arXiv subjects

Stefan Sint

Publications and source records attributed to Stefan Sint.

At least 37 records · Page 2Linked to original sources

arXiv2013

Numerical Stochastic Perturbation Theory in the Schrödinger Functional

The Schrödinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.

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arXiv2012

Lattice artefacts in the Schrödinger Functional coupling for strongly interacting theories

Models of Dynamical Electroweak Symmetry Breaking are expected to display a quasi-conformal scaling behaviour in order to accommodate experimental constraints. The scaling properties of a theory can be studied using finite volume renormalisation schemes. Among these, the most practical ones are based on the Schrödinger Functional (SF). However, lattices accessible in nu- merical simulations suffer from potentially large cutoff effects and special care has to be taken to remove these effects. Here we will study the standard setup of the SF with Wilson quarks and a setup with chirally rotated boundary conditions. We study the step scaling function for SU(2) and SU(3) gauge groups in the fundamental, 2-index symmetric and adjoint representations. We per- form the O(a)-improvement of both setups to 1-loop order in perturbation theory, and we describe a way of minimising higher order cutoff effects by a redefinition of the renormalised coupling.

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arXiv2012

An O(a) modified lattice set-up of the Schrödinger functional in SU(3) gauge theory

The set-up of the QCD Schrödinger functional (SF) on the lattice with staggered quarks requires an even number of points $L/a$ in the spatial directions, while the Euclidean time extent of the lattice, $T/a$, must be odd. Identifying a unique renormalisation scale, $L=T$, is then only possible up to O($a$) lattice artefacts. In this article we study such lattices in the pure SU(3) gauge theory, where we can also compare to the standard set-up. We consider the SF coupling as obtained from the variation of an SU(3) Abelian and spatially constant background field. The O($a$) lattice artefacts can be cancelled by the existing O($a$) boundary counterterm. However, its coefficient, $\ct$, differs at the tree-level from its standard value, so that one first needs to re-determine the induced background gauge field. The perturbative one-loop correction to the coupling allows to determine $\ct$ to one-loop order. A few numerical simulations serve to demonstrate that residual cutoff effects in the step scaling function are small in both cases, $T=L\pm a$ and comparable to the standard case with $T=L$.

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arXiv2011

Perturbative lattice artefacts in the SF coupling for technicolor-inspired models

Viable candidate theories for electroweak dynamical symmetry breaking are expected to show (near) conformal behaviour in order to accommodate current phenomenological constraints. In principle, renormalisation group studies using finite volume renormalisation schemes are well-suited to verify this property in a given model. The most practical schemes are based on the Schrodinger functional (SF), but suffer from potentially large O(a) effects. Some care has to be taken to remove these effects and to set up a scheme where cutoff effects are small and under control. We here take a step in this direction by analysing various set-ups for the SF coupling at one-loop order in perturbation theory.

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arXiv2011

The chirally rotated Schrödinger functional with Wilson fermions and automatic O(a) improvement

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 ($χ$SF). On the lattice with Wilson fermions the relation is not exact, suggesting some interesting tests of universality. The main advantage of the $χ$SF 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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arXiv2010

Testing universality and automatic O(a) improvement in massless lattice QCD with Wilson quarks

The chirally rotated Schroedinger functional provides a test bed for universality and automatic O(a) improvement. We here report on extensive quenched simulations of lattice QCD with Wilson quarks in the massless limit. We demonstrate that, after proper tuning of a dimension 3 boundary counterterm, the expected chirally rotated boundary conditions are indeed obtained. This implies automatic O(a) improvement which we then verify in a few examples. Universality of properly renormalized correlation functions is confirmed by comparing to the standard set-up of the Schroedinger functional. As a by-product of this study the non-singlet current renormalisation constants Z_A and Z_V are obtained from ratios of 2-point functions.

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arXiv2010

Non-perturbative running of the coupling from four flavour lattice QCD with staggered quarks

Using the Schrödinger functional (SF) with a single staggered fermion field we calculate the SF coupling in four-flavour QCD for a wide range of energies and lattice sizes up to $L/a=16$. Preliminary results for the continuum extrapolation of the step-scaling function are presented. To reduce cutoff effects, one-loop ${\rm O}(a)$ improvement has been implemented. Various cross checks are made possible by the use of two independent sets of lattices with either $T=L+a$ or $T=L-a$.

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arXiv2007

Lattice QCD with a chiral twist

In these lectures I explain how chiral symmetry of continuum QCD naturally leads to a class of lattice regularisations known as twisted mass QCD (tmQCD). As compared to standard Wilson quarks, its advantages are the absence of unphysical zero modes, the possibility to circumvent lattice renormalisation problems and automatic O(a) improvement. On the other hand, the physical parity and flavour symmetries are explicitly broken. I discuss these aspects and then turn to the theory in a finite space-time volume with Schroedinger functional boundary conditions. Again, chiral transformations of the continuum theory may be used as a guide to formulate an alternative lattice regularisation of the Schrödinger functional, with interesting applications to renormalization problems in QCD.

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arXiv2005

The Schrodinger functional with chirally rotated boundary conditions

Using orbifold techniques I construct the Schrodinger functional (SF) for a doublet of Wilson quarks with chirally rotated boundary conditions. This allows to perform checks of universality: for instance, the renormalized SF coupling constant, defined with either boundary conditions, must have a unique continuum limit. Similarly, SF correlation functions in twisted mass QCD and standard QCD can be defined such that they share a common continuum limit. An additional benefit of the new set-up consists in the observation that all the bulk O(a) counterterms to the action and composite operators become irrelevant in the chiral limit. This implies that (ratios of) SF renormalization constants can be automatically O(a) improved, up to the effect of unavoidable boundary counterterms. As a first application we calculate the running coupling for Nf=2 flavours in the SF-scheme to one-loop order of perturbation theory. Universality of the continuum limit is confirmed and the irrelevance of the Sheikholeslami-Wohlert term in the action is demonstrated explicitly

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arXiv2005

The Kaon B-parameter in quenched QCD

I report on a recent determination by the ALPHA collaboration of the kaon B-parameter using lattice QCD with Wilson type quarks. An effort is made to control all systematic errors except for the quenched approximation. The preliminary result for the renormalization group invariant parameter is $\hat{B}_K = 0.834(37)$, which translates to $B_K^MSbar(2 GeV)=0.604(27)$ in the MSbar scheme with anticommuting $γ_5$.

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arXiv2004

NLO anomalous dimension of multiplicatively renormalizable four-fermion operators in Schroedinger Functional schemes

Renormalization constants for multiplicatively renormalizable parity-odd four-fermion operators are computed in various different Schroedinger Functional (SF) schemes and lattice regularizations with Wilson quarks at one-loop order in perturbation theory. Our results are used in the calculation of their NLO anomalous dimensions, through matching to continuum schemes. They also enable a comparison of the two-loop perturbative RG running to the previously obtained nonperturbative one in the region of small renormalized coupling.

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arXiv2002

A precise determination of the charm quark's mass in quenched QCD

We present a lattice determination of the charm quark's mass, using the mass of the D_s meson as experimental input. All errors are under control with the exception of the quenched approximation. Setting the scale with F_K=160 MeV, our final result for the renormalization group invariant (RGI) quark mass is M_c = 1.654(45) GeV, which translates to m_c(m_c) =1.301(34) GeV for the running mass in the MSbar scheme. A 6 percent increase of the RGI quark mass is observed when the scale is set by the nucleon mass. This is a typical quenched scale ambiguity, which is reduced to about 3 percent for m_c(m_c), and to 4 percent for the mass ratio M_c/M_s. In contrast, the mass splitting m(Dstar_s)-m(D_s) changes from 117(11) MeV to 94(11) MeV, which is significantly smaller than the experimental value of 144 MeV.

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arXiv2001

Some remarks on O(a) improved twisted mass QCD

Twisted mass QCD (tmQCD) has been introduced as a solution to the problem of unphysical fermion zero modes in lattice QCD with quarks of the Wilson type. We here argue that O(a) improvement of the tmQCD action and simple quark bilinear operators can be more economical than in the standard framework. In particular, an improved and renormalized estimator of the pion decay constant in two-flavour QCD is available, given only the Sheikholeslami-Wohlert coefficient c_sw and an estimate of the critical mass m_c.

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arXiv2001

The charm quark's mass in quenched QCD

We present our preliminary result for the charmed quark mass, which follows from taking the D_s and K meson masses from experiment and r0=0.5 fm (or, equivalently F_K=160 MeV) to set the scale. For the renormalization group invariant quark mass we obtain M_c = 1684(64) MeV, which translates to m_c(m_c)= 1314 (40)(20)(7) MeV for the running mass in the MSbar scheme. Renormalization is treated non-perturbatively, and the continuum limit has been taken, so that the only uncontrolled systematic error consists in the use of the quenched approximation.

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arXiv2001

First results on the running coupling in QCD with two massless flavours

We report on the non-perturbative computation of the running coupling of two-flavour QCD in the Schr"odinger functional scheme. The corresponding Lambda-parameter, which describes the coupling strength at high energy, is related to a low energy scale which still remains to be connected to a hadronic ``experimentally'' observable quantity. We find the non-perturbative evolution of the coupling indispensable to avoid untolerable errors in the estimated Lambda-parameter.

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arXiv2001

O(a) improved twisted mass lattice QCD

Lattice QCD with Wilson quarks and a chirally twisted mass term (tmQCD) has been introduced in refs. [1,2]. We here apply Symanzik's improvement programme to this theory and list the counterterms which arise at first order in the lattice spacing a. Based on the generalised transfer matrix, we define the tmQCD Schrodinger functional and use it to derive renormalized on-shell correlation functions. By studying their continuum approach in perturbation theory we then determine the new O(a) counterterms of the action and of a few quark bilinear operators to one-loop order.

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arXiv2001

Lattice QCD with a chirally twisted mass term

Lattice QCD with Wilson quarks and a chirally twisted mass term represents a promising alternative regularization of QCD, which does not suffer from unphysical fermion zero modes. We show how the correlation functions of the renormalized theory are related to the theory with a standard parameterization of the mass term. In particular we discuss the conditions under which these relations take the same form as obtained from naive continuum considerations. We discuss in detail some applications and comment on potential benefits and problems of this framework.

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arXiv2000

Non-perturbative Renormalization in Lattice Field Theory

I review the strategies which have been developped in recent years to solve the non-perturbative renormalization problem in lattice field theories. Although the techniques are general, the focus will be on applications to lattice QCD. I discuss the momentum subtraction and finite volume schemes, and their application to scale dependent renormalizations. The problem of finite renormalizations is illustrated with the example of explicit chiral symmetry breaking, and I give a short status report concerning Symanzik's improvement programme to O($a$).

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