Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The three-loop hadronic vacuum polarization in chiral perturbation theory

Mattias Sjö, Laurent Lellouch, Alessandro Lupo, Kálmán Szabo, Pierre Vanhove

Abstract

Hadronic vacuum polarization is a key observable in low-energy QCD, and is famously the greatest contributor to the theoretical uncertainty in the muon magnetic moment. Its long-distance part in particular is a weak point of the current best lattice QCD computations. In this summary of our recent work, we present its computation to next-to-next-to-next-to-leading order in chiral perturbation theory, capturing the lowest-energy hadronic contributions to unprecedented precision and opening the door for improved control over lattice finite volume effects. The result depends on a small number of low-energy constants, whose values are mostly under good control. This calculation pushes the envelope of high-order chiral perturbation theory and of the evaluation of multiloop integrals with massive propagators, thereby extending the toolbox for precision calculations in very low-energy QCD.

The three-loop hadronic vacuum polarization in chiral perturbation theory

Abstract

Hadronic vacuum polarization is a key observable in low-energy QCD, and is famously the greatest contributor to the theoretical uncertainty in the muon magnetic moment. Its long-distance part in particular is a weak point of the current best lattice QCD computations. In this summary of our recent work, we present its computation to next-to-next-to-next-to-leading order in chiral perturbation theory, capturing the lowest-energy hadronic contributions to unprecedented precision and opening the door for improved control over lattice finite volume effects. The result depends on a small number of low-energy constants, whose values are mostly under good control. This calculation pushes the envelope of high-order chiral perturbation theory and of the evaluation of multiloop integrals with massive propagators, thereby extending the toolbox for precision calculations in very low-energy QCD.
Paper Structure (5 sections, 17 equations, 3 figures)

This paper contains 5 sections, 17 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Theory
  3. Loop integrals
  4. Results
  5. Conclusions

Figures (3)

  • Figure 1: The FVE on the HVP contribution to the muon anomalous magnetic moment from ChPT and lattice QCD, including a projection of the ultimate result of this work.
  • Figure 2: All diagrams used in the HVP calculation, categorized by power-counting order and number of loops. Dots, squares and triangles represent NLO, NNLO and N$^3$LO counterterms, respectively.
  • Figure 3: $E_{1,2,3}(2;t)$, domain-colored in their native elliptic habitat. Each point in the complex $t$-plane is represented infinitely many times in each circle, but you will find one instance of $t=\infty$ at the center of the circle, $t=16$ (the four-pion threshold) just to the left of that where $E_2(2;t)$ goes singular, $t=4$ (the two-pion threshold) at the large saddle point above, and $t=0$ on the rightmost edge, amidst the raging essential singularity.