We present a general method for deriving the energy shift of an interacting system of N spinless particles in a finite volume. To this end, we use the nonrelativistic effective field theory (NREFT), and match the pertinent low-energy constants to the scattering amplitudes. Relativistic corrections are explicitly included up to a given order in the 1/L expansion. We apply this method to obtain the ground state of N particles, and the first excited state of two and three particles to order L−6 in terms of the threshold parameters of the two- and three-particle relativistic scattering amplitudes. We use these expressions to analyze the N-particle ground state energy shift in the complex φ4 theory.

We present an exploratory investigation of the parity odd Δ = 1 pion-nucleon coupling ℎ 1 from lattice QCD. Based on the PCAC relation, we study the parity-conserving effective Hamiltonian and extract the coupling by determining the nucleon mass splitting arising from the effective 4-quark interactions using the Feynman-Hellmann theorem. We present preliminary results of the mass shift for a 32 3 × 64 ensemble of = 2 + 1 + 1 twisted mass fermions at pion mass 260 MeV and lattice spacing = 0.097 fm.

We present an exploratory investigation of the parity odd Δ𝐼 = 1 pion-nucleon coupling ℎ 1 𝜋 from lattice QCD. Based on the PCAC relation, we study the parity-conserving effective Hamiltonian and extract the coupling by determining the nucleon mass splitting arising from the effective 4-quark interactions using the Feynman-Hellmann theorem. We present preliminary results of the mass shift for a 32 3 × 64 ensemble of 𝑁 𝑓 = 2 + 1 + 1 twisted mass fermions at pion mass 260 MeV and lattice spacing 𝑎 = 0.097 fm.

We present results for an exploratory lattice calculation of the leading parity-violating pion-nucleon coupling ℎ 1 𝜋 . Based on the PCAC relation we use a parity-conserving Lagrangian and focus on the techniques to determine the nucleon matrix elements of the effective 4-quark operators. For our study we employ an ensemble of twisted mass fermions with 260 MeV pion mass. Barring mixing with lower-dimensional operators and renormalization at this stage, we discuss our estimate for ℎ 1 𝜋 .