Charged Particle Scattering in Renormalizable Pionless Effective Field Theory at Next-to-Leading Order: The $pd$, $dd$, and p³He Case

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 apd3/2 = 12.76(29)\,fm and rpd3/2 = 1.17(7)\,fm; for $dd$ scattering in the spin-quintet channel, we find add² = 6.26(3)\,fm and rdd² = 1.41(7)\,fm; and for p³He scattering, the spin-singlet and spin-triplet channels are characterized by ap³He⁰ = 11.26(4)\,fm, rp³He⁰ = 1.65(26)\,fm and ap³He¹ = 9.06(4)\,fm, rp³He¹ = 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 (Pionless EFT) for charged few-nucleon systems.