arXiv subjects
Publications and source records attributed to S. Peris.
It is shown that the commonly accepted relationship between the Landau singularity in the running coupling constant of QED or QCD and the renormalon singularities in the Borel sums of perturbation theory expansions is only a particular feature of the restriction of the perturbative $β$--function to the one loop level.
We discuss, within the framework of the Standard Model, the calculation of the two-loop electroweak contributions to the anomalous magnetic moment of the muon involving triangle fermionic loops of leptons and quarks. Because of the large ratios of masses involved, these contributions are rather large. The result we obtain differs from a previous estimate reported in the literature. The discrepancy originates in the cancellation of anomalies in $SU(3)_c\times SU(2)_L\times U(1)_Y$, a cancellation that requires the consideration of both leptons {\it and} quarks within each generation and that had been previously overlooked.
We discuss the QCD corrections to the large-$m_t$ electroweak contributions to $Δr$ and to the process $Z\to b \bar b$ as two of the most representative examples. This needs the construction of an effetive field theory below the top quark. We discuss the issue of what $μ$ scale is the appropriate one at every stage and argue that, while matching corrections do verify the simple prescription of taking $μ\simeq m_t$ in $α_s(μ)$, logarithmic (i.e. $\sim \log m_t$) corrections do not, and require the use of the running $α_s(μ)$ in the corresponding renormalization group equations. In particular we obtain the $α_s$ correction to the non-universal $\log m_t$ contribution to the $Zb\bar b$ vertex.
By using effective field theory techniques for the standard model, we discuss the issue of what $μ$ scale is the appropriate one in the QCD corrections to the large-$\mt$ electroweak contributions to $Δr$. This needs the construction of an effective field theory below the top quark. We argue that, while matching corrections do verify the simple prescription of taking $μ\simeq \mt$ in $\a(\m)$, logarithmic (i.e. $\sim \log \mt$) corrections do not, and require the use of the running $\a(μ)$ in the corresponding renormalization group equation.
Next-to-leading $1/\N$ corrections to the upper bound on $M_η/M_{η'}$ recently obtained by Georgi are considered. These corrections are just what is needed to reconcile the bound with the observed $η$ and $η'$ masses.