Two-loop leading-colour QCD helicity amplitudes for two-photon plus jet production at the LHC

Abstract

We calculate the complete set of two-loop leading-colour QCD helicity amplitudes for γγj-production at hadron colliders. Our results are presented in a compact, fully-analytical form.

Two-loop leading-colour QCD helicity amplitudes for Higgs boson production in association with a bottom-quark pair at the LHC

“…of the important ingredients in the amplitude computation -are available for the fully massless five-particle processes [8][9][10][11][12][13], allowing for several two-loop QCD amplitudes to be derived analytically [14][15][16][17][18][19][20][21][22][23][24][25], improving on previous results that were obtained numerically [26][27][28][29]. These new results have been achieved thanks to technological breakthroughs in the method of differential equations [30][31][32][33][34], integral reduction algorithms [35][36][37][38][39] and the use of finite-field arithmetic to tame the algebraic complexity of multi-leg and multiscale problems [40][41][42][43][44][45].…”

NNLO QCD corrections to diphoton production with an additional jet at the LHC

“…The scaleindependent part H (2) (s 12 ) is included in the leading color approximation as derived in ref. [40] with the help of refs. [41][42][43] (an equivalent expression for the spin-averaged twoloop squared amplitude has also been derived in ref.…”

Renormalization and non-renormalization of scalar EFTs at higher orders

“…For example, the Large Hadron Collider (LHC) is a powerful driver for advancing the boundaries of perturbative QCD and electroweak theory calculations, where S-matrix elements are needed at higher loop order to match the precision measurements, and may involve many 'legs' (number of external particles) to describe the large multiplicity processes offered by the high collision energy. For instance, recent years have witnessed state of the art QCD amplitude calculations being pushed to three-loops for up to four external legs [1], and to two-loops for up to five external legs, see for instance [2][3][4]. Similarly, extremely precise measurements of the fine structure constant from atom interferometry [5,6] and the magnetic dipole moment of the electron [7] have pushed calculations up to five loops in QED [8][9][10].…”

“…In [82] it was shown that the EFT operator basis can be identified as the set of conformal primary operators (in [84,85] these primaries were further identified as harmonics of the manifold of phase space). 3 This represents a mathematically singled out (up to rotations in the space of primaries) basis for the S-matrix, i.e. the number of on-shell physical measurements one can make in a theory.…”