The partonic structure of the electron at the next-to-leading logarithmic accuracy in QED

By working in QED, we obtain the electron, positron, and photon Parton Distribution Functions (PDFs) of the unpolarised electron at the next-to-leading logarithmic accuracy. The PDFs account for all of the universal effects of initial-state collinear origin, and are key ingredients in the calculations of cross sections in the so-called structure-function approach. We present both numerical and analytical results, and show that they agree extremely well with each other. The analytical predictions are defined by means of an additive formula that matches a large-$z$ solution that includes all orders in the QED coupling constant $\alpha$, with a small- and intermediate-$z$ solution that includes terms up to ${\cal O}(\alpha^3)$.Comment: 60 pages, 25 figures; the overall normalisation of eq.(5.56) and eq.(5.57), and a couple of grammatical mistakes, have been correcte

Precise QCD predictions for W-boson production in association with a charm jet

The production of a $W$-boson with a charm quark jet provides a highly sensitive probe of the strange quark distribution in the proton. Employing a novel flavour dressing procedure to define charm quark jets, we compute $W$+charm-jet production up to next-to-next-to-leading order (NNLO) in QCD. We study the perturbative stability of production cross sections with same-sign and opposite-sign charge combinations for the $W$ boson and the charm jet. A detailed breakdown according to different partonic initial states allows us to identify particularly suitable observables for the study of the quark parton distributions of different flavours.Comment: 26 pages, 15 figures, 5 table

Precise QCD predictions for W-boson production in association with a charm jet

The production of a W-boson with a charm quark jet provides a highly sensitive probe of the strange quark distribution in the proton. Employing a novel flavour dressing procedure to define charm quark jets, we compute W+charm-jet production up to next-to-next-to-leading order (NNLO) in QCD. We study the perturbative stability of production cross sections with same-sign and opposite-sign charge combinations for the W boson and the charm jet. A detailed breakdown according to different partonic initial states allows us to identify particularly suitable observables for the study of the quark parton distributions of different flavours

The muon parton distribution functions

We compute the Parton Distribution Functions (PDFs) of the unpolarised muon for the leptons, the photon, the light quarks, and the gluon. We discuss in detail the issues stemming from the necessity of evaluating the strong coupling constant at scales of the order of the typical hadron mass, and compare our novel approach with those currently available in the literature. While we restrict our phenomenological results to be leading-logarithmic accurate, we set up our formalism in a way that renders it straightforward to achieve next-to-leading logarithmic accuracy in the QED, QCD, and mixed QED×QCD contributions

SUBSTRUCTURE AT COLLIDERS

In this PhD thesis we investigate several aspects of parton distribution functions (PDFs) and jets as applicable to the physics underpinning the Large Hadron Collider (LHC) as well as future colliders. We first discuss jet observables at the LHC, focusing on the single-jet inclusive cross section. We introduce possible alternative definitions, which weigh the individual contributions coming from each jet in the event and are thus unitary by construction. We also clarify the origin of some problematic aspects of the standard definition. Secondly, within the hadronic PDF fitting framework of the NNPDF collaboration, we investigate the inclusion of single-jet inclusive and dijet measurements into a global PDF fit, using QCD next-to-next-to-leading order predictions for jet processes. We field-test which observables lead to better perturbative stability, better PDF compatibility with other data, better fit quality, and more stringent constraints on the PDFs. Thirdly, we focus on an analytical understanding of machine learning techniques used for quark versus gluon discrimination, a hot topic in jet substructure studies. We construct a new version of the widely used N -subjettiness variable, which features a simpler theoretical behaviour than the original one, while maintaining, if not exceeding, the discriminating power. We input these new observables to the simplest possible neural network, with only one neuron, and we study analytically the network behaviour at leading logarithmic accuracy. We also compare our analytic findings to a more realistic neural network trained with Monte Carlo pseudo-data. Fourthly, we compute the unpolarised electron, positron, and photon PDFs at next- to-leading logarithmic accuracy in QED, which are crucial for high-precision predictions needed for future e + e 12 colliders. We present both numerical and analytical results. The analytical predictions, defined by means of a specific additive formula, provide a large-z analytical solution that includes all orders in the QED coupling constant \u3b1, with a small- and intermediate-z solution that includes terms up to O(\u3b1 3 ). The content of this thesis is based on arXiv:1906.11850, arXiv:1911.12040, arXiv:2005.11327, and arXiv:2007.04319

The muon parton distribution functions

Abstract We compute the Parton Distribution Functions (PDFs) of the unpolarised muon for the leptons, the photon, the light quarks, and the gluon. We discuss in detail the issues stemming from the necessity of evaluating the strong coupling constant at scales of the order of the typical hadron mass, and compare our novel approach with those currently available in the literature. While we restrict our phenomenological results to be leading-logarithmic accurate, we set up our formalism in a way that renders it straightforward to achieve next-to-leading logarithmic accuracy in the QED, QCD, and mixed QED×QCD contributions

Towards machine learning analytics for jet substructure

The past few years have seen a rapid development of machine-learning algorithms. While surely augmenting performance, these complex tools are often treated as black-boxes and may impair our understanding of the physical processes under study. The aim of this paper is to move a first step into the direction of applying expert-knowledge in particle physics to calculate the optimal decision function and test whether it is achieved by standard training, thus making the aforementioned black-box more transparent. In particular, we consider the binary classification problem of discriminating quark-initiated jets from gluon-initiated ones. We construct a new version of the widely used N-subjettiness, which features a simpler theoretical behaviour than the original one, while maintaining, if not exceeding, the discrimination power. We input these new observables to the simplest possible neural network, i.e. the one made by a single neuron, or perceptron, and we analytically study the network behaviour at leading logarithmic accuracy. We are able to determine under which circumstances the perceptron achieves optimal performance. We also compare our analytic findings to an actual implementation of a perceptron and to a more realistic neural network and find very good agreement

The partonic structure of the electron at the next-to-leading logarithmic accuracy in QED

By working in QED, we obtain the electron, positron, and photon Parton Distribution Functions (PDFs) of the unpolarised electron at the next-to-leading logarithmic accuracy. The PDFs account for all of the universal effects of initial-state collinear origin, and are key ingredients in the calculations of cross sections in the so-called structure-function approach. We present both numerical and analytical results, and show that they agree extremely well with each other. The analytical predictions are defined by means of an additive formula that matches a large-$z$ solution that includes all orders in the QED coupling constant $\alpha$, with a small- and intermediate-$z$ solution that includes terms up to ${\cal O}(\alpha^3)$

Improving methods and predictions at high-energy e+e−e^+e^- colliders within collinear factorisation

We illustrate how electron Parton Distribution Functions (PDFs) with next-to-leading collinear logarithmic accuracy must be employed in the context of perturbative predictions for high-energy $e^+e^-$-collision processes. In particular, we discuss how the renormalisation group equation evolution of such PDFs is affected by the presence of multiple fermion families and their respective mass thresholds, and by the dependences on the choices of the factorisation and renormalisation schemes. We study the impact of the uncertainties associated with the PDFs on physical cross sections, in order to arrive at realistic precision estimates for observables computed with collinear-factorisation formulae. We do so by presenting results for the production of a heavy neutral object as well as for $t\bar{t}$ and $W^+W^-$ pairs, including next-to-leading-order effects of electroweak origin

NNLO QCD predictions for Z-boson production in association with a charm jet within the LHCb fiducial region

We compute next-to-next-to-leading order (NNLO) QCD corrections to neutral vector boson production in association with a charm jet at the LHC. This process is studied in the forward kinematics at s√=13 TeV, which may provide valuable constraints on the intrinsic charm component of the proton. A comparison is performed between fixed order and NLO predictions matched to a parton shower showing mutual compatibility within the respective uncertainties. NNLO corrections typically lead to a reduction of theoretical uncertainties by a factor of two and the perturbative convergence is further improved through the introduction of a theory-inspired constraint on the transverse momentum of the vector boson plus jet system. A comparison between these predictions with data will require an alignment of a flavour-tagging procedure in theory and experiment that is infrared and collinear safe