On the Impact of Lepton PDFs

In this paper we discuss the effect of the complete leading-order QED corrections to the DGLAP equations in the perturbative evolution of parton distribution functions (PDFs). This requires the extension of the purely QCD DGLAP evolution, including a PDF for the photons and, consistently, also for the charged leptons $e^{\pm}$, $\mu^\pm$ and $\tau^\pm$. We present the implementation of the QED-corrected DGLAP evolution in the presence of photon and lepton PDFs in the APFEL program and, by means of different assumptions for the initial scale PDFs, we produce for the first time PDF sets containing charged lepton distributions. We also present phenomenological studies that aim to assess the impact of the presence of lepton PDFs in the proton for some relevant SM (and BSM) processes at the LHC at 13 TeV and the FCC-hh at 100 TeV. The impact of the photon PDF is also outlined for those processes.Comment: 32 pages, 19 figures, matches published version in JHE

The complete NLO corrections to dijet hadroproduction

We study the production of jets in hadronic collisions, by computing all contributions proportional to $\alpha_S^n\alpha^m$, with $n+m=2$ and $n+m=3$. These correspond to leading and next-to-leading order results, respectively, for single-inclusive and dijet observables in a perturbative expansion that includes both QCD and electroweak effects. We discuss issues relevant to the definition of hadronic jets in the context of electroweak corrections, and present sample phenomenological predictions for the 13-TeV LHC. We find that both the leading and next-to-leading order contributions largely respect the relative hierarchy established by the respective coupling-constant combinations.Comment: 30 pages, 14 figures; v2 contains minor changes to the text and to one label in fig.1, plus additional material in the form of an ancillary file that reports cross sections computed in various HT range

A certified RB method for PDE-constrained parametric optimization problems

Abstract We present a certified reduced basis (RB) framework for the efficient solution of PDE-constrained parametric optimization problems. We consider optimization problems (such as optimal control and optimal design) governed by elliptic PDEs and involving possibly non-convex cost functionals, assuming that the control functions are described in terms of a parameter vector. At each optimization step, the high-fidelity approximation of state and adjoint problems is replaced by a certified RB approximation, thus yielding a very efficient solution through an "optimize-then-reduce" approach. We develop a posteriori error estimates for the solutions of state and adjoint problems, the cost functional, its gradient and the optimal solution. We confirm our theoretical results in the case of optimal control/design problems dealing with potential and thermal flows

Application of Graph Theory to the elaboration of personal genomic data for genealogical research

In this communication a representation of the links between DNA-relatives based on Graph Theory is applied to the analysis of personal genomic data to obtain genealogical information. The method is tested on both simulated and real data and its applicability to the field of genealogical research is discussed. We envisage the proposed approach as a valid tool for a streamlined application to the publicly available data generated by many online personal genomic companies. In this way, anonymized matrices of pairwise genome sharing counts can help to improve the retrieval of genetic relationships between customers who provide explicit consent to the treatment of their data