Related papers: Studying the gradient flow coupling in the Schr\"o…
We examine the proposal by Grabowska and Kaplan (GK) to use the infinite gradient flow in the domain-wall formulation of chiral lattice gauge theories. We consider the case of Abelian theories in detail, for which L\"uscher's exact…
We measure the evolution of the coupling constant using the Schroedinger functional method in the lattice formulation of SU(2) gauge theory with two massless Dirac fermions in the adjoint representation. We observe strong evidence for an…
The non-perturbatively defined running quark mass introduced by the ALPHA collaboration is based on the PCAC relation between correlation functions derived from the Schr\"odinger functional (SF). In order to complete its definition it…
We study the Schr\"odinger functional coupling for lattice Yang-Mills theory coupled to an improved bosonic spinor field, which corresponds to QCD with minus two light flavors. This theory serves as a less costly testcase than QCD for the…
Parton distribution functions (PDFs) are central to precision QCD phenomenology. Their Mellin moments can be computed on the lattice, but direct determinations using local operators, besides $\langle x \rangle$, face severe challenges from…
The gradient (Wilson) flow has been introduced recently in order to provide a solid theoretical framework for the smoothing of ultraviolet noise in lattice gauge configurations. It is interesting to ask how it compares with other, more…
We investigate the dynamics of a cosmological dark matter fluid in the Schr\"odinger formulation, seeking to evaluate the approach as a potential tool for theorists. We find simple wave-mechanical solutions of the equations for the…
Quantum Chromodynamics with a relatively large number of fundamentally charged quark flavours in the chiral limit is considered. A self-consistent solution of the quark, gluon and ghost propagator Dyson-Schwinger equations in Landau gauge…
We consider a definition of the QCD running coupling constant $\alpha(\mu)$ related to Wilson loops of size $r{\times}t$ with arbitrary fixed $t/r$. The schemes defined by these couplings are very close to the $\overline{\rm MS}$ scheme…
In the exploration of viable models of dynamical electroweak symmetry breaking, it is essential to locate the lower end of the conformal window and know the mass anomalous dimensions there for a variety of gauge theories. We calculate, with…
The gradient property of the renormalisation group (RG) is examined to four-loop order in scalar-fermion systems in $d=4$ and $d=4-\varepsilon$ dimensions. The crucial role played by the beta shift, which is a modification of the standard…
In these lectures, we discuss different types of renormalization problems in QCD and their non-perturbative solution in the framework of the lattice formulation. In particular the recursive finite size methods to compute the…
As a prerequisite to dynamical fermion simulations a detailed study of optimal parameters and scaling behavior is conducted for the quenched Schr\"odinger functional at fixed renormalized coupling. We compare standard hybrid overrelaxation…
The Yang-Mills gradient flow for QCD-like theories is generalized by including a fermionic matter term in the gauge field flow equation. We combine this with two different flow equations for the fermionic degrees of freedom. The solutions…
We report on a numerical study of axisymmetric flow of liquid metal in a circular duct with rectangular cross-section. The flow is forced through the combination of an axial magnetic field and a radial current. Sweeping a wide range of…
We study the flow equation of the O($N$) $\varphi^4$ model in $d$ dimensions at the next-to-leading order (NLO) in the $1/N$ expansion. Using the Schwinger-Dyson equation, we derive 2-pt and 4-pt functions of flowed fields. As the first…
The two loop coefficient of the expansion of the Schroedinger functional coupling in terms of the lattice coupling is calculated for the SU(3) Yang-Mills theory. This coefficient is required to relate lattice data to the MS-bar-coupling. As…
We study scaling solutions of the RG flow equation for the Z_2-effective potential in continuous dimension. As the dimension is lowered from d=4 we first observe the appearance of the Ising scaling solution and successively the apparence of…
We present an evaluation of the quark mass renormalization factor for Nf=2+1 QCD. The Schroedinger functional scheme is employed as the intermediate scheme to carry out non-perturbative running from the low energy to deep in the high energy…
We consider a definition of the QCD running coupling constant $\alpha(\mu)$ related to Wilson loops of size $r{\times}t$ with arbitrary fixed $t/r$. The schemes defined by these couplings are very close to the $\overline{\rm MS}$ scheme for…