Finite-Volume Effects in (g-2)μHVP,LO.

An analytic expression is derived for the leading-order finite-volume effects arising in lattice QCD calculations of the hadronic-vacuum-polarization contribution to the muon's magnetic moment aμHVP,LO≡(g-2)μHVP,LO/2. For calculations in a finite spatial volume with periodicity L, aμHVP,LO(L) admits a transseries expansion with exponentially suppressed L scaling. Using a Hamiltonian approach, we show that the leading finite-volume correction scales as exp[-MπL] with a prefactor given by the (infinite-volume) Compton amplitude of the pion, integrated with the muon-mass-dependent kernel. To give a complete quantitative expression, we decompose the Compton amplitude into the spacelike pion form factor Fπ(Q²) and a multiparticle piece. We determine the latter through next-to leading order in chiral perturbation theory and find that it contributes negligibly and through a universal term that depends only on the pion decay constant, with all additional low-energy constants dropping out of the integral. [ABSTRACT FROM AUTHOR]