We present the first results on the third order corrections to on-shell form factor (FF) of the Konishi operator in N = 4 supersymmetric Yang-Mills theory using Feynman diagrammatic approach in modified dimensional reduction (DR) scheme. We show that it satisfies KG equation in DR scheme while the result obtained in four dimensional helicity (FDH) scheme needs to be suitably modified not only to satisfy the KG equation but also to get the correct ultraviolet (UV) anomalous dimensions. We find that the cusp, soft and collinear anomalous dimensions obtained to third order are same as those of the FF of the half-BPS operator confirming the universality of the infrared (IR) structures of on-shell form factors. In addition, the highest transcendental terms of the FF of Konishi operator are identical to those of half-BPS operator indicating the probable existence of deeper structure of the on-shell FF. We also confirm the UV anomalous dimensions of Konishi operator up to third order providing a consistency check on the both UV and universal IR structures in N = 4. PACS numbers: 12.38BxThe ability to accomplish the challenging job of calculating quantities is of fundamental importance in any potential mathematical theory. In quantum field theory (QFT), this manifests itself in the quest for computing the multi-loop and multi-leg scattering amplitudes under the glorious framework of age-old perturbation theory. The fundamental quantities to be calculated in any gauge theory are the scattering amplitudes or the correlation functions. Recently, there have been surge of interest to study form factors (FFs) as they connect fully on-shell amplitudes and correlation functions. The FFs are a set of quantities which are constructed out of the scattering amplitudes involving on-shell states consisting of elementary fields and an off-shell state described through a composite operator. These are operator matrix elements of the form p σ1 1 , · · · , p σ l l |O|0 where, O represents a gauge invariant composite operator which generates a multiparticle on-shell state |p σ1 1 , · · · , p σ l l upon operating on the vacuum of the theory. p i are the momenta and σ i encapsulate all the other quantum numbers of the particles. More precisely, FFs are the amplitudes of the processes where classical current or field, coupled through gauge invariant composite operator O, produces some quantum state. Studying these quantities not only help to understand the underlying ultraviolet and infrared structures of the theory, but also enable us to calculate the anomalous dimensions of the associated composite operator.The Sudakov FFs (l = 2) in N = 4 maximally supersymmetric Yang-Mills (SYM) theory [1, 2] were initially considered by van Neerven in [3], almost three decades back, where a half-BPS operator belonging to the stressenergy supermultiplet, that contains the conserved currents of N = 4 SYM, was investigated to 2-loop order:Very recently, this was extended to 3-loop in [4]. We will represent scalar and pseudo-scalar fields by φ a m and χ a m ...

We compute the two-loop massless QCD corrections to the four-point amplitude g+g → H +H resulting from effective operator insertions that describe the interaction of a Higgs boson with gluons in the infinite top quark mass limit. This amplitude is an essential ingredient to the third-order QCD corrections to Higgs boson pair production. We have implemented our results in a numerical code that can be used for further phenomenological studies.

McMule is a framework for fully differential higher-order QED calculations of scattering and decay processes involving leptons. It keeps finite lepton masses, which regularises collinear singularities. Soft singularities are treated with dimensional regularisation and using FKS^\ellℓ subtraction. We describe the implementation of the framework in Fortran 95, list the processes that are currently implemented, and give instructions on how to run the code. In addition, we present new phenomenological results for muon-electron scattering and lepton-proton scattering, including the dominant NNLO corrections. While the applications presented focus on MUonE, MUSE, and P2, the code can be used for a large number of planned and running experiments.

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In this manuscript, we report the outcome of the topical workshop: paving the way to alternative NNLO strategies (https://indico.ific.uv.es/e/WorkStop-ThinkStart_3.0), by presenting a discussion about different frameworks to perform precise higher-order computations for high-energy physics. These approaches implement novel strategies to deal with infrared and ultraviolet singularities in quantum field theories. A special emphasis is devoted to the local cancellation of these singularities, which can enhance the efficiency of computations and lead to discover novel mathematical properties in quantum field theories.