Hadronic vacuum polarization to three loops in chiral perturbation theory

Abstract

Hadronic vacuum polarization at low virtualities limits the precision of experimental tests of the standard model via important physical observables. Here we compute that effect in two-flavor chiral perturbation theory to three loops. Among the master integrals that describe the amplitude, six are elliptic functions of the momentum. Of these five are new to this work, although all can be related to the three-loop sunset integral. The renormalizability of the amplitude hinges on relations between the master integrals that were not previously known and that are not consequences of the integration-by-parts reduction. Our result is intended to serve as a starting point for phenomenological calculations, as well as the computation of finite-volume corrections in lattice QCD.

arXiv comment45 pages, 2 figures, 2 tables; implementation code available at https://github.com/mssjo/HVP-3loop; v2 updated according to changes made for publication in JHEP

References in corpus (46)

• Leading hadronic contribution to the muon magnetic moment from lattice QCD
• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• Connection between Feynman integrals having different values of the space-time dimension
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Weak transition matrix elements from finite-volume correlation functions
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• The Mesonic Chiral Lagrangian of Order $p^6$
• Two-loop two-point functions with masses: asymptotic expansions and Taylor series, in any dimension
• Mesonic low-energy constants
• Renormalization of chiral perturbation theory to order p^6
• The three loop on-shell renormalization of QCD and QED
• Lattice QCD and the Timelike Pion Form Factor
• Elliptic integral evaluations of Bessel moments
• Two-point Functions at Two Loops in Three Flavour Chiral Perturbation Theory
• A Feynman integral via higher normal functions
• Critical points and number of master integrals
• The anomalous magnetic moment of the muon in the Standard Model: an update
• Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph
• Light quark vacuum polarization at the physical point and contribution to the muon $g-2$
• A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec
• Charged Pion-Pair Production and Pion Polarizabilities to two Loops
• Schouten identities for Feynman graph amplitudes; the Master Integrals for the two-loop massive sunrise graph
• An analytic solution for the equal-mass banana graph
• Feynman integral relations from parametric annihilators
• On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order
• Two-Loop Analysis of Vector Current Propagators in Chiral Perturbation Theory
• The Vector and Scalar Form Factors of the Pion to Two Loops
• On the evaluation of sunset-type Feynman diagrams
• Finite-volume effects in the muon anomalous magnetic moment on the lattice
• Numerical Scattering Amplitudes with pySecDec
• The three-loop equal-mass banana integral in $\epsilon$-factorised form with meromorphic modular forms
• Algorithms for minimal Picard-Fuchs operators of Feynman integrals
• Finite-volume effects in $(g-2{)}_{\mu }^{\text{HVP,LO}}$
• Integration by parts identities in integer numbers of dimensions. A criterion for decoupling systems of differential equations
• The order $p^8$ mesonic chiral Lagrangian
• Finite-volume and thermal effects in the leading-HVP contribution to muonic $(g-2)$
• Vector two-point functions in finite volume using partially quenched chiral perturbation theory
• $\epsilon$-regular basis for non-polylogarithmic multiloop integrals and total cross section of the process $e^{+}{e}^{-}\to 2(Q\bar{Q})$
• On the application of Effective Field Theory to finite-volume effects in $a_{\mu }^{\mathrm{HVP}}$
• Parametrization-free determination of the shape parameters for the pion electromagnetic form factor
• Laurent series expansion of sunrise-type diagrams using configuration space techniques
• The Pion Mass and Decay Constant at Three Loops in Two-Flavour Chiral Perturbation Theory
• Two-Point Functions and S-Parameter in QCD-like Theories
• Analytic decay width of the Higgs boson to massive bottom quarks at order ${\alpha }_s^3$
• Master integrals for bipartite cuts of three-loop photon self energy