Role of three-body dynamics in nucleon-deuteron correlation functions

Correlation functions of hadrons can be accessed in high-energy collisions of atomic nuclei, revealing information about the underlying interaction. This work complements experimental efforts to study nucleon-deuteron $Nd$ -- with $N=p$ (proton) or $N=n$ (neutron) -- correlations with theory evaluations using different techniques. The correlation functions $C_{nd}$ and $C_{pd}$ are calculated based on scattering wave function, extending previous benchmarks for the $Nd$ scattering matrix to this new observable. We use hyperspherical harmonics and Faddeev techniques with one of the widely used nucleon-nucleon ($NN$) interactions, the Argonne $v_{18}$ potential. Moreover, in the low-energy region we perform additional calculations in the framework of pionless effective field theory. The $pd$ correlation function is computed in the large-energy region to make contact with a recent measurement by the ALICE Collaboration. We show that the scattering wave function has the proper dynamical input to describe an initial rise and subsequent oscillations of $C_{pd}$ as a function of the energy. Effects on the observables using different $NN$ and three-nucleon potentials are evaluated with the conclusion that variations of around $2\%$ are observed. Although these effects are small, future measurements can go beyond this accuracy allowing for new detailed studies of strong interaction in light nuclear systems. The present study supports the current efforts devoted to the measurement of correlation functions in systems dominated by the strong interactions, such as $pd$, $ppp$, $\Lambda d$ and $pp\Lambda$.