arXiv subjects

Anna Hasenfratz

Publications and source records attributed to Anna Hasenfratz.

At least 73 records · Page 4Linked to original sources

arXiv2014

Improving the continuum limit of gradient flow step scaling

We introduce a non-perturbative improvement for the renormalization group step scaling function based on the gradient flow running coupling, which may be applied to any lattice gauge theory of interest. Considering first SU(3) gauge theory with $N_f = 4$ massless staggered fermions, we demonstrate that this improvement can remove $O(a^2)$ lattice artifacts, and thereby increases our control over the continuum extrapolation. Turning to the 12-flavor system, we observe an infrared fixed point in the infinite-volume continuum limit. Applying our proposed improvement reinforces this conclusion by removing all observable $O(a^2)$ effects. For the finite-volume gradient flow renormalization scheme defined by $c = \sqrt{8t} / L = 0.2$, we find the continuum conformal fixed point to be located at $g_\star^2 = 6.2(2)$

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arXiv2013

Finite size scaling of conformal theories in the presence of a near-marginal operator

The slowly evolving gauge coupling of gauge-fermion systems near the conformal window makes numerical investigations of these models challenging. We consider finite size scaling and show that this often used technique leads to inconsistent results if the leading order scaling corrections are neglected. When the corrections are included the results become consistent not only between different operators but even when data obtained at different gauge couplings or with different lattice actions are combined. Our results indicate that the SU(3) 12-fermion system is conformal with mass anomalous dimension $γ_m=0.235(15)$.

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arXiv2013

Improved Lattice Renormalization Group Techniques

We compute the bare step-scaling function $s_b$ for SU(3) lattice gauge theory with $N_f = 12$ massless fundamental fermions, using the non-perturbative Wilson-flow-optimized Monte Carlo Renormalization Group two-lattice matching technique. We use a short Wilson flow to approach the renormalized trajectory before beginning RG blocking steps. By optimizing the length of the Wilson flow, we are able to determine an $s_b$ corresponding to a unique discrete $β$ function, after a few blocking steps. We carry out this study using new ensembles of 12-flavor gauge configurations generated with exactly massless fermions, using volumes up to $32^4$. The results are consistent with the existence of an infrared fixed point (IRFP) for all investigated lattice volumes and number of blocking steps. We also compare different renormalization schemes, each of which indicates an IRFP at a slightly different value of the bare coupling, as expected for an IR-conformal theory.

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arXiv2013

Determining the mass anomalous dimension through the eigenmodes of Dirac operator

We define a scale-dependent effective mass anomalous dimension from the scaling of the mode number of the massless Dirac operator, which connects the perturbative $γ_m$ of an asymptotically-free system to the universal $γ_m^{\star}$ at a conformal fixed point. We use a stochastic algorithm to measure the mode number up to the cutoff scale on lattices as large as $48^4$. Focusing on SU(3) lattice gauge theory with $N_f = 12$ massless fundamental fermions, we examine systematic effects due to finite volumes and non-zero fermion masses. Our results suggest the existence of an infrared fixed point with $γ_m^{\star} \approx 0.25$. Our method provides a unique probe to study systems from the UV to the IR. It is universal and can be applied to any lattice model of interest, including both chirally-broken and IR-conformal systems.

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arXiv2013

Finite size scaling and the effect of the gauge coupling in 12 flavor systems

Finite size scaling is a powerful tool to study the critical properties of systems governed by one relevant operator, assuming all irrelevant operators have scaling dimensions much smaller then zero. This condition is likely not satisfied in many-fermion conformal systems where perturbation theory predicts a nearly-marginal irrelevant gauge coupling. In this work we carry out a new investigation of SU(3) lattice gauge theory with 12 fundamental flavors. Analyzing data at many different gauge couplings, our preliminary results indicate that a finite size scaling analysis that takes into account the effect of a nearly-marginal gauge coupling can resolve many of the inconsistencies observed previously in this system, leading to results consistent with conformal infrared dynamics and predicting a mass scaling anomalous around $γ_m=0.25$.

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arXiv2013

Lattice Gauge Theories at the Energy Frontier

This White Paper has been prepared as a planning document for the Division of High Energy Physics of the U. S. Department of Energy. Recent progress in lattice-based studies of physics beyond the standard model is summarized, and major current goals of USQCD research in this area are presented. Challenges and opportunities associated with the recently discovered 126 GeV Higgs-like particle are highlighted. Computational resources needed for reaching important goals are described. The document was finalized on February 11, 2013 with references that are not aimed to be complete, or account for an accurate historical record of the field.

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arXiv2013

Scale-dependent mass anomalous dimension from Dirac eigenmodes

We investigate the eigenmodes of the massless Dirac operator to extract the scale-dependent fermion mass anomalous dimension gamma_m(mu). By combining simulations on multiple lattice volumes, and when possible several gauge couplings, we are able to measure the anomalous dimension across a wide range of energy scales. The method that we present is universal and can be applied to any lattice model of interest, including both conformal or chirally broken systems. We consider SU(3) lattice gauge theories with Nf=4, 8 and 12 light or massless fermions. The 4-flavor model behaves as expected for a QCD-like system and demonstrates that systematic effects are manageable in practical lattice calculations. Our 12-flavor results are consistent with the existence of an infrared fixed point, at which we predict the scheme-independent mass anomalous dimension gamma_m^*=0.32(3). For the 8-flavor model we observe a large anomalous dimension across a wide range of energy scales. Further investigation is required to determine whether Nf=8 is chirally broken and walking, or if it possesses a strongly-coupled conformal fixed point.

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arXiv2013

Reaching the chiral limit in many flavor systems

We present a brief overview of our recent lattice studies of SU(3) gauge theory with N_f = 8 and 12 fundamental fermions, including some new and yet-unpublished results. To explore relatively unfamiliar systems beyond lattice QCD, we carry out a wide variety of investigations with the goal of synthesizing the results to better understand the non-perturbative dynamics of these systems. All our findings are consistent with conformal infrared dynamics in the 12-flavor system, but with 8 flavors we observe puzzling behavior that requires further investigation. Our new Monte Carlo renormalization group technique exploits the Wilson flow to obtain more direct predictions of a 12-flavor IR fixed point. Studies of N_f = 12 bulk and finite-temperature transitions also indicate IR conformality, while our current results for the 8-flavor phase diagram do not yet provide clear signs of spontaneous chiral symmetry breaking. From the Dirac eigenvalue spectrum we extract the mass anomalous dimension gamma_m, and predict gamma*_m = 0.32(3) at the 12-flavor fixed point. The N_f = 8 system again shows interesting behavior, with a large anomalous dimension across a wide range of energy scales. We use the eigenvalue density to predict the chiral condensate, and compare this approach with direct and partially-quenched measurements.

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arXiv2012

MCRG study of 8 and 12 fundamental flavors

We study the renormalization group properties of SU(3) gauge theories with N_f=8 and 12 nearly-massless fermions, using Monte Carlo Renormalization Group (MCRG) two-lattice matching techniques to predict bare step-scaling functions s_b. Traditional MCRG two-lattice matching requires that the renormalization scheme be optimized for each bare lattice coupling, so that s_b is a composite of many different discrete beta functions. We propose an improved procedure that uses the Wilson flow to eliminate the need for this optimization of the RG blocking transformation. While our 12-flavor results indicate an infrared fixed point, s_b for N_f=8 is significantly different from zero until strong-coupling lattice artifacts obstruct two-lattice matching. Although both procedures produce qualitatively similar bare step-scaling functions, the new s_b obtained by combining the Wilson flow with MCRG two-lattice matching have the distinct advantage of corresponding to unique discrete beta functions.

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arXiv2012

Bulk and finite-temperature transitions in SU(3) gauge theories with many light fermions

We investigate finite-temperature transitions in SU(3) lattice gauge theories with Nf=8 and 12 staggered fermions in the fundamental representation. For both of these systems, we have observed a strongly-coupled lattice phase in which the single-site shift symmetry of the staggered action is spontaneously broken. Here we report new results for finite-temperature transitions on 24^3x12 and 32^3x16 lattice volumes, contrasting the 8- and 12-flavor systems. While the Nf=12 finite-temperature transitions accumulate at the bulk transition bounding the strongly-coupled lattice phase, the Nf=8 finite-temperature transitions are able to pass through the bulk transition, and behave as expected for a QCD-like system. We discuss our current results and the work in progress to complete our investigation of the finite-temperature phase diagram.

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arXiv2012

Mass anomalous dimension from Dirac eigenmode scaling in conformal and confining systems

The mode number of the Dirac operator scales with an exponent related to the mass anomalous dimension gamma_m. This relation holds both in IR-conformal systems, as well as in confining systems for large enough eigenvalues. We investigate the Nf=4, 8 and 12 flavor SU(3) systems at several couplings near the chiral limit, and show that in general the scaling exponent varies with the eigenvalue, describing the dependence of gamma_m on the energy (or, equivalently, on the running coupling). This energy dependence can be explored even with fixed lattice parameters (bare coupling and mass). We find that for the 4 flavor system the mass anomalous dimension decreases as the energy increases, consistent with perturbative expectations. For the 8 flavor system the energy dependence is too weak to be observable at present. The 12 flavor system at our strongest couplings shows the anomalous dimension increasing with energy, consistent with backward flow and the presence of an infrared fixed point. At weaker couplings we determine a preliminary value for the mass anomalous dimension of the 12 flavor system at the infrared fixed point, gamma_m^*=0.27(3).

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arXiv2012

Novel phase in SU(3) lattice gauge theory with 12 light fermions

We study the phase structure of SU(3) lattice gauge theory with Nf=12 staggered fermions in the fundamental representation, for both zero and finite temperature at strong gauge couplings. For small fermion masses we find two transitions at finite temperature that converge to two well-separated bulk phase transitions. The phase between the two transitions appears to be a novel phase. We identify order parameters showing that the single-site shift symmetry of staggered fermions is spontaneously broken in this phase. We investigate the eigenvalue spectrum of the Dirac operator, the static potential and the meson spectrum, which collectively establish that this novel phase is confining but chirally symmetric. The phase is bordered by first-order phase transitions, and since we find the same phase structure with Nf=8 fermions, we argue that the novel phase is most likely a strong-coupling lattice artifact, the existence of which does not imply IR conformality.

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arXiv2011

MCRG study of 12 fundamental flavors with mixed fundamental-adjoint gauge action

I discuss the infrared behavior of the SU(3) gauge model with 12 fundamental fermions. Using a Monte Carlo renormalization group technique I investigate the fixed point structure in the chiral limit and show that this system has an infrared fixed point and consequently conformal infrared dynamics. I am able to reach the FP by using a new analysis method for the 2-lattice matching MCRG technique that significantly reduces finite volume effects and by choosing a lattice action that avoids a spurious ultraviolet fixed point created by strong coupling lattice artifacts.

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arXiv2011

Infrared fixed point of the 12-fermion SU(3) gauge model based on 2-lattice MCRG matching

I investigate an SU(3) gauge model with 12 fundamental fermions. The physically interesting region of this strongly coupled system can be influenced by an ultraviolet fixed point due to lattice artifacts. I suggest to use a gauge action with an additional negative adjoint plaquette term that lessens this problem. I also introduce a new analysis method for the 2-lattice matching Monte Carlo renormalization group technique that significantly reduces finite volume effects. The combination of these two improvements allows me to measure the bare step scaling function in a region of the gauge coupling where it is clearly negative, indicating a positive renormalization group $β$ function and infrared conformality.

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arXiv2010

Conformal or Walking? Monte Carlo renormalization group studies of SU(3) gauge models with fundamental fermions

Strongly coupled gauge systems with many fermions are important in many phenomenological models. I use the 2-lattice matching Monte Carlo renormalization group method to study the fixed point structure and critical indexes of SU(3) gauge models with 8 and 12 flavors of fundamental fermions. With an improved renormalization group block transformation I am able to connect the perturbative and confining regimes of the N_f=8 flavor system, thus verifying its QCD-like nature. With N_f=12 flavors the data favor the existence of an infrared fixed point and conformal phase, though the results are also consistent with very slow walking. I measure the anomalous mass dimension in both systems at several gauge couplings and find that they are barely different from the free field value.

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arXiv2009

Scaling properties of many-fermion systems from MCRG studies

Monte Carlo renormalization group methods were designed to study the phase structure and critical behavior of statistical systems. They are well suited to determine the running coupling and to investigate the properties of fixed points of gauge-fermion models, including the existence of conformal infrared fixed points in many-fermion systems. I discuss the implementation of the 2-lattice matching method and present results for SU(3) gauge theories with N_f=0,12 and 16 fundamental fermion flavors.

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arXiv2009

Comments on lattice gauge theories with infrared-attractive fixed points

Theories of interacting gauge fields and fermions can possess a running gauge coupling with an infrared attractive fixed point (IRFP). We present a minimal description of the physics of these systems and comment on some simple expectations for results from lattice simulations done within the basin of attraction of the IRFP in these theories.

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arXiv2009

Investigating the critical properties of beyond-QCD theories using Monte Carlo Renormalization Group matching

Monte Carlo Renormalization Group (MCRG) methods were designed to study the non-perturbative phase structure and critical behavior of statistical systems and quantum field theories. I adopt the 2-lattice matching method used extensively in the 1980's and show how it can be used to predict the existence of non-perturbative fixed points and their related critical exponents in many flavor SU(3) gauge theories. This work serves to test the method and I study relatively well understood systems: the $N_f=0$, 4 and 16 flavor models. The pure gauge and $N_f=4$ systems are confining and chirally broken and the MCRG method can predict their bare step scaling functions. Results for the $N_f=16$ model indicate the existence of an infrared fixed point with nearly marginal gauge coupling. I present preliminary results for the scaling dimension of the mass at this new fixed point.

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