Precise determination of muon shower content from shower universality property
A. Yushkov, M. Ambrosio, C. Aramo, F. Guarino, D. D'Urso, L. Valore
aa r X i v : . [ a s t r o - ph . H E ] O c t Precise determination of muon shower contentfrom shower universality property
A. Yushkov ∗ , M. Ambrosio , C. Aramo , F. Guarino , , D. D’Urso , L. Valore INFN Sezione di Napoli, 80125, via Cintia, Napoli, Italia Universit`a di Napoli “Federico II”, 80125, via Cintia, Napoli, Italia
Abstract
It is shown, that highly accurate estimation of muon shower content can be performed on the basisof knowledge of only vertical depth of shower maximum X vmax and total signal in ground detector. Theestimate is almost independent on primary energy and particle type and on zenith angle. The study isperformed for 21500 showers, generated with CORSIKA 6.204 from spectrum E − in the energy rangelog 10( E ) [eV]=18.5–20 and uniformly in cos θ in zenith angle interval θ = 0 ◦ − ◦ for QGSJET II/Flukainteraction models. Muon shower content is the key parameter for studies of primary mass composition and test of hadronicinteraction models. Using universality property of extensive air showers (EAS) development [1–6] we proposea simple and precise method to determine muon shower content from vertical depth of shower maximumand total signal (signal in water tanks or in scintillator detector). The study is performed for 21500 showers,generated with CORSIKA 6.204 [7] from spectrum E − in the energy range log 10( E ) [eV]=18.5–20 (withdifferent statistics in 3 energy bins 18.5–19.0, 19.0–19.5 and 19.5–20.0) and uniformly in cos θ in zenithangle interval θ = 0 ◦ − ◦ for QGSJET II [8–10]/Fluka [11, 12] interaction models. Electromagnetic (EM)component thinning was set to 10 − , the observation level was at 870 g/cm . All longitudinal showerscharacteristics and charged particles density were taken directly from CORSIKA output files. The expectedsignal in Auger-like tanks was calculated according to the procedure described in [13, 14] with the use of thesame GEANT 4 lookup tables as in [14].From different aspects of universality of shower development we will be interested only in the dependenceof electromagnetic and muon signals on the distance of shower maximum to the ground. We will beginour consideration from Auger-like experimental setup and consider signal in water Cherenkov tanks at 1000meters. In this case one deals with the situation, where muon contribution to the detector is much largercompared to the EM one due to higher energy losses of muons in tanks. The common way to expressuniversality of electromagnetic signal is to plot it against slant distance to the ground (Fig. 1 and alsoFigure 1 in [4]), showing its quasi-independence on primary particle type. The muon signal functionaldependence on slant distance to the ground DG is also very similar for both proton and iron, but thereis a shift in the normalization (Fig. 1). Since iron showers reach X max earlier than showers from protons,comparison of set of showers from p and Fe at equal DG means the comparison between showers withdifferent zenith angles, but at the same development stage. Passing to comparison of shower characteristicsdependence on vertical distance to ground DG V reveals a very interesting property (see Fig. 2): in thiscase the similarity of functional dependence of muon and EM signals on DG V between p and Fe primariesis preserved, but now also EM signal normalizations are different. This happens because one confrontsshowers, which have the same vertical distance from X vmax to the ground, but once again proton showersare more inclined than iron ones and their EM component attenuates more while reaching the ground from X vmax . The ratio S FeEM /S pEM turns out to be almost equal to the S Fe µ /S p µ one and this allows to state the ∗ Corresponding author; e-mail: [email protected] Muon signal includes only signal from muons, crossing the tank, signal from electromagnetic particles, originating frommuon decays is included in the electromagnetic signal. the ratio of the muon signal to the EM one S µ /S EM is the same for allshowers, reaching the maximum at the same vertical depth X vmax , independently on the primary particle type,primary energy and incident zenith angle (at the least for the energy and angular ranges considered here).This property is illustrated in Fig. 3, where it is shown the dependence of S µ /S EM on X vmax for p, O and Feprimaries in four different energy bins. The functional dependence between X vmax and S µ /S EM turns out tobe very simple and quasi-universal for all energies and primaries. The function in the form X vmax = A ( S µ /S EM + a ) b (1)fits well the data and the fit parameters are quite stable across entire energy range. Having in hand thefunctional dependence of X vmax on ( S µ /S EM ) and using S tot = S EM + S µ one easily gets the equation, whichallows to obtain muon signal from shower vertical depth and total signal in tanks: S fit µ = S tot / (( X vmax /A ) /b − a ) . (2)We calculated the difference between the Monte-Carlo (MC) simulated muon signal S MC µ and the muonsignal, obtained from the fit S fit µ , an example distributions of this value are shown in Fig. 4. In Table 1 wegive mean and RMS values of such distributions for various energy bins, obtained with the unique set of fitparameters A = 538, b = − .
25 and a = − .
22. It is seen, that the estimates of muon signals are unbiasedwith less than 1% deviation of mean reconstructed muon signal from the MC one for all 3 primaries andthe RMS values are small: 8% for protons and around 5% for oxygen and iron. Certainly, application ofspecific coefficients for every energy bin or narrowing of zenith angle interval, or using of more sophisticatedfit functions can even slightly improve the performance of the method, which anyhow is good in its simpleand universal form. The described universal dependence of S µ /S EM on X vmax holds true in the wide intervalof distances and in Fig. 5 we show examples for the distances 200 and 1500 meters from the core, though fordistances closer to the core the function in the form (1) does not describe accurately the data in the entireangular range 0 ◦ − ◦ and it is needed or to split it in two parts or to apply more complex parametrization.The same universality principle holds true in the case of detectors using scintillators and effectivelymeasuring density of charged particles [15]. We have performed the reconstruction of muon densities usingthe dependence of the ratio (muon density D µ )/(electron density D e ) on X vmax in the form same to (1) (seeTable 2 and Fig. 6). It is seen, that when muons and electrons equally contribute to the detector signalthe shower fluctuations play more important role and the accuracy of parametrization is only within 15%,though the estimate is still unbiased.Hence, the new universality property allows to obtain accurate estimates of the muon signal, which arealmost independent on the primary particle type, primary energy and zenith angle for various types ofground detectors. Taking in consideration that the shower universality property was established for differentinteraction models [1–6], we expect that the proposed approach to muon content derivation is not specificonly to QGSJET II/Fluka case.The discovered simple shower universality property in respect to (muon signal/EM signal) ratio, givingaccess to the muon shower content, can open new possibilities as in solution of the global problems, suchas derivation of primary mass composition and understanding of hadronic interactions properties, so in thenumber of more particular tasks (e.g. estimations of primary energy on the basis of pure electromagneticsignal, primary particle type independent corrections to the missing energy in experiments using fluorescentlight etc.). Acknowledgements
We are very grateful to Maximo Ave and Fabian Schmidt for kind permission to use their GEANT 4 lookuptables in our calculations of signal from different particles in Auger water tanks.2
200 0 200 400 600 800 1000 1200 140051015202530 o -65 o o -65 o PSfrag replacements S E M , V E M DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X vmax , g/cm ( D MC µ − D fit µ ) /D MC µ , % D µ /D e Showers -200 0 200 400 600 800 1000 1200 1400468101214161820 o -65 o o -65 o PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , V E M S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X vmax , g/cm ( D MC µ − D fit µ ) /D MC µ , % D µ /D e ShowersFigure 1: EM and muon signals from proton (red squares) and iron (blue crosses) in water Cherenkov tanksat 1000 m vs slant distance from shower maximum to the ground DG in log 10( E )[eV]=18.9–19.0 energy bin -100 0 100 200 300 400 500 60051015202530 o -65 o o -65 o PSfrag replacements S E M , V E M DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X vmax , g/cm ( D MC µ − D fit µ ) /D MC µ , % D µ /D e Showers -100 0 100 200 300 400 500 600468101214161820 o -65 o o -65 o PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , V E M S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X vmax , g/cm ( D MC µ − D fit µ ) /D MC µ , % D µ /D e ShowersFigure 2: EM and muon signals from proton (red squares) and iron (blue crosses) in water Cherenkov tanksat 1000 m vs vertical distance from shower maximum to the ground DG V in log 10( E )[eV]=18.9–19.0 energybin 3 -65 o o -65 o PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X v m a x , g/ c m ( D MC µ − D fit µ ) /D MC µ , % D µ /D e Showers -65 o o -65 o PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X v m a x , g/ c m ( D MC µ − D fit µ ) /D MC µ , % D µ /D e Showers -65 o o -65 o PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X v m a x , g/ c m ( D MC µ − D fit µ ) /D MC µ , % D µ /D e Showers -65 o o -65 o PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X v m a x , g/ c m ( D MC µ − D fit µ ) /D MC µ , % D µ /D e ShowersFigure 3: Ratio of signals in water Cherenkov tanks S µ /S EM at 1000 m vs vertical depth of shower maximum X vmax in four energy bins. Protons — red squares, oxygen — brown diamonds, iron — blue crosses4
20 -10 0 10 200102030405060708090
PEntries 524Mean -0.1739RMS 7.389OEntries 756Mean -0.3392RMS 4.719FeEntries 533Mean -0.9083RMS 4.243 o -65 o -20 -10 0 10 200102030405060708090 PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X vmax , g/cm ( D MC µ − D fit µ ) /D MC µ , % D µ /D e Sh o w e r s -40 -30 -20 -10 0 10 20 30020406080100120 PEntries 476Mean 0.4177RMS 8.32OEntries 758Mean -0.2603RMS 4.791FeEntries 513Mean -0.5534RMS 4.336 o -65 o -40 -30 -20 -10 0 10 20 30020406080100120 PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X vmax , g/cm ( D MC µ − D fit µ ) /D MC µ , % D µ /D e Sh o w e r s -30 -20 -10 0 10 20051015202530354045 PEntries 300Mean 0.9655RMS 7.512OEntries 206Mean 0.2456RMS 6.011FeEntries 361Mean 0.06442RMS 4.388 o -65 o -30 -20 -10 0 10 20051015202530354045 PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X vmax , g/cm ( D MC µ − D fit µ ) /D MC µ , % D µ /D e Sh o w e r s -30 -20 -10 0 10 20 300510152025303540 PEntries 330Mean 1.107RMS 8.969OEntries 192Mean 0.1269RMS 5.84FeEntries 345Mean -0.1776RMS 4.857 o -65 o -30 -20 -10 0 10 20 300510152025303540 PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X vmax , g/cm ( D MC µ − D fit µ ) /D MC µ , % D µ /D e Sh o w e r s Figure 4: Distributions of relative difference between MC simulated muon signals in Cherenkov water tanks S MC µ and muon signals derived from the fit S fit µ at 1000 m. Protons — red line, oxygen — brown line,iron — blue line. -65 o o -65 o PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X v m a x , g/ c m ( D MC µ − D fit µ ) /D MC µ , % D µ /D e Showers -65 o o -65 o PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X v m a x , g/ c m ( D MC µ − D fit µ ) /D MC µ , % D µ /D e ShowersFigure 5: Ratio of signals in water Cherenkov tanks S µ /S EM at 200 m and 1500 m vs vertical depth ofshower maximum X vmax in log 10( E )[eV]=18.9–19.0 energy bin. Protons — red squares, oxygen — browndiamonds, iron — blue crosses 5able 1: Means and RMS of distributions of relative difference between MC simulated muon signals inCherenkov water tanks S MC µ and muon signals derived from the fit S fit µ at 1000 m (see also Fig. 4) ( S MC µ − S fit µ ) /S MC µ , %, calculated with the unique set of parameters for all energy bins: A = 538, b = − . a = − .
22 log 10( E ) [eV] proton oxygen ironMean RMS Mean RMS Mean RMS18.5 – 18.6 -0.1 7.4 -0.3 4.7 -0.8 4.218.6 – 18.7 -0.3 7.2 -0.2 5.0 -0.8 3.918.7 – 18.8 0.1 8.1 -0.2 4.9 -0.8 4.518.8 – 18.9 -0.1 8.3 -0.3 5.2 -0.5 4.218.9 – 19.0 0.5 8.3 -0.2 4.8 -0.5 4.319.0 – 19.1 -0.1 7.2 0.4 5.2 -0.3 4.219.1 – 19.2 0.4 8.5 0.2 5.1 -0.1 4.619.2 – 19.3 0.3 7.8 0.3 5.1 -0.1 3.919.3 – 19.4 0.2 7.9 0.0 5.2 0.2 4.519.4 – 19.5 0.6 8.0 0.1 5.4 -0.1 4.319.5 – 19.6 1.0 7.5 0.3 6.0 0.1 4.419.6 – 19.7 0.2 7.7 -0.0 5.1 0.0 4.719.7 – 19.8 0.7 8.1 0.3 4.9 -0.2 4.819.8 – 19.9 0.2 7.2 0.5 4.9 0.4 4.919.9 – 20.0 1.2 9.0 0.2 5.8 -0.1 4.918.5 - 20.0 0.3 7.9 0.1 5.1 -0.2 4.46 -65 o o -65 o PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X v m a x , g/ c m ( D MC µ − D fit µ ) /D MC µ , % D µ /D e Showers -65 o o -65 o PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X v m a x , g/ c m ( D MC µ − D fit µ ) /D MC µ , % D µ /D e Showers -40 -20 0 20 40010203040506070
PEntries 524Mean -0.258RMS 14.73OEntries 756Mean -0.3011RMS 10.76FeEntries 533Mean -1.768RMS 10.3 o -65 o -40 -20 0 20 40010203040506070 PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X vmax , g/cm ( D MC µ − D fit µ ) /D MC µ , % D µ /D e Sh o w e r s -60 -40 -20 0 20 4001020304050 PEntries 581Mean 1.321RMS 16.63OEntries 573Mean 0.1489RMS 12.73FeEntries 498Mean 0.2673RMS 11.66 o -65 o -60 -40 -20 0 20 4001020304050 PSfrag replacements S EM , VEM DG , g/cm DG V , g/cm S µ , VEM S µ /S EM ( S MC µ − S fit µ ) /S MC µ , % S µ /S S µ /S X vmax , g/cm ( D MC µ − D fit µ ) /D MC µ , % D µ /D e Sh o w e r s Figure 6: Top: ratio of muon density to the electron one at 1000 m vs vertical depth of shower maximum X vmax for two energy bins; bottom: distributions of relative difference between MC simulated muon density D MC µ and muon density derived from the fit D fit µ at 1000 m. The data are given for two energy bins,protons — red, oxygen — brown, iron — blue. 7able 2: Means and RMS of distributions of relative difference between MC simulated muon density D MC µ and muon density derived from the fit D fit µ at 1000 m (see also Fig. 6) ( D MC µ − D fit µ ) /D MC µ , %, calculatedwith the unique set of parameters for all energy bins A = 475, b = − . a = − . E ) [eV] proton oxygen ironMean RMS Mean RMS Mean RMS18.5 – 18.6 -0.3 15 -0.3 11 -1.8 1018.6 – 18.7 -1.0 15 -0.1 11 -1.4 1018.7 – 18.8 -0.0 16 -0.8 11 -0.9 1018.8 – 18.9 -1.7 16 -0.2 11 -0.9 1018.9 – 19.0 1.1 17 -0.8 12 -0.4 1119.0 – 19.1 -0.2 15 0.6 12 -1.1 1119.1 – 19.2 0.7 16 0.3 12 -0.5 1119.2 – 19.3 0.3 15 0.5 13 -0.0 1119.3 – 19.4 0.8 16 -0.9 12 0.4 1119.4 – 19.5 1.3 17 0.1 13 0.3 1219.5 – 19.6 1.3 17 1.5 13 0.3 1219.6 – 19.7 -1.2 16 -0.4 13 0.7 1219.7 – 19.8 0.9 17 -0.7 14 -0.8 1219.8 – 19.9 0.2 16 -0.1 13 0.6 1319.9 – 20.0 1.6 19 0.5 14 0.4 1218.5 - 20.0 0.3 16 -0.1 12 -0.4 118 eferences [1] M. Giller, A. Kacperczyk, J. Malinowski, et al., Similarity of extensive air showers with respect to theshower age , J. Phys.
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