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

Splitting type, global sections and Chern classes for torsion free sheaves on P^N

In this paper we compare a torsion free sheaf \FF on \PP^N and the free vector bundle \oplus_{i=1}^n\OPN(b_i) having same rank and splitting type. We show that the first one has always "less" global sections, while it has a higher second Chern class. In both cases bounds for the difference are found in terms of the maximal free subsheaves of \FF. As a consequence we obtain a direct, easy and more general proof of the "Horrocks' splitting criterion", also holding for torsion free sheaves, and lower bounds for the Chern classes c_i(\FF(t)) of twists of \FF, only depending on some numerical invariants of \FF. Especially, we prove for rank $n$ torsion free sheaves on \PP^N, whose splitting type has no gap (i.e. $b_i\geq b_{i+1}\geq b_i-1$ for every $i=1, ...,n-1$), the following formula for the discriminant: \Delta(\FF):=2nc_2-(n-1)c_1^2\geq -{1/12}n^2(n^2-1) Finally in the case of rank $n$ reflexive sheaves we obtain polynomial upper bounds for the absolute value of the higher Chern classes c_3(\FF(t)), ..., c_n(\FF(t)), for the dimension of the cohomology modules H^i\FF(t) and for the Castelnuovo-Mumford regularity of \FF; these polynomial bounds only depend only on c_1(\FF), c_2(\FF), the splitting type of \FF and $t$.Comment: Final version, 15 page

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