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Register a new userExperimental Tests of Asymptotic Freedom
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Siegfried Bethke
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Measurements which probe the energy dependence of $alpha_s$, the coupling strength of the strong interaction, are reviewed. Jet counting in $e^+ e^-$ annihilation, combining results obtained in the centre of mass energy range from 22 to 133 GeV, provides direct evidence for an asymptotically free coupling, without the need to determine explicit values of $alpha_s$. Recent results from jet production in $e p$ and in $p overline{p}$ collisions, obtained in single experiments spanning large ranges of momentum transfer, $Q^2$, are in good agreement with the running of $alpha_s$ as predicted by QCD. Mass spectra of hadronic decays of $tau$-leptons are analysed to probe the running $alpha_s$ in the very low energy domain, $0.7 GeV^2 < Q^2 < M_tau^2$. An update of the world summary of measurements of $alpha_s(Q^2)$ consistently proves the energy dependence of $alpha_s$ and results in a combined average of $alpha_s(M_Z) = 0.118 pm 0.006$.
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We provide strong evidence that the asymptotically free (1+1)-dimensional non-linear O(3) sigma model can be regularized using a quantum lattice Hamiltonian, referred to as the Heisenberg-comb, that acts on a Hilbert space with only two qubits per spatial lattice site. The Heisenberg-comb consists of a spin-half anti-ferromagnetic Heisenberg-chain coupled anti-ferromagnetically to a second local spin-half particle at every lattice site. Using a world-line Monte Carlo method we show that the model reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200,000 in lattice units and argue how the continuum limit could emerge. We provide a quantum circuit description of time-evolution of the model and argue that near-term quantum computers may suffice to demonstrate asymptotic freedom.
Based on the spontaneous breaking of chiral symmetry, chiral perturbation theory (ChPT) is believed to approximate confinement scale QCD. Dedicated and increasingly accurate experiments and improving lattice calculations are confirming this belief, and we are entering a new era in which we can test confinement scale QCD in some well chosen reactions. This is demonstrated with an overview of low energy experimental tests of ChPT predictions of $pipi$ scattering, pion properties, $pi$N scattering and electromagnetic pion production. These predictions have been shown to be consistent with QCD in the meson sector by increasingly accurate lattice calculations. At present there is good agreement between experiment and ChPT calculations, including the $pipi$ and $pi$N s wave scattering lengths and the $pi^{0}$ lifetime. Recent, accurate pionic atom data are in agreement with chiral calculations once isospin breaking effects due to the mass difference of the up and down quarks are taken into account, as was required to extract the $pipi$ scattering lengths. In addition to tests of the theory, comparisons between $pipi$ and $pi$N interactions based on general chiral principles are discussed. Lattice calculations are now providing results for the fundamental, long and inconclusively studied, $pi$N $sigma$ term and the contribution of the strange quark to the mass of the proton. Increasingly accurate experiments in electromagnetic pion production experiments from the proton which test ChPT calculations (and their energy region of validity) are presented. These experiments are also beginning to measure the final state $pi$N interaction. This paper is based on the concluding remarks made at the Chiral Dynamics Workshop CD12 held at Jefferson Lab in Aug. 2012.
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An effective field theory model of the massive Yang-Mills theory is considered. Assuming that the renormalized coupling constants of non-renormalizable interactions are suppressed by a large scale parameter it is shown that in analogy to the non-abelian gauge invariant theory the dimensionless coupling constant vanishes logarithmically for large values of the renormalization scale parameter.
${Z}_2$-Yukawa-QCD models are a minimalistic model class with a Yukawa and a QCD-like gauge sector that exhibits a regime with asymptotic freedom in all its marginal couplings in standard perturbation theory. We discover the existence of further asymptotically free trajectories for these models by exploiting generalized boundary conditions. We construct such trajectories as quasi-fixed points for the Higgs potential within different approximation schemes. We substantiate our findings first in an effective-field-theory approach, and obtain a comprehensive picture using the functional renormalization group. We infer the existence of scaling solutions also by means of a weak-Yukawa-coupling expansion in the ultraviolet. In the same regime, we discuss the stability of the quasi-fixed point solutions for large field amplitudes. We provide further evidence for such asymptotically free theories by numerical studies using pseudo-spectral and shooting methods.
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