Multi-pion correlations in high energy collisions

Any-order pion inclusive distribution for a chaotic source in high energy collisions are given which can be used in both theory and experiment to analyze any-order pion interferometry. Multi-pion correlations effects on twopion and three-pion interferometry are discussed. PACS number(s): 13.85 Hd, 05.30Jp, 12.40 Ee. Hanbury-Brown and Twiss [1] were the first who applied the Bose-Einstein (BE) correlations to measure the size of distant stars. The method was first applied to particle physics by Goldhaber et al.(GGLP) [2] in 1959. Since then the size of the interaction region has been measured by numerous experiments in high energy collisions using different types of particles. Two-pion BE correlation is widely used in high energy collisions to provide the information of the space-time structure, degree of coherence and dynamics of the region where the pions were produced [3]. Ultrarelativistic hadronic collisions provide the environment for creating dozens of pions [4–7], therefore one must take into account the effects of multi-pion BE correlations in those processes. Because the bosonic nature of the pion should affect the single and i-pion spectra and distort the i(i ≥ 2)-pion correlation function, thus, it is very interesting to analyze the multi-pion BE correlation effects on i-pion interferometry [8–15]. On the other hand, one also want to study higher-order pion interferometry directly to see what additional information can be extracted from higher-order pion interferometry. Now this aspect has aroused great interests among physicists [6,7,13,16–18]. Unfortunately all present analyses of multi-pion correlations are based on pure “multi-pion interferometry formula” without considering the higher-order pion correlation effects on the lower-order