The basic problem that we consider in this section is to find the possible solutions for a set of form factors\(F_i(s)\),\(i=1\ldots n\), ordered in increasing value of their thresholds\(s_{\mathrm{th};i}\). Each of the\(F_i(s)\) has LHC for\(s<s_L\) and RHC for\(s>s_\mathrm{th}\), where\(s_\mathrm{th}\) is the lightest of all the thresholds\(s_{\mathrm{th};i}\) involved and\(s_L\) was defined above.

1. 1.

   More rigorously we should say thatL(s) diverges less strong than\(s^{m-1}\),\(m\ge 1\), to avoid just a logarithmic vanishing of\(L(s)/s^m\). However, for the statement above we always have in mind a power-like vanishing,\(|L(s)/s^m|<|s|^{-\gamma }\),\(\gamma >0\), for\(s\rightarrow \infty \).

2. 2.

   The number of open channels changes. However,\(\varPhi (s)\) is a continuous function ofs along the RHC.

3. 3.

   We assume that the zeroes and poles of\(\varDelta (s)\) do not occur at the threshold\(s_R\).

Authors and Affiliations

1. Departamento de Física, Universidad de Murcia, Murcia, Spain

   José Antonio Oller

Corresponding author

Correspondence toJosé Antonio Oller.

Reprints and permissions

© 2019 The Author(s), under exclusive licence to Springer Nature Switzerland AG

Policies and ethics