Study of the rare decays of B 0 s and B 0 mesons into muon pairs using data collected during 2015 and 2016 with the ATLAS detector The ATLAS Collaboration A study of the decays B 0 s → µ + µ − and B 0 → µ + µ − has been performed using 26.3 fb −1 of 13 TeV LHC proton-proton collision data collected with the ATLAS detector in 2015 and 2016. Since the detector resolution in µ + µ − invariant mass is comparable to the B 0 s -B 0 mass difference, a single fit determines the signal yields for both decay modes. This results in a measurement of the branching fraction B(B 0 s → µ + µ − ) = 3.2 +1.1 −1.0 × 10 −9 and an upper limit B(B 0 → µ + µ − ) < 4.3 × 10 −10 at 95% confidence level. The result is combined with the Run 1 ATLAS result, yielding B(B 0 s → µ + µ − ) = 2.8 +0.8 −0.7 ×10 −9 and B(B 0 → µ + µ − ) < 2.1×10 −10 at 95% confidence level. The combined result is consistent with the Standard Model prediction within 2.4 standard deviations in the B(B 0 → µ + µ − )-B(B 0 s → µ + µ − ) plane.

Angular analysis of B 0 d → K * µ + µ − decays in p p collisions at √ s = 8 TeV with the ATLAS detector The ATLAS Collaboration An angular analysis of the decay B 0 d → K * µ + µ − is presented, based on proton-proton collision data recorded by the ATLAS experiment at the LHC. The study is using 20.3 fb −1 of integrated luminosity collected during 2012 at centre-of-mass energy of √ s = 8 TeV. Measurements of the K * longitudinal polarisation fraction and a set of angular parameters obtained for this decay are presented. The results are compatible with the Standard Model predictions.Flavour-changing neutral currents (FCNC) have played a significant role in the construction of the Standard Model of particle physics (SM). These processes are forbidden at tree level and can proceed only via loops, hence are rare. An important set of FCNC processes involve the transition of a b-quark to an sµ + µ − final state mediated by electroweak box and penguin diagrams. If heavy new particles exist, they may contribute to FCNC decay amplitudes, affecting the measurement of observables related to the decay under study. Hence FCNC processes allow searches for contributions from sources of physics beyond the SM (hereafter referred to as new physics). This analysis focuses on the decay B 0 d → K * 0 (892)µ + µ − , where K * 0 (892) → K + π − . Hereafter, the K * 0 (892) is referred to as K * and charge conjugation is implied throughout, unless stated otherwise. In addition to angular observables such as the forward-backward asymmetry A FB 1, there is considerable interest in measurements of the charge asymmetry, differential branching fraction, isospin asymmetry, and ratio of rates of decay into dimuon and dielectron final states, all as a function of the invariant mass squared of the dilepton system q 2 . All of these observable sets can be sensitive to different types of new physics that allow for FCNCs at tree or loop level. The BaBar, Belle, CDF, CMS, and LHCb collaborations have published the results of studies of the angular distributions forThe LHCb Collaboration has reported a potential hint, at the level of 3.4 standard deviations, of a deviation from SM calculations [3,4] in this decay mode when using a parameterization of the angular distribution designed to minimise uncertainties from hadronic form factors. Measurements using this approach were also reported by the Belle and CMS Collaborations [6,8] and they are consistent with the LHCb experiment's results and with the SM calculations. This paper presents results following the methodology outlined in Ref. [3] and the convention adopted by the LHCb Collaboration for the definition of angular observables described in Ref. [9]. The results obtained here are compared with theoretical predictions that use the form factors computed in Ref. [10].This article presents the results of an angular analysis of the decay B 0 d → K * µ + µ − with the ATLAS detector, using 20.3 fb −1 of pp collision data at a centre-of-mass energy √ s = 8 TeV delivered by the Large Hadron Collider (LHC...

A certain representation for the Heisenberg algebra in finite difference operators is established. The Lie algebraic procedure of discretization of differential equations with isospectral property is proposed. Using sl 2-algebra based approach, (quasi)-exactly-solvable finite difference equations are described. It is shown that the operators having the Hahn, Charlier and Meissner polynomials as the eigenfunctions are reproduced in the present approach as some particular cases. A discrete version of the classical orthogonal polynomials (like Hermite, Laguerre, Legendre and Jacobi ones) is introduced.

It is shown that the spectrum of the asymmetric rotor can be realized quantum mechanically in terms of a system of interacting bosons. This is achieved in the SU(3) limit of the interacting boson model by considering higher-order interactions between the bosons. The spectrum corresponds to that of a rigid asymmetric rotor in the limit of infinite boson number.It is well known that the dynamical symmetry limits of the simplest version of the interacting boson model (IBM) [1,2], IBM-1, correspond to particular types of collective nuclear spectra. A Hamiltonian with U(5) dynamical symmetry [3] has the spectrum of an anharmonic vibrator, the SU(3) Hamiltonian [4] has the rotation-vibration spectrum of vibrations around an axially symmetric shape and the SO(6) Hamiltonian [5] yields the spectrum of a γ-unstable nucleus [6]. There exists another interesting type of spectrum frequently used to interpret nuclear collective excitations which corresponds to the rotation of a rigid asymmetric top [7] and which, up to now, has found no realization in the context of the IBM-1. The purpose of this letter is to extend the IBM-1 towards high-order terms such that a realization of the rigid non-axial rotor of Davydov and Filippov becomes possible. A pure group-theoretical approach is used that allows to establish the connection between algebraic and geometric Hamiltonians not only from the comparison of their spectra but also from the underlying group properties.Let us first recall some of the aspects that have enabled a geometric understanding of the IBM. The relation between the Bohr-Mottelson collective model [8] and the IBM has been established [9,10] on the basis of an intrinsic (or coherent) state for the IBM. Via this coherent-state formalism, a potential energy surface E(β, γ) in the quadrupole deformation variables β and γ can be derived for any IBM Hamiltonian and the equilibrium deformation parameters β 0 and γ 0 are then found by minimizing E(β, γ). It is by now well established that a one-and two-body IBM-1 Hamiltonian can give rise only to axially symmetric equilibrium shapes (γ 0 = 0 o or 60 o ) [9,10] and that a triaxial minimum in the potential energy surface requires at least three-body interactions [11].Since the relationship between γ-unstable model and rigid triaxial rotor was always an open question, Otsuka et al. [12,13] investigated in detail the SO(6) solutions of one-and two-body IBM-1 Hamiltonian. They found out that the triaxial intrinsic state with γ 0 = 30 o produces after the angular momentum projection the exact SO(6) eigenfunctions for small numbers of bosons N. Thus they conclude that for finite boson systems triaxiality reduces to γ-unstability.