Abstract
Given a discontinuity of a PWA along the LHC, \(\varDelta (p^2)\), the first-iterated N / D solution is obtained from the N / 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.
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Notes
- 1.
If there where some s-channel exchange of a bare particle this would give rise to a pole in V(s) that could be straightforwardly accommodated by a adding a pole in the DR for \(V(p^2)\), cf. Eq. (4.4).
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Oller, J.A. (2019). The First-Iterated N / D Solution with Perturbative \(\varDelta (p^2)\). In: A Brief Introduction to Dispersion Relations. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-13582-9_12
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DOI: https://doi.org/10.1007/978-3-030-13582-9_12
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