Given a discontinuity of a PWA along the LHC,\(\varDelta (p^2)\), the first-iteratedN / D solution is obtained from theN / D DRs, cf. Eqs. (11.4) and (11.5), by iterating once along the RHC. This implies to substituting\(D(q^2)\rightarrow 1\) in the equation for\(N(p^2)\), Eq. (11.5). As a result the DR for\(N(p^2)\) corresponds to the perturbative amplitude\(V(p^2)\) with only LHC, which can be calculated by performing the corresponding integration, whose integrand is known now. Furthermore, the most common situation is that\(V(p^2)\) is an input function already calculated from some theory. The integrand for\(D(p^2)\) in Eq. (11.4) is also known.

1. 1.

   If there where somes-channel exchange of a bare particle this would give rise to a pole inV(s) that could be straightforwardly accommodated by a adding a pole in the DR for\(V(p^2)\), cf. Eq. (4.4).

Authors and Affiliations

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

   José Antonio Oller

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Correspondence toJosé Antonio Oller.

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