PPPC4DMID.html

If you are interested in the assessment of QCD uncertainties on the fluxes at production, please see the numerical results (by S. Amoroso et al.) and cite:
    S. Amoroso, S. Caron, A. Jueid, R. Ruiz de Austri, P. Skands,
    "Estimating QCD uncertainties in Monte Carlo event generators for gamma-ray dark matter searches",
    arXiv 1812.07424, JCAP 05 (2019) 007.

Propagation functions for electrons and positrons everywhere in the Galaxy:

Energy loss coefficient function b[E, r, z] for electrons and positrons in the Galaxy: Mathematica function btot.m, refer to the notebook Sample.nb for usage.

Annihilation
Positrons:	The file ElectronHaloFunctGalaxyAnn.m provides the halo functions I(x,E_s,r,z) at a point (r,z) in the Galaxy. [Note: very large file, almost 4GB.] The notebook Sample.nb shows how to load and use it.

Decay
Positrons:	The file ElectronHaloFunctGalaxyDec.m provides the halo functions I(x,E_s,r,z) at a point (r,z) in the Galaxy. [Note: very large file, almost 4GB.] The notebook Sample.nb shows how to load and use it.

Propagation functions for charged cosmic rays at the location of the Earth:

Annihilation
Positrons:	The file ElectronHaloFunctEarthAnn.m provides the halo functions I(x,E_s,r_Earth) at the location of the Earth. The notebook Sample.nb shows how to load and use it.

	Table of fit coefficients for the reduced halo function I(λ) (in the approximated formalism - see paper).

Antiprotons:	Table of fit coefficients for the propagation function R(T).

Antideuterons:	Table of fit coefficients for the propagation function R(T).

Decay
Positrons:	The file ElectronHaloFunctEarthDec.m provides the halo functions I(x,E_s,r_Earth) at the location of the Earth. The notebook Sample.nb shows how to load and use it.

	Table of fit coefficients for the reduced halo function I(λ) (in the approximated formalism - see paper).

Antiprotons:	Table of fit coefficients for the propagation function R(T).

Antideuterons:	Table of fit coefficients for the propagation function R(T).

Fluxes of charged cosmic rays at the Earth, after propagation:

Annihilation
Positrons:	Mathematica function: the file ElectronFluxAnn.m provides the spectra Log₁₀ [d Φ/d Log₁₀ E ]. Refer to the notebook Sample.nb for usage.

	Numerical table: provides the spectra dΦ/d Log₁₀E. The columns are: [ m_DM, halo, propagation, Log₁₀E , dΦ/d Log₁₀E for 28 primary channels ]. The spectra are computed at a benchmark annihilation cross of <σv> = 10^-26 cm³/s and renormalized multiplying by (m_DM/GeV)². Units are particles/(cm² s sr).

Antiprotons:	Mathematica function: the file ProtonFluxELDRAnn.m provides the spectra Log₁₀ [d Φ/d Log₁₀ K ]. Refer to the notebook Sample.nb for usage.

	Numerical table: provides the spectra dΦ/d Log₁₀K. The columns are: [ m_DM, halo, propagation, Log₁₀K , dΦ/d Log₁₀K for 28 primary channels ]. The spectra are computed at a benchmark annihilation cross of <σv> = 10^-26 cm³/s and renormalized multiplying by (m_DM/GeV)². Units are particles/(m² s sr).
	The file ProtonFluxAnn.m provides the spectra without ELDR (Energy Losses including tertiaries and Diffusive Reacceleration, see 1412.5696 for details): this is now superseded and provided here only for the purpose of comparison with previous calculations.

Antideuterons:	Mathematica function: the file DeuteronFluxAnn.m provides the spectra Log₁₀ [d Φ/d Log₁₀ (K_d/n) ]. Refer to the notebook Sample.nb for usage.

	Numerical table: provides the spectra dΦ/d Log₁₀(K_d/n). The columns are: [ m_DM, halo, propagation, Log₁₀(K_d/n) , dΦ/d Log₁₀(K_d/n) for 28 primary channels ]. The spectra are computed at a benchmark annihilation cross of <σv> = 10^-26 cm³/s and renormalized multiplying by (m_DM/GeV)². Units are particles/(m² s sr).

Decay
Positrons:	Mathematica function: the file ElectronFluxDec.m provides the spectra Log₁₀ [d Φ/d Log₁₀ E ]. Refer to the notebook Sample.nb for usage.

	Numerical table: provides the spectra dΦ/d Log₁₀E. The columns are: [ m_DM, halo, propagation, Log₁₀E , dΦ/d Log₁₀E for 28 primary channels ]. The spectra are computed at a benchmark decay life of τ = 10²⁶ s and renormalized multiplying by (m_DM/GeV). Units are particles/(cm² s sr).

Antiprotons:	Mathematica function: the file ProtonFluxELDRDec.m provides the spectra Log₁₀ [d Φ/d Log₁₀ K ]. Refer to the notebook Sample.nb for usage.

	Numerical table: provides the spectra dΦ/d Log₁₀K. The columns are: [ m_DM, halo, propagation, Log₁₀K , dΦ/d Log₁₀K for 28 primary channels ]. The spectra are computed at a benchmark decay life of τ = 10²⁶ s and renormalized multiplying by (m_DM/GeV). Units are particles/(m² s sr).
	The file ProtonFluxDec.m provides the spectra without ELDR (Energy Losses including tertiaries and Diffusive Reacceleration, see 1412.5696 for details): this is now superseded and provided here only for the purpose of comparison with previous calculations.

Antideuterons:	Mathematica function: the file DeuteronFluxDec.m provides the spectra Log₁₀ [d Φ/d Log₁₀ (K_d/n) ]. Refer to the notebook Sample.nb for usage.

	Numerical table: provides the spectra dΦ/d Log₁₀(K_d/n). The columns are: [ m_DM, halo, propagation, Log₁₀(K_d/n) , dΦ/d Log₁₀(K_d/n) for 28 primary channels ]. The spectra are computed at a benchmark decay life of τ = 10²⁶ s and renormalized multiplying by (m_DM/GeV). Units are particles/(m² s sr).

J factors for prompt gamma rays:

Annihilation

Mathematica function: the file JAnn.m provides Log₁₀ [J(θ)].
Refer to the notebook Sample.nb for usage.

Decay

Mathematica function: the file JDec.m provides Log₁₀ [J(θ)].
Refer to the notebook Sample.nb for usage.

Fluxes of Inverse Compton gamma rays:

Annihilation

Mathematica function: the file IICAnn.m provides the Inverse Compton halo functions I_IC(E_s,E_γ,l,b).
Refer to the notebook Sample.nb for usage.

Such notebook contains also a Mathematica code bite to compute the resulting IC flux.

Decay

Mathematica function: the file IICDec.m provides the Inverse Compton halo functions I_IC(E_s,E_γ,l,b).
Refer to the notebook Sample.nb for usage.

Such notebook contains also a Mathematica code bite to compute the resulting IC flux.

Fluxes of bremsstrahlung gamma rays:

Annihilation

Mathematica function: the file IBremAnn.m provides the bremsstrahlung halo functions Ibrem(E_s,E_γ,l,b).
Refer to the notebook Sample.nb for usage.

Decay

Mathematica function: the file IBremDec.m provides the bremsstrahlung halo functions I_brem(E_s,E_γ,l,b).
Refer to the notebook Sample.nb for usage.

Fluxes of synchrotron radiation:

Annihilation

Mathematica function: the file ISynAnn.m provides the synchrotron halo functions Isyn(E_s,ν,l,b).
Refer to the notebook Sample.nb for usage.

Decay

Mathematica function: the file ISynDec.m provides the synchrotron halo functions I_brem(E_s,ν,l,b).
Refer to the notebook Sample.nb for usage.

Fluxes of extragalactic gamma rays:

Cosmological Boost factor B: Mathematica function BoostF.m, refer to the notebook Sample.nb for usage.

Optical Depth of the Universe: transparency factor Exp[-τ ] for gamma rays: Mathematica function OpticalDepth.m, refer to the notebook Sample.nb for usage.

Annihilation

Mathematica function: the file EGgammaFluxAnn.m provides the spectra Log₁₀ [d Φ/d Log₁₀ E ].
Refer to the notebook Sample.nb for usage.

Decay

Mathematica function: the file EGgammaFluxDec.m provides the spectra Log₁₀ [d Φ/d Log₁₀ E ].
Refer to the notebook Sample.nb for usage.

DMν : Neutrinos from the Sun:

DM annihilation rate in the Sun: Mathematica function GammaAnn.m, refer to the notebook Sample.nb for usage.
Neutrino energy spectra at production: Mathematica function dlNnudlxEW.m, refer to the notebook Sample.nb for usage. [03 jun 2015] Warning: some bugs in these files have been brought to our attention, we are working to fix them. Sorry for the inconvenience.
Neutrino energy spectra at detection: Mathematica function dlNnudlxEarth.m, refer to the notebook Sample.nb for usage. [03 jun 2015] Warning: some bugs in these files have been brought to our attention, we are working to fix them. Sorry for the inconvenience.

Log of changes and releases:

[30 oct 2011] Fixed typo in Sample.nb about the units of the spectra of positrons (the units are particles/(cm^2 sec sr), not particles/(m^2 sec sr)). No new Release.

[30 oct 2011] Fixed bug in the labelling of the files 'JAnn.m' and 'JDec.m' (which was causing runaway loops when evaluated for some profiles). No new Release.

[29 may 2012] Uploaded new version of extragalactic gamma rays. They are an anticipation of a new Release, which will appear soon.

[21 aug 2012] New Release: 2.0 . Main modifications:

Included higgs boson channel hh with mass mh =125 GeV. All previous channels hmhm removed.
Fixed normalization and interpolation problems in 'dlNdlxEW.m' and 'dlNdlxPythia.m' (and, as a consequence, in all derived ingredients), notably in the γγ channel.
New version of extragalactic gamma rays, fixing some mistakes in the redshift dependence, the energy dependences and the impact of absorption. Also improved interpolation.
New version of the 'Optical Depth of the Universe', employing updated models of EBL (Extragalactic Background Light), fixing the redshift dependence and with a better interpolation.

This Release corresponds to version 4 of 1012.4515 on arXiv and to the Erratum on JCAP.

[21 mar 2013] Fixed 2 broken links.

[23 dec 2013] Fixed some typos in Sample.nb file.

[23 dec 2013] New Release: 3.0 . Main modification: addition of the section 'DMν : Neutrinos from the Sun', based on 1312.6408.

[03 aug 2014] Note on Mathematica v10 compatibility: Mathematica v10, released in 2014, does not assure compatibility with the InterpolatingFunction feature of the previous versions. Wolfram Customer Support can only provide a manual solution (highly unpractical). We suggest that you keep using Mathematica v9.

[16 nov 2014] Note on Mathematica v10 compatibility: the issue above is now solved (Wolfram released a patch of Mathematica v10).

[17 nov 2014] Fixed an interpolation issue mainly affecting ProtonFluxAnn and ProtonFluxDec at DM masses larger than 50 TeV and 100 TeV respectively. No new Release.

[15 jan 2015] New Release: 4.0 . Main modification: addition of 'ELDR' (Energy Losses including tertiaries and Diffusive Reacceleration) in the computation of the antiproton fluxes, based on 1412.5696.

[06 may 2015] New Release: 5.0 based on the results in 1505.01049. Main additions and modifications:

New version of the 'Energy loss coefficient function' b[E,r,z].
New version of the 'Propagation functions for electrons and positrons everywhere in the Galaxy'.
New version of the 'Propagation functions for charged cosmic rays at the location of the Earth', for positrons.
New version of the 'Fluxes of charged cosmic rays at the Earth, after propagation', for positrons.
New version of the 'Fluxes of Inverse Compton gamma rays', functions IICAnn.m and IICDec.m.
Addition of the 'Fluxes of bremsstrahlung gamma rays'.
Addition of the 'Fluxes of synchrotron radiation'.

[03 and 14 nov 2015] Fixed some broken links.

[09 dec 2015] Fixed bug in the labels for magnetic fields in one of the numerical tables for positrons at the Earth, after propagation (affected file: AfterPropagation_Ann_positrons.dat).

[13 jan 2016] New Release: 6.0 based on the results in 1511.08787 on spectra at production in models with cascade decays in the hidden sector. These results are contributed by G. Elor, N. Rodd, T. Slatyer and W. Xue.

[23 may 2016] Improvements and bug fixing in the section 'Code bites to compute fluxes of ICS gamma rays' in the Sample.nb file. No new release.

[28 jan 2018] Fixed bug in the fluxes of positrons at Earth after propagation. The code was returning 'Indeterminate', instead of a very small number, for energies near the DM mass (affected files: ElectronFluxAnn.m, ElectronFluxDec.m, AfterPropagation_Ann_positrons.dat, AfterPropagation_Dec_positrons.dat). No new release.

[31 jan 2021] Refined the energy resolution in the fluxes of positrons at Earth after propagation (affected files: ElectronFluxAnn.m, ElectronFluxDec.m, AfterPropagation_Ann_positrons.dat, AfterPropagation_Dec_positrons.dat). No new release.

Contact: marco.cirelli@gmail.com .

Last updated: Sun 23 Oct 2022

Mathematica functions:	The file dlNdlxEW.m provides the spectra Log₁₀ [d N/d Log₁₀ x ]. The notebook Sample.nb shows how to load and use it.

Numerical tables:	Each table provides the spectra dN/d Log₁₀x of stable SM particles (positrons, antiprotons...), normalized per one annihilation. The columns are: [ m_DM, Log₁₀x , dN/d Log₁₀x for 28 primary channels ]. The primary channels are: DM DM --> e_L⁺e_L^-, e_R⁺e_R^-, e⁺e^-, μ_L⁺μ_L^-, μ_R⁺μ_R^-, μ⁺μ^-, τ_L⁺τ_L^-, τ_R⁺τ_R^-,τ⁺τ^-, qq, cc, bb, tt, W_L⁺W_L^-, W_T⁺W_T^-,W⁺W^-, Z_LZ_L, Z_TZ_T, ZZ, gg, γγ, hh, ν_eν_e, ν_μν_μ, ν_τν_τ, VV → 4e, VV → 4μ, VV → 4τ. The non-polarized fluxes are just obtained as the appropriate average of the Left and Right or Longitudinal and Transverse ones. The channel into Higgs bosons assumes a Higgs mass of 125 GeV.
	Positrons
	Antiprotons
	Gamma rays
	Electron Neutrinos
	Muon Neutrinos
	Tau Neutrinos
	Antideuterons
	all of the above	All the 7 tables, in a single zipped file.

Mathematica functions:	The file dlNdlxPythia.m provides the spectra Log₁₀ [d N/d Log₁₀ x ]. The notebook Sample.nb shows how to load and use it.

Numerical tables:	Same as above, but here the primary channels are the following 12: DM DM --> e⁺e^-, μ⁺μ^-, τ⁺τ ^-, qq, cc, bb, tt, W⁺W^-, ZZ, gg, γγ, hh.
	Positrons
	Antiprotons
	Gamma rays
	Electron Neutrinos
	Muon Neutrinos
	Tau Neutrinos
	Antideuterons
	all of the above	All the 7 tables, in a single zipped file.

PPPC 4 DM ID - A Poor Particle Physicist Cookbook for Dark Matter Indirect Detection