Equilibration Processes in Statistical Hadronization
Explore the rate equation approach to J-equilibration in the context of SHM+J processes, as discussed by Philipp Bahavar at a transport meeting. The results cover statistical hadronization, charm conservation, and production equivalency, shedding light on chemical equilibrium measures and the role of QGP scattering in multiplicity production.
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Presentation Transcript
Rate equation approach to J/ equilibration Philipp Bahavar Transport Meeting - 08.07.2015
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Outline 1. ?/? in the statistical hadronization model 2. Production and dissociation processes 3. Rate equation approach 4. Results Philipp Bahavar Transport Meeting - 08.07.2015 1
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Statistical hadronization Multiplicity given by T, , V: ? ? =???? 1?+1?? ??? ? ?? 2?2?? ??2 ?=1 T, : ratio fits V: charged hadron multiplicity Philipp Bahavar Transport Meeting - 08.07.2015 2
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Exact charm conservation (hadron picture) Balance equation: ? ? + ??2?? ? ?1????? ?0????? ???=1 ? ?? ? 2????? ??: charm fugacity (hadronic picture) ??/? ? ??/?= ??2??/??? ???/? ? ??/? ?2 2?2 ? ?=1 Philipp Bahavar Transport Meeting - 08.07.2015 3
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Exact charm conservation (QGP picture) Balance equation: ? ???? 2?2?? 1?+1?? ??? ? ???= ?? ???? = ?? ? ?? ? ??2 ?=1 ?? ?: charm fugacity (QGP picture) ??/? ? 2??/??? 2?2 ???/? ? ??/?= ?? ? ??/? ?2 ? ?=1 Philipp Bahavar Transport Meeting - 08.07.2015 4
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Production equivalency ?? and ?? ? are connected measures of chemical equilibrium Strong dependence on ??! PB, Uphoff, Greiner: PRC 90 (2014) 6, 061901 Philipp Bahavar Transport Meeting - 08.07.2015 5
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Motivation Simultaneous production of hadrons fits ?/? ????> ???: QGP picture should hold Can QGP scatterings produce statistical ?/? multiplicities? Philipp Bahavar Transport Meeting - 08.07.2015 6
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Processes Bhanot-Peskin gluon dissociation 32 ??0 1 ??0 211 27 1 5 3? ?? Bhanot, Peskin: Nucl. Phys. B 156 (1979) 391 Philipp Bahavar Transport Meeting - 08.07.2015 7
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Processes Quasi-free quark dissociation 2 2???2 2??? + ?? 2???2 2??? + ?? 1 +2 2??? + ?? 2 2 ?0 4??2 9 2???2 2 ?0 2)log 2(2??? + ?? 2 2?0 Combridge: Nucl. Phys. B 151 (1979) 429 Philipp Bahavar Transport Meeting - 08.07.2015 8
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Processes Quasi-free gluon dissociation 2??2 2???2 ?2 ?2 4 ?2 9??? 2 2 1 +4 ??+ ? ? 2+?0 + 4????+ ? log?0 ? ?0 9 ? ?2 ?2 2 3 5?? ? 2? 4 +2 ?? log2??? ?0 2??? ?+ 8?? 1 2 1 +16?? 1 1 2?2 2??? ? 2 9 ? 9 ?0 2??? ?0 Combridge: Nucl. Phys. B 151 (1979) 429 Philipp Bahavar Transport Meeting - 08.07.2015 9
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Potential model Binding radius from screened potential: ? = 4 ? ?? ???+ ? ??(1 ? ???) 3 ???2 4 ? ? ?? ???+ ? ??(1 ? ???) ? = 2??+ 3 ???3+ ? +4 2? ? ? 1 ?+ ?? ? ???= 0 3 Karsch, Mehr, Satz: Z. Phys. C 37, 617 (1988) Philipp Bahavar Transport Meeting - 08.07.2015 10
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Melting Philipp Bahavar Transport Meeting - 08.07.2015 11
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Modifications Cross sections increase with radius ?2? ?2(0) ? ? = ? 0 Philipp Bahavar Transport Meeting - 08.07.2015 12
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Dissociation rate d3? 2?3???????/????? = ??2+1+ ?? ?/? d? ???/?log1 ? ??? 2?2?? ??,? = ??2+1 ?? ?/? 1 ? ?0 ?2???/? ??/? 1 for ?? = 0 ?? 2?2 T = d? ?0 Philipp Bahavar Transport Meeting - 08.07.2015 13
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Rates ??= 1.65 GeV ??= 1.87 GeV Philipp Bahavar Transport Meeting - 08.07.2015 14
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Rates ??= 1.65 GeV ?2? ?2(0)= ??= 1.87 GeV Philipp Bahavar Transport Meeting - 08.07.2015 15
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Rate equation d? = gain rate loss rate ? ? loss ? = ??? ?? = 0 gain = ??? ?? ??= ? ? ??? Philipp Bahavar Transport Meeting - 08.07.2015 16
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Explicit form ? ? = ?????. ??= ?? ?? ? ? ?? 1 ? = ? 2? 2??2 ?? ???= ?? ? ? ? ??? ??2 ?? ??= ? ? ? ? 2??? ? ? ?? Philipp Bahavar Transport Meeting - 08.07.2015 17
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Static box ??= 1.65 GeV ??= 1.87 GeV Philipp Bahavar Transport Meeting - 08.07.2015 18
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Cooling and expanding Schenke, Jeon, Gale: Phys. Lett. B 702 (2011) 59 Philipp Bahavar Transport Meeting - 08.07.2015 19
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Dynamic equilibration ??= 1.65 GeV ??= 1.87 GeV Philipp Bahavar Transport Meeting - 08.07.2015 20
Rate equation approach to J/ equilibration SHM+J/ Processes Rate equation Results Summary Systematic approach cross sections equilibration times External temperature profiles Equilibration possible for ??= 1.65 GeV To do: external flow profiles Philipp Bahavar Transport Meeting - 08.07.2015 21
