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Subtleties and controversies related to the strangeness signature

As was pointed out originally by Redlich et al.[49] and later by Kapusta and Mekjian [52], McLerran [50], and Baym [51], strangeness per unit of entropy is larger in the hadron gas in flavour equilibrium than it is in the plasma, due to the fact that a significant fraction of entropy in the plasma is carried by gluons. During the return to the confined state, the entropy is conserved while the disappearing free gluons give birth to mesons. The $K/\pi$ ratio immediately after the phase transition approximates the strangeness to entropy ratio in QGP well. The problem however is that the $K/\pi$ ratio we measure reflects the rescattering in the hadron gas phase before the system freezes out. In particular, reaction 5.8 works to convert some pions into kaons.

Thus, an observation of strangeness enhancement should be regarded as an indirect and conditional QGP signature. At most it can testify to the state of flavour equilibrium reached by the hadron gas, and it remains to be proven that such a state was reached via a descent from a deconfined state. Kinetic theory calculations of the number of strange quarks in the hadronic gas resulting from the deconfined phase have been carried out in [22]. It was concluded that on the time scale of the collision (10 fm/c), the hadron gas can not equilibrate its flavour composition unless a transient QGP phase boosts the process. In the baryonic medium, kaons ($\bar{s}q$) equilibrate faster than strange antibaryons.

The topic of flavour equilibrium is approached by fitting particle ratios with statistical models. Statistical models are based on the following postulates[75]:

• In a certain volume, a system of $N$ secondary particles is formed as a result of strong interaction of the primary particles
• $N$ is large enough to justify statistical description
• By the time when the statistical equilibrium is established (relaxation time), the states of individual particles are statistically independent. In other words, the only remaining correlations are due to energy-momentum conservation. (To avoid misunderstanding: the effect of HBT interference of like particles, used to characterize system size, is a final state effect and it remains in this case[53]!)

It has been noticed that the rarer a particular baryon is, the less reliable its description via statistical model becomes[73]. From a logical point of view, even a perfect fit of data with a statistical model is merely a consistency check, rather than a proof of equilibration, since the statistical assumption inherent in such a model cuts off alternative explanations of the same behaviour by construction.

There is, moreover, another important component in resolving the dilemma between the QGP/non-QGP strangeness production scenarios, which makes the issue more complicated than just a choice between the purely hadronic and the QGP flavour equilibration mechanism. Very early in the collision, some strangeness production takes place in the energetic primary collisions. Its physics is neither that of the thermalized hadron gas, nor that of the thermalized QGP. Mattiello et al. (the RQMD group) showed [54] that kaon production in the primary hard collisions explains the enhanced production of $K^+$ in the $Si+Au$ collisions at AGS. Via color rope mechanism[57], RQMD can also explain $\Lambda$ and $\bar{\Lambda}$ production at the SPS[69].