arXiv subjects

Tomasz Korzec

Publications and source records attributed to Tomasz Korzec.

At least 55 records · Page 3Linked to original sources

arXiv2017

Power corrections from decoupling of the charm quark

Decoupling of heavy quarks at low energies can be described by means of an effective theory as shown by S. Weinberg in Ref. [1]. We study the decoupling of the charm quark by lattice simulations. We simulate a model, QCD with two degenerate charm quarks. In this case the leading order term in the effective theory is a pure gauge theory. The higher order terms are proportional to inverse powers of the charm quark mass $M$ starting at $M^{-2}$. Ratios of hadronic scales are equal to their value in the pure gauge theory up to power corrections. We show, by precise measurements of ratios of scales defined from the Wilson flow, that these corrections are very small and that they can be described by a term proportional to $M^{-2}$ down to masses in the region of the charm quark mass.

hep-lat↗

arXiv2017

Setting the scale for the CLS $2 + 1$ flavor ensembles

We present measurements of a combination of the decay constants of the light pseudoscalar mesons and the gradient flow scale $t_0$, which allow to set the scale of the lattices generated by CLS with $2 + 1$ flavors of non-perturbatively improved Wilson fermions. Mistunings of the quark masses are corrected for by measuring the derivatives of observables with respect to the bare quark masses.

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arXiv2016

Impact of dynamical charm quarks

We compute and compare the continuum limits of several quantities in QCD with and without a dynamical charm quark. We consider both low energy quantities, like the hadronic scales $r_0$ and $t_0$, and high energy quantities, like the charmonium masses.

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arXiv2016

The determination of $α_s$ by the ALPHA collaboration

We review the ALPHA collaboration strategy for obtaining the QCD coupling at high scale. In the three-flavor effective theory it avoids the use of perturbation theory at $α> 0.2$ and at the same time has the physical scales small compared to the cutoff $1/a$ in all stages of the computation. The result $Λ_\overline{MS}^{(3)}=332(14)$~MeV is translated to $α_\overline{MS}(m_Z)=0.1179(10)(2)$ by use of (high order) perturbative relations between the effective theory couplings at the charm and beauty quark "thresholds". The error of this perturbative step is discussed and estimated as $0.0002$.

hep-lat↗

arXiv2016

Determination of the QCD $Λ$-parameter and the accuracy of perturbation theory at high energies

We discuss the determination of the strong coupling $α_\mathrm{\overline{MS}}^{}(m_\mathrm{Z})$ or equivalently the QCD $Λ$-parameter. Its determination requires the use of perturbation theory in $α_s(μ)$ in some scheme, $s$, and at some energy scale $μ$. The higher the scale $μ$ the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the $Λ$-parameter in three-flavor QCD, we perform lattice computations in a scheme which allows us to non-perturbatively reach very high energies, corresponding to $α_s = 0.1$ and below. We find that (continuum) perturbation theory is very accurate there, yielding a three percent error in the $Λ$-parameter, while data around $α_s \approx 0.2$ is clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.

hep-ph↗

arXiv2016

Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\rm f}=3$ QCD

Using a finite volume Gradient Flow (GF) renormalization scheme with Schrödinger Functional (SF) boundary conditions, we compute the non-perturbative running coupling in the range $2.2 \lesssim {\bar g}_\mathrm{GF}^2(L) \lesssim 13$. Careful continuum extrapolations turn out to be crucial to reach our high accuracy. The running of the coupling is always between one-loop and two-loop and very close to one-loop in the region of $200\,{\rm MeV} \lesssim μ=1/L \lesssim 4\,{\rm GeV}$. While there is no convincing contact to two-loop running, we match non-perturbatively to the SF coupling with background field. In this case we know the $μ$ dependence up to $\sim 100\,{\rm GeV}$ and can thus connect to the $Λ$-parameter.

hep-lat↗

arXiv2015

A status update on the determination of $Λ_{\overline{\rm MS}}^{N_{\rm f}=3}$ by the ALPHA collaboration

The ALPHA collaboration aims to determine $α_s(m_Z)$ with a total error below the percent level. A further step towards this goal can be taken by combining results from the recent simulations of 2+1-flavour QCD by the CLS initiative with a number of tools developed over the years: renormalized couplings in finite volume schemes, recursive finite size techniques, two-loop renormalized perturbation theory and the (improved) gradient flow on the lattice. We sketch the strategy, which involves both the standard SF coupling in the high energy regime and a gradient flow coupling at low energies. This implies the need for matching both schemes at an intermediate switching scale, $L_{\rm swi}$, which we choose roughly in the range 2-4 GeV. In this contribution we present a preliminary result for this matching procedure, and we then focus on our almost final results for the scale evolution of the SF coupling from $L_{\rm swi}$ towards the perturbative regime, where we extract the $N_{\rm f} = 3$ $Λ$-parameter, $Λ_{\overline{\rm MS}}^{N_{\rm f}=3}$, in units of $L_{\rm swi}$ . Connecting $L_{\rm swi}$ and thus the $Λ$-parameter to a hadronic scale such as $F_K$ requires 2 further ingredients: first, the connection of $L_{\rm swi}$ to $L_{\rm max}$ using a few steps with the step-scaling function of the gradient flow coupling, and, second, the continuum extrapolation of $L_{\rm max} F_K$.

hep-lat↗

arXiv2015

Triviality of $ϕ^4_4$ in the broken phase revisited

We define a finite size renormalization scheme for $ϕ^4$ theory which in the thermodynamic limit reduces to the standard scheme used in the broken phase. We use it to re-investigate the question of triviality for the four dimensional infinite bare coupling (Ising) limit. The relevant observables all rely on two-point functions and are very suitable for a precise estimation with the worm algorithm. This contribution updates an earlier publication by analysing a much larger dataset.

hep-lat↗

arXiv2015

Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions

We describe a new set of gauge configurations generated within the CLS effort. These ensembles have N_f=2+1 flavors of non-perturbatively improved Wilson fermions in the sea with the Luescher-Weisz action used for the gluons. Open boundary conditions in time are used to address the problem of topological freezing at small lattice spacings and twisted-mass reweighting for improved stability of the simulations. We give the bare parameters at which the ensembles have been generated and how these parameters have been chosen. Details of the algorithmic setup and its performance are presented as well as measurements of the pion and kaon masses alongside the scale parameter t_0.

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arXiv2014

On the extraction of spectral quantities with open boundary conditions

We discuss methods to extract decay constants, meson masses and gluonic observables in the presence of open boundary conditions. The ensembles have been generated by the CLS effort and have 2+1 flavors of O(a)-improved Wilson fermions with a small twisted-mass term as proposed by Lüscher and Palombi. We analyse the effect of the associated reweighting factors on the computation of different observables.

hep-lat↗

arXiv2013

Simulating the Random Surface representation of Abelian Gauge Theories

We present a Monte-Carlo algorithm for the simulation of the all-order strong coupling expansion of the Z2 gauge theory. This random surface ensemble is equivalent to the standard formulation, but allows to measure some quantities, like Polyakov loop correlators or excess free energies, with an accuracy that could not have been easily achieved with traditional simulation methods. One interesting application of the algorithm is the investigation of effective string theories.

hep-lat↗

arXiv2013

Simulated random surfaces and effective string models in 3D Z(2) gauge theory

All-order strong coupling simulations have been used to derive precise energies of string states in the confined phase of three dimensional Z(2) lattice gauge theory. The behavior of the ground state energy is here compared with predictions of effective string theory. Our new data reported here are consistent with known universal terms of the long string length ($L_0$) expansion known from effective string models in the continuum limit. Our precision is however still not sufficient to disentangle non-univeral terms of order $L_0^{-7}

hep-lat↗

arXiv2013

Simulating the All-Order Strong Coupling Expansion V: Ising Gauge Theory

We exactly rewrite the Z(2) lattice gauge theory with standard plaquette action as a random surface model equivalent to the untruncated set of its strong coupling graphs. By extending the worm approach applied to spin models we simulate such surfaces including Polyakov line defects that randomly walk over the lattice. Our Monte Carlo algorithms for the graph ensemble are reasonably efficient but not free of critical slowing down. Polyakov line correlators can be measured in this approach with small relative errors that are independent of the separation. As a first application our results are confronted with effective string theory predictions. In addition, the excess free energy due to twisted boundary conditions becomes an easily accessible observable. Our numerical experiments are in three dimensions, but the method is expected to work in any dimension.

hep-lat↗

arXiv2011

Performance of a worm algorithm in $ϕ^4$ theory at finite quartic coupling

Worm algorithms have been very successful with the simulation of sigma models with fixed length spins which result from scalar field theories in the limit of infinite quartic coupling lambda. Here we investigate closer their algorithmic efficiency at finite and even vanishing lambda for the one component model in dimensions D = 2, 3, 4.

hep-lat↗

arXiv2010

A worm-inspired algorithm for the simulation of Abelian gauge theories

We present an algorithm in which the all-order strong coupling expansion of the Abelian U(1) gauge theory with Wilson plaquette action is sampled. In addition to the vacuum closed surface graphs of the partition function we propose to also allow for a class of defects (boundaries) related to Wilson loops in the ensemble. The efficiency of our scheme in estimating various observables is compared to a standard Metropolis algorithm.

hep-lat↗

arXiv2010

Axial and pseudoscalar form-factors of the Delta^+(1232)

We present first results on the axial and pseudoscalar $Δ$ form factors. The analysis is carried out in the quenched approximation where statistical errors are small and the lattice set-up can be investigated relatively quickly. We also present an analysis with a hybrid action using staggered sea quarks and domain-wall valence fermions.

hep-lat↗

arXiv2009

Quark transverse charge densities in the $Δ(1232)$ from lattice QCD

We extend the formalism relating electromagnetic form factors to transverse quark charge densities in the light-front frame to the case of a spin-3/2 baryon and calculate these transverse densities for the $Δ(1232)$ isobar using lattice QCD. The transverse charge densities for a transversely polarized spin-3/2 particle are characterized by monopole, dipole, quadrupole, and octupole patterns representing the structure beyond that of a pure point-like spin-3/2 particle. We present lattice QCD results for the $Δ$-isobar electromagnetic form factors for pion masses down to approximatively 350 MeV for three cases: quenched QCD, two-degenerate flavors of dynamical Wilson quarks, and three flavors of quarks using a mixed action that combines domain wall valence quarks and dynamical staggered sea quarks. We extract transverse quark charge densities from these lattice results and find that the $Δ$ is prolately deformed, as indicated by the fact that the quadrupole moment $G_{E2}(0$) is larger than the value -3 characterizing a point particle and the fact that the transverse charge density in a $Δ^+$ of maximal transverse spin projection is elongated along the axis of the spin.

hep-ph↗

arXiv2008

Nucleon form factors with dynamical twisted mass fermions

The electromagnetic and axial form factors of the nucleon are evaluated in twisted mass QCD with two degenerate flavors of light, dynamical quarks. The axial charge g_A, magnetic moment and the Dirac and Pauli radii are determined for pion masses in the range 300 MeV to 500 MeV.

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