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We propose a general method for the description of arbitrary single spin-j states transforming according to (j,0)+(0,j) carrier spaces of the Lorentz algebra in terms of Lorentz-tensors for bosons, and tensor-spinors for fermions, and by means of second order Lagrangians. The method allows to avoid the cumbersome matrix calculus and higher partial^{2j} order wave equations inherent to the Weinberg-Joos approach. We start with reducible Lorentz-tensor (tensor-spinor) representation spaces hosting one sole (j,0)+(0,j) irreducible sector and design there a representation reduction algorithm based on one of the Casimir invariants of the Lorentz algebra. This algorithm allows us to separate neatly the pure spin-j sector of interest from the rest, while preserving the separate Lorentz- and Dirac indexes. However, the Lorentz invariants are momentum independent and do not provide wave equations. Genuine wave equations are obtained by conditioning the Lorentz-tensors under consideration to satisfy the Klein-Gordon equation. In so doing, one always ends up with wave equations and associated Lagrangians that are second order in the momenta. Specifically, a spin-3/2 particle transforming as (3/2,0)+ (0,3/2) is comfortably described by a second order Lagrangian in the basis of the totally antisymmetric Lorentz tensor-spinor of second rank, Psi_[ mu u]. Moreover, the particle is shown to propagate causally within an electromagnetic background. In our study of (3/2,0)+(0,3/2) as part of Psi_[mu u] we reproduce the electromagnetic multipole moments known from the Weinberg-Joos theory. We also find a Compton differential cross section that satisfies unitarity in forward direction. The suggested tensor calculus presents itself very computer friendly with respect to the symbolic software FeynCalc.
We use the Laplace/Borel sum rules (LSR) and the finite energy/local duality sum rules (FESR) to investigate the non-strange $udbar ubar d$ and hidden-strange $usbar ubar s$ tetraquark states with exotic quantum numbers $J^{PC}=0^{+-}$ . We systemati
We present a formalism that extends the Majorana-construction to arbitrary spin (j,0)+(0,j) representation spaces. For the example case of spin-1, a wave equation satisfied by the Majorana-like (1,0)+(0,1) spinors is constructed and its physical cont
A boson of spin-j>1 can be described in one of the possibilities within the Bargmann-Wigner framework by means of one sole differential equation of order twice the spin, which however is known to be inconsistent as it allows for non-local, ghost and
We study the decay processes of $bar{B}^0 to J/psi bar{K}^{*0} K^0$ and $bar{B}^0 to J/psi f_1(1285)$ to analyse the $f_1(1285)$ resonance. By the calculation within chiral unitary approach where $f_1(1285)$ resonance is dynamically generated from th
We present the first study of the process $J/psi rightarrow gammaetapi^{0}$ using $(223.7pm1.4)times10^{6}$ $J/psi$ events accumulated with the BESIII detector at the BEPCII facility. The branching fraction for $J/psi rightarrow gammaetapi^{0}$ is me