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Khuri-Treiman equations for $3\pi$ decays of particles with spin

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arxiv 1910.03107 v1 pith:JK5XOFNK submitted 2019-10-07 hep-ph hep-exhep-thnucl-th

JPAC Collaboration: M. Albaladejo , D. Winney , I. V.~Danilkin , C. Fernandez-Ramirez , V. Mathieu , M. Mikhasenko , A. Pilloni , J.A. Silva-Castro
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A. P. Szczepaniak
This is my paper · ORCID
classification hep-phhep-exhep-thnucl-th
keywords amplitudesdecayscrossingequationsfinalhelicitykhuri-treimanparticles
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abstract

Khuri-Treiman equations have proven to be a useful theoretical tool in the analysis of 3-body decays, specially into the $3\pi$ final state. In this work we present in full detail the necessary generalization of the formalism to study the decays of particles with arbitrary spin, parity, and charge conjugation. To this extent, we find it most convenient to work with helicity amplitudes instead of the so-called invariant amplitudes, specially when dealing with the unitarity relations. The isobar expansions in the three possible ($s$-, $t$-, and $u$-) final channels are related with the appropriate crossing matrices. We pay special attention to the kinematical singularities and constraints of the helicity amplitudes, showing that these can be derived by means of the crossing matrix.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Production Effects and Final-state Interactions in $\pi_1 \to 3\pi$

    hep-ph 2026-07 conditional novelty 6.0 of 10

    A Khuri-Treiman model with contact and one-pion-exchange production terms fits COMPASS's π1→3π freed-isobar data and produces a smooth 1.6 GeV structure in the extracted production strengths.

  2. Deep Neural Network Driven Simulation Based Inference Method for Pole Position Estimation under Model Misspecification

    hep-ph 2025-07 conditional novelty 5.0 of 10

    Simulation-based inference trained on synthetic scattering data yields rho(770) pole estimates closer to reference values than chi-squared minimization in the tested misspecification cases.

  3. $\phi \to 3\pi$ and $\phi\pi^{0}$ transition form factor from Khuri-Treiman equations

    hep-ph 2025-05 accept novelty 5.0 of 10

    A once-subtracted Khuri-Treiman analysis describes KLOE phi to 3pi and phi to pi0 gamma* data simultaneously, with a fitted subtraction constant near the sum-rule value.

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