Two-pion exchange for coupled-channel scattering of two heavy mesons

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Abstract
To improve the theoretical understanding of multiquark states like Z b ( 10610 ) and Z b ( 10650 ) , we calculate the heavy-meson heavy-(anti)meson scattering potential up to next-to-leading order, O ( Q 2 ) , within chiral effective field theory ( χ EFT ) employing a power counting scheme that explicitly keeps track with the large momentum scale Q ∼ 2 μ δ (where δ = m V − m P is the vector-pseudoscalar mass difference and μ their reduced mass) introduced by the coupled channel dynamics. We provide expressions for the two-pion exchange (TPE) terms up to O ( Q 2 ) and their partial-wave decomposition. We show that these potentials are well approximated by contact terms at O ( Q 2 ) , with minor residual nonanalytic TPE contributions, supporting χ EFT convergence in the theoretical predictions for Z b ( 10610 ) and Z b ( 10650 ) , as well as their spin partners. These findings are also relevant for D ( * ) D ( * ) scattering, especially for the T c c state, for both physical and lattice quantum chromodynamics (QCD) data with moderately larger pion masses. We further demonstrate that the differences between isovector and isoscalar potentials for heavy mesons are naturally explained by the TPE contributions. Published by the American Physical Society 2025
Funding Information
  • National Natural Science Foundation of China (11621131001)
  • Deutsche Forschungsgemeinschaft (CRC110)

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