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Hadrochemistry

Here we summarize the present understanding of how inelastic hadronic rescattering in a thermal hadron gas can change flavour composition and influence relative abundances of particle species.

Koch, Rafelski and Muller [24,22] pointed out that in the thermally equilibrated fireball, the usual reaction

$$N+N \leftrightarrow N+Y+\bar{K},$$ (40)

where $Y=\Lambda$ or $\Sigma$, plays almost no role because, first, the majority of collisions are $\pi N$ and $\pi\pi$, not $NN$, and second, the following $\pi N$ and $\pi\pi$ reactions have lower threshold :

$$\pi+N \leftrightarrow \bar{K} + Y$$ (41)

$$\pi+Y \leftrightarrow \bar{K} + \Xi$$ (42)

$$\pi+\Xi \leftrightarrow \bar{K} + \Omega$$ (43)

$$\pi + \bar{N} \leftrightarrow K + \bar{Y}$$ (44)

$$\pi + \bar{Y} \leftrightarrow K + \bar{\Xi}$$ (45)

$$\pi + \bar{\Xi} \leftrightarrow K + \Bar{\Omega}$$ (46)

$$\pi + \pi \leftrightarrow K + \bar{K}$$ (47)

For charged kaons, $\bar{K}$ is $K^+$ ($u\bar{s}$) and $K$ is $K^-$ ($s\bar{u}$). In $Pb+Pb$ collisions at SPS, the $\bar{p}/p$ ratio was reported to be around 0.07 [47,48], and $p/\pi$ around 0.16 (as seen by collecting the data from [47,48] and the present work [26]). Therefore it is clear that the reactions above enhance $K^+$ whereas $K^-$ is little affected. The effect of the pion rescattering 5.9,5.10 on the $\Lambda$, $\Sigma$ and $\Xi$ will be depletion, since the left hand side of these reactions is a more common state.

There is another side to the question of how rescattering affects strange particle yields. The strangeness exchange reactions

$$K+N \leftrightarrow Y + \pi$$ (48)

$$K+Y \leftrightarrow \Xi + \pi$$ (49)

$$K+\Xi \leftrightarrow \Omega + \pi$$ (50)

$$\bar{K}+\bar{N} \leftrightarrow \bar{Y} + \pi$$ (51)

$$\bar{K}+\bar{Y} \leftrightarrow \bar{\Xi} + \pi$$ (52)

$$\bar{K} + \bar{\Xi} \leftrightarrow \bar{\Omega} + \pi$$ (53)

are exothermic when they proceed from the left to the right. When the system cools down, kaons and hyperons are already present and cooling down will shift the balance to favour the right hand side.