Related papers: Analytic Continuation of Massless Two-Loop Four-Po…
We present for numerical use the analytic continuations to complex arguments of those basic Mellin transforms, which build the harmonic sums contributing to the 3--loop anomalous dimensions. Eight new basic functions contribute in addition…
Rotations on the 3-dimensional Euclidean vector-space can be represented by real quaternions, as was shown by Hamilton. Introducing complex quaternions allows us to extend the result to elliptic and hyperbolic rotations on the Minkowski…
We present an unfolded off-shell formulation for free massless higher-spin fields in 4d Minkowski space in terms of spinorial variables. This system arises from the on-shell one by the addition of external higher-spin currents, for which we…
We present the analytic computation of all the planar master integrals which contribute to the two-loop scattering amplitudes for Higgs$\to 3$ partons, with full heavy-quark mass dependence. These are relevant for the NNLO corrections to…
Crossing symmetry suggests that deep inelastic scattering and semi inclusive electron-positron annihilation are governed by analytic continuations of a single forward amplitude. Drell, Levy, and Yan proposed that the hadronic tensor admits…
Pushing the reach of NNLO QCD predictions to $2\to3$ production processes is one of the pillars of precision phenomenology program at the LHC. In this talk we will overview recent results and developments in the calculation of two-loop…
We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct non-selfadjoint operators representing operator roots of the transfer…
In this paper we will consider quantum aspects of a non-local, infinite-derivative scalar field theory - a $\it toy \, model$ depiction of a covariant infinite-derivative, non-local extension of Einstein's general relativity which has…
In this paper, we have made the attempt to classify the integrand basis of all two-loop diagrams in pure four-dimension space-time. Our classification includes the topology of two-loop diagrams which determines the structure of…
We present a review of the one-loop photon ($\Pi$) and neutrino ($\Sigma$) two-point functions in a covariant and deformed $\rm U(1)$ gauge-theory on the 4-dimensional noncommutative spaces, determined by a constant antisymmetric tensor…
The higher-order corrections become increasingly important with experiments reaching sub-percent level of uncertainty as they look for physics beyond the Standard Model. Our goal is to address the full set of two-loop electroweak…
We write spectral decomposition of the hypergeometric differential operator on the contour $Re z=1/2$ (multiplicity of spectrum is 2). As a result, we obtain an integral transform that differs from the Jacobi (or Olevsky) transform. We also…
We derive the hard functions for all 2->2 processes in massless QCD up to next-to-next-to-leading order (NNLO) in the strong coupling constant. By employing the known one- and two-loop helicity amplitudes for these processes, we obtain…
We highlight the latest developments in computing higher-order scattering amplitudes with massive internal propagators. The contributing Feynman integrals often lead to special classes of functions, for example, functions associated with…
We generalize the result of our recent paper on the massless single off-shell scalar box integral to the case of two non-adjacent end points off the light cone. An analytic result in $d=4-2\varepsilon$ dimensions is established in terms of…
Dynamics of a one-dimensional system of Brownian particles with short-range repulsive interaction (diameter sigma) is studied with a liquid-theoretical approach. The mean square displacement, the two-particle displacement correlation, and…
The leading-order equations of the $1/N$ -- expansion for a vector-matrix model with interaction $g\phi_a^*\phi_b\chi_{ab}$ in four dimensions are investigated. This investigation shows a change of the asymptotic behavior in the deep…
Experiments at the future colliders LHC and ILC will, for the first time, explore electroweak reactions at energies in the TeV region, i.e. far beyond the masses of the W and Z bosons. In exclusive processes without the emission of massive…
We studied the two-loop non-factorizable Feynman diagrams for the $t$-channel single-top production process in quantum chromodynamics. We present a systematic computation of master integrals of the two-loop Feynman diagrams with one…
We evaluate the two-point functions of the electromagnetic field in (D+1) -dimensional spatially flat Friedmann-Robertson-Walker universes with a power-law scale factor, assuming that the field is prepared in the Bunch-Davies vacuum state.…