Dissecting the collinear structure of quark splitting at NNLL

We explore the collinear limit of final-state quark splittings at order $$ {\alpha}_s^2 $$ α s 2 . While at general NLL level, this limit is described simply by a product of leading-order 1 → 2 DGLAP splitting functions, at the NNLL level we need to consider 1 → 3 splitting functions. Here, by performing suitable integrals of the triple-collinear splitting functions, we demonstrate how one may extract $$ {\mathrm{\mathcal{B}}}_2^q(z) $$ ℬ 2 q z , a differential version of the coefficient $$ {\mathrm{\mathcal{B}}}_2^q $$ ℬ 2 q that enters the quark form factor at NNLL and governs the intensity of collinear radiation from a quark. The variable z corresponds to the quark energy fraction after an initial 1 → 2 splitting, and our results yield effective higher-order splitting functions, which may be considered as a step towards the construction of NNLL parton showers. Further, while in the limit z → 1 we recover the standard soft limit results involving the CMW coupling with scale kt, the z dependence we obtain also motivates the extension of the notion of a physical coupling beyond the soft limit.

The two-loop remainder function for eight and nine particles

Two-loop MHV amplitudes in planar $$ \mathcal{N} $$ N = 4 supersymmetric Yang Mills theory are known to exhibit many intriguing forms of cluster-algebraic structure. We leverage this structure to upgrade the symbols of the eight- and nine-particle amplitudes to complete analytic functions. This is done by systematically projecting onto the components of these amplitudes that take different functional forms, and matching each component to an ansatz of multiple polylogarithms with negative cluster-coordinate arguments. The remaining additive constant can be determined analytically by comparing the collinear limit of each amplitude to known lower-multiplicity results. We also observe that the nonclassical part of each of these amplitudes admits a unique decomposition in terms of a specific A3 cluster polylogarithm, and explore the numerical behavior of the remainder function along lines in the positive region.

Groomed jet mass as a direct probe of collinear parton dynamics

We study the link between parton dynamics in the collinear limit and the logarithmically enhanced terms of the groomed jet mass distribution, for jets groomed with the modified mass-drop tagger (mMDT). While the leading-logarithmic (LL) result is linked to collinear evolution with leading-order splitting kernels, here we derive the NLL structure directly from triple-collinear splitting kernels. The calculation we present is a fixed-order calculation in the triple-collinear limit, independent of resummation ingredients and methods. It therefore constitutes a powerful cross-check of the NLL results previously derived using the SCET formalism and provides much of the insight needed for resummation within the traditional QCD approach.

N-jettiness beam functions at N3LO

We present the first complete calculation for the quark and gluon N-jettiness ($$ {\mathcal{T}}_N $$ T N ) beam functions at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. Our calculation is based on an expansion of the differential Higgs boson and Drell-Yan production cross sections about their collinear limit. This method allows us to employ cutting edge techniques for the computation of cross sections to extract the universal building blocks in question. The class of functions appearing in the matching coefficents for all channels includes iterated integrals with non-rational kernels, thus going beyond the one of harmonic polylogarithms. Our results are a key step in extending the $$ {\mathcal{T}}_N $$ T N subtraction methods to N3LO, and to resum $$ {\mathcal{T}}_N $$ T N distributions at N3LL′ accuracy both for quark as well as for gluon initiated processes.

Transverse momentum dependent PDFs at N3LO

We compute the quark and gluon transverse momentum dependent parton distribution functions at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. Our calculation is based on an expansion of the differential Drell-Yan and gluon fusion Higgs production cross sections about their collinear limit. This method allows us to employ cutting edge multiloop techniques for the computation of cross sections to extract these universal building blocks of the collinear limit of QCD. The corresponding perturbative matching kernels for all channels are expressed in terms of simple harmonic polylogarithms up to weight five. As a byproduct, we confirm a previous computation of the soft function for transverse momentum factorization at N3LO. Our results are the last missing ingredient to extend the qT subtraction methods to N3LO and to obtain resummed qT spectra at N3LL′ accuracy both for gluon as well as for quark initiated processes.

Massive event-shape distributions at N2LL

In a recent paper we have shown how to optimally compute the differential and cumulative cross sections for massive event-shapes at $$ \mathcal{O}\left({\alpha}_s\right) $$ O α s in full QCD. In the present article we complete our study by obtaining resummed expressions for non-recoil-sensitive observables to N2LL + $$ \mathcal{O}\left({\alpha}_s\right) $$ O α s precision. Our results can be used for thrust, heavy jet mass and C-parameter distributions in any massive scheme, and are easily generalized to angularities and other event shapes. We show that the so-called E- and P-schemes coincide in the collinear limit, and compute the missing pieces to achieve this level of accuracy: the P-scheme massive jet function in Soft-Collinear Effective Theory (SCET) and boosted Heavy Quark Effective Theory (bHQET). The resummed expression is subsequently matched into fixed-order QCD to extend its validity towards the tail and far- tail of the distribution. The computation of the jet function cannot be cast as the dis- continuity of a forward-scattering matrix element, and involves phase space integrals in d = 4 − 2ε dimensions. We show how to analytically solve the renormalization group equation for the P-scheme SCET jet function, which is significantly more complicated than its 2-jettiness counterpart, and derive rapidly-convergent expansions in various kinematic regimes. Finally, we perform a numerical study to pin down when mass effects become more relevant.

Production of prompt photons associated with jets at LHC in kT-factorization

We use the kT–factorization approach to calculate total and differential cross sections of associated production of prompt photons and hadronic jets at the LHC energies. Our consideration relies on the pegasus Monte-Carlo generator with implemented ℴ(αα2s) off-shell gluon–gluon fusion subprocess g*g* → γqq− and several subleading quark-initiated contributions from ℴ(ααs) and ℴ(αα2s) subprocesses, taken into account in the collinear limit. Using Monte-Carlo generators CASCADE and PYTHIA, we investigate parton showering effects and compare our predictions with the data, taken by CMS and ATLAS collaborations at the LHC. We demostrate reasonabledescription of the data and the importance of parton shower effects in the kT–factorization.