Researchers have developed a new basis for describing meromorphic pion scattering amplitudes in the large-N limit, a regime where quantum chromodynamics (QCD) simplifies. This basis is constructed from linear combinations of Lovelace-Shapiro-like amplitudes, which intrinsically satisfy fundamental properties such as analyticity, crossing symmetry, and Regge behavior. The work focuses on ensuring that these amplitudes are physically consistent, especially in specific kinematic regimes like the high-energy fixed-angle limit.

A crucial aspect of this development is the treatment of unitarity. Although unitarity is not directly imposed in the initial construction of the basis, the authors enforce it a posteriori by requiring positivity in the partial-wave decomposition. This condition is formulated as an optimization problem and solved numerically. This approach, termed "primal bootstrap," yields meromorphic amplitudes that satisfy all necessary physical constraints, ensuring that the results are consistent with fundamental principles of field theory.

The results obtained from this method have been compared with bounds derived from dual positivity conditions, demonstrating that the generated family of amplitudes spans the allowed parameter space. This methodology not only provides a robust tool for the study of pion scattering but is also adaptable. With appropriate modifications, the technique could be extended to construct amplitude families for a broader range of applications within particle physics and field theory, opening new avenues for the analysis of fundamental interactions.