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On some low energy experiments on hadron spectroscopyState Research Center ‘Institute of High Energy Physics’, ul. Pobedy 1, Protvino, Moscow Region, 142280, Russian Federation Possibilities to carry out low energy experiments (at E$^{\operatorname{lab}}$ $\sim$ 2--10 GeV) on the searches and studies of exotic hadrons and rare decays of mesons are considered: 1) search for baryonic states of $\mathrm{qqqs\bar s}$, $\mathrm{qqss\bar s}$, and $\mathrm{qqqg}$ types in direct channel; 2) search for exotic mesons in baryon exchange processes pN $\to$ (M)$_f$ + (pN;p$\pi$N); 3) study of exotic mesons in OPE hadron reactions and in photoproduction processes; 4) study of the rare electromagnetic decays of mesons; 5) study of the isotopic invariance violation.
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