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Register a new userA new three-loop sum-integral of mass dimension two
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We evaluate a new 3-loop sum-integral which contributes to the Debye screening mass in hot QCD. While we manage to derive all divergences analytically, its finite part is mapped onto simple integrals and evaluated numerically.
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In order to prepare the ground for evaluating classes of three-loop sum-integrals that are presently needed for thermodynamic observables, we take a fresh and systematic look on the few known cases, and review their evaluation in a unified way using coherent notation. We do this for three important cases of massless bosonic three-loop vacuum sum-integrals that have been frequently used in the literature, and aim for a streamlined exposition as compared to the original evaluations. In passing, we speculate on options for generalization of the computational techniques that have been employed.
We present the full analytic result for the three-loop angle-dependent cusp anomalous dimension in QCD. With this result, infrared divergences of planar scattering processes with massive particles can be predicted to that order. Moreover, we define a closely related quantity in terms of an effective coupling defined by the light-like cusp anomalous dimension. We find evidence that this quantity is universal for any gauge theory, and use this observation to predict the non-planar $n_{f}$-dependent terms of the four-loop cusp anomalous dimension.
We integrate three-loop sunrise-type vacuum diagrams in $D_0=4$ dimensions with four different masses using configuration space techniques. The finite parts of our results are in numerical agreement with corresponding three-loop calculations in momentum space. Using some of the closed form results of the momentum space calculation we arrive at new integral identities involving truncated integrals of products of Bessel functions. For the non-degenerate finite two-loop sunrise-type vacuum diagram in $D_0=2$ dimensions we make use of the known closed form $p$-space result to express the moment of a product of three Bessel functions in terms of a sum of Claussen polylogarithms. Using results for the nondegenerate two-loop sunrise diagram from the literature in $D_0=2$ dimensions we obtain a Bessel function integral identity in terms of elliptic functions.
We present the details of the analytic calculation of the three-loop angle-dependent cusp anomalous dimension in QCD and its supersymmetric extensions, including the maximally supersymmetric $mathcal{N}=4$ super Yang-Mills theory. The three-loop result in the latter theory is new and confirms a conjecture made in our previous paper. We study various physical limits of the cusp anomalous dimension and discuss its relation to the quark-antiquark potential including the effects of broken conformal symmetry in QCD. We find that the cusp anomalous dimension viewed as a function of the cusp angle and the new effective coupling given by light-like cusp anomalous dimension reveals a remarkable universality property -- it takes the same form in QCD and its supersymmetric extensions, to three loops at least. We exploit this universality property and make use of the known result for the three-loop quark-antiquark potential to predict the special class of nonplanar corrections to the cusp anomalous dimensions at four loops. Finally, we also discuss in detail the computation of all necessary Wilson line integrals up to three loops using the method of leading singularities and differential equations.
Pseudo-goldstinos appear in the scenario of multi-sector SUSY breaking. Unlike the true goldstino which is massless and absorbed by the gravitino, pseudo-goldstinos could obtain mass from radiative effects. In this note, working in the scenario of two-sector SUSY breaking with gauge mediation, we explicitly calculate the pseudo-goldstino mass at the leading three-loop level and provide the analytical results. In our calculation we consider the general case of messenger masses (not necessarily equal) and include the higher order terms of SUSY breaking scales. Our results can reproduce the numerical value estimated previously at the leading order of SUSY breaking scales with the assumption of equal messenger masses. It turns out that the results are very sensitive to the ratio of messenger masses, while the higher order terms of SUSY breaking scales are rather small in magnitude. Depending on the ratio of messenger masses, the pseudo-goldstino mass can be as low as ${{cal O} (0.1)}$ GeV.
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