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143 results on '"Celeghini, Enrico"'

1. Gelfand Triplets, Continuous and Discrete Bases and Legendre Polynomials

Author

Celeghini, Enrico, Gadella, Manuel, and del Olmo, Mariano A.

Subjects
Mathematical Physics, 33C50, 46E20
Abstract

We consider a basis of square integrable functions on a rectangle, contained in $R^2$, constructed with Legendre polynomials, suitable, for instance, for the analogical description of images on the plane or in other fields of application of the Legendre polynomials in higher dimensions. After extending the Legendre polynomials to any arbitrary interval of the form [a,b], from its original form on [-1,1], we generalize the basis of Legendre polynomials to two dimensions. This is the first step to generalize the basis to n-dimensions. We present some mathematical constructions such as Gelfand triples appropriate on this context. ``Smoothness'' of functions on space of test functions and some other properties are revisited, as well as te continuity of generators of $su(1,1)$ on this context., Comment: 18 pages, 8 figures

Published
2023

2. Hermite functions and Fourier series

Author

Celeghini, Enrico, Gadella, Manuel, and del Olmo, Mariano. A.

Subjects
Mathematical Physics, Mathematics - Functional Analysis, 42C10, 42A38, 46E20, 46E30
Abstract

Using normalized Hermite functions, we construct bases in the space of square integrable functions on the unit circle ($L^2(\mathcal C)$) and in $l_2(\mathbb Z)$, which are related to each other by means of the Fourier transform and the discrete Fourier transform. These relations are unitary. The construction of orthonormal bases requires the use of the Gramm--Schmidt method. On both spaces, we have provided ladder operators with the same properties as the ladder operators for the one-dimensional quantum oscillator. These operators are linear combinations of some multiplication- and differentiation-like operators that, when applied to periodic functions, preserve periodicity. Finally, we have constructed riggings for both $L^2(\mathcal C)$ and $l_2(\mathbb Z)$, so that all the mentioned operators are continuous., Comment: 29 pages

Published
2020

3. Zernike functions, rigged Hilbert spaces and potential applications

Author

Celeghini, Enrico, Gadella, Manuel, and del Olmo, Mariano A

Subjects
Mathematical Physics, Physics - Optics
Abstract

We revise the symmetries of the Zernike polynomials that determine the Lie algebra su(1,1) + su(1,1). We show how they induce discrete as well continuous bases that coexist in the framework of rigged Hilbert spaces. We also discuss some other interesting properties of Zernike polynomials and Zernike functions. One of the interests of Zernike functions has been their applications in optics. Here, we suggest that operators on the spaces of Zernike functions may play a role in optical image processing., Comment: 16 pages, 9 figures

Published
2019
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4. Theory of Images and Quantum Mechanics, a common Paradigm

Author

Celeghini, Enrico

Subjects
Physics - General Physics, Quantum Physics
Abstract

The Paradigms introduced in philosophy of science one century ago are shown to be quite more satisfactory of that introduced by Galileo. This is particularly evident in the physics based on Hilbert Spaces and related mathematical structures that we apply in this paper to Quantum Mechanics and to Theory of Images. An exhaustive discussion, that include the algebraic analysis of the operators acting on them, exhibits that the Hilbert Spaces -- that have fixed dimension -- must be generalized to the Rigged Hilbert Spaces that contains right inside spaces with continuous and discrete dimensions. This is the property of Rigged Hilbert Spaces that allows a consistent formal description of the physics we are considering. Theory of Quantum Mechanics and of Images are similar and the fundamental difference between them come from the definition of measure that is outside the theory of the spaces: while in Quantum Mechanics the measure is a probabilistic action, in Images it is a classical functional. KEYWORDS: Optics, Quantum Mechanics, Rigged Hilbert Spaces, Lie Algebras, Comment: 11 pages, 0 figures Submitted to Journal of Physics: Conferences Series

Published
2019
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5. Hermite functions, Lie groups and Fourier analysis

Author

Celeghini, Enrico, Gadella, Manuel, and del Olmo, Mariano A.

Subjects
Mathematical Physics, Quantum Physics, 42A16, 42C10, 46E20, 22D10, 81P16
Abstract

In this paper, we present recent results in harmonic analysis in the real line R and in the half-line R^+, which show a closed relation between Hermite and Laguerre functions, respectively, their symmetry groups and Fourier analysis. This can be done in terms of a unified framework based in the use of rigged Hilbert spaces. We find a relation between the universal enveloping algebra of the symmetry groups with the fractional Fourier transform. The results obtained are relevant in quantum mechanics as well as in signal processing as Fourier analysis has a close relation with signal filters. Also, we introduce some new results concerning a discretized Fourier transform on the circle. We introduce new functions on the circle constructed with the use of Hermite functions with interesting properties under Fourier transformations., Comment: 18 pages

Published
2018
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6. Lie algebra representations and rigged Hilbert spaces: the SO(2) case

Author

Celeghini, Enrico, Gadella, Manuel, and del Olmo, Mariano A

Subjects
Mathematical Physics, Quantum Physics, 81Q99, 46C99, 22C05
Abstract

It is well known that related with the irreducible representations of the Lie group $SO(2)$ we find a discrete basis as well a continuous one. In this paper we revisited this situation under the light of Rigged Hilbert spaces, which are the suitable framework to deal with both discrete and bases in the same context and in relation with physical applications., Comment: 12

Published
2017

7. Algebraic Image Processing

Author

Celeghini, Enrico

Subjects
Electrical Engineering and Systems Science - Image and Video Processing, Computer Science - Computer Vision and Pattern Recognition
Abstract

We propose an approach to image processing related to algebraic operators acting in the space of images. In view of the interest in the applications in optics and computer science, mathematical aspects of the paper have been simplified as much as possible. Underlying theory, related to rigged Hilbert spaces and Lie algebras, is discussed elsewhere, Comment: 8 pages

Published
2017

8. SU(2), Associated Laguerre Polynomials and Rigged Hilbert Spaces

Author

Celeghini, Enrico, Gadella, Manuel, and del Olmo, Mariano A.

Subjects
Mathematical Physics, Mathematics - Group Theory, 33C45, 42C20, 43A65, 43A75
Abstract

We present a family of unitary irreducible representations of SU(2) realized in the plane, in terms of the Laguerre polynomials. These functions are similar to the spherical harmonics defined on the sphere. Relations with an space of square integrable functions defined on the plane, $L^2(\R^2)$, are analyzed. We have also enlarged this study using rigged Hilbert spaces that allow to work with iscrete and continuous bases like is the case here., Comment: 10 pages

Published
2015

9. A constructive presentation of rigged Hilbert spaces

Author

Celeghini, Enrico

Subjects
Mathematical Physics, Quantum Physics
Abstract

We construct a rigged Hilbert space for the square integrable functions on the line L^2(R) adding to the generators of the Weyl-Heisenberg algebra a new discrete operator, related to the degree of the Hermite polynomials. All together, continuous and discrete operators, constitute the generators of the projective algebra io(2. L^2(R) and the vector space of the line R are shown to be isomorphic representations of such an algebra and, as both these representations are irreducible, all operators defined on the rigged Hilbert spaces L^2(R) or R are shown to belong to the universal enveloping algebra of io(2). The procedure can be extended to orthogonal and pseudo-orthogonal spaces of arbitrary dimension by tensorialization. Circumventing all formal problems the paper proposes a kind of toy model, well defined from a mathematical point of view, of rigged Hilbert spaces where, in contrast with the Hilbert spaces, operators with different cardinality are allowed., Comment: 9 pages, 7th Int. Workshop DICE2014, Sept. 15-19, 2014, Castiglioncello (Italy)

Published
2015

10. Quantum Physics and Signal Processing in Rigged Hilbert Spaces by means of Special Functions, Lie Algebras and Fourier and Fourier-like Transforms

Author

Celeghini, Enrico and del Olmo, Mariano A.

Subjects
Mathematical Physics, Physics - Computational Physics, Quantum Physics, 81R15, 81Q10, 33C45, 42A38
Abstract

Quantum Mechanics and Signal Processing in the line R, are strictly related to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variable that measures the degree of the Hermite functions and allows to obtain the projective algebra io(2). A Rigged Hilbert space is found and a new discrete basis in R obtained. The operators {O[R]} defined on R are shown to belong to the Universal Enveloping Algebra UEA[io(2)] allowing, in this way, their algebraic discussion. Introducing in the half-line a Fourier-like Transform, the procedure is extended to R^+ and can be easily generalized to R^n and to spherical reference systems., Comment: 12 pages, Contribution to the 30th International Colloquium on Group Theoretical Methods in Physics, July 14-18, 2014, Gent (Belgium)

Published
2014
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12. Non-cyclic phases for neutrino oscillations in quantum field theory

Author

Blasone, Massimo, Capolupo, Antonio, Celeghini, Enrico, and Vitiello, Giuseppe

Subjects
High Energy Physics - Theory
Abstract

We show the presence of non-cyclic phases for oscillating neutrinos in the context of quantum field theory. Such phases carry information about the non-perturbative vacuum structure associated with the field mixing. By subtracting the condensate contribution of the flavor vacuum, the previously studied quantum mechanics geometric phase is recovered.

Published
2009
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13. Quantum Bases in Uq(g)

Author

Celeghini, Enrico

Subjects
Mathematics - Quantum Algebra, 81R50, 17B35, 17B37, 17B62
Abstract

This paper is devoted to analize inside the infinitely many possible bases of Uq(g), same that can be considered "more equal then others". The element of selection has been a privileged relation with the bialgebra. A new parameter z' has been found that determines the commutation relations, independent from the z=log(q) that defines Uq(g). Both z and z' are necessary to fix the relations between the basic set and its coproducts. Three cases are particularly relevant: the analytical set with z'=z, the Lie set with Lie-like commutation relations (for z'=0) and the canonical/crystal basis with z' infinity. To simplify the exposition, we discuss in details the easy generalizable case of Uq(su(2))., Comment: Latex, 10 pages, no figures

Published
2008

15. Bose Condensation and Temperature

Author

Celeghini, Enrico and Rasetti, Mario

Subjects
Condensed Matter - Statistical Mechanics
Abstract

A quantitative analysis of the process of condensation of bosons both in harmonic traps and in gases is made resorting to two ingredients only: Bose classical distribution and spectral discretness. It is shown that in order to take properly into account statistical correlations, temperature must be defined from first principles, based on Shannon entropy, and turns out to be equal to $\beta^{-1}$ only for $T > T_c$ where the usual results are recovered. Below $T_c$ a new critical temperature $T_d$ is found, where the specific heat exhibits a sharp spike, similar to the $\lambda$-peak of superfluidity., Comment: 4 pages, 5 figures

Published
2001

16. Bosons and Environment

Author

Celeghini, Enrico and Rasetti, Mario

Subjects
Condensed Matter - Statistical Mechanics
Abstract

The role of background in bosonic quantum statistics is discussed in the frame of a new approach in terms of coherent states. Bosons are indeed detected in different physical situations where they exhibit different and apparently unconnected properties. Besides Bose gas we consider bosons in particle physics and bosons in harmonic traps. In particle physics bosons are dealt with in a context where the number of observed particles is finite: here the relevant features are the canonical commutation relations, which we shall show to be related to a Boltzmann-like distribution. A further case is Bose condensate in harmonic traps, where discrete spectrum leads us to predict, below T_c, a new critical temperature. The unified approach proposed shows that all defferences can be ascribed to the environment., Comment: 8 pages, 1 figure, contribution to "Spin-Statistics Connection and Commutation Relations", R.C.Hilborn and G.M.Tino eds. (AIP, New York, 2000)

Published
2000
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17. Discrete Spectrum in Bose Condensation

Author

Celeghini, Enrico and Rasetti, Mario

Subjects
Condensed Matter - Statistical Mechanics
Abstract

A quantitative description of the whole process of condensation of bosons in an harmonic trap is given resorting only to Gibbs and Bose postulates, without assuming equipartition nor continuum statistics. Below Tc discrete spectrum theory predicts for the thermo-dynamical variables a behavior different from the continuum case. In particular a new critical temperature is found where the specific heat exhibits a lambda-like spike. Numerical values of the relevant quantities depend on the experimental set-up. The theory does not take into account collective effects in the ground state., Comment: 4 Latex pages, 4 eps figures, uses AMS fonts. 4 misprints corrected

Published
2000

18. Quantum (1+1) extended Galilei algebras: from Lie bialgebras to quantum R-matrices and integrable systems

Author

Ballesteros, Angel, Celeghini, Enrico, and Herranz, Francisco J.

Subjects
Mathematics - Quantum Algebra
Abstract

The Lie bialgebras of the (1+1) extended Galilei algebra are obtained and classified into four multiparametric families. Their quantum deformations are obtained, together with the corresponding deformed Casimir operators. For the coboundary cases quantum universal R-matrices are also given. Applications of the quantum extended Galilei algebras to classical integrable systems are explicitly developed., Comment: 16 pages, LaTeX. A detailed description of the construction of integrable systems is carried out

Published
1999
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21. A universal non-quasitriangular quantization of the Heisenberg group

Author

Ballesteros, A., Celeghini, Enrico, Herranz, F. J., del Olmo, M. A., and Santander, M.

Subjects
High Energy Physics - Theory, Mathematics - Quantum Algebra
Abstract

A universal R--matrix for the quantum Heisenberg algebra h(1)q is presented. Despite of the non--quasitriangularity of this Hopf algebra, the quantum group induced from it coincides with the quasitriangular deformation already known., Comment: 5 pages

Published
1994
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22. Exponential mapping for non semisimple quantum groups

Author

Bonechi, F., Celeghini, Enrico, Giachetti, R., Pereña, C. M., Sorace, E., and Tarlini, M.

Subjects
High Energy Physics - Theory, Mathematics - Quantum Algebra
Abstract

The concept of universal T matrix, recently introduced by Fronsdal and Galindo in the framework of quantum groups, is here discussed as a generalization of the exponential mapping. New examples related to inhomogeneous quantum groups of physical interest are developed, the duality calculations are explicitly presented and it is found that in some cases the universal T matrix, like for Lie groups, is expressed in terms of usual exponential series., Comment: 12 pages

Published
1993
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23. Italian workshop on quantum groups

Author

Celeghini, Enrico and Tarlini, M.

Subjects
High Energy Physics - Theory, Mathematics - Quantum Algebra
Abstract

The first ``Convegno Informale su Quantum Groups'' was held in Florence from February 3 to 6, 1993. This Convegno was conceived as an informal meeting to bring together all the italian people working in the field of quantum groups and related topics. We are very happy indeed that about 30 theoretical physicists decided to take part presenting many aspects of this interesting and live subject of research. We thank all the participants for the stimulating and nice atmosphere that has characterized the meeting. This paper has the intent to give a quick review in english of the contributions and related references. We think useful to include the complete addresses and coordinate data of the participants. It is our intention to diffuse these proceedings by e-mail trough electronic data banks., Comment: 42 pages

Published
1993

24. Quantum algebras and Lie groups

Author

Celeghini, Enrico

Subjects
High Energy Physics - Theory, Mathematics - Quantum Algebra
Abstract

Lie groups and quantum algebras are connected through their common universal enveloping algebra. The adjoint action of Lie group on its algebra is naturally extended to related q-algebra and q-coalgebra. In such a way, quantum structure can be dealt more or less as the Lie one and we do not need to introduce the not easy to handle topological groups. Composed system also is described by the suitably symmetrized q-coalgebra. A physical application to the phonon, irreducible unitary representation of E_q(1,1), shows both the transformation under the group action of one phonon state and the fusion of two phonons, by means of the coproduct, in only one phonon lying on a branch of the appropriate dispersion relation., Comment: 9 pages

Published
1992

31. Groups, Jacobi functions, and rigged Hilbert spaces

Author

Celeghini, Enrico and Celeghini, Enrico

Abstract

This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations of their algebra of symmetry, that induce discrete and continuous bases coexisting on a rigged Hilbert space supporting the representation. Meaningful operators are shown to be continuous on the spaces of test vectors and its dual. Here, the chosen special functions, called “Algebraic Jacobi Functions” are related to the Jacobi polynomials and the Lie algebra is su(2, 2). These functions with m and q fixed, also exhibit a su(1, 1)-symmetry. Different discrete and continuous bases are introduced. An extension in the spirit of the associated Legendre polynomials and the spherical harmonics is presented introducing the “Jacobi Harmonics” that are a generalization of the spherical harmonics to the three-dimensional hypersphere S3.

Published
2020

35. Spherical harmonics and rigged Hilbert spaces

Author

Celeghini, Enrico and Celeghini, Enrico

Abstract

Producción Científica, This paper is devoted to study discrete and continuous bases for spaces supporting representations of SO(3) and SO(3, 2) where the spherical harmonics are involved. We show how discrete and continuous bases coexist on appropriate choices of rigged Hilbert spaces. We prove the continuity of relevant operators and the operators in the algebras spanned by them using appropriate topologies on our spaces. Finally, we discuss the properties of the functionals that form the continuous basis, Ministerio de Economía, Industria y Competitividad (Project MTM2014-57129-C2-1-P with EU-FEDER support), Junta de Castilla y León (programa de apoyo a proyectos de investigación - Ref. VA057U16)

Published
2018

36. Searches for lepton number violation and resonances in K± → πμμ decays

Author

Batley, J. R., Kalmus, G., Lazzeroni, C., Munday, D. J., Slater, M. W., Wotton, S. A., Arcidiacono, R., Bocquet, G., Cabibbo, N., Ceccucci, A., Cundy, D., Falaleev, V., Fidecaro, M., Gatignon, L., Gonidec, A., Kubischta, W., Maier, A., Massri, K., Norton, A., Patel, M., Peters, A., Balev, S., Frabetti, P. L., Gersabeck, E., Goudzovski, E., Hristov, P., Kekelidze, V., Kozhuharov, V., Litov, L., Madigozhin, D., Molokanova, N., Polenkevich, I., Potrebenikov, Y. U., Stoynev, S., Zinchenko, A., Monnier, E., Swallow, E., Winston, R., Rubin, P., Walker, A., Baldini, W., Cotta Ramusino, A., Dalpiaz, P., Damiani, C., Fiorini, M., Gianoli, A., Martini, M., Petrucci, F., Savriã©, M., Scarpa, M., Wahl, H., Bizzeti, A., Lenti, M., Veltri, M., Calvetti, Mario, Celeghini, Enrico, Iacopini, Enrico, Ruggiero, Giuseppe, Behler, M., Eppard, K., Kleinknecht, K., Marouelli, P., Masetti, L., Moosbrugger, U., Morales Morales, C., Renk, B., Wache, M., Wanke, R., Winhart, A., Coward, D., Dabrowski, A., Fonseca Martin, T., Shieh, M., Szleper, M., Velasco, M., Wood, M. D., Cenci, P., Pepe, M., Petrucci, M. C., Anzivino, G., Imbergamo, E., Nappi, A., Piccini, M., Raggi, M., Valdata nappi, M., Cerri, C., Fantechi, R., Collazuol, G., Dilella, L., Lamanna, G., Mannelli, I., Michetti, A., Costantini, F., Doble, N., Fiorini, L., Giudici, S., Pierazzini, G., Sozzi, M., Venditti, S., Bloch devaux, B., Cheshkov, C., Chãze, J. B., De Beer, M., Derrã©, J., Marel, G., Mazzucato, E., Peyaud, B., Vallage, B., Holder, M., Ziolkowski, M., Biino, C., Cartiglia, N., Marchetto, F., Bifani, S., Clemencic, M., Goy Lopez, S., Dibon, H., Jeitler, M., Markytan, M., Mikulec, I., Neuhofer, G., and Widhalm, L.

Subjects
Nuclear and High Energy Physics
Published
2017

40. Detailed study of the K ± → π 0 π 0 e ± ν (K e4 00 ) decay properties

Author

Batley, J. R., Kalmus, G., Lazzeroni, C., Munday, D. J., Slater, M. W., Wotton, S. A., Arcidiacono, R., Bocquet, G., Cabibbo, N., Ceccucci, A., Cundy, D., Falaleev, V., Fidecaro, M., Gatignon, L., Gonidec, A., Kubischta, W., Norton, A., Maier, A., Patel, M., Peters, A., Balev, S., Frabetti, P. L., Gersabeck, E., Goudzovski, E., Hristov, P., Kekelidze, V., Kozhuharov, V., Litov, L., Madigozhin, D., Molokanova, N., Polenkevich, I., Potrebenikov, Y. u., Stoynev, S., Zinchenko, A., Monnier, E., Swallow, E., Winston, R., Rubin, P., Walker, A., Baldini, W., Ramusino, A. Cotta, Dalpiaz, P., Damiani, C., Fiorini, M., Gianoli, A., Martini, M., Petrucci, F., Savrié, M., Scarpa, M., Wahl, H., Bizzeti, A., Lenti, M., Veltri, M., Calvetti, Mario, Celeghini, Enrico, Iacopini, Enrico, Ruggiero, G., Behler, M., Eppard, K., Gersabeck, M., Kleinknecht, K., Marouelli, P., Masetti, L., Moosbrugger, U., Morales, C. Morales, Renk, B., Wache, M., Wanke, R., Winhart, A., Coward, D., Dabrowski, A., Martin, T. Fonseca, Shieh, M., Szleper, M., Velasco, M., Wood, M. D., Cenci, P., Pepe, M., Petrucci, M. C., Anzivino, G., Imbergamo, E., Nappi, A., Piccini, M., Raggi, M., Valdata Nappi, M., Cerri, C., Fantechi, R., Collazuol, G., Dilella, L., Lamanna, G., Mannelli, I., Michetti, A., Costantini, F., Doble, N., Fiorini, L., Giudici, S., Pierazzini, G., Sozzi, M., Venditti, S., Bloch Devaux, B., Cheshkov, C., Chèze, J. B., De Beer, M., Derré, J., Marel, G., Mazzucato, E., Peyaud, B., Vallage, B., Holder, M., Ziolkowski, M., Biino, C., Cartiglia, N., Marchetto, F., Bifani, S., Clemencic, M., Lopez, S. Goy, Dibon, H., Jeitler, M., Markytan, M., Mikulec, I., Neuhofer, G., and Widhalm, L.

Subjects
Mesoni K
Published
2014

41. A new measurement of the K-+/- -> pi(+/-)gamma gamma decay at the NA48/2 experiment

Author

Batley, Jr, 21 Kalmus G, 1, 1 Lazzeroni C, 1 Munday DJ, 1 Slater MW, 1 Wotton SA, 1 Arcidiacono R, 2 Bocquet G, 2 Cabibbo N, 2 Ceccucci A, 2 Cundy D, 2 Falaleev V, 2 Fidecaro M, 2 Gatignon L, 2 Gonidec A, 2 Kubischta W, 2 Norton A, 2 Maier A, 2 Patel M, 2 Peters A, 2 Balev S, 3 Frabetti PL, 3 Gersabeck E, 3 Goudzovski E, 3 Hristov P, 3 Kekelidze V, 3 Kozhuharov V, 3 Litov L, 3 Madigozhin D, 3 Molokanova N, 3 Polenkevich I, 3 Potrebenikov Y, 3 Stoynev S, 3 Zinchenko A, 3 Monnier E, 4 Swallow E, 4 Winston R, 4 Rubin P, 5 Walker A, 5 Baldini Wander 6, 7 Cotta Ramusino Angelo 6, 7 Dalpiaz Pietro 6, 7 Damiani Chiara 6, 7 Fiorini Massimiliano 6, 7 Gianoli Alberto 6, 7 Martini Mara 6, 7 Petrucci Ferruccio 6, 7 Savrie' Mauro 6, 7 Scarpa Marcella 6, 7 Wahl Heinrich 6, 7 Bizzeti Andrea, Lenti, Massimo, Veltri, Michele, Calvetti, Mario, Celeghini, Enrico, Iacopini, Enrico, Ruggiero Giuseppe 8, 9 Behler M, 10 Eppard, K, 10 Kleinknecht, K, 10 Marouelli, P, 10 Masetti, L, 10 Moosbrugger, U, 10 Morales CM, 10 Renk, B, 10 Wache, M, 10 Wanke, R, 10 Winhart, A, 10 Coward, D, 11 Dabrowski, A, 11 Martin TF, 11 Shieh, M, 11 Szleper, M, 11 Velasco, M, 11 Wood MD, 11 Cenci Patrizia 12 Pepe Monica 12 Petrucci Maria Carmela 12 Anzivino Giuseppina 12, 13 Imbergamo Ermanno 12, 13 Nappi Aniello 12, 13 Piccini Mauro 12, 13 Raggi Mauro 12, 13 Valdata Nappi, M, 13 Cerri Claudio 14 Fantechi Riccardo 14 Collazuol Gianmaria 14, 15 DiLella, L, 15 Lamanna Gianluca 14, 15 Mannelli Italo 14, 15 Michetti Andrea 14, 15 Costantini Flavio 14, 16 Doble, N, 16 Fiorini Luca 14, 16 Giudici Sergio 14, 16 Pierazzini Giuseppe 14, 16 Sozzi Marco 14, 16 Venditti Stefano 14, 16 Bloch Devaux, B, 17 Cheshkov, C, 17 Cheze JB, 17 De Beer, M, 17 Derre, J, 17 Marel, G, 17 Mazzucato, E, 17 Peyaud, B, 17 Vallage, B, 17 Holder, M, 18 Ziolkowski, M, 18 Biino Cristina 19 Cartiglia Nicolo' 19 Marchetto Flavio Pietro 19 Bifani Simone 19, 20 Clemencic Marco 19, 20 Goy Lopez Silvia 19, 20 Dibon, H, 21 Jeitler, M, 21 Markytan, M, 21 Mikulec, I, 21 Neuhofer, G, and 21 Widhalm, L.

Published
2014

42. Precise tests of low energy QCD from $K_{e4}$ decay properties

Author

Batley, Jr, Kalmus, G, Lazzeroni, C, Munday, Dj, Slater, Mw, Wotton, Sa, Arcidiacono, Roberta, Bocquet, G, Cabibbo, Nicola, Ceccucci, A, Cundy, D, Falaleev, V, Fidecaro, M, Gatignon, L, Gonidec, A, Kubischta, W, Norton Alan Robert, Maier, A, Patel, M, Peters, A, Balev, S, Frabetti, Pl, Goudzovski, E, Hristov, P, Kekelidze, V, Kozhuharov, V, Litov, L, Madigozhin, D, Marinova Evelina Mihova, Molokanova, N, Polenkevich, I, Potrebenikov, Y, Stoynev, S, Zinchenko, A, Monnier, E, Swallow, E, Winston, R, Rubin, P, Walker, A, Baldini, Wander, Cotta Ramusino Angelo, Dalpiaz, Pietro, Damiani, Chiara, Fiorini, Massimiliano, Gianoli, Alberto, Martini, Marco, Petrucci, Fabrizio, Savrie', Mauro, Scarpa, Marcella, Wahl, Heinrich, Bizzeti, Andrea, Lenti, Massimo, Veltri, Michele, Calvetti, Mario, Celeghini, Enrico, Iacopini, Enrico, Ruggiero, Giuseppe, Behler, M, Eppard, K, Kleinknecht, K, Marouelli, P, Masetti, L, Moosbrugger, U, Morales, Cm, Renk, B, Wache, M, Wanke, R, Winhart, A, Coward, D, Dabrowski, A, Martin, Tf, Shieh, M, Szleper, M, Velasco, M, Wood, Md, Cenci, Patrizia, Pepe, Monica, Petrucci Maria Carmela, Anzivino, Giuseppina, Imbergamo, Ermanno, Nappi, Aniello, Piccini, Mauro, Raggi, Mauro, Valdata, Marisa, Cerri, Claudio, Fantechi, Riccardo, Collazuol, Gianmaria, Dilella, L, Lamanna, Gianluca, Mannelli, Italo, Michetti, Andrea, Costantini, Flavio, Doble, N, Fiorini, Luca, Giudici, Sergio, Pierazzini, Giuseppe, Sozzi, Marco, Venditti, Stefano, Bloch Devaux, B, Cheshkov, C, Cheze, Jb, De Beer, M, Derre, J, Marel, G, Mazzucato, E, Peyaud, B, Vallage, B, Holder, M, Ziolkowski, M, Biino, Cristina, Cartiglia, Nicolo', Marchetto Flavio Pietro, Bifani, Simone, Clemencic, Marco, Goy Lopez Silvia, Dibon, H, Jeitler, M, Markytan, M, Mikulec, I, Neuhofer, G, and Widhalm, L.

Subjects
LENGTHS, MONTE-CARLO, KE4 DECAYS, PI-PI SCATTERING, FORM-FACTORS, ONE-LOOP, CONSTANTS, EQUATION, ISOSPIN BREAKING, PHASE-SHIFTS, Particle Physics - Experiment
Abstract

We report results from the analysis of the $K^{\pm} \rightarrow \pi^{+} \pi^{-} e^{\pm} \nu$ (Ke4) decay by the NA48/2 collaboration at the CERN SPS, based on the total statistics of 1.13 million decays collected in 2003-2004. The hadronic form factors in the S- and P-wave and their variation with energy are obtained. The phase difference between the S- and P-wave states of the $\pi \pi$ system is accurately measured and allows a precise determination of $a_{0}^{0}$ and $a_{0}^{2}$, the I=0 and I=2 S-wave $\pi \pi$ scattering lengths: $a_{0}^{0} = 0.2220 \pm 0.0128_{stat} \pm 0.0050_{syst} \pm 0.0037_{th}, a_{0}^{2}$ = $-0.0432 \pm 0.0086_{stat} \pm 0.0034_{syst} \pm 0.0028_{th}.$ Combination of this result with the other NA48/2 measurement obtained in the study of $K^{\pm} \rightarrow \pi^{0} \pi^{0} \pi^{\pm}$ decays brings an improved determination of $a_{0}^{0}$ and the first precise experimental measurement of $a_{0}^{2}$, providing a stringent test of Chiral Perturbation Theory predictions and lattice QCD calculations. Using constraints based on analyticity and chiral symmetry, even more precise values are obtained: $a_{0}^{0} = 0.2196 \pm 0.0028_{stat} \pm 0.0020_{syst}$ and $a_{0}^{2} = -0.0444 \pm 0.0007_{stat} \pm 0.0005_{syst} \pm 0.0008_{ChPT}$.

Published
2010

45. Measurement of the direct emission and interference terms and search for CP violation in the decay $\K^pm -> pi^pm pi^0 \gamma$

Author

Batley, Jr, Kalmus, G, Lazzeroni, C, Munday, Dj, Slater, Mw, Wotton, Sa, Arcidiacono, Roberta, Bocquet, G, Cabibbo, Nicola, Ceccucci, A, Cundy, D, Falaleev, V, Fidecaro, M, Gatignon, L, Gonidec, A, Kubischta, W, Norton Alan Robert, Maier, A, Patel, M, Peters, A, Balev, S, Frabetti, Pierluigi, Goudzovski, E, Hristov, P, Kekelidze, V, Kozhuharov, V, Litov, L, Madigozhin, D, Marinova Evelina Mihova, Molokanova, N, Polenkevich, I, Potrebenikov, Y, Stoynev, S, Zinchenko, A, Monnier, E, Swallow, E, Winston, R, Rubin, P, Walker, A, Baldini, Wander, Cotta Ramusino Angelo, Dalpiaz, Pietro, Damiani, Chiara, Fiorini, Massimiliano, Gianoli, Alberto, Martini, Marco, Petrucci, Fabrizio, Savrie', Mauro, Scarpa, Marcella, Wahl, Heinrich, Bizzeti, Andrea, Lenti, Massimo, Veltri, Michele, Calvetti, Mario, Celeghini, Enrico, Iacopini, Enrico, Ruggiero, Giuseppe, Behler, M, Eppard, K, Kleinknecht, K, Marouelli, P, Masetti, L, Moosbrugger, U, Morales, Cm, Renk, B, Wache, M, Wanke, R, Winhart, A, Coward, D, Dabrowski, A, Martin, Tf, Shieh, M, Szleper, M, Velasco, M, Wood, Md, Cenci, Patrizia, Petrucci Maria Carmela, Pepe, Monica, Anzivino, Giuseppina, Imbergamo, Ermanno, Nappi, Aniello, Piccini, Mauro, Raggi, Mauro, Valdata, Marisa, Cerri, Claudio, Fantechi, Riccardo, Collazuol, Gianmaria, Dilella, L, Lamanna, Gianluca, Mannelli, Italo, Michetti, Andrea, Costantini, Flavio, Doble, N, Fiorini, Luca, Giudici, Sergio, Pierazzini, Giuseppe, Sozzi, Marco, Venditti, Stefano, Bloch Devaux, B, Cheshkov, C, Cheze, Jb, De Beer, M, Derre, J, Marel, G, Mazzucato, E, Peyaud, B, Vallage, B, Holder, M, Ziolkowski, M, Bifani, Simone, Biino, Cristina, Cartiglia, Nicolo', Clemencic, Marco, Goy Lopez Silvia, Marchetto Flavio Pietro, Dibon, H, Jeitler, M, Markytan, M, Mikulec, I, Neuhofer, G, and Widhalm, L.

Published
2010

46. Precise measurement of the K±->π±e+e− decay

Author

Batley, Jr, Culling, Aj, Kalmus, G, Lazzeroni, C, Munday, Dj, Slater, Mw, Wotton, Sa, Arcidiacono, Roberta, Bocquet, G, Cabibbo, Nicola, Ceccucci, A, Cundy, D, Falaleev, V, Fidecaro, M, Gatignon, L, Gonidec, A, Kubischta, W, Norton Alan Robert, Maier, A, Patel, M, Peters, A, Balev, S, Frabetti, Pierluigi, Goudzovski, E, Hristov, P, Kekelidze, V, Kozhuharov, V, Litov, L, Madigozhin, D, Marinova, E, Molokanova, N, Polenkevich, I, Potrebenikov, Y, Stoynev, S, Zinchenko, A, Monnier, E, Swallow, E, Winston, R, Rubin, P, Walker, A, Baldini, Wander, Cotta Ramusino Angelo, Dalpiaz, Pietro, Damiani, Chiara, Fiorini, Massimiliano, Gianoli, Alberto, Martini, Marco, Petrucci, Fabrizio, Savrie', Mauro, Scarpa, Marcella, Wahl, Heinrich, Bizzetti, A, Calvetti, Mario, Celeghini, Enrico, Iacopini, Enrico, Lenti, Massimo, Martelli, Filippo, Ruggiero, Giuseppe, Veltri, Michele, Behler, M, Eppard, K, Kleinknecht, K, Marouelli, P, Masetti, L, Moosbrugger, U, Morales, Cm, Renk, B, Wache, M, Wanke, R, Winhart, A, Coward, D, Dabrowski, A, Martin, Tf, Shieh, M, Szleper, M, Velasco, M, Wood, Md, Anzivino, Giuseppina, Cenci, Patrizia, Imbergamo, Ermanno, Nappi, Aniello, Pepe, Monica, Petrucci Maria Carmela, Piccini, Mauro, Raggi, Mauro, Valdata, Marisa, Cerri, Claudio, Fantechi, Riccardo, Collazuol, Gianmaria, Dilella, L, Lamanna, Gianluca, Mannelli, Italo, Michetti, Andrea, Costantini, Flavio, Doble, N, Fiorini, Luca, Giudici, Sergio, Pierazzini, Giuseppe, Sozzi, Marco, Venditti, Stefano, Bloch Devaux, B, Cheshkov, C, Cheze, Jb, De Beer, M, Derre, J, Marel, G, Mazzucato, E, Peyaud, B, Vallage, B, Holder, M, Ziolkowski, M, Bifani, Simone, Biino, Cristina, Cartiglia, Nicolo', Clemencic, Marco, Goy Lopez Silvia, Marchetto Flavio Pietro, Dibon, H, Jeitler, M, Markytan, M, Mikulec, I, Neuhofer, G, and Widhalm, L.

Published
2009

47. First observation and measurement of the decay K± -> π±e+e-γ

Author

Batley, Jr, Culling, Aj, Kalmus, G, Lazzeroni, C, Munday, Dj, Slater, Mw, Wotton, Sa, Arcidiacono, Roberta, Bocquet, G, Cabibbo, Nicola, Ceccucci, A, Cundy, D, Falaleev, V, Fidecaro, M, Gatignon, L, Gonidec, A, Kubischta, W, Norton Alan Robert, Maier, A, Patel, M, Peters, A, Balev, S, Frabetti, Pierluigi, Goudzovski, E, Hristov, P, Kekelidze, V, Kozhuharov, V, Litov, L, Madigozhin, D, Marinova, E, Molokanova, N, Polenkevich, I, Potrebenikov, Y, Stoynev, S, Zinchenko, A, Monnier, E, Swallow, E, Winston, R, Rubin, P, Walker, A, Baldini, Wander, Cotta Ramusino Angelo, Dalpiaz, Pietro, Darniani, C, Fiorini, Massimiliano, Gianoli, Alberto, Martini, Marco, Petrucci, Fabrizio, Savrie', Mauro, Scarpa, Marcella, Wahl, Heinrich, Bizzeti, Andrea, Calvetti, Mario, Celeghini, Enrico, Lacopini, E, Lenti, Massimo, Martelli, Filippo, Ruggiero, Giuseppe, Veltri, Michele, Behler, M, Eppard, K, Handel, C, Kleinknecht, K, Marouelli, P, Masetti, L, Moosbrugger, U, Morales, Cm, Renk, B, Wache, M, Wanke, R, Winhart, A, Coward, D, Dabrowski, A, Martin, Tf, Shieh, M, Szleper, M, Velasco, M, Wood, Md, Anzivino, Giuseppina, Cenci, Patrizia, Imbergarno, E, Nappi, Aniello, Pepe, Monica, Petrucci Maria Carmela, Piccini, Mauro, Raggi, Mauro, Valdata, Marisa, Cerri, Claudio, Collazuol, Gianmaria, Costantini, Flavio, Dilella, L, Doble, N, Fantechi, Riccardo, Fiorini, Luca, Giudici, Sergio, Lamanna, Gianluca, Mannelli, Italo, Michetti, Andrea, Pierazzini, Giuseppe, Sozzi, Marco, Bloch Devaux, B, Cheshkov, C, Cheze, Jb, De Beer, M, Derre, J, Marel, G, Mazzucato, E, Peyaud, B, Vallage, B, Holder, M, Ziolkowski, M, Bifani, Simone, Biino, Cristina, Cartiglia, Nicolo', Clernencic, A, Goy Lopez Silvia, Marchetto Flavio Pietro, Dibon, H, Jeitler, A, Markytan, A, Mikulec, I, Neuhofer, G, and Widhalm, L.

Published
2008

48. First observation and measurement of the decay $K^{\pm} \to\pi^{\pm}e^{+}e^{-}\gamma$

Author

Batley, J.R., Culling, A.J., Kalmus, George E., Lazzeroni, Cristina, Munday, D.J., Slater, M.W., Wotton, S.A., Arcidiacono, Roberta, Bocquet, G., Cabibbo, N., Ceccucci, Augusto, Cundy, D., Falaleev, V., Fidecaro, M., Gatignon, L., Gonidec, A., Kubischta, W., Norton, A., Maier, A., Patel, M., Peters, A., Balev, S., Frabetti, P.L., Goudzovski, E., Hristov, Peter, Kekelidze, V., Kozhuharov, V., Litov, Leandar, Madigozhin, D., Marinova, E., Molokanova, N., Polenkevich, I., Stoynev, S., Zinchenko, A., Monnier, E., Swallow, E., Winston, R., Rubin, Philip D., Walker, A., Baldini, W., Cotta Ramusino, A., Dalpiaz, P., Damiani, C., Fiorini, M., Gianoli, Alberto, Martini, M., Petrucci, F., Savrie, M., Scarpa, M., Wahl, H., Bizzeti, A., Calvetti, M., Celeghini, Enrico, Iacopini, E., Lenti, M., Martelli, F., Ruggiero, G., Veltri, M., Behler, M., Eppard, K., Handel, C., Kleinknecht, Konrad, Marouelli, P., Masetti, L., Moosbrugger, U., Morales Morales, C., Renk, B., Wache, M., Wanke, R., Winhart, A., Coward, D.H., Dabrowski, A., Fonseca Martin, T., Shieh, M., Szleper, M., Velasco, M., Wood, M.D., Anzivino, Giuseppina, Cenci, P., Imbergamo, E., Nappi, Nello, Pepe, M., Petrucci, M.C., Piccini, M., Raggi, M., Valdata-Nappi, Marisa, Cerri, C., Collazuol, G., Costantini, Flavio, Di, L., Doble, Niels, Fantechi, R., Fiorini, L., Giudici, S., Lamanna, G., Mannelli, Italo, Michetti, A., Pierazzini, G., Sozzi, Marco S., Bloch-Devaux, Brigitte, Cheshkov, C., Cheze, J.B., De Beer, M., Derre, J., Marel, G., Mazzucato, E., Peyaud, B., Vallage, B., Holder, M., Ziolkowski, M., Bifani, S., Biino, C., Cartiglia, N., Clemencic, M., Goy Lopez, S., Marchetto, Flavio Pietro, Dibon, Heinz, Jeitler, Manfred, Markytan, M., Mikulec, I., Neuhofer, G., and Widhalm, L.

Subjects
Particle Physics - Experiment
Abstract

Using the full data set of the NA48/2 experiment, the decay $K^{\pm} \rightarrow \pi^{\pm} e^{+} e^{-}\gamma$ is observed for the first time, selecting 120 candidates with $7.3 \pm 1.7$ estimated background events. With $K^{\pm} \rightarrow \pi^{\pm} \pi^{0}_{D}$ as normalisation channel, the branching ratio is determined in a model-independent way to be Br$(K^{\pm} \rightarrow \pi^{\pm} e^{+} e^{-}\gamma, m_{ee\gamma} > 260$ MeV/c$^{2}) = (1.19 \pm 0.12_{stat} \pm 0.04_{syst}) \times 10^{-8}$. This measured value and the spectrum of the $e^{+}e^{-}\gamma$ invariant mass allow a comparison with predictions of Chiral Perturbation Theory. Using the full data set of the NA48/2 experiment, the decay K±→π±e+e−γ is observed for the first time, selecting 120 candidates with 7.3±1.7 estimated background events. With K±→π±πD0 as normalisation channel, the branching ratio is determined in a model-independent way to be Br(K±→π±e+e−γ,meeγ>260 MeV/c2)=(1.19±0.12stat±0.04syst)×10−8 . This measured value and the spectrum of the e+e−γ invariant mass allow a comparison with predictions of chiral perturbation theory. Using the full data set of the NA48/2 experiment, the decay K+- -> pi+- e+ e- gamma is observed for the first time, selecting 120 candidates with 7.3 +- 1.7 estimated background events. With K+- -> pi+- pi0D as normalisation channel, the branching ratio is determined in a model-independent way to be Br(K+- -> pi+- e+ e- gamma, m_eegamma > 260 MeV/c^2) = (1.19 +- 0.12_stat +- 0.04_syst) x 10^-8. This measured value and the spectrum of the e+ e- gamma invariant mass allow a comparison with predictions of Chiral Perturbation Theory.

Published
2007

49. Measurement of the Dalitz plot slopes of the K±-> π±π+π- decay

Author

Batley, Jr, Culling, Aj, Kalmus, G, Lazzeroni, C, Munday, Dj, Slater, Mw, Wotton, Sa, Arcidiacono, Roberta, Bocquet, G, Cabibbo, Nicola, Ceccucci, A, Cundy, D, Falaleev, V, Fidecaro, M, Gatignon, L, Gonidec, A, Kubischta, W, Norton Alan Robert, Maier, A, Patel, M, Peters, A, Balev, Spasimir, Frabetti, Pierluigi, Goudzovski, E, Hristov, P, Kekelidze, V, Kozhuharov, V, Litov, L, Madigozhin, D, Marinova, E, Molokanova, N, Polenkevich, I, Potrebenikov, Y, Stoynev, S, Zinchenko, A, Monnier, E, Swallow, E, Winston, R, Rubin, P, Walker, A, Baldini, Wander, Ramusino, Ac, Dalpiaz, Pietro, Damiani, Chiara, Fiorini, Massimiliano, Gianoli, Alberto, Martini, Mara, Petrucci, Ferruccio, Savrie', Mauro, Scarpa, Marcella, Wahl, Heinrich, Bizzeti, Andrea, Calvetti, Mario, Celeghini, Enrico, Iacopini, Enrico, Lenti, Massimo, Martelli, Filippo, Ruggiero, Giuseppe, Veltri, Michele, Behler, M, Eppard, K, Kleinknecht, K, Marouelli, P, Masetti, L, Moosbrugger, U, Morales, Cm, Renk, B, Wache, M, Wanke, R, Winhart, A, Coward, D, Dabrowski, A, Martin, Tf, Shieh, M, Szleper, M, Velasco, M, Wood, Md, Anzivino, Giuseppina, Cenci, Patrizia, Imbergamo, Ermanno, Nappi, Aniello, Pepe, Monica, Petrucci Maria Carmela, Piccini, Mauro, Raggi, Mauro, Valdata, Marisa, Cerri, Claudio, Collazuol, Gianmaria, Costantini, Flavio, Dilella, L, Doble, N, Fantechi, Riccardo, Fiorini, Luca, Giudici, Sergio, Lamanna, Gianluca, Mannelli, Italo, Michetti, Andrea, Pierazzini, Giuseppe, Sozzi, Marco, Bloch Devaux, B, Cheshkov, C, Cheze, Jb, De Beer, M, Derre, J, Marel, G, Mazzucato, E, Peyaud, B, Vallage, B, Holder, M, Ziolkowski, M, Bifani, Simone, Biino, Cristina, Cartiglia, Nicolo', Clemencic, Marco, Goy Lopez Silvia, Marchetto Flavio Pietro, Dibon, H, Jeitler, M, Markytan, M, Mikulec, I, Neuhofer, G, and Widhalm, L.

Published
2007

50. Search for direct CP-violation in K± -> π± π0 π0 decays

Author

Batley, Jr, Culling, Aj, Kalmus, G, Lazzeroni, C, Munday, Dj, Slater, Mw, Wotton, Sa, Arcidiacono, Roberta, Bocquet, G, Cabibbo, Nicola, Ceccucci, A, Cundy, D, Falaleev, V, Fidecaro, M, Gatignon, L, Gonidec, A, Kubischta, W, Norton Alan Robert, Maier, A, Patel, M, Peters, A, Balev, Spasimir, Frabetti, Pl, Goudzovski, E, Hristov, P, Kekelidze, V, Kozhuharov, V, Litov, L, Madigozhin, D, Marinova, E, Molokanova, N, Polenkevich, I, Potrebenikov, Y, Stoynev, S, Zinchenko, A, Monnier, E, Swallow, E, Winston, R, Rubin, P, Walker, A, Baldini, Wander, Cotta Ramusino Angelo, Dalpiaz, Pietro, Damiani, Chiara, Fiorini, Massimiliano, Gianoli, Alberto, Martini, Mara, Petrucci, Ferruccio, Savrie', Mauro, Scarpa, Marcella, Wahl, Heinrich, Bizzeti, Andrea, Calvetti, Mario, Celeghini, Enrico, Iacopini, Enrico, Lenti, Massimo, Martelli, Filippo, Ruggiero, Giuseppe, Veltri, Michele, Behler, M, Eppard, K, Kleinknecht, K, Marouelli, P, Masetti, Lorenzo, Moosbrugger, U, Morales, Cm, Renk, B, Wache, M, Wanke, R, Winhart, A, Coward, D, Dabrowski, A, Martin, Tf, Shieh, M, Szleper, M, Velasco, M, Wood, Md, Anzivino, Giuseppina, Cenci, Patrizia, Imbergamo, Ermanno, Nappi, Aniello, Pepe, Monica, Petrucci, Mc, Piccini, Mauro, Raggi, Mauro, Valdata, Marisa, Cerri, Claudio, Collazuol, Gianmaria, Costantini, Flavio, Dilella, L, Doble, N, Fantechi, Riccardo, Fiorini, Luca, Giudici, Sergio, Lamanna, Gianluca, Mannelli, Italo, Michetti, Andrea, Pierazzini, Giuseppe, Sozzi, Marco, Bloch Devaux, B, Cheshkov, C, Cheze, Jb, De Beer, M, Derre, J, Marel, G, Mazzucato, E, Peyaud, B, Vallage, B, Holder, A, Ziolkowski, M, Bafani, S, Biino, Cristina, Cartiglia, Nicolo', Clemencic, Marco, Goy Lopez Silvia, Marchetto Flavio Pietro, Dibon, H, Jeitler, M, Markytan, M, Mikulec, I, Neuhofer, G, and Widhalm, L.

Published
2006

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