The $\pi\pi$ scattering amplitude at large N$_{c}$

Hernández, Pilar; Romero-López, Fernando; Baeza Ballesteros, Jorge

Preprint

PUBDB-2025-05693

The $\pi\pi$ scattering amplitude at large N$_{c}$

Hernández, P. ; Romero-López, F. ; Baeza Ballesteros, J. (Corresponding author)DESY*

2025

[10.3204/PUBDB-2025-05693]

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Please use a persistent id in citations: doi:10.3204/PUBDB-2025-05693

Report No.: DESY-25-040; MIT-CTP/5850; arXiv:2503.13978

Abstract: We study the scaling of meson-meson scattering amplitudes with the number of colors, N$_{c}$. We use lattice calculations in a theory with N$_{f}$ = 4 degenerate flavors, with N$_{c}$ = 3 – 6 and pion mass M$_{π}$ ≈ 560 MeV. We focus on three different scattering channels, two of which have the same quantum numbers as some tetraquark candidates recently found at LHCb: the $ {T}_{cs0}^0(2900) $, $ {T}_{c\overline{s}0}^{++}(2900) $, $ {T}_{c\overline{s}0}^0(2900) $ and $ {T}_{cs1}^0(2900) $ states. Finite-volume energies are extracted using a large set of operators, containing two-particle operators with the form of two pions or two vector mesons, and local tetraquark operators. The resulting energy spectra is used to constrain the infinite-volume scattering amplitude by means of Lüscher’s quantization condition. We consider polynomial parametrizations of the phase shift, as well as one-loop chiral perturbation theory (ChPT) predictions. We find that our lattice results follow the expected N$_{c}$ scaling and are sensitive to subleading N$_{c}$ corrections. In addition, we constrain the scaling of different combinations of low-energy constants from matching to large N$_{c}$ ChPT. The results for the channel corresponding to a $ \left({\pi}^{+}{D}_s^{+}-{K}^{+}{D}^{+}\right) $ state show evidence of a virtual bound state with energy E$_{virtual}$ = 1.63(10)M$_{π}$ for N$_{c}$ = 3, while this pole disappears at N$_{c}$ > 3. This may be connected to the exotic states found in experiment.

Keyword(s): 1/N Expansion ; Hadronic Spectroscopy ; Structure and Interactions ; Lattice QCD ; Chiral Lagrangian

Classification:

ddc:530

Note: 66 pages including 3 appendices, 20 figures, 18 tables. Full list of operators included as ancillary file. v2: References added, minor corrections that do not affect the results. v3: Matches published version

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