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Register a new userCorrespondence of multiplicity and energy distributions
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The evaluation of the number of ways we can distribute energy among a collection of particles in a system is important in many branches of modern science. In particular, in multiparticle production processes the measurements of particle yields and kinematic distributions are essential for characterizing their global properties and to develop an understanding of the mechanism for particle production. We demonstrate that energy distributions are connected with multiplicity distributions by their generating functions.
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Multiplicity distributions exhibit, after closer inspection, peculiarly enhanced void probability and oscillatory behavior of the modified combinants. We discuss the possible sources of these oscillations and their impact on our understanding of the multiparticle production mechanism. Theoretical understanding of both phenomena within the class of compound distributions is presented.
Multiplicity distributions, P(N), provide valuable information on the mechanism of the production process. We argue that the observed P(N) contain more information (located in the small N region) than expected and used so far. We demonstrate that it can be retrieved by analysing specific combinations of the experimentally measured values of P(N) which we call {it modified combinants, Cj, and which show distinct oscillatory behavior, not observed in the usual phenomenological forms of the P(N) used to fit data. We discuss the possible sources of these oscillations and their impact on our understanding of the multiparticle production mechanism.
We study the modification of the multiplicity distributions in MLLA due to the presence of a QCD medium. The medium is introduced though a multiplicative constant ($f_{med}$) in the soft infrared parts of the kernels of QCD evolution equations. Using the asymptotic ansatz for quark and gluons mean multiplicities $<n_G>=e^{gamma y}$ and $<n_Q>=r^{-1}e^{gamma y}$ respectively, we study two cases: fixed $gamma$ as previously considered in the literature, and fixed $alpha_s$. We find opposite behaviors of the dispersion of the multiplicity distributions with increasing $f_{med}$ in both cases. For fixed $gamma$ the dispersion decreases, while for fixed $alpha_s$ it increases.
The unitarity of the $S$-matrix requires that the absorptive part of the elastic scattering amplitude receives contributions from both the inelastic and the elastic channels. We explore this unitarity condition in order to describe, in a connected way, hadron-hadron observables like the total and elastic differential cross sections, the ratio of the real to imaginary part of the forward scattering amplitude and the inclusive multiplicity distributions in full phase space, over a large range of energies. We introduce non-perturbative QCD effects in the forward scattering amplitude by using the infrared QCD effective charge dependent on the dynamical gluon mass. In our analysis we pay special attention to the theoretical uncertainties in the predictions due to this mass scale variation. We also present quantitative predictions for the $H_{q}$ moments at high energies. Our results reproduce the moment oscillations observed in experimental data, and are consistent with the behavior predicted by QCD.
As shown recently, one can obtain additional information from the measured multiplicity distributions, $P(N)$, by extracting the so-called modified combinants, $C_j$. This information is encoded in their specific oscillatory behavior, which can be described only by some combinations of compound distributions, the basic part of which is the Binomial Distribution. So far this idea was applied to $pp$ and $pbar{p}$ processes; in this note we show that an even stronger effect is observed in the $C_j$ deduced from $e^+e^-$ collisions. We present its possible explanation in terms of the so called Generalised Multiplicity Distribution (GMD) proposed some time ago.
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