Higher-loop Contributions Research Articles

Renormalization scheme and higher loop stability in hadronic $\tau$ decay within analytic perturbation theory

We apply an analytic description to the inclusive decay of the $\tau$ lepton. We argue that this method gives not only a self-consistent description of the process both in the timelike region by using the initial expression for $R_\tau$ and in the spacelike domain by using the analytic properties of the hadronic correlator, but also leads to the fact that theoretical uncertainties associated with unknown higher-loop contributions and renormalization scheme dependence can be reduced dramatically.

Divergences in real-time classical field theories at nonzero temperature

The classical approximation provides a non-perturbative approach to time-dependent problems in finite temperature field theory. We study the divergences in hot classical field theory perturbatively. At one-loop, we show that the linear divergences are completely determined by the classical equivalent of the hard thermal loops in hot quantum field theories, and that logarithmic divergences are absent. To deal with higher-loop diagrams, we present a general argument that the superficial degree of divergence of classical vertex functions decreases by one with each additional loop: one-loop contributions are superficially linearly divergent, two-loop contributions are superficially logarithmically divergent, and three- and higher-loop contributions are superficially finite. We verify this for two-loop SU(N) self-energy diagrams in Feynman and Coulomb gauges. We argue that hot, classical scalar field theory may be completely renormalized by local (mass) counterterms, and discuss renormalization of SU(N) gauge theories.

Diagrammatic approach to soft non-Abelian dynamics at high temperature

The dynamics of soft (| p |∼ g 2 T) non-Abelian gauge fields at finite temperature is non-perturbative. The effective theory for the soft scale is determined by diagrams with external momenta p 0≲ g 2 T, | p |∼ g 2 T and loop momenta larger than g 2 T. We consider the polarization tensor beyond the hard thermal loop approximation, which accounts for loop momenta of order T. There are higher loop diagrams, involving also the scale gT, which are as important as the hard thermal loops. These higher loop contributions are characteristic for non-Abelian gauge theories and their calculation is simplified by using the hard thermal loop effective theory. Remarkably, the effective one-loop polarization tensor is found to be gauge fixing independent and transverse at leading order in the gauge coupling g. The transversality indicates that this approach leads to a gauge invariant effective theory.

Cancellation of quantum-mechanical higher loop contributions to the gravitational chiral anomaly.

We give an explicit demonstration, using the rigorous Feynman rules developed by de Boer et al., that the regularized trace $\mathrm{Tr}{\ensuremath{\gamma}}_{5}{e}^{\ensuremath{-}\ensuremath{\beta}{\D}^{2}}$ for the gravitational chiral anomaly expressed as an appropriate quantum-mechanical path integral is $\ensuremath{\beta}$ independent up to the two-loop level. Identities and diagrammatic notation are developed to facilitate rapid evaluation of graphs given by these rules.

Vacuum energy for Yang-Mills fields inR d �S 1: One-loop, two-loop, and beyond

The vacuum energy is calculated for Yang-Mills (YM) system defined in $D$ dimensional space-time of $S^1\times R^d$ ($D=d+1$), where the possibility of the YM fields to acquire the vacuum expectation values on $S^1$ is taken into account. The vacuum energy has already been obtained to the order of one-loop in many people. Here we calculate the vacuum energy in $D$ dimensions to two-loop order. With an intention to reach higher loops, an approximation method is proposed, which is especially effective in higher dimensions. By this method, we can treat the higher-loop contributions of YM interactions as easily as we treat one-loop effect. As a check, we show reproduction of the two-loop contribution ($D$-dependence of the coefficient as well as the functional form) when the coupling constant is small. This approximation method is useful not only for the Kaluza-Klein theories but also for the finite temperature-density system (as a quark-gluon plasma).

Higher loop contributions to an effective potential of the gauge theory at high temperature

Higher perturbative contributions to an effective potential for the temporal component of the gauge field ( A p a =const.) for nonabelian gauge theory at high temperature are discussed. It is shown that one of the most important contributions is due to Debye gluons. The condensate of the field A 0∝ gT( g→0) does not appear if we take into account one-and two-loop Debye contributions only. The behaviour of infra-red leading perturbative contributions is investigated. It is argued that asymptotic behaviour of these terms still indicates a possible formation of the A 0∝ gT condensate. High perturbative contributions for the Debye mass are also discussed.

Central charge of the Virasoro algebra for supersymmetric sigma models on Calabi-Yau manifolds

It is shown that the central charge of the Virasoro algebra for a conformally invariant supersymmetric σ-model on a Calabi-Yau manifold remains equal to its free field value to order α′ 4 despite the non-Ricci-flatness of the background metric. Various possibilities for higher loop contributions are discussed.

Covariant supergraphs: (I). Yang-Mills theory

We describe covariant D-algebra methods for the evaluation of supergraphs in supersymmetric Yang-Mills theories. These methods lead to simplifications in the evaluation of higher-loop contributions.