Toward an Improved Determination of Tc with 2+1 Flavors of Asqtad Fermions
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Transcript of Toward an Improved Determination of Tc with 2+1 Flavors of Asqtad Fermions
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Toward an Improved Determination of Tc with 2+1 Flavors of Asqtad Fermions
C. DeTar
University of Utah
The HotQCD Collaboration
July 30, 2007
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HotQCD Collaboration
• T. Battacharya (LANL)
• M. Cheng (Columbia)
• N. Christ (Columbia)
• C. DeTar (Utah)
• S. Gottlieb (Indiana)
• R. Gupta (LANL)
• U. Heller (APS)
• K. Huebner (BNL)
• C. Jung (BNL)
• F. Karsch (BNL/Bielefeld)
• E. Laermann (Bielefeld)
• L. Levkova (Utah)
• T. Luu (LLNL)
• R. Mawhinney (Columbia)
• P. Petreczky (BNL)
• D. Renfrew (Columbia)
• C. Schmidt (BNL)
• R. Soltz (LLNL)
• W. Soeldner (BNL)
• R. Sugar (UCSB)
• D. Toussaint (Arizona)
• P. Vranas (LLNL)
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Physics Goals
• Accurate determination of Tc– Energy density ~ T^4 sensitive to errors in T
• Equation of State (zero and nonzero density)– Needed for modeling heavy ion collisions.
• Spectral Functions
• Spatial and temporal correlators versus T
• Transport coefficients of the quark gluon plasma
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Data Sample
• Algorithm:– Asqtad 2+1 flavor RHMC
• Ensembles– Line of constant physics: m_l/m_s = 0.1– 32^3 x 8 ~12000 trajectories each– 13 beta values along line of constant physics– 32^4 couple hundred trajectories for now
• I will be focusing on Asqtad results for Nt = 8, m_l/m_s = 0.1 throughout this talk.
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How to Measure Tc
• “Chiral” phenomena Tchiral
– Peaks in chiral susceptibilities
– Singular at critical point (no ambiguity there)
• “Deconfinement” phenomena Tdeconf
– Inflection points in ReP, energy density vs T
– May be linked at chiral critical point
• How large are the differences in these measures at the physical quark mass?– Aoki et al (Wuppertal – Budapest) Phys Lett B 643:46 (2006)
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Sources of Error
• Algorithm R vs RHMC
• Finite volume
• Peak or inflection point determination
• Statistics (sample size)
• Extrapolation to physical quark mass and continuum
• Scale error
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Asqtad R vs RHMC
Differences are very small
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Chiral susceptibilities
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Connected Chiral Susceptibility
Finite size effect increases values at low T
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Disconnected chiral susceptibility
Larger volume is important
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Singlet chiral susceptibility
Finite size effect tends to decrease Tc slightly
16^3: 184(2)MeV
32^3: 186(2)
Statistical error for this fit model only! Systematic errors to be determined.
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Renormalized singlet susceptibility (Wuppertal-Budapest)
Small difference in peak position
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Quark number susceptibilities
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Strange quark number susceptibility
It is more difficult to locate an inflection point than a peak.
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Polyakov Loop
Unrenormalized
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Summary of Tc Determination (Nt=8, 0.1ms)
• All methods give answers in the range 180-195 MeV
• “Chiral” measures tend to give a bit lower Tc than “deconfining” measures
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Error budget beyond Nt = 8, 0.1ms
• Extrapolation to physical masses and
continuum depends on extrapolation model:
Estimated error: a few MeV from previous Asqtad studies
• Scale error in determination of lattice spacing (theorists can use r1 Tc)
Estimated error: 4 MeV
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Error budget conclusions
• R vs RHMC: insignificant
• Finite size: couple MeV
• Peak or inflection point determination: couple to several MeV
• Statistics (to be determined)
• Extrapolation (to be determined)
• Scale (few MeV)
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To be Done
• Complete Nt=8 simulations• Finish analysis of all the variables • Combine Nt=4,6,8 calculations• Extract transition temperature at which bulk
quantities show largest fluctuations• Is there a difference in temperature for
chiral and deconfinement phenomena at the physical quark mass?