Search results for "Renormalization Group"
showing 10 items of 206 documents
Fully coupled functional equations for the quark sector of QCD
2021
We present a comprehensive study of the quark sector of $2+1$ flavour QCD, based on a self-consistent treatment of the coupled system of Schwinger-Dyson equations for the quark propagator and the full quark-gluon vertex. The individual form factors of the quark-gluon vertex are expressed in a special tensor basis obtained from a set of gauge-invariant operators. The sole external ingredient used as input to our equations is the Landau gauge gluon propagator with $2+1$ dynamical quark flavours, obtained from studies with Schwinger-Dyson equations, the functional renormalisation group approach, and large volume lattice simulations. The appropriate renormalisation procedure required in order t…
Renormalization group analysis of the gluon mass equation
2014
In the present work we carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass. A detailed, all-order analysis of the complete kernel appearing in this particular equation reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained sol…
Critical reflections on asymptotically safe gravity
2020
Asymptotic safety is a theoretical proposal for the ultraviolet completion of quantum field theories, in particular for quantum gravity. Significant progress on this program has led to a first characterization of the Reuter fixed point. Further advancement in our understanding of the nature of quantum spacetime requires addressing a number of open questions and challenges. Here, we aim at providing a critical reflection on the state of the art in the asymptotic safety program, specifying and elaborating on open questions of both technical and conceptual nature. We also point out systematic pathways, in various stages of practical implementation, towards answering them. Finally, we also take…
Running Immirzi Parameter and Asymptotic Safety
2011
We explore the renormalization group (RG) properties of quantum gravity, using the vielbein and the spin connection as the fundamental field variables. We require the effective action to be invariant under the semidirect product of spacetime diffeomorphisms and local frame rotations. Starting from the corresponding functional integral we review the construction of an appropriate theory space and an exact funtional RG equation operating on it. We then solve this equation on a truncated space defined by a three parameter family of Holst-type actions which involve a running Immirzi parameter. We find evidence for the existence of an asymptotically safe fundamental theory. It is probably inequi…
Approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom
1999
We construct an approximate renormalization transformation that combines Kolmogorov-Arnold-Moser (KAM)and renormalization-group techniques, to analyze instabilities in Hamiltonian systems with three degrees of freedom. This scheme is implemented both for isoenergetically nondegenerate and for degenerate Hamiltonians. For the spiral mean frequency vector, we find numerically that the iterations of the transformation on nondegenerate Hamiltonians tend to degenerate ones on the critical surface. As a consequence, isoenergetically degenerate and nondegenerate Hamiltonians belong to the same universality class, and thus the corresponding critical invariant tori have the same type of scaling prop…
Why the Cosmological Constant Seems to Hardly Care About Quantum Vacuum Fluctuations: Surprises From Background Independent Coarse Graining
2020
International audience; Background Independence is a sine qua non for every satisfactory theory of Quantum Gravity. In particular if one tries to establish a corresponding notion of Wilsonian renormalization, or coarse graining, it presents a major conceptual and technical difficulty usually. In this paper we adopt the approach of the gravitational Effective Average Action and demonstrate that generically coarse graining in Quantum Gravity and in standard field theories on a non-dynamical spacetime are profoundly different. By means of a concrete example, which in connection with the cosmological constant problem is also interesting in its own right, we show that the surprising and sometime…
Structural properties ofSi1−xGexalloys: A Monte Carlo simulation with the Stillinger-Weber potential
1995
The structural properties of binary silicon-germanium alloys are investigated by means of large-scale constant-pressure Monte Carlo simulations of the Stillinger-Weber model. At low temperatures, the binary-mixture phase separates into Si-rich and Ge-rich phases. The two-phase coexistence region is terminated by a critical point that belongs to the mean-field universality class. We also studied the structural properties of pure Si and Ge as well as the binary mixture. In particular, we found that the linear thermal expansions for both Si and Ge are in agreement with experiments, and that V\'egard's law is valid at temperatures above the critical point. Finally, we compare the bond-length an…
Multiscaling and the classification of continuous phase transitions
1992
Multiscaling of the free energy is obtained by generalizing the classification of phase transitions proposed by Ehrenfest. The free energy is found to obey a new generalized scaling form which contains as special cases standard and multiscaling forms. The results are obtained by analytic continuation from the classification scheme of Ehrenfest.
Critical point Higgs inflation in the Palatini formulation
2021
We study Higgs inflation in the Palatini formulation with the renormalisation group improved potential in the case when loop corrections generate a feature similar to an inflection point. Assuming that there is a threshold correction for the Higgs quartic coupling $\lambda$ and the top Yukawa coupling $y_t$, we scan the three-dimensional parameter space formed by the two jumps and the non-minimal coupling $\xi$. The spectral index $n_s$ can take any value in the observationally allowed range. The lower limit for the running is $\alpha_s>-3.5\times10^{-3}$, and $\alpha_s$ can be as large as the observational upper limit. Running of the running is small. The tensor-to-scalar ratio is $2.2\tim…
Effective field theory after a new-physics discovery
2018
When a new heavy particle is discovered at the LHC or at a future high-energy collider, it will be interesting to study its decays into Standard Model particles using an effective field-theory framework. We point out that the proper effective theory can not be constructed as an expansion in local, higher-dimensional operators; rather, it must be based on non-local operators defined in soft-collinear effective theory (SCET). For the interesting case where the new resonance is a gauge-singlet spin-0 boson, which is the first member of a new sector governed by a mass scale $M$, we show how a consistent scale separation between $M$ and the electroweak scale $v$ is achieved up to next-to-next-to…