The SF running coupling with four flavours of staggered quarks

Rubio, Paula Pérez; Sint, Stefan

doi:10.22323/1.042.0249

Cited by 9 publications

(20 citation statements)

References 6 publications

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“…For this we need the fermionic boundary fields, ζ, ζ ′ andζ,ζ ′ , which are naturally included in the mapping (3.15) by identifying them with the non-Dirichlet components near the time boundaries. More precisely we set 19) thus leaving the α-dependence implicit. This should not lead to any confusion, as the fermionic boundary fields mostly appear as insertions into correlation functions with the subscripts indicating the projectors used for the boundary conditions.…”

Section: Relating Correlation Functions At Different Values Of αmentioning

confidence: 99%

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The chirally rotated Schrödinger functional with Wilson fermions and automatic improvement

Sint¹

2011

Nuclear Physics B

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117

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A modified formulation of the Schrödinger functional (SF) is proposed. In the continuum it is related to the standard SF by a non-singlet chiral field rotation and therefore referred to as the chirally rotated SF (χSF). On the lattice with Wilson fermions the relation is not exact, suggesting some interesting tests of universality. The main advantage of the χSF consists in its compatibility with the mechanism of automatic O(a) improvement. In this paper the basic set-up is introduced and discussed. Chirally rotated SF boundary conditions are implemented on the lattice using an orbifold construction. The lattice symmetries imply a list of counterterms, which determine how the action and the basic fermionic two-point functions are renormalised and O(a) improved. As with the standard SF, a logarithmically divergent boundary counterterm leads to a multiplicative renormalisation of the fermionic boundary fields. In addition, a finite dimension 3 boundary counterterm must be tuned in order to preserve the chirally rotated boundary conditions in the interacting theory. Once this is achieved, O(a) effects originating from the bulk action or from insertions of composite operators in the bulk can be avoided by the mechanism of automatic O(a) improvement. The remaining O(a) effects arise from the boundaries and can be cancelled by tuning a couple of O(a) boundary counterterms. The general results are illustrated in the free theory where the Sheikholeslami-Wohlert term is shown to affect correlation functions only at O(a 2 ), irrespective of its coefficient.

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Section: Relating Correlation Functions At Different Values Of αmentioning

confidence: 99%

“…This has been largely solved, and formulations of the SF with staggered and Ginsparg-Wilson-type fermions have been given in [18][19][20] and [21][22][23][24][25], respectively.…”

Section: Introductionmentioning

confidence: 99%

The chirally rotated Schrödinger functional with Wilson fermions and automatic improvement

Sint¹

2011

Nuclear Physics B

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117

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“…It is therefore not possible to set T = L exactly. We define T = T + sa with s = ±1 and take the continuum limit at fixed T = L [12,14]. This modified continuum approach required a major effort to re-compute the O(a) improvement coefficient c t at the tree and one-loop level of perturbation theory [14].…”

Section: The Set-up and Resultsmentioning

confidence: 99%

The running of the Schrödinger functional coupling from four-flavour lattice QCD with staggered quarks

Rubio

Sint

2011

AIP Conference Proceedings

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Mesonic eightfold way from dynamics and confinement in strongly coupled lattice quantum chromodynamics J. Math. Phys. 49, 072301 (2008) Bosonic color-flavor transformation for the special unitary group J. Math. Phys. 46, 072306 (2005) Charge superselection sectors for QCD on the lattice J. Math. Phys. 46, 032303 (2005) Consistent and mimetic discretizations in general relativity J. Math. Phys. 46, 032501 (2005) Additional information on AIP Conf. Proc. Abstract. We present preliminary results for the running coupling in the Schrödinger functional scheme in QCD with four flavours. A single-component staggered quark field is used on lattices of size (L/a) 3 × (L/a ± 1). This provides us with 2 different regularisations of the same renormalized coupling, and thus some control over the size of lattice artefacts. These are found to be comparatively large, calling for a more refined analysis, which still remains to be done.

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“…Actually, on that lattice, the time dependence of the background field is not uniform anymore. Therefore we extend our algorithm to this case, the details of the extended algorithm are shown in Appendix D. A preliminary result for the gauge sector by making use of the algorithm was already presented in [9,22].…”

Section: Discussionmentioning

confidence: 99%

“…Since any parallel transporter is composed of the elementary single link variables, by starting from a set for the link variable whose elements are shown in eq. (9) and by repeating the above multiplication one can obtain a set for arbitrary parallel transporters. This is the origin of the name "bottom up".…”

Section: Bottom Up Algorithmmentioning

confidence: 99%

Automatic generation of Feynman rules in the Schrödinger functional

Takeda

2009

Nuclear Physics B

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We provide an algorithm to generate vertices for the Schrödinger functional with an abelian background gauge field. The background field has a non-trivial color structure, therefore we mainly focus on a manipulation of the color matrix part. We propose how to implement the algorithm especially in python code. By using python outputs produced by the code, we also show how to write a numerical expression of vertices in the time-momentum as well as the coordinate space into a Feynman diagram calculation code. As examples of the applications of the algorithm, we provide some one-loop results, ratios of the Λ parameters between the plaquette gauge action and the improved gauge actions composed from sixlink loops (rectangular, chair and parallelogram), the determination of the O(a) boundary counter term to this order, and the perturbative cutoff effects of the step scaling function of the Schrödinger functional coupling constant.

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The SF running coupling with four flavours of staggered quarks

Cited by 9 publications

References 6 publications

The chirally rotated Schrödinger functional with Wilson fermions and automatic improvement

The chirally rotated Schrödinger functional with Wilson fermions and automatic improvement

The running of the Schrödinger functional coupling from four-flavour lattice QCD with staggered quarks

Automatic generation of Feynman rules in the Schrödinger functional

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