Bootstrapping the deuteron

Abstract: Bootstrap is a novel and ambitious paradigm for quantum physics. It aims to solve the target problems by exploiting theoretical constraints from general physical principles and self-consistency conditions. The bootstrap philosophy dates back to the 1960s. Its real power has been recognized only recently in, e.g., conformal field theories and relativistic scattering amplitudes. Inspired by [X. Han, S. A. Hartnoll, and J. Kruthoff, Phys. Rev. Lett. 125, 041601 (2020)], we report the first bootstrap results in low-energy nuclear physics, where deuteron, with its Hamiltonian given by pionless effective field theory in harmonic oscillator space, is solved by directly exploiting the most fundamental quantum mechanical requirement that probability should never be negative. Our study shows that the bootstrap method can be helpful in studying realistic nuclear systems.