We present a theoretical study of the two-particle spectrum $\omega \left(K\right)$ for the chiral waveguide QED setup of an array of two-level atoms directionally interacting with photons propagating along the waveguide. We demonstrate that for each pair center-of-mass momentum $K$ there exist distinct solutions with $\mathrm{Im}\omega \le 0$ in the two-particle spectrum, corresponding to bound, antibound, and resonance states, in addition to the continuum of scattering states. Contrary to previous studies, which showed the bound and resonance-state spectra only over a limited range of $K$, the calculated spectrum is consistent across all $K$ values. An interesting finding is that the real part of the spectrum $\text{Re}\omega \left(K\right)$ in the chiral model is gapless. The calculated dispersion law $\omega \left(K\right)$ provides an effective model for the bound photon pairs also in a finite-size array, manifesting the topological non-Hermitian skin effect.

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• Collective effects in quantum optics
• Topological effects in photonic systems
• Non-Hermitian systems