Strangeness enhancement as a signal of Quark-Gluon Plasma

anda signal of the onset of

deconfinement

Therese Renstrøm

• Confinement• Deconfinement, asymptotic freedom• Quark-Gluon Plasma

Fig.1 The effective coupling constant in QCD, dependence of momentum exchange between the interacting hadrons

• How to get so hot and dense?• Answer: Ultrarelativistic heavy ion collisions

Fig. 2 An incredibly simplified picture of the creation of Quark-Gluon Plasma

QGP

Signatures of Quark-Gluon Plasma

• Electromagnetic probes (direct photons and dileptons)

• J/psi-suppression• High pT suppression• Jet modification and correlations• Elliptic flow• Strangeness enhancement

Strangeness Content: for matter at thermal and chemical equlibrium

Schwinger model for particle production gives production probability

In a nucleon-nucleon collision the ratio of strange to non-strange pairs is ca 0.1

Strangeness in hadron gas Counting the valence quarks of kaons and pions, gives the relation

In nucleon-nucleon collision this ratio is very small (p-Be, ratio=0.05)

• What about nucleus-nucleus collisions?• Produced hadrons: mainly pions and kaons• What is the ratio of strange to non-strange pairs if it is allowed to

reach thermal and chemical equlibrium?• Obtain strangeness content fraction by treating the system of

pions and kaons as an electrically neutral(!) boson gas in thermal and chemical equlibrium

• Use of Bose-Einstein statistics, and setting the chemical potential to zero is justified.

Strangeness in hadron gas at thermal and chemical equilibrium

Now we can express the density one type of meson as

The above intergral leads to the result

Where K2 is the Bessel function of order 2

At temperature T=200MeV

And following the ratio of strange to non-strange particles:

Notice that the ratio is considerably enhanced! (0.05 for p-Be)

Notice that the summands of the two sums converge rapidly Considering only the first summand in both sums, corresponds to using the Maxwell-Boltzman distribution

• Strangeness content in QGP is governed by the dynamical state of the plasma

• Thermal equilibrium- momentum distribution of particles do not change

• Chemical equilibrium- densities of particles reach steady state

• What are the densities of the different kinds of quarks if the plasma has a lifetime long enough to establish thermal and chemical equlibrium?

Strangeness in QGP in thermal and chemical equlibrium

Quarks = fermions, using Fermi-Dirac statistics

The presence of an antiquark corresponds to the absence of a quark in a negative energy state, so

Current mass, since deconfinement

We have the following number density of one type of quark

Strongly suggests strangeness enhancement as a signature of QGP!

Looking at chemical potential equals zero, we see that the predicted number density of s quarks equals that of u and d quarks. Gives a strange/nonstrange ratio of 1/2!

Approaching chemical equilibrium in QGM

So what are the mechanisms of strange pair production in QGP?

Fig. Lowest order Feynman diagrams for strange anti-strange production from quark antiquark annihilation (a) and gluon fusion (b),(c),(d).

Cross-sections for the reactions

Rate of production of strange anti-strange pairs from quark annihilatons and gluon fusion

So, the final expressions for the rate of production per unit space-time are:

Notice the similarites of the these two integrals.The cross sections are of the same order of magnitude,The difference between the Fermi-Dirac and the Bose-Einsteindistribution functions are negible at high temperatures,

The main difference comes from the degeneracy factors

We can conclude that the main source of strangenessproduction in QGP comes from gluon fusionThis was theoretically predicted by J.Rafelski and B.Mullerin 1982

The equalibration time of the strangeness production

The knowledge of the equilibrium strange quark denstity and the rate of change gives us an estimate of the equilibration time

Phase-transitionsStrangeness as a way of determining the order of phasetransition

• Three characteristics were predicted to exist if the fasetransition from the hadron gas to QGP was of first order

• The theory was tested experimentally of the NA49-collaboration

• The experimental results confirmed the theory

The kink, horn and step

The kink

Fig. Energy dependence of the mean pion multiplicity per wounded nucleon.

The horn

Fig. Energy dependence of the <K+>/<π+>

The step

Fig. Energy dependence of the mean inverse slope parameter T for K+ spectra.