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Abstract

We apply the general framework of multiple dispersive bounds, firstly discussed in the companion paper [1], to the study of sub-threshold branch-cuts. We propose the simultaneous application of a double dispersive bound as a proper way to take into account unitarity constraints within phenomenological analyses of hadronic form factors in the presence of sub-threshold branch-cuts. Accordingly, the standard $z$-expansion of hadronic form factors, commonly referred to as the Boyd-Grinstein-Lebed approach [2-5], is modified by including simultaneously the dispersive bounds related to the pair-production and to the sub-threshold regions. For the latter one the effects of above-threshold poles are described through a new resonance model and the possible choices of the outer function outside the pair-production region are discussed. A detailed numerical analysis of the experimental data or lattice QCD results in the spacelike region for the charged kaon form factor is presented as a direct application of the procedure of double dispersive bound. The comparison with other methodologies present in literature and with the $z$-expansion based on the single, total dispersive bound clearly shows that the $z$-expansion including the double dispersive bound provides the most precise extrapolation at large momentum transfer as well as the most stable results with respect to the choice of the outer function outside the pair-production region.