Beyond Intermittency: Erraticity

Erraticity analysis of multiparticle production data is introduced as a way of extracting the maximum amount of information on self-similar fluctuations. It is presented as the next logical step to take beyond the intermittency analysis. An erraticity spectrum e(α) can be determined analogous to the multifractal spectrum f(α). An analytical example is presented to elucidate the method of analysis and the type of results that can be obtained. 1 A historical overview Andrzej Bia las has played an influential role in the physics of hadronic and nuclear collisions throughout his career. The work that he did with Robi Peschanski on intermittency has dominated the attention of physicists working on multiparticle production in the last ten years. It is fitting at this point to review the significance of intermittency and ask where we can go from here. When many particles are produced in high-energy collisions, the very natural quantities to study theoretically and experimentally are averages, such as the mean multiplicity 〈n〉, the first few moments of the multiplicity distribution Pn, and the rapidity distribution dn/dy. Indeed, those were the quantities investigated intensively in the beginning of the era of multiparticle production. Then as the collision energy was increased, the total rapidity range Y became large enough to permit meaningful partitioning of Y into smaller bins of various sizes δ. It was found that the distributions Pn(δ) can be well fitted by negative binomial distributions with the normalized width increasing, as δ decreases [1, 2]. Thus began the interest in the study of multiplicity fluctuation as a function of the bin size. Such studies did not catch fire until the significance of intermittency, proposed by Bia las and Peschanski [3], was fully appreciated.