Here we take the point of view of calculating perturbatively in an EFT the discontinuity of a PWA along the LHC, that we denoted above as\(\varDelta (p^2)\). Once\(\varDelta (p^2)\) is approximated in this way one can then solve the IE that follows from theN / D method in order to calculateD(s) along the LHC, and then the fullT(s).

1. 1.

   By this we mean that

   $$\begin{aligned} \int _0^1dy \int _0^1 dx\, K(x, y)^2<\infty ~,\\ \int _0^1 dy\, f(y)^2 <\infty ~.\nonumber \end{aligned}$$

   (11.17)
2. 2.

   The only exception might be if the factor\(\frac{\lambda m}{4\pi ^2}(-L)^{\gamma + \frac{1}{2}}\) multiplying the integral in Eq. (11.15) coincided with an eigenvalue of the kernelK(y, x). Nonetheless, since\(\lambda \) is continuous and the eigenvalues of a kernel are discrete we could employ a smooth continuation to find the solution in the a priori unlikely case of such coincidence.

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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