A planar four-loop form factor and cusp anomalous dimension in QCD

Four-loop collinear anomalous dimensions in QCD and $\mathcal{N} = 4$ super Yang-Mills

“…To be precise, we continue its decimal expansion in all possible ways out to a maximum of fifteen significant digits. 3 After each digit is added by our trial code, a PSLQ fit is attempted and then judged according to the simplicity and similarity criteria of the previous paragraph. We find it remarkable that, all the way out to fifteen decimal digits, no other possible PSLQ fit looks nearly as natural as (28) above.…”

“…Over the last several years, significant attention has been given to the calculation of cusp and collinear anomalous dimensions in massless perturbation theory. The light-like cusp anomalous dimensions [1] enter the leading infrared poles of massless scattering amplitudes and have recently been calculated to four-loop order both in Quantum Chromodynamics (QCD) and N = 4 supersymmetric Yang-Mills theory (N = 4 SYM) [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. The collinear anomalous dimensions enter the subleading infrared poles and can be extracted from the 1/ǫ poles of vertex form factors [18,19,20,21,22,23,24].…”

“…The collinear anomalous dimensions enter the subleading infrared poles and can be extracted from the 1/ǫ poles of vertex form factors [18,19,20,21,22,23,24]. Partial results are available at four-loop order both in QCD [3,6,7,11,8,25,26,17] and N = 4 supersymmetric Yang-Mills theory (N = 4 SYM) [27,28,29]. In this article, we consider the analytically unknown four-loop contributions to the collinear anomalous dimensions.…”

“…By experimenting with our sample expressions, we found that fewer significant digits are generally required for a fit in terms of {ζ 7 , ζ 5 ζ 2 , ζ 4 ζ 3 }, which is therefore the default ansatz for our actual PSLQ runs 3. It turns out that all weight seven terms of our 318 sample expansion coefficients can be reconstructed by running the PSLQ algorithm with fifteen significant digit input precision.…”

Quark and gluon form factors in four-loop QCD

“…The results, which are presented in this Letter, finalize a long-running effort to compute QCD form factors to four loops. First results have been obtained in 2016 [36,37] where planar diagrams for F q have been presented in the large-N c limit. Fermionic corrections with two closed fermion bubbles are available from [38] and the complete contribution from color structure (d abcd F ) 2 has 2 Fq :…”