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Equation of state in 2+1 flavor QCD P é ter Petreczky HotQCD Collaboration

Equation of state in 2+1 flavor QCD P é ter Petreczky HotQCD Collaboration. EoS is usually calculated from the trace anomaly, ε -3p. Status of trace anomaly calculations in 2011:. Bazavov, arXiv:1201.5345v1. Bazavov et al, PRD 85 (2012) 054503.

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Equation of state in 2+1 flavor QCD P é ter Petreczky HotQCD Collaboration

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  1. Equation of state in 2+1 flavor QCD Péter Petreczky HotQCD Collaboration EoS is usually calculated from the trace anomaly, ε-3p Status of trace anomaly calculations in 2011: Bazavov, arXiv:1201.5345v1 Bazavov et al, PRD85 (2012) 054503 significant discrepancies in ε-3pwhile the temperature and cutoff dependence of other quantities turns out to be similar for stout and for HISQ/tree => detailed study of the dependence on the cutoff and scale setting procedure is needed with HISQ/tree and asqtad action

  2. Trace anomaly calculations with HISQ/tree action HISQ/tree action, ml=ms/20 scale setting using r1scale statistics for the T>0 runs: 163x4: 4K TU 243x6: 5K-30K TU 323x8: 12K-30K TU 403x10: 10K-20K TU 483x12: 30K-40K TU statistics for the T=0 runs: 243x32: 3K-4K TU 324, 323x64: 2K-5K TU 484: 4K-5K TU 483x64: 5K TU in molecular dynamic time units (TU)

  3. Scale setting and Nτdependence of the trace anomaly no tree level improve- ment for stout For Nτ=6 the difference are large;fK scale improves the agreement between different actions

  4. Scale setting and Nτdependence of the trace anomaly no tree level improve- ment for stout for Nτ=10 and 12 the differences between different actions are not significant for HISQ/tree Nτ=10,12 calculations the scale setting with fK gives the same result

  5. Trace anomaly at high temperatures • The Nτdependence of the ideal gas is not seen in the trace anomaly for HISQ/tree action even for T≈700 MeV • The trace anomaly agrees reasonably well with resummed perturbative calculations that uses 1-loop (dashed lines ) and 2-loop (solid lines ) running coupling, • Andersen et al, PRD 84 (2011) 087703

  6. Trace anomaly at low temperatures • the effect of taste symmetry breaking • in the ps meson sector (splitting of the ps • meson masses) is smaller for • the trace anomaly => the Nτ –dependence • is difficult to see • the continuum limit is approached from below • the lattices results are larger than • the hadron resonance gas (HRG) model Bazavov et al, PRD85 (‘12) 054503

  7. Summary and conclusions • The Nτ =10 and 12 HISQ/tree data for ε-3pagree with previous Nτ =8 data • for T>230MeV, while in the peak region ( T ≈ 200 MeV ) they are slightly smaller • The differences between HISQ/tree and stout data are statistically not significant for • Nτ≥ 8 • The scale setting procedure could • make a difference, the use of fK scale • improves the agreement between • different actions, though the • effect is negligible for HISQ/tree • Nτ=10,12 • The expected cutoff dependence • of the pressure at high temperatures • is not seen in the trace anomaly • The cutoff dependence at low T • can be understood qualitatively in • terms of HRG

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