Mellin-Barnes approach to hadronic vacuum polarization and gμ−2

Abstract

It is shown that with a precise determination of a few derivatives of the hadronic vacuum polarization (HVP) self-energy function ΠðQ 2 Þ at Q 2 ¼ 0, from lattice QCD (LQCD) or from a dedicated low-energy experiment, one can obtain an evaluation of the lowest order HVP contribution to the anomalous magnetic moment of the muon a HVP μ with an accuracy comparable to the one reached using the e þ e − annihilation cross section into hadrons. The technique of Mellin-Barnes approximants (MBa) that we propose is illustrated in detail with the example of the two loop vacuum polarization function in QED. We then apply it to the first few moments of the hadronic spectral function obtained from experiment and show that the resulting MBa evaluations of a HVP μ converge very quickly to the full experimental determination.

Hadronic corrections to μ-e scattering at NNLO with space-like data

“…Even if so far with a larger uncertainty, lattice QCD provides an alternative evaluation of a HLO µ [10][11][12][13][14][15][16][17][18]. Other proposed methods exploit the hadronic vacuum polarization within dispersive QCD approach [19], Schwinger's sum rules [20] and Mellin-Barnes approximants [21].…”

On Constraints Between $Δα_{\rm had}(M_Z^2)$ and $(g_μ-2)_{\rm HVP}$

“…This representation has been proposed as a possible way to obtain successive approximations to a HVP µ from the knowledge of the moments M(s) at s = 0, −1, −2 • • • and their extrapolation at all s-values using Mellin-Barnes approximants (see refs. [15,16] and references therein).…”

Constraints between Δαhad(MZ2) and Rafael1 2020Phys. Rev. DSelf Cite330210View full textAdd to dashboardCite

“…Mellin-Barnes representations are particularly useful to obtain asymptotic expansions of functions. In the case of a HVP μ [16]: [17,18] and references therein).…”

“…which govern the ðg μ − 2Þ had contribution [16][17][18]. Therefore, within this perspective, the possibility of relating the two observables Δα ð5Þ had ðM 2 Z Þ and ðg μ − 2Þ had seems a priori a rather difficult task, unless of course one uses data or a model for the hadronic spectral function, or performs fully dedicated LQCD evaluations of both observables.…”

“…As discussed in Refs. [16][17][18] they provide excellent tests to confront LQCD evaluations of the lhs with experimental results, but they invoke a totally different Q 2 -region to the one which applies to Eq. (2.9).…”