arXiv subjects

Anna Hasenfratz

Publications and source records attributed to Anna Hasenfratz.

At least 37 records · Page 2Linked to original sources

arXiv2022

Gradient flow step-scaling function for SU(3) with $N_f=8$ fundamental flavors

The step-scaling function, the lattice analog of the renormalization group $β$ function, is presented for the SU(3) gauge system with eight flavors in the fundamental representation. Our investigation is based on generating dynamical eight flavor gauge field configurations using stout-smeared Möbius domain wall fermions and Symanzik gauge action. On these gauge field configurations we perform gradient flow measurements using the Zeuthen, Wilson, or Symanzik kernel and consider the Symanzik, Wilson plaquette, or clover operators to determine step-scaling functions for a scale change $s=2$ including large, up to $48^4$, volumes. Considering different flows and operators as well as the optional use of tree-level improvement allows us to check for possible systematic effects. Our result covers the range of renormalized coupling up to $g_c^2 \lesssim 10$. In the case of $N_f=8$ we observe that the reach in $g_c^2$ is limited due to an unphysical first order bulk phase transition caused by large ultra-violet fluctuations. We compare our findings to $N_f=4$, 6, 10 or 12 flavors results that are obtained using the same lattice action and analysis. In addition we investigate the phase structure for simulations with different number of flavors using stout-smeared Möbius domain wall fermions and Symanzik gauge actions to shed some light on the limited reach in $g_c^2$.

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arXiv2022

Lattice QCD and Particle Physics

Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021).

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arXiv2022

Gradient flow step-scaling function for SU(3) with $N_f$ = 6 or 4 fundamental flavors

Nonperturbative determinations of the renormalization group (RG) $β$ function are crucial to understand properties of gauge-fermion systems at strong coupling and connect lattice simulations and the perturbative ultraviolet regime. Choosing well-understood, QCD-like systems with SU(3) gauge group and either six or four fundamental flavors, we investigate their step-scaling $β$ function. In both cases we push the simulations to the boundary of chiral symmetry breaking and study the regime $g^2_{GF} \lesssim 8.2$ with six, and $g^2_{GF} \lesssim 6.6$ with four flavors. We carefully consider the lattice discretization errors by comparing three different gradient flows (GF), and for each flow three operators to estimate the renormalized finite volume coupling. We also consider the tree level improvement of the coupling. Noteworthy outcome is that nonperturbatively determined $β$ functions run much slower than perturbatively predicted.

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arXiv2022

Report of the Snowmass 2021 Topical Group on Lattice Gauge Theory

Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy Physics. Whether it is to enable precision quark- and lepton-flavor physics, to uncover signals of new physics in nucleons and nuclei, to elucidate hadron structure and spectrum, to serve as a numerical laboratory to reach beyond the Standard Model, or to invent and improve state-of-the-art computational paradigms, the lattice-gauge-theory program is in a prime position to impact the course of developments and enhance discovery potential of a vibrant experimental program in High-Energy Physics over the coming decade. This projection is based on abundant successful results that have emerged using lattice gauge theory over the years: on continued improvement in theoretical frameworks and algorithmic suits; on the forthcoming transition into the exascale era of high-performance computing; and on a skillful, dedicated, and organized community of lattice gauge theorists in the U.S. and worldwide. The prospects of this effort in pushing the frontiers of research in High-Energy Physics have recently been studied within the U.S. decadal Particle Physics Planning Exercise (Snowmass 2021), and the conclusions are summarized in this Topical Report.

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arXiv2022

Emergent strongly coupled ultraviolet fixed point in four dimensions with 8 Kähler-Dirac fermions

The existence of a strongly coupled ultraviolet fixed point in 4-dimensional lattice models as they cross into the conformal window has long been hypothesized. The SU(3) gauge system with 8 fundamental fermions is a good candidate to study this phenomenon as it is expected to be very close to the opening of the conformal window. I study the system using staggered lattice fermions in the chiral limit. My numerical simulations employ improved lattice actions that include heavy Pauli-Villars (PV) type bosons. This modification does not affect the infrared dynamics but greatly reduces the ultraviolet fluctuations, thus allowing the study of stronger renormalized couplings than previously possible. I consider two different PV actions and find that both show an apparent continuous phase transition in the 8-flavor system. I investigate the critical behavior using finite size scaling of the renormalized gradient flow coupling. The finite size scaling curve-collapse analysis predicts a first order phase transition consistent with discontinuity exponent $ν=1/4$ in the system without PV bosons. The scaling analysis with the PV boson actions is not consistent with a first order phase transition. The numerical data are well described by "walking scaling" corresponding to a renormalization group $β$ function that just touches zero, $β(g^2) \sim (g^2 - g^2_\star)^2$, though second order scaling cannot be excluded. Walking scaling could imply that the 8-flavor system is the opening of the conformal window, an exciting possibility that could be related to t'Hooft anomaly cancellation of the system.

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arXiv2022

A novel nonperturbative renormalization scheme for local operators

The gradient flow exponentially suppresses ultraviolet field fluctuations and removes ultraviolet divergences (up to a multiplicative fermionic wavefunction renormalization). It can be used to describe real-space Wilsonian renormalization group transformations and determine the corresponding beta function. We propose a new nonperturbative renormalization scheme for local composite fermionic operators that uses the gradient flow and is amenable to lattice QCD calculations. We present preliminary nonperturbative results for the running of quark bilinear operators in this scheme and outline the calculation of perturbative matching to the MS-bar scheme.

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arXiv2021

Determination of the continuous $β$ function of SU(3) Yang-Mills theory

In infinite volume the gradient flow transformation can be interpreted as a continuous real-space Wilsonian renormalization group (RG) transformation. This approach allows one to determine the continuous RG $β$ function, an alternative to the finite-volume step-scaling function. Unlike step-scaling, where the lattice must provide the only scale, the continuous $β$ function can be used even in the confining regime where dimensional transmutation generates a physical scale $Λ_{\mathrm{QCD}}$. We investigate a pure gauge SU(3) Yang-Mills theory both in the deconfined and the confined phases and determine the continuous $β$ function in both. Our investigation is based on simulations done with the tree-level Symanzik gauge action on lattice volumes up to $32^4$ using both Wilson and Zeuthen gradient flow (GF) measurements. Our continuum GF $β$ function exhibits considerably slower running than the universal 2-loop perturbative prediction, and at strong couplings it runs even slower than the 1-loop prediction.

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arXiv2021

Taming lattice artifacts with Pauli--Villars fields

As fermions are added to a lattice gauge theory, one is driven to stronger bare coupling in order to maintain the same renormalized coupling. Stronger bare couplings are usually associated with larger gauge fluctuations, leading to larger cutoff effects and more expensive simulations. In theories with many light fermions, sometimes the desired physical region cannot be reached before encountering a phase boundary. We show that these undesired effects can be reduced by adding Pauli--Villars fields. We reach significantly larger renormalized couplings while at the same time damping short-distance fluctuations of the gauge field. This may allow for controlled continuum extrapolations from large lattice spacings.

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arXiv2021

Near-conformal dynamics in a chirally broken system

Composite Higgs models must exhibit very different dynamics from quantum chromodynamics (QCD) regardless whether they describe the Higgs boson as a dilatonlike state or a pseudo-Nambu-Goldstone boson. Large separation of scales and large anomalous dimensions are frequently desired by phenomenological models. Mass-split systems are well-suited for composite Higgs models because they are governed by a conformal fixed point in the ultraviolet but are chirally broken in the infrared. In this work we use lattice field theory calculations with domain wall fermions to investigate a system with four light and six heavy flavors. We demonstrate how a nearby conformal fixed point affects the properties of the four light flavors that exhibit chiral symmetry breaking in the infrared. Specifically we describe hyperscaling of dimensionful physical quantities and determine the corresponding anomalous mass dimension. We obtain $y_m=1+γ^*= 1.47(5)$ suggesting that $N_f=10$ lies inside the conformal window. Comparing the low energy spectrum to predictions of dilaton chiral perturbation theory, we observe excellent agreement which supports the expectation that the 4+6 mass-split system exhibits near-conformal dynamics with a relatively light $0^{++}$ isosinglet scalar.

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arXiv2020

Composite Higgs scenario in mass-split models

Mass-split composite Higgs models naturally accommodate the experimental observation of a light 125 GeV Higgs boson and predict a large scale separation to other heavier resonances. We explore the SU(3) gauge system with four light (massless) and six heavy (massive) flavors by performing numerical simulations. Since the underlying system with degenerate and massless ten flavors appears to be infrared conformal, this system inherits conformal hyperscaling and allows to study near-conformal dynamics. Carrying out nonperturbative lattice field theory simulations, we present the low-lying particle spectrum. We demonstrate hyperscaling, predict the anomalous mass dimension of the corresponding conformal fixed point, and show that in the investigated mass regime the data are described by dilaton chiral perturbation theory. The proximity of a conformal infrared fixed point leads to a highly predictive particle spectrum which is quite distinct from QCD. Further we present initial results of our finite temperature investigations.

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arXiv2020

Gradient flow step-scaling function for SU(3) with ten fundamental flavors

We calculate the step scaling function, the lattice analog of the renormalization group $β$-function, for an SU(3) gauge theory with ten fundamental flavors. We present a detailed analysis including the study of systematic effects of our extensive data set generated with ten dynamical flavors using the Symanzik gauge action and three times stout smeared Möbius domain wall fermions. Using up to $32^4$ volumes, we calculate renormalized couplings for different gradient flow schemes and determine the step-scaling $β$ function for a scale change $s=2$ on up to five different lattice volume pairs. In an accompanying paper we discuss that gradient flow can promote lattice dislocations to instanton-like objects, introducing nonperturbative lattice artifacts to the step scaling function. Motivated by the observation that Wilson flow sufficiently suppresses these artifacts, we choose Wilson flow with the Symanzik operator as our preferred analysis. We study systematic effects by calculating the step-scaling function based on alternative flows (Zeuthen or Symanzik), alternative operators (Wilson plaquette, clover), and also explore the effects of the perturbative tree-level improvement. Further we investigate the effects due to the finite value of $L_s$.

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arXiv2020

Dislocations under gradient flow and their effect on the renormalized coupling

Non-zero topological charge is prohibited in the chiral limit of gauge-fermion systems because any instanton would create a zero mode of the Dirac operator. On the lattice, however, the geometric $Q_\text{geom}=\langle F{\tilde F}\rangle /32π^2$ definition of the topological charge does not necessarily vanish even when the gauge fields are smoothed for example with gradient flow. Small vacuum fluctuations (dislocations) not seen by the fermions may be promoted to instanton-like objects by the gradient flow. We demonstrate that these artifacts of the flow cause the gradient flow renormalized gauge coupling to increase and run faster. In step-scaling studies such artifacts contribute a term which increases with volume. The usual $a/L\to 0$ continuum limit extrapolations can hence lead to incorrect results. In this paper we investigate these topological lattice artifacts in the SU(3) 10-flavor system with domain wall fermions and the 8-flavor system with staggered fermions. Both systems exhibit nonzero topological charge at the strong coupling, especially when using Symanzik gradient flow. We demonstrate how this artifact impacts the determination of the renormalized gauge coupling and the step-scaling $β$ function.

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arXiv2020

Continuous renormalization group $β$ function from lattice simulations

We present a real-space renormalization group transformation with continuous scale change to calculate the continuous renormalization group $β$ function in non-perturbative lattice simulations. Our method is motivated by the connection between Wilsonian renormalization group and the gradient flow transformation. It does not rely on the perturbative definition of the renormalized coupling and is also valid at non-perturbative fixed points. Although our method requires an additional extrapolation compared to traditional step scaling calculations, it has several advantages which compensates for this extra step even when applied in the vicinity of the perturbative fixed point. We illustrate our approach by calculating the $β$ function of 2-flavor QCD and show that lattice predictions from individual lattice ensembles, even without the required continuum and finite volume extrapolations, can be very close to the result of the full analysis. Thus our method provides a non-perturbative framework and intuitive understanding into the structure of strongly coupled systems, in addition to being complementary to existing lattice determinations.

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arXiv2019

Constructing a composite Higgs model with built-in large separation of scales

Experimentally the existence of a light 125 GeV Higgs boson is well established but so far no other heavier resonances have been observed. Viable models to describe the Higgs boson as composite particle require hence to exhibit a large separation of scales. This occurs naturally in systems located near a conformal fixed point irrespective whether the system lies outside or inside the conformal window. We demonstrate the latter case by investigating a mass-split model with four light and six heavy flavors. By construction mass-split models exhibit a large separation of scales and feature in addition a highly constrained hadron spectrum. We present results based on the low-lying connected meson spectrum. Although the light sector is chirally broken, we show that it exhibits hyperscaling which is typical for conformal systems.

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arXiv2019

Continuous $β$ function for the SU(3) gauge systems with two and twelve fundamental flavors

The gradient flow transformation can be interpreted as continuous real-space renormalization group transformation if a coarse-graining step is incorporated as part of calculating expectation values. The method allows to predict critical properties of strongly coupled systems including the renormalization group $β$ function and anomalous dimensions at nonperturbative fixed points. In this contribution we discuss a new analysis of the continuous renormalization group $β$ function for $N_f=2$ and $N_f=12$ fundamental flavors in SU(3) gauge theories based on this method. We follow the approach developed and tested for the $N_f=2$ system in arXiv:1910.06408. Here we present further information on the analysis, emphasizing the robustness and intuitive features of the continuous $β$ function calculation. We also discuss the applicability of the continuous $β$ function calculation in conformal systems, extending the possible phase diagram to include a 4-fermion interaction. The numerical analysis for $N_f=12$ uses the same set of ensembles that was generated and analyzed for the step scaling function in arXiv:1909.05842. The new analysis uses volumes with $L \ge 20$ and determines the $β$ function in the $c=0$ gradient flow renormalization scheme. The continuous $β$ function predicts the existence of a conformal fixed point and is consistent between different operators. Although determinations of the step scaling and continuous $β$ function use different renormalization schemes, they both predict the existence of a conformal fixed point around $g^2\sim 6$.

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arXiv2019

Gradient flow step-scaling function for SU(3) with twelve flavors

We calculate the step scaling function, the lattice analog of the renormalization group $β$-function, for an SU(3) gauge theory with twelve flavors. The gauge coupling of this system runs very slowly, which is reflected in a small step scaling function, making numerical simulations particularly challenging. We present a detailed analysis including the study of systematic effects of our extensive data set generated with twelve dynamical flavors using the Symanzik gauge action and three times stout smeared Möbius domain wall fermions. Using up to $32^4$ volumes, we calculate renormalized couplings for different gradient flow schemes and determine the step-scaling $β$ function for a scale change $s=2$ on up to five different lattice volume pairs. Our preferred analysis is fully $O(a^2)$ Symanzik improved and uses Zeuthen flow combined with the Symanzik operator. We find an infrared fixed point within the range $5.2 \le g_c^2 \le 6.4$ in the $c=0.250$ finite volume gradient flow scheme. We account for systematic effects by calculating the step-scaling function based on alternative flows (Wilson or Symanzik) as well as operators (Wilson plaquette, clover) and also explore the effects of the perturbative tree-level improvement.

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arXiv2019

Stochastic Renormalization Group and Gradient Flow in Scalar Field Theory

Recently, the connections between gradient flow and renormalization group have been explored analytically and numerically. Gradient flow (when modified by a field rescaling) can be characterized as a continuous blocking transformation. In this work, we draw a connection between gradient flow and functional renormalization group by describing how FRG can be represented by a stochastic process, and how the stochastic observables relate to gradient flow observables. The relation implies correlator scaling formulae that can be applied numerically in lattice simulations. We present preliminary results on anomalous dimensions obtained from such measurements in the context of 3-dimensional lattice $ϕ^4$ theory.

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arXiv2019

Lattice Gauge Theory for Physics Beyond the Standard Model

This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice field theory research to make an impact on models of new physics beyond the Standard Model, including composite Higgs, composite dark matter, and supersymmetric theories.

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