A lattice study of ππ scattering at large Nc
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13130_2022_Article_18529.pdf
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Author(s)
Baeza-Ballesteros, Jorge
Hernández, Pilar
Romero-López, Fernando
Date Issued
June 9, 2022
Publisher
Springer Berlin Heidelberg
Citation
Journal of High Energy Physics. 2022 Jun 09;2022(6):49
Version
Final published version
Abstract
Abstract
We present the first lattice study of pion-pion scattering with varying number of colors, Nc. We use lattice simulations with four degenerate quark flavors, Nf = 4, and Nc = 3 − 6. We focus on two scattering channels that do not involve vacuum diagrams. These correspond to two irreducible representations of the SU(4) flavor group: the fully symmetric one, SS, and the fully antisymmetric one, AA. The former is a repulsive channel equivalent to the isospin-2 channel of SU(2). By contrast, the latter is attractive and only exists for Nf ≥ 4. A representative state is
D
s
+
π
+
−
D
+
K
+
/
2
$$ \left(\left.\left|{D}_s^{+}{\pi}^{+}\right.\right\rangle -\left.\left|{D}^{+}{K}^{+}\right.\right\rangle \right)/\sqrt{2} $$
. Using Lüscher’s formalism, we extract the near-threshold scattering amplitude and we match our results to Chiral Perturbation Theory (ChPT) at large Nc. For this, we compute the analytical U(Nf) ChPT prediction for two-pion scattering, and use the lattice results to constrain the Nc scaling of the relevant low-energy couplings.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP06(2022)049
