How to retrieve additional information from the multiplicity distributions

Abstract

Multiplicity distributions P (N ) measured in multiparticle production processes are most frequently described by the Negative Binomial Distribution (NBD). However, with increasing collision energy some systematic discrepancies have become more and more apparent. They are usually attributed to the possible multi-source structure of the production process and described using a multi-NBD form of the multiplicity distribution. We investigate the possibility of keeping a single NBD but with its parameters depending on the multiplicity N . This is done by modifying the widely known clan model of particle production leading to the NBD form of P (N ). This is then confronted with the approach based on the so-called cascadestochastic formalism which is based on different types of recurrence relations defining P (N ). We demonstrate that a combination of both approaches allows the retrieval of additional valuable information from the multiplicity distributions, namely the oscillatory behavior of the counting statistics apparently visible in the high energy data.

Oscillations in counting statistics

“…One can see that only our MNBD fit reproduces the experimentally obtained coefficients C j . In [3] it is also shown that the amplitude of these oscillations decrease with the narrowing of the pseudo-rapidity window, |η|, in which the data are collected (eventually they vanish for small |η|) and that the same behavior is also observed for the ALICE data [6] (albeit with stronger oscillations in this case). A word of caution is in order at this point.…”

“…Both m(N) and the probability of particle emission p(N) are now non-monotonic functions of N (p(N) = const in the standard NBD). This non-monoticity is located in the region of small multiplicities N [3]. Note that such a spout-like form of the proposed modification is just one of the simplest possible choices of parametrization bringing agreement with data.…”

“…Instead we concentrate on another example of oscillations, this time connected with the multiplicity distributions, P(N). We demonstrate that some combinations of the experimentally measured values of P(N), calculated from recurrence relations widely used in the description of the cascade-stochastic processes in quantum optics, exhibit distinct oscillatory behavior not observed in the usual Negative Binomial Distributions used to fit data [3]. These oscillations provide therefore one more example of oscillations seen in counting statistics in many different, apparently very disparate, branches of physics, further demonstrating the universality of this phenomenon [3].…”

“…2, and still adhere to the single NBD form of P(N), one has to modify it. We provide such a modification in [3] (and call it the Modified Negative Binomial Distribution -MNBD). It consists of allowing the parameter m in Eq.…”

“…The important feature of Eq. ( 4) is that it can be easily inverted, i.e., knowing (for example, from the measurement process) all P(N), one can use this experimental information to deduce the corresponding C j by means of the following recurrence relation [3],…”