Multichannel 1 → 2 transition amplitudes in a finite volume

Journal Article · Tue Feb 03 00:00:00 EST 2015 · Physical Review. D, Particles, Fields, Gravitation and Cosmology

DOI:https://doi.org/10.1103/PhysRevD.91.034501· OSTI ID:1169162

Briceno, Raul A. ^[1]; Hansen, Maxwell T. ^[2]; Walker-Loud, Andre ^[3]

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1. Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
2. Univ. of Washington, Seattle, WA (United States)
3. Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States)

We perform a model-independent, non-perturbative investigation of two-point and three-point finite-volume correlation functions in the energy regime where two-particle states can go on-shell. We study three-point functions involving a single incoming particle and an outgoing two-particle state, relevant, for example, for studies of meson decays (e.g., B⁰ → K*l⁺l⁻) or meson photo production (e.g., πγ* → ππ). We observe that, while the spectrum solely depends upon the on-shell scattering amplitude, the correlation functions also depend upon off-shell amplitudes. The main result of this work is a non-perturbative generalization of the Lellouch-Luscher formula relating matrix elements of currents in finite and infinite spatial volumes. We extend that work by considering a theory with multiple, strongly-coupled channels and by accommodating external currents which inject arbitrary four-momentum as well as arbitrary angular-momentum. The result is exact up to exponentially suppressed corrections governed by the pion mass times the box size. We also apply our master equation to various examples, including two processes mentioned above as well as examples where the final state is an admixture of two open channels.

• Research Organization: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Nuclear Physics (NP)
• DOE Contract Number: AC05-06OR23177
• OSTI ID: 1169162
• Report Number(s): JLAB-THY-14-1909; DOE/OR/23177-3128; arXiv:1406.5965; PRVDAQ; ArticleNumber: 034501
• Journal Information: Physical Review. D, Particles, Fields, Gravitation and Cosmology, Vol. 91, Issue 3; ISSN 1550-7998
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English