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Smearing the bare quantum fields in lattice calculations before applying composite hadron creation operators has a long record of substantially improving overlaps onto low-lying energy eigenstates. A technique called distillation which defines smearing for quark fields as a low-rank linear projection operator into a small vector space of smooth gauge-covariant fields has proven to be both effective and versatile in hadron spectroscopy calculations albeit with significant computational cost . In this paper, more general operators in this space of smooth fields are introduced and optimised, which enhances the performance of the method when tested on systems of heavy quark-anti-quark pairs close to the charmonium energy scale., 19 pages, 19 figures, 6 tables

Physics letters / B 807, 135571 - (2020). doi:10.1016/j.physletb.2020.135571, We propose a new strategy for the determination of the QCD coupling. It relies on a coupling computed in QCD with $N_{\rm f} \geq 3$ degenerate heavy quarks at a low energy scale $\mu_{\rm dec}$, together with a non-perturbative determination of the ratio $\Lambda/\mu_{\rm dec}$ in the pure gauge theory. We explore this idea using a finite volume renormalization scheme for the case of $N_{\rm f} = 3$ QCD, demonstrating that a precise value of the strong coupling $\alpha_s$ can be obtained. The idea is quite general and can be applied to solve other renormalization problems, using finite or infinite volume intermediate renormalization schemes., Published by North-Holland Publ., Amsterdam

The energy spectrum of a system containing a static quark anti-quark pair is computed for a wide range of source separations using lattice QCD with $N_\mathrm{f}=2+1$ dynamical flavours. By employing a variational method with a basis including operators resembling both the gluon string and systems of two separated static mesons, the first three energy levels are determined up to and beyond the distance where it is energetically favourable for the vacuum to screen the static sources through light- or strange-quark pair creation, enabling both these screening phenomena to be observed. The separation dependence of the energy spectrum is reliably parameterised over this saturation region with a simple model which can be used as input for subsequent investigations of quarkonia above threshold and heavy-light and heavy-strange coupled-channel meson scattering., 12 pages, 3 figures; version accepted for publication in Physics Letters B

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., Comment: 20 pages, 3 figures, 3 tables, v2: Introduction and Conclusions expanded, new fits added to Figure 2 and 3, References updated

We present the construction of constraint HMC algorithms for gauge-Higgs models in order to measure the effective Higgs potential. In particular we focus on SU(2) Gauge-Higgs Unification models in five dimensions. Previous simulations have identified regions in the Higgs phase of these models which have properties of 4D adjoint or Abelian Higgs models. We want to test this relationship by comparing the effective potentials in five and four dimensions., Presented at The 36th Annual International Symposium on Lattice Field Theory (LATTICE2018) 22-28 July, 2018, Michigan State University, East Lansing, Michigan, USA

We report on the progress in the study of a five-dimensional SU(2) Gauge-Higgs Unification model. In this non-perturbative study, the Higgs mechanism is triggered by the spontaneous breaking of a global symmetry. In the same region of the phase diagram, we observe both dimensional reduction and the ratio of Higgs and Z boson masses to take the value known from experiment. We present the first results on the construction of a line of constant physics in this region, including the prediction for the mass scale of the first excited states of the Higgs and gauge bosons., Comment: Proceedings from the 34th annual International Symposium on Lattice Field Theory, 24-30 July 2016, University of Southampton, UK, Modified acknowledgements

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., 7 pages, 7 figures, 34th International Symposium on Lattice Field Theory (lattice 2016), 24-30 July 2016, Southampton, UK

We consider the determination of the finite temperature phase transition in the Yang--Mills SU(3) gauge theory. We compute the difference of the spatial and temporal energy density at a physical Wilson flow time. This difference is zero in the confined phase and becomes non zero in the deconfined phase. We locate the phase transition by using a new technique based on an exponential smoothing spline. This method is an alternative to the determination of the phase transition based on the Polyakov loop susceptibility and can also be used with dynamical fermions., 13 pages, 6 figures; clarification added in section 2.4; version accepted for publication in JHEP

The hadro-quarkonium picture [S. Dubinskiy and M.B. Voloshin, Phys. Lett. B 666, 344 (2008)] provides one possible interpretation for the pentaquark candidates with hidden charm, recently reported by the LHCb Collaboration, as well as for some of the charmonium-like "X,Y,Z" states. In this picture, a heavy quarkonium core resides within a light hadron giving rise to four- or five-quark/antiquark bound states. We test this scenario in the heavy quark limit by investigating the modification of the potential between a static quark-antiquark pair induced by the presence of a hadron. Our lattice QCD simulations are performed on a Coordinated Lattice Simulations (CLS) ensemble with $N_f = 2+1$ flavours of non-perturbatively improved Wilson quarks at a pion mass of about 223 MeV and a lattice spacing of about 0.0854 fm. We study the static potential in the presence of a variety of light mesons as well as of octet and decuplet baryons. In all these cases, the resulting configurations are favoured energetically. The associated binding energies between the quarkonium in the heavy quark limit and the light hadron are found to be smaller than a few MeV, similar in strength to deuterium binding. It needs to be seen if the small attraction survives in the infinite volume limit and supports bound states or resonances., 16 pages, 17 figures, V2: 1 figure added, changes to the abstract and various places in the text for enhanced clarity, update of references

We study the phase diagram and mass spectrum of an $SU(2)$ Gauge-Higgs Unification scenario on a five-dimensional orbifold.We observe spontaneous symmetry breaking within the Higgs phase of the theory and, in the vicinity of a newly discovered phase, we find that the ratio of Higgs to gauge boson masses takes a Standard Model-like value. Precisely in this region of the phase diagram, we observe dimensional reduction via localisation., 7 pages, 5 figures. Proceedings for the 33rd international symposium on Lattice Field Theory, Kobe, Japan, 14-18 July 2015

We study the viability of five-dimensional gauge theories as candidates for the origin of the Higgs field and its mechanism for spontaneous symmetry breaking. Within the framework of lattice field theory, we consider the simplest model of an $SU(2)$ gauge theory. We construct this theory on a five-dimensional orbifold which explicitly breaks the gauge symmetry to $U(1)$ at the fixed points of the orbifold. Using anisotropic gauge couplings, we find that this theory exhibits three distinct phases which we label as confined, Higgs and hybrid. Within the Higgs phase, close to the Higgs-hybrid phase transition, we find that the ratio of the Higgs to gauge boson masses takes Standard Model-like values. Precisely in this region of the phase diagram, we find dimensional reduction via localisation., Version accepted for publication in JHEP. 36 pages, 13 figures

We simulate a theory with $N_f=2$ heavy quarks of mass $M$. At energies much smaller than $M$ the heavy quarks decouple and the theory can be described by an effective theory which is a pure gauge theory to leading order in $1/M$. We present results for the mass dependence of ratios such as $t_0(M)/t_0(0)$. We compute these ratios from simulations and compare them to the perturbative prediction. The latter relies on a factorisation formula for the ratios which is valid to leading order in $1/M$., Comment: 7 pages, 3 figures, Proceedings of the 33rd International Symposium on Lattice Field Theory, 14-18 July 2015, Kobe, Japan

We study a five-dimensional pure SU(2) gauge theory formulated on the orbifold and discretized on the lattice by means of Monte Carlo simulations. The gauge symmetry is explicitly broken to U(1) at the orbifold boundaries. The action is the Wilson plaquette action with a modified weight for the boundary U(1) plaquettes. We study the phase transition and present results for the spectrum and the shape of the static potential on the boundary. The latter is sensitive to the presence of a massive Z-boson, in good agreement with the directly measured Z-boson mass. The results may support an alternative view of the lattice orbifold (stemming from its mean-field study) as a 5d bosonic superconductor., 9 pages, 10 figures, PoS(LATTICE 2013)061; changed section 2.2

Erratum to “One flavor mass reweighting in lattice QCD” [Nucl. Phys. B 877 (2) (2013) 441–456] ✩ Jacob Finkenrath , Francesco Knechtli , Bjorn Leder a,b a Department of Physics, Bergische Universitat Wuppertal, Gaussstr. 20, D-42119 Wuppertal, Germany b Department of Mathematics, Bergische Universitat Wuppertal, Gaussstr. 20, D-42119 Wuppertal, Germany Received 14 January 2014; received in revised form 22 January 2014; accepted 26 January 2014

We analyze the fluctuations in the case of mass reweighting for N_f=2 Wilson fermions. We use a domain decomposition factorization of the fermion determinant. Ratios of determinants are estimated stochastically. We study the stochastic and the ensemble fluctuations as a function of the volume V and the mass shift Delta m. With our result it is possible to estimate the cost and the effectiveness of mass reweighting. In addition we introduce a stochastic estimation for the one flavor case without using the square root., 7 pages,6 figures. Proceedings of the 30th International Symposium on Lattice Field Theory, June 24-29 2012, Cairns, Australia. Figure 3 replaced

We study Gauge-Higgs Unification in five dimensions on the lattice by means of the mean-field expansion. We formulate it for the case of an SU(2) pure gauge theory and orbifold boundary conditions along the extra dimension, which explicitly break the gauge symmetry to U(1) on the boundaries. Our main result is that the gauge boson mass computed from the static potential along four-dimensional hyperplanes is nonzero implying spontaneous symmetry breaking. This observation supports earlier data from Monte Carlo simulations [12]., 33 pages, 8 figures; text improved; references corrected; version accepted for publication in Nucl. Phys. B

The fermion determinant is a highly non-local object and its logarithm is an extensive quantity. For these reasons it is widely believed that the determinant cannot be treated in acceptance steps of gauge link configurations that differ in a large fraction of the links. However, for exact factorisations of the determinant that separate the ultraviolet from the infra-red modes of the Dirac operator it is known that the latter show less variation under changes of the gauge field compared to the former. Using a factorisation based on recursive domain decomposition allows for a hierarchical algorithm that starts with pure gauge updates of the links within the domains and ends after a number of filters with a global acceptance step. We find that the global acceptance rate is high on moderate lattice sizes. Whether this type of algorithm can help in curing the problem of critical slowing down is presently under study., Adds a clarification of fig. 3 in section 6

The phase diagram of five-dimensional SU(2) gauge theories is explored using Monte Carlo simulations of the theory discretized on a Euclidean lattice using the Wilson plaquette action and periodic boundary conditions. We simulate anisotropic gauge couplings which correspond to different lattice spacings a_4 in the four dimensions and a_5 along the extra dimension. In particular we study the case where a_5>a_4. We identify a line of first order phase transitions which separate the confined from the deconfined phase. We perform simulations in large volume at the bulk phase transition staying in the confined vacuum. The static potential measured in the hyperplanes orthogonal to the extra dimension hint at dimensional reduction. We also locate and analyze second order phase transitions related to breaking of the center along one direction., 28 pages, 22 figures, 4 tables; few explanations and references added; version accepted for publication in Nucl. Phys. B

We calculate analytically the improvement coefficients of the static axial and vector currents in O(a) improved lattice QCD at one-loop order of perturbation theory. The static quark is described by the hypercubic action, previously introduced in the literature in order to improve the signal-to-noise ratio of static observables. Within a Schroedinger Functional setup, we derive the Feynman rules of the hypercubic link in time-momentum representation. The improvement coefficients are obtained from on-shell correlators of the static axial and vector currents. As a by-product, we localise the minimum of the static self-energy as a function of the smearing parameters of the action at one-loop order and show that the perturbative minimum is close to its non-perturbative counterpart., Comment: 24 pages, 7 figures

Spontaneous symmetry breaking has been observed in lattice simulations of five-dimensional gauge theories on an orbifold. This effect is reproduced by perturbation theory if it is modified to account for a finite cut-off. We present a comparison of lattice and analytic results for bulk gauge group SU(2)., 7 pages, 5 figures. Presented at International Europhysics Conference on High Energy Physics (EPS-HEP2007), Manchester, England, 19-25 Jul 2007

We investigate the two flavor chiral Gross-Neveu model in the Schroedinger functional on the lattice. The procedure necessary to recover chiral symmetry in the continuum limit of this model with Wilson fermions is discussed. We introduce several useful observables and present a first demonstration of the feasibility of Monte-Carlo simulations in this model., Lattice 2005

The computation of the step scaling function for the finite size mass-gap in the O(N) sigma model at large N is reviewed. Practically exact nonperturbative results become available for both finite and vanishing lattice spacing. We use them as a testbed to investigate standard procedures of continuum extrapolation in lattice field theory., 6 pages, 2 figures, contribution of U.W. to Lat05, Dublin

We study the finite temperature phase transition of four and two flavor staggered fermions with hypercubic smeared link actions. These preliminary studies suggest that the improved flavor symmetry of the fermionic action can have a significant effect on the finite temperature phase diagram., 3 pages, 4 figures, Lattice2001(hightemp)

We measure the static potential from Wilson loops constructed using hypercubic blocked (HYP) links. The HYP potential agrees with the potential measured using thin links for distances r/a>=2. We calculated the lowest order perturbative expansion of the lattice Coulomb potential of HYP links. These results are used in analyzing the static potential both on quenched and dynamical lattices. The statistical accuracy of the potential with HYP links improves by about an order of magnitude, giving a reliable scale even with limited statistics both on quenched and dynamical lattices., 3 pages, 5 figures, Lattice2001(heavyquark)

We introduce a new smearing transformation, the hypercubic (HYP) fat link. The hypercubic fat link mixes gauge links within hypercubes attached to the original link only. Using quenched lattices at beta = 5.7 and 6.0 we show that HYP fat links improve flavor symmetry by an order of magnitude relative to the thin link staggered action. The static potential measured on HYP smeared lattices agrees with the thin link potential at distances r/a >= 2 and has greatly reduced statistical errors. These quenched results will be used in forthcoming dynamical simulations of HYP staggered fermions., 18 pages, 8 figures, few comments added in section 3 and new figures 6 and 7 split for better presentation, few references added

We study the potential of a static quark anti-quark pair in the confinement ``phase'' of the SU(2) Higgs model. Around separation r_b, the confining string of the gauge field breaks by formation of a dynamical pair of light quarks. The ground state and first excited state static potentials are determined by a variational technique from a matrix correlation in which suitably smeared gauge and Higgs fields enter. Our results at beta=2.4 clearly show string breaking (r_b ~ 1.9r_0). The investigation of properly defined overlaps confirms the interpretation of string breaking as a level crossing phenomenon between string-type and meson-type states. We study the scaling properties of the static potentials along a line of constant physics, varying the lattice spacing by a factor of 2. Our results show compatibility with scaling within tiny errors., 21 pages, 9 figures

We consider pure SU(N) gauge theories defined on an orbifold lattice, analogous to the S^1/Z_2 gauge theory orbifolds of the continuum, which according to the perturbative analysis do not have a Higgs phase. Non-perturbatively the conclusion for N even is the opposite, namely that spontaneous symmetry breaking does take place and some of the gauge bosons become massive. We interpret this new, non-perturbative phenomenon both mathematically and physically., 25 pages, 1 figure; figure added and text improved

We compute the fermionic contribution to the strong coupling $\alpha_{qq}$ extracted from the static force in Lattice QCD up to order $g^4$ in perturbation theory. This allows us to subtract the leading fermionic lattice artifacts from recent determinations of $\alpha_{qq}$ produced in simulations of two dynamical charm quarks. Moreover, by using a suitable parametrization of the $\beta_{qq}$-function, we can evaluate the charm loop effects on $\alpha_{qq}$ in the continuum limit., Comment: 8 pages, 2 figures; Proceedings of the 35th International Symposium on Lattice Field Theory, Granada, Spain