On the measurement of the proton-air cross section using air shower data
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1 On the measurement of the proton-air cross section using air shower data Ralf Ulrich J. Blümer, R. Engel, F. Schüssler, M. Unger KIT, Forschungszentrum Karlsruhe Aspen 2007
2 Introduction Analysis methods Unaccompanied hadrons Frequency attenuation Distribution of X max RMS tail shape Sources of systematic uncertainties Cosmic ray composition Methodical Air shower fluctuations Hadronic interaction models Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 1 / 25
3 Overview Cross section (proton-air) [mb] Equivalent c.m. energy 2 3 Mielke et al Aglietta et al Baltrusaitis et al Honda et al Knurenko et al Nam et al Siohan et al Belov et al. Tevatron (p-p) [GeV] 4 QGSJET01 EPOS NEXUS3 SIBYLL2.1 QGSJETII log (Energy/eV) Energy [GeV] s pp LHC (p-p) LHC (C-C) 5 Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 2 / 25
4 Contributions to total cross section Ralf Ulrich On the measurement of the proton-air cross section using air shower data 3 / 25
5 First interaction and fluctuations in air showers primary particle atmospheric boundary fluctuations fluctuations (fluctuations) (fluctuations) ground level Ralf Ulrich On the measurement of the proton-air cross section using air shower data 4 / 25
6 Air shower profile fluctuations 6 N / electrons 19 protons, ev N / muons (N) RMS of log 0.3 minimum of shower fluctuations slant depth [gcm ] all simulations performed with CONEX Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 5 / 25
7 Air shower profile development (extended Heitler model) primary n=1 inel charged neutral n=2 π + π- πo n=3 n(charged) n(neutral) = 2 1 X max λ inel + λ e.m. ln( E 0 n mult E c ) Oppenheimer, Heitler, Matthews (2005) Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 6 / 25
8 High energy hadronic interaction models probability EPOS, protons at ev 19 QGSJET, protons at ev 19 QGSJETII, protons at ev 19 SIBYLL, protons at ev 19 NEXUS, protons at ev probability E max / E total EPOS, protons at ev 19 QGSJET, protons at ev 19 QGSJETII, protons at ev 19 SIBYLL, protons at ev 19 NEXUS, protons at ev E e.m. / E total probability EPOS, protons at ev 19 QGSJET, protons at ev 19 QGSJETII, protons at ev 19 SIBYLL, protons at ev 19 NEXUS, protons at ev dp dx max P(n mult ) P(n inel ) P(r e.m. ) log (multiplicity) Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 7 / 25
9 HE models microscopic parameters... parton distribution diffraction fragmentation... model cross section multiplicity elasticity... macroscopic parameters all macroscopic parameters are correlated Ralf Ulrich On the measurement of the proton-air cross section using air shower data 8 / 25
10 Composition - impact on X max fraction -1 SIBYLL 19 ev proton (58%) helium (30%) iron (%) gamma (2%) sum X max [gcm ] Uncertain composition above 15.5 ev impacts all air shower observables Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 9 / 25
11 Unaccompanied hadrons protons satellite ballone atmospheric boundary hadron calorimeter anti-coincidence array ground level experimental results from: Nam et al. (1975), Siohan et al. (1978), Mielke et al. (1994),... Ralf Ulrich On the measurement of the proton-air cross section using air shower data / 25
12 Unaccompanied hadrons protons satellite ballone atmospheric boundary hadron calorimeter anti-coincidence array ground level experimental results from: Nam et al. (1975), Siohan et al. (1978), Mielke et al. (1994),... Ralf Ulrich On the measurement of the proton-air cross section using air shower data / 25
13 Unaccompanied hadrons protons heavier primaries satellite ballone atmospheric boundary hadron calorimeter anti-coincidence array ground level experimental results from: Nam et al. (1975), Siohan et al. (1978), Mielke et al. (1994),... Ralf Ulrich On the measurement of the proton-air cross section using air shower data / 25
14 Unaccompanied hadrons - cross section φ(x) = 1 λ e X/λ Top of atmosphere φ top = φ(x top = 0gcm 2 ) by satellites, or φ top = φ(x top 5gcm 2 ) ballones Bottom of atmosphere φ bottom = φ(x ground ) measured by calorimeter Flux attenuation λ prod = X/ log(φ top /φ bottom ) with X = X bottom X top σ prod = σ tot σ el σ q el σ diffr Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 11 / 25
15 Frequency attenuation Attenuation of shower cascades in the atmosphere same energy proton showers atmospheric boundary N e air shower ground array ground level constant N µ equal E 0 constant N e same distance to X max experimental results from: Honda et al. (1993), Hara et al. (1999), Aglietta et al. (1999),... Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 12 / 25
16 Frequency attenuation Attenuation of shower cascades in the atmosphere same energy proton showers atmospheric boundary deeply penetrating N e N e air shower ground array ground level constant N µ equal E 0 constant N e same distance to X max experimental results from: Honda et al. (1993), Hara et al. (1999), Aglietta et al. (1999),... Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 12 / 25
17 Frequency attenuation Attenuation of shower cascades in the atmosphere same energy proton showers atmospheric boundary deeply penetrating Ne Ne air shower ground array Ne ground level constant N µ equal E 0 constant N e same distance to X max experimental results from: Honda et al. (1993), Hara et al. (1999), Aglietta et al. (1999),... Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 12 / 25
18 Frequency attenuation - examples AGASA like experiment (X obs =920gcm 2, (Ne) N e = 0.05, (Nµ) N µ = 0.1) (toy detector simulation, Φ E 2.7, 0 < θ < 60, protons only) frequency [arbitrary units] 3 frequency of events in (N /N µ ) bin e exponential attenuation, Λ= gcm entries < θ/deg < hist_ < θ/deg Entries < < θ/deg Mean < RMS < θ/deg < < log (N (E >1GeV)) < 6.25 µ µ 8.2 < log (N (E >1MeV)) < 8.4 e e sec(θ) X obs -X 1 [gcm ] observed attenuation is only partly due to cross section compare for example Alvarez-Muniz et al. (2002) Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 13 / 25
19 N e sensitivity (proton-air) [mb] 1400 qgsjet 1200 qgsjetii sibyll 00 σ tot Energy reconstruction/selection accurate (E 0 = EeV), (Ne) N e Λ(attenuation) [gcm ] = 0.05, X obs =920gcm 2 Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 14 / 25
20 N e sensitivity (proton-air) [mb] 1400 qgsjet 1200 qgsjetii sibyll 00 σ tot Λ 5gcm 2 σ 300mb Energy reconstruction/selection accurate (E 0 = EeV), (Ne) N e Λ(attenuation) [gcm ] = 0.05, X obs =920gcm 2 Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 14 / 25
21 X max distribution: tail and fluctuations fraction -1-3 RMS tail (exp(-x/λ)) λ int = k Λ obs = <M> σ int -4 all detector effects and fluctuations are contained in k X max [gcm ] RMS Walker & Watson (Havera Park, 1982) Linsley (1985) tail Baltrusaitis et al. (Fly s eye, 1984) Knurenko et al. (Yakutsk, 1999) Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 15 / 25
22 X max sensitivity (proton-air) [mb] (proton-air) [mb] qgsjet qgsjetii sibyll σ tot 00 σ tot Λ(X ) [gcm ] max RMS(X ) [gcm ] max X max-resolution is 30gcm 2. Energy reconstruction is accurate (E 0 = EeV). Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 16 / 25
23 X max sensitivity (proton-air) [mb] (proton-air) [mb] qgsjet qgsjetii sibyll σ tot 00 σ tot Λ(X ) [gcm ] max RMS(X ) [gcm ] max X max-resolution is 30gcm 2. Energy reconstruction is accurate (E 0 = EeV). Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 16 / 25
24 Deconvolution of X max -distribution X max = X 1 + X probability -1-3 probability = -1-3 probability X max / gcm X 1 / gcm X /gcm P Xmax (X max ) = 0 dx 1 P X1 (X 1 ) P X ( X X 1 ; HEM) method proposed by Belov et al. (HiRes) Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 17 / 25
25 Independence of X-distribution from X 1 QGSJET01, protons 18 ev ( profiles): Probability 0< X 2 /gcm < 13 (n=53876) first < X /gcm first 2 39< X /gcm first 2 78< X /gcm first < 39 (n=70785) < 78 (n=52277) < 533 (n=38958) X 1 and X are independent parameters X / gcm P X ( X X 1 ) = P X ( X) (confirmed for NEXUS3, SIBYLL2.1, QGSJETII.3, QGSJET01 for protons at 18 ev and 19 ev) Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 18 / 25
26 Dependence on HE model dn / d X -3 CONEX, QGSJETII, EeV QGSJETII, sibyll_0.5 factor=0.5 QGSJETII, Entries factor= QGSJETII, Mean factor= QGSJETII, RMS factor= QGSJETII, factor=0.9 QGSJETII, factor=1.0 QGSJETII, factor=1.2 QGSJETII, factor=1.4 QGSJETII, factor=1.6 QGSJETII, factor=1.8 QGSJETII, factor= X [gcm similar dependence on multiplicity expected ] P X is a function of σ and other correlated HE model parameters (multiplicity,...) Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 19 / 25
27 X-distribution for different HE-models probability qgsjet sibyll -3-4 nexus qgsjetii X / gcm Position of maximum shifts up to 60gcm 2 Exponential slope after maximum changes up to a factor of 1.36 Model-dependence Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 20 / 25
28 Sensitivity of deconvolution - σ true [mb] σ rec X(QGSJET), X (QGSJET) max X(QGSJETII), X (QGSJETII) max σ modified - σ model [mb] E 0 = 19 ev Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 21 / 25
29 Sensitivity of deconvolution - σ true [mb] σ rec X(QGSJET), X (QGSJET) max X(QGSJETII), X (QGSJETII) max X(QGSJET), X (SIBYLL) max X(QGSJET), X (QGSJETII) max model uncertainty band σ modified - σ model [mb] E 0 = 19 ev Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 21 / 25
30 Summary measuring σ p air means measuring EAS fluctuations assuming CR primary interaction length the only source of EAS fluctuations is not enough. At least needed: Additional HE interaction characteristics (multiplicity,...) The first few interactions at still extreme energy diffraction Meaningful estimate of uncertainty needs: HE model dependence and CR composition x Future better understanding of fluctuations measurement of composition new experiments (fluorescence/cherenkov, muons,...) Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 22 / 25
31 Summary measuring σ p air means measuring EAS fluctuations assuming CR primary interaction length the only source of EAS fluctuations is not enough. At least needed: Additional HE interaction characteristics (multiplicity,...) The first few interactions at still extreme energy diffraction Meaningful estimate of uncertainty needs: HE model dependence and CR composition x Future better understanding of fluctuations measurement of composition new experiments (fluorescence/cherenkov, muons,...) Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 22 / 25
32 Summary measuring σ p air means measuring EAS fluctuations assuming CR primary interaction length the only source of EAS fluctuations is not enough. At least needed: Additional HE interaction characteristics (multiplicity,...) The first few interactions at still extreme energy diffraction Meaningful estimate of uncertainty needs: HE model dependence and CR composition x Future better understanding of fluctuations measurement of composition new experiments (fluorescence/cherenkov, muons,...) Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 22 / 25
33 Final rating method HE-model composition fluctuations unaccompanied hadrons frequency attenuation X max RMS X max tail ( ) X max deconvolution Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 23 / 25
34 Final - conservative picture Cross section (proton-air) [mb] Mielke et al Nam et al Siohan et al lower limits Equivalent c.m. energy 2 3 Tevatron (p-p) [GeV] 4 QGSJET01 EPOS NEXUS3 SIBYLL2.1 QGSJETII log (Energy/eV) Energy [GeV] s pp LHC (p-p) LHC (C-C) 5 Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 24 / 25
35 Final - progressive picture Cross section (proton-air) [mb] Equivalent c.m. energy 2 3 Mielke et al Baltrusaitis et al Nam et al Siohan et al % confidence limit Tevatron (p-p) [GeV] 4 QGSJET01 EPOS NEXUS3 SIBYLL2.1 QGSJETII log (Energy/eV) Energy [GeV] s pp LHC (p-p) weak constraints on HE interaction models 5 LHC (C-C) Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 25 / 25 HE model
36 Changing composition - data ] 2 <X max > [g/cm HiRes-MIA HiRes Yakutsk 2001 Fly s Eye Yakutsk 1993 γ-ray proton iron QGSJET01 SIBYLL 2.1 DPMJET Energy [ev] Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 26 / 25
37 Composition - model by Hillas Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 27 / 25
38 Equal intensity cut intensity [arbitrary units] < log (N ) < 8.25 ch 8.25 < log (N ) < 8.5 ch 8.5 < log (N ) < 8.75 ch 8.75 < log (N ) < 9 ch sec(θ) constant intensity same primary energy (isotropic flux) relates shower size N ch at different zenith angle with primary energy Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 28 / 25
39 Equal intensity cut intensity [arbitrary units] < log (N ) < 8.25 ch 8.25 < log (N ) < 8.5 ch 8.5 < log (N ) < 8.75 ch 8.75 < log (N ) < 9 ch constant intensity sec(θ) constant intensity same primary energy (isotropic flux) relates shower size N ch at different zenith angle with primary energy Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 28 / 25
40 Equal intensity cut intensity [arbitrary units] < log (N ) < 8.25 ch 8.25 < log (N ) < 8.5 ch 8.5 < log (N ) < 8.75 ch 8.75 < log (N ) < 9 ch constant intensity sec(θ) constant intensity same primary energy (isotropic flux) relates shower size N ch at different zenith angle with primary energy Ralf Ulrich (ralf.ulrich@ik.fzk.de) On the measurement of the proton-air cross section using air shower data 28 / 25
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