ABSTRACT
Focusing on three-pion states with maximal isospin (π^{+}π^{+}π^{+}), we present the first nonperturbative determination of an energy-dependent three-hadron scattering amplitude from first-principles QCD. The calculation combines finite-volume three-hadron energies, extracted using numerical lattice QCD, with a relativistic finite-volume formalism, required to interpret the results. To fully implement the latter, we also solve integral equations that relate an intermediate three-body K matrix to the physical three-hadron scattering amplitude. The resulting amplitude shows rich analytic structure and a complicated dependence on the two-pion invariant masses, represented here via Dalitz-like plots of the scattering rate.
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.
