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Large-$N$ $π^+π^+$ scattering from twisted Eguchi--Kawai reduction

Year: 2026
Type: preprint
Abstract: We present the first computation of the $π^+π^+$ scattering length in large-$N$ QCD in the 't Hooft limit, $N_{\scriptscriptstyle{\rm f}}/N\to 0$, using the twisted Eguchi--Kawai formulation of the lattice theory. We employ values of $N$ up to 1156 and consider several quark masses and lattice spacings to achieve controlled large-$N$, continuum, and chiral limits. The chiral behavior of the scattering length is compared with next-to-leading-order Chiral Perturbation Theory predictions. Our result for the low-energy coupling describing the sub-leading quark-mass dependence is consistent with existing S-matrix bootstrap bounds. Combining TEK results with previous lattice QCD data obtained using standard methods for $3\le N\le 6$, we are also able to extract sub-leading $\mathcal{O}(1/N)$ corrections to the large-$N$ scattering length.
DOI: 10.48550/arxiv.2610.35176
Authors: Bonanno, Claudio, Pérez, Margarita García, González-Arroyo, Antonio, Ishikawa, Ken-Ichi, Okawa, Masanori, Romero-López, Fernando
Language: English
Open Access status: green
Funders: University of Bern, European Commission, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, University of Tsukuba, Agencia Estatal de Investigación, NextGenerationEU
Awards: G1799927510, G282847690, G318412399, G3454045019, G4993905653, G5195188938, G5785939682, G6520718613, G993971353
OpenAlex ID: W7223931110
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