Charged Particle Scattering in Renormalizable Pionless Effective Field Theory at Next-to-Leading Order: The $pd$, $dd$, and $p^3\mathrm{He}$ Case

Abstract

We formulate a renormalizable pionless effective field theory (Pionless EFT) with a non-perturbative treatment of the Coulomb interaction up to next-to-leading order (NLO) for few-nucleon systems. We extract scattering observables for charged clusters by employing two-, three-, and four-body contact interactions and using the stochastic variational method with a Coulomb-corrected harmonic oscillator trap. Our NLO results yield a $pd$ spin-quartet scattering length and effective range of $a_{pd}^{3/2}=12.76(29)\mathrm{fm}$ and $r_{pd}^{3/2}=1.17(7)\mathrm{fm}$; for $dd$ scattering in the spin-quintet channel, we find $a_{dd}^2=6.26(3)\mathrm{fm}$ and $r_{dd}^2=1.41(7)\mathrm{fm}$; and for $p^3\mathrm{He}$ scattering, the spin-singlet and spin-triplet channels are characterized by $a_{p^3\mathrm{He}}^0=11.26(4)\mathrm{fm}$, $r_{p^3\mathrm{He}}^0=1.65(26)\mathrm{fm}$ and $a_{p^3\mathrm{He}}^1=9.06(4)\mathrm{fm}$, $r_{p^3\mathrm{He}}^1=1.36(25)\mathrm{fm}$, respectively. Our predictions exhibit mild cutoff dependence and agree well with existing experimental phase shift analyses and potential model calculations. This demonstrates the predictive power of (Pionless EFT) for charged few-nucleon systems.

Comments: Data in figures are publicly accessible: DOI:10.5281/zenodo.16290109