1 / 29

Do small systems equilibrate chemically?

Do small systems equilibrate chemically?. Ingrid Kraus TU Darmstadt. Outline. Introduction to the Statistical Model Ensembles, partition function Grand canonical ensemble Comparison to data Extrapolation and predictions for heavy-ion collisions at LHC

ide
Download Presentation

Do small systems equilibrate chemically?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Do small systems equilibrate chemically? Ingrid Kraus TU Darmstadt

  2. Outline • Introduction to the Statistical Model • Ensembles, partition function • Grand canonical ensemble • Comparison to data • Extrapolation and predictions for heavy-ion collisions at LHC • Experimental observables for T and μB determination • Relevance of resonances • From Pb+Pb to p+p: system size and energy dependence • Canonical suppression • Concept of equilibrated clusters • Comparison to data • Summary Hot Quarks 2006, Sardinia, May 16, 2006

  3. T, Vb, Nb T, V, N T, Vb, Nb T, V, m Statistical Ensembles • Micro-canonical • closed system • E, V, N fix • Canonical • heat bath • T, V, N fix • Grand-canonical • open system • heat bath and particle reservoir • T, V, m fix E, V, N Laplace transformation SE SN Hot Quarks 2006, Sardinia, May 16, 2006

  4. Partition function and its derivations • Partition function of a grand canonical ensemble • Energy density Entropy density • Particle number density Pressure • Grand-canonical partition function • i: species in the system • Mesons m < 1.5 GeV, Baryons m < 2 GeV Hot Quarks 2006, Sardinia, May 16, 2006

  5. Partition function and model parameters • Partition function for species i with degenaracy factor gi • with • (+) for fermions, (-) for bosons • Model parameters • T and mBmS constrained by strangeness neutrality • V cancels in ratios mQ constrained by charge of nuclei Hot Quarks 2006, Sardinia, May 16, 2006

  6. Comparison to Experimental Data A.Andonic, P. Braun-Munzinger, J. Stachel, nucl-th/0511071 • Accurancy in T, mB: few MeV • Different data selected for fits Hot Quarks 2006, Sardinia, May 16, 2006

  7. T - mB – systematics, extrapolation to LHC Chemical decoupling conditions extracted from SIS up to RHIC Feature common behavior On the freeze-out curve: TLHC ≈ TRHIC ≈ 170 MeV T ≤ TC ≈ 170 MeV μB from parametrised freeze-out curve: μB(√(sNN) = 5.5TeV) = 1 MeV Nucl. Phys. A 697 (2002) 902 Grand canonical ensemble for Pb+Pb predictions hep-ph/0511094 Hot Quarks 2006, Sardinia, May 16, 2006

  8. Predictions for Pb+Pb • Reliable for stable particles • Benchmark for resonances • Errors: T = 170 +/- 5 MeV μB = 1 + 4 MeV - 1 All calculations with THERMUS hep-ph/0407174 Hot Quarks 2006, Sardinia, May 16, 2006

  9. Extraction of thermal parameters from data _ • determine μB from p/p • sensitivity on T • increases with mass difference • decay contribution affect lighter particles stronger • increasing feed-down with increasing T • decay dilutes T dependence • T from W / p and/or W / K Hot Quarks 2006, Sardinia, May 16, 2006

  10. Resonance Decays • Hadron Resonance gas • W no resonance contribution • X • 50% from feed-down • both exhibit same T dependence • K decay exceeds thermal at LHC • p • thermal production ≈ constant • resonance contribution dominant • 75% of all p from resonances Hot Quarks 2006, Sardinia, May 16, 2006

  11. T, Vb, Nb T, V, N T, Vb, Nb T, V, m Canonical suppression • Grand canonical ensemble • large systems, large number of produced hadrons • Canonical ensemble • small systems / peripheral collisions, low energies • suppressed phase-space for particles related to conserved charges • density of particle i with strangeness S approxiamtely • S: order of Bessel functions • x: sum over strange hadrons, related to volume • Volume enters as additional parameter V • here: radius R of spherical volume V Hot Quarks 2006, Sardinia, May 16, 2006

  12. Canonical suppression • Stronger suppression for multi-strange hadrons • Suppression depends on strangeness content, not difference (expected from gS) Hot Quarks 2006, Sardinia, May 16, 2006

  13. Suppression by undersatured phase-space • Stronger suppression for multi-strange hadrons • Suppression depends on difference of strangeness content (power of gS) Hot Quarks 2006, Sardinia, May 16, 2006

  14. Suppression in small systems • Suppressed strangeness production beyond canonical suppression • addressed by canonical treatment and undersaturation factor gS • new: equilibrated clusters SPS √(sNN) = 17 AGeV Hot Quarks 2006, Sardinia, May 16, 2006

  15. Modification of the model • Statistical Model approach: T and μB • Volume for yields → radius R used here • Deviations: strangeness undersaturation factor gS • Fit parameter • Alternative: small clusters (RC) in fireball (R): RC ≤ R • Chemical equilibrium in subvolumes: canonical suppression • RC free parameter R RC Hot Quarks 2006, Sardinia, May 16, 2006

  16. Fit Example • All Fits were performed with THERMUS hep-ph/0407174 • Fits with gS / RC give better description of data Hot Quarks 2006, Sardinia, May 16, 2006

  17. System size and energy dependence of T and mB • T independent of • System size • Data selection • Energy • μB smaller at RHIC Hot Quarks 2006, Sardinia, May 16, 2006

  18. System size and energy dependence of the cluster size • Small clusters in all systems • Small system size dependence • p+p • energy dependence? • Pb+Pb • depends on data selection (multistrange hadrons needed) Hot Quarks 2006, Sardinia, May 16, 2006

  19. System size and energy dependence of the cluster size • A+A: clusters smaller than fireball • RC not well defined for RC ≥ 2 fm because suppression vanishes Hot Quarks 2006, Sardinia, May 16, 2006

  20. Canonical Suppression • Particle ratios saturate at RC ≈ 2 - 3 fm • no precise determination for small strangeness suppression Hot Quarks 2006, Sardinia, May 16, 2006

  21. Summary • Canonical ensemble • volume dependend suppression • stronger suppression modeled with smaller, thermally equilibrated clusters • successful description of p+p, C+C, Si+Si data • strangeness production in small systems reproduced with equilibrated subvolumes • Outlook • strangeness production in p+p at LHC • Grand canonical ensemble • successful description of Au+Au, Pb+Pb data • extrapolations allow for predictions • determination of thermal parameters with few particle ratios • proper treatment of resonances is mandatory Hot Quarks 2006, Sardinia, May 16, 2006

  22. Going into formulas • performing the momentum integration • (+) for bosons, (-) for fermions • mi: mass of hadron i • Particle number density Hot Quarks 2006, Sardinia, May 16, 2006

  23. Density and Ratios • Approx. modified Bessel function • Particle ratio • Antiparticle/Particle ratio Hot Quarks 2006, Sardinia, May 16, 2006

  24. System size dependence of T and mB • μB decreases at mid-rapidity in small systems …. • …. as expected from increasing antibaryon / baryon ratio Hot Quarks 2006, Sardinia, May 16, 2006

  25. System size dependence of the cluster size Same trend as K / p Hot Quarks 2006, Sardinia, May 16, 2006

  26. More SPS and RHIC 200 GeV Data Hot Quarks 2006, Sardinia, May 16, 2006

  27. Model setting with gS • gS • sensitive on data sample • increase with size • increase with energy Hot Quarks 2006, Sardinia, May 16, 2006

  28. Extrapolation to LHC • does strangeness in p+p at LHC behave grand canonical ? • multiplicity increases with √(sNN) • canonical and grand canon. event classes? plot from PPR Vol I Hot Quarks 2006, Sardinia, May 16, 2006

  29. Prediction for p+p • significant increase of ratios at RC ≈ 1.5 fm • K / p and W / X behave differently • multistrange hadrons suffer stronger suppression • RC will be determined with ALICE data Hot Quarks 2006, Sardinia, May 16, 2006

More Related