Lattice energy-momentum tensor from the Yang-Mills gradient flow--inclusion of fermion fields

We compute the renormalized running coupling of SU(3) gauge theory coupled to N f = 8 flavors of massless fundamental Dirac fermions. The recently proposed finite volume gradient flow scheme is used. The calculations are performed at several lattice spacings allowing for a controlled continuum extrapolation. The results for the discrete β-function show that it is monotonic without any sign of a fixed point in the range of couplings we cover. As a cross check the continuum results are compared with the wellknown perturbative continuum β-function for small values of the renormalized coupling and perfect agreement is found.

Section: Jhep06(2015)019mentioning

confidence: 99%

The running coupling of 8 flavors and 3 colors

Fodor

Holland

Kuti

et al. 2015

“…Using ringed fermions, which do not require any multiplicative wavefunction renormalization [25,26], the corresponding lattice matrix elements remain finite in the continuum limit. This approach evades the problem of the power-divergence associated with the Wilson line operator that defines the quasi PDF.…”

Section: Jhep03(2017)116mentioning

confidence: 99%

“…First, the gradient flow serves as a gauge-invariant ultraviolet regulator. Second, given a renormalized theory at zero flow time, the matrix elements of smeared fields are automatically finite, up to a multiplicative wave-function renormalization for the fermion fields [24], which can be removed by introducing ringed fermion fields [25,26]. Third, the lattice matrix elements of smeared fields remain finite in the continuum limit, provided the flow time is fixed in physical units [24,35].…”

Section: Smeared Quasi Pdfsmentioning

confidence: 99%

“…We can now relate the moments of the smeared quasi PDF b (s,twist−2) n √ τ Λ QCD , which are local matrix elements of smeared fields, to the renormalized moments of the lightfront PDFs, by using the properties of the gradient flow that arise from a short distance expansion [23,25,26,41,42]. The exponentially local nature of the smearing procedure allows for a short distance expansion of the smeared local operators in terms of renormalized operators in some renormalization scheme, such as the M S scheme.…”

Section: Short-distance Expansionmentioning

confidence: 99%

See 1 more Smart Citation

Quasi parton distributions and the gradient flow

Monahan

Orginos

2017

We propose a new approach to determining quasi parton distribution functions (PDFs) from lattice quantum chromodynamics. By incorporating the gradient flow, this method guarantees that the lattice quasi PDFs are finite in the continuum limit and evades the thorny, and as yet unresolved, issue of the renormalization of quasi PDFs on the lattice. In the limit that the flow time is much smaller than the length scale set by the nucleon momentum, the moments of the smeared quasi PDF are proportional to those of the lightfront PDF. We use this relation to derive evolution equations for the matching kernel that relates the smeared quasi PDF and the light-front PDF.

“…Recent extensive analyses of the energy-momentum tensor for Yang-Mills theory in the gradient flow scheme are found in [16][17][18][19][20].…”

Section: Jhep03(2016)021mentioning

confidence: 99%

The gradient flow in λϕ 4 theory

Fujikawa

2016

A gradient flow equation for λφ 4 theory in D = 4 is formulated. In this scheme the gradient flow equation is written in terms of the renormalized probe variable Φ(t, x) and renormalized parameters m 2 and λ in a manner analogous to the higher derivative regularization. No extra divergence is induced in the interaction of the probe variable Φ(t, x) and the 4-dimensional dynamical variable φ(x) which is defined in renormalized perturbation theory. The finiteness to all orders in perturbation theory is established by power counting argument in the context of D + 1 dimensional field theory. This illustrates that one can formulate the gradient flow for the simple but important λφ 4 theory in addition to the well-known Yang-Mills flow, and it shows the generality of the gradient flow for a wider class of field theory.