The impact of stout-link smearing in lattice fermion actions is examined
through the consideration of the mass and renormalization functions of the
overlap quark propagator over a variety of smeared configurations. Up to six
sweeps of stout-link smearing are investigated. For heavy quark masses, the
quark propagator is strongly affected by the smearing procedure. For moderate
masses, the effect appears to be negligible. A small effect is seen for light
quark masses, where dynamical mass generation is suppressed through the
smearing procedure.Comment: 7 pages, 3 figures, presented at the XXVII International Symposium on
  Lattice Field Theory - LAT2009, July 26-31 2009, Peking University, Beijing,
  Chin

Bowman, Patrick O.

Leinweber, Derek B.

Moran, Peter J.

Williams, Anthony G.

Zhang, J. B.

English

arXiv

The impact of stout-link smearing in lattice fermion actions is examined through the consideration of the mass and renormalization functions of the overlap quark propagator over a variety of smeared configurations. Up to six sweeps of stout-link smearing are investigated. For heavy quark masses, the quark propagator is strongly affected by the smearing procedure. For moderate masses, the effect appears to be negligible. A small effect is seen for light quark masses, where dynamical mass generation is suppressed through the smearing procedure.Peter J. Moran, Patrick O. Bowman, Derek B. Leinweber, Anthony G. Williams and J. B. Zhan

Moran, P.

Bowman, P.

Leinweber, D.

Williams, A.

Zhang, J.

Adelaide Research &amp; Scholarship

PUBLISHED VERSION   Peter J. Moran, Patrick O. Bowman, Derek B. Leinweber, Anthony G. Williams and J. B. Zhang Impact of Stout-link smearing in lattice fermion actions Proceedings of the XXVII International Symposium on Lattice Field Theory (LAT 2009), pp. 023-1-023-7.  Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.                           http://hdl.handle.net/2440/59000  PERMISSIONS http://pos.sissa.it/POSlicense.html   Given the Open Access nature of this proceedings collection, PoS has chosen to apply the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.    11th September 2015 PoS(LAT2009)023Impact of stout-link smearing in lattice fermionactionsPeter J. Morana, Patrick O. Bowmanb, Derek B. Leinweber∗a, Anthony G. Williamsaand J. B. ZhangacaSpecial Research Center for the Subatomic Structure of Matter (CSSM) andDepartment of Physics, University of Adelaide 5005, AustraliabCentre for Theoretical Chemistry and Physics and Institute of Natural Sciences,Massey University (Albany), Private Bag 102904,North Shore City 0745, New ZealandcZIMP and Department of Physics, Zhejiang University, Hangzhou, 310027,People’s Republic of ChinaE-mail: peter.moran@adelaide.edu.au, P.O.Bowman@massey.ac.nz,dleinweb@physics.adelaide.edu.au, anthony.williams@arcs.org.au,jzhang@physics.adelaide.edu.auThe impact of stout-link smearing in lattice fermion actions is examined through the consider-ation of the mass and renormalization functions of the overlap quark propagator over a varietyof smeared configurations. Up to six sweeps of stout-link smearing are investigated. For heavyquark masses, the quark propagator is strongly affected by the smearing procedure. For moderatemasses, the effect appears to be negligible. A small effect is seen for light quark masses, wheredynamical mass generation is suppressed through the smearing procedure.The XXVII International Symposium on Lattice Field Theory - LAT2009July 26-31 2009Peking University, Beijing, China∗Speaker.c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(LAT2009)023Impact of Stout-link smearing in lattice fermion actions Derek B. Leinweber1. IntroductionThe term “fat-link fermions” is used to describe a class of actions in which smeared, or fat,gauge links are incorporated into the standard Wilson or Clover actions. Because the smearingalgorithms remove short-distance physics from the gauge field, these actions are also often referredto as UV-filtered actions. There is some flexibility in how these fat links are included in the Diracoperator. They can be used in all terms of the action [1, 2, 3, 4, 5], in just the relevant terms [6], oronly in the irrelevant terms [7, 8, 9, 10]. The fat-link irrelevant clover (FLIC) action is an exampleof the last of these choices.The FLIC action is O(a)-improved [8, 10], and by only including fat-links in the irrelevantWilson and Clover terms, the short-distance physics in the relevant operators is preserved. Thisallows relatively cheap access to the light quark mass regime [9], and excellent scaling with smallO(a2) errors that provide near continuum results at a finite lattice spacing a [10].S. Dürr et al. advocate [11] a fat-link fermion action in which all gauge links are smeared.Using a tree level, clover improved Wilson action with six sweeps of stout-link smearing, they suc-cessfully reproduced the light hadron spectrum. While six sweeps of smearing may seem exces-sive, there is no clear prescription for determining the correct number of smearing sweeps. Indeed,smearing only introduces extra irrelevant terms into the action, and so as long as the number ofsweeps and the smearing parameter are held fixed, the smearing should not alter the continuumlimit of the action.Although not a direct physical observable, the quark propagator is a fundamental componentof QCD, with many physical quantities depending on its properties. By studying the momentum-dependent quark mass function in the infrared region, one can gain valuable insights into the mech-anisms of dynamical chiral symmetry breaking and the associated dynamical generation of mass.In the following, we investigate the properties of the momentum space overlap quark prop-agator over a variety of smeared quenched configurations. Of particular interest is how the massand renormalization functions of the fermion propagator change as the gauge fields undergo moresmearing.As the configurations are smeared, the short-distance, ultraviolet fluctuations are removedfrom the gauge field. For heavy quarks one might expect that the Compton wavelength wouldbe short enough to reveal the void in gluon interactions left by the smearing procedure. As moresmearing sweeps are applied, this should cause the asymptotic value of the mass function to ap-proach the bare input mass.The ultraviolet physics that is most affected by the smearing algorithm is linked to the infraredphysics through approximate zero modes. In the QCD vacuum, there is a finite density of zeromodes of the Dirac operator, ρ(0), due to the presence of topologically nontrivial, instanton-likeobjects. The Dirac zero modes are intimately related to dynamical chiral symmetry breaking viathe Banks-Casher relation,〈q¯q〉=−pi ρ(0), as mq → 0 . (1.1)One might therefore expect that at light quark masses, the removal of short-distance, nontrivialtopological fluctuations through smearing would suppress the generation of approximate zero-modes. This would compromise dynamical mass generation, through dynamical chiral symmetrybreaking, for fat-link fermion actions.2PoS(LAT2009)023Impact of Stout-link smearing in lattice fermion actions Derek B. Leinweber2. Overlap quark propagatorThe massive overlap operator can be written as [12]D(µ) = 12[1+ µ +(1−µ)γ5ε(Hw)] , (2.1)where Hw(x,y) = γ5Dw(x,y) is the Hermitian Wilson-Dirac operator, ε(Hw) = Hw/√H2w is thematrix sign function, and the dimensionless quark mass parameter µ isµ ≡ m02mw, (2.2)where m0 is the bare quark mass and mw is the Wilson quark mass which, in the free case, must liein the range 0 < mw < 2.In a covariant gauge, the continuum, renormalized quark propagator has the formSζ (p) =Zζ (p2)ip/+ M(p2). (2.3)Whereas on the lattice we have at tree level,S(0)(p)≡ 1iq/+ m0, (2.4)where we have defined the kinematic lattice momentum q. The lattice mass and renormalizationfunctions are then defined by [13],Sζ (p) =Zζ (p2)iq/+ M(p2). (2.5)3. Simulation detailsWe consider 163×32 lattices, generated with a tadpole-improved Lüscher-Weisz action, witha lattice spacing of a = 0.093 fm [14]. To these configurations we apply standard, isotropic stout-link smearing [15] with ρ = 0.1, to create ensembles of 1, 3, and 6-sweep smeared configurations.Each level of smearing is then fixed to O(a2)-improved Landau gauge [16].We use the mean-field improved Wilson action in the overlap fermion kernel. The value κ =0.19163 is used in the Wilson action, which provides mwa = 1.391 for the Wilson regulator mass inthe interacting case [17]. The overlap quark propagator is calculated for 15 bare quark masses oneach ensemble and we report results for three different bare quark masses; m0 = 53 MeV (light),177 MeV (moderate), and 531 MeV (heavy). All data is cylinder cut [18]. Statistical uncertaintiesare estimated via a second-order, single-elimination jackknife.In a standard lattice simulation, one begins by tuning the value of the input bare quark mass m0to give the desired renormalized quark mass. However, smearing a lattice configuration filters outthe ultraviolet physics and gives a different renormalized quark mass. The input bare quark massmust then be re-tuned in order to reproduce the same physical behavior as on the unsmeared config-uration. We replicate this re-tuning procedure in our results by interpolating between neighboringquark masses, such that the functions agree at a given reference momentum ζ . For full details seeRef. [13].3PoS(LAT2009)023Impact of Stout-link smearing in lattice fermion actions Derek B. LeinweberFigure 1: The interpolated mass and renormalization functions for the moderate bare quark mass, m0 =177 MeV, with the three choices of ζ . The effective bare quark masses are given in square brackets. Apartfrom a splitting of the renormalization function for ζ = 2.0 GeV, the smearing has little effect on the quarkpropagator.4. ResultsWe begin with an analysis of the moderate bare quark mass, m0 = 177 MeV. The interpolatedmass and renormalization functions, for three choices of reference momentum, are shown in Fig. 1.For this choice of bare quark mass the smearing algorithm appears to have little effect on the quarkpropagator. The most obvious dependence is in the UV region of the renormalization function forζ = 2.0 GeV, where the smearing introduces a splitting of the curves.Next we consider the lighter quark mass, m0 = 53 MeV. The mass and renormalization func-tions are given in Fig. 2. As in the case of the moderate quark mass there appears to be little effecton the quark propagator. However when the quark masses are matched in the UV at ζ = 6.0 GeVthere is a significant suppression of dynamical mass generation for nsw = 6.Finally, we consider the heavy quark mass, m0 = 531 MeV, and provide the relevant functionsin Fig. 3. The impact of smearing is most apparent for this heavy mass. The most interesting4PoS(LAT2009)023Impact of Stout-link smearing in lattice fermion actions Derek B. LeinweberFigure 2: The interpolated mass and renormalization functions for the small bare quark mass, m0 = 53 MeV,with three choices of ζ . As with the moderate quark mass, the smearing has little effect on the propagator.However when the quark masses are matched in the UV at ζ = 6.0 GeV there is a significant suppression ofdynamical mass generation for nsw = 6.effect is in the mass function with the choice of ζ = 2.0 GeV, matching the infrared physics. Herethe mass function decreases dramatically as progressively more smearing is applied. We see thatsmearing the gauge field causes the asymptotic value of the mass function to approach the input barequark mass, clearly illustrating the short-distance void created by 6 sweeps of stout-link smearing.5. ConclusionSmearing all links in the gauge field only has a strong effect on the quark propagator for heavyquarks. Here suppression of the short distance physics through smearing spoils the physics of thetheory above about 2 to 3 GeV. Renormalization of the bare quark mass is not enough to restorethe flattening of the bare quark mass at large momenta. We also saw that the asymptotic value ofthe mass function approaches the input bare quark mass.5PoS(LAT2009)023Impact of Stout-link smearing in lattice fermion actions Derek B. LeinweberFigure 3: The interpolated mass and renormalization functions for the heavy bare quark mass, m0 =531 MeV, for the three choices of ζ . The effective bare quark masses are given in square brackets. Forthis choice of m0 the smearing has a strong impact on the quark propagator.For all values of the quark mass considered, the effect of one sweep of smearing on the renor-malization function is negligible. The small discrepancies, which are of the order of 2%, areinsensitive to the value of the quark mass. We also note a significant reduction in the statisticalerror, even after a single sweep of smearing.At the lightest quark mass, the anticipated suppression of dynamical mass generation is appar-ent. In the case of six smearing sweeps, we find an order 2σ reduction in the infrared dynamicalmass generation when the quark masses are matched. In this case, we also see that for p < 2 to3 GeV, the mass function for six sweeps of smearing lies systematically low. This effect is clearlyillustrated in the lower left panel of Fig. 2.AcknowledgmentsWe thank both eResearch SA and the NCI National Facility for generous grants of supercom-puter time which have enabled this project. This work is supported by the Australian Research6PoS(LAT2009)023Impact of Stout-link smearing in lattice fermion actions Derek B. LeinweberCouncil. J. B. Zhang is partly supported by Chinese NSFC-Grant No. 10675101 and 10835002.POB is supported by the Marsden Fund administered by the Royal Society of New Zealand.References[1] MILC Collaboration, T. A. DeGrand, A. Hasenfratz and T. G. Kovacs, Optimizing the chiralproperties of lattice fermion actions, hep-lat/9807002.[2] T. A. DeGrand, A. Hasenfratz and T. G. Kovacs, Instantons and exceptional configurations with theclover action, Nucl. Phys. B547 (1999) 259–280 [hep-lat/9810061].[3] A. Hasenfratz, R. Hoffmann and S. Schaefer, Hypercubic smeared links for dynamical fermions,JHEP 05 (2007) 029 [hep-lat/0702028].[4] S. Capitani, S. Durr and C. Hoelbling, Rationale for uv-filtered clover fermions, JHEP 11 (2006) 028[hep-lat/0607006].[5] S. Durr et. al., Scaling study of dynamical smeared-link clover fermions, Phys. Rev. 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Impact of Stout-link smearing in lattice fermion actions

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Impact of stout-link smearing in lattice fermion actions

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