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Finite-volume pionless effective field theory for few-nucleon systems with differentiable programming

Finite-volume pionless eﬀective ﬁeld theory provides an eﬃcient framework for the extrapolation of nuclear spectra and matrix elements calculated at ﬁnite volume in lattice QCD to inﬁnite volume, and to nuclei with larger atomic number. In this work, it is demonstrated how this framework may be implemented via a set of correlated Gaussian wavefunctions optimised using diﬀerentiable programming and via solution of a generalised eigenvalue problem. This approach is shown to be signiﬁcantly more eﬃcient than a stochastic implementation of the variational method based on the same form of correlated Gaussian wavefunctions, yielding comparably accurate representations of the ground-state wavefunctions with an order of magnitude fewer terms. The eﬃciency of representation allows such calculations to be extended to larger systems than in previous work. The method is demonstrated through calculations of the binding energies of nuclei with atomic number A ∈ { 2 , 3 , 4 } in ﬁnite volume, matched to lattice QCD calculations at quark masses corresponding to m π = 806 MeV, and inﬁnite-volume eﬀective ﬁeld theory calculations of A ∈ { 2 , 3 , 4 , 5 , 6 } systems based on this matching.