Four-loop cusp anomalous dimension in QED

TL;DR

This paper analytically computes 4-loop and 5-loop contributions to the cusp anomalous dimension and related quantities in QED, confirming recent numerical results and providing complete analytical expressions up to 4 loops.

Contribution

It presents the first complete analytical 4-loop results for the cusp anomalous dimension and related anomalous dimensions in QED, extending previous numerical findings.

Findings

Analytical 4-loop cusp anomalous dimension in QED obtained.

Confirmed agreement with recent numerical results.

Provided small-phi expansion up to phi^6 at 4 loops.

Abstract

The 4-loop $C_F^3 T_F n_l$ and 5-loop $C_F^4 T_F n_l$ terms in the HQET field anomalous dimension $\gamma_h$ are calculated analytically (the 4-loop one agrees with the recent numerical result [arXiv:1801.08292]). The 4-loop $C_F^3 T_F n_l$ and 5-loop $C_F^4 T_F n_l$ terms in the cusp anomalous dimension $\Gamma(\varphi)$ are calculated analytically, exactly in $\varphi$ (the $\varphi\to\infty$ asymptotics of the 4-loop one agrees with the recent numerical result [arXiv:1707.08315]). Combining these results with the recent 4-loop $d_{FF} n_l$ contributions to $\gamma_h$ and to the small-$\varphi$ expansion of $\Gamma(\varphi)$ up to $\varphi^4$ [arXiv:1708.01221] (recently extended to $\varphi^6$ [arXiv:1807.05145]) we now have the complete analytical 4-loop result for the Bloch--Nordsieck field anomalous dimension in QED, and the small-$\varphi$ expansion of the 4-loop QED cusp anomalous dimension up to $\varphi^6$.