Advanced parametrisations for hadronic form factors

The rich analytic structure of hadronic form factors makes a theoretically consistent yet easily applicable parametrisation cumbersome. Consequently, most parametrisations are limited to reproducing the simplest analytic features sufficient to describe form factors on their first Riemann sheet. Here, we introduce two novel form factor parametrisations that allow resonance poles and left-hand cuts on the second Riemann sheet to be studied, while also making the connection to partial-wave amplitudes manifest.

💡 Research Summary

The paper addresses a longstanding limitation in the parametrisation of hadronic two‑particle form factors (FFs). Traditional approaches, most notably the z‑expansion, map the entire first Riemann sheet of the complex‑s plane onto the unit disc, placing the right‑hand (unitarity) cut on the unit circle. While this works well for describing the space‑like region and the low‑energy timelike region below the first inelastic threshold, it fails to provide a convergent representation when one needs to describe the second Riemann sheet, where resonance poles, virtual states and a left‑hand cut (LHC) reside. In particular, the LHC is mapped to the interval