The anomalous magnetic moment of the tau lepton, a_tau = (g_tau - 2)/2, is a sensitive probe new physics but extremely difficult to measure precisely in contrast electron and muon moments. best experimental limits were set by DELPHI collaboration more than 15 years ago studies ditau production e+e -> e+e+tau+tau process. Ultra-peripheral collisions (UPCs) heavy ions at LHC may provide unique opportunity improve constraints Pb+Pb Pb+Pb+tau+tau We review recent proposals study via...

Photon-induced reactions in ultra-peripheral collisions (UPCs) of heavy nuclei at the LHC have been studied using ALICE detector for several years. The can measure photoproduction cross section vector mesons various rapidities, centre-of-mass energies and collision systems. In addition to recent studies rapidity momentum transfer dependence coherent $\rm{J/\psi}$ photoproduction, new results on incoherent will be discussed. These complement measurements provide additional sensitivity probing...

Precision measurements of the anomalous electromagnetic moment leptons ( a l ) may serve as one most promising directions in search for new physics beyond Standard Model. While experimental value electron magnetic agrees with theoretical predictions up to 11 significant digits, muon shows deviations from Model at level 4.2 sigma, indicating possible occurrence effects. Although τ tau lepton its heavy mass is expected be ${{m_\tau ^2} \mathord{\left/ {\vphantom {{m_\tau {m_\mu ^2}}} \right....

In the framework of quaternionic Clifford analysis in Euclidean space $\mathbb{R}^{4p}$, which constitutes a refinement and Hermitian analysis, Fischer decomposition complex valued polynomials is obtained terms spaces so--called (adjoint) symplectic spherical harmonics, are irreducible modules for group Sp$(p)$. Its Howe dual partner determined to be $\mathfrak{sl}(2,\mathbb{C}) \oplus \mathfrak{sl}(2,\mathbb{C}) = \mathfrak{so}(4,\mathbb{C})$.

The main aim of this paper is to construct explicitly orthogonal bases for the spaces k-homogeneous polynomial solutions Hodge-de Rham system in Euclidean space R^m which take values s-vectors. Actually, we describe even so-called Gelfand-Tsetlin such terms Gegenbauer polynomials. As an application, obtain algorithm how compute basis homogeneous a generalized Moisil-Theodoresco R^m.

Introducing a quaternionic structure on Euclidean space, the fundaments for and symplectic Clifford analysis are studied in detail from viewpoint of invariance group action.

Quaternionic Clifford analysis is a recent new branch of analysis, higher dimensional function theory which refines harmonic and generalizes to dimension the holomorphic functions in complex plane. So-called quaternionic monogenic satisfy system first order linear differential equations expressed terms four interrelated Dirac operators. The conceptual significance unraveled by showing that monogenicity can be characterized means generalized gradients sense Stein Weiss. At same time,...

Recently, the Fischer decomposition for polynomials on superspace R^{m|2n} (that is, in m commuting and 2n anti-commuting variables) has been obtained unless superdimension M=m-2n is even non-positive. In this case, it turns out that of into spherical harmonics quite analogous as R^m an irreducible under natural action Lie superalgebra osp(m|2n). paper, we describe explicitly exceptional case when M particular, show that, osp(m|2n), not, general, a but indecomposable pieces.

In this paper, we study generating functions for the standard orthogonal bases of spherical harmonics and monogenics in R^m. Here are polynomial solutions Dirac equation particular, obtain recurrence formula which expresses function dimension m terms that m-1. Hence can find closed formulae R^m by induction on m.

In [J. Bures, R. Lavicka, V. Soucek, Elements of quaternionic analysis and Radon transform, Textos de Matematica 42, Departamento Matematica, Universidade Coimbra, 2009], the authors describe a link between holomorphic functions depending on parameter monogenic defined R^(n+1) using dual transforms. The main aim this paper is to further develop approach. fact, transform for with values in Clifford algebra R_n mapping solutions generalized Cauchy-Riemann equation, i.e., functions, parametric...

Recently the Gelfand-Tsetlin construction of orthogonal bases has been explicitly described for spaces k-homogeneous polynomial solutions Hodge-de Rham system in Euclidean space R^m which take values s-vectors. In this paper, we give another these and, mainly, show that even form complete Appell systems. Moreover, study corresponding Taylor series expansions. As an application, construct quite homogeneous arbitrary generalized Moisil-Theodoresco system.

The determination of the luminosity is a key element in measurement cross sections at LHC. uncertainty this has major impact on accuracy measured physics quantities. definition and main strategy its estimation by ALICE, ATLAS, CMS LHCb experiments are presented. van der Meer technique associated corrections discussed. Finally, summary current results

It turns out that harmonic analysis on the superspace R^{m|2n} is quite parallel to classical theory Euclidean space R^{m} unless superdimension M:=m-2n even and non-positive. The underlying symmetry given by orthosymplectic superalgebra osp(m|2n). In this paper, when reduced osp(m-1|2n) we describe explicitly corresponding branching laws for spherical harmonics also in exceptional cases. unexceptional cases, these are well-known analogous as framework.

The aim of the paper is to study relations between polynomial solutions generalized Moisil-Theodoresco (GMT) systems and Hodge-de Rham and, using these relations, describe GMT systems. We decompose space homogeneous system a given homogeneity into irreducible pieces under action group O(m) we characterize individual by their highest weights compute dimensions.

Recently the Fischer decomposition for H-action of Pin group on Clifford algebra valued polynomials has been obtained. We apply this tool to get various decompositions special monogenic and inframonogenic in terms two sided ones.

The classical Fischer decomposition of spinor-valued polynomials is a key result on solutions the Dirac equation in Euclidean space R^m. As well-known, it can be understood as an irreducible with respect to so-called L-action Pin group Pin(m). But, Clifford algebra valued polynomials, we consider also H-action In this paper, corresponding for obtained. It turns out that, case, basic building blocks are spaces homogeneous Hodge-de Rham system. Moreover, shown that viewed even refinement one.