APFEL++: A new PDF evolution library in C++

I present a preliminary version of {\tt APFEL++}, a C++ rewriting of the Fortran 77 evolution code {\tt APFEL}. In this contribution I discuss the new philosophy adopted for the numerical computation of the convolutions, demonstrate the ability to reproduce old results in an accurate and fast way, and present an original application to the computation of the semi-inclusive deep-inelastic-scattering cross section to next-to-leading order in QCD.Comment: 7 pages, 4 figures, proceedings of the DIS2017 conferenc

The photon PDF from high-mass Drell-Yan data at the LHC

I present a determination of the photon PDF from a fit to the recent ATLAS measurements of high-mass Drell-Yan lepton-pair production at $\sqrt{s} = 8$ TeV. This analysis is based on the {\tt xFitter} framework interfaced to the {\tt APFEL} program, that accounts for NLO QED effects, and to the {\tt aMCfast} code to account for the photon-initiated contributions within {\tt MadGraph5\_aMC@NLO}. The result is compared with other recent determinations of the photon PDF finding a general good agreement.Comment: 8 pages, 6 figures, Proceedings of the PHOTON'17 worksho

Parton Distributions with the Combined HERA Charm Production Cross Sections

Heavy quark structure functions from HERA provide a direct handle on the medium and small-x gluon PDF. In this contribution, we discuss ongoing progress on the implementation of the FONLL General-Mass scheme with running heavy quark masses, and of its benchmarking with the HOPPET and OpenQCDrad codes, and then present the impact of the recently released combined HERA charm production cross sections in the NNPDF2.3 analysis. We find that the combined charm data contribute to constraining the gluon and quarks at small values of Bjorken-x.Comment: 4 pages, 2 figures, 2 tables, contribution to the proceedings of the DIFFRACTION 2012 Workshop, Sep 10-15, Puerto del Carmen, Spai

APFEL: A PDF Evolution Library with QED corrections

Quantum electrodynamics and electroweak corrections are important ingredients for many theoretical predictions at the LHC. This paper documents APFEL, a new PDF evolution package that allows for the first time to perform DGLAP evolution up to NNLO in QCD and to LO in QED, in the variable-flavor-number scheme and with either pole or MSbar heavy quark masses. APFEL consistently accounts for the QED corrections to the evolution of quark and gluon PDFs and for the contribution from the photon PDF in the proton. The coupled QCD+QED equations are solved in x-space by means of higher order interpolation, followed by Runge-Kutta solution of the resulting discretized evolution equations. APFEL is based on an innovative and flexible methodology for the sequential solution of the QCD and QED evolution equations and their combination. In addition to PDF evolution, APFEL provides a module that computes Deep-Inelastic Scattering structure functions in the FONLL general-mass variable-flavor-number scheme up to O($\alpha_s^2$). All the functionalities of APFEL can be accessed via a Graphical User Interface, supplemented with a variety of plotting tools for PDFs, parton luminosities and structure functions. Written in Fortran 77, APFEL can also be used via the C/C++ and Python interfaces, and is publicly available from the HepForge repository.Comment: 34 pages, 5 figures. Final version, to be published in CPC. Several corrections and improvements. Program available from http://apfel.hepforge.org

Doped Parton Distributions

Calculations of high-energy processes involving the production of b-quarks are typically performed in two different ways, the massive four-flavour scheme (4FS) and the massless five-flavour scheme (5FS). For processes where the combination of the 4FS and 5FS results into a matched calculation is technically difficult, it is possible to define a hybrid scheme known as the doped scheme, where above the b-quark threshold the strong coupling runs with $n_f=5$, as in the massless calculation, while the DGLAP splitting functions are those of the $n_f=4$ scheme. In this contribution we present NNPDF3.0 PDF sets in this doped scheme, compare them with the corresponding 4FS and 5FS sets, and discuss their relevance for LHC phenomenology.Comment: 5 pages, 5 figures, to appear in the proceedings of the 27th Rencontres de Blois on Particle Physics and Cosmology, Blois, May 31 to June 05, 201

APFELgrid: a high performance tool for parton density determinations

We present a new software package designed to reduce the computational burden of hadron collider measurements in Parton Distribution Function (PDF) fits. The APFELgrid package converts interpolated weight tables provided by APPLgrid files into a more efficient format for PDF fitting by the combination with PDF and $\alpha_s$ evolution factors provided by APFEL. This combination significantly reduces the number of operations required to perform the calculation of hadronic observables in PDF fits and simplifies the structure of the calculation into a readily optimised scalar product. We demonstrate that our technique can lead to a substantial speed improvement when compared to existing methods without any reduction in numerical accuracy.Comment: 13 pages, 2 figures. Submitted to CPC. Code available from https://github.com/nhartland/APFELgri

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

Exclusive meets inclusive at small Bjorken-xBx_B: how to relate exclusive measurements to PDFs based on evolution equations

Exclusive heavy-vector-meson photoproduction is a prominent signal in collider experiments with hadron beams. At the highest photon-hadron collision energies, this process is considered as a candidate to constrain gluon parton distribution functions (PDFs) at small longitudinal momentum fractions. However, in the framework of collinear factorisation, exclusive particle production is described in terms of generalised parton distributions (GPDs). In this contribution, we investigate at the leading order in $\alpha_s$ the connection between GPDs and PDFs. Our main result is a proposal to quantify the systematic uncertainty inherent to this connection. We put our approach into context with respect to the Shuavev transform. Our uncertainty estimate can be straightforwardly adapted to higher fixed orders and small-$x$ resummations. The question of extrapolating GPDs to vanishing skewness is paramount for the programme of the Electron Ion Collider (EIC), notably for the extraction of the radial distributions of partons.Comment: 17 pages, 7 figure

A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties

We present NNFF1.0, a new determination of the fragmentation functions (FFs) of charged pions, charged kaons, and protons/antiprotons from an analysis of single-inclusive hadron production data in electron-positron annihilation. This determination, performed at leading, next-to-leading, and next-to-next-to-leading order in perturbative QCD, is based on the NNPDF methodology, a fitting framework designed to provide a statistically sound representation of FF uncertainties and to minimise any procedural bias. We discuss novel aspects of the methodology used in this analysis, namely an optimised parametrisation of FFs and a more efficient $\chi^2$ minimisation strategy, and validate the FF fitting procedure by means of closure tests. We then present the NNFF1.0 sets, and discuss their fit quality, their perturbative convergence, and their stability upon variations of the kinematic cuts and the fitted dataset. We find that the systematic inclusion of higher-order QCD corrections significantly improves the description of the data, especially in the small-$z$ region. We compare the NNFF1.0 sets to other recent sets of FFs, finding in general a reasonable agreement, but also important differences. Together with existing sets of unpolarised and polarised parton distribution functions (PDFs), FFs and PDFs are now available from a common fitting framework for the first time.Comment: 50 pages, 22 figures, 5 table