Termination of the Radial Ladder in Mixed-Flavor Heavy Mesons
Abstract
A fundamental open question in hadron spectroscopy is whether the radial excitation ladder of heavy mesons terminates at a finite level once confinement is screened by light-quark pair creation. We address this question for the mixed-flavor mesons Ds, Bs, and Bc by solving a screened Godfrey--Isgur Hamiltonian with the Gaussian expansion method. The screening length is fixed by threshold-dependent string breaking analysis, and is matched to the charmonium and bottomonium anchors. The calculated spectra saturate at $3.36$, $6.78$, and 8.19 GeV in Ds, Bs, and Bc families, while the RMS radii grow by several fm and mass gaps fall below 10 MeV. Mass-radius decoupling places the end of the safe radial ladder at nsafe≈ 4--$6$ for Ds, $5−−7$ for Bs, and $9−−11$ for Bc, so the ladder terminates first in Ds, then in Bs, and last in Bc. Above the limiting-mass windows, at $3.49$, $6.86$, and 8.24 GeV, states of the radial ladder cannot be discovered. This termination is directly testable with forthcoming high-statistics data from BESIII, Belle II, and LHCb.
Related
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BibTeX
@misc{zhang2026termination,
title = {{Termination of the Radial Ladder in Mixed-Flavor Heavy Mesons}},
author = {Wen-Xuan Zhang and Wen-Nian Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34734},
eprint = {2609.34734},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34734},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Termination of the Radial Ladder in Mixed-Flavor Heavy Mesons
AU - Wen-Xuan Zhang
AU - Wen-Nian Liu
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34734
UR - https://arxiv.org/abs/2609.34734
AB - A fundamental open question in hadron spectroscopy is whether the radial excitation ladder of heavy mesons terminates at a finite level once confinement is screened by light-quark pair creation. We address this question for the mixed-flavor mesons D_s, B_s, and B_c by solving a screened Godfrey--Isgur Hamiltonian with the Gaussian expansion method. The screening length is fixed by threshold-dependent string breaking analysis, and is matched to the charmonium and bottomonium anchors. The calculated spectra saturate at $3.36$, $6.78$, and 8.19 GeV in D_s, B_s, and B_c families, while the RMS radii grow by several fm and mass gaps fall below 10 MeV. Mass-radius decoupling places the end of the safe radial ladder at n_safe≈ 4--$6$ for D_s, $5−−7$ for B_s, and $9−−11$ for B_c, so the ladder terminates first in D_s, then in B_s, and last in B_c. Above the limiting-mass windows, at $3.49$, $6.86$, and 8.24 GeV, states of the radial ladder cannot be discovered. This termination is directly testable with forthcoming high-statistics data from BESIII, Belle II, and LHCb.
ER -