Accelerating LHC phenomenology with analytic one-loop amplitudes

The evaluation of one-loop matrix elements is one of the main bottlenecks in precision calculations for the high-luminosity phase of the Large Hadron Collider. To alleviate this problem, a new C++ interface to the "Image missing" parton-level Monte Carlo is introduced, giving access to an extensive library of analytic results for one-loop amplitudes. Timing comparisons are presented for a large set of Standard Model processes. These are relevant for high-statistics event simulation in the context of experimental analyses and precision fixed-order computations.

One-loop string corrections for AdS Kaluza-Klein amplitudes

We discuss the string corrections to one-loop amplitudes in AdS5×S5, focussing on their expressions in Mellin space. We present the leading (α′)3 corrections to the family of correlators $$ \left\langle {\mathcal{O}}_2{\mathcal{O}}_2{\mathcal{O}}_p{\mathcal{O}}_p\right\rangle $$ O 2 O 2 O p O p at one loop and begin the exploration of the form of correlators with multiple channels. From these correlators we extract some string corrections to one- loop anomalous dimensions of families of operators of low twist.

Tropical fans, scattering equations and amplitudes

We describe a family of tropical fans related to Grassmannian cluster algebras. These fans are related to the kinematic space of massless scattering processes in a number of ways. For each fan associated to the Grassmannian Gr(k, n) there is a notion of a generalised ϕ3 amplitude and an associated set of scattering equations which further generalise the Gr(k, n) scattering equations that have been recently introduced. Here we focus mostly on the cases related to finite Grassmannian cluster algebras and we explain how face variables for the cluster polytopes are simply related to the scattering equations. For the Grassmannians Gr(4, n) the tropical fans we describe are related to the singularities (or symbol letters) of loop amplitudes in planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We show how each choice of tropical fan leads to a natural class of polylogarithms, generalising the notion of cluster adjacency and we describe how the currently known loop data fit into this classification.

Loops in AdS: from the spectral representation to position space. Part II

We continue the study of AdS loop amplitudes in the spectral representation and in position space. We compute the finite coupling 4-point function in position space for the large-N conformal Gross Neveu model on AdS3. The resummation of loop bubble diagrams gives a result proportional to a tree-level contact diagram. We show that certain families of fermionic Witten diagrams can be easily computed from their companion scalar diagrams. Thus, many of the results and identities of [1] are extended to the case of external fermions. We derive a spectral representation for ladder diagrams in AdS. Finally, we compute various bulk 2-point correlators, extending the results of [1].

Mixed EW-QCD two-loop amplitudes for $$ q\overline{q}\to {\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} $$ and γ5 scheme independence of multi-loop corrections

We perform a dedicated study of the $$ q\overline{q} $$ q q ¯ -initiated two-loop electroweak-QCD Drell-Yan scattering amplitude in dimensional regularization schemes for vanishing light quark and lepton masses. For the relative order α and αs one-loop Standard Model corrections, details of our comparison to the original literature are given. The infrared pole terms of the mixed two-loop amplitude are governed by a known generalization of the dipole formula and we show explicitly that exactly the same two-loop polarized hard scattering functions are obtained in both the standard ’t Hooft-Veltman-Breitenlohner-Maison γ5 scheme and Kreimer’s anticommuting γ5 scheme.

Two-loop leading colour QCD corrections to $$ q\overline{q} $$ → γγg and qg → γγq

We present the leading colour and light fermionic planar two-loop corrections for the production of two photons and a jet in the quark-antiquark and quark-gluon channels. In particular, we compute the interference of the two-loop amplitudes with the corresponding tree level ones, summed over colours and polarisations. Our calculation uses the latest advancements in the algorithms for integration-by-parts reduction and multivariate partial fraction decomposition to produce compact and easy-to-use results. We have implemented our results in an efficient C++ numerical code. We also provide their analytic expressions in Mathematica format.