Theoretical uncertainties
on prompt neutrino fluxes
M.V. Garzelli,
S.-O. Moch
and
G. Sigl
II Institute for Theoretical Physics, University of Hamburg, Germany
mainly on the basis of JHEP 1510 (2015) 115 [arXiv:1507.01570]
Atmospheric Neutrino Workshop ANW’16
Cluster of Excellence “Universe”
München, February 7 - 9 th, 2016
Prompt neutrino flux hadroproduction in the
atmosphere: theoretical predictions in literature
∗ Long non-exhaustive list of papers, including, among the others:
Lipari, Astropart. Phys. 1 (1993) 195
Battistoni, Bloise, Forti et al., Astropart. Phys. 4 (1996) 351
Gondolo, Ingelman, Thunman, Astropart. Phys. 5 (1996) 309
Bugaev, Misaki, Naumov et al., Phys. Rev. D 58 (1998) 054001
Pasquali, Reno, Sarcevic, Phys. Rev. D 59 (1999) 034020
Enberg, Reno, Sarcevic, Phys. Rev. D 78 (2008) 043005
∗ Updates and recently renewed interest:
Bhattacharya, Enberg, Reno et al., JHEP 1506 (2015) 110
Fedynitch, Gaisser et al. ICRC 2015, TAUP 2015... → talk by A. Fedynitch
Garzelli, Moch, Sigl, JHEP 1510 (2015) 115 → this talk
Gauld, Rojo, Sarkar, Rottoli, Talbert, arXiv:1511.06346 → talk by J. Talbert
Halzen, Wille, arXiv:1601.03044 → talk by L. Wille
motivated by new results from VLVνT’s and updated theory and new
results from LHC
Neutrino Astronomy and VLVνT
Observation of high-energy ν’s by large volume neutrino telescopes,
as a window to better understand the high-energy Universe, in
particular the relation between these ν and high-energy Cosmic
Rays, and particle acceleration in possible sources like AGNs,
GRBs, Starburst galaxies, SNRs.
This is possible thanks to
ν weak interactions (6= Cosmic Rays)
ν propagation not bended by galactic and extra-galactic magnetic
fields (6= Cosmic Rays)
under-water neutrino telescopes: Baikal, now under upgrade to
GVD/Baikal and ANTARES/NEMO/NESTOR, now working in a
joint effort towards the KM3NeT Mediterranean Neutrino
Observatory, with an instrumented volume similar to that of
IceCube.
in-ice neutrino telescopes: IceCube 1 km3 instrumented volume
already allowed for the actual detection of a high-energy ν flux.
The astrophysical case:
IceCube high-energy events
([arXiv:1405.5303] + ICRC 2015)
∗ 2013: 662-day analysis, with 28 candidates in the energy range [50 TeV - 2 PeV].
(4.1 σ excess over the expected atmospheric background).
∗ 2014: 988-day analysis, with a total of 37 events with energy [30 TeV - 2 PeV]
(5.7 σ excess), no events in the energy range [400 TeV - 1 PeV], spectral Γ = −2.3 ± 0.3.
∗ 2015: 1347-day analysis,
with a total ofenergy
53 + 1 spectrum
events, previous
energy gap partially filled,��
(4 years)
ν
(7 σ excess), spectral Γ = −2.58 ± 0.25.�����������������������������������������������������������������
Events per 988 Days
102
Background Atmospheric Muon Flux
Bkg. Atmospheric Neutrinos (π/K)
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Background Uncertainties
Atmospheric Neutrinos ��
(90%
CL Charm Limit)
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Bkg.+Signal Best-Fit Astrophysical (best-fit slope E . )
Bkg.+Signal Best-Fit Astrophysical (fixed slope E )
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Data
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−2 3
101
100
10-1
−2
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10
102 ��������������������������
103
Deposited EM-Equivalent Energy in Detector (TeV)
2014
figures from the presentation of C. Kopper, ICRC2015
* high-energy diffuse flux further testable by KM3Net/ARCA
2015
Candidate sources for HESE
considered so far in literature
1) Astrophysical Sources:
extragalactic: AGNs, GRBs, Starburst galaxies, galaxy clusters...
galactic: SNRs, pulsars, microquasars, Fermi bubbles, Galactic halo
2) Heavy DM decay, DM-DM annihilation
3) Atmospheric leptons
May be a combination of some of the previous ones ?
Precise predictions/measurements of the atmospheric ν fluxes have to
be taken into account in the analyses, because they represent a “background” for any astrophysical or BSM hypothesis.
Atmospheric ν flux:
conventional and prompt components
Cosmic Rays + Atmospheric Nuclei → hadrons → neutrinos + X
∗ Two contributing mechanisms, following two different power-law regimes:
- conventional ν flux from the decay of π ± and K ±
- prompt ν flux from charmed and heavier hadrons (D’s, Λ±
c ’s.....)
∗ Transition point: still subject of investigation......
Standard procedure to get fluxes: from cascade
equations to Z -moments [review in Gaisser, 1990; Lipari, 1993 ]
Solve a system of coupled differential equations regulating particle evolution in the
atmosphere (interaction/decay/(re)generation):
X k→j
φj (Ej , X ) φj (Ej , X ) X k→j
dφj (Ej , X )
j→j
=−
−
+
Sprod (Ej , X ) +
Sdecay (Ej , X ) + Sreg
(Ej , X )
dX
λj,int (Ej )
λj,dec (Ej )
k6=j
k6=j
Under assumption that X dependence of fluxes factorizes from E dependence,
analytical approximated solutions in terms of Z -moments:
− Particle Production:
Z ∞
φk (Ej , X )
φk (Ek , X ) 1 dσk→j (Ek , Ej )
k→j
∼
Zkj (Ej )
Sprod
(Ej , X ) =
dEk
λk (Ek ) σk
dEj
λk (Ej )
Ej
− Particle Decay:
j→l
Sdecay
(El , X ) =
Z
∞
dEj
El
φj (Ej , X ) 1 dΓj→l (Ej , El )
φj (El , X )
∼
Zjl (El )
λj (Ej ) Γj
dEl
λj (El )
Solutions available for Ej >> Ecrit, j and for Ej << Ecrit, j , respectively,
are interpolated geometrically.
Z -moments for heavy hadron production and decay
∗ CR + Air interactions producing heavy hadrons (in particular including charm)
parameterized in terms of p-p collisions
∗ Integration variable: xE = Eh /Ep
∗ Z -moments for intermediate hadron production:
Z 1
dσpp→cc̄→h+X
dxE φp (Eh /xE )
Aair
Zph (Eh ) =
(Eh /xE )
tot,inel
x
φ
(E
)
dxE
p h
E
σ
(Eh )
0
p−Air
∗ These hadrons are then decayed semileptonically, producing leptons (+ X)
∗ Integration variable: xE0 = El /Eh
∗ Z -moments for intermediate hadron decay:
Z
φh (El /xE 0 )
Zhl (El ) = dxE0
Fh→l (xE0 )
φh (El )
The QCD core of the Z -moments for prompt fluxes:
dσ(pp → cc̄)/dxE
∗ We used QCD in the standard collinear factorization formalism.
σH1 H2 →X
=
XZ
dx1 dx2 fi/H1 (xi , µ2F )fj/H2 (xj , µ2F )σ̂ij→X (xi p1 , xj p2 ; αS , µ2R , µ2F )
i,j
where
xi = pz,i /pz,H1 = Bjorken variable
fi/H1 (xi , µ2F ) = PDFs (long-distance physics) reabsorb infrared collinear singularities uncancelled within the hard-scattering and are universal (process independent). At a given scale,
they are non-perturbative objects, but their evolution with µF is governed by perturbation
theory (DGLAP equation).
σ̂ij→X = partonic hard-scattering cross-section (short-distance physics), computable by
pQCD.
µF = factorization scale: separates long-distance physics (non-perturbative QCD) from
short-distance physics (perturbative QCD).
µR = renormalization scale: renormalization eliminates UV divergences, by reabsorbing the
divergences in renormalized quantities.
The QCD core of the Z -moments for prompt fluxes:
dσ(pp → charmed hadrons)/dxE
∗ We used QCD in the standard collinear factorization formalism.
∗ So far this has been succesfully employed not only to explain ATLAS and CMS
results (central pseudorapidities), but even many observables at LHCb (mid-forward
pseudorapidities 2 < η < 5).
∗ LHCf is able to investigate in very-forward rapidity regions (8.4 < η < ∞) the
production of γ’s, π 0 ’s, neutrons and light neutral hadrons, no charmed charged
particles :-(
∗ total cross-section for cc̄ pair hadroproduction using NNLO QCD radiative corrections in pQCD.
∗ differential cross-section for cc̄ pair hadroproduction not yet available at NNLO;
use of a NLO QCD + Parton Shower + hadronization + decay approach.
∗ QCD parameters of computation and uncertainties due to the missing
higher orders fixed by theory, i.e. by looking at the convergence of the
perturbative series (LO/NLO/NNLO comparison).
p-p and p-p̄ collision overview (LHC and Tevatron)
}
parton shower
QED shower
⇤QCD = 200 M eV
hadronization
hadron decay
}
underlying event
pile-up (overlap of
di↵erent collisions).
���������������������������������������������
����������������������
�������������������������
�������������
hard scattering
How do experimental data enter in this approach ?
∗ Parameters and scales entering the hard-scattering are fixed by theoretical considerations.
∗ Fits to experimental data together with theoretical considerations are used to fix:
x dependence of parton distribution functions (PDF) fi/h (x, Q 2 )
z dependence of Fragmetation Functions (FF) Dah (z, Q 2 )
and the Fragmentation Fractions
However these fits are universal: i.e. it is supposed that PDFs and FFs describe
equally well reactions different from those considered here, i.e. that they are independent from the parton-parton scattering (basis of the factorization theorem).
⇒ the same PDFs and FFs used in this work are routinely used at LHC, there is
not any “ad hoc” assumption......
∗ Comparison with recent experimental data on D-hadrons is done “a posteriori”
and can confirm (or not) the validity of the whole theoretical framework.
σ(pp → cc̄) at LO, NLO, NNLO QCD
10
2
10
σpp → cc- [mb]
10
10
10
σpp → cc- [mb]
10
pole mc = 1.40 GeV
1
10
2
mc(mc) = 1.27 GeV
1
LO
-1
10
NLO
NNLO
-2
10
-3
10
3
5
10
10
Elab [GeV]
7
pole mass scheme
10
9
10
-1
-2
-3
10
3
5
10
10
Elab [GeV]
7
10
9
running mass scheme
exp data from fixed target exp + colliders (STAR, PHENIX, ALICE, ATLAS, LHCb).
(Elab = 106 GeV ∼ Ecm = 1.37 TeV)
(Elab = 108 GeV ∼ Ecm = 13.7 TeV)
(Elab = 1010 GeV ∼ Ecm = 137 TeV)
∗ Assumption: pQCD in DGLAP formalism valid on the whole energy
range.
σ(pp → cc̄): scale and mass dependence
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Elab = 106 GeV
σpp → cc- [mb]
pole mass mcpole
mc = 1.25 GeV
↓
mc = 1.40 GeV
mc = 1.55 GeV
1
10
10
2
µF [GeV]
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Elab = 106 GeV
σpp → cc- [mb]
––––
MS mass mc(mc)
mc = 1.24 GeV
mc = 1.27 GeV
mc = 1.30 GeV
↓
1
10
10
2
µF [GeV]
¯ scheme
∗ PDG running mass in the MS
mc (mc ) = 1.275 ± 0.025 GeV
∗ Conversion to the pole mass scheme suffers from poor convergence:
mc (mc ) = 1.27 GeV → mcpole = 1.48 GeV at 1-loop
mc (mc ) = 1.27 GeV → mcpole = 1.67 GeV at 2-loop
∗ Furthermore, accuracy of the pole mass limited to be of the order of O(ΛQCD )
by the renormalon ambiguity.
⇒ We fix mcpole = 1.4 ± 0.15 GeV. With this choice the cross-section in the pole
mass scheme approximately reproduces that in the running mass scheme.
σ(pp → cc̄): scale dependence
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
σpp → cc- [mb]
pole mc = 1.40 GeV
Elab = 106 GeV
↓
1
µR = µF/2
µR = µF
µR = 2µF
10
10
2
µF [GeV]
∗ Minimal sensitivity to radiative corrections is reached at a scale
µR ∼ µF ∼ 2mcharm .
q
2
∗ This translates into a dynamical scale pT2 ,charm + 4mcharm
to better catch dynamics in differential distributions.
σ(pp → cc̄): PDFs
10
and their behaviour at low Bjorken x
2
10
σpp → cc- [mb]
10
10
10
σpp → cc- [mb]
10
ABM11 with PDF unc.
1
10
2
NN30 with PDF unc.
1
NLO
-1
10
NNLO
-2
10
-3
10
3
5
10
10
Elab [GeV]
7
10
9
10
NLO
-1
NNLO
-2
-3
10
3
5
10
10
Elab [GeV]
7
10
9
∗ Probing higher astrophysical energies allows to probe smaller x region,
down to values where no data constrain PDFs yet (at least at present).
∗ f (x, µ2F ): µ2F evolution fixed by DGLAP equations, x dependence non-perturbative:
ansatz + extraction from experimental data.
∗ Different behaviour of different PDF parameterizations:
- ABM parameterization constrains PDFs at low x;
- NNPDF parameterization in LHAPDF reflects the absence of constraints from
experimental data at low x.
PROSA PDF fit
[O. Zenaiev, A. Geiser et al. [arXiv:1503.04585]]
First fit already including some LHCb data (charm and bottom) appeared in arXiv.
∗ ABM PDFs, although non including any info from LHCb, in agreement with
PROSA fit → good candidates for ultra-high-energy applications.
∗ CT10 PDFs in marginal agreement with PROSA fit.
∗ NNPDF PDFs: at present still the largest uncertainties, at least when looking
to the public release available in LHAPDF, they recenly worked at
incorporating PROSA idea in their fit as well (Gauld et al. [arXiv:1506.08025]).
Comparison of our theoretical predictions
with LHCb data on pp → D + + X
D+ 2 < y < 2.5
dσ / dpT ( pb / GeV )
108
107
106
108
107
106
105
105
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
pT ( GeV )
5
5.5
6
mass var + scale var scale var (µR, µF) in ([0.5,2],[0.5,2])
mass var in (1.25 - 1.55) GeV
mcharm = 1.4 GeV, µR = µF = sqrt(pT2 + 4 mc2)
LHCb experimental data
109
ratio
dσ / dpT ( pb / GeV )
109
ratio
D+ 3.5 < y < 4
mass var + scale var scale var (µR, µF) in ([0.5,2],[0.5,2])
mass var in (1.25 - 1.55) GeV
mcharm = 1.4 GeV, µR = µF = sqrt(pT2 + 4 mc2)
LHCb experimental data
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
pT ( GeV )
∗ Data within theoretical uncertainties due to scale and mass variation
both for central and for more peripheral collisions.
∗ Theoretical improvement looks to be required to match the accuracy
of the experimental data.
Comparison of our theoretical predictions
with LHCb data on pp → D 0 + X
D0 2 < y < 2.5
106
108
107
106
108
107
106
105
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
ratio
105
ratio
105
0
0.5
1
1.5
2
2.5
3
pT ( GeV )
3.5
4
4.5
5
5.5
6
6.5
7
7.5
0
0.5
1
1.5
2
2.5
3
dσ / dpT ( pb / GeV )
107
106
ratio
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
2.5
3
3.5
4
4.5
pT ( GeV )
5.5
6
6.5
7
106
105
2
5
107
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
1.5
4.5
108
105
1
4
5
5.5
6
mass var + scale var scale var (µR, µF) in ([0.5,2],[0.5,2])
mass var in (1.25 - 1.55) GeV
mcharm = 1.4 GeV, µR = µF = sqrt(pT2 + 4 mc2)
LHCb experimental data
109
108
0.5
3.5
pT ( GeV )
D0 4 < y < 4.5
mass var + scale var scale var (µR, µF) in ([0.5,2],[0.5,2])
mass var in (1.25 - 1.55) GeV
mcharm = 1.4 GeV, µR = µF = sqrt(pT2 + 4 mc2)
LHCb experimental data
109
0
8
pT ( GeV )
D0 3.5 < y < 4
dσ / dpT ( pb / GeV )
0
mass var + scale var scale var (µR, µF) in ([0.5,2],[0.5,2])
mass var in (1.25 - 1.55) GeV
mcharm = 1.4 GeV, µR = µF = sqrt(pT2 + 4 mc2)
LHCb experimental data
109
dσ / dpT ( pb / GeV )
dσ / dpT ( pb / GeV )
107
D0 3 < y < 3.5
mass var + scale var scale var (µR, µF) in ([0.5,2],[0.5,2])
mass var in (1.25 - 1.55) GeV
mcharm = 1.4 GeV, µR = µF = sqrt(pT2 + 4 mc2)
LHCb experimental data
109
108
ratio
dσ / dpT ( pb / GeV )
ratio
D0 2.5 < y < 3
mass var + scale var scale var (µR, µF) in ([0.5,2],[0.5,2])
mass var in (1.25 - 1.55) GeV
mcharm = 1.4 GeV, µR = µF = sqrt(pT2 + 4 mc2)
LHCb experimental data
109
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
pT ( GeV )
Data within theoretical uncertainties in all measured rapidity bins
7.5
8
dσ(pp → cc̄ → D 0 + X )/dxE :
scale and mass uncertainties
D0 hadron
D0 hadron
1011
(µR, µF) scale variation
µR = µF = sqrt(pT2 + 4 mc2)
1011
dσ / d xE ( pb )
dσ / d xE ( pb )
pole mass variation
mcharm = 1.40 GeV
mcharm=1.25 GeV
mcharm=1.55 GeV
1010
1010
109
108
107
109
108
107
106
106
105
ratio
ratio
105
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
xE 1.6
1.4
1.2
1
0.8
0.6
0.4
0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
xE ∗ Here plots for pp collisions at Ep, lab = 107 GeV, shape remains similar at
different energies.
All-particle Cosmic Ray flux
1x1025
5x1024
This Model - Fe Excess
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E 3 x dNdE Hm-2 s-1 sr-1 eV-2L
−− This Model - Rigidity Dependency
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ø
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à
23
5x10
àà
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òò
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109
1010
1011
1012
1013
1014
1015
1016
ø
ø
ø
1017
1018
EHeVnucleusL
Experimental data cover lab energies up to Elab ∼ 1020 eV
(although with a suppressed flux, cut-off at Ecm = 300 - 400 TeV)
1019
1020
The all-nucleon CR spectra: considered hypotheses
Cosmic Ray primary all-nucleon flux
108
power-law CR
E3 dN / dE
( GeV2 m-2 s-1 sr-1 )
Gaisser 2012 - var 1 CR
Gaisser 2012 - var 2 CR
107
Gaisser 2014 - var 1 CR
Gaisser 2014 - var 2 CR
106
105
104
103
104
105
106
Elab
107
108
109
1010
1011
1012
( GeV )
∗ All-nucleon spectra obtained from all-particles ones under different assumptions
as for the CR composition at the highest energies.
∗ Models with 3 (2 gal + 1 extra-gal) or 4 (2 gal + 2 extra-gal) populations
are available.
(νµ + ν̄µ ) fluxes: scale and mass variation νµ + anti-νµ flux
νµ + anti-νµ flux
10-2
E3 dN / dE ( GeV2 cm-2 s-1 sr-1 )
scale var (µR, µF) in ([0.5,2],[0.5,2]) power-law CR
10-3
10-4
10-5
10-6
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
mcharm = 1.40 GeV
mcharm = 1.25 GeV
mcharm = 1.55 GeV
10-3
10-4
10-5
10-6
1.4
ratio
ratio
E3 dN / dE ( GeV2 cm-2 s-1 sr-1 )
10-2
power law CR
1.2
1
0.8
0.6
103
104
105
106
107
108
103
Elab,ν ( GeV )
104
105
106
107
108
Elab,ν ( GeV )
∗ scale uncertainty slowly changes with Elab,ν ,
it accounts for missing higher orders (pQCD).
∗ mcharm mass uncertainty decreases with increasing Elab,ν ,
because configurations with smaller xE = Ehad /Ep become possible.
(νµ + ν̄µ ) fluxes: PDF variation -
power law CR
νµ + anti-νµ flux
E3 dN / dE ( GeV2 cm-2 s-1 sr-1 )
10-2
10-3
ABM11-nlo-3fl, pdf var in (1,28) sets
power-law CR
CT10-nlo-3fl, set 0
NNPDF3.0-nlo-3fl, set 0
10-4
10-5
ratio
10-6
1.4
1.2
1
0.8
0.6
103
104
105
Elab,ν ( GeV )
106
107
108
(νµ + ν̄µ ) fluxes: (scale + mass + PDF) variation
summary
νµ + anti-νµ flux
10-3
νµ + anti-νµ flux
10-2
scale var (µR, µF) in ([0.5,2],[0.5,2]) power-law CR
Gaisser 2012 - var 1 CR
Gaisser 2012 - var 2 CR
Gaisser 2014 - var 1 CR
Gaisser 2014 - var 2 CR
E3 dN / dE ( GeV2 cm-2 s-1 sr-1 )
E3 dN / dE ( GeV2 cm-2 s-1 sr-1 )
10-2
10-4
10-5
10-6
10-3
mcharm = 1.25-1.55 GeV
power-law CR
Gaisser 2012 - var 1 CR
Gaisser 2012 - var 2 CR
Gaisser 2014 - var 1 CR
Gaisser 2014 - var 2 CR
10-4
10-5
10-6
103
104
105
106
107
108
103
104
Elab,ν ( GeV )
νµ + anti-νµ flux
10-3
106
107
108
106
107
108
νµ + anti-νµ flux
10-2
ABM11-nlo-3fl, pdf var in (1,28) sets
power-law CR
Gaisser 2012 - var 1 CR
Gaisser 2012 - var 2 CR
Gaisser 2014 - var 1 CR
Gaisser 2014 - var 2 CR
E3 dN / dE ( GeV2 cm-2 s-1 sr-1 )
E3 dN / dE ( GeV2 cm-2 s-1 sr-1 )
10-2
105
Elab,ν ( GeV )
10-4
10-5
10-6
10-3
scale var + mcharm var + PDF var
power-law CR
Gaisser 2012 - var 1 CR
Gaisser 2012 - var 2 CR
Gaisser 2014 - var 1 CR
Gaisser 2014 - var 2 CR
10-4
10-5
10-6
103
104
105
Elab,ν ( GeV )
106
107
108
103
104
105
Elab,ν ( GeV )
(νµ + ν̄µ ) fluxes: variation in the total inelastic σp−Air
νµ + anti-νµ flux
analytical formula, 1998
600
σ(N-air) QGSJet0.1c
500
other measurements
E3 dN / dE ( GeV2 cm-2 s-1 sr-1 )
700
σ(p-Air) Sybill 2.1
AUGER exp data
400
σp,airtot, inel variation p-Air approx 1998
p-Air Sibyll 2.1
p-Air QGSJet0.1c
10-3
10-4
10-5
10-6
1.4
ratio
300
200
103
104
105
106
107
108
109 1010
1.2
1
0.8
0.6
Elab ( GeV )
103
104
105
Elab,ν ( GeV )
νµ + anti-νµ flux
10-2
E3 dN / dE ( GeV2 cm-2 s-1 sr-1 )
σtot, inel (p + Air) ( mb )
10-2
power-law CR
Gaisser 2012 - var 1 CR
Gaisser 2012 - var 2 CR
Gaisser 2014 - var 1 CR
Gaisser 2014 - var 2 CR
10-3
10-4
10-5
10-6
103
104
105
Elab,ν ( GeV )
106
107
108
106
107
108
(νµ + ν̄µ ) fluxes: comparison with other predictions
νµ + anti-νµ flux
E3 dN / dE ( GeV2 cm-2 s-1 sr-1 )
10-2
scale var + mcharm var + PDF var
arXiv:1507.01570, power-law CR
TIG 1998
BERSS 2015
ERS 2008 (dipole model)
SIBYLL 2.3 RC1 (2015)
GRRST 2015
10-3
10-4
10-5
10-6
103
104
105
106
107
108
Elab,ν ( GeV )
Our uncertainty band is an envelope of theoretical uncertainties, not only
normalization but even shape of ν fluxes can change within the envelope.
Conclusions
∗ Prompt lepton fluxes are background for astrophysical high-energy ν seen by
in-ice or under-water large volume neutrino telescopes.
∗ We provide a new estimate of the prompt ν component, on the basis of up-to-date
QCD theoretical results + recent knowledge in astrophysical CR fluxes. Theoretical
predictions were compared a posteriori with LHCb experimental data.
∗ We got a sizable uncertainty band, larger than those previously (under)estimated,
dominated by QCD renormalization and factorization scale uncertainties very slowly
varying with Elab,ν energy.
∗ Central predictions by other groups who made public their results in 2015 are
within our uncertainty band. The ERS 2008 central prediction is larger than our
one, but still in our uncertainty band.
∗ At increasing energies above the transition region, the uncertainties on primary
cosmic ray origin (galactic/extragalactic) and composition (p/heavy ions) become
increasingly more important (and comparable to QCD uncertainty): more investigation is needed from EAS experiments.
∗ A web page with our most recent predictions is available:
http://promptfluxes.desy.de