Chiral extrapolation of the magnetic polarizability of the neutral pion

TL;DR

This paper uses lattice QCD and chiral perturbation theory to accurately extrapolate the magnetic polarizability of the neutral pion to physical quark masses, incorporating effects of quark quenching.

Contribution

It introduces a formalism that preserves leading nonanalytic terms in chiral extrapolation of lattice results, improving the accuracy of neutral pion magnetic polarizability estimates.

Findings

Calculated the neutral pion magnetic polarizability as 3.44(19)(37)×10^{-4} fm^3.

Demonstrated that electro-quenching does not affect the leading-loop contribution.

Provided a more precise estimate close to experimental bounds.

Abstract

The magnetic polarizability of the neutral pion has been calculated in the background magnetic-field formalism of Lattice QCD. In this investigation, the chiral extrapolation of these lattice results is considered in a formalism preserving the exact leading nonanalytic terms of chiral perturbation theory. The $n_f = 2 + 1$ numerical simulations are electro-quenched, such that the virtual sea-quarks of the QCD vacuum do not interact with the background field. To understand the impact of this, we draw on partially quenched chiral perturbation theory and identify the leading contributions of quark-flow connected and disconnected diagrams. While electro-quenching does not impact the leading-loop contribution to the magnetic polarizability, the loops which generate the leading term have yet to be considered in lattice QCD simulations. Lattice QCD results are used to constrain the analytic terms in the chiral expansion and supplementing those with the two-loop result from chiral perturbation theory enables an evaluation of the polarizability at the physical quark mass. The resulting magnetic polarizability of the neutral pion is $\beta_{\pi^0}=3.44(19)^{\rm stat}(37)^{\rm syst}\times 10^{-4}$ fm$^3$, which lies just above the $1 \sigma$ error bound of the experimental measurement.