From Colour--Casimir Recoupling to Near-Threshold Scattering: Algebraic Diagnostics and a Pion-Mass Test for the Tcc+ Channel
Abstract
The near-threshold Tcc+ is a clean testing ground for how constituent-level colour structure connects to hadronic scattering. We report three results and state what each does and does not establish. (i)~\emph{Colour algebra.} In the two-dimensional colour-singlet basis of ccu̅d̅, a general pairwise colour operator has direct DD* matrix element VMM=−4/3(v13+v24), containing only the two intra-meson coefficients, while meson--hidden-colour mixing is VMHoff=√2/3Δv with Δv=v14+v23−v12−v34; uniform edges give no mixing. The projection is exact within this basis and is checked numerically on 10\,000 random edge assignments. A same-Hamiltonian decomposition shows that it re-expresses the central colour operator ($116.46$ MeV off-diagonal) rather than adding an independent dynamical input. (ii)~\emph{Negative dynamical results.} For Coulomb-type Gaussian edges the hidden-colour diagonal lies below the meson diagonal, so the attractive second-order shift −2Δv2/(9ΔH) does not apply. In a Gaussian constituent Hamiltonian calibrated to MD and MD*, the lowest compact level lies $148.6$ MeV above its model DD* threshold (iii)~\emph{Pion-mass test.} Couplings fixed at the mπ≃280 MeV lattice pole (−5.2 MeV) are carried to mπ≃391 MeV by changing only the reduced mass and compact-sector gap, both refitted to the lattice D and D* masses. A one-channel separable Lippmann--Schwinger benchmark (Λ=650 MeV, μ=967.7 MeV, CG≃−36.15 GeV−2) is calibrated to the $5.2$ MeV pole and serves only as a regulator-sensitivity study. We do not reproduce the complex lattice pole or perform a full coupled-channel calculation.
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BibTeX
@misc{monemzadeh2026from,
title = {{From Colour--Casimir Recoupling to Near-Threshold Scattering: Algebraic Diagnostics and a Pion-Mass Test for the $T_cc^+$ Channel}},
author = {M. Monemzadeh and N. Tazimi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39787},
eprint = {2610.39787},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39787},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From Colour--Casimir Recoupling to Near-Threshold Scattering: Algebraic Diagnostics and a Pion-Mass Test for the T_cc^+ Channel
AU - M. Monemzadeh
AU - N. Tazimi
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39787
UR - https://arxiv.org/abs/2610.39787
AB - The near-threshold T_cc^+ is a clean testing ground for how constituent-level colour structure connects to hadronic scattering. We report three results and state what each does and does not establish. (i)~\emph{Colour algebra.} In the two-dimensional colour-singlet basis of ccu̅d̅, a general pairwise colour operator has direct DD^* matrix element V_MM=−4/3(v_13+v_24), containing only the two intra-meson coefficients, while meson--hidden-colour mixing is V_MH^off=√2/3Δ_v with Δ_v=v_14+v_23−v_12−v_34; uniform edges give no mixing. The projection is exact within this basis and is checked numerically on 10\,000 random edge assignments. A same-Hamiltonian decomposition shows that it re-expresses the central colour operator ($116.46$ MeV off-diagonal) rather than adding an independent dynamical input. (ii)~\emph{Negative dynamical results.} For Coulomb-type Gaussian edges the hidden-colour diagonal lies below the meson diagonal, so the attractive second-order shift −2Δ_v^2/(9Δ_H) does not apply. In a Gaussian constituent Hamiltonian calibrated to M_D and M_D^*, the lowest compact level lies $148.6$ MeV above its model DD^* threshold (iii)~\emph{Pion-mass test.} Couplings fixed at the m_π≃280 MeV lattice pole (−5.2 MeV) are carried to m_π≃391 MeV by changing only the reduced mass and compact-sector gap, both refitted to the lattice D and D^* masses. A one-channel separable Lippmann--Schwinger benchmark (Λ=650 MeV, μ=967.7 MeV, C_G≃−36.15 GeV^−2) is calibrated to the $5.2$ MeV pole and serves only as a regulator-sensitivity study. We do not reproduce the complex lattice pole or perform a full coupled-channel calculation.
ER -