Toward an Improved Determination of Tc with 2+1 Flavors of Asqtad Fermions

C. DeTar

University of Utah

The HotQCD Collaboration

July 30, 2007

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)

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

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.

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)

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

Asqtad R vs RHMC

Differences are very small

Chiral susceptibilities

Connected Chiral Susceptibility

Finite size effect increases values at low T

Disconnected chiral susceptibility

Larger volume is important

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.

Renormalized singlet susceptibility (Wuppertal-Budapest)

Small difference in peak position

Quark number susceptibilities

Strange quark number susceptibility

It is more difficult to locate an inflection point than a peak.

Polyakov Loop

Unrenormalized

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

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

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)

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?