Coulomb effects in the decays $\Upsilon (4S) \rightarrow B\bar B$

TL;DR

This paper introduces an exactly solvable model for $S$ decays into B mesons, analyzing Coulomb effects and showing they influence decay spectra and ratios, challenging common factorization assumptions.

Contribution

It presents a novel exactly solvable model that accurately describes Coulomb effects in $S$ decays, revealing non-factorizable influences on decay spectra and ratios.

Findings

Coulomb effects alter the peaks in decay spectra.

The decay ratio is a nontrivial energy-dependent function.

Factorization of Coulomb effects is not valid.

Abstract

A simple exactly solvable model is proposed for describing the decays $\Upsilon (4S) \rightarrow B^0\bar B^0$ and $\Upsilon (4S) \rightarrow B^+B^-$. Our predictions agree with available experimental data. Using this model, we analyze the Coulomb effects in the spectra of these decays. It is shown that the frequently used assumption of factorization of Coulomb effects is not fulfilled. The Coulomb interaction leads to the difference in the positions and heights of the peaks corresponding to the charged and neutral modes. As a result, the ratio of probability of $\Upsilon (4S)\rightarrow B^+B^-$ decay and $\Upsilon (4S) \rightarrow B^0\bar B^0$ decay is a nontrivial function of energy.