Towards high partial waves in lattice QCD with a dumbbell-like operator

An extended two-hadron operator is developed to extract the spectra of irreducible representations (irreps) in the finite volume. The irreps of the group for the finite volume system are projected using a coordinate-space operator. The correlation function of this operator is computationally efficient to extract lattice spectra of the specific irrep. In particular, this new formulation only requires propagators to be computed from two distinct source locations, at fixed spatial separation. We perform a proof-of-principle study on a $24^3 \times 48$ lattice volume with $m_\pi\approx 900$ MeV by isolating various spectra of the $\pi\pi$ system with isospin-2 including a range of total momenta and irreps. By applying the L\"uscher formalism, the phase shifts of $S$-, $D$- and $G$-wave $\pi\pi$ scattering with isospin-2 are extracted from the spectra.