A determination of the charm content of the proton: The NNPDF Collaboration

Evidence for intrinsic charm quarks in the proton

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 predictions^1,5.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.

Study of Z Bosons Produced in Association with Charm in the Forward Region

Events containing a Z boson and a charm jet are studied for the first time in the forward region of proton-proton collisions. The data sample used corresponds to an integrated luminosity of 6  fb^{-1} collected at a center-of-mass energy of 13 TeV with the LHCb detector. In events with a Z boson and a jet, the fraction of charm jets is determined in intervals of Z-boson rapidity in the range 2.0<y(Z)<4.5. A sizable enhancement is observed in the forwardmost y(Z) interval, which could be indicative of a valencelike intrinsic-charm component in the proton wave function.

Can New Physics Hide inside the Proton?

Modern global analyses of the structure of the proton include collider measurements which probe energies well above the electroweak scale. While these provide powerful constraints on the parton distribution functions (PDFs), they are also sensitive to beyond the standard model (BSM) dynamics if these affect the fitted distributions. Here we present a first simultaneous determination of the PDFs and BSM effects from deep-inelastic structure function data by means of the NNPDF framework. We consider representative four-fermion operators from the SM effective field theory (SMEFT), quantify to which extent their effects modify the fitted PDFs, and assess how the resulting bounds on the SMEFT degrees of freedom are modified. Our results demonstrate how BSM effects that might otherwise be reabsorbed into the PDFs can be systematically disentangled.

The sea of quarks and antiquarks in the nucleon

The quark and gluon structure of the proton has been under intense experimental and theoretical investigation for five decades. Even for the distributions of the well-studied valence quarks, challenges such as the value of the down quark to up quark ratio at high fractional momenta remain. Much of the sea of quark-antiquark pairs emerges from the splitting of gluons and is well described by perturbative evolution in quantum chromodynamics. However, experiments confirm that there is a non-perturbative component to the sea that is not well understood and hitherto has been difficult to calculate with ab initio non-perturbative methods. This non-perturbative structure shows up, perhaps most directly, in the flavor dependence of the sea antiquark distributions. While some of the general trends can be reproduced by models, there are features of the data that do not seem to be well described. This article discusses the experimental situation, the status of calculations and models, and the directions where these studies will progress in the near future.

Z boson production in bottom-quark fusion: a study of b-mass effects beyond leading order

We compute the total cross-section for Z boson production in bottom-quark fusion, applying to this case the method we previously used for Higgs production in bottom fusion. Namely, we match, through the FONLL procedure, the next-to-next-to-leading-log five-flavor scheme result, in which the b quark is treated as a massless parton, with the next-to-leading-order O ( α s 3 ) four-flavor scheme computation in which bottom is treated as a massive final-state particle. Also, we add to our formalism the possibility of varying the heavy quark matching scale. The results obtained with the FONLL formalism can thus be compared directly to recent results obtained in various approximations, and used as a proxy to assess and discuss the issues of scale dependence and treatment of heavy quarks. Finally, We use our results in order to improve the prediction for the total Z production cross-section.

Direct photon production and PDF fits reloaded

Direct photon production in hadronic collisions provides a handle on the gluon PDF by means of the QCD Compton scattering process. In this work we revisit the impact of direct photon production on a global PDF analysis, motivated by the recent availability of the next-to-next-to-leading (NNLO) calculation for this process. We demonstrate that the inclusion of NNLO QCD and leading-logarithmic electroweak corrections leads to a good quantitative agreement with the ATLAS measurements at 8 and 13 TeV, except for the most forward rapidity region in the former case. By including the ATLAS 8 TeV direct photon production data in the NNPDF3.1 NNLO global analysis, we assess its impact on the medium-x gluon. We also study the constraining power of the direct photon production measurements on PDF fits based on different datasets, in particular on the NNPDF3.1 no-LHC and collider-only fits. We also present updated NNLO theoretical predictions for direct photon production at 13 TeV that include the constraints from the 8 TeV measurements.

Precision determination of the strong coupling constant within a global PDF analysis: NNPDF Collaboration

We present a determination of the strong coupling constant α s ( m Z ) based on the NNPDF3.1 determination of parton distributions, which for the first time includes constraints from jet production, top-quark pair differential distributions, and the Z p T distributions using exact NNLO theory. Our result is based on a novel extension of the NNPDF methodology - the correlated replica method - which allows for a simultaneous determination of α s and the PDFs with all correlations between them fully taken into account. We study in detail all relevant sources of experimental, methodological and theoretical uncertainty. At NNLO we find α s ( m Z ) = 0.1185 ± 0 . 0005 (exp) ± 0 . 0001 (meth) , showing that methodological uncertainties are negligible. We conservatively estimate the theoretical uncertainty due to missing higher order QCD corrections (N 3 LO and beyond) from half the shift between the NLO and NNLO α s values, finding Δ α s th = 0.0011 .

Parton distributions with small-x resummation: evidence for BFKL dynamics in HERA data

We present a determination of the parton distribution functions of the proton in which NLO and NNLO fixed-order calculations are supplemented by NLLx small-x resummation. Deep-inelastic structure functions are computed consistently at NLO+NLL x or NNLO+NLL x , while for hadronic processes small-x resummation is included only in the PDF evolution, with kinematic cuts introduced to ensure the fitted data lie in a region where the fixed-order calculation of the hard cross-sections is reliable. In all other respects, the fits use the same methodology and are based on the same global dataset as the recent NNPDF3.1 analysis. We demonstrate that the inclusion of small-x resummation leads to a quantitative improvement in the perturbative description of the HERA inclusive and charm-production reduced cross-sections in the small x region. The impact of the resummation in our fits is greater at NNLO than at NLO, because fixed-order calculations have a perturbative instability at small x due to large logarithms that can be cured by resummation. We explore the phenomenological implications of PDF sets with small-x resummation for the longitudinal structure function F L at HERA, for parton luminosities and LHC benchmark cross-sections, for ultra-high-energy neutrino-nucleus cross-sections, and for future high-energy lepton-proton colliders such as the LHeC.

Measurement of associated Z + charm production in proton-proton collisions at s = 8 TeV

A study of the associated production of a Z boson and a charm quark jet ( Z + c ), and a comparison to production with a b quark jet ( Z + b ), in p p collisions at a centre-of-mass energy of 8TeV are presented. The analysis uses a data sample corresponding to an integrated luminosity of 19.7fb - 1 , collected with the CMS detector at the CERN LHC. The Z boson candidates are identified through their decays into pairs of electrons or muons. Jets originating from heavy flavour quarks are identified using semileptonic decays of c or b flavoured hadrons and hadronic decays of charm hadrons. The measurements are performed in the kinematic region with two leptons withp T ℓ > 20 GeV ,| η ℓ | < 2.1 , 71 < m ℓ ℓ < 111 GeV , and heavy flavour jets withp T jet > 25 GeV and| η jet | < 2.5 . The Z + c production cross section is measured to be σ ( p p → Z + c + X ) B ( Z → ℓ + ℓ - ) = 8.8 ± 0.5 (stat) ± 0.6 (syst) pb . The ratio of the Z + c and Z + b production cross sections is measured to be σ ( p p → Z + c + X ) / σ ( p p → Z + b + X ) = 2.0 ± 0.2 (stat) ± 0.2 (syst) . The Z + c production cross section and the cross section ratio are also measured as a function of the transverse momentum of the Z boson and of the heavy flavour jet. The measurements are compared with theoretical predictions.

CTEQ-TEA parton distribution functions with intrinsic charm

We present a study in which the possibility of a (sizable) nonperturbative contribution to the charm parton distribution function (PDF) in a nucleon is investigated together with theoretical issues arising in its interpretation. The separation of the universal component of the nonperturbative charm from the rest of the radiative contributions is also discussed. We illustrate the potential impact of a nonperturbative charm PDF on LHC scattering processes. An estimate of nonperturbative charm magnitude in the CT14 and CT14HERA2 global QCD analyses at the next-to-next-to leading order (NNLO) in the QCD coupling strength is given by including the latest experimental data from HERA and the Large Hadron Collider. We show a comparison between different models of intrinsic charm and illustrate prospects for standard candle observables at the LHC.

Impact of the heavy-quark matching scales in PDF fits

We investigate the impact of displaced heavy-quark matching scales in a global fit. The heavy-quark matching scale μ m determines at which energy scale μ the QCD theory transitions from N F toN F + 1 in the variable flavor number scheme (VFNS) for the evolution of the parton distribution functions (PDFs) and strong couplingα S ( μ ) . We study the variation of the matching scales, and their impact on a global PDF fit of the combined HERA data. As the choice of the matching scale μ m effectively is a choice of scheme, this represents a theoretical uncertainty; ideally, we would like to see minimal dependence on this parameter. For the transition across the charm quark (fromN F = 3 to 4), we find a largeμ m = μ c dependence of the global fit χ 2 at NLO, but this is significantly reduced at NNLO. For the transition across the bottom quark (fromN F = 4 to 5), we have a reducedμ m = μ b dependence of the χ 2 at both NLO and NNLO as compared to the charm. This feature is now implemented in xFitter 2.0.0, an open source QCD fit framework.

Parton distributions from high-precision collider data: NNPDF Collaboration

We present a new set of parton distributions, NNPDF3.1, which updates NNPDF3.0, the first global set of PDFs determined using a methodology validated by a closure test. The update is motivated by recent progress in methodology and available data, and involves both. On the methodological side, we now parametrize and determine the charm PDF alongside the light-quark and gluon ones, thereby increasing from seven to eight the number of independent PDFs. On the data side, we now include the D0 electron and muon W asymmetries from the final Tevatron dataset, the complete LHCb measurements of W and Z production in the forward region at 7 and 8 TeV, and new ATLAS and CMS measurements of inclusive jet and electroweak boson production. We also include for the first time top-quark pair differential distributions and the transverse momentum of the Z bosons from ATLAS and CMS. We investigate the impact of parametrizing charm and provide evidence that the accuracy and stability of the PDFs are thereby improved. We study the impact of the new data by producing a variety of determinations based on reduced datasets. We find that both improvements have a significant impact on the PDFs, with some substantial reductions in uncertainties, but with the new PDFs generally in agreement with the previous set at the one-sigma level. The most significant changes are seen in the light-quark flavor separation, and in increased precision in the determination of the gluon. We explore the implications of NNPDF3.1 for LHC phenomenology at Run II, compare with recent LHC measurements at 13 TeV, provide updated predictions for Higgs production cross-sections and discuss the strangeness and charm content of the proton in light of our improved dataset and methodology. The NNPDF3.1 PDFs are delivered for the first time both as Hessian sets, and as optimized Monte Carlo sets with a compressed number of replicas.

A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties: The NNPDF Collaboration

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 [Formula: see text] 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.