Triangle singularity enhancing isospin violation in $\bar B_s^0 \to J/\psi \pi^0 f_0(980)$

Abstract

We perform calculations for the $\bar B_s^0 \to J/\psi \pi^0 f_0(980)$ and $\bar B_s^0 \to J/\psi \pi^0 a_0(980)$ reactions, showing that the first one is isospin-suppressed while the second one is isospin-allowed. The reaction proceeds via a triangle mechanism, with $\bar B_s^0 \to J/\psi K^* \bar K +c.c.$, followed by the decay $K^* \to K\pi$ and a further fusion of $K\bar K$ into the $f_0(980)$ or $a_0(980)$. We show that the mechanism develops a singularity around the $\pi^0 f_0(980)$ or $\pi^0 a_0(980)$ invariant mass of 1420 MeV where the $\pi^0 f_0$ and $\pi^0 a_0$ decay modes are magnified and also the ratio of $\pi^0 f_0$ to $\pi^0 a_0$ production. Using experimental information for the $\bar B_s^0 \to J/\psi K^* \bar K +c.c.$ decay, we are able to obtain absolute values for the reactions studied which fall into the experimentally accessible range. The reactions proposed and the observables evaluated, when contrasted with actual experiments should be very valuable to obtain information on the nature of the low lying scalar mesons.