Speaker
Bing An Li
(University of Kentucky)
Description
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\begin{document}
\title{$\Upsilon(1S)\rightarrow \gamma( \eta', \eta, f_2(1270))$ decays }
\author{Bing An Li\\Department of Physics, Univ. of Kentucky, Lexington, USA}
%KY, 40506, USA}
\maketitle
In this talk the study of $\Upsilon(1S)\rightarrow \gamma (\eta', \eta, f_2(1270))$ decays
is presented.
Comparing with decays $J/\psi\rightarrow\gamma (\eta', \eta, f_2(1270))$,
very small upper limits
\[B(\Upsilon(1s)\rightarrow\gamma\eta)<1.0\times10^{-6},\;\;
B(\Upsilon(1s)\rightarrow\gamma\eta')<1.9\times10^{-6}\]
and larger
\[B(\Upsilon(1S)\rightarrow\gamma f_2(1270))=(10.2\pm0.8\pm0.7)\times 10^{-5},\]
%\[B(\Upsilon(1S)\rightarrow\gamma f_2(1270))=(10.5\pm1.6(stat)^{+1.9}_{-1.8}(syst))\times 10^{-5}\]
have been reported by CLEO.
Dependence on quark mass plays key roles in these decays of $J/\psi, \Upsilon(1S)$. An approach
in which $\eta'$ and $f_2(1270)$ are strongly coupled to gluons has been used to study these decays.
This approach has successfully predicted
\[\frac{\Gamma(J/\psi\rightarrow\gamma\eta')}{\Gamma(J/\psi\rightarrow\gamma\eta)}=5.1\]
and very small \(y=T_2/T_0\)($J/\psi\rightarrow\gamma f_2$) which agrees with data well.
By using this approach very strong quark mass dependence
\[\frac{B(\Upsilon\rightarrow\gamma\eta')}{B(J/\psi\rightarrow\gamma\eta')}=
0.29\frac{\alpha_s(m_c)}{\alpha_s(m_b)}({m_c\over m_b})^7\]
is obtained. Inputting $B(J/\psi\rightarrow\gamma\eta')$,
\[B(\Upsilon\rightarrow\gamma\eta')=1.04\times10^{-7},\;\;B(\Upsilon\rightarrow\gamma\eta)=0.23\times10^{-8}\]
are obtained. They are in good agreement with data. The study shows that
d-wave dominance in $\Upsilon(1S)\rightarrow\gamma f_2(1270)$ is the consequence of the strong coupling
between $f_2$ and gluons and an enhancement factor, $\frac{p^4_\Upsilon}{p^4_J}$, in the ratio of the decay rates is resulted
in the d-wave dominance. Like $\Upsilon(1s)\rightarrow\gamma\eta'$ there is suppress factor by $m_b$ in
$\Upsilon(1S)\rightarrow\gamma f_2(1270)$. The combination of these two factors lead to larger
$B(\Upsilon(1S)\rightarrow\gamma f_2(1270))$. On the other hand, very small ratios of the helicity amplitudes
are predicted and they agree with data.
Right quark mass dependencies of $\Upsilon(1s)\rightarrow\gamma(\eta', \eta, f_2(1270))$ are revealed from the
couplings between the mesons and gluons. Theoretical results agree with data well. In this study \(m_c=1.3GeV\) and
$\bar{MS}$
mass of b-quark are taken.
\end{document}
Author
Bing An Li
(University of Kentucky)
