Related papers: Rotation-invariant observables as Density Matrix i…
The di-fermion angular distribution observed in decays of inclusively produced vector particles is characterized by two frame-independent observables, reflecting the average spin-alignment of the produced particle and the magnitude of…
We derive the four-fold angular distribution for the semileptonic decay $\bar{B}\to D_2^*(\to D \pi)\,\ell \bar{\nu}$ where $D_2^*$(2460) is a tensor meson. We start with the most general beyond the Standard Model (SM) dimension-six…
We discuss how the angular distribution of lepton pairs from decays of vector mesons depends on the choice of reference frame, and provide a geometrical description of the transformations of the coefficients of the angular distribution.…
The coefficients determining the dilepton decay angular distribution of vector particles obey certain positivity constraints and a rotation-invariant identity. These relations are a direct consequence of the covariance properties of angular…
Polarization measurements provide a detailed method to test the Standard Model and to search for new physics. Most previous studies depend on pre-selected coordinates, which blurs the significance of the results. The construction of two…
This short note is concerned with the rotational invariance of the stored energy density in continuum physics as a scalar function of a few vectors. A simple derivation is presented for the determination of the general form of the energy…
Invariant tensors are states in the (local) SU(2) tensor product representation but invariant under global SU(2) action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An…
In two meson photoproduction off a nucleon, for the case in which two of the three final state hadrons are products of the decay of an intermediate resonance, general expressions for its decay distribution and for polarization observables…
The rotational properties of angular momentum eigenstates imply the existence of a frame-independent relation among the parameters of the decay distribution of vector mesons into fermions. This relation is a generalization of the Lam-Tung…
For homogeneous higher gradient elasticity models we discuss frame-indifference and isotropy requirements. To this end, we introduce the notions of local versus global SO(3)-invariance and identify frame-indifference (traditionally) with…
The joint angular distribution of the decay B \to J/\Psi V, where V is an axial vector or vector resonance, followed by the subsequent decay processes of the J/\Psi and V is calculated using the covariant density method. In particular, the…
Observables in random tensor theory are polynomials in the entries of a tensor of rank $d$ which are invariant under $U(N)^d$. It is notoriously difficult to evaluate the expectations of such polynomials, even in the Gaussian distribution.…
Recent measurements of the lepton flavor universality ratios $R^{\mu e}_{K}$ and $R^{\mu e}_{K^*}$ in $B\to \left(K, K^*\right)\mu^{+}\mu^{-}\left(e^+e^-\right)$ at LHCb align with the Standard Model predictions, necessitating search for…
Models, describing relativistic particles, where Lagrangian densities depend linearly on both the curvature and the torsion of the trajectories, are revisited in D=3 space forms. The moduli spaces of trajectories are completely and…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
We develop a curvilinear invariant set of the diffusion tensor which may be applied to Diffusion Tensor Imaging measurements on tissues and porous media. This new set is an alternative to the more common invariants such as fractional…
The observable consequences of a lowering of the restmasses of vector mesons on dilepton spectra in the SIS energy regime (HADES) and on photoabsorption cross sections on nuclei are studied in a transporttheoretical framework. We also…
In general there are nine observables in the decay of a B meson to two vector mesons defined in terms of polarization correlations of these mesons. Only six of these can be detected via the subsequent decay angular distributions because of…
Real or complex tensor model observables, the backbone of the tensor theory space, are classical (unitary, orthogonal, symplectic) Lie group invariants. These observables represent as colored graphs, and that representation gives an handle…
We investigate the weak semileptonic decays of the charmonium $J/\psi$ and bottomonium $\Upsilon(1S)$ into a pseudoscalar meson, namely, the $J/\psi\to D_{(s)}\ell\bar{\nu}_\ell$ and $\Upsilon(1S)\to B_{(c)}\ell\bar{\nu}_\ell$ decays. We…