Integrals of Bessel functions
We use the operator method to evaluate a class of integrals involving Bessel or Bessel-type functions. The technique we propose is based on the formal reduction of these family of functions to Gaussians.
math.CA↗
arXiv subjects
D. Babusci
Publications and source records attributed to D. Babusci.
Observation of the rare eta->e+e-e+e- decay with the KLOE experiment
We report the first observation of the rare eta->e+e-e+e- decay based on 1.7 fb^{-1} collected by the KLOE experiment at the DAFNE phi-factory. The selection of the e+e-e+e- final state is fully inclusive of radiation. We have identified 362 +- 29 events resulting in a branching ratio of (2.4 +- 0.2_stat+bckg +- 0.1_syst) x 10^{-5}.
hep-ex↗
Measurement of $Γ(η\to π^+π^-γ)/Γ(η\to π^+π^-π^0)$ with KLOE experiment
We report the measurement of the ratio $Γ(η\to π^+π^-γ)/Γ(η\to π^+π^-π^0)$ analyzing a large sample of $ϕ\to ηγ$ decays recorded with the KLOE experiment at the DA$Φ$NE $e^+ e^-$ collider, corresponding to an integrated luminosity of 558 pb$^{-1}$. The $η\to π^+π^-γ$ process is supposed to proceed both via a resonant contribution, mediated by the $ρ$ meson, and a non resonant direct term, connected to the box anomaly. The presence of the direct term affects the partial width value. Our result $R_η=Γ(η\to π^+ π^- γ)/Γ(η\to π^+ π^- π^0)= 0.1838\pm 0.0005_{stat} \pm 0.0030_{syst}$ is in agreement with a recent CLEO measurement, which differs by more 3 $σ$ from the average of previous results.
hep-ex↗
The algebra of factorial polynomials
We discuss the formal aspects of the factorial polynomials and of the associated series. We develop the theory using the formalism of quasi-monomials and prove the usefulness of the method for the solutions of nontrivial difference equations.
math.AP↗
$γγ$ physics with the KLOE experiment
The processes $e^+e^-\to e^+e^-X$, with $X$ being either the $η$ meson or $π^0π^0$, are studied at DA$Φ$NE, with $e^+e^-$ beams colliding at $\sqrt{s}\simeq1$ GeV, below the $ϕ$ resonance peak. The data sample is from an integrated luminosity of 240 pb$^{-1}$, collected by the KLOE experiment without tagging of the outgoing $e^+e^-$. Preliminary results are presented on the observation of the $γγ\toη$ process, with both $η\toπ^+π^-π^0$ and $η\toπ^0π^0π^0$ channels, and the evidence for $γγ\toπ^0π^0$ production at low $π^0π^0$ invariant mass.
hep-ex↗
U boson searches at KLOE
The existence of a secluded gauge sector could explain several puzzling astrophysical observations. This hypothesis can be tested at low energy e+e- colliders such as DAPHNE. Preliminary results obtained with KLOE data and perpectives for the KLOE-2 run, where a larger data sample is expected, are discussed.
hep-ex↗
Relativistic equations with fractional and pseudo-differential operators
In this paper we use different techniques from the fractional and pseudo-operators calculus to solve partial differential equations involving operators with non integer exponents. We apply the method to equations resembling generalizations of the heat equations and discuss the possibility of extending the procedure to the relativistic Schrödinger and Dirac equations.
math-ph↗
A note on the extension of the Dirac method
In this note we extend the Dirac method to partial differential equations involving higher order roots of differential operators.
math-ph↗
The Ramanujan master theorem and its implications for special functions
We study a number of possible extensions of the Ramanujan master theorem, which is formulated here by using methods of Umbral nature. We discuss the implications of the procedure for the theory of special functions, like the derivation of formulae concerning the integrals of products of families of Bessel functions and the successive derivatives of Bessel type functions. We stress also that the procedure we propose allows a unified treatment of many problems appearing in applications, which can formally be reduced to the evaluation of exponential- or Gaussian-like integrals.
math-ph↗
On Ramanujan Master Theorem
In this short note we use the umbral formalism to derive the Ramanujan Master Theorem and discuss its extension to more general cases.
math-ph↗
Complex-type numbers and generalizations of the Euler identity
We consider different generalizations of the Euler formula and discuss the properties of the associated trigonometric functions. The problem is analyzed from different points of view and it is shown that it can be formulated in a natural way in algebraic and geometric terms.
math.CA↗
On integrals involving Hermite polynomials
We show how the combined use of the generating function method and of the theory of multivariable Hermite polynomials is naturally suited to evaluate integrals of gaussian functions and of multiple products of Hermite polynomials.
math-ph↗
Operational methods and Lorentz-type equations of motion
We propose an operational method for the solution of differential equations involving vector products. The technique we propose is based on the use of the evolution operator, defined in such a way that the wealth of techniques developed within the context of quantum mechanics can also be exploited for classical problems. We discuss the application of the method to the solution of the Lorentz-type equations.
math-ph↗
Generalization of the Airy function and the operational methods
In this brief note the operatorial methods are applied to the study of the Airy function and its generalizations.
math-ph↗
Integral equations, fractional calculus and shift operator
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the exponential shift operator.
math-ph↗
Proposal for taking data with the KLOE-2 detector at the DA$Φ$NE collider upgraded in energy
This document reviews the physics program of the KLOE-2 detector at DA$Φ$NE upgraded in energy and provides a simple solution to run the collider above the $ϕ$-peak (up to 2, possibly 2.5 GeV). It is shown how a precise measurement of the multihadronic cross section in the energy region up to 2 (possibly 2.5) GeV would have a major impact on the tests of the Standard Model through a precise determination of the anomalous magnetic moment of the muon and the effective fine-structure constant at the $M_Z$ scale. With a luminosity of about $10^{32}$cm$^{-2}$s$^{-1}$, DA$Φ$NE upgraded in energy can perform a scan in the region from 1 to 2.5 GeV in one year by collecting an integrated luminosity of 20 pb$^{-1}$ (corresponding to a few days of data taking) for single point, assuming an energy step of 25 MeV. A few years of data taking in this region would provide important tests of QCD and effective theories by $γγ$ physics with open thresholds for pseudo-scalar (like the $η'$), scalar ($f_0,f'_0$, etc...) and axial-vector ($a_1$, etc...) mesons; vector-mesons spectroscopy and baryon form factors; tests of CVC and searches for exotics. In the final part of the document a technical solution for the energy upgrade of DA$Φ$NE is proposed.
hep-ex↗
The Lamb-Bateman integral equation and the fractional derivatives
The Lamb-Bateman integral equation was introduced to study the solitary wave diffraction and its solution was written in terms of an integral transform. We prove that it is essentially the Abel integral equation and its solution can be obtained using the formalism of fractional calculus.
math-ph↗
Physics with the KLOE-2 experiment at the upgraded DA$ϕ$NE
Investigation at a $ϕ$--factory can shed light on several debated issues in particle physics. We discuss: i) recent theoretical development and experimental progress in kaon physics relevant for the Standard Model tests in the flavor sector, ii) the sensitivity we can reach in probing CPT and Quantum Mechanics from time evolution of entangled kaon states, iii) the interest for improving on the present measurements of non-leptonic and radiative decays of kaons and eta/eta$^\prime$ mesons, iv) the contribution to understand the nature of light scalar mesons, and v) the opportunity to search for narrow di-lepton resonances suggested by recent models proposing a hidden dark-matter sector. We also report on the $e^+ e^-$ physics in the continuum with the measurements of (multi)hadronic cross sections and the study of gamma gamma processes.
hep-ex↗