Form Factor Analysis Derived from the Gluon Emission Model Applied to the $\Psi(2S)$ and the $\Upsilon(2S)$

Abstract

In a recent article it has been shown that form factors may be derived through the use of the Gluon Emission Model (GEM) theoretical structure describing the widths of vector mesons; such form factors, $f$, are such that $(1-f)$ represents the fraction of the original quark $(Q)$ --- anti-quark $(Q^*)$ pair comprising a given vector meson that remains part of the decay scheme, the remainder, $f$, making a transition to a $QQ^*$ state comprising quarks of the next lightest mass compared to the original (remaining) ones. In conjunction with representative Feynman Diagrams we employ said form factors in order to calculate the various partial widths of the $\Psi(2S)$ and the $\Upsilon(2S)$. Excellent agreement with experiment is reached, and we are able to show that the matrix elements involved in the $\Psi(2S) \to \Psi(1S) + Z$ decay, where $Z$ represents any other product, and in the $\Upsilon(2S) \to \Upsilon(1S)+ Z$ decay are roughly four ninths the magnitude of those associated with the $\Psi(2S) \to Z_{1} + Z_{2}$ decay and the $\Upsilon(2S) \to Z_{1} + Z_{2}$ decay, where $Z_{1}$ and $Z_{2}$ each represent any decay product other than $\Psi(1S)$ or $\Psi(2S)$, respectively.