Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLattice computation of the Dirac eigenvalue density in the perturbative regime of QCD
44
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The eigenvalue spectrum $rho(lambda)$ of the Dirac operator is numerically calculated in lattice QCD with 2+1 flavors of dynamical domain-wall fermions. In the high-energy regime, the discretization effects become significant. We subtract them at the leading order and then take the continuum limit with lattice data at three lattice spacings. Lattice results for the exponent $partiallnrho/partiallnlambda$ are matched to continuum perturbation theory, which is known up to $O(alpha_s^4)$, to extract the strong coupling constant $alpha_s$.
rate research
Read More
The determination of renormalization factors is of crucial importance. They relate the observables obtained on finite, discrete lattices to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. They are always present because simulations are done at lattice spacings $a$ and momenta $p$ with $ap$ not necessarily small. In this paper we try to suppress these artifacts by subtraction of one-loop contributions in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of $O(a^2)$.
We review the long term project of the ALPHA collaboration to compute in QCD the running coupling constant and quark masses at high energy scales in terms of low energy hadronic quantities. The adapted techniques required to numerically carry out the required multiscale non-perturbative calculation with our special emphasis on the control of systematic errors are summarized. The complete results in the two dynamical flavor approximation are reviewed and an outlook is given on the ongoing three flavor extension of the programme with improved target precision.
Recent developments in non-perturbative renormalization for lattice QCD are reviewed with a particular emphasis on RI/MOM scheme and its variants, RI/SMOM schemes. Summary of recent developments in Schroedinger functional scheme, as well as the summary of related topics are presented. Comparison of strong coupling constant and the strange quark mass from various methods are made.
We propose a fully non-perturbative method to compute inelastic lepton-nucleon ($ell N$) scattering cross sections using lattice QCD. The method is applicable even at low energies, such as the energy region relevant for the recent and future neutrino-nucleon ($ u N$) scattering experiments, for which perturbative analysis is invalidated. The basic building block is the forward Compton-scattering amplitude, or the hadronic tensor, computed on a Euclidean lattice. Total cross section is constructed from the hadronic tensor by multiplying a phase space factor and integrating over the energy and momentum of final hadronic states. The energy integral that induces a sum over all possible final states is performed implicitly by promoting the phase space factor to an operator written in terms of the transfer matrix on the lattice. The formalism is imported from that of the inclusive semileptonic B meson decay [P. Gambino, S. Hashimoto, arXiv:2005.13730]. It can be generalized to compute the $ell N$ scattering cross sections and their moments, as well as the virtual correction to the nuclear $beta$-decay. Necessary quark-line contractions for two current insertions corresponding to the Compton amplitude to be computed on the lattice are summarized.
We compute the spectral density of the (Hermitean) Dirac operator in Quantum Chromodynamics with two light degenerate quarks near the origin. We use CLS/ALPHA lattices generated with two flavours of O(a)-improved Wilson fermions corresponding to pseudoscalar meson masses down to 190 MeV, and with spacings in the range 0.05-0.08 fm. Thanks to the coverage of parameter space, we can extrapolate our data to the chiral and continuum limits with confidence. The results show that the spectral density at the origin is non-zero because the low modes of the Dirac operator do condense as expected in the Banks-Casher mechanism. Within errors, the spectral density turns out to be a constant function up to eigenvalues of approximately 80 MeV. Its value agrees with the one extracted from the Gell-Mann-Oakes-Renner relation.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
