# ICHEP 2020

July 28, 2020 to August 6, 2020
virtual conference
Europe/Prague timezone

## Inclusive $\Upsilon (1S) \to \eta^{(\prime)} + X$ Decays with Account of $\alpha_s$ Running in Effective $\eta^{(\prime)} g^* g$-Vertex

Jul 31, 2020, 1:48 PM
3m
virtual conference

#### virtual conference

Poster 06. Strong Interactions and Hadron Physics

### Speaker

Alexander Parkhomenko (P.G. Demidov Yaroslavl State University, Yaroslavl, Russia)

### Description

The $\eta^\prime$-meson energy spectrum in the inclusive $\Upsilon (1S) \to \eta^\prime g g g \to \eta^\prime X$ decay measured by the CLEO Collaboration in 2002 allowed one to constrain the lowest Gegenbauer coefficients $B^q_2$ and $B^g_2$ of the quark-antiquark and gluonic distribution amplitudes of the $\eta^\prime$-meson entering the $\eta^\prime g^* g$ effective vertex function (EVF). The fitting procedure of the CLEO data on the hard part of the $\eta^\prime$-meson energy spectrum was based on the theoretical expression calculated in the leading-order perturbative QCD in the static-quark limit for the orthoquarkonium. The resulting constraints were combined with the existing ones on these coefficients from an analysis of the $\eta^\prime - \gamma$ transition form factor. The updated measurements of the $\eta^\prime$-meson energy spectrum by the CLEO Collaboration in 2006 results a worser consistency with theoretical expectations and require some improvements from a theory. As a first step, we assume the dependence of the strong coupling constant in the $\eta^\prime g^* g$ EVF on the quark energy the $\eta^\prime$-meson and repeat the fitting procedure within the improved approach. The corresponding results for the Gegenbauer coefficients are presented. With this values we plot the
QCD-based $\eta$-meson energy spectrum in the inclusive $\Upsilon (1S) \to \eta g g g \to \eta + X$ decay in the leading-order perturbative QCD in the static-quark limit for the orthoquarkonium. Both the $\eta$- and $\eta^\prime$-meson energy spectra in the decays considered can be checked by the Belle Collaboration based on the existing and forthcoming data on $\Upsilon (1S)$-meson.

### Primary author

Alexander Parkhomenko (P.G. Demidov Yaroslavl State University, Yaroslavl, Russia)

### Co-authors

Ahmed Ali (DESY) Alexander Rusov (P.G. Demidov Yaroslavl State University)