Three-particle bound states in a finite volume: Unequal masses and higher partial waves

An explicit expression for the finite-volume energy shift of shallow three-body bound states for nonidentical particles is obtained in the unitary limit. The inclusion of the higher partial waves is considered. To this end, the method of Meißner, Rìos, and Rusetsky [Phys. Rev. Lett. 114, 091602 (2015)] is generalized for the case of unequal masses and arbitrary angular momenta. It is shown that in the S-wave and in the equal-mass limit, the result from Meißner, Rìos, and Rusetsky is reproduced.

Figure 1

The coefficients $C_1$ (solid line) and $C_2=C_3$ (dashed line) as a function of the mass ratio $z=m_1/m_2=m_1/m_3$; see Eq. (34).