A state-of-the-art calculation of atmospheric lepton fluxes 35 th International Cosmic Ray Conference 2017, Bexco, Busan, South Korea Anatoli Fedynitch In collaboration with: DESY Zeuthen Hans Dembinski (Bartol, MPIK) Felix Riehn (KIT, LIP) Ralph Engel (KIT) Tom K. Gaisser (Bartol) Todor Stanev (Bartol)
Importance of high precision atmospheric lepton flux prediction > Conventional and prompt leptons are backgrounds for astrophysical neutrino measurements > Estimation of spectral index and normalization depends on the shape of the atmospheric expectation > Accuracy of calculations at lower energies limits neutrino properties measurements with atmospheric neutrinos Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 2
Importance of high precision atmospheric lepton flux prediction IceCube Collaboration, ICRC 2015 > Conventional and prompt leptons are backgrounds for astrophysical neutrino measurements > Estimation of spectral index and normalization depends on the shape of the atmospheric expectation > Accuracy of calculations at lower energies limits neutrino properties measurements with atmospheric neutrinos Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 3 IceCube, PRD 91, 072004 (2015)
Transport equations (hadronic cascade equations) System of non-linear PDE for each particle species h (~62 x #E-bins) : Interactions with air Decays Energy losses (radiative) Re-injection from interactions Re-injection from decays Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 4
Transport equations (hadronic cascade equations) System of non-linear PDE for each particle species h (~62 x #E-bins) : cosmic ray physics Interactions with air Decays atmospheric physics Energy losses (radiative) Re-injection from interactions Re-injection from decays particle physics Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 5
Our tools: MCEq - open-source cascade equation solver > Simultaneous integration of several thousands kinetic equations > Energy range 1 (30) GeV – 10 11 GeV > All models included > High optimization: multi- core, GPU, … (BLAS, MKL, CUDA) (~milli-seconds) > MIT licensed @ https://github.com/afedynitch/MCEq CORSIKA: A. Fedynitch, J. Becker Tjus and P. Desiati, PRD 2012 MCEq: A. Fedynitch, R. Engel, T. K. Gaisser, F. Riehn and S. Todor. PoS ICRC 2015, 1129 Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 6
Models of the comic ray spectrum at the top of the atmosphere > None of the shown models extends over entire energy range and provides error estimates > GST-X and HXa are quite extreme assumptions for UHECR HXa : T. K. Gaisser, Astropart. Phys. 35 (2012) 801 – 806 GH : T. K. Gaisser and M. Honda, Ann. Rev. Nucl. Part. Sci. 52 (2002) 153 – 199 GST-X : T. K. Gaisser, T. Stanev, and S. Tilav, Front. Phys.(Beijing) 8 (2013) 748 – 758 Update of GH (not shown) : J. Evans, D. Porzio et al., 1612.03219 Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 7
GSF flux model (talk by H. Dembinski 19 th July 14:45) Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 8
GSF flux model (talk by H. Dembinski 19 th July 14:45) > Wavy feature at lower energies are due to the hardening of proton and He spectra (see also a recent update of GH model by Evans et al. 1612.03219) > Increase of error around 10 TeV because of the gap between direct and indirect exp. > Higher flux at the knee and harder specrtal index between knee and ankle > Latter effect comes from the lighter composition at the knee as in other models > Mainly driven by KASKADE Gr. and latest data from IceTop and TUNKA Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 9
SIBYLL 2.3c with charm and improved kaon distributions More details in F. Riehn et al., PoS(ICRC2017)301 Talk by Ralph Engel right now Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 10
Implementation of “Barr et al.” in a numerical scheme > Compute partial derivatives wrt. phase-space Original scheme regions, i.e. > No correlations between phase-space regions (as in Barr et al.) or add. correlations Elements of Jacobian (numerical) Extension for charm Charm Error propagation CH_B + CH_A Energy dependence G. D. Barr, S. Robbins, T. K. Gaisser, and T. Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 11 Stanev, Phys. Rev. D 74, 094009 (2006)
Implementation of “Barr et al.” in a numerical scheme > Compute partial derivatives wrt. phase-space Original scheme regions, i.e. > No correlations between phase-space regions (as in Barr et al.) or add. correlations Elements of Jacobian (numerical) Extension for charm Charm Charm Error propagation CH_B + 70 % + max. 25 % CH_A 10 % Energy dependence Energy dependence G. D. Barr, S. Robbins, T. K. Gaisser, and T. Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 12 Stanev, Phys. Rev. D 74, 094009 (2006)
Uncertainties of lepton fluxes Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 13
Uncertainties of lepton fluxes > Similar error band for each interaction model > Error from Barr et al. scheme approximately universal for all current models > Hadronic interaction models produce compatible results Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 14
Uncertainties of lepton ratios Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 15
Uncertainties of lepton ratios > Only very few benchmark measurements available > Ratios are more sensitive to the leading particle effect > SIBYLL 2.1 and 2.3 known to have problems with K+ > Newer models all compatible Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 16
Prompt neutrinos from decays of charmed mesons > SIBYLL 2.3c is the only full MC model > Compatible with LHC data and IceCube limit > New CR flux model (GSF) changes situation a bit > Uncertainties from QCD theory are large and calculations are compatible within bands IceCube: Astrophys.J. 833 (2016) GMS: Garzelli et al., JHEP 1510 (2015) 115 BERSS: Bhattacharya et al. JHEP 2015: 110 Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 17
Prompt neutrinos from decays of charmed mesons > SIBYLL 2.3c is the only full MC model > Compatible with LHC data and IceCube limit > New CR flux model (GSF) changes situation a bit > Uncertainties from QCD theory are large and calculations are compatible within bands IceCube: Astrophys.J. 833 (2016) GMS: Garzelli et al., JHEP 1510 (2015) 115 BERSS: Bhattacharya et al. JHEP 2015: 110 Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 18
Conclusions > We developed a high -performance open-source code for atmospheric lepton calculations (Updated version of MCEq soon @ https://github.com/afedynitch/MCEq) > Uncertainties are dominated by hadronic interactions and cosmic ray flux errors > The CR flux errors are quantified using a new global fit to experimental data (GSF); the model changes the expectation of the very high energy neutrinos > Hadronic errors are quantified using a scheme after Barr et al., which can be used as a starting point for further studies; the error bands weakly depend on the initial choice of the interaction model > The high performance of the code together with the error propagation scheme can be used to constrain hadronic interactions in a phase-space inaccessible to colliders Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 19
Hadronic uncertainties: current state of the art > “ Uncertainties in atmospheric neutrino fluxes ”, G. D. Barr, S. Robbins, T. K. Gaisser, and T. Stanev, Phys. Rev. D 74, 094009 (2006) > Cut phase-space in regions/slices in E lab and x lab and assign uncertainty to each slice (uncorrelated) > Draw-back 1 : Uncorrelated uncertainty assigned by hand and judged only from availability of experimental data (not how well TARGET described it) > Draw-back 2 : The “central value” is assumed to be TARGET. Scheme doesn’t tell anything about ”best estimate”. Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 20
Hadronic uncertainties computed with different interaction models Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 21
Hadronic uncertainties computed with different interaction models 1. If models with known problems are excluded, then errors are ~ universal = approx. independent on the choice of interaction model Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 22 “Bracketing” with different models can be a good estimate, sometimes 2.
Hadronic uncertainties below 200 GeV Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 23
Hadronic uncertainties for high energy leptons Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 24
Relevant particles for lepton production Muon neutrinos Electron neutrinos charm decay pion decay kaon decay charm decay muon decay kaon decay Anatoli Fedynitch | 35 th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 25
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