Supersymmetric Decomposition Research Articles

Full Angle Dependence of the Four-Loop Cusp Anomalous Dimension in QED.

The angle-dependent cusp anomalous dimension governs divergences coming from soft gluon exchanges between heavy particles, such as top quarks. We focus on the matter-dependent contributions and compute the first truly nonplanar terms. They appear at four loops and are proportional to a quartic Casimir operator in color space. Specializing our general gauge theory result to U(1), we obtain the full QED four-loop angle-dependent cusp anomalous dimension. While more complicated functions appear at intermediate steps, the analytic answer depends only on multiple polylogarithms with singularities at fourth roots of unity. It can be written in terms of four rational structures and contains functions of up to maximal transcendental weight seven. Despite this complexity, we find that numerically the answer is tantalizingly close to the appropriately rescaled one-loop formula, over most of the kinematic range. We take several limits of our analytic result, which serves as a check and allows us to obtain new, power-suppressed terms. In the antiparallel lines limit, which corresponds to production of two massive particles at threshold, we find that the subleading power correction vanishes. Finally, we compute the quartic Casimir contribution for scalars in the loop. Taking into account a supersymmetric decomposition, we derive the first nonplanar corrections to the quark antiquark potential in maximally supersymmetric gauge theory.

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

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 by {left.{Gamma}_{mathrm{cusp},mathrm{A}}right|}_{alpha_s^4}=-{left(frac{alpha_sN}{pi}right)}^4left[frac{73{pi}^6}{20160}+frac{zeta_3^2}{8}+frac{1}{N^2}left(frac{31{pi}^6}{5040}+frac{9{zeta}_3^2}{4}right)right]. Our 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 four-loop 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.

All-multiplicity one-loop amplitudes in Born-Infeld electrodynamics from generalized unitarity

We initiate a study of non-supersymmetric Born-Infeld electrodynamics in 4d at the quantum level. Explicit all-multiplicity expressions are calculated for the purely rational one-loop amplitudes in the self-dual (+ + … +) and next-to-self-dual (− + … +) helicity sectors. Using a supersymmetric decomposition, d-dimensional unitarity cuts of the integrand factorize into tree-amplitudes in a 4d model of Born-Infeld photons coupled to a massive complex scalar. The two-scalar tree-amplitudes needed to construct the Born-Infeld integrand are computed using two complimentary approaches: (1) as a double-copy of Yang-Mills coupled to a massive adjoint scalar with a dimensionally reduced form of Chiral Perturbation Theory, and (2) by imposing consistency with low-energy theorems under a reduction from 4d to 3d and T-duality. The Born-Infeld integrand is integrated in d = 4 − 2ϵ dimensions at order mathcal{O}left({in}^0right) using the dimension-shifting formalism. We comment on the implications for electromagnetic duality in quantum Born-Infeld theory.

Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation.

A soft function relevant for transverse-momentum resummation for Drell-Yan or Higgs production at hadron colliders is computed through to three loops in the expansion of strong coupling, with the help of the bootstrap technique and supersymmetric decomposition. The corresponding rapidity anomalous dimension is extracted. An intriguing relation between anomalous dimensions for transverse-momentum resummation and threshold resummation is found.

Hidden structures in quantum mechanics

It is shown that some operators in quantum mechanics have hidden structures that are unobservable in principle. These structures are based on a supersymmetric decomposition of the momentum operator, and a nonassociative decomposition of the spin operator.

Six-photon amplitudes in scalar QED

The analytical result for the six-photon helicity amplitudes in scalar QED is presented. To compute the loop, a recently developed method based on multiple cuts is used. The amplitudes for QED and $QED^{\caln=1}$ are also derived using the supersymmetric decomposition linking the three theories.

Recursive calculation of one-loop QCD integral coefficients

We present a new procedure using on-shell recursion to determine coefficients of integral functions appearing in one-loop scattering amplitudes of gauge theories, including QCD. With this procedure, coefficients of integrals, including bubbles and triangles, can be determined without resorting to integration. We give criteria for avoiding spurious singularities and boundary terms that would invalidate the recursion. As an example where the criteria are satisfied, we obtain all cut-constructible contributions to the one-loop n-gluon scattering amplitude, A_n^{oneloop}(...--+++...), with split-helicity from an N=1 chiral multiplet and from a complex scalar. Using the supersymmetric decomposition, these are ingredients in the construction of QCD amplitudes with the same helicities. This method requires prior knowledge of amplitudes with sufficiently large numbers of legs as input. In many cases, these are already known in compact forms from the unitarity method.