Lattice QCD with chemical potential

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Derivatives Derivatives of log Z can be expressed in terms of derivatives of Z. The latter can be constructed by the chain rule. Z f = ∂Z ∂µ f = ∫ DUe −S Tr M −1 f M ′ f. Note: M ′ = γ 0 and M −1 = ψψ, so Tr M −1 M ′ = ψ † ψ. Odd derivatives vanish for µ f = 0 by CP symmetry. S. Gottlieb et al., Phys. Rev. Lett., 59 (1987) 2247 1 2 11 111 21 3 S. Gupta, Acta Phys. Pol., B 33 (2002) 4259 Chemical potential/S. Gupta: IMSc, 2003 to plan, Phases, Reweight, Expansion, QNS, strangeness, EOS, masses, end 9
Quark number susceptibilities: phenomena • Fluctuations of conserved quantities in heavy-ion collisions are related to χ uu . Isospin fluctuations are related to χ 3 = χ uu − χ ud , charge fluctuations can also be constructed out of these. M. Asakawa et al., Phys. Rev. Lett., 85 (2000) 2072; S. Jeon and V. Koch, ibid., 85 (2000) 2076 • Under certain conditions strangeness production rate can be related to the strange susceptibility, χ ss . R. V. Gavai et al., Phys. Rev., D 65 (2002) 054506 • The pressure at finite chemical potential is essentially determined by the susceptibility. R. V. Gavai and S. Gupta, Phys. Rev. D 68 (2003) 034506. • χ 3 is the zero momentum Euclidean finite temperature vector propagator and hence closely related to a transport coefficient— the DC electrical conductivity of quark matter. S. Gupta, hep-lat/0301006. Chemical potential/S. Gupta: IMSc, 2003 to plan, Phases, Reweight, Expansion, QNS, strangeness, EOS, masses, end 10
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 8 and 9: Reweighting: lattice artifacts Chem
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

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