilepton production from hadrons and resonances

Dileptons from the decay of charm particles

Drell-Yann processes

In the Drell-Yann process for a nucleus-nucleus collision, a valence quark of a nucleon interacts with a sea antiquark of a nucleon of the other nucleus.

They annihilate into a virtual photon which subsequently decays into a dilepton pair.

Such process is especially important for large values of the invariant mass of the lepton-lepton pair.

A,B = nucleons

Correlation among the nucleons are not important in such case, and the production of dileptons under the Drell-Yann process in heavy ion collisions may be considered as arising from independent NN collisions.

It can be shown that the dilepton differential cross section arising from Drell-Yann processes is approximately

The parameters Ai depend on the value of Q2 (square of the invariant mass of the dilepton pair)

The Drell-Yann dilepton differential cross section at y=0 behaves as if there is an effective temperature TDY arising from the motion of quarks and antiquarks in the nucleon:

How to take into account these Drell-Yann processes in nucleus-nucleus collisions?

Using results from the Glauber model, for a collision between 2 nuclei A and B at an impact parameter b, the total probability for the occurrence of a Drell-Yann process in such collision is

Probability to find a nucleon in the proper volume element

Probability for a nucleon-nucleon Drell-Yann process

Following such arguments, the differential number of lepton pairs with an invariant mass M and a rapidity y is given by

and, integrating over the transverse area

T(b)=thickness function

In particular, for a central collision of two equal nuclei (A=B), the number of dilepton pairs from the Drell-Yann process scales as A4/3.

Dilepton production from hadrons and resonances

Hadron collisions may produce dileptons.

For instance π+π- l+l-

Dilepton pairs may also come from the decay of hadron resonances, such as ρ, ω, φ, J/Ψ

Both of them are then additional sources of dileptons, and must be identified in order to look at dileptons originating from QGP

To evaluate the contribution from the hadronic matter, consider for simplicity that it consists only of pions.

The cross section for such process is estimated similarly to the cross section from QGP, with the following replacements

Then one gets

with a form factor

Mass and width of the ρ-meson

M

Hadron resonances will show up as sharp peaks in the invariant mass spectrum of the lepton pairs, with a width related to the lifetime of that resonance and a magnitude depending on the abundance of the resonance.

Such resonances may be produced in nucleus-nucleus collisions even before thermalization.

Resonance B.R. (e+e-) Main decay mode

ρ(770) 4.49E-5 ππ (≈100 %)

ω(782) 7.07E-5 π+π-π0 (88.8 %)

Φ(1020) 2.91E-4 K+K- (49.2 %)

Dileptons from the decay of charm particles

Charmed mesons (D+, D-) may be produced by such processes

Since a charm meson D+ is a composite particle which consists of a charm quark and an antiquark (u,d or s), one may produce D+D- pairs, which subsequently decay into lepton pairs.

Possible processes are

The dileptons produced via charm production have an approximately exponential shape for the invariant mass distribution, with a slope parameter corresponding to an effective temperature much smaller than for the Drell-Yann process.

Question: Is the dilepton yield arising from QGP large enough to make it observable? To allow for this, the intensity should be comparable or even larger than the yields from other sources.

Invariant masses below 1 GeV:

Decays from ρ, ω, φ dominate over the possible contribution from QGP. Also hadron collision and decay from charm have low temperature, so they contribute to the low mass region. It is then difficult to observe any contribution from QGP.

Invariant masses greater than 1.5 GeV:

Away from resonance peaks, the dominant non-QGP contribution comes from the Drell-Yann process. Dileptons from QGP should have a temperature of a few hundred MeV.

Dileptons from Drell-Yann have a temperature dependent on √s. At RHIC, the temperature expected is in the order 10-20 GeV (much greater than for QGP). Then the dilepton yield from Drell-Yann will be larger than the dilepton yield from QGP at large invariant masses.

The dilepton yield from QGP will however depend on the QGP temperature.

If the QGP temperature is higher than 350 MeV, the observation of dileptons from the QGP should be possible in the region 1-3 GeV. At lower temperatures, observation could be possible at lower masses (1-2 GeV) but not so clean.

The experimental situation

Results from the NA45/CERES Collaboration@CERN SPS

The NA45/CERES set-up is a dielectron spectrometer focused on the detection of e+e-

pairs in the invariant mass range < 1 GeV/c2.

NA45 Set-up

The acceptance, fully symmetric in azimuth, covers from 2.11 to 2.64 in pseudorapidity (a window of about 0.5 units around midrapidity).

Two Si-drift detectors provide angle measurement of the particles and reconstruct the primary vertex.

The main discrimination between the (rare) electron pairs and the (abundant) hadrons is done with Ring Imaging Cherenkov Detectors (RICH).

A TPC (added in 1999) improves the reconstruction of momenta and then the invariant mass resolution to 2%.

One of the experimental problems in measuring dielectron pairs is the low probability of electromagnetic decay and the large amount of combinatorial background from photon conversion and Dalitz decay.

A very good electron identification is needed against pions: In NA45 the pion rejection factor is about 0.999

Once identified, electron pairs from direct photon conversion and Dalitz decay have to be eliminated by their topology (small opening angle and small momentum)

A measure of the combinatorial background is given by the comparison between like-sign and unlike-sign invariant mass spectra.

In a series of systematic measurements, NA45 has studied dielectron production in pA and AA collisions at CERN SPS, up to 200 A GeV.

Large difference have been found between the

p-nucleus case (pBe and pAu at 450 GeV)

and the

nucleus-nucleus case (S+Au @200 A GeV and Pb+Au @160 A GeV)

In the proton case, the superposition of known electromagnetic decays of produced neutral mesons can successfull account for the observed yield of dielectron pairs.

In the nucleus-nucleus case a strong excess of dielectrons above the expectations from meson decays is observed.

Dielectrons from proton-nucleus collisions at 450 GeV

Results may be interpreted in terms of hadron decays

Enhancement factor over conventional sources: 5 ± 0.7 at low invariant masses

Dielectrons from S+Au at 200 A GeV

Dielectrons from Pb+Au at 158 A GeV

Confirm results from S+Au@200 A GeV

Enhancement factor: 3.5 ± 0.4

Enhancement for different centrality bins

Pb+Au @ 158 A GeV

Pb+Au @ 158 A GeV

Enhancement at low transverse momentum

Pb+Au @ 158 A GeV: Transverse momentum dependence

For small masses, agreement with hadron decays, enhancement at larger masses

These results have started an experimental and theoretical program of activity, leading to new results in very recent years.

To examine the dependence of such effect on baryon density and temperature, experiments have been carried at different bombarding energies (40 A GeV) in 1999.

At 40 A GeV, the temperature is lower and the baryon density is 1.5 higher than at 160 A GeV.

Results at 40 A GeV point out again a strong excess (with an enhancement factor of 5.4, higher than at 160 A GeV) with respect to the expectations from meson decay.

For masses below 0.2 GeV/c2, the spectrum is dominated by the Dalitz decay of π0 and η into γe+e-, and a good agreement with predictions is found.

For larger masses, a structureless continuum is seen above the hadron decay level, extending up to the region of the φ.

The enhancement factor is 5.9 ± 1.5(stat).

The transverse momentum distributions are extracted for low and higher invariant masses of the dielectron system, again showing the excess at large masses.

Recent, improved NA45 set-up

Recent results from NA45 on low mass dielectrons

Recent results from NA45 on low mass dielectrons: centrality dependence

Recent results from NA45 on low mass dielectrons: comparison to recent models

Results on dimuons

The NA50 set-up

Upgrade of NA38 set-up

Angle/momentum of muons are measured in a magnetic spectrometer, protected by a hadron absorber. Muon pairs are detected between η=2.8 and η=4.

The most important sources of low mass dileptons (muon pairs) are 2-body and Dalitz decays of light neutral mesons

Also the contributions from charmed D mesons, J/Ψ and Drell-Yann process need to be included

Dimuons in S+U and S+Cu collisions@200 A GeV (NA38/NA50)

Dimuons in Pb+Pb collisions@158 A GeV (NA50)

Introducing additional ingredients in the hadronic scenario

Tentative summary (so far)

Experiments on dilepton production are difficult: small cross sections, huge background, specific detectors needed

Mainly two sets of results:

a) Intermediate invariant mass range (1-3 GeV)

NA38, NA50, Helios-3

a) Low invariant mass range (< 1 GeV)

NA45/CERES (dielectrons), NA38/NA50 (dimuons)

Features of e+e- results:

Mass spectrum in p-nucleus well explained by known sourcesSignificant enhancement in heavy-ion collisions at SPS energies w.r.t. hadron cocktailEnhancement increases with centrality and with low pt.

Features of μ+μ- results:

Mass spectrum in p-nucleus compatible with known sources

Small enhancement observed in heavy-ion collisions

Only high transverse momenta probed so far

Meson modifications may result in significant change of the predicted spectrum

Study of dielectrons at GSI near the production threshold: The HADES experiment

HADES (High Acceptance Dielectron Spectrometer) is a second generation experiment aimed at the study of electron pairs in proton, pion and heavy ion-induced reactions at GSI (2 A GeV).

The main part of the HADES experimental program is focused on studies of the in-medium properties of the vector mesons ρ(770), ω(782), φ(1020).

The meson spectral functions inside nuclear matter are directly accessible through their decay into electron pairs, since such electrons do not suffer further interactions.

HADES set-up

Due to the dielectron excess observed at SPS energies from NA45 (and the claim as a QGP signature), HADES wants also to investigate dielectrons to check possible alternative explanations based on hadronic models with significant alterations of the in-medium properties.

Previous experiments at SIS showed that in pp collisions the dielectrons yields could be explained by conventional mechanisms. For heavy-ion collisions (C+C and Ca+Ca), an excess of electron pairs was found in the low mass range (200-600 MeV/c2)

Such excess could not be explained even with in-medium modifications of vector mesons.

HADES is exploring such process through the study of several channels, with proton, pion and heavy ion beams.

Preliminary results with C+C collisions at 2 A GeV showed some evidence of dielectron excess over the combinatorial background.

Exclusive measurements (with well defined final states) carried out in 2005 with proton and pion projectiles to separate the contribution from different channels.