How to measure E-by-E fluctuations of identified particles Anar Rustamov for the NA49 and NA61/SHINE Collaborations NICA/JINR-FAIR Bilateral Workshop “Matter at highest baryon densities in the laboratory and in space” Frankfurt Institute for Advanced Studies (FIAS), April 2 – 4, 2012 Outline: Phase diagrams Critical point E-by-E fluctuations Identity method Application to data Summary and outlook

Phases of matter phase diagram of water Hypothetical phase diagram of strongly interacting matter phase diagram of water (electromagnetically interacting matter) first order liquid-gas phase transition line ends in a second order critical point A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Critical point, fluctuations Smoluchowski, Annalen der Physik, 25, 1908. Einstein, Annalen der Physik, 33, 1910. Large fluctuations near the critical point leads to well-known phenomena of Critical Opalescence A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Predicted signals Initial Stage Early Stage (ES) Freeze-Out (FO) Phys. Rev. D 82, 074008 (2010) Initial Stage Early Stage (ES) Freeze-Out (FO) A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Selected fluctuation measures Multiplicity fluctuations Poisson case: Chemical (particle composition) fluctuations NA49: STAR: Independent Poisson distributions: Some other measures A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Particle ratio fluctuations K/p and K/π results from NA49 and STAR are significantly different at low energies. What is the reason for this discrepancy ? Acceptance effects Centrality selection Bias in the used methods ? Wrong results ? A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

NA49 particle identification Charge Momentum vector Mass Production point π p K e e π K p p A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

NA49 fluctuation analysis Event mixing is used to remove: Artificial correlations 2. Statistical fluctuations For each particle from inclusive fit define: PDFs of dE/dx: PDFs of momentum: using Maximum Likelihood method extract e-b-e particle ratios, Introduces artificial correlations! No analytical derivation! A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Identity method “in a nutshell” Phys. Rev. C 83, 054907 (2011) ,Phys. Rev. C 84, 024902 (2011) A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Identity method, defining the problem Available information: Inclusive dE/dx spectra Mean multiplicities dE/dx value for every track Given this information we want to estimate moments of the unknown multiplicity distributions A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Identities (3-particle example) Calculated for each event A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

W distributions (simulation) π K p Wπ, nπ A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

W distributions (simulation) Wπ, nπ π K p A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

W distributions (simulation) Wπ, nπ π K p A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

W distributions (simulation) Wπ, nπ π K p A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Is there a relation between moments of W quantities and unknown multiplicity distributions A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Identity method, second moments Main idea is to find a relation between known moments of the W quantities and unknown moments of multiplicity distributions. For example in case of 2 particle types (p, k) Known in term of inclusive dE/dx distributions Known in term of inclusive dE/dx distributions Phys. Rev. C 83, 054907 (2011) Phys. Rev. C 84, 024902 (2011) (2- component system) (n- component or matrix method) A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Identity method, second moments Complete example in case of 2 particle types, p and k (in general works for any number of particle species) 3 equations, 3 unknowns Phys. Rev. C 84, 024902 (2011) A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Identity method, third moments Main idea is to find a relation between known moments of the W quantities and unknown moments of multiplicity distributions. For example in case of 2 particle types (p, k) ready for publication A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Application to the data A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

NA49 data set Reaction P [GeV/c] s1/2 [GeV] F [GeV1/2] 0-3.5% Pb + Pb 20 6.271 1.918 30 7.621 2.233 40 8.766 2.471 80 12.325 3.101 158 17.27 3.812 A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

W distributions (experiment) With Simple-4-Gaussian dE/dx fits A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Perfect agreement with both, published results of NA49, and STAR ! NA49, Pb+Pb, 0-3.5% (identity method) NA49, Pb+Pb, 0-3.5% (e-by-e fit) STAR, Au+Au, 0-5% preliminary Error calculation for identity method: ongoing Statistical errors are expected to be similar to those from e-by-e fit A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Increasing trend at low energies reported by NA49 is confirmed NA49, Pb+Pb, 0-3.5% (identity method) NA49, Pb+Pb, 0-3.5% (e-by-e fit) STAR, Au+Au, 0-5% preliminary Error calculation for identity method: ongoing Statistical errors are expected to be similar to those from e-by-e fit A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Increasing trend at low energies reported by NA49 is confirmed NA49, Pb+Pb, 0-3.5% (identity method) NA49, Pb+Pb, 0-3.5% (e-by-e fit) STAR, Au+Au, 0-5% preliminary Error calculation for identity method: ongoing Statistical errors are expected to be similar to those from e-by-e fit A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

The differences are still there preliminary preliminary NA49 (identity method) NA49 (e-by-e fit) STAR Independent analysis of NA49 data by different method confirms p/pi k/p and k/pi energy dependence published by NA49 What is the reason for this difference in k/p and k/pi? Acceptance effects Centrality selection Bias in the used methods Wrong results? NA49 (checked) STAR results can be verified with the identity method preliminary A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

NA61 Road Map Tchem [MEV] μB [MEV] p+p Be+Be p+p C+C Si+Si Pb+Pb Tchem [MEV] μB [MEV] A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

NA61 Road Map /12 A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Summary and Outlook Summary A new unbiased approach to study multiplicity fluctuations of identified particles has been developed Identity method allows to study higher cumulants predicted to better probe the critical point The method was used to verify published NA49 results. It is programmed in a separate package which can be compiled under the ROOT and used in any experiments Outlook The Identity method can also be applied to STAR data It will also be used for the NA61/SHINE data A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Phase diagram Spontaneous symmetry braking: Chiral symmetry SU(2)L x SU(2)R order parameter: Center symmetry Z(3) (of SU(3)C) A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Critical point, fluctuations Large fluctuations near the critical point leads to well-known phenomena of Critical Opalescence I order phase transition II order phase transition A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012

Multi-4-Gaussian dE/dx fit A. Rustamov, NICA/JINR-FAIR Workshop, FIAS, 02-04.04.2012