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Towards event-by-event studies of the ultrahigh-energy cosmic-ray composition 6th Rencontres du Vietnam, Challenges in Particle Astrophysics Hanoi, 6-12 August, 2006 Dmitry S. Gorbunov astro-ph/0601449 astro-ph/0606442 astro-ph/06xxxxx In collaboration with G.I. Rubtsov, S.V. Troitsky, MSU, Yakutsk Collaboration [email protected] Institute for Nuclear Research, Moscow D. Gorbunov Towards event-by-event composition studies – p. 1/19 Motivation What can we learn from GZK-studies, if the cutoff would be observed? Astrophysics sources: accelaration mechanism, local backgrounds space: -background, magnetic fileds D. Gorbunov Particle physics interactions at Ecm 300 TeV: cross section, inelasticity, multiplicity, PT -distribution, new physics phenomena? Towards event-by-event composition studies – p. 2/19 Motivation What can we learn from GZK-studies, if the cutoff would be observed? Astrophysics sources: accelaration mechanism, local backgrounds space: -background, magnetic fileds Particle physics interactions at Ecm 300 TeV: cross section, inelasticity, multiplicity, PT -distribution, new physics phenomena? chemical composition D. Gorbunov Towards event-by-event composition studies – p. 2/19 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 AGASA and Yakutsk events, low energy Yakutsk events What else? D. Gorbunov Towards event-by-event composition studies – p. 3/19 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 EAS are measured significant fluctuations degeneracy: similar values for different primaries azimuth angle dependence D. Gorbunov Towards event-by-event composition studies – p. 4/19 Interesting questions: a given event For a given observed event (several parameters of EAS are measured): conservative study (negative knowledge): what is the probability, that it could not be initiated by the primary A? (positive knowledge): what is the probability, that it could be initiated by a primary of a given type Ai (say, Ai = p, , . . . , Fe)? ... D. Gorbunov Towards event-by-event composition studies – p. 5/19 What is the primary of an observed event? energy-related parameters of EAS (S600 ,. . . ) composition-related parameters of EAS ( 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 Eobs would rather produce a shower with these parameters equal to Erec : gE (Erec , Eobs ) The probability distribution that a shower with measured c-parameters equal to c could produce detector readings corresponding to c : gc (c , c). D. Gorbunov Towards event-by-event composition studies – p. 6/19 Steps 1. for each primary one generates a library of simulated showers : the same direction, Es Eobs , e.g. 0.5Eobs < Es < 2Eobs 2. following the experimental procedure for each event one finds rec ) Erec (e.g., S600 3. one assigns to each simulated shower a weight w1 = gE (Eobs , Erec ) 4. one assigns to each simulated shower an additional weight w2 = (Es /Eobs ) 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 fA(c) = D. Gorbunov 1 gc (c, ciA)w1,iAw2,iA i Towards event-by-event composition studies – p. 7/19 Example The highest energy AGASA event 2.46 1020 eV: (1000) c= 0.5 0.4 log 2 (Erec /Eobs ) 2 2 l e 2 l c )2 2 2 c (c c )2 2 2 c (c 0.3 l = 0.104 E/E = 0.25 gE (Eobs , Erec ) = e 0.2 gc (c , c) = e dc 0 c 0.1 5 10 15 20 Ρ Μ H1000L 25 = 0.4c 30 Distributions of muon densities fA of simulated events: thin dark line, A = ; thick gray line, A = p; dashed line, A =Fe. D. Gorbunov Towards event-by-event composition studies – p. 8/19 Results If the event is unlikely being initiated by the primary A, one can estimate the probability of it could be initiated by the primary A: fA(c)dc pA = FA(cobs ) fA (c) fA(cobs ) one can test the hypothesis that the primary was either A1 or A2 . Then pA1 + pA2 = 1 and 0.5 pAk = 0.4 fAk (cobs ) fA1 (cobs )+fA2 (cobs ) , k = 1, 2 0.3 0.2 0.1 5 D. Gorbunov 10 15 20 Ρ Μ H1000L 25 30 Towards event-by-event composition studies – p. 9/19 Interesting questions: combined set Chemical composition of UHECR within a given energy interval ) (within a given solid angle, etc.): Emin < E < Emax ( (negative knowledge): the upper limit on the primary A (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 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,. . . 2. for each event j one compares the parameters of simulated EAS of various primaries to parameters of observed EAS and estimates the probabilities pi (j) that it could (not) be initiated by a primary Ai of energy within 3. pi (j) enables one to estimate the probability that among N events ni were (not) initiated by primary Ai — combinatorics 4. one estimates the most probable chemical composition i or set the upper bound on a primary Ai , 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 The upper limit on a fraction of primary A 1. Input set of N observed events with energies , (+)j (+)j (+)j ( )j generally pA + pA = 1 pA , pA , Steps 2. Probability (n1 , n2 ): among N observed events, n1 initiated by A with and n2 initiated by A with : A pA(+)mn , A mn =ij ,kl - , , kl (n1 , n2 ) one sums over all subsets ( ij , kl ) ij , kl , mn / & % # 1 N D. Gorbunov . . . ' . , . . i1 <i2 < <in 1 k1 <k2 < <kn ,ij =kl 2 ij , kl / (n1 , n2 ) = % # " + To calculate p(+)mn ' ij * 1 ) p(+)kl pA - # = ) (+)ij & % ij , kl % $#" ( ! The probability to have i1 -th, . . . , in1 -th events (i1 < < in1 ) induced by < kn2 , ij = kl ) induced by A A with and k1 -th, . . . , kn2 -th events (k1 < with : Towards event-by-event composition studies – p. 12/19 The upper limit on a fraction of primary A Let A be the fraction of A in 3. Let ( A) be the probability that the observed results are reproduced for a given A. Hence n1 +n2 N A) (1 ) n1 A (n1 , n2 ) ( A) = n2 n1 ,n2 P( A) 1 0 0 at a given confidence level : ) A 1 4. Upper limit on D. Gorbunov + 1 2 A 2 A, true = ) mlost , = m 2 5. Correction because of cuts: A Towards event-by-event composition studies – p. 13/19 Example all AGASA events with known muon content and energies Eobs > 8 1019 eV: N=6 p(+) 1.000 0.998 0.921 0.887 0.580 0.565 1 3 p(+) 0.000 0.001 0.013 0.003 0.000 0.000 3 Event 1 2 3 4 5 6 0.8 P 0.6 0.4 68% C.L. 0.2 95% C.L. 0.2 0.4 0.6 0.8 1 < 0.50 at 95% C.L. ,true < 0.36 ,true 3 3 Result: AGASA+Yakutsk, E > 1020 eV, muons: ΕΓ Rubtsov et al, astro-ph/0601449 D. Gorbunov Towards event-by-event composition studies – p. 14/19 Low energy Yakutsk data 0.8 ΕΓ 0.6 0.4 D. Gorbunov 4 EY > 2 1019 eV, NY = 47 Z-burst PRELIMINARY A HP PA 19 Y A A 0.2 0 EY > 4 1019 eV, NY = 15 4 AY: Rubtsov et al, astro-ph/0601449 Y: D.G, Rubtsov, Troitsky, Yakutsk Coll., astro-ph/06xxxxx RH HP AY SHDM TD Y 19.5 Log E 20 20.5 Towards event-by-event composition studies – p. 15/19 The most probable chemical composition 1. Input set of N observed events with energies , (+)j (+)j (+)j ( )j generally pA1 + pA2 = 1 pA1 , pA2 , Steps 2. Probability (n1 , n2 ): among N observed events, n1 initiated by A1 with and n2 initiated by A2 with : * n pA(+)m 1 mn =ij ,kl kl - , , (n1 , n2 ) one sums over all subsets ( ij , kl ) ij , kl , mn / & % # 1 N D. Gorbunov . . . ' . , . . i1 <i2 < <in 1 k1 <k2 < <kn ,ij =kl 2 ij , kl / (n1 , n2 ) = % # " + To calculate n pA(+)m ;, 2 ' ij 1 ) l pA(+)k 2 pA1 - # = ) (+)ij & % ij , kl % # " ( ! The probability to have i1 -th, . . . , in1 -th events (i1 < < in1 ) induced by < kn2 , ij = kl ) induced by A1 with and k1 -th, . . . , kn2 -th events (k1 < A2 with : Towards event-by-event composition studies – p. 16/19 The most probable chemical composition ) Let us suppose that A1,2 are the fractions of A1,2 3. Let ( A1 ) be the probability that the observed results are reproduced for a given set ( A1 , A2 = 1 A1 ). Hence A1 ) 1 " n1 A1 (n1 , n2 ) A1 ) = ( & n1 +n2 N n2 n1 ,n2 0 at a given confidence level : 1 0 ( D. Gorbunov A2 ) 2 A1 ( A1 2 + ) A1 1 ) = A2 ) A1 ) 2 A1 (1 2 true A1 ) mlost , = m 2 4.b The most probable composition: maximization of 5. Correction because of cuts: A1 ) ) P( 1 A1 4.a The allowed . Towards event-by-event composition studies – p. 17/19 Example Two AGASA and two Yakutsk events with known muon content and energies Eobs > 1.5 1020 eV: N=4 , A1 = p, A2 = F e 0.5 Event 1 2 7 8 pp(+) (+) pFe 0.254 0.295 0.186 0.413 0.136 0.135 0.814 0.587 0.4 P 0.3 0.2 68% C.L. 95% C.L. 0.1 0.2 0.4 0.6 0.8 1 D. Gorbunov = 0.35 , Fe = 0.65 < 0.54 at 68% C.L. most probable 0.15 < p Result: Εp p Towards event-by-event composition studies – p. 18/19 What else? With this method one can consider Many types of c-parameters Many types of primaries Only 0.8 ΕΓ 0.6 0.4 depends on energy systematics Z-burst PRELIMINARY RH A HP PA 19 D. Gorbunov Y A A 0.2 0 Unknown primary HP AY SHDM TD Y 19.5 Log E 20 20.5 Towards event-by-event composition studies – p. 19/19