Document Type

Article

Publication Date

5-2020

DOI

10.1103/PhysRevD.101.094508

Publication Title

Physical Review D

Volume

101

Issue

9

Pages

094508 (16 pp.)

Abstract

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.

Comments

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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

ORCID

0000-0003-1109-1473 (Briceño), 0000-0002-3249-5410 (Jackura)

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