Anomalous dimensions in multiparticle collisions and the empty bin effect

Using the random cascade model, we systematically analyze various conditions where realistic multiparticle distributions from cascading processes are affected by systematic and statistical biases at high resolution. We show, both analytically and numerically, that the effect of such conditions (empty bin effect) is to produce, in some cases, a modification of the power law of factorial moments as a function of the bin size that is, of the anomalous dimensions governing the dynamical fluctuations. We examine how these may influence the intermittency analysis of multiparticle data. Simulations based on the -model parametrization of random cascading are suggested to take into account the empty bin effects in the intermittency analysis. A systematic comparison of the fluctuation effects of known distributions, including the log-normal, negative binomial and Lévy-stable laws is performed in terms of the anomalous dimensions, in view of their use as useful approximations.Supported by the World Laboratory/HED and the CERN/LAA Projects     

Quasi-Gaussian fixed points and factorial cumulants in nuclear multifragmentation

We re-analyze the conditions for the phenomenon of intermittency (self-similar fluctuations) to occur in models of multifragmentation. Analyzing two different mechanisms, the bond-percolation and the ERW (Elattari, Richert and Wagner) statistical fragmentation models, we point out a common quasi-Gaussian shape of the total multiplicity distribution in the critical range. The fixed-point property is also observed for the multiplicity of the second bin. Fluctuations are studied using scaled factorial cumulants instead of scaled factorial moments. The second-order cumulant displays the intermittency signal while higher order cumulants are equal to zero, revealing a large information redundancy in scaled factorial moments. A practical criterion is proposed to identify the Gaussian feature of light-fragment production, distinguishing between a self-similarity mechanism (ERW) and the superposition of independent sources (percolation).     

Intermittency in 3.7 A GeV ^16O-emulsion interactions

The intermittency effect has been studied for an interaction of 3.7 A GeV ^16O with emulsion using the distributions of both the pseudorapidity intervals and the azimuthal angle intervals of the shower particles emitted in a central rapidity region. The scaled factorial moments, reduced scaled factorial moments and multifractal moments as functions of the bin size in pseudorapidity and in azimuthal angle have been calculated and have revealed the presence of an intermittent behaviour which may be due to the random cascading property of the reaction. The anomalous fractal dimension has been found to increase with the increase of rank of the moment.     

高能碰撞多粒子末态间歇现象与关联积分的研究

用理论分析和Monte Carlo模拟表明:研究间歇现象时用关联积分代替阶乘矩的统计会改变快度bin减小时的反常标度行为. 指出,关联函数积分与阶乘矩可能分别反映不同的物理内容.提出了一种随机移动分bin起点的统计阶乘矩方法以消除分bin造成的人为因素.证明了,“钉子”事件对间歇指数有重要贡献.     

Intermittency in the Ginzburg-Landau model for parton-hadron phase transitions

The formalism of squeezed states within Ginzburg-Landau theory is used to describe parton-hadron phase transitions in processes involving the production of rather high energy densities. Normalized factorial moments are studied as functions of a bin width of phase space at various squeezing parameters. The intermittency effect and scaling behavior of the moments under consideration are revealed. The values obtained for the scaling exponent agree with experimental data at small values of the squeezing parameter.     

Intermittency and correlations in hadronic Z^0 decays

A multidimensional study of local multiplicity fluctuations and multiparticle correlations of hadrons produced in Z decays is performed. The study is based on the data sample of more than events recorded with the OPAL detector at LEP. The fluctuations and correlations are analysed in terms of the normalized scaled factorial moments and cumulants up to the fifth order. The moments are observed to have intermittency-like behaviour, which is found to be more pronounced with increasing dimension. The large data sample allows for the first time a study of the factorial cumulants in annihilation. The analysis of the cumulants shows the existence of genuine multiparticle correlations with a strong intermittency rise up to higher orders. These correlations are found to be stronger in higher dimensions. The decomposition of the factorial moments into lower-order correlations shows that the dynamical fluctuations have important contributions from genuine many-particle correlations. The Monte Carlo models Jetset 7.4 and Herwig 5.9 are found to reproduce the trend of the measured moments and cumulants but they underestimate the magnitudes. The results are found to be consistent with QCD jet formation dynamics, although additional contributions from other mechanisms cannot be excluded. Received: 8 February 1999 / Published online: 8 September 1999     

Angular intermittency in QCD jets

Using two methods, via fluctuations and correlations, an analytical formula is derived for the factorial multiplicity moments in a QCD jet at the Double Leading Logarithm accuracy. The resulting self-similar dependence on the solid-angle cell size is characteristic of an intermittency behaviour in angular variables. The intermittency indices depend on the diffusion angle through the running of α_S. Physical features of jet fluctuations such as collimation at large angles and saturation at small angles are well described in the perturbative framework. A parameter-free prediction of angular intermittency is proposed for Z⁰ decays into hadrons, assuming hadronparton duality.

     

高能非线性现象研究的新进展

经典色动力学有混沌解,但是量子混沌是一个困难的理论问题,因而高能物理中的非线性目前还只能用唯象方法进行研究.80年代末,实验观察到多粒子未态相空间中有局域大起伏,激发了对高能非线性现象——间歇与分形研究的热潮.实验发现,一维阶乘矩有饱和现象,这被解释为高维间歇投影到低维的结果;但是,三维阶乘矩也并没有严格的反常标度性.这一困难在一段时间里曾使得间歇(分形)的研究陷于停顿.以后发现,其原因在于高能多粒子未态相空问高度各向异性,因而相应的分形是自仿射分形.只有对相空间进行正确的各向异性分割,才能观察到反常标度性.这一预言已在NA22和NA27的实验数据中得到证实,成功地观察到了反常标度性,从而使高能非线性的研究取得突破性进展.本文介绍这一进展,并作一些讨论.     

Intermittency and scaling relations

We show that to a very good approximation there exists in general an equivalence between intermittency and the assumption that the first factorial correlatorF ₁₁ is independent of bin size. We further show that strict bin size independence imposes for the possible values of the intermittency index?, ?=0, or?=1.     

Investigation of intermittency in muon-proton scattering at 280 GeV

In this paper intermittency is investigated in hadron production by muon proton interactions at 280 GeV, using data of the European Muon Collaboration. Intermittent behaviour is observed in the dependence of the scaled factorial moments on the rapidity bin width. This behaviour is stronger for positive than for all charged hadrons; it increases with the hadronic cms energyW, and is larger in the central region than in the fragmentation regions. The data are compared with the predictions of the Webber model, the Lund model, and of short-range ordering     

Event-by-event efficiency fluctuations and efficiency correction for cumulants of superposed multiplicity distributions in relativistic heavy-ion collision experiments

We performed systematic studies on the effects of event-by-event efficiency fluctuations on efficiency correction for cumulant analysis in relativistic heavy-ion collision experiments. Experimentally, particle efficiencies of events measured under different experimental conditions should be different. For fluctuation measurements, the final event-by-event multiplicity distributions should be the superposed distributions of various type of events measured under different conditions. We demonstrate efficiency fluctuation effects using numerical simulation, in which we construct an event ensemble consisting of events with two different efficiencies. By using the mean particle efficiencies, we find that the efficiency corrected cumulants show large deviations from the original inputs when the discrepancy between the two efficiencies is large. We further studied the effects of efficiency fluctuations for the cumulants of net-proton distributions by implementing the UrQMD events of Au+Au collisions at sNN~(1/2) = 7.7 GeV in a realistic STAR detector acceptance. We consider the unequal efficiency in two sides of the Time Projection Chamber(TPC), multiplicity dependent efficiency, and the event-by-event variations of the collision vertex position along the longitudinal direction(V_z). When the efficiencies fluctuate dramatically within the studied event sample,the effects of efficiency fluctuations have significant impacts on the efficiency corrections of cumulants with the mean efficiencies. We find that this effect can be effectively suppressed by binning the entire event ensemble into various sub-event samples, in which the efficiency variations are relatively small. The final efficiency corrected cumulants can be calculated from the weighted average of the corrected factorial moments of the sub-event samples with the mean efficiencies.     

Intermittency and fractals in nuclear collisions at 1.52 A GeV

The techniques of scaled factorial moments and multifractals have been employed to study the dynamical fluctuations of the produced singly charged particles in collisions of⁸⁴Kr ions at 1.52 A GeV in nuclear emulsion. The power law behaviors are observed in the data. The generalized dimensions are determined by using the methods of intermittency and multifractals.     

α模型中不固定多重数下的阶乘矩、粒子数关联矩

利用二维相空间自仿射分形的随机级联α模型,采用蒙特卡罗模拟的方法,研究了阶乘矩､粒子数关联矩在不固定多重数下,对应于多重数相对起伏强度n_f的依赖关系,得到:阶乘矩、粒子数关联矩依赖于多重数相对起伏n_f,但间歇指数一般不依赖于n_f,当n_f较小时这种依赖性得以消除.     

Moment analysis and Zipf law

The moment analysis method and nuclear Zipf's law of fragment size distributions are reviewed to study nuclear disassembly. In this report, we present a compilation of both theoretical and experimental studies on moment analysis and Zipf law performed so far. The relationship of both methods to a possible critical behavior or phase transition of nuclear disassembly is discussed. In addition, scaled factorial moments and intermittency are reviewed.     

Factorial Moments and Factorial Correlations in α Model for Non-Fixing Multiplicity

Using the self-affine fractal of two-dimensional phase space and Monte Carlo simulation, the dependence of the factorial moments and the factorial correlations on the multiplicity relative strength of fluctuation are studied for non-fixing multiplicity. It is discovered that the factorial moments and the factorial correlations depend on the muldplicity relative strength of fluctuation n_f, but the intermittency does not depend on n_f When n_f is smaller, these dependence are dispelled.     

Fluctuations of moments of density in random cascade models

It is suggested that measurements of fluctuations of the moments of particle density may be helpful in the search for the origin of intermittency. These fluctuations are calculated for the random cascade model. They are related to the moments themselves by relations, which do not depend on the parameters of the model and thus provide a valuable test of random cascading. A simple method of comparing the predictions with experiment is proposed.     

Comparison of particle production in Pb(158 GeV/nucleon)-AgBr collisions with the VENUS and FRITIOF models

Data on multiparticle production in interactions of 158 GeV/nucleon lead ions with the heavy nuclei in emulsions (Ag,Br) are compared with the predictions of the VENUS and FRITIOF models. It is found that total multiplicities of produced charged particles are reasonably well reproduced by both models. On the other hand, discrepancies between the data and the predictions are observed for the forward charge and pseudorapidity distributions. Furthermore, dynamical fluctuations, revealed in the data by application of the method of factorial moments, are absent from the model simulations. The dynamical fluctuations observed in the data can be at least partly due to Bose-Einstein correlations.     

Intermittency or Something Else in High Dimensions

A regular two-particle correlation function is proposed to explain the intermittency behavior in pp collision at √3= 630 GeV. It is found that the intermittency behaviors in all dimensions in the experiments can be reproduced with a regular two-particle correlation function. Maybe the existence of intermittency in a serious sense in high dimensions is still a puzzle and the factorid moments of order-two would saturate in the limit of small bin sizes of phase space in high dimensions at last.     

Quadrupole moments of medium-weight and heavy hypernuclei with the NΛ configurations (N = p and n)

Using the shell model wave functions, we have studied quadrupole moments of medium-weight and heavy hypernuclei, and obtained the shell model values of quadrupole moments of NΛ systems ( N = p and n). With the use of the first-order perturbation theory, we have also estimated the configuration mixing effects on quadrupole moments of these NΛ hypernuclei. We show that the hyperon-induced configuration mixing effects are small and the nucleon-induced configuration mixing effects are large in many cases. Received: 22 February 2000 / Accepted: 2 August 2000     

Multiplicity fluctuations of pions and protons at SPS energy — An in-depth analysis with factorial correlator

We compute the factorial correlators to study the dynamical fluctuations of pions and a combination of pions and protons (compound multiplicity) in ³²S-AgBr interactions at 200 A GeV. The study reveals that for both pion and compound multiplicity the correlated moments increase with the decrease in bin-bin separation D, following a power-law, which suggests the self-similarity of multiplicity fluctuation in each case. The results of the analysis also show a consistency with the prediction of α-model for the existence of intermittency in both cases.