A
bstract
We analytically calculate one-loop five-point Master Integrals,
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 Mathematica package 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.
A
bstract
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.
A
bstract
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.
A
bstract
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
→
3 scattering processes of interest at the LHC, especially for the leading-color
W
+ 2 jets production.
Resummation methods for Master Integrals Canko, Dhimiter D.; Syrrakos, Nikolaos
The journal of high energy physics,
02/2021, Letnik:
2021, Številka:
2
Journal Article
Recenzirano
Odprti dostop
A
bstract
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 →
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.
A
bstract
We present analytic results for the two tennis-court integral families relevant to 2 → 2 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.
A
bstract
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
→
ggg
,
H
→
q
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.
We compute the planar three-loop Quantum Chromodynamics (QCD) corrections to the helicity amplitudes involving a vector boson V=Z,W±,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 N3, N2Nf, NNf2 and Nf3. We provide the finite remainders of the independent helicity amplitudes in terms of multiple polylogarithms, continued to all kinematic regions and in a form which is compact and lends itself to efficient numerical evaluation. The presented amplitude respects the conjectured symbol-adjacency constraints for amplitudes with three massless and one massive leg.
A
bstract
We compute the two-loop Quantum Chromodynamics (QCD) corrections to all partonic channels relevant for the production of an electroweak boson
V
=
Z, W
±
, γ
*
and a jet at hadron colliders. ...We consider the decay of a vector boson
V
to three partons
V
→
q
q
¯
g
,
V
→
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
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
O
(
ϵ
2
). We provide finite remainders of the helicity amplitudes analytically continued to all relevant scattering regions
q
q
¯
→
Vg
,
qg
→
Vq
and
gg
→
Vg
. The axial vector contribution to the gluon-induced channel completes the set of two-loop amplitudes for this process, while the extension to
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.
A
bstract
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.
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