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arXiv · 2606.16781

QCD-like theories at next-to-next-to-leading order with $N_F=2$ non-degenerate fermions

Johan Bijnens·Daniil Krichevskiy
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Abstract

QCD-like theories with $N_F=2$ fermion flavours in real and pseudoreal representations are studied within Chiral Perturbation Theory. For the pseudoreal symmetry-breaking pattern $SU(4)/Sp(4)$, the reduced NLO Lagrangian is derived. The NLO and NNLO corrections to the pion masses, decay constants, and vacuum condensates are calculated for non-degenerate fermion masses, extending previous results obtained for degenerate masses and for the non-degenerate case at NLO. Using the available spectroscopic and scattering lattice data for the $Sp(N_c=4)$ gauge theory with two fermion flavours, fits of the NLO low-energy constants are performed at NNLO precision. It is found that higher-order corrections are important for reproducing lattice observables and have a significant impact on the phenomenology of strongly interacting pionic dark matter, particularly in the regime of big $M_\pi/F_\pi$.

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Johan Bijnens, Daniil Krichevskiy. 2026-06-15. QCD-like theories at next-to-next-to-leading order with $N_F=2$ non-degenerate fermions. https://arxiv.org/abs/2606.16781

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