Signature decay modes of the compact doubly-heavy tetraquarks T₁₁ₔ ₃ and T₁₂ₔ ₃

Based on the expectations that the lowest-lying double-bottom tetraquark T₁₁ ₔ ₃ (JP=1^+) and the bottom-charm tetraquark T₁₂ ₔ ₃ (JP=0^+) are stable against strong and electromagnetic decays, we work out a number of semileptonic and non-leptonic weak decays of these hadrons, making use of the heavy quark symmetry. In doing this, we concentrate on the exclusive decays involving also tetraquarks in the final states, i. e. , transitions such as T₁₁ ₔ ₃ T₁₂ ₔ ₃ (^- _, h^-) and T₁₂ ₔ ₃ T₂₂ ₔ ₃ (^- _, h^-), where h^-=^-, ^-, a₁^-. So far, only the JP=1^+ tetraquark T₂₂ ₔ ₃ has been discovered, which we identify with the I=0 T₂₂^+ object, compatible with JP=1^+ and having the mass and decay widths m =M (T₂₂^+) - (M (D^*+) - M (D⁰) ) = -360 40 ^+4-₀ keV and (T₂₂^+) =48^+2-₁₄ keV. Experimental discoveries of the transitions worked out here will go a long way in establishing the nature of these tetraquarks as (mainly) compact four-quark objects.