Entanglement and Accidental Symmetries in Nuclear Effective Field Theory

Abstract

Effective field theory descriptions of nuclear forces automatically account for sym metries that are manifest in the underlying theory of quantum chromodynamics. In contrast, the consequences of accidental nuclear symmetries, such as Wigner SU(4) and Serber symmetries, often remain hidden. Wigner SU(4) symmetry dictates spin- and isospin-independent interactions while the orbital-parity Serber symmetry requires that the interaction is zero in partial waves with odd parity. Furthermore, recent work has highlighted an interesting connection between spin-entanglement suppression and Wigner SU(4) symmetry. In this thesis, we incorporate these accidental symmetries into chiral effective field theory (χEFT) and perform a quantitative study of their effects from an en tanglement perspective. We construct five modified versions of the leading order Weinberg power counting (WPC) potential and study pure spin entanglement for the neutron-proton system. Consequently, this study serves as a first step in the investigation of a possible entanglement-guided power counting in χEFT. We show that a Wigner SU(4) and Serber symmetric interaction results in a scattering-amplitude matrix that is proportional to the zero-entangling identity op erator for all scattering angles and for lab energies less than 300 MeV. Meanwhile, a short-distance breaking of Wigner SU(4) symmetry results in entanglement solely at low energies which, in the very-low-energy limit, depends sensitively on the specific values of the S-wave low-energy constants. At intermediate energies, the Wigner breaking tensor interaction in the leading order WPC potential is responsible for a large contribution to entanglement while Serber breaking in odd-parity spin-singlet waves results in entanglement in forward and backward scattering directions. The order-by-order entanglement pattern for WPC up to next-to-leading order is also presented and compared with the results obtained with the phenomenological Ni jmegenI potential. We conclude that entanglement provides a new perspective on the relative importance of different terms in the nuclear force. This work there fore advocates for future studies on entanglement-guided power-counting schemes in nuclear effective field theory.