arXiv subjects

Oliver Witzel

Publications and source records attributed to Oliver Witzel.

At least 37 records · Page 2Linked to original sources

arXiv2022

Gradient flow scale setting with tree-level improvement

Lattice scales defined using gradient flow are typically very precise, while also easy to calculate. However, different definitions of flows and operators can differ significantly, suggesting possible systematical effects. Using a subset of RBC-UKQCD's 2+1 flavor domain wall fermion and Iwasaki gauge action ensembles, we explore differences between $\sqrt{t_0}$ and $w_0$ gradient flow scales, compare the impact of different operators to define the energy density, and study the effect of using tree-level improvement for the gradient flow. We find that for this set of gauge field ensembles Zeuthen flow with Symanzik operators has the most consistent approach to the continuum limit and exhibit very small cutoff corrections. Tree-level improvement, traditionally used in step-scaling studies, significantly reduces the spread between different operators, but does not lead to an overall improvement when it comes to reducing cutoff effects for gradient flow scales $\sqrt{t_0}$ or $w_0$.

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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

A lattice QCD perspective on weak decays of b and c quarks Snowmass 2022 White Paper

Lattice quantum chromodynamics has proven to be an indispensable method to determine nonperturbative strong contributions to weak decay processes. In this white paper for the Snowmass community planning process we highlight achievements and future avenues of research for lattice calculations of weak $b$ and $c$ quark decays, and point out how these calculations will help to address the anomalies currently in the spotlight of the particle physics community. With future increases in computational resources and algorithmic improvements, percent level (and below) lattice determinations will play a central role in constraining the standard model or identifying new physics.

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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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arXiv2022

Semileptonic $D \rightarrow π\ell ν$, $D \rightarrow K \ell ν$ and $D_s \rightarrow K \ell ν$ decays with 2+1f domain wall fermions

We present the status of our project to calculate $D \to π\ell ν$, $D \to K \ell ν$ and $D_s \to K \ell ν$ semileptonic form factors using domain wall fermions for both heavy and light quarks. Our computations are performed using RBC/UKQCD's set of 2+1 flavour domain wall fermion and Iwasaki gauge field ensembles. We plan to calculate three-point functions covering the full, physically allowed kinematic range. Given that the signal decays faster than the noise, unambiguously and reliably extracting the ground state is critical for success. We include an analysis of operator diagonalisation within several possible $2 \times 2$ operator bases and find an admixture of gauged fixed wall and $\mathbb{Z} \left( 2 \right)$ wall sources to be acceptable at both zero and non-zero momentum. Initial results for semileptonic form factors are presented for first ensembles.

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arXiv2021

Form factors for semileptonic $B\toπ$, $B_s\to K$ and $B_s\to D_s$ decays

We report on our determinations of $B\to π\ellν$, $B_s\to K \ell ν$ and $B_s\to D_s \ell ν$ semileptonic form factors. In addition we discuss the determination of $R$-ratios testing lepton-flavor universality and suggest an improved ratio. Our calculations are based on the set of 2+1 flavor domain-wall Iwasaki gauge field configurations generated by the RBC/UKQCD collaboration with three lattice spacings of $1/a = 1.78$, $2.38$, and $2.79\,\text{GeV}$. We use the relativistic heavy quark action for $b$ quarks and charm quarks are simulated with the Möbius domain-wall fermion action.

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arXiv2021

BSM $B - \bar{B}$ mixing on JLQCD and RBC/UKQCD $N_f=2+1$ DWF ensembles

We are presenting our ongoing Lattice QCD study on $B - \bar{B}$ mixing on several RBC/UKQCD and JLQCD ensembles with 2+1 dynamical-flavour domain-wall fermions, including physical-pion-mass ensembles. We are extracting bag parameters $B_{B_d}$ and $B_{B_s}$ using the full 5-mixing-operator basis to study both Standard-Model mixing as well as Beyond the Standard Model mixing, using a fully correlated combined fit to two-point functions and ratios of three-point and two-point functions. Using 15 different lattice ensembles we are simulating a range of heavy-quark masses from below the charm-quark mass to just below the bottom-quark mass.

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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

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

Nonperturbative calculations of form factors for exclusive semileptonic $B_{(s)}$ decays

Precise theoretical predictions derived from the Standard Model are a key ingredient in searches for new physics in the flavor sector. The large mass and long lifetime of the $b$ quark make processes involving $b$ quarks of particular interest. We use lattice simulations to perform nonperturbative QCD calculations for semileptonic $B_{(s)}$ decays. We present results from our determinations of $B_s\to D_s \ell ν$ and $B_s\to K \ell ν$ semileptonic form factors and provide an outlook for our $B\to π\ellν$ calculation. In addition we discuss the determination of $R$-ratios testing lepton-flavor universality and suggest use of an improved ratio. Our calculations are based on the set of 2+1 flavor domain wall Iwasaki gauge field configurations generated by the RBC-UKQCD collaboration featuring three lattice spacings of $1/a = 1.78$, $2.38$, and $2.79\,\text{GeV}$. Heavy $b$-quarks are simulated using the relativistic heavy quark action.

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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

SU(3)-breaking ratios for $D_{(s)}$ and $B_{(s)}$ mesons

We present results for the $SU(3)$ breaking ratios of decay constants $f_{D_s}/f_D$ and $f_{B_s}/f_B$ and - for the first time with physical pion masses - the ratio of bag parameters $B_{B_s}/B_{B_d}$, as well as the ratio $ξ$, forming the ratio of the nonpeturbative contributions to neutral $B_{(s)}$ meson mixing. Our results are based on Lattice QCD simulations with chirally symmetric 2+1 dynamical flavors of domain wall fermions. Eight ensembles at three different lattice spacing in the range $a = 0.11 - 0.07\,\mathrm{fm}$ enter the analysis two of which feature physical light quark masses. Multiple heavy quark masses are simulated ranging from below the charm quark mass to half the bottom quark mass. The $SU(3)$ breaking ratios display a very benign heavy mass behaviour allowing for extrapolation to the physical bottom quark mass. The results in the continuum limit including all sources of systematic errors are $f_{D_s}/f_D = 1.1740(51)_\mathrm{stat}(^{+68}_{-68})_\mathrm{sys}$, $f_{B_s}/f_B = 1.1949(60)_\mathrm{stat}(^{+\hphantom{0}95}_{-175})_\mathrm{sys}$, $B_{B_s}/B_{B_d} = 0.9984(45)_\mathrm{stat}(^{+80}_{-63})_\mathrm{sys}$ and $ξ= 1.1939(67)_\mathrm{stat}(^{+\hphantom{0}95}_{-177})_\mathrm{sys}$. Combining these with experimentally measured values we extract the ratios of CKM matrix elements $|V_{cd}/V_{cs}| = 0.2164(57)_\mathrm{exp}(^{+12}_{-12})_\mathrm{lat}$ and $|V_{td}/V_{ts}| = 0.20329(41)_\mathrm{exp}(^{+162}_{-301})_\mathrm{lat}$.

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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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