CTA 報告 187:
ハドロン相互作用モデルとCTA
M. Ohishi1, L. Arbeletche2, V. de Souza2, G. Maier3, K. Bernlöhr4,
A. Moralejo5, J. Bregeon6, L. Arrabito6, T. Yoshikoshi1
1ICRR, the Univ. of Tokyo, 2IFSC, Univ. of Saõ Paulo,

3DESY, 4MPIK, 5IFAE, The Barcelona Inst. of Sci. & Tech.,
6LUPM, Univ. of Montpellier

Contents of this talk based on
Ohishi M et al., J. Phys. G: Nucl. Part. Phys. 48 075201 (2021)

Outline• Introduction• Simulation without detector response– p0 spectrum• Simulation with detector response (CTA prod3b, baseline
configuration)– Reconstructed energy– Basic shower parameters– Multivariate Analysis (MVA) parameter– g-ray sensitivity• Possibility of the interaction model verification with CTA• Conclusion
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Introduction: indirect/direct g-ray observations
Directprimary charge→ most important info for thescreening of charged cosmicrays

Indirectprimary charge → cannot be measured*
Primary particle
identification byshower images
IACT:Imaging
Atmospheric
Cherenkov
Telescope

Cherenkov lightIACTs(figure from NASA GSFC website)2,000 m a.s.l.

ExtensiveAir Shower (EAS)

surface particle
detectors
4,000 m a.s.l.

muons → strong evidence of
hadronic origin of the primary✓ Particle identification (g or not) is more difficult in indirect observations→ higher background level due to charged cosmic rays
* Except for IACT observations of heavy nuclei in limited situations2

Proton-induced shower images in IACTs••

EASs from cosmic-ray protons : sub-structures‒ EM sub-showers from p0‒ Muons from pWide variation in observed images

Schematic diagram of a protoninduced EAS
primaryprotonCherenkov Image samples for 1 TeV protonz : 0 deg, Impact Parameter : 120 m,
first interaction height : 20km, target nucleus: Nitrogen (all fixed)pv

m-arcmmv
sub-showers

sub-showers

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Proton-induced shower images in IACTs•

Previous studies on nature of g-like proton events:
Maier+ (2007), Sitarek+ (2018), Sobczyńska (2008, 2015) etc.

••

Schematic diagram of a g-like EAS

Emission of energetic p0 → g -like shower
Rate of g-like events depends on p0 spectrum

In case ofEp0 close to Eprimaryprimaryproton

High max Ep0 image samples for 1 TeV protonz : 0 deg, Impact Parameter : 120 m,first interaction height : 20km, target nucleus: Nitrogen (all fixed)

pmv

mv

… g- like…

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g-ray sensitivity (CTA case)Dif. Sens. of CTA South array, 50 h, z = 20deg, point sourcet: obs. time

• Background  misidentified
cosmic-ray protons andelectrons

t0
approximately  𝑆/ 𝐵*

t-1• Efficiency of BG rejection in
the analysis affects thesensitivity

BGrate [1/s]t-1/2e- dominates• At the trigger level, g-ray eventsaccount for only <1 % (even forbright sources)

BG rate• Event selection is optimized
considering a balance of BG
rejection and signal loss

* Li &Ma (1983) Eq. (17) with a = 0.2,for CTA case5

Monte Carlo Simulations• Tested hadronic interaction models– QGSJET-II-03 (pre-LHC) in CORSIKA 6.99
– QGSJET-II-04, SIBYLIL2.3c, EPOS-LHC (post-LHC) inCORSIKA 7.69
• Simulation w/o detector response– p0 spectra, energy fraction consumed in EM
components
Current public CTA
performance plot:• Simulation w/ detector (CTA) response”Alpha configuration"– prod3b baseline configuration (“Omegais used as the first
construction phaseconfiguration”), South site array– Reconstructed energy, collection area,
basic shower parameters, MVA parameter, g-ray
sensitivity
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Simulation w/o det. response: p0 spectrum
0.1 

Eprimaryp0 spectra for mono-energetic
primary proton of 1 TeV

Eprimary• p0 spectrum at the high energyedge affects g-like event rate
• Tested models show differentfeatures• Harder spectrum→ higher BG rate is expected
EPOS-LHC → SIBYLL2.3c→ QGSJET-II-03  QGSJET-II-04

Difference 
toward high-E region

As for g-like event rate, effect of• different model characteristics
is stronger than• parameter tuning by LHC data(since QGSJET-II-03  QGSJET-II-04)

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Simulation w/ detector response:
Reconstructed energy
Mean Reconstructed Energy Erecg/True Energy VS True Energy
Trigger bias& m →e + 𝜈 + 𝜈ҧp →m + n• Proton events,
before g-like event
selection• Erecg is estimatedp + N → p0 + p  + 
1/3
assuming all theevents are g-rays• Mean Erecg
5%approaches to 1/3(= energyconsumed in p0) inmoderately low-Eregion• In mean Erecg, a difference of 5-7 % between models is seen
• Difference in Erecg propagates to a difference of 8-12% in proton shower rate
at a certain Erecg, assuming spectral index of -2.62

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Simulation w/ detector response:
Reconstructed energy
Mean Reconstructed Energy Erecg/True Energy VS True EnergypTrigger bias
& m →e + 𝜈 + 𝜈ҧp →m + nmp + N → p0 + p  + n1/3p5%mn• In mean Erecg, a difference of 5-7 % between models is seen
• Difference in Erecg propagates to a difference of 8-12% in proton shower rate
at a certain Erecg, assuming spectral index of -2.62

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Basic shower parameters
MRSW, Erecg : 1 -10 TeV

Width : lateral size of an EAS
Length : longitudinal size of an EAS

normalized byhistogram areas
MRSL

Height of Shower max.

MRSW/L: Mean Reduced Scaled
Width/Length (Aharonian+ 2006)

E> 1 TeV : lateral size is the mostimportant for g/h separation• EPOS-LHC & SIBYLL2.3c have more
events in g-like regions• QGSJET-II-03  QGSJET-II-04
in g-like region, but they are
different in large MRSW(proton-like) region

10Multivariate analysis (MVA) parameters• A single index for g/h separation• Boosted Decision Tree (BDT) in this work with 11 input parameters• EPOS-LHC and SIBYLL2.3c show higher residual BG rate than the two QGSJET-IImodels at a same signal acceptance
BDT distribution, 0log10(Erec/TeV)0.75

BG acceptance VS signal acceptanceHigh BG

normalizedby areasLow BG

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g-ray sensitivity (prod3b, South site array)
Differential sensitivity, z=20deg, point source

Background rate
50 h case

50 h case

••

+30%

+100%

Differences of factor 2 (+100%) in BG rate, ~30% in g-ray sensitivity between models
Relation between models and its energy dependence is consistent with theexpectations from simulations without detector response

12Possibility of the interaction model
verification with CTA
MVA (BDT) parameter, Erecg : 1- 10 TeV

g-likep-like

contribution of e- is considered+100%

An identical BDT (trained with QGSJET-II-03 proton and g)
is used to evaluate BDT response• CTA → expected to have asignificant capability of model
verification with variousobservables:‒ cosmic ray rate
‒ shower shape parameters‒ muon numbers‒ g-like event rateetc.
• Merit of using g-like event rate:‒ Difference between models
becomes large (due to p0spectral feature)‒ Verification with almost pure
proton (among CR nuclei) ispossible• No dedicated observation data isneeded13

Possibility of the interaction model
verification with CTA• One of the problems in theverification of interaction models
with air shower experiments:Composition?

Interaction?

e.g. muon production depends on both of primary
nuclei type and hadronic interaction.....

TeVZyla et al. (Particle Data Group, 2020)• Recent direct measurements at veryhigh energy limit uncertainty incosmic ray composition• Feedback from the current IACTs on
the interaction model verification isencouraged!
(VERITAS, H.E.S.S., MAGIC….)
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Conclusion• Effect of the uncertainty in the hadronic interaction models on theestimation of the g-ray sensitivity of CTA was investigated• Regarding the South site array of prod3b baseline configuration,differences of– factor 2 in background rate
– ~30% in differential g-ray sensitivity (in 1 – 30 TeV)
are seen between the tested four interaction models(QGSJET-II-03, QGSJET-II-04, EPOS-LHC, SIBYLL2.3c)• These results are consistent with the features of the secondary
particles in EASs, especially p0 spectrum• CTA will have a significant capability for verification of interaction
models, without requiring any dedicated observation time
• Feedback from current IACTs is also encouraged!
For more detail, see:
Ohishi M et al., J. Phys. G: Nucl. Part. Phys. 48 075201 (2021)

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