Effects of finite volume on the K _{L} – K _{S} mass difference
Phenomena that involve two or more onshell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher and Lellouch and Lüscher, which determine the leadingorder effects of finite volume on the twoparticle spectrum and twoparticle decay amplitudes to determine the finitevolume effects in the secondorder mixing of the K⁰ and K⁰⁻ states. We extend the methods of Kim, Sachrajda, and Sharpe to provide a direct, uniform treatment of these three, related, finitevolume corrections. In particular, the leading, finitevolume corrections to the K _{L} – K _{S} mass difference ΔM _{K} and the CPviolating parameter εK are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finitevolume, twopion state.
 Authors:

^{[1]};
^{[1]};
^{[2]};
^{[3]}
 Columbia Univ., New York, NY (United States)
 Trieste and INFN Sezione di Roma La Sapienza, Roma (Italy)
 Univ. of Southampton (United Kingdom)
 Publication Date:
 Grant/Contract Number:
 SC0011941
 Type:
 Publisher's Accepted Manuscript
 Journal Name:
 Physical Review. D, Particles, Fields, Gravitation and Cosmology
 Additional Journal Information:
 Journal Name: Physical Review. D, Particles, Fields, Gravitation and Cosmology Journal Volume: 91 Journal Issue: 11; Journal ID: ISSN 15507998
 Publisher:
 American Physical Society
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 OSTI Identifier:
 1188516
Christ, N. H., Feng, X., Martinelli, G., and Sachrajda, C. T.. Effects of finite volume on the KL – KS mass difference. United States: N. p.,
Web. doi:10.1103/PhysRevD.91.114510.
Christ, N. H., Feng, X., Martinelli, G., & Sachrajda, C. T.. Effects of finite volume on the KL – KS mass difference. United States. doi:10.1103/PhysRevD.91.114510.
Christ, N. H., Feng, X., Martinelli, G., and Sachrajda, C. T.. 2015.
"Effects of finite volume on the KL – KS mass difference". United States.
doi:10.1103/PhysRevD.91.114510.
@article{osti_1188516,
title = {Effects of finite volume on the KL – KS mass difference},
author = {Christ, N. H. and Feng, X. and Martinelli, G. and Sachrajda, C. T.},
abstractNote = {Phenomena that involve two or more onshell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher and Lellouch and Lüscher, which determine the leadingorder effects of finite volume on the twoparticle spectrum and twoparticle decay amplitudes to determine the finitevolume effects in the secondorder mixing of the K⁰ and K⁰⁻ states. We extend the methods of Kim, Sachrajda, and Sharpe to provide a direct, uniform treatment of these three, related, finitevolume corrections. In particular, the leading, finitevolume corrections to the KL – KS mass difference ΔMK and the CPviolating parameter εK are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finitevolume, twopion state.},
doi = {10.1103/PhysRevD.91.114510},
journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
number = 11,
volume = 91,
place = {United States},
year = {2015},
month = {6}
}