Analysis of variances of quasirapidities in collisions of gold nuclei with track-emulsion nuclei
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EMENTARY PARTICLES AND FIELDS Theory
Analysis of Variances of Quasirapidities in Collisions of Gold Nuclei with Track-Emulsion Nuclei K. G. Gulamov, S. I. Zhokhova, V. V. Lugovoi*, V. S. Navotny** , N. S. Saidkhanov, and V. M. Chudakov Physical–Technical Institute, Fizika–Solntse Research and Production Association, Uzbek Academy of Sciences, ul. Mavlyanova 2b, Tashkent, 700084 Republic of Uzbekistan Received June 16, 2011; in final form, October 12, 2011
Abstract—A new method of an analysis of variances was developed for studying n-particle correlations of quasirapidities in nucleus–nucleus collisions for a large constant number n of particles. Formulas that generalize the results of the respective analysis to various values of n were derived. Calculations on the basis of simple models indicate that the method is applicable, at least for n ≥ 100. Quasirapidity correlations statistically significant at a level of 36 standard deviations were discovered in collisions between gold nuclei and track-emulsion nuclei at an energy of 10.6 GeV per nucleon. The experimental data obtained in our present study are contrasted against the theory of nucleus–nucleus collisions. DOI: 10.1134/S1063778812040059
1. INTRODUCTION A comparison of the results of Monte Carlo calculations with experimental data on the distribution of rapidities and their correlations is a widespread method for testing models of multiparticle hadron production. The mathematical-statistics method known as an analysis of variances was used in [1, 2], and a coherent diffractive dissociation of baryons was discovered for the first time with the aid of this method. A large number N of events featuring the same small number n of secondary particles were studied there. In the present study, we apply an analysis of variances of quasirapidities in exploring their correlations and extend it to the case of nucleus– nucleus collisions for various large values of n at a large total number of events but a small number N of events characterized by the same multiplicity n. We also propose a new method for an analysis of variances. 2. RATIO OF VARIANCES In the theory of an analysis of variances, use is made of the quantity F = nS12 /S22 ,
(1)
where S12 = (N − 1)−1
N (ηi − η)2 , i=1
* **
E-mail: [email protected] E-mail: [email protected]
(2)
S22 = N −1
N
⎡ −1
⎣(n − 1)
i=1
ηi = n
−1
n
⎤ n (ηij − ηi )2 ⎦ , j=1
ηij ,
η = N
−1
N
j=1
ηi ,
(3)
i=1
N is the total number of events characterized by the same multiplicity n, and ηij is the quasirapidity of the jth particle in the ith event. In the case of N = ∞, events of the same multiplicity n form an ensemble called a general set of independent events. In the case of a random numbering of particles in an event, n quantities ηj are distributed identically. If they are independent of one another, then the ratio of variances is F = 1 for N = ∞. Let us consider a nonuniform ensemble of particles. One can readily break it down into subensembles differing in the rapidity distribution of secondary particle
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