Prompt neutrino fluxes in the atmosphere with PROSA parton distribution functions

Journal of High Energy Physics, May 2017

Effects on atmospheric prompt neutrino fluxes of present uncertainties affecting the nucleon composition are studied by using the PROSA fit to parton distribution functions (PDFs). The PROSA fit extends the precision of the PDFs to low x, which is the kinematic region of relevance for high-energy neutrino production, by taking into account LHCb data on charm and bottom hadroproduction collected at the center-of-mass energy of \( \sqrt{s}=7 \) TeV. In the range of neutrino energies explored by present Very Large Volume Neutrino Telescopes, it is found that PDF uncertainties are far smaller with respect to those due to renormalization and factorization scale variation and to assumptions on the cosmic ray composition, which at present dominate and limit our knowledge of prompt neutrino fluxes. A discussion is presented on how these uncertainties affect the expected number of atmospheric prompt neutrino events in the analysis of high-energy events characterized by interaction vertices fully contained within the instrumented volume of the detector, performed by the IceCube collaboration.

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Prompt neutrino fluxes in the atmosphere with PROSA parton distribution functions

Received: November Prompt neutrino uxes in the atmosphere with PROSA parton distribution functions M.V. Garzelli 0 1 3 5 S. Moch 0 1 3 5 O. Zenaiev 0 1 5 A. Cooper-Sarkar 0 1 2 5 A. Geiser 0 1 5 K. Lipka 0 1 5 R. Placakyte 0 1 3 5 G. Sigl 0 1 3 5 Open Access 0 1 5 c The Authors. 0 1 5 0 Keble Road, Oxford OX1 3RH, U.K 1 Luruper Chaussee 149 , D 2 Department of Physics, University of Oxford 3 II. Institute for Theoretical Physics, Hamburg University 4 22607 Hamburg , Germany 5 t to parton distribution E ects on atmospheric prompt neutrino uxes of present uncertainties a ecting the nucleon composition are studied by using the PROSA functions (PDFs). The PROSA t extends the precision of the PDFs to low x, which is the kinematic region of relevance for high-energy neutrino production, by taking into account LHCb data on charm and bottom hadroproduction collected at the center-of-mass energy of p s = 7 TeV. In the range of neutrino energies explored by present Very Large Volume Neutrino Telescopes, it is found that PDF uncertainties are far smaller with respect to those due to renormalization and factorization scale variation and to assumptions on the cosmic ray composition, which at present dominate and limit our knowledge of prompt neutrino uxes. A discussion is presented on how these uncertainties a ect the expected number of atmospheric prompt neutrino events in the analysis of high-energy events characterized by interaction vertices fully contained within the instrumented volume of the detector, performed by the IceCube collaboration. NLO Computations; QCD Phenomenology Contents 1 Introduction 2 3 4 IceCube upper limit s = 7 and 13 TeV Charm hadroproduction in QCD and parton distribution functions Predictions for prompt neutrino uxes and their uncertainties analysis and comparison of the prompt ( ux with the present Introduction tal techniques, accurate predictions for atmospheric lepton uxes are of crucial importance traditional searches for atmospheric neutrino oscillations. the conventional component at energies larger than 105 GeV [6]. At present, poor knowledge of the charm hadroproduction process [6, 8]. of parton distribution functions (PDFs) a ect prompt neutrino uxes, by making use of the PROSA PDF t [9], and we compare this uncertainty to that from QCD and astrophysical origin. Current PDF ts are based on data collected at the HERA ep collider, the LHCb charm data at p t, by using the contains a full PDF t in the self-consistent xed avour number scheme employed, and also includes LHCb data on Ds , D the laboratory frame, i.e. E ; lab 106 GeV. In this context it is important to note factor of order O(10{1000). Further, Ep; lab 108 GeV corresponds to Epp; cm and on beauty hadroproduction [16] at p s = 7 TeV. by using additional selected LHCb charm data at p 3 < y < 3:5 were discarded. from an instrumented ducial volume of 1 km3 to a larger one, of 10 km3, has been ratory energies in the EeV range, i.e. increased by a factor of 1000. In nucleon-nucleon hundred TeV. upper limit on the prompt ( ) ux recently obtained by the IceCube collaboration in a complementary analysis, restricted to 350000 up-going events from the Northern volume [20]. at center-of-mass energy p s = 7 and 13 TeV. when early colliders were built. The attention focused on the production of charmlarge enough with respect to QCD, so that the use of perturbative QCD is justi ed to the HESE sample. PYTHIA8 generator and A14 tune are used by default, unless stated otherwise. The POWHEGBOX framework includes hard-scattering matrix-elements for charm out the calculation of the scattering amplitudes performed in the avour number in association with PYTHIA8 and the Monash 2013 tune. when performing the original PROSA t for PDFs, in the computation of theoretical hadroproduction [41] in pp collisions at p with LHCb experimental data. In particular, data for D , Ds , , D0 and D0 of the PROSA PDF t in association with our POWHEGBOX + PYTHIA8/PYTHIA6 setup in comparison with these data at both p emphasize here that the PROSA PDFs used in this paper were derived by tting the ratios of LHCb rapidity distributions in each xed pT bin. It turns out that we obtain theoretical approaches. Predictions for prompt neutrino uxes and their uncertainties ulating particle ux evolution through an air column of slant depth X, representing the Z-moment approach initially proposed in refs. [43, 44] (see also refs. [6, 39]). The necessary Z-moments, e.g., Zp hc for charm hadroproduction in the factorization and renormalization scales as R = F = 0 = F were allowed to vary independently in the range 0=2 < pole mass was xed to mc = 1:40 0:15 GeV, as in ref. [6]. All other moments Zhc ` , Zhc hc and ZN N were computed as in ref. [6] (see also refs. [39, 40]). The resulting predictions for the ( ) uxes are presented in gures 1, 2 and 3. pT;c + mc2. The scales PDF uncertainty component Number of variations t + exp. stat. + exp. syst. parametrization Uncertainty source data uncertainties Q20, Duv , DU , DD the list of the corresponding uncertainty sources. s(MZ ), the strangeness fraction fs in the PDF t, the minimum virtuality cut Q2min on F , and the parameters K of the charm and beauty fragmentation functions [50]. Q20 of the QCD evolution, as well as the value of the starting scale. framework [59] for gure 4 ensures the extrapolation of the PDFs to the low-x region beyond the kinematic range provided and tted by the individual groups [52{58]. The parameterizations adopted. in the PROSA t, these theoretical uncertainties are strongly reduced, since variations of -1)10-3 r -1)10-3 r -1)10-3 r total PDF uncertainty fit PDF uncertainty total PDF uncertainty model PDF uncertainty total PDF uncertainty parameterization PDF uncertainty ) atmospheric ux as a function of the on the Earth atmosphere is used as input, cf. ref. [6]. scale + mcharm + PDF uncertainty total scale uncertainty total PDF uncertainty total mcharm uncertainty 1)10-3 scale + mcharm + PDF uncertainty, PY8, A14 scale + mcharm + PDF uncertainty, PY6, Perugia uncertainty contributions due to F scale variation around 0, mc and the PDF eigenvalues within the PROSA t, are shown separately by bands of di erent styles and colors, together with ux as in gure 1 is used as input. Right: comparison between central predictions and (scale (not plotted here) turn out to be even closer to those with PYTHIA6. ux the scale variations in the matrix elements were performed independently of 0:15 GeV adopted here are compatible and The of QCD uncertainties a ecting ( ) uxes is shown in gure 2 again for the broken power-law primary cosmic-ray input spectrum as in gure 1. The di erences between by di erent tunes (A14 or Monash 2013 vs. Perugia), as shown in gure 2.b, amount to maximum ( 14, +6)%.3 On the other hand, from gure 2.a it is evident that, at 1)10-3 1)10-3 scale + mcharm + PDF uncertainty total scale uncertainty total PDF uncertainty total mcharm uncertainty scale + mcharm + PDF uncertainty total scale uncertainty total PDF uncertainty total mcharm uncertainty 1)10-3 1)10-3 scale + mcharm + PDF uncertainty total scale uncertainty total PDF uncertainty total mcharm uncertainty scale + mcharm + PDF uncertainty total scale uncertainty total PDF uncertainty total mcharm uncertainty The upper two panels correspond to the GST t described in refs. [47, 48], whereas the lower two panel: GST-4, left lower panel: H3p). respect we would like to note that the present PROSA t extends down to x 10 6, while tail extending down to x by a factor 50 with respect to its maximum. HERAPDF2.0_NLO PROSA_1503_04581 MMHT2014nlo68cl NNPDF30_nlo_as_0118 NNPDF30 + LHCb 2016 PROSA_1503_04581 ­6100­8 10­7 10­6 10­5 10­4 10­3 10­2 10­1 x 1 ­6100­8 10­7 10­6 10­5 10­4 10­3 10­2 10­1 x 1 Note that the ABM11, PROSA and JR14 PDFs employ the avour number scheme (with NNPDF3.0 + LHCb use di erent implementations of the variable avour number scheme, so the latter distributions should only be compared qualitatively to the former ones. to be already far better constrained than the scale ones, and amount to (+42%, and (+52%, 13:5%), respectively, for the power-law cosmic ray spectrum. These values (+25.8%, 20%) at 1 and 2 PeV, respectively. PDF variation may become a more critical issue. by satellites or balloon-born experiments, because the ux of cosmic rays decreases too component seen by uorescence telescopes pointing to the upper layer of the Earth's at In order to have an idea of the e ect of these uncertainties on prompt ( ) uxes, comparing one with each other the various panels of gure 3. central values of the ( ) uxes, together with their scale and total QCD uncertainties, are shown separately in the two panels of gure 5. For both uxes the scale uncertainties R = pT;c + 4mc2 whereas the PROSA pre PROSA flux - scale uncertainty GMS 2015 flux - scale uncertainty PROSA flux - (scale + mcharm + PDF) uncertainty GMS 2015 flux - (scale + mcharm + PDF) uncertainty ) uxes obtained with PROSA PDFs (solid line) as compared to pT;c + 4mc2 for the GMS 2015 uxes. pT;c + mc2, leads to uncertainty bands larger than for the scale which retains full consistency with the PROSA PDF t. putation of cosmic ray interactions with atmospheric nuclei. In gure 7 we compare the scale var + mcharm var + PDF var PROSA flux, power-law CR scale var + mcharm var + PDF var PROSA flux, power-law CR ERS 2008 (dipole model) SIBYLL 2.3 RC1 (2015) scale var + mcharm var + PDF var PROSA flux, power-law CR BEJKRSS 2016, nCTEQ15-14 scale var + mcharm var + PDF var PROSA flux, power-law CR BEJKRSS 2016, EPS09 ) uxes with the PROSA proton PDFs and not accounted for in these plots. For consistency with ref. [40], and di erently from gure 5 and 6, the cosmic ray primary ux H3p is used in all these predictions, cf. gure 3. { 13 { new developments on this issue for the future. HESE analysis and comparison of the prompt ( ux with the present IceCube upper limit ing to a 4.1 excess in the year 2013 [1]. These results were updated in the year 2014, day analysis [19], which has collected 54 events, corresponding to a rejection of the GST - 4 CR Deposited EM-Equivalent Energy in Detector ( GeV ) latter include leptons of both atmospheric and astrophysical origin. the basis of PROSA predictions for prompt neutrino uxes, is shown in gure 8 for the nergies deposited, limited to 2 PeV, the di erence between the variants of Gaisser CR predictions for prompt uxes turn out to lie below the data, thus con rming a di erent origin for those most energetic IceCube events, also shown in the plot. Deposited EM-Equivalent Energy in Detector ( GeV ) and astrophysical origin. computed by using di erent models is shown in gure 9, considering as a basis for the cosmic ray primary ux the H3a model. In particular, predictions computed by using the GMS 2015 central ux [6] and those reported in ref. [39] are shown. These earlier of scale variations (with R 6= F ) and also the PDF uncertainties, not considered in [39]. any additional uncertainty.5 The IceCube upper limit on the total neutrino ux at 90% 5Actually, deeply comprehensive studies on the uncertainties on conventional neutrino uxes are still missing, especially in the high-energy region explored by VLV Ts. Thus, instead of not quoting any that this ux has an uncertainty around at least 20{30%. total (PROSA + Honda 2015) total (BERSS + Honda 2015) IceCube atmo nu upper limit 90% C.L. Deposited EM-Equivalent Energy in Detector ( GeV ) conventional Honda 2015 total (PROSA + Honda 2015) IceCube atmo nu upper limit 90% C.L. Deposited EM-Equivalent Energy in Detector ( GeV ) The H3a cosmic ray primary ux is used as input. On the top the central predictions are shown and reproduced in ref. [18] is shown in magenta. The comparison of the most recent IceCube estimate of this limit [20] 6IceCube HESE samples include events initiated by neutrinos of all possible avours, e, This has been indeed taken into account by reasonable assumptions on the ratio e : when adapting events from the Northern hemisphere. PROSA scale var + mcharm var + PDF var PROSA, µR = µF = sqrt(pT2 + mc2) PROSA, µR = µF = sqrt(pT2 + 4 mc2) GMS 2015, H3p CR IceCube prompt upper limit (90% C.L.) - (H3p CR + ERS) ( GeV ) ) ux using the PROSA PDFs with the present for modelling prompt neutrinos. Central predictions using the scale R = F = pp2T + 4mc2 and the H3p CR ux. gure 11. Again, the published IceCube upper limit, although being larger than revising the model assumptions in the aforementioned IceCube analyses. information on the physics related to charm hadroproduction. Conclusions PDF uncertainties on the prompt neutrino ux increase with increasing neutrino energies. renormalization and factorization scale variation. Our ux turns out to be compatible theoretical predictions on ( ) uxes with the IceCube upper limit published in comupper limit on prompt neutrino uxes at 90% con dence level, published by IceCube, al ) ux obtained in this study, but well inside our global QCD uncertainty band. in their astrophysical sources, during propagation and in the atmosphere. In future, the LHCb measurements of charm hadroproduction at p s = 13 TeV [14] could peared LHCb charm data at p cosmic ray nuclei with the nuclei of our atmosphere will be left for future work. at https://prosa.desy.de. Acknowledgments ing Fund of the Helmholtz Association. s = 7 and 13 TeV verse momentum of D , D0 + D0, Ds at p the range pT 2 [0; 8] GeV in a di erent rapidity interval. theoretical central predictions. Figures 15{17 contain the same study for LHCb experimental data [14] at p s = 13 TeV. tum spectrum in the range pT 2 [0; 15] GeV. in the plots. out to lie above the central theoretical predictions.7 This tendency remains essentially contribution actually dominate the total prompt neutrino ux at the neutrino energies our present uncertainty bands. in this paper. mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2, PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2, PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 mesons in pp collisions at POWHEGBOX + PYTHIA8 (blue solid line)/PYTHIA6 (red dotted line) predictions for 0 = 7 TeV. scale variation (green), to mc (magenta) and to PROSA PDF (light-blue hatched) predictions by POWHEGBOX + PYTHIA8. mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2, PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 Figure 13. Same as gure 12, for (D + D0) hadroproduction at s = 7 TeV. mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2, PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 Figure 14. Same as gure 12, for D hadroproduction at s = 7 TeV. mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV LHCb experimental data mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV LHCb experimental data mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV LHCb experimental data mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV LHCb experimental data mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV LHCb experimental data mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 s = 13 TeV. gure 12, for the LHCb experimental data [14] on D hadroproduction at mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV LHCb experimental data mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV LHCb experimental data mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV LHCb experimental data mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV LHCb experimental data mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV LHCb experimental data mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 Figure 16. Same as gure 15, for (D0 D0) hadroproduction at s = 13 TeV. mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV LHCb experimental data mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV LHCb experimental data mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV LHCb experimental data mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV LHCb experimental data mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 mass var + scale var + PDF var scale var (µR, µF) in ([0.5,2],[0.5,2]) mass var in (1.25 - 1.55) GeV LHCb experimental data mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY8 mc = 1.4 GeV, µR = µF = sqrt(pT2 + mc2), PY6 Figure 17. 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M. V. Garzelli, S. Moch, O. Zenaiev, A. Cooper-Sarkar, A. Geiser, K. Lipka, R. Placakyte, G. Sigl, The PROSA collaboration. Prompt neutrino fluxes in the atmosphere with PROSA parton distribution functions, Journal of High Energy Physics, 2017, 4, DOI: 10.1007/JHEP05(2017)004