Investigation of the lightest hybrid meson candidate with a coupled-channel analysis of $${{\bar{p}}p}$$-, $$\pi ^- p$$- and $${\pi \pi }$$-Data

A sophisticated coupled-channel analysis is presented that combines different processes: the channels $${\pi ^0\pi ^0\eta }$$ π 0 π 0 η , $${\pi ^0\eta \eta }$$ π 0 η η and $${K^+K^-\pi ^0}$$ K + K - π 0 from $${{\bar{p}}p}$$ p ¯ p annihilations, the P- and D-wave amplitudes of the $$\pi \eta $$ π η and $$\pi \eta ^\prime $$ π η ′ systems produced in $$\pi ^-p$$ π - p scattering, and data from $${\pi \pi }$$ π π -scattering reactions. Hence our analysis combines the data sets used in two independent previous analyses published by the Crystal Barrel experiment and by the JPAC group. Based on the new insights from these studies, this paper aims at a better understanding of the spin-exotic $$\pi _1$$ π 1 resonances in the light-meson sector. By utilizing the K-matrix approach and realizing the analyticity via Chew-Mandelstam functions the amplitude of the spin-exotic wave can be well described by a single $$\pi _1$$ π 1 pole for both systems, $$\pi \eta $$ π η and $$\pi \eta ^\prime $$ π η ′ . The mass and the width of the $$\pi _1$$ π 1 -pole are measured to be $$(1623 \, \pm \, 47 \, ^{+24}_{-75})\, \mathrm {MeV/}c^2$$ ( 1623 ± 47 - 75 + 24 ) MeV / c 2 and $$(455 \, \pm 88 \, ^{+144}_{-175})\, \mathrm {MeV}$$ ( 455 ± 88 - 175 + 144 ) MeV .

Optimal Perturbation Technique within the Asymptotic Iteration Method for Heavy-Light Meson Mass Splittings

For further insight into the perturbation technique within the framework of the asymptotic iteration method (PAIM), we suggest this method to be used as an alternative method to the traditional well-known perturbation techniques. We show by means of very simple algebraic manipulations that PAIM can be directly applied to obtain the symbolic expectation value of any perturbed potential piece without using the eigenfunction of the unperturbed problem. One of the fundamental advantages of PAIM is its ability to extract a reference unperturbed potential piece or pieces from the total Hamiltonian which can be solved exactly within AIM. After all, one can easily compute the symbolic expectation values of the remaining potential pieces. As an example, the present scheme is applied to the semi-relativistic wave equation with the harmonic-oscillator potential implemented with the Fermi–Breit potential terms. In particular, the non-trivial symbolic expectation values of the Dirac delta function, and the momentum-dependent orbit–orbit coupling terms are successfully calculated. Results are then used, as an illustration, to compute the semi-relativistic s-wave heavy-light meson masses. We obtain good agreement with experimental data for the meson mass splittings cu¯, cd¯, cs¯, bu¯, bd¯, bs¯.