Abstract
We compute the fermionic contributions to the cusp anomalous dimension in QCD at four loops as an expansion for small cusp angle. As a byproduct we also obtain the respective terms of the four-loop HQET wave function anomalous dimension. Our new results at small angles provide stringent tests of a recent conjecture for the exact angle dependence of the matter terms in the four-loop cusp anomalous dimension. We find that the conjecture does not hold for two of the seven fermionic color structures, but passes all tests for the remaining terms. This provides strong support for the validity of the corresponding conjectured expressions with full angle dependence. Taking the limit of large Minkowskian angle, we extract novel analytic results for certain terms of the light-like cusp anomalous dimension. They agree with the known numerical results. Finally, we study the anti-parallel lines limit of the cusp anomalous dimension. In a conformal theory, the latter is proportional to the static quark-antiquark potential. We use the new four-loop results to determine parts of the conformal anomaly term.
Highlights
In addition to the light-like limit, there are two more interesting limits, the anti-parallel lines and the small angle limit
We compute the fermionic contributions to the cusp anomalous dimension in QCD at four loops as an expansion for small cusp angle
Those are the diagrams with a fermion box subdiagram, where the four gluons are directly attached to the Wilson lines as shown in the sample diagram in table 1
Summary
We start with the definition of the cusp anomalous dimension in QCD To this end we consider a closed Wilson loop with a time-like integration contour C. We considered the angle dependent cusp anomalous dimension Γcusp(φ, αs), originating from the UV divergences of a cusped Wilson loop with a time-like integration contour. Pij(x) govern the evolution of the parton distribution functions [40,41,42] In this context the light-like cusp anomalous dimension is relevant for the threshold limit x → 1 [43]. The corresponding HQET heavy quark field anomalous dimension depends on the strong coupling αs, and on the gauge. The relevant terms of the corresponding anomalous dimension can e.g. be found in [38]
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