[en] We evaluate the prompt atmospheric neutrino flux at high energies using three different frameworks for calculating the heavy quark production cross section in QCD: NLO perturbative QCD, k$_{T}$ factorization including low-x resummation, and the dipole model including parton saturation. We use QCD parameters, the value for the charm quark mass and the range for the factorization and renormalization scales that provide the best description of the total charm cross section measured at fixed target experiments, at RHIC and at LHC. Using these parameters we calculate differential cross sections for charm and bottom production and compare with the latest data on forward charm meson production from LHCb at 7 TeV and at 13 TeV, finding good agreement with the data. In addition, we investigate the role of nuclear shadowing by including nuclear parton distribution functions (PDF) for the target air nucleus using two different nuclear PDF schemes. Depending on the scheme used, we find the reduction of the flux due to nuclear effects varies from 10% to 50% at the highest energies. Finally, we compare our results with the IceCube limit on the prompt neutrino flux, which is already providing valuable information about some of the QCD models.
Disciplines :
Physics
Author, co-author :
Bhattacharya, Atri ; Université de Liège > Département d'astrophys., géophysique et océanographie (AGO) > Inter. fondamentales en physique et astrophysique (IFPA)
Enberg, Rikard
Jeong, Yu Seon
Kim, C. S.
Reno, Mary Hall
Sarcevic, Ina
Stasto, Anna
Language :
English
Title :
Prompt atmospheric neutrino fluxes: perturbative QCD models and nuclear effects
IceCube collaboration, M.G. Aartsen et al., First observation of PeV-energy neutrinos with IceCube, Phys. Rev. Lett. 111 (2013) 021103 [arXiv:1304.5356] [INSPIRE].
IceCube collaboration, M.G. Aartsen et al., Evidence for High-Energy Extraterrestrial Neutrinos at the IceCube Detector, Science 342 (2013) 1242856 [arXiv:1311.5238] [INSPIRE].
M. Honda, T. Kajita, K. Kasahara, S. Midorikawa and T. Sanuki, Calculation of atmospheric neutrino flux using the interaction model calibrated with atmospheric muon data, Phys. Rev. D 75 (2007) 043006 [astro-ph/0611418] [INSPIRE].
G.D. Barr, T.K. Gaisser, P. Lipari, S. Robbins and T. Stanev, A three-dimensional calculation of atmospheric neutrinos, Phys. Rev. D 70 (2004) 023006 [astro-ph/0403630] [INSPIRE].
T.K. Gaisser and S.R. Klein, A new contribution to the conventional atmospheric neutrino flux, Astropart. Phys. 64 (2015) 13 [arXiv:1409.4924] [INSPIRE].
P. Gondolo, G. Ingelman and M. Thunman, Charm production and high-energy atmospheric muon and neutrino fluxes, Astropart. Phys. 5 (1996) 309 [hep-ph/9505417] [INSPIRE].
L. Pasquali, M.H. Reno and I. Sarcevic, Lepton fluxes from atmospheric charm, Phys. Rev. D 59 (1999) 034020 [hep-ph/9806428] [INSPIRE].
L. Pasquali and M.H. Reno, Tau-neutrino fluxes from atmospheric charm, Phys. Rev. D 59 (1999) 093003 [hep-ph/9811268] [INSPIRE].
A.D. Martin, M.G. Ryskin and A.M. Stasto, Prompt neutrinos from atmospheric cc and bb production and the gluon at very small x, Acta Phys. Polon. B 34 (2003) 3273 [hep-ph/0302140] [INSPIRE].
R. Enberg, M.H. Reno and I. Sarcevic, Prompt neutrino fluxes from atmospheric charm, Phys. Rev. D 78 (2008) 043005 [arXiv:0806.0418] [INSPIRE].
A. Bhattacharya, R. Enberg, M.H. Reno, I. Sarcevic and A. Stasto, Perturbative charm production and the prompt atmospheric neutrino flux in light of RHIC and LHC, JHEP 06 (2015) 110 [arXiv:1502.01076] [INSPIRE].
M.V. Garzelli, S. Moch and G. Sigl, Lepton fluxes from atmospheric charm revisited, JHEP 10 (2015) 115 [arXiv:1507.01570] [INSPIRE].
R. Gauld, J. Rojo, L. Rottoli and J. Talbert, Charm production in the forward region: constraints on the small-x gluon and backgrounds for neutrino astronomy, JHEP 11 (2015) 009 [arXiv:1506.08025] [INSPIRE].
R. Gauld, J. Rojo, L. Rottoli, S. Sarkar and J. Talbert, The prompt atmospheric neutrino flux in the light of LHCb, JHEP 02 (2016) 130 [arXiv:1511.06346] [INSPIRE].
LHCb collaboration, Prompt charm production in pp collisions at s=7 TeV, Nucl. Phys. B 871 (2013) 1 [arXiv:1302.2864] [INSPIRE].
LHCb collaboration, Measurements of prompt charm production cross-sections in pp collisions at s=13 TeV, JHEP 03 (2016) 159.
P. Nason, S. Dawson and R.K. Ellis, The Total Cross-Section for the Production of Heavy Quarks in Hadronic Collisions, Nucl. Phys. B 303 (1988) 607 [INSPIRE].
P. Nason, S. Dawson, R.K. Ellis, The One Particle Inclusive Differential Cross-Section for Heavy Quark Production in Hadronic Collisions, Nucl. Phys. B 327 (1989) 49.
[Erratum ibid. B 335 (1990) 260] [INSPIRE].
M.L. Mangano, P. Nason and G. Ridolfi, Heavy quark correlations in hadron collisions at next-to-leading order, Nucl. Phys. B 373 (1992) 295 [INSPIRE].
M. Cacciari, M.L. Mangano and P. Nason, Gluon PDF constraints from the ratio of forward heavy-quark production at the LHC at S=7 and 13TeV, Eur. Phys. J. C 75(2015) 610 [arXiv:1507.06197] [INSPIRE].
M. Cacciari and M. Greco, Large pT hadroproduction of heavy quarks, Nucl. Phys. B 421 (1994) 530 [hep-ph/9311260] [INSPIRE].
M. Cacciari, M. Greco and P. Nason, The pT spectrum in heavy flavor hadroproduction, JHEP 05 (1998) 007 [hep-ph/9803400] [INSPIRE].
M. Cacciari, S. Frixione and P. Nason, The pT spectrum in heavy flavor photoproduction, JHEP 03 (2001) 006 [hep-ph/0102134] [INSPIRE].
P. Nason, A new method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040 [hep-ph/0409146] [INSPIRE].
N.N. Nikolaev and B.G. Zakharov, Color transparency and scaling properties of nuclear shadowing in deep inelastic scattering, Z. Phys. C 49 (1991) 607 [INSPIRE].
A.H. Mueller, Soft gluons in the infinite momentum wave function and the BFKL Pomeron, Nucl. Phys. B 415 (1994) 373 [INSPIRE].
N.N. Nikolaev, G. Piller and B.G. Zakharov, Inclusive heavy flavor production from nuclei, Z. Phys. A 354 (1996) 99 [hep-ph/9511384] [INSPIRE].
K.J. Golec-Biernat and M. Wusthoff, Saturation effects in deep inelastic scattering at low Q 2 and its implications on diffraction, Phys. Rev. D 59 (1998) 014017 [hep-ph/9807513] [INSPIRE].
J.R. Forshaw, G. Kerley and G. Shaw, Extracting the dipole cross-section from photoproduction and electroproduction total cross-section data, Phys. Rev. D 60 (1999) 074012 [hep-ph/9903341] [INSPIRE].
A.M. Stasto, K.J. Golec-Biernat and J. Kwiecinski, Geometric scaling for the total γ ∗ p cross-section in the low x region, Phys. Rev. Lett. 86 (2001) 596 [hep-ph/0007192] [INSPIRE].
J. Bartels, K.J. Golec-Biernat and H. Kowalski, A modification of the saturation model: DGLAP evolution, Phys. Rev. D 66 (2002) 014001 [hep-ph/0203258] [INSPIRE].
B.Z. Kopeliovich and A.V. Tarasov, Gluon shadowing and heavy flavor production off nuclei, Nucl. Phys. A 710 (2002) 180 [hep-ph/0205151] [INSPIRE].
J. Raufeisen and J.-C. Peng, Relating parton model and color dipole formulation of heavy quark hadroproduction, Phys. Rev. D 67 (2003) 054008 [hep-ph/0211422] [INSPIRE].
H. Kowalski and D. Teaney, An Impact parameter dipole saturation model, Phys. Rev. D 68 (2003) 114005 [hep-ph/0304189] [INSPIRE].
E. Iancu, K. Itakura and S. Munier, Saturation and BFKL dynamics in the HERA data at small x, Phys. Lett. B 590 (2004) 199 [hep-ph/0310338] [INSPIRE].
V.P. Goncalves and M.V.T. Machado, Saturation Physics in Ultra High Energy Cosmic Rays: Heavy Quark Production, JHEP 04 (2007) 028 [hep-ph/0607125] [INSPIRE].
G. Soyez, Saturation QCD predictions with heavy quarks at HERA, Phys. Lett. B 655 (2007) 32 [arXiv:0705.3672] [INSPIRE].
J.L. Albacete, N. Armesto, J.G. Milhano and C.A. Salgado, Non-linear QCD meets data: A global analysis of lepton-proton scattering with running coupling BK evolution, Phys. Rev. D 80 (2009) 034031 [arXiv:0902.1112] [INSPIRE].
J.L. Albacete, N. Armesto, J.G. Milhano, P. Quiroga-Arias and C.A. Salgado, AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks, Eur. Phys. J. C 71 (2011) 1705 [arXiv:1012.4408] [INSPIRE].
V.P. Goncalves, M.S. Kugeratski, M.V.T. Machado and F.S. Navarra, Saturation physics at HERA and RHIC: An unified description, Phys. Lett. B 643 (2006) 273 [hep-ph/0608063] [INSPIRE].
J.L. Albacete, N. Armesto, J.G. Milhano, P. Quiroga-Arias and C.A. Salgado, AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks, Eur. Phys. J. C 71 (2011) 1705 [arXiv:1012.4408] [INSPIRE].
C. Ewerz, A. von Manteuffel and O. Nachtmann, On the Energy Dependence of the Dipole-Proton Cross section in Deep Inelastic Scattering, JHEP 03 (2011) 062 [arXiv:1101.0288] [INSPIRE].
Y.S. Jeong, C.S. Kim, M.V. Luu and M.H. Reno, Color dipole cross section and inelastic structure function, JHEP 11 (2014) 025 [arXiv:1403.2551] [INSPIRE].
M.M. Block, L. Durand and P. Ha, Connection of the virtual γ ∗ p cross section of ep deep inelastic scattering to real γp scattering and the implications for νN and ep total cross sections, Phys. Rev. D 89 (2014) 094027 [arXiv:1404.4530] [INSPIRE].
S. Catani, M. Ciafaloni and F. Hautmann, High-energy factorization and small x heavy flavor production, Nucl. Phys. B 366 (1991) 135 [INSPIRE].
J.C. Collins and R.K. Ellis, Heavy quark production in very high-energy hadron collisions, Nucl. Phys. B 360 (1991) 3 [INSPIRE].
E.M. Levin, M.G. Ryskin, Yu.M. Shabelski and A.G. Shuvaev, Heavy quark production in parton model and in QCD, Sov. J. Nucl. Phys. 54 (1991) 867 [INSPIRE].
M.G. Ryskin, Yu.M. Shabelski and A.G. Shuvaev, Heavy quark production in parton model and in QCD, Z. Phys. C 69 (1996) 269 [hep-ph/9506338] [INSPIRE].
K. Kovarik et al., nCTEQ15 — Global analysis of nuclear parton distributions with uncertainties in the CTEQ framework, Phys. Rev. D 93 (2016) 085037 [arXiv:1509.00792] [INSPIRE].
K.J. Eskola, H. Paukkunen and C.A. Salgado, EPS09: A New Generation of NLO and LO Nuclear Parton Distribution Functions, JHEP 04 (2009) 065 [arXiv:0902.4154] [INSPIRE].
T.K. Gaisser, Spectrum of cosmic-ray nucleons, kaon production and the atmospheric muon charge ratio, Astropart. Phys. 35 (2012) 801 [arXiv:1111.6675] [INSPIRE].
T.K. Gaisser, T. Stanev and S. Tilav, Cosmic Ray Energy Spectrum from Measurements of Air Showers, Front. Phys. (Beijing) 8 (2013) 748 [arXiv:1303.3565] [INSPIRE].
T. Stanev, T.K. Gaisser and S. Tilav, High energy cosmic rays: sources and fluxes, Nucl. Instrum. Meth. A 742 (2014) 42 [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
P. Marquard, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Quark Mass Relations to Four-Loop Order in Perturbative QCD, Phys. Rev. Lett. 114 (2015) 142002 [arXiv:1502.01030] [INSPIRE].
R.E. Nelson, R. Vogt and A.D. Frawley, Narrowing the uncertainty on the total charm cross section and its effect on the J/ ψ cross section, Phys. Rev. C 87 (2013) 014908 [arXiv:1210.4610] [INSPIRE].
S. Dulat et al., New parton distribution functions from a global analysis of quantum chromodynamics, Phys. Rev. D 93 (2016) 033006 [arXiv:1506.07443] [INSPIRE].
F. Olness and A. Kusina, private communication.
ALICE collaboration, Measurement of charm production at central rapidity in proton-proton collisions at s=2.76 TeV, JHEP 07 (2012) 191 [arXiv:1205.4007] [INSPIRE].
ATLAS collaboration, Measurement of D ∗±, D ± and Ds ± meson production cross sections in pp collisions at s=7 TeV with the ATLAS detector, Nucl. Phys. B 907 (2016) 717 [arXiv:1512.02913] [INSPIRE].
PHENIX collaboration, A. Adare et al., Measurement of high-pT single electrons from heavy-flavor decays in p+p collisions at s=200 GeV, Phys. Rev. Lett. 97 (2006) 252002 [hep-ex/0609010] [INSPIRE].
STAR collaboration, L. Adamczyk et al., Measurements of D 0 and D ∗ Production in p + p Collisions at s=200 GeV, Phys. Rev. D 86 (2012) 072013 [arXiv:1204.4244] [INSPIRE].
HERA-B collaboration, I. Abt et al., Measurement of D 0, D +, Ds + and D ∗+ Production in Fixed Target 920-GeV Proton-Nucleus Collisions, Eur. Phys. J. C 52 (2007) 531 [arXiv:0708.1443] [INSPIRE].
PHENIX collaboration, A. Adare et al., Cross section for bb production via dielectrons in d+Au collisions at sNN=200 GeV, Phys. Rev. C 91 (2015) 014907 [arXiv:1405.4004] [INSPIRE].
ALICE collaboration, Beauty production in pp collisions at s=2.76 TeV measured via semi-electronic decays, Phys. Lett. B 738 (2014) 97 [arXiv:1405.4144] [INSPIRE].
ALICE collaboration, Measurement of prompt J/ ψ and beauty hadron production cross sections at mid-rapidity in pp collisions at s=7 TeV, JHEP 11 (2012) 065 [arXiv:1205.5880] [INSPIRE].
UA1 collaboration, C. Albajar et al., Beauty production at the CERN pp¯ collider, Phys. Lett. B 256 (1991).
[Erratum ibid. B 262 (1991) 497] [INSPIRE].
LHCb collaboration, Measurement of J/ ψ production in pp collisions at s=7 TeV, Eur. Phys. J. C 71 (2011) 1645 [arXiv:1103.0423] [INSPIRE].
C. Lourenco and H.K. Wohri, Heavy flavour hadro-production from fixed-target to collider energies, Phys. Rept. 433 (2006) 127 [hep-ph/0609101] [INSPIRE].
I. Balitsky, Operator expansion for high-energy scattering, Nucl. Phys. B 463 (1996) 99 [hep-ph/9509348] [INSPIRE].
Y.V. Kovchegov, Small x F(2) structure function of a nucleus including multiple Pomeron exchanges, Phys. Rev. D 60 (1999) 034008 [hep-ph/9901281] [INSPIRE].
C.A. Argüelles, F. Halzen, L. Wille, M. Kroll and M.H. Reno, High-energy behavior of photon, neutrino and proton cross sections, Phys. Rev. D 92 (2015) 074040 [arXiv:1504.06639] [INSPIRE].
N. Armesto, C.A. Salgado and U.A. Wiedemann, Relating high-energy lepton-hadron, proton-nucleus and nucleus-nucleus collisions through geometric scaling, Phys. Rev. Lett. 94 (2005) 022002 [hep-ph/0407018] [INSPIRE].
H. De Vries, C.W. De Jager and C. De Vries, Nuclear charge and magnetization density distribution parameters from elastic electron scattering, Atom. Data Nucl. Data Tabl. 36 (1987) 495 [INSPIRE].
N. Armesto, A Simple model for nuclear structure functions at small x in the dipole picture, Eur. Phys. J. C 26 (2002) 35 [hep-ph/0206017] [INSPIRE].
V.P. Goncalves and M.V.T. Machado, Nuclear heavy quark photoproduction in a saturation model, Eur. Phys. J. C 30 (2003) 387 [hep-ph/0305045] [INSPIRE].
L.N. Lipatov, Reggeization of the Vector Meson and the Vacuum Singularity in Nonabelian Gauge Theories, Sov. J. Nucl. Phys. 23 (1976) 338 [INSPIRE].
E.A. Kuraev, L.N. Lipatov and V.S. Fadin, Multi-Reggeon Processes in the Yang-Mills Theory, Sov. Phys. JETP 44 (1976) 443 [INSPIRE].
E.A. Kuraev, L.N. Lipatov and V.S. Fadin, The Pomeranchuk Singularity in Nonabelian Gauge Theories, Sov. Phys. JETP 45 (1977) 199 [INSPIRE].
I.I. Balitsky and L.N. Lipatov, The Pomeranchuk Singularity in Quantum Chromodynamics, Sov. J. Nucl. Phys. 28 (1978) 822 [INSPIRE].
T. Altinoluk, N. Armesto, G. Beuf, A. Kovner and M. Lublinsky, Heavy quarks in proton-nucleus collisions — the hybrid formalism, Phys. Rev. D 93 (2016) 054049 [arXiv:1511.09415] [INSPIRE].
J. Kwiecinski, A.D. Martin and A.M. Stasto, A unified BFKL and GLAP description of F2 data, Phys. Rev. D 56 (1997) 3991 [hep-ph/9703445] [INSPIRE].
K. Kutak and J. Kwiecinski, Screening effects in the ultrahigh-energy neutrino interactions, Eur. Phys. J. C 29 (2003) 521 [hep-ph/0303209] [INSPIRE].
K. Kutak and A.M. Stasto, Unintegrated gluon distribution from modified BK equation, Eur. Phys. J. C 41 (2005) 343 [hep-ph/0408117] [INSPIRE].
K. Kutak and S. Sapeta, Gluon saturation in dijet production in p-Pb collisions at Large Hadron Collider, Phys. Rev. D 86 (2012) 094043 [arXiv:1205.5035] [INSPIRE].
R. Gauld, Forward D predictions for pPb collisions and sensitivity to cold nuclear matter effects, Phys. Rev. D 93 (2016) 014001 [arXiv:1508.07629] [INSPIRE].
T.K. Gaisser, Cosmic rays and particle physics. Cambridge University Press (1990).
P. Lipari, Lepton spectra in the earth’s atmosphere, Astropart. Phys. 1 (1993) 195 [INSPIRE].
T.K. Gaisser, Spectrum of cosmic-ray nucleons, kaon production and the atmospheric muon charge ratio, Astropart. Phys. 35 (2012) 801 [arXiv:1111.6675] [INSPIRE].
B.A. Kniehl and G. Kramer, Charmed-hadron fragmentation functions from CERN LEP1 revisited, Phys. Rev. D 74 (2006) 037502 [hep-ph/0607306] [INSPIRE].
M. Lisovyi, A. Verbytskyi and O. Zenaiev, Combined analysis of charm-quark fragmentation-fraction measurements, Eur. Phys. J. C 76 (2016) 397 [arXiv:1509.01061] [INSPIRE].
B.A. Kniehl, G. Kramer, I. Schienbein and H. Spiesberger, Finite-mass effects on inclusive B meson hadroproduction, Phys. Rev. D 77 (2008) 014011 [arXiv:0705.4392] [INSPIRE].
LHCb collaboration, Measurement of b-hadron production fractions in 7 TeV pp collisions, Phys. Rev. D 85 (2012) 032008 [arXiv:1111.2357] [INSPIRE].
E. Braaten, K.-m. Cheung, S. Fleming and T.C. Yuan, Perturbative QCD fragmentation functions as a model for heavy quark fragmentation, Phys. Rev. D 51 (1995) 4819 [hep-ph/9409316] [INSPIRE].
M. Cacciari and P. Nason, Charm cross-sections for the Tevatron Run II, JHEP 09 (2003) 006 [hep-ph/0306212] [INSPIRE].
T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 Physics and Manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].
E. Norrbin and T. Sjöstrand, Production mechanisms of charm hadrons in the string model, Phys. Lett. B 442 (1998) 407 [hep-ph/9809266] [INSPIRE].
E. Norrbin and T. Sjöstrand, Production and hadronization of heavy quarks, Eur. Phys. J. C 17 (2000) 137 [hep-ph/0005110] [INSPIRE].
S. Frixione, P. Nason and C. Oleari, Matching NLO QCD computations with Parton Shower simulations: the POWHEG method, JHEP 11 (2007) 070 [arXiv:0709.2092] [INSPIRE].
S. Alioli, P. Nason, C. Oleari and E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX, JHEP 06 (2010) 043 [arXiv:1002.2581] [INSPIRE].
S. Frixione, P. Nason and G. Ridolfi, A positive-weight next-to-leading-order Monte Carlo for heavy flavour hadroproduction, JHEP 09 (2007) 126 [arXiv:0707.3088] [INSPIRE].
T. Pierog and K. Werner, EPOS Model and Ultra High Energy Cosmic Rays, Nucl. Phys. Proc. Suppl. 196 (2009) 102 [arXiv:0905.1198] [INSPIRE].
S. Iyer, M.H. Reno and I. Sarcevic, Searching for νμ → ντ oscillations with extragalactic neutrinos, Phys. Rev. D 61 (2000) 053003 [hep-ph/9909393] [INSPIRE].
F. Becattini and S. Bottai, Extreme energy neutrino(tau) propagation through the Earth, Astropart. Phys. 15 (2001) 323 [astro-ph/0003179] [INSPIRE].
A. Bulmahn and M.H. Reno, Secondary atmospheric tau neutrino production, Phys. Rev. D 82 (2010) 057302 [arXiv:1007.4989] [INSPIRE].
IceCube collaboration, L. Rädel et al., A measurement of the diffuse astrophysical muon neutrino flux using multiple years of IceCube data, PoS (ICRC2015) 1079.
S.J. Brodsky, P. Hoyer, C. Peterson and N. Sakai, The Intrinsic Charm of the Proton, Phys. Lett. B 93 (1980) 451 [INSPIRE].
T.J. Hobbs, J.T. Londergan and W. Melnitchouk, Phenomenology of nonperturbative charm in the nucleon, Phys. Rev. D 89 (2014) 074008 [arXiv:1311.1578] [INSPIRE].
S. Dulat et al., Intrinsic Charm Parton Distribution Functions from CTEQ-TEA Global Analysis, Phys. Rev. D 89 (2014) 073004 [arXiv:1309.0025] [INSPIRE].
NNPDF collaboration, R.D. Ball et al., A Determination of the Charm Content of the Proton, arXiv:1605.06515 [INSPIRE].
T. Boettcher, P. Ilten and M. Williams, Direct probe of the intrinsic charm content of the proton, Phys. Rev. D 93 (2016) 074008 [arXiv:1512.06666] [INSPIRE].
F. Halzen, Y.S. Jeong and C.S. Kim, Charge Asymmetry of Weak Boson Production at the LHC and the Charm Content of the Proton, Phys. Rev. D 88 (2013) 073013 [arXiv:1304.0322] [INSPIRE].
F. Halzen and L. Wille, Upper Limit on Forward Charm Contribution to Atmospheric Neutrino Flux, arXiv:1601.03044 [INSPIRE].
F. Halzen and L. Wille, Charm contribution to the atmospheric neutrino flux, Phys. Rev. D 94 (2016) 014014 [arXiv:1605.01409] [INSPIRE].
R. Laha and S.J. Brodsky, IC at IC: IceCube can constrain the intrinsic charm of the proton, arXiv:1607.08240 [INSPIRE].
LHCf collaboration, O. Adriani et al., Measurements of longitudinal and transverse momentum distributions for neutral pions in the forward-rapidity region with the LHCf detector, Phys. Rev. D 94 (2016) 032007 [arXiv:1507.08764] [INSPIRE].
TOTEM collaboration, G. Antchev et al., Measurement of the forward charged particle pseudorapidity density in pp collisions at s=8 TeV using a displaced interaction point, Eur. Phys. J. C 75 (2015) 126 [arXiv:1411.4963] [INSPIRE].
IceCube collaboration, M.G. Aartsen et al., Observation and Characterization of a Cosmic Muon Neutrino Flux from the Northern Hemisphere using six years of IceCube data, arXiv:1607.08006 [INSPIRE].
ALICE collaboration, Measurement of Ds+ production and nuclear modification factor in Pb-Pb collisions at sNN=2.76 TeV, JHEP 03 (2016) 082 [arXiv:1509.07287] [INSPIRE].
LHCb collaboration, Measurement of B meson production cross-sections in proton-proton collisions at s=7 TeV, JHEP 08 (2013) 117 [arXiv:1306.3663] [INSPIRE].
E.V. Bugaev, A. Misaki, V.A. Naumov, T.S. Sinegovskaya, S.I. Sinegovsky and N. Takahashi, Atmospheric muon flux at sea level, underground and underwater, Phys. Rev. D 58 (1998) 054001 [hep-ph/9803488] [INSPIRE].
H. Pietschmann, Weak Interactions — Formulae, Results and Derivations, Springer-Verlag, (1984).
