arXiv subjects

Nikolaos Syrrakos

Publications and source records attributed to Nikolaos Syrrakos.

14 recordsLinked to original sources

arXiv2024

Graded transcendental functions: an application to four-point amplitudes with one off-shell leg

Several recent works have demonstrated the powerful algebraic simplifications that can be achieved for scattering amplitudes through a systematic grading of transcendental quantities. We develop these concepts to construct a minimal basis of functions tailored to a scattering amplitude in a general way. Starting with formal solutions for all master integral topologies, we organise the appearing functions by properties such as their symbol alphabet or letter adjacency. We rotate the basis such that functions with spurious features appear in the least possible number of basis elements. Since their coefficients must vanish for physical quantities, this approach avoids complex cancellations. As a first application, we evaluate all integral topologies relevant to the three-loop $Hggg$ and $Hgq\bar{q}$ amplitudes in the leading-colour approximation and heavy-top limit. We describe the derivation of canonical differential equation systems and present a method for fixing boundary conditions without the need for a full functional representation. Using multiple numerical reductions, we test the maximal transcendentality conjecture for $Hggg$ and identify a new letter which appears in functions of weight 4 and 5. In addition, we provide the first direct analytic computation of a three-point form factor of the operator $\mathrm{Tr}(ϕ^2)$ in planar $\mathcal{N}=4$ sYM and find agreement with numerical and bootstrapped results.

hep-th↗

arXiv2023

Planar three-loop QCD helicity amplitudes for $V$+jet production at hadron colliders

We compute the planar three-loop Quantum Chromodynamics (QCD) corrections to the helicity amplitudes involving a vector boson $V=Z,W^\pm,γ^*$, two quarks and a gluon. These amplitudes are relevant to vector-boson-plus-jet production at hadron colliders and other precision QCD observables. The planar corrections encompass the leading colour factors $N^3$, $N^2 N_f$, $N N_f^2$ and $N_f^3$. We provide the finite remainders of the independent helicity amplitudes in terms of multiple polylogrithms, continued to all kinematic regions and in a form which is compact and lends itself to efficient numerical evaluation.

hep-ph↗

arXiv2023

Two-loop helicity amplitudes for $H+$jet production to higher orders in the dimensional regulator

In view of the forthcoming High-Luminosity phase of the LHC, next-to-next-to-next-to-leading (N$^3$LO) calculations for the most phenomenologically relevant processes become necessary. In this work, we take the first step towards this goal for H$+$jet production by computing the one- and two-loop helicity amplitudes for the two contributing processes, $H\to ggg$, $H\to q\bar{q}g$, in an effective theory with infinite top quark mass, to higher orders in the dimensional regulator. We decompose the amplitude in scalar form factors related to the helicity amplitudes and in a new basis of tensorial structures. The form factors receive contributions from Feynman integrals which were reduced to a novel canonical basis of master integrals. We derive and solve a set of differential equations for these integrals in terms of Multiple Polylogarithms (MPLs) of two variables up to transcendental weight six.

hep-ph↗

arXiv2023

Three-loop master integrals for H+jet production at N$^3$LO: Towards the non-planar topologies

We discuss the recent progress that has been made towards the computation of three-loop non-planar master integrals relevant to next-to-next-to-next-to-leading-order (N$^3$LO) corrections to processes such as H+jet production at the LHC. We describe the analytic structure of these integrals, as well as several technical issues regarding their analytic computation using canonical differential equations. Finally, we comment on the remaining steps towards the computation of all relevant three-loop topologies and their application to amplitude calculations.

hep-ph↗

arXiv2023

Two-loop helicity amplitudes for $V+$jet production including axial vector couplings to higher orders in $ε$

We compute the two-loop Quantum Chromodynamics (QCD) corrections to all partonic channels relevant for the production of an electroweak boson $V=Z,W^\pm,γ^*$ and a jet at hadron colliders. We consider the decay of a vector boson $V$ to three partons $ V \to q\bar{q}g$, $ V \to ggg$ with a vector and axial vector coupling in both channels, including singlet and non-singlet contributions. For the quark channel, we use a recent tensor decomposition and extend the calculation to $\mathcal{O}(ε^2)$. For the gluonic channel, we define a new tensor decomposition which allows us to compute the vector and the axial vector amplitudes at once and to perform the computation of the amplitudes to $\mathcal{O}(ε^2)$. We provide finite remainders of the helicity amplitudes analytically continued to all relevant scattering regions $q\bar{q} \to V g$, $q g \to V q$ and $gg \to V g$. The axial vector contribution to the gluon-induced channel completes the set of two-loop amplitudes for this process, while the extension to $\mathcal{O}(ε^2)$ represents the first step in the calculation of next-to-next-to-next-to-leading-order (N$^3$LO) QCD corrections to $Z$+jet production at hadron colliders.

hep-ph↗

arXiv2023

Two-loop master integrals for a planar and a non-planar topology relevant for single top production

We provide analytic results for two-loop four-point master integrals with one massive propagator and one massive leg relevant to single top production. Canonical bases of master integrals are constructed and the Simplified Differential Equations approach is employed for their analytic solution. The necessary boundary terms are computed in closed form in the dimensional regulator, allowing us to obtain analytic results in terms of multiple polylogarithms of arbitrary transcendental weight. We provide explicit solutions of all two-loop master integrals up to transcendental weight six and discuss their numerical evaluation for Euclidean and physical phase-space points.

hep-ph↗

arXiv2022

Two-loop non-planar hexa-box integrals with one massive leg

Based on the Simplified Differential Equations approach, we present results for the two-loop non-planar hexa-box families of master integrals. We introduce a new approach to obtain the boundary terms and establish a one-dimensional integral representation of the master integrals in terms of Generalised Polylogarithms, when the alphabet contains non-factorisable square roots. The results are relevant to the study of NNLO QCD corrections for $W,Z$ and Higgs-boson production in association with two hadronic jets.

hep-ph↗

arXiv2022

Planar three-loop master integrals for $2 \to 2$ processes with one external massive particle

We present analytic results for the two tennis-court integral families relevant to $2\to2$ scattering processes involving one massive external particle and massless propagators in terms of Goncharov polylogarithms of up to transcendental weight six. We also present analytic results for physical kinematics for the ladder-box family and the two tennis-court families in terms of real-valued polylogarithmic functions, making our solutions well-suited for phenomenological applications.

hep-ph↗

arXiv2021

Multiscale pentagon integrals to all orders

We present analytical results for one-loop five-point master integrals with up to three off-shell legs. The method of canonical differential equations along with the Simplified Differential Equations approach is employed. All necessary boundary terms are given in closed form, resulting to solutions in terms of Goncharov Polylogarithms of arbitrary weight. Explicit results up to weight six will be presented.

hep-ph↗

arXiv2021

$N^3LO$ calculations for $2 \to 2$ processes using Simplified Differential Equations

We present the computation of the massless three-loop ladder-box family with one external off-shell leg using the Simplified Differential Equations (SDE) approach. We also discuss the methods we used for finding a canonical differential equation for the two tennis-court families with one off-shell leg, and the application of the SDE approach on these two families.

hep-ph↗

arXiv2021

One-loop Feynman integrals for $2\to3$ scattering involving many scales including internal masses

We study several multiscale one-loop five-point families of Feynman integrals. More specifically, we employ the Simplified Differential Equations approach to obtain results in terms of Goncharov polylogarithms of up to transcendental weight four for families with two and three massive external legs and massless propagators, as well as with one massive internal line and up to two massive external legs. This is the first time this computational approach is applied to cases involving internal masses.

hep-ph↗

arXiv2021

Pentagon integrals to arbitrary order in the dimensional regulator

We analytically calculate one-loop five-point Master Integrals, \textit{pentagon integrals}, with up to one off-shell leg to arbitrary order in the dimensional regulator in $d=4-2ε$ space-time dimensions. A pure basis of Master Integrals is constructed for the pentagon family with one off-shell leg, satisfying a single-variable canonical differential equation in the Simplified Differential Equations approach. The relevant boundary terms are given in closed form, including a hypergeometric function which can be expanded to arbitrary order in the dimensional regulator using the \texttt{Mathematica} package \texttt{HypExp}. Thus one can obtain solutions of the canonical differential equation in terms of Goncharov Polylogartihms of arbitrary transcendental weight. As a special limit of the one-mass pentagon family, we obtain a fully analytic result for the massless pentagon family in terms of pure and universally transcendental functions. For both families we provide explicit solutions in terms of Goncharov Polylogartihms up to weight four.

hep-ph↗

arXiv2020

Resummation methods for Master Integrals

We present in detail two resummation methods emerging from the application of the Simplified Differential Equations approach to a canonical basis of master integrals. The first one is a method which allows for an easy determination of the boundary conditions, since it finds relations between the boundaries of the basis elements and the second one indicates how using the $x \rightarrow 1$ limit to the solutions of a canonical basis, one can obtain the solutions to a canonical basis for the same problem with one mass less. Both methods utilise the residue matrices for the letters $\{0,1\}$ of the canonical differential equation. As proof of concept, we apply these methods to a canonical basis for the three-loop ladder-box with one external mass off-shell, obtaining subsequently a canonical basis for the massless three-loop ladder-box as well as its solution.

hep-ph↗

arXiv2020

Analytic representation of all planar two-loop five-point Master Integrals with one off-shell leg

We present analytic expressions in terms of polylogarithmic functions for all three families of planar two-loop five-point Master Integrals with one off-shell leg. The calculation is based on the Simplified Differential Equations approach. The results are relevant to the study of many $2\to 3$ scattering processes of interest at the LHC, especially for the leading-color $W+2$ jets production.

hep-ph↗