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Register a new userScaling of factorial moments in cumulative variables
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A search for power-law fluctuations within the framework of the intermittency method is ongoing to locate the critical point of the strongly interacting matter. In particular, experimental data on proton and pion production in heavy-ion collisions are analyzed in transverse-momentum, $p_T$, space. In this regard, we have studied the dependence of the second scaled factorial moment $F_2$ of particle multiplicity distribution on the number of subdivisions of transverse momentum-interval used in the analysis. The study is performed using a simple model with a power-law two-particle correlation function in $p_T$. We observe that $F_2$ values depend on the size and position of the $p_T$ interval. However, when we convert the non-uniform transverse-momentum distribution to uniform one using cumulative transformation, $F_2$ calculated in subdivisions of the cumulative $p_T$ becomes independent of the cumulative-$p_T$ interval. The scaling behaviour of $F_2$ for the cumulative variable is observed. Moreover, $F_2$ follows a power law with the number of subdivisions of the cumulative-$p_T$ interval with the intermittency index close to the correlation functions exponent.
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The effect of momentum resolution on factorial moments due to the power-law correlation function is studied. The study is motivated by the search for the critical point of the strongly interacting matter in heavy-ion collisions using the intermittency method. We observe that factorial moments are significantly affected by the finite momentum resolution. The effect is superficially significant compared to intuitive expectations. The results depend on the power of the correlation function and the number of uncorrelated particles.
We derive joint factorial moment identities for point processes with Papangelou intensities. Our proof simplifies previous approaches to related moment identities and includes the setting of Poisson point processes. Applications are given to random transformations of point processes and to their distribution invariance properties.
We study the factorial moments (Fq), the factorial cumulants (Kq) and the ratio of Kq to Fq (Hq = Kq=Fq) in pp/pp collisions using an updated approach, in which the multiplicity distribution is related to the eikonal function. The QCD inspired eikonal model adopted contains contributions of quark-quark, quark-gluon and gluon-gluon interactions. Our work shows that the approach can reproduce the collision energy dependence of the Fq moments, correctly predicts that the first minimum of the Hq lies around q = 5 and qualitatively reproduces the oscillations of the Hq moments, as shown in the experimental data and predicted by QCD at preasymptotic energy. The result of this study seems to indicate that the Hq oscillations are manifestation of semihard component in the multiparticle production process. Predictions for multiplicity distribution and Hq moments at the LHC energy of 14 TeV are presented.
We discuss properties and applications of factorial cumulants of various particle numbers and for their mixed channels measured by the event-by-event analysis in relativistic heavy-ion collisions. After defining the factorial cumulants for systems with multi-particle species, their properties are elucidated. The uses of the factorial cumulants in the study of critical fluctuations are discussed. We point out that factorial cumulants play useful roles in understanding fluctuation observables when they have underlying physics approximately described by the binomial distribution. As examples, we suggest novel utilization methods of the factorial cumulants in the study of the momentum cut and rapidity window dependences of fluctuation observables.
Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative probability distribution of the sum of some number of exponential variables, with potentially differing constants in their exponents. In this article we present a pedagogical derivation of the cumulative distribution, which reproduces the known formula from power density analyses in the limit that all of the constants are equal, and which assumes no prior knowledge of combinatorics except for some of the properties of a class of symmetric polynomials in $n$ variables (Schur polynomials).
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