T_c for staggered quarks

In QCD with dynamical quarks there is a scale in the Lagrangian: the quark mass. As a result, extraction of T_c requires extrapolation in this parameter to a realistic value of the mass. Trading the quark mass for m_ρ, we can extrapolate to realistic values of this mass. A simultaneous test of scaling is to investigate this extrapolation in terms of a plot of T_c/Λ_MS against m_ρ/Λ_MS, as shown above. The data has been taken from the literature; results for staggered quarks are collected in the table below. For the physical value of m_ρ/Λ_MS we find that T_c/Λ_MS=0.49 (2).

Additional unpublished material

Compilation of critical couplings

Nt	Ns	ma	m/Tc	mπ/mρ	βc	mρ/Tc	Tc/ΛMS	Ref
4	8	0.15	0.6	0.67 (2)	5.400 (25)	5.76 (12)	1.3 (2)	[6]
4	8	0.1	0.4	0.57 (1)	5.375 (20)	5.632 (44)	?	[1,5]
4	8	0.1	0.4	0.57 (2)	5.375 (25)	5.64 (20)	1.3 (2)	[6]
4	8	0.05	0.2	0.41 (3)	5.320 (10)	5.624 (192)	?	[1,5]
4	8	0.05	0.2	0.45 (2)	5.325 (25)	5.16 (20)	1.2 (2)	[6]
4	8	0.025	0.1	0.31 (3)	5.2875 (25)	5.37 (18)	?	[1,5]
6	12	0.1	0.6	0.68 (1)	5.525 (40)	7.260 (96)	?	[1,5]
6	12	0.05	0.3	0.65 (3)	5.470 (40)	5.62 (27)	?	[1,5]
6	12	0.025	0.15	0.52 (12)	5.438 (40)	5.1 (4)	?	[1,5]
6	12	0.025	0.15	?	5.44-5.45	5.40 (12)	?	[2]
6	24	0.01667	0.1	?	5.425 (5)	?	?	[8]
6	12	0.0125	0.075	?	5.41-5.43	5.40 (12)	?	[2]
8	16	0.0125	0.1	?	5.54 (2)	5.36 (8)	?	[3,7]
12	?	0.016	0.192	?	5.75-5.8	?	?	[4]
12	?	0.008	0.096	?	5.65-5.7	?	?	[4]

Citations for the compilation

1. S. Gottlieb et al, Phys. Rev. Lett. 59 (1987) 1513. (N_t=4,6, β_c)
2. C. Bernard et al, Phys. Rev. D 45 (1992) 3854. (N_t=6, thermodynamics, screening)
3. S. Gottlieb et al, Phys. Rev. D 47 (1993) 3619. (N_t=8, β_c, screening)
4. C. Bernard et al, Phys. Rev. D 54 (1996) 4585. (N_t=12, β_c)
5. S. Gottlieb et al, PRD 38 (1988) 2245. (plaquette and masses)
6. R.V. Gavai and S. Gupta, Phys. Rev. D 66 (2002) 094510 (N_t=4 β_c, masses, plaquette)
7. S. Gottlieb et al, PRD 47 (1993) 3619. (β_c, plaquette)
8. R. V. Gavai and S. Gupta, PRD 78 (2008) 114503. (β_c)