We formulate a renormalizable pionless effective field theory ($\cancel{\pi }\mathrm{EFT}$) 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 $a_{pd}^{3/2}=12.76\left(29\right)\mathrm{fm}$ and $r_{pd}^{3/2}=1.17\left(7\right)\mathrm{fm}$; for $dd$ scattering in the spin-quintet channel we find $a_{dd}^2=6.26\left(3\right)\mathrm{fm}$ and $r_{dd}^2=1.41\left(7\right)\mathrm{fm}$; and for $p^3\mathrm{He}$ scattering the spin-singlet and spin-triplet channels are characterized by $a_{p^3\mathrm{He}}^0=11.26\left(4\right)\mathrm{fm}, r_{p^3\mathrm{He}}^0=1.65\left(26\right)\mathrm{fm}$ and $a_{p^3\mathrm{He}}^1=9.06\left(4\right)\mathrm{fm}, r_{p^3\mathrm{He}}^1=1.36\left(25\right)\mathrm{fm}$, 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 $\cancel{\pi }\mathrm{EFT}$ for charged few-nucleon systems.

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• Few-body systems
• Nuclear forces
• Nucleon-nucleon interactions