Large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>N</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>limit reduces the number of independent few-body parity-violating low-energy constants in pionless effective field theory

Abstract

The symmetries of the standard model dictate that for very low energies, where nucleon dynamics can be described in terms of a pionless effective field theory $(\text{EFT}(\ensuremath{\pi}\phantom{\rule{-0.5em}{0ex}}/))$, the leading-order parity-violating nucleon-nucleon Lagrangian contains five independent unknown low-energy constants (LECs). We find that imposing the approximate symmetry of QCD that appears when the number of colors ${N}_{c}$ becomes large reduces the number of independent LECs to two at leading order in the combined $\text{EFT}(\ensuremath{\pi}\phantom{\rule{-0.5em}{0ex}}/)$ and large-${N}_{c}$ expansions. We also find a relation between the two isoscalar LECs in the large-${N}_{c}$ limit. This has important implications for the number of experiments and/or lattice calculations necessary to confirm this description of physics. In particular, we find that a future measurement of the parity-violating asymmetry in $\stackrel{P\vec}{\ensuremath{\gamma}}d\ensuremath{\rightarrow}np$ together with the existing result for parity-violating $\stackrel{P\vec}{p}p$ scattering would constrain all leading-order (in the combined expansion) LECs. This is a considerable improvement on the previous understanding of the system.