Charged particle scattering in renormalizable pionless effective field theory at next-to-leading order: The pd, dd, and p³He cases

We formulate a renormalizable pionless effective field theory (π/EFT) with a nonperturbative 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 a³ _pd ^/2 = 12.76(29) fm and r_pd ³/² = 1.17(7) fm; for dd scattering in the spin-quintet channel we find a_dd ² = 6.26(3) fm and r_dd ² = 1.41(7) fm; and for p³He scattering the spin-singlet and spin-triplet channels are characterized by a⁰ _p3He = 11.26(4) fm, r_p ⁰_3He = 1.65(26) fm and a¹ _p3He = 9.06(4) fm, r_p ¹_3He = 1.36(25) 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 π/EFT for charged few-nucleon systems.