Physical Review D
094508 (16 pp.)
Using the general formalism presented in [Phys. Rev. D 94, 013008 (2016); Phys. Rev. D 100, 034511 (2019)], we study the finite-volume effects for the 2 þ J → 2 matrix element of an external current coupled to a two-particle state of identical scalars with perturbative interactions. Working in a finite cubic volume with periodicity L, we derive a 1=L expansion of the matrix element through O(1=L5) and find that it is governed by two universal current-dependent parameters, the scalar charge and the threshold two particle form factor. We confirm the result through a numerical study of the general formalism and additionally through an independent perturbative calculation. We further demonstrate a consistency with the Feynman-Hellmann theorem, which can be used to relate the 1=L expansions of the ground-state energy and matrix element. The latter gives a simple insight into why the leading volume corrections to the matrix element have the same scaling as those in the energy, 1=L3, in contradiction to Phys. Rev. D 91, 074509 (2015), which found a 1=L2 contribution to the matrix element. We show here that such a term arises at intermediate stages in the perturbative calculation, but cancels in the final result.
Original Publication Citation
Briceño, R. A., Hansen, M. T., & Jackura, A. W. (2020). Consistency checks for two-body finite-volume matrix elements. II. Perturbative systems. Physical Review D, 101(9), 094508. doi: 10.1103/PhysRevD.101.094508
0000-0003-1109-1473 (Briceño), 0000-0002-3249-5410 (Jackura)
Briceño, Raúl A.; Hansen, Maxwell T.; and Jackura, Andrew W., "Consistency Checks for Two-Body Finite-Volume Matrix Elements. II. Perturbative Systems" (2020). Physics Faculty Publications. 423.