Finite-volume and thermal effects in the leading-HVP contribution to muonic $(g-2)$

Understand

The leading finite-volume and thermal effects, arising in numerical lattice QCD calculations of $a^{\text{HVP,LO}}_\mu \equiv (g-2)^{\text{HVP,LO}}_\mu/2$, are determined to all orders with respect to the interactions of a generic, relativistic effective field theory of pions.

• In contrast to earlier work based in the finite-volume Hamiltonian, the results presented here are derived by formally summing all Feynman diagrams contributing to the Euclidean electromagnetic-current two-point function, with any number of internal pion loops and interaction vertices.
• As was already found in our previous publication, the leading finite-volume corrections to $a^{\text{HVP,LO}}_\mu$ scale as $\exp[- m L]$ where $m$ is the pion mass and $L$ is the length of the three periodic spatial directions.
• In this work we additionally control the two sub-leading exponentials, scaling as $\exp[- \sqrt{2} m L]$ and $\exp[- \sqrt{3} m L]$.