Lattice QCD with chemical potential

More documents

Recommendations

Info

Reweighting: lattice artifacts Chemical potential on the lattice is prescription dependent. Why? The continuum Dirac operator specifies effects of an infinitesimal time translation. On the lattice we deal with finite translations (by lattice spacing a). There are many ways of doing this which lead to the same infinitesimal transformation. This is the origin of problems with reweighting: it gives no indication of how large the lattice artifacts are. Taylor series expansion is prescription dependent beyond 2nd order at every finite lattice spacing a, but prescription independent for a → 0. With explicit Taylor expansion we can take the continuum limit. R. V. Gavai and S. Gupta, Phys. Rev. D 68 (2003) 034506. Chemical potential/S. Gupta: IMSc, 2003 to plan, Phases, Reweight, Expansion, QNS, strangeness, EOS, masses, end 7
The Taylor Expansion Since P V = −F = T log Z, the Taylor expansion of P is the same as of F ! 1 V P (T, µ u, µ d ) = 1 V P (T, 0, 0) + ∑ f n f µ f + 1 2! where the quark number densities and susceptibilities are— ∑ χ fg µ f µ g + · · · fg n f = T V χ fg = T V χ fgh··· = T V ∂ log Z ∂µ f ∣ ∣∣∣µf =0 ∣ ∂ 2 log Z ∣∣∣µf ∂µ f ∂µ g =µ g =0 ∂ n log Z ∣ ∂µ f ∂µ g ∂µ h · · · ∣ µf =µ g =···=0 Chemical potential/S. Gupta: IMSc, 2003 to plan, Phases, Reweight, Expansion, QNS, strangeness, EOS, masses, end 8
Page 1: Lattice QCD with chemical potential
Page 4 and 5: What’s the problem? Z = e −F/T
Page 6 and 7: Reweighting and other direct approa
Page 10 and 11: Derivatives Derivatives of log Z ca
Page 12 and 13: Some notation With two degenerate f
Page 14 and 15: Perturbation theory 1.0 1 0.9 NL HT
Page 16 and 17: Event to event fluctuations Each he
Page 18 and 19: The pressure P (T, µ) = −F/V = P
Page 20 and 21: Radius of convergence: distance to
Page 22: Summary of Results More than one me

Lattice QCD with chemical potential

Create successful ePaper yourself

Delete template?

Save as template?