Two- and three-body interactions in $$\varphi ^4$$ φ4 theory from lattice simulations

• Main Authors: F. Romero-López, A. Rusetsky, C. Urbach
• Format: Article
• Language: English
• Published: SpringerOpen 2018-10-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-018-6325-8

Abstract We calculate the one-, two- and three-particle energy levels for different lattice volumes in the complex $$\varphi ^4$$ φ4 theory on the lattice. We argue that the exponentially suppressed finite-volume corrections for the two- and three-particle energy shifts can be reduced significantly by using the single particle mass, which includes the finite-size effects. We show numerically that, for a set of bare parameters, corresponding to the weak repulsive interaction, one can reliably extract the two- and three-particle energy shifts. From those, we extract the scattering length, the effective range and the effective three-body coupling. We show that the parameters, extracted from the two- and three-particle energy shifts, are consistent. Moreover, the effective three-body coupling is significantly different from zero.