Continuum limit improved lattice action for pure Yang-Mills theory (II)

“…The perturbative Symanzik approach to improvement is in this work represented by three actions; a tree-level version with a plaquette and a 1×2 rectangle [1] (abbreviation: S) and two one-loop actions, one with a 1 3 parallelogram (x,y,z,-x,-y,-z) [1,2] (S1) and the other with both parallelogram and a 2 × 2 large square [3] (S1S) as additional operators. Of these also the tadpole improved (TI) versions (STI, S1TI, S1STI) are considered.…”

Section: The Actionsmentioning

confidence: 99%

Comparing improved actions for SU(2)

Pennanen

Peisa

1998

Nuclear Physics B - Proceedings Supplements

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In order to help the user in choosing the right action a performance comparison is done for seven improved actions. Six of them are Symanzik improved, one at tree-level and two at one-loop, all with or without tadpole improvement. The seventh is an approximate fixed point action. Observables are static on-and off-axis two-body potentials and four-body binding energies, whose precision is compared when the same amount of computer time is used by the programs.We were motivated to consider using improved actions after noting the slowness of a four-quark flux distribution measurement code. In this case the lattice spacing has to be small, a ≈ 0.1 fm, to achieve sufficient resolution. In this work we compare actions at that scale and at a ≈ 0.2 fm. The actionsThe perturbative Symanzik approach to improvement is in this work represented by three actions; a tree-level version with a plaquette and a 1×2 rectangle[1] (abbreviation: S) and two one-loop actions, one with a 1 3 parallelogram (x,y,z,-x,-y,-z) [1,2] (S1) and the other with both parallelogram and a 2 × 2 large square [3] (S1S) as additional operators. Of these also the tadpole improved (TI) versions (STI, S1TI, S1STI) are considered. TI for the S1 action follows Ref.[4] using results for SU(2) in Ref.[2]. The non-perturbative approach to improvement is represented by a truncated fixed point action (FP) which includes first to fourth powers of the plaquette and the parallelogram [5]. The taskThe measurements consist of static two-quark potentials for R = 1, . . . , 6 on-axis, R = (1, 1), (2, 1), . . . , (3, 3) off-axis and the binding energies of four quarks at the corners of a regular * Presented by P. Pennanen, Petrus@hip.fi † Janne.Peisa@helsinki.fi tetrahedron, the cube surrounding it having sides of length R = 1, 2, 3. Here binding energies mean E 4 − 2V 2 , where E 4 is the energy of four quarks and 2V 2 the energy of the lowest-lying two-body pairing -see [6,7]. In order to separate the ground state a variational basis of fuzzing levels 13 and 2 is used. An update step consisted of four overrelaxations and one heatbath sweep, except for the FP case for which the latter was replaced by ten Metropolis sweeps. Table 1 shows the β values and corresponding scales used for the comparison. Scales were set by fitting plateau two-body potentials at R = 2, . . . , 6 with the continuum parameterization V fit = −e/R + b S R + V 0 and using Sommer's equation r 2 0 F (r 0 ) = c with c = 2.44, corresponding to r 0 ≈ 0.66 fm. These scales agree with the determination using √ b S = 440 MeV. The plateau was taken to be reached when the difference of potentials at T +1 and T was smaller than the bootstrap error on this difference.

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“…We obtain new results for non-planar Wilson loops in the pure gauge case in Table 1, and for various dynamical fermion actions in Table 2. The results for planar small Wilson loops in pure gauge theory are well known [1,2,5,6]. The extraction of α s with massive dynamical quarks in a "partially quenched" analysis, where the scale is set before extrapolation in the quark mass, is somewhat subtle since it depends on both the perturbative plaquette, and on the connection to M S. In Figure 1 we show the mass dependence of the perturbative plaquette with the Wilson gauge action and both (improved) Wilson quark and Kogut-Susskind quark actions with massive dynamical quarks.…”

Section: Small Wilson Loopsmentioning

confidence: 99%

“…Further, while the calculation of the static potential has been well understood in the literature [1][2][3], and in particular for quenched SU(2) gauge theory [4], we present results for the static potential in SU (3) both with and without dynamical fermions.…”

Section: Introductionmentioning

confidence: 99%

The static potential to O(α2) in lattice perturbation theory

Boyle

Bali

2002

Nuclear Physics B - Proceedings Supplements

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We present a calculation of Wilson loops, and the static inter-quark potential to O(α 2 ) in lattice perturbation theory. This is carried out with the Wilson, Symanzik-Weisz, and Iwasaki gauge actions and the Wilson, Sheikholeslami-Wohlert, and Kogut-Susskind dynamical fermion action for small Wilson loops, and with the Wilson gauge action and each of the dynamical quark actions in the case of the static potential.

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Continuum limit improved lattice action for pure Yang-Mills theory (II)

Cited by 190 publications

References 17 publications

Square Symanzik action to one-loop order

Square Symanzik action to one-loop order

Comparing improved actions for SU(2)

The static potential to O(α2) in lattice perturbation theory

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