The anomalous magnetic moment of the muon in the Standard Model

194 pages, 103 figures, bib files for the citation references are available from: https://muon-gm2-theory.illinois.eduWe review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant $\alpha$ and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including $\mathcal{O}(\alpha^5)$ with negligible numerical uncertainty. The electroweak contribution is suppressed by $(m_\mu/M_W)^2$ and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at $\mathcal{O}(\alpha^2)$ and is due to hadronic vacuum polarization, whereas at $\mathcal{O}(\alpha^3)$ the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads $a_\mu^\text{SM}=116\,591\,810(43)\times 10^{-11}$ and is smaller than the Brookhaven measurement by 3.7$\sigma$. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics

Floral Assemblages and Patterns of Insect Herbivory during the Permian to Triassic of Northeastern Italy

To discern the effect of the end-Permian (P-Tr) ecological crisis on land, interactions between plants and their insect herbivores were examined for four time intervals containing ten major floras from the Dolomites of northeastern Italy during a Permian-Triassic interval. These floras are: (i) the Kungurian Tregiovo Flora;(ii) the Wuchiapingian Bletterbach Flora;(iii) three Anisian floras;and (iv) five Ladinian floras. Derived plant-insect interactional data is based on 4242 plant specimens (1995 Permian, 2247 Triassic) allocated to 86 fossil taxa (32 Permian, 56 Triassic), representing lycophytes, sphenophytes, pteridophytes, pterido-sperms, ginkgophytes, cycadophytes and coniferophytes from 37 million-year interval (23 m. yr. Permian, 14 m. yr. Triassic). Major Kungurian herbivorized plants were unaffiliated taxa and pteridosperms;later during the Wuchiapingian cycadophytes were predominantly consumed. For the Anisian, pteridosperms and cycadophytes were preferentially consumed, and subordinately pteridophytes, lycophytes and conifers. Ladinian herbivores overwhelming targeted pteridosperms and subordinately cycadophytes and conifers. Throughout the interval the percentage of insect-damaged leaves in bulk floras, as a proportion of total leaves examined, varied from 3.6% for the Kungurian (N = 464 leaves), 1.95% for the Wuchiapingian (N = 1531), 11.65% for the pooled Anisian (N = 1324), to 10.72% for the pooled Ladinian (N = 923), documenting an overall herbivory rise. The percentage of generalized consumption, equivalent to external foliage feeding, consistently exceeded the level of specialized consumption from internal feeding. Generalized damage ranged from 73.6% (Kungurian) of all feeding damage, to 79% (Wuchiapingian), 65.5% (pooled Anisian) and 73.2% (pooled Ladinian). Generalized-to-specialized ratios show minimal change through the interval, although herbivore component community structure (herbivore species feeding on a single plant-host species) increasingly was partitioned from Wuchiapingian to Ladinian. The Paleozoic plant with the richest herbivore component community, the coniferophyte Pseudovoltzia liebeana, harbored four damage types (DTs), whereas its Triassic parallel, the pteridosperm Scytophyllum bergeri housed 11 DTs, almost four times that of P. liebeana. Although generalized DTs of P. liebeana were similar to S. bergeri, there was expansion of Triassic specialized feeding types, including leaf mining. Permian-Triassic generalized herbivory remained relatively constant, but specialized herbivores more finely partitioned plant- host tissues via new feeding modes, especially in the Anisian. Insect-damaged leaf percentages for Dolomites Kungurian and Wuchiapingian floras were similar to those of lower Permian, north-central Texas, but only one-third that of southeastern Brazil. Global herbivore patterns for Early Triassic plant-insect interactions remain unknown

The anomalous magnetic moment of the muon in the Standard Model

We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant α and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including O(α5) with negligible numerical uncertainty. The electroweak contribution is suppressed by (mμ∕MW)2 and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at O(α2) and is due to hadronic vacuum polarization, whereas at O(α3) the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads aμSM=116591810(43)×10−11 and is smaller than the Brookhaven measurement by 3.7σ. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future – which are also discussed here – make this quantity one of the most promising places to look for evidence of new physics