It is common lore that Parton Distribution Functions (PDFs) in the $$ \overline{\mathrm{MS}} $$ MS ¯ factorization scheme can become negative beyond leading order due to the collinear subtraction which is needed in order to define partonic cross sections. We show that this is in fact not the case and next-to-leading order (NLO) $$ \overline{\mathrm{MS}} $$ MS ¯ PDFs are actually positive in the perturbative regime. In order to prove this, we modify the subtraction prescription, and perform the collinear subtraction in such a way that partonic cross sections remain positive. This defines a factorization scheme in which PDFs are positive. We then show that positivity of the PDFs is preserved when transforming from this scheme to $$ \overline{\mathrm{MS}} $$ MS ¯ , provided only the strong coupling is in the perturbative regime, such that the NLO scheme change is smaller than the LO term.

The theory of the strong force, quantum chromodynamics, describes the proton in terms of quarks and gluons. The proton is a state of two up quarks and one down quark bound by gluons, but quantum theory predicts that in addition there is an infinite number of quark–antiquark pairs. Both light and heavy quarks, whose mass is respectively smaller or bigger than the mass of the proton, are revealed inside the proton in high-energy collisions. However, it is unclear whether heavy quarks also exist as a part of the proton wavefunction, which is determined by non-perturbative dynamics and accordingly unknown: so-called intrinsic heavy quarks1. It has been argued for a long time that the proton could have a sizable intrinsic component of the lightest heavy quark, the charm quark. Innumerable efforts to establish intrinsic charm in the proton2 have remained inconclusive. Here we provide evidence for intrinsic charm by exploiting a high-precision determination of the quark–gluon content of the nucleon3 based on machine learning and a large experimental dataset. We disentangle the intrinsic charm component from charm–anticharm pairs arising from high-energy radiation4. We establish the existence of intrinsic charm at the 3-standard-deviation level, with a momentum distribution in remarkable agreement with model predictions1,5.We confirm these findings by comparing them to very recent data on Z-boson production with charm jets from the Large Hadron Collider beauty (LHCb) experiment6.

We present a new QCD evolution library for unpolarized parton distribution functions: . The program solves DGLAP equations up to next-to-next-to-leading order. The unique feature of is the computation of solution operators, which are independent of the boundary condition, can be stored and quickly applied to evolve several initial PDFs. The approach combines the power of N-space solutions with the flexibility of a x-space delivery, that allows for an easy interface with existing codes. The code is fully open source and written in Python, with a modular structure in order to facilitate usage, readability and possible extensions. We provide a set of benchmarks with similar available tools, finding good agreement.

We discuss the sensitivity of theoretical predictions of observables used in searches for new physics to parton distributions (PDFs) at large momentum fraction x. Specifically, we consider the neutral-current Drell–Yan production of gauge bosons with invariant masses in the TeV range, for which the forward–backward asymmetry of charged leptons from the decay of the gauge boson in its rest frame is a traditional probe of new physics. We show that the qualitative behaviour of the asymmetry depends strongly on the assumptions made in determining the underlying PDFs. We discuss and compare the large-x behaviour of various different PDF sets, and find that they differ significantly. Consequently, the shape of the asymmetry observed at lower dilepton invariant masses, where all PDF sets are in reasonable agreement because of the presence of experimental constraints, is not necessarily reproduced at large masses where the PDFs are mostly unconstrained by data. It follows that the shape of the asymmetry at high masses may depend on assumptions made in the PDF parametrization, and thus deviations from the traditionally expected behaviour cannot be taken as a reliable indication of new physics. We demonstrate that forward–backward asymmetry measurements could help in constraining PDFs at large x and discuss the accuracy that would be required to disentangle the effects of new physics from uncertainties in the PDFs in this region.

We review our recent paper, where we proved Parton distributions functions (PDFs) to be positive at NLO in the \overline{MS}MS¯ factorization scheme. We present some additional material that was useful in completing the steps for the actual proof, but we won’t attempt to report on the full proof, but referring the reader to the paper itself.