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We propose a new regularization scheme to study the bound state oftwo-nucleon systems in Lattice Effective Field Theory. Inspired by continuumEFT calculation, we study an exponential regulator acting on the leading-order(LO) and next-to-leading order (NLO) interactions, consisting of local contactterms. By fitting the low-energy coefficients (LECs) to deuteron binding energyand the asymptotic normalization coefficient (ANC) on a lattice simulation, weextract the effective range expansion (ERE) parameters in the $^3S_1$ channelto order $p^2$. We explore the impact of different powers of the regulator onthe extracted ERE parameters for the lattice spacing $a=1.97$ fm. Moreover, weinvestigate how the implementation of the regularization scheme improves thepredicted ERE parameters on the lattice spacing in the range of $1.4 \le a \le2.6$ fm. Our numerical analysis indicates that for lattice spacing greater than$2$ fm, the predicted observables are very close to the experimental data.

A Novel Regularization Scheme for Nucleon-Nucleon Lattice Simulations with Effective Field Theory