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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)

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A state-of-the-art calculation of atmospheric lepton fluxes

35th International Cosmic Ray Conference 2017, Bexco, Busan, South Korea

Anatoli Fedynitch DESY Zeuthen In collaboration with: Hans Dembinski (Bartol, MPIK) Felix Riehn (KIT, LIP) Ralph Engel (KIT) Tom K. Gaisser (Bartol) Todor Stanev (Bartol)

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 2

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

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 3

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

IceCube, PRD 91, 072004 (2015)

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Anatoli Fedynitch | 35th 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) : Interactions with air Decays Energy losses (radiative) Re-injection from interactions Re-injection from decays

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 5

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 particle physics atmospheric physics cosmic ray physics

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 6

Our tools: MCEq - open-source cascade equation solver

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

> Simultaneous integration of several thousands kinetic equations > Energy range 1 (30) GeV – 1011 GeV > All models included > High optimization: multi-core, GPU, … (BLAS, MKL, CUDA) (~milli-seconds) > MIT licensed @ https://github.com/afedynitch/MCEq

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 7

Models of the comic ray spectrum at the top of the atmosphere

> None of the shown models extends

ver 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

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 8

GSF flux model (talk by H. Dembinski 19th July 14:45)

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 9

GSF flux model (talk by H. Dembinski 19th 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

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 10

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 

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 11

Implementation of “Barr et al.” in a numerical scheme

> Compute partial derivatives wrt. phase-space regions, i.e. > No correlations between phase-space regions (as in Barr et al.) or add. correlations

Original scheme

Elements of Jacobian (numerical) Error propagation Charm

CH_A CH_B + Energy dependence

G. D. Barr, S. Robbins, T. K. Gaisser, and T.

Stanev, Phys. Rev. D 74, 094009 (2006)

Extension for charm

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 12

Implementation of “Barr et al.” in a numerical scheme

> Compute partial derivatives wrt. phase-space regions, i.e. > No correlations between phase-space regions (as in Barr et al.) or add. correlations

Original scheme

Elements of Jacobian (numerical) Error propagation Charm

CH_A CH_B + Energy dependence

Charm

10 % 70 % + max. 25 % Energy dependence

G. D. Barr, S. Robbins, T. K. Gaisser, and T.

Stanev, Phys. Rev. D 74, 094009 (2006)

Extension for charm

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 13

Uncertainties of lepton fluxes

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 14

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

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 15

Uncertainties of lepton ratios

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 16

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

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Anatoli Fedynitch | 35th 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

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 18

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

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 19

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

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 20

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 Elab and xlab 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”.

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 21

Hadronic uncertainties computed with different interaction models

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 22

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 2. “Bracketing” with different models can be a good estimate, sometimes

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 23

Hadronic uncertainties below 200 GeV

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 24

Hadronic uncertainties for high energy leptons

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 25

Relevant particles for lepton production

pion decay kaon decay charm decay muon decay kaon decay charm decay Muon neutrinos Electron neutrinos

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 26

Relation between lepton and cosmic ray energy

Energy range covered by particle accelerators.

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Anatoli Fedynitch | 35th ICRC, 2017, Busan, South Korea | 2017/07/10 | Page 27

A state-of-the-art calculation of atmospheric lepton fluxes

35th International Cosmic Ray Conference 2017, Bexco, Busan, South Korea

Importance of high precision atmospheric lepton flux prediction

Importance of high precision atmospheric lepton flux prediction

Transport equations (hadronic cascade equations)

Transport equations (hadronic cascade equations)

Our tools: MCEq - open-source cascade equation solver

> Simultaneous integration of several thousands kinetic equations > Energy range 1 (30) GeV – 1011 GeV > All models included > High optimization: multi-core, GPU, … (BLAS, MKL, CUDA) (~milli-seconds) > MIT licensed @ https://github.com/afedynitch/MCEq

Models of the comic ray spectrum at the top of the atmosphere

> None of the shown models extends

error estimates > GST-X and HXa are quite extreme assumptions for UHECR

GSF flux model (talk by H. Dembinski 19th July 14:45)

GSF flux model (talk by H. Dembinski 19th July 14:45)

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 

Implementation of “Barr et al.” in a numerical scheme

> Compute partial derivatives wrt. phase-space regions, i.e. > No correlations between phase-space regions (as in Barr et al.) or add. correlations

Elements of Jacobian (numerical) Error propagation Charm

Implementation of “Barr et al.” in a numerical scheme

> Compute partial derivatives wrt. phase-space regions, i.e. > No correlations between phase-space regions (as in Barr et al.) or add. correlations

Elements of Jacobian (numerical) Error propagation Charm

Charm

Uncertainties of lepton fluxes

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

Uncertainties of lepton ratios

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

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

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

Conclusions

We developed a high >

Hadronic uncertainties: current state of the art

Hadronic uncertainties computed with different interaction models

Hadronic uncertainties computed with different interaction models

Hadronic uncertainties below 200 GeV

Hadronic uncertainties for high energy leptons

Relevant particles for lepton production

Relation between lepton and cosmic ray energy

Energy range covered by particle accelerators.

Hadrons in MCEq