Analytical Representation of the Longitudinal Hadronic Shower Development

The analytical representation of the longitudinal hadronic shower development from the face of a calorimeter is presented and compared with experimental data. The suggested formula is particularly useful at designing, testing and calibration of huge calorimeter complex like in ATLAS at LHC.Comment: 5 pages, 1 figur

On Poisson–Tweedie mixtures

Poisson-Tweedie mixtures are the Poisson mixtures for which the mixing measure is generated by those members of the family of Tweedie distributions whose support is non-negative. This class of non-negative integer-valued distributions is comprised of Neyman type A, back-shifted negative binomial, compound Poisson-negative binomial, discrete stable and exponentially tilted discrete stable laws. For a specific value of the “power” parameter associated with the corresponding Tweedie distributions, such mixtures comprise an additive exponential dispersion model. We derive closed-form expressions for the related variance functions in terms of the exponential tilting invariants and particular special functions. We compare specific Poisson-Tweedie models with the corresponding Hinde-Demétrio exponential dispersion models which possess a comparable unit variance function. We construct numerous local approximations for specific subclasses of Poisson-Tweedie mixtures and identify Lévy measure for all the members of this three-parameter family

Non-Compensation of the Barrel Tile Hadron Module-0 Calorimeter

The detailed experimental information about the electron and pion responses, the electron energy resolution and the e/h ratio as a function of incident energy E, impact point Z and incidence angle $\Theta$ of the Module-0 of the iron-scintillator barrel hadron calorimeter with the longitudinal tile configuration is presented. The results are based on the electron and pion beams data for E = 10, 20, 60, 80, 100 and 180 GeV at $\eta$ = -0.25 and -0.55, which have been obtained during the test beam period in 1996. The results are compared with the existing experimental data of TILECAL 1m prototype modules, various iron-scintillator calorimeters and with some Monte Carlo calculations.Comment: 33 pages, 20 figure

Non-compensation of an Electromagnetic Compartment of a Combined Calorimeter

The method of extraction of the $e/h$ ratio, the degree of non-compensation, of the electromagnetic compartment of the combined calorimeter is suggested. The $e/h$ ratio of $1.74\pm0.04$ has been determined on the basis of the 1996 combined calorimeter test beam data. This value agrees with the prediction that $e/h > 1.7$ for this electromagnetic calorimeter.Comment: LATEX, 17 pages, 7 figure

Longitudinal Hadronic Shower Development in a Combined Calorimeter

This work is devoted to the experimental study of the longitudinal hadronic shower development in the ATLAS barrel combined prototype calorimeter consisting of the lead-liquid argon electromagnetic part and the iron-scintillator hadronic part. The results have been obtained on the basis of the 1996 combined test beam data which have been taken on the H8 beam of the CERN SPS, with the pion beams of 10, 20, 40, 50, 80, 100, 150 and 300 GeV/c. The degree of description of generally accepted Bock parameterization of the longitudinal shower development has been investigated. It is shown that this parameterization does not give satisfactory description for this combined calorimeter. Some modification of this parameterization, in which the e/h ratios of the compartments of the combined calorimeter are used, is suggested and compared with the experimental data. The agreement between such parameterization and the experimental data is demonstrated.Comment: Latex, 21 pages, 10 figure

The evaluation of a weighted sum of Gauss hypergeometric functions and its connection with Galton–Watson processes

We evaluate a weighted sum of Gauss hypergeometric functions for certain ranges of the argument, weights and parameters. We establish the domain of absolute convergence of this series by determining the growth of the hypergeometric function for large summation index. We present an application to Galton–Watson branching processes arising in the theory of stochastic processes. We introduce a new class of positive integer-valued distributions with power tails

Low-temperature specific heat of real crystals: Possibility of leading contribution of optical and short-wavelength acoustical vibrations

We point out that the repeatedly reported glass-like properties of crystalline materials are not necessarily associated with localized (or quasilocalized) excitations. In real crystals, optical and short-wavelength acoustical vibrations remain damped due to defects down to zero temperature. If such a damping is frequency-independent, e.g. due to planar defects or charged defects, these optical and short-wavelength acoustical vibrations yield a linear-in-$T$ contribution to the low-temperature specific heat of the crystal lattices. At low enough temperatures such a contribution will prevail over that of the long-wavelength acoustical vibrations (Debye contribution). The crossover between the linear and the Debye regime takes place at $T^* \propto \sqrt N$, where $N$ is the concentration of the defects responsible for the damping. Estimates show that this crossover could be observable.Comment: 5 pages. v4: Error in Appendix corrected, which does not change the main results of the pape

The e/h Method of Energy Reconstruction for Combined Calorimeter

The new simple method of the energy reconstruction for a combined calorimeter, which we called the e/h method, is suggested. It uses only the known e/h ratios and the electron calibration constants and does not require the determination of any parameters by a minimization technique. The method has been tested on the basis of the 1996 test beam data of the combined calorimeter and demonstrated the correctness of the reconstruction of the mean values of energies. The obtained fractional energy resolution is $[(58\pm3)$. This algorithm can be used for the fast energy reconstruction in the first level trigger

Lie conformal algebra cohomology and the variational complex

We find an interpretation of the complex of variational calculus in terms of the Lie conformal algebra cohomology theory. This leads to a better understanding of both theories. In particular, we give an explicit construction of the Lie conformal algebra cohomology complex, and endow it with a structure of a g-complex. On the other hand, we give an explicit construction of the complex of variational calculus in terms of skew-symmetric poly-differential operators.Comment: 56 page