Victor Ananyev | Searcharxiv

arXiv2021

Approximating the mode of the non-central chi-squared distribution

In this paper we consider the probability density function (PDF) of the non-central $χ^2$ distribution with arbitrary number of degrees of freedom and non-centrality. For this function we find the approximate location of the maximum and discuss related edge cases of 1 and 2 degrees of freedom. We also use this expression to demonstrate the improved performance of the C++ Boost's implementation of the non-central $χ^2$ and extend the domain of its applicability.

math.CA↗

arXiv2020

Light-by-light scattering sum rule for radiative transitions of bottomonia

We generalize a forward light-by-light scattering sum rule to the case of heavy quarkonium radiative transitions. We apply such sum rule to the bottomonium states, and use available data on radiative transitions in its evaluation. For the transitions that are not known experimentally, we provide theoretical estimates within a potential model, and consider the spread between similar approaches in the literature as an estimate for the model error. For the $Υ(1S)$, $Υ(2S)$, and $Υ(3S)$ states we observe that, due to a cancellation between transitions involving $χ_{b0}, χ_{b1}$, and $χ_{b2}$ states, the sum rule is satisfied within experimental and theoretical error estimates. Having tested this sum rule for the low-lying bottomonium states, it may be used as a tool to investigate the nature of exotic states in the charmonium and bottomonium spectrum through the corresponding radiative transitions.

hep-ph↗