Investigation of rainbow-ladder truncation for excited and exotic mesons

Si-xue Qin, Lei Chang, Yu-xin Liu, Craig D. Roberts, and David J. Wilson

Phys. Rev. C 85, 035202 – Published 6 March 2012

Abstract

Ground-state, radially excited, and exotic scalar, vector, and flavored-pseudoscalar mesons are studied in rainbow-ladder truncation using an interaction kernel that is consonant with modern Dyson-Schwinger equation and lattice-QCD results. The inability of this truncation to provide realistic predictions for the masses of excited and exotic states is confirmed and explained. However, its application does provide information that is potentially useful when working beyond this leading-order truncation, e.g.: assisting with the development of projection techniques that ease the computation of excited-state properties; placing qualitative constraints on the long-range behavior of the interaction kernel; and highlighting and illustrating some features of hadron observables that do not depend on details of the dynamics.

Received 15 September 2011

DOI:https://doi.org/10.1103/PhysRevC.85.035202

Authors & Affiliations

Si-xue Qin¹, Lei Chang², Yu-xin Liu^1,3, Craig D. Roberts^1,2,4, and David J. Wilson²

¹Department of Physics, Center for High Energy Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
²Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
³Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000, China
⁴Department of Physics, Illinois Institute of Technology, Chicago, Illinois 60616-3793, USA

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Vol. 85, Iss. 3 — March 2012

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Figure 1
Pseudoscalar mesons. Relative difference between the mass computed with all the amplitudes in Eq. (10) and that obtained when the identified $i \geq 2$ amplitude is omitted. Circles: ground-state pion; Squares: $J^{P C} = 0^{- -}$ exotic; and Diamonds: first pseudoscalar radial excitation. In all cases, $ω = 0.6$ GeV, $D ω = {(1.1 GeV)}^{3}$ . There is only minor quantitative variation with $ω \in [0.4, 0.6]$ GeV. The $i = 1$ amplitude is never omitted, it specifies the reference value.Reuse & Permissions
Figure 2
Scalar mesons. Relative difference between the mass computed with all the amplitudes in Eq. (11) and that obtained when the identified $i \geq 2$ amplitude is omitted. Circles: ground state $u = d$ scalar; Squares: $J^{P C} = 0^{+ -}$ exotic; and Diamonds: first pseudoscalar radial excitation. In all cases $ω = 0.6$ GeV, $D ω = {(1.1 GeV)}^{3}$ . There is only minor quantitative variation with $ω \in [0.4, 0.6]$ GeV. The $i = 1$ amplitude is never omitted, it specifies the reference value.Reuse & Permissions
Figure 3
Vector mesons. Relative difference between the mass computed with all the amplitudes in Eq. (12) and that obtained when the identified $i \geq 2$ amplitude is omitted. Circles: ground state $u = d$ vector; Squares: $J^{P C} = 1^{- +}$ exotic; and Diamonds: first vector radial excitation. In all cases $ω = 0.6$ GeV, $D ω = {(1.1 GeV)}^{3}$ . While there are quantitative changes with $ω$ , the pattern of amplitude importance is unchanged. The $i = 1$ amplitude is never omitted, it specifies the reference value.Reuse & Permissions
Figure 4
Pseudoscalar mesons. $ω$ dependence of low-order Chebyshev projections of leading invariant amplitude for ground, radially excited, and exotic states. Upper four panels, ground and radial; lower four panels, ground and exotic. In all panels, solid line—zeroth moment, ground state; dashed line—leading moment, comparison state; dash-dotted line—subleading moment, comparison state. Row-1, left, $ω = 0.4$ GeV; Row-1, right, $ω = 0.5$ GeV; Row-2, left, $ω = 0.6$ GeV; and Row-2, right, $ω = 0.7$ GeV. This pattern is repeated in the next two rows. The normalization is chosen such that $^{0} E_{π_{0}} (k^{2} = 0) = 1$ and $D ω = {(1.1 GeV)}^{3}$ .Reuse & Permissions
Figure 5
Vector mesons. $ω$ dependence of low-order Chebyshev projections of leading invariant amplitude for ground, radially excited, and exotic states. Upper four panels, ground and radial; lower four panels, ground and exotic. In all panels, solid line—zeroth moment, ground state; dashed line—leading moment, comparison state; dash-dotted line—subleading moment, comparison state. Row-1, left, $ω = 0.4$ GeV; Row-1, right, $ω = 0.5$ GeV; Row-2, left, $ω = 0.6$ GeV; and Row-2, right, $ω = 0.7$ GeV. This pattern is repeated in the next two rows. The normalization is chosen such that $^{0} E_{ρ_{0}} (k^{2} = 0) = 1$ and $D ω = {(1.1 GeV)}^{3}$ .Reuse & Permissions
Figure 6
$ω$ dependence of leptonic decay constants for pseudoscalar and vector mesons. Ground-state pion, solid line; radially excited pion, dashed line; ground-state $ρ$ meson, dotted line; and radially excited $ρ$ meson, dash-dotted line. [ $D ω = {(1.1 GeV)}^{3}$ .]Reuse & Permissions

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