In this thesis, the infrared structure of squared matrix elements in quantum chromodynamics (QCD) is scrutinised. Specifically, the triple-collinear splitting functions are decomposed and improvements to antenna subtraction are sought through the construction of idealised antenna functions. The antenna-subtraction technique has demonstrated remarkable effectiveness in handling next-to-next-to-leading order (NNLO) infrared divergences for a wide range of QCD processes relevant for colliders. However, since antenna functions were historically extracted from matrix elements, they did not have uniform properties, which made the generation of subtraction terms complex. Antenna subtraction up to NNLO is reviewed, including the role of antenna functions. A general algorithm is detailed in order to re-build antenna functions, with idealised features, directly from a specified list of unresolved limits, for any number of real and virtual emissions. Using this general algorithm, together with the decomposition of the triple-collinear splitting functions, all the antenna functions required for NNLO QCD calculations in the final-final configuration are constructed and it is demonstrated that they form a consistent NNLO subtraction scheme. The idealised antenna functions should simplify the generation of subtraction terms and minimise the introduction of spurious limits. Additionally, the general algorithm sets out an initial blueprint for next-to-NNLO (N$^3$LO) idealised antennae for use in N$^3$LO QCD calculations.
We determine, in the antenna subtraction framework for handling infrared divergences in higher order QCD calculations, the real-virtual antenna functions for processes involving the production of a pair of massive quarks by an uncolored initial state at NNLO QCD. The integrated leading and subleading color real-virtual antenna functions are computed analytically in terms of (cyclotomic) harmonic polylogarithms. As a by-product and check we compute $R_Q=σ(e^+e^-\to γ^*\to Q\bar{Q}X)/σ(e^+e^-\to γ^*\toμ^+μ^-)$ and compare with existing results. Our result for $R_Q$ is exact to order $α_s^2$.
We present a complete set of helicity-dependent 2->3 antenna functions for QCD initial- and final- state radiation. The functions are implemented in the Vincia shower Monte Carlo framework and are used to generate showers for hadron-collider processes in which helicities are explicitly sampled (and conserved) at each step of the evolution. Although not capturing the full effects of spin correlations, the explicit helicity sampling does permit a significantly faster evaluation of fixed-order matrix-element corrections. A further speed increase is achieved via the implementation of a new fast li…
We present a formalism for a fully coherent QED parton shower. The complete multipole structure of photonic radiation is incorporated in a single branching kernel. The regular on-shell 2 to 3 kinematic picture is kept intact by dividing the radiative phase space into sectors, allowing for a definition of the ordering variable that is similar to QCD antenna showers. A modified version of the Sudakov veto algorithm is discussed that increases performance at the cost of the introduction of weighted events. Due to the absence of a soft singularity, the formalism for photon splitting is very simila…
We report on our recent progress towards including the photon fragmentation contribution in next-to-next-to-leading order (NNLO) QCD predictions for photon production cross sections. This extension to previous NNLO calculations requires the identification of the photon in singular parton-photon collinear limits. We discuss how these limits can be subtracted within antenna subtraction using fragmentation antenna functions and we outline their integration.
We extend the antenna subtraction method to include hadron fragmentation processes up to next-to-next-to-leading order (NNLO) in QCD in $e^+e^-$ collisions. To handle collinear singularities associated with the fragmentation process, we introduce fragmentation antenna functions in final-final kinematics with associated phase space mappings. These antenna functions are integrated over the relevant phase spaces, retaining their dependence on the momentum fraction of the fragmenting parton. The integrated antenna functions are cross-checked against the known NNLO coefficient functions for identif…
We present the colourful antenna subtraction method, a reformulation of the antenna subtraction scheme for next-to-next-to-leading order (NNLO) calculations in QCD. The aim of this new approach is to achieve a general and process-independent construction of the subtraction infrastructure at NNLO. We rely on the predictability of the infrared singularity structure of one- and two-loop amplitudes in colour space to generate virtual subtraction terms and, subsequently, we define an automatable procedure to systematically infer the expression of the real subtraction terms, guided by the correspond…
We present the NNLO corrections to top pair production in the quark-antiquark channel proportional to the number of light quark flavors $N_l$. While the double real corrections were derived previously, here we compute the real-virtual and virtual-virtual contributions in this partonic channel. Using the antenna subtraction formalism, we show that the subtraction terms correctly approximate the real-virtual contributions in all their infrared limits. Combined with the integrated forms of the double real and real-virtual subtraction terms, we show analytically that the explicit infrared poles ca…
We present a new implementation of the NNLO QCD corrections to three-jet final states and related event-shape observables in electron--positron annihilation. Our implementation is based on the antenna subtraction method, and is performed in the NNLOJET framework. The calculation improves upon earlier results by taking into account the full kinematical information on the initial state momenta, thereby allowing the event orientation to be computed to NNLO accuracy. We find the event-orientation distributions at LEP and SLC to be very robust under higher order QCD corrections.
We compute the next-to-leading order (NLO) QCD corrections to the gluon-fusion subprocess of diphoton-plus-jet production at the LHC. We compute fully differential distributions by combining two-loop virtual corrections with one-loop real radiation using antenna subtraction to cancel infrared divergences. We observe significant corrections at NLO which demonstrate the importance of combining these corrections with the quark-induced diphoton-plus-jet channel at next-to-next-to-leading order (NNLO).
We describe the details of the calculation of the full colour NNLO QCD corrections to jet production observables at the LHC with antenna subtraction. All relevant matrix elements for the process $pp \to jj$ at NNLO in full colour are colour-decomposed and given in a $N_c$ and $n_f$ expansion, making identification of leading and subleading colour contributions transparent. The colour-ordered antenna subtraction method has previously successfully been used to construct the NNLO subtraction terms for processes with up to five partons or in the leading colour approximation. However, it is challen…
We present the first public implementation of antenna-based QCD initial- and final-state showers. The shower kernels are $2\to 3$ antenna functions, which capture not only the collinear dynamics but also the leading soft (coherent) singularities of QCD matrix elements. We define the evolution measure to be inversely proportional to the leading poles, hence gluon emissions are evolved in a $p_\perp$ measure inversely proportional to the eikonal, while processes that only contain a single pole (e.g., $g\to q\bar{q}$) are evolved in virtuality. Non-ordered emissions are allowed, suppressed by an …
The theoretical description of photon production at particle colliders combines direct photon radiation and fragmentation processes, which can not be separated from each other for definitions of photon isolation used in experimental measurements. The theoretical description of these processes must account for collinear parton-photon configurations, retaining the dependence on the photon momentum fraction, and includes the parton-to-photon fragmentation functions. We extend the antenna subtraction method to include photon fragmentation processes up to next-to-next-to-leading order (NNLO) in QCD…
We consider the probability for a colour-singlet qqbar pair to emit a gluon, in strongly and smoothly ordered antenna showers. We expand to second order in alphaS and compare to the second-order QCD matrix elements for Z -> 3 jets, neglecting terms suppressed by 1/NC^2. We give a prescription that corrects the shower to the matrix-element result at this order for both soft and hard emissions, thereby explicitly reducing its dependence on evolution- and renormalization-scale choices. We confirm that the choice of pT for both of these scales absorbs all logarithms through order alphaS^2, and con…
Gluon radiation from a QCD antenna with realistic parton-medium interactions
École polytechnique（巴黎综合理工学院）；Institut Polytechnique de Paris（巴黎理工学院）；LIP - Laboratório de Instrumentação e Física Experimental de Partículas（粒子物理与实验仪器实验室）；Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高级技术学院物理系）；Instituto Galego de Física de Altas Enerxías IGFAE, Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学加利西亚高能物理研究所）
We compute the factorising second-order QCD corrections to the electroweak production of a Higgs boson through vector boson fusion. Our calculation is fully differential in the kinematics of the Higgs boson and of the final state jets, and uses the antenna subtraction method to handle infrared singular configurations in the different parton-level contributions. Our results allow us to reassess the impact of the next-to-leading order (NLO) QCD corrections to electroweak Higgs-plus-three-jet production and of the next-to-next-to-leading order (NNLO) QCD corrections to electroweak Higgs-plus-two-…
We present the computation of the double real and real-virtual contributions to top-antitop pair production in the quark-antiquark channel at leading colour. The $q \bar q \to t \bar{t} g$ amplitudes contributing to the real-virtual part are computed with OpenLoops, and their numerical stability in the soft and collinear regions is found to be sufficiently high to perform a realistic NNLO calculation in double precision. The subtraction terms required at real-real and real-virtual levels are constructed within the antenna subtraction formalism extended to deal with the presence of coloured mas…
NNLOJET: a parton-level event generator for jet cross sections at NNLO QCD accuracy
CERN（欧洲核子研究组织）；Universität Zürich（苏黎世大学）；University of Durham（杜伦大学）；ETH（苏黎世联邦理工学院）；Shandong University（山东大学）；Max-Planck-Institut für Physik, Werner-Heisenberg-Institut（马克斯·普朗克物理研究所）；KIT（卡尔斯鲁厄理工学院）；TU Dresden（德累斯顿工业大学）；LIP（葡萄牙粒子与核物理研究所）；Universidade de Lisboa（里斯本大学）；University of Wuppertal（伍珀塔尔大学）；Georg-August-Universität Göttingen（哥廷根大学）
We consider the decay of a neutral Higgs boson of arbitrary CP nature to a massive quark antiquark pair at next-to-next-to-leading order in perturbative QCD. Our analysis is made at the differential level using the antenna subtraction framework. We apply our general set-up to the decays of a CP-even and CP-odd heavy Higgs boson to a top-quark top-antiquark pair and to the decay of the 125 GeV Higgs boson to a massive bottom-quark bottom-antiquark pair. In the latter case we calculate, in particular, the two-jet, three-jet, and four-jet decay rates and, for two-jet events, the energy distributi…
We set up a formalism, within the antenna subtraction framework, for computing the production of a massive quark-antiquark pair in electron positron collisions at next-to-next-to-leading order in the coupling $α_s$ of quantum chromodynamics at the differential level. Our formalism applies to the calculation of any infrared-safe observable. We apply this set-up to the production of top-quark top antiquark pairs in the continuum. We compute the production cross section and several distributions. We determine, in particular, the top-quark forward-backward asymmetry at order $α_s^2$. Our result ag…
We discuss and illustrate the properties of several parton-shower algorithms available in Pythia and Vincia, in the context of Higgs production via vector boson fusion (VBF). In particular, the distinctive colour topology of VBF processes allows to define observables sensitive to the coherent radiation pattern of additional jets. We study a set of such observables, using the Vincia sector-antenna shower as our main reference, and contrast it to Pythia's transverse-momentum-ordered DGLAP shower as well as Pythia's dipole-improved shower. We then investigate the robustness of these predictions a…
