Evaluation of the CALET
Cosmic-Ray Electron Spectrumwith regard to Dark Matter
ダークマターの懇談会 2019
Waseda University

Holger Motz
Global Center for Science and Engineering,
Faculty of Science and Engineering,
Waseda University

Dark Matter Search inElectron+Positron Cosmic Rays
●Basic Idea (as in most indirect DM search):–

Background is astrophysical power law spectrum
from stochastic acceleration–Signal is peaked due to cut off at (half) the mass ofthe dark matter particle from annihilation (decay)→ Search for “structures” in the spectrum●Complications:–Dark Matter spectrum softened by decay of primaryannihilation (decay) products and propagation–

Astrophysical background spectrum from multiple
sources, deviation from power law due to escapemechanism and propagation effects possible

CALET Electron+Positron Spectrum
Structures ! (?)

Interpretation of structures
as Dark Matter signatures

O. Adriani et al.
Phys. Rev. Lett. 120,261102 (2018)–

Interesting speculation–

Allows to compare
model with hints fromother search methods→ to be taken seriously
if finding agreement

Explanation of structures by astrophysical origin–

Refine background model for Dark Matter search,
investigate if it impacts the constraints that can be
set on Dark Matter properties (limits)

Background Model
The background model should describe thedata well (give a good fit) with as few
parameters as possible● It should be as much as possible physics
motivated and variation of parameters shouldreflect uncertainty in physical processes● It should take into account correlation withother results e.g. consider the source of thepositron excess→ assume pulsar(s) as mundane option*→ to constrain their properties CALET e- + e+
data combined with AMS-02 e+-only data
●AMS-02 Positron Flux up to 1 TeV
M. Aguilar et al.
Phys. Rev. Lett. 122, 041102 (2019)
Error on energy converted toerror on flux using the publishedpower law index: σ Φ(E )=Φ( σ E / E)( γ−1)

* compared to:- DM-only origin of thepositron excess- more complicatedsecondary production in
CR propagation thanstandard assumptionModel for the Local e & e Spectra-●Primary electron spectrum with low-energy spectral break and exponential cut-off,secondary electrons, secondary positrons, extra pulsar source for positron excess
Φ ele = C e E●+−(γ e − Δ γ e )EΔ γe s −Ecuts( ( ) )E1+EBe( ) +C Φds-s(e )+Φ ex ; Φ pos = C s Φ s (e ) +Φ ex ; Φ tot =Φ ele +Φ pos-

Fitted to CALET data and AMS-02 positron flux for E>10GeV(E<10 GeV: charge and time dependent solar modulation)

Smooth break in the
primary electron spectrum

Pulsar electron + positron

Pulsar positron

Secondarypositrons

Exponential
cut-offof primaryelectronspectrum
at Ecut = 4 TeV

Solar modulation:● force fieldapproximation● potential for bothcharge signs:
500 MVPropagation Model(Calculation with DRAGON)●Nuclei spectra independent of local source distribution→ Propagation parameters tuned to explain nuclei measurements
Proton Spectrum:

Boron/Carbon ratio:

CALET measured stronger
hardening → working on
revision of model28

2D0 =1.3⋅10 cm /s @ 4 GV
δ=0.6(R >300 GV →0.33)
L=±3 kpc
γ i=2.32

Smooth break in
diffusion coefficient:R δR δ −s δ
D=D0/ 1+R0Rbs( )( ( ) )llh

No break in injection
spectrum needed

Flux of secondary electrons and positrons interpolated and used infitting with rescaling factor Cs as free parameter in range [0.5 , 2.0]
● Propagation parameters consistently used also for pulsar and DM●

Model for the Local e & e Spectra-●Primary electron spectrum with low-energy spectral break and exponential cut-off,secondary electrons, secondary positrons, extra pulsar source for positron excess
Φ ele = C e E●+−(γ e − Δ γ e )EΔ γe s −Ecuts( ( ) )E1+EBe( ) +C Φds-s(e )+Φ ex ; Φ pos = C s Φ s (e ) +Φ ex ; Φ tot =Φ ele +Φ pos-

Fitted to CALET data and AMS-02 positron flux for E>10GeV(E<10 GeV: charge and time dependent solar modulation)

Smooth break in the
primary electron spectrum

Pulsar electron + positron

Pulsar positron

Secondarypositrons

Exponential
cut-offof primaryelectronspectrum
at Ecut = 4 TeV

Solar modulation:● force fieldapproximation● potential for bothcharge signs:500 MV

Calculation of Flux from Pulsars
Analytic solution of propagation equation for instantaneous
point source (Green's function) [e.g. Eur. Phys. J. C. 76:229 (2016)]
adapted to propagation model with break in diffusion coefficient
Q0 ηE1−Emax

2E / Ecutr
γ−2 −−
1− E / E max r 2dif( )D( E) t E
E1r =21− 1−; E =()√ 1−δ(EE) E [ E E ] d [log(D (bE))]t
D( E)= D ( ) / 1+( ); δ ( E)=( E )Ed [log ( E)]ϕpulsar =π3/2 3difr

difE−γe(1−δ(E ))maxdifmaxmax

δh−δl ssδl000 difb

free parameters: efficiency η, index γ , cutoff energy Ecutdetermined parameters: D 0 , δl , δh , E B , s , b 0 (from propagation model)
total energy Q 0 , distance r , diffusion time t dif (from ATNF catalog)Model for the Local e & e Spectra-●Primary electron spectrum with low-energy spectral break and exponential cut-off,secondary electrons, secondary positrons, extra pulsar source for positron excessΦ ele = C e E●+−(γ e − Δ γ e )EΔ γe s −Ecuts( ( ) )E1+EBe( ) +C Φds-s(e )+Φ ex ; Φ pos = C s Φ s (e ) +Φ ex ; Φ tot =Φ ele +Φ pos-

Fitted to CALET data and AMS-02 positron flux for E>10GeV(E<10 GeV: charge and time dependent solar modulation)

Smooth break in the
primary electron spectrum

Pulsar electron + positron

Pulsar positron

Secondarypositrons

Exponential
cut-offof primaryelectronspectrum
at Ecut = 4 TeV

Solar modulation:● force fieldapproximation● potential for bothcharge signs:500 MV

Systematic Uncertainties as
Fitted Nuisance Parameters
Systematic uncertainties with energy
dependence listed in the paper’s S.M.
● Normalization● Tracking● Charge Selection● Electron Identification● Monte Carlo

Systematic shift of fit function, squared weight ofeach uncertainty added to the total χ² of the fit:(2χ 2CALET = ∑i(ϕi + ∑k Δ k wk −J i )σ2i)+ ∑ w 2kki: data point index
k: uncertainty index
Uncertainties ofTrigger andBDT (protonrejection) arestill added
quadratically tostatistical error
Nuisance
parameter
weights
contribute
2.13 to χ²

Model for the Local e & e Spectra-●Primary electron spectrum with low-energy spectral break and exponential cut-off,secondary electrons, secondary positrons, extra pulsar source for positron excess
Φ ele = C e E●+−(γ e − Δ γ e )E
Δ γe s −Ecuts( ( ) )E1+
EBe( ) +C Φds-s(e )+Φ ex ; Φ pos = C s Φ s (e ) +Φ ex ; Φ tot =Φ ele +Φ pos-Fitted to CALET data and AMS-02 positron flux for E>10GeV(E<10 GeV: charge and time dependent solar modulation)

Smooth break in theprimary electron spectrum

Pulsar electron + positron

Pulsar positron

Secondarypositrons

Exponential
cut-offof primaryelectronspectrum
at Ecut = 4 TeV

Solar modulation:● force fieldapproximation● potential for bothcharge signs:
500 MVAdding Dark Matter●●Initial assumption that the Monogem pulsar is the reason for the positron excess
Starting from this pulsar-only fit, flux from Dark Matter annihilation(calculated with PYTHIA, propagated with DRAGON using common propagation
parameters, NFW profile, 0.3 GeV/cm3 local density) is added and the boost
factor increased while repeating the fit each time to adapt other parameters
Example: 350 GeV DM annihilation
to electron + positron

DM flux
increasedAdding (too much) Dark Matter●●If adding Dark Matter flux with large scale (boost) factor, the data does notmatch the resulting spectral feature → χ2 increases
Boost factor at which χ2 reaches 95 % CL corresponds to a limit on the DarkMatter annihilation rate → repeat for many Dark Matter masses ...
Example: 350 GeV DM annihilation
to electron + positron
Fit withDark Matterexcluded at
95%CLDM flux
increased

Limits on Dark Matter Annihilation
as a Function of Dark Matter Mass
Fermi-LAT limits fromPhys. Rev. Lett. 115,231301 (2015) (SM)electron+positroncomplementary togamma-ray search→ different sensitivity toannihilation channels→ different target region(galactic neighborhood
vs. dwarf galaxies)

Limits on Dark Matter Decay as aFunction of Dark Matter Mass

Adding (a bit of) Dark Matter●●χ2 decreases initially before increasing →best fit INCLUDING Dark Matter signal
Structure near 350 GeV better modeled

Example: 350 GeV DM annihilation
to electron + positron
Fit withDark Matter
better than
without

Pulsar +DM flux

Small
addition ofDM flux

Fit Improvement byModeling 350 GeV Step-like
Structure with Dark Matter Signature
Pulsar onlyPulsar + 350 GeV DM- χ2 improvement compared to single pulsar case:
Full energy range (CALET & AMS-02 data) : Δχ2 = 6.6 (33.9 → 27.3)
100 GeV – 3 TeV (CALET data only) : Δχ2 = 7.0 (13.3 → 6.3)

Fit Improvement and Best x-Section
against Dark Matter Mass
Direct annihilation of Dark Matter to electron-positron pair
350 GeV

BF
101.4 TeV

Fit Improvement and Best Lifetime
against Dark Matter Mass
Direct decay of Dark Matter to electron-positron pair
700 GeV

2.8 TeVFit Improvement byModeling ~ 1 TeV Step/Peak-like
Structure with Dark Matter Signature
Pulsar only

Pulsar + 1.4 TeV DM- χ2 improvement compared to single pulsar case:
Full energy range (CALET & AMS-02 data) : Δχ2 = 3.9 (33.9 → 30.0)
100 GeV – 3 TeV (CALET data only) : Δχ2 = 4.8 (13.3 → 8.5)
The spectrum from DM annihilation to electron-positron pairs can’t model this“peak” well, but significance anyway limited due so larger statistical errors

Refining the Pulsar Model●Accelerated particles may be trapped in pulsar wind nebula for the lifetime of thenebula, assumed to be up to ~ 100000 years [e.g. Phys. Rev. D. 80.063005 ]→ Introduce release time Tr as additional free parameter subtracted from the age ofthe pulsar to get time of cosmic ray propagation tdif●

Scan in steps of 1000 years → optimal value for Monogem: 20000 years●

Scan over cutoff energy of primary energy spectrum, best value 10 TeV
χ2 improvesby 2.2 from33.9 to 31.7

Multi-Pulsar Model●●●

Calculate flux of all pulsars in ATNF catalog with age < 1 Myr and distance < 1 kpc(22 pulsars) scanning over power law index [1..3] and release time [0 .. 100 kyr]Select pulsars contributing more then 5% of total pulsar flux at any energy under any
condition → 13 “relevant” pulsars used in fit
Same free parameters (γ, η, Ecut, Tr ) assumed for all pulsars, but initial energy,distance and age different (calculated from ATNF catalog data)

Fit Improvement byModeling 350 GeV Step-like
Structure with Multiple Pulsars
Monogem only

13 Pulsars- χ2 improvement compared to optimized single pulsar case:
Full energy range (CALET & AMS-02 data) : Δχ2 = 5.5 (31.7 → 26.2)
100 GeV – 3 TeV (CALET data only) : Δχ2 = 3.6 (11.4 → 7.8)
No additional free parameters→ multiple pulsar model clearly favored over single pulsar (Monogem)

Limits on Dark Matter Annihilation
with Multi-Pulsar Background

Only small deviation fromsingle-pulsar limits especially fordirect electron+positron channel

Variability of Background●●Why not vary the parameters of all the pulsars individually?
–

Technical: Fitting not feasible, since minimized function notconstrained enough (no unique minimum)–

Physical: Pulsar parameters should be assumed approximately
equal with limited random variation for individual pulsars, notfine-tuned to hide the dark matter signal.

To improve the limits on Dark Matter, the individual nearby sourcesof the astrophysical background (SNR and pulsars) and theirparameters must be identified, a goal to which CALET contributes

Summary, Conclusions and Outlook
●●

●

●

●

●

Structures exist in the CALET spectrum, a significant improvement of the fit quality
can be achieved by modeling the step near 350 GeV:–

By adding the predicted signal from Dark Matter annihilation into
electron-positron pairs–

By combining the flux from all known nearby pulsars with same injection
parameters as the extra source causing the positron excess

Limits on Dark Matter annihilation and decay from the CALET electron+positron
spectrum give a strong constraint on two-body annihilation or decay of Dark Matterdirectly to electron+positron pairs
The limits change only slightly if using the multi-pulsar model as backgroundinstead of single pulsar model
The observed structure is potentially statistically significant and could be a hint forthe presence of individual local astrophysical sources ( or Dark Matter ? )The variability in astrophysical background necessary to explain it does notinvalidate the Dark Matter limits from using a simpler single-pulsar model
Reduction of systematic errors and better understanding of their energy
dependence expected to further increase the precision of the CALET measurementin the future, improving the limits and possibly the significance of structures (if real)
These results are part of the research outcome of Waseda University Grant for Special Research Projects No. 2019C-539