On influence of p t (x Lab ) dependence in h-ah interactions on lateral features of most energetic particles in young EAS cores

Transcription

1 On influence of p t (x Lab ) dependence in h-ah interactions on lateral features of most energetic particles in young EAS cores Rauf Mukhamedshin Institute for Nuclear Research, Moscow, Russia Masanobu Tamada Kinki University, Osaka, Japan Janusz Kempa Warsaw University of Technology

2 Introduction All the ground-based astrophysical experiments must simulate air cascade development. 2

3 Introduction All the ground-based astrophysical experiments must simulate air cascade development. A number of models of hadron-air air nucleus interactions with different features were proposed. 3

4 Introduction All the ground-based astrophysical experiments must simulate air cascade development. A number of models of hadron-air nucleus interactions with different features were proposed. CORSIKA includes QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 and EPOS 2.1, NEXUS and other models 4

5 Introduction All the ground-based astrophysical experiments must simulate air cascade development. A number of models of hadron-air nucleus interactions with different features were proposed. CORSIKA includes QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 and EPOS 2.1, NEXUS and other models Different models give different PCR mass composition 5

6 Introduction All the ground-based astrophysical experiments must simulate air cascade development. A number of models of hadron-air nucleus interactions with different features were proposed. CORSIKA includes QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 and EPOS 2.1, NEXUS and other models Different models give different PCR mass composition The most adequate model is not chosen yet 6

7 Introduction All the ground-based astrophysical experiments must simulate air cascade development. A number of models of hadron-air nucleus interactions with different features were proposed. CORSIKA includes QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 and EPOS 2.1, NEXUS and other models Different models give different PCR mass composition The most adequate model is not chosen yet. Why? 7

8 Introduction All the ground-based astrophysical experiments must simulate air cascade development. A number of models of hadron-air nucleus interactions with different features were proposed. CORSIKA includes QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 and EPOS 2.1, NEXUS and other models Different models give different PCR mass composition The most adequate model is not chosen yet. Why? Models are tuned on basis of sea-level EAS data 8

9 Introduction All the ground-based astrophysical experiments must simulate air cascade development. A number of models of hadron-air nucleus interactions with different features were proposed. CORSIKA includes QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 and EPOS 2.1, NEXUS and other models Different models give different PCR mass composition The most adequate model is not chosen yet. Why? Models are tuned on basis of sea-level EAS data high-mountain EAS data and X-ray X emulsion chamber (XREC) results are not taken into account 9

10 XREC experiments High-altitude PAMIR s X-ray emulsion chambers 10

11 XREC experiments X-ray Emulsion Chamber s s observables Spectra of single gamma-rays (γ/e( ± ) & hadrons (h) γ-h family = bundle of most high-energy correlated particles (γ,(, e ±, h) in young-eas core Particle energies E γ, E hγ > 4 TeV Energy & number of particles p per γ- h family Particle parameters Parameters of single γ-h families Parameters of fam families N fam Measurement accuracy ΣE tot =ΣE γ +ΣE hγ ~ TэВT n γ,n 4 x i, y i = coordinates R i = distance from center E i = single particle energy X 0, Y 0 = center coordinates R = ΣR i / n γ,h ; ER = Σ(E i R i )/ n γ,h Anisotropy parameters: λ n etc R = Σ R / N fam ; ER = ΣER/ N fam Anisotropy parameters, intensity, energy spectra of families x, y ~ 10 µm, θ < 3, 3 ϕ < 15 σ E /E ~ Examples of γ -families R.Mukhamedshin,, Moscow, Russia 11

12 XREC experiments Important: Dominant part of γ-ray families is produced by PCR protons uncertainties related to the PCR mass composition are decreased R.Mukhamedshin,, Moscow, Russia 12

13 XREC experiments Important: Dominant part of γ-ray families is produced by PCR protons uncertainties related to the PCR mass composition are decreased γ-ray families are sensitive to the kinematic fragmentation range (x( Lab > 0.01 ) R.Mukhamedshin,, Moscow, Russia 13

14 XREC experiments Important: Dominant part of γ-ray families is produced by PCR protons uncertainties related to the PCR mass composition are decreased γ-ray families are sensitive to the kinematic fragmentation range (x Lab >0.01 ) XREC γ-ray families are actually more model-sensitive than EAS R.Mukhamedshin,, Moscow, Russia 14

15 XREC experiments Important: Dominant part of γ-ray families is produced by PCR protons uncertainties related to the vague PCR mass composition are decreased γ-ray families are sensitive to the kinematic fragmentation range (x Lab >0.01 ) XREC γ-ray families are actually more model-sensitive than EAS Data on γ-ray families can give some information being useful to test fragmentation-range range parameters of models R.Mukhamedshin,, Moscow, Russia 15

16 XREC experiments Important: Dominant part of γ-ray families is produced by PCR protons uncertainties related to the vague PCR mass composition are decreased γ-ray families are sensitive to the kinematic fragmentation range (x Lab >0.01 ) XREC γ-ray families are actually more model-sensitive than EAS Data on γ-ray families can give some information being useful to test fragmentation-range parameters of models The talk considers correlations between p t (x Lab ) behavior at x Lab 0.01 and lateral size of γ-ray families R.Mukhamedshin,, Moscow, Russia 16

17 XREC experiments Important: average energy of primary protons initiating γ-ray families with ΣE γ = TeV is E 0 p 10 PeV = ev at any more or less rational PCR composition R.Mukhamedshin,, Moscow, Russia 17

18 XREC experiments Important: average energy of primary protons initiating γ-ray families with ΣE γ = TeV is E 0 p 10 PeV = ev at any more or less rational PCR composition Assumption: main features of γ-families are determined by first interaction (as in the EAS case) R.Mukhamedshin,, Moscow, Russia 18

19 XREC experiments Important: average energy of primary protons initiating γ-ray families with ΣE γ = TeV is E 0 p 10 PeV = ev at any more or less rational PCR composition Assumption: main features of γ-families are determined by first interaction (as in the EAS case) Aim: Search for p-airp air-interaction interaction p t -dependent parameters P(p t ) giving most adequate correlation at E 0 =10 16 ev with R γ p of proton-initiated γ-ray families R.Mukhamedshin,, Moscow, Russia 19

20 XREC experiments Correlation between R γ and p t doubly averaged radius of γ-families, R γ,, is easily measured R γ is sensitive to variations of transversal momentum p t : the higher p t, the larger R γ mass of PCR particle: the larger mass (p He, e.g.), the larger R γ Double averaging of radius means that at first stage averaging is made over particles of each separate event. At the second stage, the required values are averaged over all events R.Mukhamedshin,, Moscow, Russia 20

21 XREC experiments Correlation between R γ and p t doubly averaged radius of γ-families, R γ, is easily measured R γ is sensitive to variations of transversal momentum p t : the higher p t, the larger R γ mass of PCR particle: the larger mass (p He, e.g.), the larger R γ Double averaging of radius means that at first stage averaging is made over particles of each separate event. At the second stage, the required values are averaged over all events R.Mukhamedshin,, Moscow, Russia 21

22 XREC experiments Correlation between R γ and p t doubly averaged radius of γ-families, R γ, is easily measured R γ is sensitive to variations of transversal momentum p t : the higher p t, the larger R γ mass of PCR particle: the larger mass (p He, e.g.),, the larger R γ Double averaging of radius means that at first stage averaging is made over particles of each separate event. At the second stage, the required values are averaged over all events R.Mukhamedshin,, Moscow, Russia 22

23 XREC experiments Correlation between R γ and p t doubly averaged radius of γ-families, R γ, is easily measured R γ is sensitive to variations of transversal momentum p t : the higher p t, the larger R γ mass of PCR particle: the larger mass (p He, e.g.), the larger R γ Double averaging of radius means that at first stage averaging is made over particles of each separate event. At the second stage, the required values are averaged over all events. How strong and in what way does R γ depend on р t? R.Mukhamedshin,, Moscow, Russia 23

24 p t -dependent parameters P(p t ) of p-air interactions 1.5 pt, GeV/c 1.0 p-air charged E 0 =10 16 ev p t (X Lab ) dependence (X Lab QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ X Lab E/E 0 the higher E, E the larger XLab X Lab Contribution of large-x Lab particles into family s s transverse features is higher than that of low-x Lab particles R.Mukhamedshin,, Moscow, Russia 24

25 p t -dependent parameters P(p t ) of p-air interactions 1.5 pt, GeV/c 1.0 p-air charged E 0 =10 16 ev p t (X Lab ) dependence (X Lab QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ X Lab E/E 0 the higher E, E the larger XLab X Lab Contribution of large-x Lab particles into family s transverse features is higher than that of low-x Lab particles Search for desired parameters as X Lab - and X 2 Lab -weighted p t - dependent parameters R.Mukhamedshin,, Moscow, Russia 25

26 p t -dependent parameters P(p t ) of p-air interactions P 1 (p t ) P 2 (p t ) P 3 (p t ) P 4 (p t ) P 1 (p t ) = standard p t P 2 (p t ), P 4 (p t ), P 6 (p t ) = x Lab -weighted parameters P 3 (p t ), P 5 (p t ), P 7 (p t ) = x 2 Lab -weighted parameters P 4 (p t ) and P 5 (p t )= partly «truncated» parameters P 5 (p t ) X min X Lab X max X min X Lab X max P 6 (p t ) P 7 (p t ) P 6 (p t ) and P 7 (p t )= completely «truncated» parameters 26

27 Correlation of p t - dependent parameters and γ-ray families R γ p R γ p is simulated for PCR proton spectrum 27

28 Correlation of p t - dependent parameters and γ-ray families R γ p R γ p is simulated for PCR proton spectrum Models are tested as follows QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 (CORSIKA package) 28

29 Correlation of p t - dependent parameters and γ-ray families R γ p R γ p is simulated for PCR proton spectrum Models are tested as follows QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 (CORSIKA package) MC0 (R.M., ~1990) 29

30 Correlation of p t - dependent parameters and γ-ray families R γ p R γ p is simulated for PCR proton spectrum Models are tested as follows QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 (CORSIKA package) MC0 (R.M., ~1990) FANSY 1.0 и FANSY 1.01 (R.M., 2006) are designed to analyze problems of γ-ray family alignment differs only in one parameter: p t (x Lab ) dependence at ~0.01 < x Lab < 0.5 and show clear influence of this x Lab range on R γ 30

31 Correlation of p t - dependent parameters and γ-ray families R γ p Search for correlations between R γ values and p t -dependent x Lab - & x 2 Lab -weighted parameters P(p t ) in whole x Lab interval at 0 X Lab 1 (all particles are included) 31

32 Correlation of p t - dependent parameters and γ-ray families R γ p Search for correlations between R γ values and p t -dependent x Lab - & x 2 Lab -weighted parameters P(p t ) in whole x Lab interval at 0 X Lab 1(all particles are included) in truncated x Lab intervals at X min X Lab X max (no low- and high-energy particles) max #) #) X min min = 0.01, 0.02, 0.03, 0.04, 0.05 (no low-energy particles) X max = 0.20, 0.25, 0.30, 0.40, 0.50 (no most energetic particle) 32

33 Correlation of p t - dependent parameters and γ-ray families R γ p Search for correlations between R γ values and p t -dependent x Lab - & x 2 Lab -weighted parameters P(p t ) in whole x Lab interval at 0 X Lab 1(all particles are included) in truncated x Lab intervals at X min X Lab X #) max (no low- and high-energy particles) as Y = m X m X + const $) #) X min = 0.01, 0.02, 0.03, 0.04, 0.05 (no low-energy particles) X max = 0.20, 0.25, 0.30, 0.40, 0.50 (no most energetic particle) $) X = P i (p t )/P FANSY 1.01 (p t ), Y = R= γ / R γ FANSY

34 Correlation of p t - dependent parameters and γ-ray families R γ p Search for correlations between R γ values and p t -dependent x Lab - & x 2 Lab -weighted parameters P(p t ) in whole x Lab interval at 0 X Lab 1(all particles are included) in truncated x Lab intervals at X min X Lab X #) max (no low- and high-energy particles) as Y = m X + const $) with m 1.25 (found by least-squares squares method) at r (determinancy coefficient) ) (for all the models excluding QGSJET II) #) X min = 0.01, 0.02, 0.03, 0.04, 0.05 (no low-energy particles) X max = 0.20, 0.25, 0.30, 0.40, 0.50 (no most energetic particle) $) X = P i (p t )/P FANSY 1.01 (p t ), Y = R γ / R γ FANSY 1.01 ) Ideal case: m = 1 at r 2 = 1 34

35 Correlation of p t - dependent parameters and γ-ray families R γ p Definitions: m m All for all models m mq1sefmf for all models excluding QGSJET II 35

36 Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 1 (p t ) QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 MC0 FANSY X Lab 1 m All = 1.99 ± 1.26 r 2 All= p0.8 t, GeV/c 0.9 no correlation of R γ & p t (small r 2 ) scatter in R γ values is much more than that in p t values 36

37 Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 2 (p t ) QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 MC0 FANSY p0.8 t x, GeV/c X Lab 1 m All = 2.03 ± 1.05 r 2 All= P 3 (p t ) QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 MC0 FANSY p t 0.8 x 2, GeV/c 0.9 m All = 0.05 ± 0.97 r 2 All= no correlation of R γ & P 2,3 (p t ) (r 2 is extremely small); scatter in R γ and P 3 ( p t ) values is large 37

38 Correlation of p t - dependent parameters and γ-ray families R γ p 25 a) P 4 (p t ) QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 MC0 FANSY X Lab 0.5 m All = 0.62 ± 0.29 r 2 All= p t x(<0.5) 0.8, GeV/c P 5 (p t ) QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 MC0 FANSY p t x 2 (<0.5), 0.8 GeV/c 0.9 m All = 0.72 ± 0.96 r 2 All= 0.10 no correlation between R γ & P 4,5 (p t ) (r 2 is small); scatter in R γ and P 4,5 (p t values is too large 38

39 Correlation of p t - dependent parameters and γ-ray families R γ p No real correlation between R γ and p t -dependent parameters P 1 (p t ) P 5 (p t ) Analysis of «truncated» parameters for different x min and x max There are different results for «truncated» intervals with different x min and x max Best results are shown below 39

40 Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 6 (p t ) QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ 10 ch p 0.8 t x tr ,GeV/c X Lab 0.25 m Q1SEFMF= 1.24 ± 0.11 r 2 Q1SEFMF= X Lab 0.20 m Q1SEFMF= 1.17 ± 0.10 r 2 Q1SEFMF= QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ p t x tr ,GeV/c 0.9 ch R.Mukhamedshin, Moscow, Russia 40

41 Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 6 (p t ) QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ 10 ch p t x tr ,GeV/c X Lab 0.20 m Q1SEFMF= 1.14 ± 0.09 r 2 Q1SEFMF=

42 Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 7 (p (7) t ) QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ 10 ch p 0.7 t x 2 tr.02-.2,gev/c X Lab 0.20 m Q1SEFMF = 1.23 ± 0.12 r 2 Q1SEFMF= a) QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ p 0.7 t x 2 tr.03-.2,gev/c X Lab 0.20 m Q1SEFMF = 1.20 ± 0.11 r 2 Q1SEFMF= 0.97 ch 42

43 Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 7 (p t ) QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ 10 ch p 0.7 t x 2 tr.04-.2,gev/c X Lab 0.20 m Q1SEFMF = 1.19 ± 0.10 r 2 Q1SEFMF= QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ p 0.7 t x 2 tr.05-.2,gev/c ch 0.05 X Lab 0.20 m Q1SEFMF = 1.17 ± 0.09 r 2 Q1SEFMF=

44 Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 7 (p t ) QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ 10 ch p 0.7 t x 2 tr.06-.2,gev/c X Lab 0.20 m Q1SEFMF = 1.15 ± 0.10 r 2 Q1SEFMF= 0.97 Clear linear dependence of R γ p on x Lab - and x 2 Lab -weighted «truncated» parameters (6) & (7) for QGSJET 01, EPOS 1.99, SYBILL 2.1, FANSY 1.0, MC0, FANSY 1.01 at ~ < X Lab < ~0.25 QGSJET II deviates from general trend 44

45 Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 7 (p t ) QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ 10 ch p 0.7 t x 2 tr.06-.2,gev/c X Lab 0.20 m Q1SEFMF = 1.15 ± 0.10 r 2 Q1SEFMF= 0.97 Clear linear dependence of R γ p on x Lab - and x 2 Lab -weighted «truncated» parameters (6) & (7) for QGSJET 01, EPOS 1.99, SYBILL 2.1, FANSY 1.0, MC0, FANSY 1.01 at ~0.02 < X Lab < ~0.25 QGSJET II deviates from general trend 45

46 Experiment and simulation PAMIR experiment data and simulation results acceptable R γ too large R γ Pamir QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY p t x tr , GeV/c 1 сh Simulation: complex composition of PCR spectrum (p,(, He, Fe) with XREC response 0.05 X Lab 0.5 P 6 (p t ) FANSY 1.01, MC0, QGSJET 01 & EPOS 1.99 results are more or less close to «Pamir» experimental data 46

47 Experiment and simulation PAMIR experiment data and simulation results acceptable R γ too large R γ Pamir QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY p t x tr , GeV/c 1 сh Simulation: complex composition of PCR spectrum (p,(, He, Fe) with XREC response 0.05 X Lab 0.5 P 6 (p t ) FANSY 1.01, MC0, QGSJET 01 & EPOS 1.99 results are more or less close to «Pamir» experimental data QGSJET II, SYBILL 2.1 & FANSY 1.0 contradict to «Pamir» data 47

48 Conclusion FANSY 1.01, MC0, QGSJET 01 & EPOS 1.99 results are more or less close to «Pamir» experimental data 48

49 Conclusion FANSY 1.01, MC0, QGSJET 01 & EPOS 1.99 results are more or less close to «Pamir» experimental data QGSJET II, SYBILL 2.1 & FANSY 1.0 results contradict to «Pamir» data 49

50 Conclusion FANSY 1.01, MC0, QGSJET 01 & EPOS 1.99 results are more or less close to «Pamir» experimental data QGSJET II, SYBILL 2.1 & FANSY 1.0 results contradict to «Pamir» data All models (excluding QGSJET II) ) show understandable dependence of γ-ray family size on p t -dependent parameters by P 6 (p t ) and P 7 (p t ) at X Lab

51 Conclusion FANSY 1.01, MC0, QGSJET 01 & EPOS 1.99 results are more or less close to «Pamir» experimental data QGSJET II, SYBILL 2.1 & FANSY 1.0 results contradict to «Pamir» data All models (excluding QGSJET II) show understandable dependence of γ-ray family size on p t -dependent parameters by P 6 (p t ) and P 7 (p t )at X Lab QGSJET II shows deviation from general trend 51

52 Conclusion FANSY 1.01, MC0, QGSJET 01 & EPOS 1.99 results are more or less close to «Pamir» experimental data QGSJET II, SYBILL 2.1 & FANSY 1.0 results contradict to «Pamir» data All models (excluding QGSJET II) show understandable dependence of γ-ray family size on p t -dependent parameters by P 6 (p t ) and P 7 (p t )at X Lab QGSJET II shows deviation from general trend The wider EAS core, the stronger imitation of more heavy nuclei: p He, p He Li etc. QGSJET II, SYBILL 2.1 & FANSY 1.0 can imitate more heavy nuclei 52

53 Conclusion p t is not related to transversal size of γ-ray families 53

54 Conclusion p t is not related to transversal size of γ-ray families Just p t (x Lab ) dependence at X Lab determines lateral divergence of beam of young EAS-core high-energy particles at initial stage 54

55 Conclusion p t is not related to transversal size of γ-ray families Just p t (x Lab ) dependence at X Lab determines lateral divergence of beam of young EAS-core high-energy particles at initial stage Optimum p t (X Lab ) 0.5 GeV/c at X Lab (E ev) 55

56 Conclusion p t is not related to transversal size of γ-ray families Just p t (x Lab ) dependence at X Lab determines lateral divergence of beam of young EAS-core high-energy particles at initial stage Optimum p t (X Lab ) 0.5 GeV/c at X Lab (E ev) X Lab - and/or X 2 Lab -weighted p t -dependent parameters defined in «truncated» x Lab ranges seem to be most adequate 56

57 Conclusion p t is not related to transversal size of γ-ray families Just p t (x Lab ) dependence at X Lab determines lateral divergence of beam of young EAS-core high-energy particles at initial stage Optimum p t (X Lab ) 0.5 GeV/c at X Lab (E ev) X Lab - and/or X 2 Lab-weighted p t -dependent parameters defined in «truncated» x Lab ranges seem to be most adequate XREC high-altitude high-threshold data give a good chance to test models of hadron-nucleus nucleus interactions at superhigh energies 57

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