#### 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. Same as
gure 15, for Ds
hadroproduction at
s = 13 TeV.
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