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Title Prospects for $\gamma^\star \gamma^\star \to \pi \pi$ via lattice QCD
Authors Raul Briceno, Andrew Jackura, Arkaitz Rodas, Juan Guerrero Teran
JLAB number JLAB-THY-22-3727
LANL number (None)
Other number DOE/OR/23177-5624
Document Type(s) (Journal Article) 
Associated with EIC: No
Supported by Jefferson Lab LDRD Funding: Yes
LDRD Numbers: 2021-LDRD-17
Funding Source: Nuclear Physics (NP)
Other Funding:DE-AC05-06OR23177

Compiled for Physical Review D
Volume 107
Page(s) 034504
Publication Abstract: The $\gamma^\star \gamma^\star \to \pi \pi$ scattering amplitude plays a key role in a wide range of phenomena, including understanding the inner structure of scalar resonances as well as constraining the hadronic contributions to the anomalous magnetic moment of the muon. In this work, we explain how the infinite-volume Minkowski amplitude can be constrained from finite-volume Euclidean correlation functions. The relationship between the finite-volume Euclidean correlation functions and the desired amplitude holds up to energies where $3\pi$ states can go on shell, and is exact up to exponentially small corrections that scale like $\mathcal{O}(e^{-m_\pi L})$, where $L$ is the spatial extent of the cubic volume and $m_\pi$ is the pion mass. In order to implement this formalism and remove all power-law finite volume errors, it is necessary to first obtain $\pi \pi \to \pi\pi$, $\pi \gamma^\star \to \pi$, $\gamma^\star \to\pi\pi$, and $\pi\pi\gamma^\star \to\pi\pi$ amplitudes; all of which can be determined via lattice quantum chromodynamic calculations.
Experiment Numbers: other
Document: pdf
Accepted Manuscript: PhysRevD.107.034504.pdf
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