Prompt neutrino fluxes from atmospheric
charm revisited
M.V. Garzelli,
S.-O. Moch
and
G. Sigl
II Institute for Theoretical Physics, University of Hamburg, Germany
arXiv:1507.01570
14th International Conference on Topics in Astroparticle and
Underground Physics, Torino, September 7 - 11 th, 2015
The astrophysical issue:
IceCube high-energy events
([arXiv:1405.5303] + ICRC 2015)
∗ 2013: 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].
energy spectrum (4 years)
ν
∗ 2015: 4-year analysis, with a total of 54�����������������������������������������������������������������
events, gap partially filled.
Events per 988 Days
102
Background Atmospheric Muon Flux
Bkg. Atmospheric Neutrinos (π/K)
�������������������������
Background Uncertainties
�����������������
Atmospheric Neutrinos
(90% CL Charm Limit)
�����������
Bkg.+Signal Best-Fit Astrophysical (best-fit slope E . )
Bkg.+Signal Best-Fit Astrophysical (fixed slope E )
��������������������������
Data
���������������������������������
�����������������
−2 3
101
100
10-1
−2
����������������������������������
�������������������
��������������������������������������
�����
104
102 ��������������������������
103
Deposited EM-Equivalent Energy in Detector (TeV)
figures from the presentation of C. Kopper, ICRC2015
��
Candidate sources for high-energy ν events
considered in literature
∗ Astrophysical sources:
AGNs, GRBs, SNRs, Starburst galaxies...
∗ Heavy DM decay, DM-DM annihilation
∗ Atmospheric leptons
May be a combination of all of them ?
Precise predictions/measurements of atmospheric ν’s have to be considered and represent a “background” for any astrophysical or BSM hypothesis.
Conventional and Prompt atmospheric ν flux
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 havier hadrons (D’s, Λ’s.....)
∗ Transition point: still subject of investigation......
Standard procedure: from cascade equations to
Z -moments
Solve a system of coupled differential equations regulating particle evolution in the
atmosphere (interaction/decay/(re)generation):
X
X
dφj
φj
φj
=−
−
+
Sprod (k → j) +
Sdecay (k → j) + Sreg (j → j)
dX
λj,int
λj,dec
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 )
Sprod (k → j) =
dEk
∼
Zkj (Ej )
λ
(E
)
σ
dE
λk (Ej )
j
k
k
k
Ej
− Particle Decay:
Z
∞
Sdecay (j → l) =
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
Aair
dxE φp (Eh /xE )
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 νl + l + X
∗ Integration variable: xE0 = El /Eh
∗ Z -moments for intermediate hadron decay:
Z
Zhl (El ) =
0
1−
eff
sX
,h
m2
h
dxE0 φh (El /xE 0 )
Fh→l (xE0 )
xE0
φh (El )
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 rapidities), but even many observables at LHCb (mid-forward rapidity).
∗ 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 looking at the convergence of the perturbative
series (LO/NLO/NNLO comparison).
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 eV ∼ Ecm = 1.37 TeV)
(Elab = 108 eV ∼ Ecm = 13.7 TeV)
(Elab = 1010 eV ∼ 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 → mcpole = 1.48 at 1-loop
mc (mc ) = 1.27 → mcpole = 1.67 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, Q 2 ): Q 2 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 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: the largest uncertainties, they are working to try to
incorporate PROSA idea in their fit as well (Gauld et al. [arXiv:1506.08025],
not yet available in the 3 flavour scheme).
The all nucleon CR spectra: considered hypotheses
Cosmic Ray primary all-nucleon flux
108
power-law CR
E2 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: interpolation between high energy
and low energy solutions - power law CR
νµ + anti-νµ flux
E3 dN / dE ( GeV2 cm-2 s-1 sr-1 )
interpolation
low energy solution
high energy solution
10-2
10-3
10-4
10-5
103
104
105
Elab,ν ( GeV )
106
107
108
(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
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 (see talk of T. Gaisser).
Garzelli, Moch, Sigl, [arXiv:1507.01570] → this talk
+ other works in preparation......
(νµ + ν̄µ ) fluxes: comparison with other predictions
νµ + anti-νµ flux
E3 dN / dE ( GeV2 cm-2 s-1 sr-1 )
10-2
10-3
scale var + mcharm var + PDF var
this work, power-law CR
TIG 1998
BERSS 2015
ERS 2008 (dipole model)
10-4
10-5
10-6
103
104
105
Elab,ν ( GeV )
106
107
108
(νµ + ν̄µ ) fluxes: comparisons with other predictions
and transition region
νµ + anti-νµ flux
νµ + anti-νµ flux
10-2
scale var + mcharm var + PDF var
this work, Gaisser 2014 - var 1 CR
BERSS 2015
Honda-2007 conventional
E3 dN / dE ( GeV2 cm-2 s-1 sr-1 )
E3 dN / dE ( GeV2 cm-2 s-1 sr-1 )
10-2
10-3
10-4
10-5
10-6
scale var + mcharm var + PDF var
this work, Gaisser 2014 - var 2 CR
BERSS 2015
Honda-2007 conventional
10-3
10-4
10-5
10-6
103
104
105
Elab,ν ( GeV )
106
107
108
103
104
105
106
107
Elab,ν ( GeV )
5
∗ Our predictions point to a transition energy Etrans = 6+12
−3 · 10 GeV:
is the last E bin where IceCube did not see events just filled by prompt ν ?
108
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.
∗ Our central predictions are in between those recently obtained by pQCD by
another group (BERSS 2015) and those previously obtained by the same group
(ERS 2008) with a phenomenological dipole model.
∗ 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.
∗ 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 predictions is under construction. Alternatively,
they can be requested to the authors (just e-mail us!)