Recently, the charge-exchange reaction \({{\pi }^{ - }}p \to \) \(\omega \phi n\) was studied with the upgraded VES facility (at the Protvino accelerator) in the interaction of a 29 GeV pion beam with a beryllium target [1]. The analysis performed showed that the observed signal in \(\omega \phi \) system can be described by the contribution of the known scalar resonance \({{f}_{0}}(1710)\) [2]. The dominant mechanism of the \({{\pi }^{ - }}p \to {{f}_{0}}(1710)n\) reaction at high energies and small momentum transfers is the one-pion exchange mechanism. This fact allowed the authors of [1] to find the product of the \({{f}_{0}}(1710) \to \pi \pi \) and \({{f}_{0}}(1710) \to \omega \phi \) branching fractions:

$$\begin{gathered} Br({{f}_{0}}(1710) \to \pi \pi )Br({{f}_{0}}(1710) \to \omega \phi ) \\ = (4.8 \pm 1.2) \times {{10}^{{ - 3}}}. \\ \end{gathered} $$
(1)

Then, using the data presented in the Review of Particle Physics (RPP) [2] for the decays \(J{\text{/}}\psi \to \) \(\gamma {\kern 1pt} {{f}_{0}}(1710)\,{\kern 1pt} \to \,{\kern 1pt} \gamma \pi \pi \) and \(J{\text{/}}\psi {\kern 1pt} \, \to \,{\kern 1pt} \gamma {\kern 1pt} {{f}_{0}}(1710)\,{\kern 1pt} \to \,{\kern 1pt} \gamma \omega \phi \), they found the product \(Br(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma \pi \pi ) \times \) \(Br(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma \omega \phi )\) = (9.5 ± 2.6) × 10−8, divided it by Eq. (1), extracted the root from this ratio and thus get the total branching fraction of the \(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710)\) decay [1]:

$$\begin{gathered} {{\left[ {\frac{{Br(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma \pi \pi )Br(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \omega \phi )}}{{Br({{f}_{0}}(1710) \to \pi \pi )Br({{f}_{0}}(1710) \to \omega \phi )}}} \right]}^{{1/2}}} \\ = Br(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710)) = (4.46 \pm 0.82) \times {{10}^{{ - 3}}}. \\ \end{gathered} $$
(2)

They compared this value with the known branching fraction for \(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710)\) → 5 channels, i.e., with \(Br(J{\text{/}}\psi \to \gamma {{f}_{0}}(1710)\) → \((\gamma \pi \pi + \gamma K\bar {K} + \gamma \eta \eta + \gamma \omega \omega + \) \(\gamma \omega \phi ))\) = (2.13 ± 0.18) × 10−3 [2], and concluded that unregistered channels account for \(Br(J{\text{/}}\psi \to \) \(\gamma {{f}_{0}}(1710)\) → \((\gamma 4\pi + \gamma \eta \eta {\kern 1pt} '\; + \gamma \pi \pi K\bar {K} + ...))\) = (2.33 ± 0.84) × 10−3 [1].

If we now divide the values given in RPP [2] for the branching fractions of the \(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma \pi \pi \), \(\gamma K\bar {K}\), \(\gamma \eta \eta \), \(\gamma \omega \omega \), \(\gamma \omega \phi \) decays by \(Br(J{\text{/}}\psi \to \) \(\gamma {\kern 1pt} {{f}_{0}}(1710))\) from Eq. (2), then we obtain the absolute branching fractions for the corresponding decays of the \({{f}_{0}}(1710)\) resonance itself. These estimates are presented in Table 1.

Table 1. Branching fractions for the \({{f}_{0}}(1710)\) decays
Full size table

Note that the factorization of the effective creation and decay coupling constants for the \({{f}_{0}}(1710)\) resonance makes it possible to evaluate the ratio \(Br({{f}_{0}} \to \pi \pi ){\text{/}}Br({{f}_{0}} \to K\bar {K})\) from the data on the radiative \(J{\text{/}}\psi \), \(\psi (2S)\), and \(\Upsilon (1S)\) decays [2] in three different ways,

$$\begin{gathered} \frac{{Br({{f}_{0}}(1710) \to \pi \pi )}}{{Br({{f}_{0}}(1710) \to K\bar {K})}} \\ = \frac{{Br(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma \pi \pi )}}{{Br(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma K\bar {K})}} = 0.40 \pm 0.07, \\ \end{gathered} $$
(3)
$$\begin{gathered} \frac{{Br({{f}_{0}}(1710) \to \pi \pi )}}{{Br({{f}_{0}}(1710) \to K\bar {K})}} \\ = \frac{{Br(\psi (2S) \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma \pi \pi )}}{{Br(\psi (2S) \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma K\bar {K})}} = 0.58 \pm 0.11, \\ \end{gathered} $$
(4)
$$\begin{gathered} \frac{{Br({{f}_{0}}(1710) \to \pi \pi )}}{{Br({{f}_{0}}(1710) \to K\bar {K})}} \\ = \frac{{Br(\Upsilon (1S) \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma \pi \pi )}}{{Br(\Upsilon (1S) \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma K\bar {K})}} = 0.36 \pm 0.17. \\ \end{gathered} $$
(5)

As is seen, these estimates are consistent with each other within the error limits. The VES result (see Eq. (2), factorization, and RPP data [2] allow us to determine the absolute branching fractions for radiative decays \(\psi (2S) \to \gamma {{f}_{0}}(1710)\) and \(\Upsilon (1S) \to \) \(\gamma {\kern 1pt} {{f}_{0}}(1710)\) in two ways (using the data on the \({{f}_{0}}(1710) \to \pi \pi \) and \({{f}_{0}}(1710) \to K\bar {K}\) channels):

$$\begin{gathered} Br(\psi (2S) \to \gamma {\kern 1pt} {{f}_{0}}(1710)) \\ = \frac{{Br(\psi (2S) \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma \pi \pi )}}{{Br(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma \pi \pi )}} \\ \times \;Br(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710)) = (4.1 \pm 1.2) \times {{10}^{{ - 5}}}, \\ \end{gathered} $$
(6)
$$\begin{gathered} Br(\psi (2S) \to \gamma {\kern 1pt} {{f}_{0}}(1710)) \\ = \frac{{Br(\psi (2S) \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma K\bar {K})}}{{Br(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma K\bar {K})}} \\ \times \;Br(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710)) = (3.1 \pm 0.7) \times {{10}^{{ - 5}}}, \\ \end{gathered} $$
(7)
$$\begin{gathered} Br(\Upsilon (1S) \to \gamma {\kern 1pt} {{f}_{0}}(1710)) \\ = \frac{{Br(\Upsilon (1S) \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma \pi \pi )}}{{Br(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma \pi \pi )}} \\ \times \;Br(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710)) = (0.93 \pm 0.27) \times {{10}^{{ - 5}}}, \\ \end{gathered} $$
(8)
$$\begin{gathered} Br(\Upsilon (1S) \to \gamma {\kern 1pt} {{f}_{0}}(1710)) \\ = \frac{{Br(\Upsilon (1S) \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma K\bar {K})}}{{Br(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710) \to \gamma K\bar {K})}} \\ \times \;Br(J{\text{/}}\psi \to \gamma {\kern 1pt} {{f}_{0}}(1710)) = (1.03 \pm 0.19) \times {{10}^{{ - 5}}}. \\ \end{gathered} $$
(9)

The properties of the \({{f}_{0}}(1710)\) resonance and its possible nature have been the subject of intense discussions for several decades, see for review [2, 3] and references therein. For now, the numerical estimates given in Table 1 are a good addition to the very scarce information available about the absolute branching fractions of the \({{f}_{0}}(1710)\) decays, see section dedicated to this state in RPP [2] (the existing data are not used by Particle Data Group for finding averages, fits, limits, etc.). Statements like “seen” in this section can be superseded by the corresponding values from Table 1.

A similar method for estimating the absolute branching fractions can be useful for other heavy scalar (tensor) multichannel resonances, for example, for \({{f}_{0}}(1370)\), \({{f}_{0}}(1500)\), \({{f}_{0}}(1770)\), and \({{f}_{0}}(2020)\) [2] that can be produced both in \(\pi N\) collisions via one-pion exchange mechanism and in radiative \(J{\text{/}}\psi \), \(\psi (2S)\), and \(\Upsilon (1S)\) decays.

In the recent work [4], we discussed the properties of the new \({{a}_{0}}(1700{\text{/}}1800)\) meson [2] assuming that it can be similar to the \({{q}^{2}}{{\bar {q}}^{2}}\) state from the MIT bag [5]. This \({{a}_{0}}\) meson has to have the isoscalar partner \({{f}_{0}}\) with a close (or even degenerate) mass [5]. The branching fractions in Table 1 will help us to understand whether the \({{f}_{0}}(1710)\) can pretend to this role. This issue will be considered elsewhere.