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D. Babusci

Publications and source records attributed to D. Babusci.

At least 55 records · Page 3Linked to original sources
arXiv2012

The spherical Bessel and Struve functions and operational methods

We review some aspects of the theory of spherical Bessel functions and Struve functions by means of an operational procedure essentially of umbral nature, capable of providing the straightforward evaluation of their definite integrals and of successive derivatives. The method we propose allows indeed the formal reduction of these family of functions to elementary ones of Gaussian type. We study the problem in general terms and present a formalism capable of providing a unifying point of view including Anger and Weber functions too. The link to the multi-index Bessel functions is also briefly discussed.

math.CA↗
arXiv2012

Measurement of Γ(η-> π^+π^-γ)/Γ(η-> π^+π^-π^0) with the KLOE Detector

The ratio R_η=Γ(η-> π^+π^-γ)/Γ(η-> π^+π^-π^0) has been measured by analyzing 22 million ϕ\to ηγdecays collected by the KLOE experiment at DA\PhiNE, corresponding to an integrated luminosity of 558 pb^{-1}. The η\to π^+π^-γproceeds both via the ρresonant contribution, and possibly a non-resonant direct term, connected to the box anomaly. Our result, R_η= 0.1856\pm 0.0005_{stat} \pm 0.0028_{syst}, points out a sizable contribution of the direct term to the total width. The di-pion invariant mass for the η-> π^+π^-γdecay could be described in a model-independent approach in terms of a single free parameter, α. The determined value of the parameter αis α= (1.32 \pm 0.08_{stat} +0.10/-0.09_{syst}\pm 0.02_{theo}) GeV^{-2}

hep-ex↗
arXiv2012

Definite integrals and operational methods

An operatorial method, already employed to formulate a generalization of the Ramanujan master theorem, is applied to the evaluation of integrals of various type. This technique provide a very flexible and powerful tool yielding new results encompassing various aspects of the special function theory.

math.CA↗
arXiv2012

Exploring quantum vacuum with low-energy photons

Although quantum mechanics (QM) and quantum field theory (QFT) are highly successful, the seemingly simplest state -- vacuum -- remains mysterious. While the LHC experiments are expected to clarify basic questions on the structure of QFT vacuum, much can still be done at lower energies as well. For instance, experiments like PVLAS try to reach extremely high sensitivities, in their attempt to observe the effects of the interaction of visible or near-visible photons with intense magnetic fields -- a process which becomes possible in quantum electrodynamics (QED) thanks to the vacuum fluctuations of the electronic field, and which is akin to photon-photon scattering. PVLAS is now close to data-taking and if it reaches the required sensitivity, it could provide important information on QED vacuum. PVLAS and other similar experiments face great challenges as they try to measure an extremely minute effect. However, raising the photon energy greatly increases the photon-photon cross-section, and gamma rays could help extract much more information from the observed light-light scattering. Here we discuss an experimental design to measure photon-photon scattering close to the peak of the photon-photon cross-section, that could fit in the proposed construction of an FEL facility at the Cabibbo Lab near Frascati (Rome, Italy).

physics.ins-det↗
arXiv2012

Relativistic harmonic oscillator

We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique is used to solve the associated Liouville equations, yielding the phase space evolution of an ensemble of relativistic particles, subject to a "harmonic" potential. The non-harmonic distortion of the spatial and momentum distributions due to the intrinsic non-linear nature of the relativistic contributions are discussed. We analyze the relativistic dynamics induced by two types of Hamiltonian, which can ascribed to those of harmonic oscillators type. Finally, we briefly discuss the quantum aspects of the problem by considering possible strategies for the solution of the associated Salpeter equation.

math-ph↗
arXiv2012

On the logarithm of the derivative operator

We study the properties of the logarithm of the derivative operator and show that its action on a constant is not zero, but yields the sum of the logarithmic function and the Euler-Mascheroni constant. We discuss more general aspects concerning the logarithm of an operator for the study of the properties of the Bessel functions.

math.CA↗
arXiv2012

Dirac factorization and fractional calculus

We show that the Dirac factorization method can be successfully employed to treat problems involving operators raised to a fractional power. The technique we adopt is based on an extension of the Pauli matrices and the properties of the roots of unity. We also comment about the possibility of using the method to linearize evolution equations containing the $n$-th root of differential operators and make a comparison with other techniques involving suitable transforms.

math-ph↗
arXiv2012

Chebyshev polynomials and generalized complex numbers

The generalized complex numbers can be realized in terms of $2\times2$ or higher-order matrices and can be exploited to get different ways of looking at the trigonometric functions. Since Chebyshev polynomials are linked to the power of matrices and to trigonometric functions, we take the quite natural step to discuss them in the context of the theory of generalized complex numbers. We also briefly discuss the two-variable Chebyshev polynomials and their link with the third-order Hermite polynomials.

math.CA↗
arXiv2012

On Mittag-Leffler function and associated polynomials

The Mittag-Leffler function plays a role of central importance in the theory of fractional derivatives. In this brief note we discuss the properties of this function and its connection with the Wright-Bessel functions and with a new family of associated heat polynomials.

math-ph↗
arXiv2012

The KLOE-2 High Energy Tagger Detector

In order to fully reconstruct to the reaction e+e- to e+e- gamma-gamma in the energy region of the phi meson production, new detectors along the DAFNE beam line have to be installed in order to detect the scattered e+e-. The High Energy Tagger (HET) detector measures the deviation of leptons from their main orbit by determining their position and timing so to tag gamma-gamma physics events and disentangle them from background. The HET detectors are placed at the exit of the DAFNE dipole magnets, 11 m away from the IP, both on positron and electron lines. The HET sensitive area is made up of a set of 28 plastic scintillators. A dedicated DAQ electronics board based on a Xilinx Virtex-5 FPGA have been developed for this detector. It provides a MultiHit TDC with a time resolution of the order of 500 ps and the possibility to acquire data any 2.5 ns, thus allowing to clearly identify the correct bunch crossing. First results of the commissioning run are presented.

physics.ins-det↗
arXiv2012

Operator solutions for fractional Fokker-Planck equations

We obtain exact results for fractional equations of Fokker-Planck type using evolution operator method. We employ exact forms of one-sided Levy stable distributions to generate a set of self-reproducing solutions. Explicit cases are reported and studied for various fractional order of derivatives, different initial conditions, and for different versions of Fokker-Planck operators.

cond-mat.stat-mech↗
arXiv2012

The Dirac factorization method and the harmonic oscillator

We apply the Dirac factorization method to the nonrelativistic harmonic oscillator and, more in general, to Hamiltonians with a generic potential. It is shown that this procedure naturally leads to a supersymmetric formulation of the problems under study. It is also speculated on the physical meaning underlying this method and it is suggested that the vacuum field fluctuations can be viewed as the spontaneous emission of the associated two-level system, whose quantization is due to the noncommuting nature of the harmonic oscillator canonical variables.

math-ph↗
arXiv2012

On the possibility to measure the (pi0 to gamma gamma) decay width and the (gamma* gamma to pi0) transition form factor with the KLOE-2 experiment

A possibility of KLOE-2 experiment to measure the width Gamma(pi0 to gamma gamma) and the (pi0 gamma gamma*) form factor F(Q^2) at low invariant masses of the virtual photon in the space-like region is considered. This measurement is an important test of the strong interaction dynamics at low energies. The feasibility is estimated on the basis of a Monte-Carlo simulation. The expected accuracy for Gamma(pi0 to gamma gamma) is at a per cent level, which is better than the current experimental world average and theory. The form factor will be measured for the first time at Q^2 less or equal 0.1 GeV^2 in the space-like region. The impact of these measurements on the accuracy of the pion-exchange contribution to the hadronic light-by-light scattering part of the anomalous magnetic moment of the muon is also discussed.

hep-ph↗
arXiv2011

Repeated derivatives of composite functions and generalizations of the Leibniz rule

We use the properties of Hermite and Kampé de Fériet polynomials to get closed forms for the repeated derivatives of functions whose argument is a quadratic or higher-order polynomial. The results we obtain are extended to product of functions of the above argument, thus giving rise to expressions which can formally be interpreted as generalizations of the familiar Leibniz rule. Finally, examples of practical interest are discussed.

math.CA↗
arXiv2011

Umbral methods and operator ordering

By using methods of umbral nature, we discuss new rules concerning the operator ordering. We apply the technique of formal power series to take advantage from the wealth of properties of the exponential operators. The usefulness of the obtained results in quantum field theory is discussed.

math-ph↗
arXiv2011

On evaluation of integrals involving Bessel functions

We introduce a symbolic method for the evaluation of definite integrals containing combinations of various functions, including exponentials, logarithm and products of Bessel functions of different types. The method we develop is naturally suited for the evaluation of integrals associated with specific Feynman diagrams.

math.CA↗