Abstract
We test an alternative proposal by Bruno and Hansen (J High Energy Phys 2021(6), https://doi.org/10.1007/JHEP06(2021)043, 2021) to extract the scattering length from lattice simulations in a finite volume. For this, we use a scalar phi ^4 theory with two mass nondegenerate particles and explore various strategies to implement this new method. We find that the results are comparable to those obtained from the Lüscher method, with somewhat smaller statistical uncertainties at larger volumes.
Highlights
As pointed out by the authors, the case of threshold kinematics is favourable as it allows for a direct extraction of the scattering length, with the π N channel being one concrete example.In this letter we test this novel approach in a scalar φ4 theory
We test an alternative proposal by Bruno and Hansen (J High Energy Phys 2021(6), https://doi.org/10. 1007/JHEP06(2021)043, 2021) to extract the scattering length from lattice simulations in a finite volume
We find that the results are comparable to those obtained from the Lüscher method, with somewhat smaller statistical uncertainties at larger volumes
Summary
As pointed out by the authors, the case of threshold kinematics is favourable as it allows for a direct extraction of the scattering length, with the π N channel being one concrete example. In this letter we test this novel approach in a scalar φ4 theory Using this theory has proven to be an excellent test bed for novel scattering studies, as shown in Refs. The standard approach is the Lüscher method [2], which relates the finitevolume spectrum obtained from the lattice to the infinitevolume scattering amplitude. The formalism has been recently extended to three particles with three different but conceptually equivalent formulations available in the literature at present [4,5,6,7,8], see Refs. [1], the authors propose a new strategy to extract scattering quantities. This will be referred to as the BH method. The hope is that this approach can be generalised more to multi-hadron processes
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