Massless propagators: applications in QCD and QED

TL;DR

This work reports two independent five-loop results for massless propagator applications in QCD and QED: (i) the $a_s^4$ correction to the absorptive part of the vector correlator at $n_f=3$, i.e., the five-loop contribution to $R(s)$, and (ii) the five-loop contribution to the $\beta$-function of quenched QED. The calculation employs infrared rearrangement, the $R^*$ operation, and Baikov-based master integral reduction to 28 masters, with a large-$D$ reconstruction and a slice strategy fixed at $n_f=3$ to determine $d_4(n_f=3)$ analytically and numerically; the results include $d_4(n_f=3)=\frac{78631453}{20736} - \frac{1704247}{432} \zeta_3 + \frac{4185}{8} \zeta_3^2 + \frac{34165}{96} \zeta_5 - \frac{1995}{16} \zeta_7 \approx 49.0757$ and the corresponding $R(s)$ expansion $1 + a_s + 1.6398 a_s^2 + 6.3710 a_s^3 - 106.8798 a_s^4$. The paper also analyzes the colour structure to outline the remaining slices needed for generic gauge groups and reports the five-loop $\beta^{qQED}$ coefficient, highlighting that the rationality observed at lower loops no longer holds at five loops. Overall, the results bear on precision $\alpha_s$ determinations from hadronic observables and deepen understanding of high-order perturbative structure in gauge theories.

Abstract

We report on two recent results based on the evaluation of five-loop massless propagators in QCD and QED: (i) corrections of order $α_s^4$ to the absorptive part of the polarization function in QCD with $n_f=3$;(ii) the five-loop contribution to the $β$ function of quenched QED.

Figures (1)

• Figure 1: (a) (a),(b) Examples of five -loop quenched Abelian diagrams of order $a_s^4 n_f^0$ . (c) A five -loop non-abelian diagram. (d) A five -loop non-quenched abelian diagram of order $a_s^4 n_f$