The full four-loop cusp anomalous dimension in $$ \mathcal{N} $$ = 4 super Yang-Mills and QCD

Abstract

We present the complete formula for the cusp anomalous dimension at four loops in QCD and in maximally supersymmetric Yang-Mills. In the latter theory it is given byOur approach is based on computing the correlation function of a rectangular light-like Wilson loop with a Lagrangian insertion, normalized by the expectation value of the Wilson loop. In maximally supersymmetric Yang-Mills theory, this ratio is a finite function of a cross-ratio and the coupling constant. We compute it to three loops, including the full colour dependence. Integrating over the position of the Lagrangian insertion gives the fourloop Wilson loop. We extract its leading divergence, which determines the four-loop cusp anomalous dimension. Finally, we employ a supersymmetric decomposition to derive the last missing ingredient in the corresponding QCD result.

Cusp and Collinear Anomalous Dimensions in Four-Loop QCD from Form Factors

“…We find very solid agreement with Table 1 of [13], suggesting that their error estimates were actually conservative. Finally, a comparison to the four-loop cusp anomalous dimension of the N = 4 model [34,69] shows that our result respects the principle of maximal transcendentality [70,71]. The collinear anomalous dimensions can be read off from the ǫ −1 poles of the logarithm of the renormalized form factors.…”

“…This generalized Casimir scaling proposal was recently corroborated by two independent theoretical studies [32,33]. Using further conjectural input from [23], an analytic form of the four-loop QCD cusp anomalous dimensions was put forward very recently in [34].…”

Factorization at subleading power and endpoint-divergent convolutions in h → γγ decay

“…where Γ cusp is the light-like cusp anomalous dimension in the fundamental representation of SU(N c ) [39], and γ q is the anomalous dimension of the quark field in light-cone gauge. The cusp anomalous dimension has recently been calculated to four-loop order [40], while γ q is known to three loops. It can be determined from the three-loop expression for the divergent part of the on-shell quark form factor in QCD [41,42].…”

Constructing d-log integrands and computing master integrals for three-loop four-particle scattering

“…Let us mention also that a variant of the spinor helicity parametrization can also be used in the case of massive external kinematics, by decomposing a massive momentum in terms of two (arbitrary) light-like momenta. Finally, we want to mention that another promising choice of paramterization is the 'improved Baikov' representation, see section 3.2 of [49].…”