Towards event-by-event studies of the ultrahigh-energy cosmic-ray composition

Transcription

1 Towards event-by-event studies of the ultrahigh-energy cosmic-ray composition 6th Rencontres du Vietnam Challenges in Particle strophysics Hanoi 6-1 ugust 006 Dmitry S. Gorbunov astro-ph/ astro-ph/ astro-ph/06xxxxx In collaboration with G.I. Rubtsov S.V. Troitsky MSU Yakutsk Collaboration Institute for Nuclear Research Moscow D. Gorbunov Towards event-by-event composition studies p. 1/19

2 Motivation What can we learn from GZK-studies if the cutoff would be observed? strophysics Particle physics sources: interactions at E cm 300 TeV: accelaration mechanism cross section local backgrounds inelasticity space: multiplicity -background P T -distribution magnetic fileds new physics phenomena? D. Gorbunov Towards event-by-event composition studies p. /19

3 Motivation What can we learn from GZK-studies if the cutoff would be observed? strophysics Particle physics sources: interactions at E cm 300 TeV: accelaration mechanism cross section local backgrounds inelasticity space: multiplicity -background P T -distribution magnetic fileds new physics phenomena? chemical composition D. Gorbunov Towards event-by-event composition studies p. /19

4 Plan The main idea: event-by-event analysis The probability of a given particle (p... to be a primary of a given observed event Chemical composition from observed events with estimated primary type Several Examples: highest energy GS and Yakutsk events low energy Yakutsk events What else? D. Gorbunov Towards event-by-event composition studies p. 3/19

5 Event-by-event analysis It is obviously important for studies of: highest energy tail evolution of chemical compoistion with energy global anisotropy (direction-dependent composition? Problems with poor statistics: just several parameters of ES are measured significant fluctuations degeneracy: similar values for different primaries azimuth angle dependence D. Gorbunov Towards event-by-event composition studies p. 4/19

6 Interesting questions: a given event For a given observed event (several parameters of ES are measured: conservative study (negative knowledge: what is the probability that it could not be initiated by the primary? (positive knowledge: what is the probability that it could be initiated by a primary of a given type i (say i = p... Fe?... D. Gorbunov Towards event-by-event composition studies p. 5/19

7 What is the primary of an observed event? energy-related parameters of ES (S composition-related parameters of ES ( 1000 E-parameters... c-parameters Both parameters are reconstructed with some errors The probability distribution that the primary particle which produced an actual shower with the observed E-parameters equal to E obs would rather produce a shower with these parameters equal to E rec : g E (E rec E obs The probability distribution that a shower with measured c-parameters equal to c could produce detector readings corresponding to c : g c (c c. D. Gorbunov Towards event-by-event composition studies p. 6/19

8 Steps 1. for each primary one generates a library of simulated showers : the same direction E s E obs e.g. 0.5E obs < E s < E obs. following the experimental procedure for each event one finds E rec (e.g. S rec one assigns to each simulated shower a weight w 1 = g E (E obs E rec 4. one assigns to each simulated shower an additional weight w = (E s /E obs to mimic the real power-law spectrum Output: The distribution of the c-parameters for the showers consistent with the real one by E-parameters is given by f (c = 1 g c (c c i w 1i w i D. Gorbunov i Towards event-by-event composition studies p. 7/19

9 Example The highest energy GS event ev: c = ( g E (E obs E rec = e E/E = 0.5 g c (c c = log (Erec/E obs e 0 e l l = l (c c c (c c c dc c = 0.4c Ρ Μ 1000 Distributions of muon densities f of simulated events: thin dark line = ; thick gray line = p; dashed line =Fe. D. Gorbunov Towards event-by-event composition studies p. 8/19

10 Results If the event is unlikely being initiated by the primary one can estimate the probability of it could be initiated by the primary : p = F (c obs f (cdc f (c f (c obs one can test the hypothesis that the primary was either 1 or. Then p 1 + p = 1 and p k = f k (c obs f 1 (c obs +f (c obs k = Ρ Μ 1000 D. Gorbunov Towards event-by-event composition studies p. 9/19

11 Interesting questions: combined set Chemical composition of UHECR within a given energy interval E min < E < E max ( (within a given solid angle etc.: (negative knowledge: the upper limit on the primary (positive knowledge: what is the most probable chemical composition (the set of possible primaries is fixed?... D. Gorbunov Towards event-by-event composition studies p. 10/19

12 Procedure to estimate the chemical composition 1. one selects the set of N observed events (E- c-parameters have been measured experimental cuts (z < 45 quality cuts.... for each event j one compares the parameters of simulated ES of various primaries to parameters of observed ES and estimates the probabilities p i (j that it could (not be initiated by a primary i of energy within 3. p i (j enables one to estimate the probability that among N events n i were (not initiated by primary i combinatorics 4. one estimates the most probable chemical composition i or set the upper bound on a primary i which are consistent with selected set of observed events likelihood 5. one takes into account possible corrections because of cuts on initial set detector acceptance etc. lost events D. Gorbunov Towards event-by-event composition studies p. 11/19

13 ! * ( & % # % ' & % # % / /... ' The upper limit on a fraction of primary 1. Input set of N observed events with energies p (+j p (+j generally p (+j + p ( j = 1 Steps. Probability (n 1 n : among N observed events n 1 initiated by with and n initiated by with : The probability to have i 1 -th... i n1 -th events (i 1 < with and k 1 -th... k n -th events (k 1 < with : < k n ij < i n1 induced by = k l induced by i j "$# k l = i j p (+ij k l p (+kl m n =i j k l 1 p (+m n p (+m n To calculate (n 1 n one sums over all subsets ( i j k l (n 1 n = i 1 <i < <in 1 k 1 <k < =k l D. Gorbunov Towards event-by-event composition studies p. 1/19... <kn ij i j " # k l 1 i j k l m n N

14 0 0 1 The upper limit on a fraction of primary Let be the fraction of in 3. Let ( be the probability that the observed results are reproduced for a given. Hence ( = n 1 +n N (n 1 n n1 (1 n n 1 n 4. Upper limit on at a given confidence level : P( 5. Correction because of cuts: 1 = m lost m true = 1 + D. Gorbunov Towards event-by-event composition studies p. 13/19

15 Example Event p (+ all GS events with known muon content and energies E obs > ev: N=6 p( P Result: GS+Yakutsk E > 10 0 ev muons: 68% C.L. 95% C.L Ε Γ true < 0.50 at 95% C.L. true < Rubtsov et al astro-ph/ D. Gorbunov Towards event-by-event composition studies p. 14/19

16 Low energy Yakutsk data 4 4 Y: Rubtsov et al astro-ph/ E Y > 4 Y: D.G Rubtsov Troitsky Yakutsk Coll. astro-ph/06xxxxx E Y > ev N Y = ev N Y = 47 ΕΓ PRELIMINRY HP Y P HP Y Y RH Z burst SHDM TD Log E D. Gorbunov Towards event-by-event composition studies p. 15/19

17 The most probable chemical composition # % + & %... ' # % ' & % ( - /! - * / 1. Input set of N observed events with energies p (+j 1 p (+j generally p (+j 1 + p ( j = 1 Steps. Probability (n 1 n : among N observed events n 1 initiated by 1 with and n initiated by with : The probability to have i 1 -th... i n1 -th events (i 1 < 1 with and k 1 -th... k n -th events (k 1 < with : < k n ij < i n1 induced by = k l induced by i j " # k l = p (+ij 1 k l p (+k l 1 p (+m n 1 p (+m n ; i j m n =i j k l To calculate (n 1 n one sums over all subsets ( i j k l (n 1 n = i 1 <i < k 1 <k < <in 1... <kn ij =k l i j " # k l 1 i j k l m n D. Gorbunov Towards event-by-event composition studies p. 16/19 N

18 The most probable chemical composition 1 0 " 0 & Let us suppose that 1 are the fractions of 1 3. Let ( 1 be the probability that the observed results are reproduced for a given set ( 1 = 1 1. Hence ( 1 = n 1 +n N (n 1 n n n n 1 n 4.a The allowed 1 at a given confidence level : P( b The most probable composition: maximization of 5. Correction because of cuts: ( 1 = m lost m true 1 = 1 ( ( 1. D. Gorbunov Towards event-by-event composition studies p. 17/19

19 Example Two GS and two Yakutsk events with known muon content and energies E obs > ev: N=4 1 = p = Fe Event p p (+ p (+ Fe Result: P % C.L. most probable 0.15 < 95% C.L Ε p p = 0.35 Fe = 0.65 p < 0.54 at 68% C.L. D. Gorbunov Towards event-by-event composition studies p. 18/19

20 What else? With this method one can consider Many types of c-parameters Many types of primaries Unknown primary Only depends on energy systematics ΕΓ PRELIMINRY HP HP Y Y P Y RH Z burst SHDM TD Log E D. Gorbunov Towards event-by-event composition studies p. 19/19