Pole position of the ${a}_{1}(1260)$ resonance in a three-body unitary framework

Open Access

Pole position of the $a_{1} (1260)$ resonance in a three-body unitary framework

Daniel Sadasivan, Andrei Alexandru, Hakan Akdag, Felipe Amorim, Ruairí Brett, Chris Culver, Michael Döring, Frank X. Lee, and Maxim Mai

Phys. Rev. D 105, 054020 – Published 18 March 2022

Abstract

Masses, widths, and branching ratios of hadronic resonances are quantified by their pole positions and residues with respect to transition amplitudes on the Riemann sheets of the complex energy plane. In this study, we discuss the analytic structure in the physical energy region of three-body scattering amplitudes on such manifolds. As an application, we determine the pole position of the $a_{1} (1260)$ meson from the ALEPH experiment by allowing for $π ρ$ coupled channels in $S$ and $D$ waves. We find it to be $\sqrt{s_{0}} = (123 2_{- 0 - 11}^{+ 15 + 9} - i 26 6_{- 22 - 27}^{+ 0 + 15}) MeV$ .

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Received 14 December 2021
Accepted 28 February 2022

DOI:https://doi.org/10.1103/PhysRevD.105.054020

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Few-body systems Particle & resonance production Resonance reactions

Nuclear Physics

Authors & Affiliations

Daniel Sadasivan ^1,*, Andrei Alexandru ^2,3,†, Hakan Akdag^4,‡, Felipe Amorim ^1,§, Ruairí Brett ^2,∥, Chris Culver^5,¶, Michael Döring^2,6,**, Frank X. Lee^2,††, and Maxim Mai ^2,4,‡‡

¹Ave Maria University, Ave Maria, Florida 34142, USA
²The George Washington University, Washington, DC 20052, USA
³Department of Physics, University of Maryland, College Park, Maryland 20742, USA
⁴Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, 53115 Bonn, Germany
⁵Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom
⁶Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA

^*daniel.sadasivan@avemaria.edu
^†aalexan@gwu.edu
^‡akdag@hiskp.uni-bonn.de
^§FelipeAugusto.deAmor@my.avemaria.edu
^∥rbrett@gwu.edu
^¶C.Culver@liverpool.ac.uk
^**doring@gwu.edu
^††fxlee@gwu.edu
^‡‡maximmai@gwu.edu

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Issue

Vol. 105, Iss. 5 — 1 March 2022

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Physical Review D

covering particles, fields, gravitation, and cosmology