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At very high energies, and in the central region ($x_F\simeq0$), thedouble-Pomeron exchange mechanism gives the dominant contribution to theproduction of hadrons with the positive $C$ parity and isospin $I=0$.Therefore, the observation of resonances in the states with $I=1$ will beindicative of their production or decay with the isotopic symmetry breaking.Here, we bear in mind the cases of the anomalous breaking of the isotopicsymmetry, i.e., when the cross section of the process breaking the isospin isnot of the order of $10^{-4}$ of the cross section of the allowed process butof the order of $1\%$. The paper draws attention to the reactions $pp\top(f_1(1285)/f_1(1420))p\to p(\pi^+\pi^-\pi^0)p$ and $pp\to p(K\bar K)p\top(a^0_0(980))p\to p(\eta\pi^0)p$ in which a similar situation can be realized,owing to the $K\bar K$ loop mechanisms of the breaking of isotopic symmetry. Wenote that there is no visible background in the $\pi^+\pi^-\pi^0$ and $\eta\pi^0$ channels. Observation of the process $pp\to p(f_1(1285))p\top(\pi^+\pi^-\pi^0)p$ would be a confirmation of the first results from the VESand BESIII detectors, indicating the very large isospin breaking in the decay$f_1(1285))\to\pi^+\pi^-\pi^0$.

physical review. d/physical review. d.

Proposal to look for the anomalous isotopic symmetry breaking in central  diffractive production of the $f_1(1285)$ and $a^0_0(980)$ resonances at the  LHC