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 a₃^3/2 = 12. 76 (29) \, fm and r₃^3/2 = 1. 17 (7) \, fm; for dd scattering in the spin-quintet channel, we find a₃₃^2 = 6. 26 (3) \, fm and r₃₃^2 = 1. 41 (7) \, fm; and for p³He scattering, the spin-singlet and spin-triplet channels are characterized by a℃₇₄⁰ = 11. 26 (4) \, fm, r℃₇₄⁰ = 1. 65 (26) \, fm and a℃₇₄¹ = 9. 06 (4) \, fm, r℃₇₄¹ = 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.
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