Abstract
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 a_{μ}^{HVP,LO}≡(g-2)_{μ}^{HVP,LO}/2. For calculations in a finite spatial volume with periodicity L, a_{μ}^{HVP,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[-M_{π}L] 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 F_{π}(Q^{2}) 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.
Highlights
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 aHμ VP;LO ≡ ðg − 2ÞHμ VP;LO=2
Using a Hamiltonian approach, we show that the leading finite-volume correction scales as exp1⁄2−MπL with a prefactor given by the Compton amplitude of the pion, integrated with the muon-mass-dependent kernel
Introduction.—The discrepancy between experimental [1,2] and theoretical [3,4,5] values and the ongoing measurements at Fermilab [6,7,8,9] and J-PARC [10,11] have motivated various lattice QCD (LQCD) collaborations to calculate the hadronic contributions to ðg − 2Þμ, which currently dominate the theoretical uncertainty [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]
Summary
Introduction.—The discrepancy between experimental [1,2] and theoretical [3,4,5] values and the ongoing measurements at Fermilab [6,7,8,9] and J-PARC [10,11] have motivated various lattice QCD (LQCD) collaborations to calculate the hadronic contributions to ðg − 2Þμ, which currently dominate the theoretical uncertainty [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]. 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 aHμ VP;LO ≡ ðg − 2ÞHμ VP;LO=2. For calculations in a finite spatial volume with periodicity L, aHμ VP;LOðLÞ admits a transseries expansion with exponentially suppressed L scaling.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
