On the renormalization of operator products: the scalar gluonic case

In this paper we study the renormalization of the product of two operators $O_1=-\frac{1}{4} G^{\mu \nu}G_{\mu \nu}$ in QCD. An insertion of two such operators $O_1(x)O_1(0)$ into a Greens function produces divergent contact terms for $x\rightarrow 0$. In the course of the computation of the operator product expansion (OPE) of the correlator of two such operators $i\int\!\mathrm{d}^4x\,e^{iqx} T\{\,O_1(x)O_1(0)\}$ to three-loop order we discovered that divergent contact terms remain not only in the leading Wilson coefficient $C_0$, which is just the VEV of the correlator, but also in the Wilson coefficient $C_1$ in front of $O_1$. As this correlator plays an important role for example in QCD sum rules a full understanding of its renormalization is desireable. This work explains how the divergences encountered in higher orders of an OPE of this correlator should be absorbed in counterterms and derives an additive renormalization constant for $C_1$ from first principles and to all orders in perturnbation theory. The method to derive the renormalization of this operator product is an extension of the ideas of a paper by Spiridonov and can be generalized to other cases.Comment: v2: this is the version accepted by JHEP; more detailed discussion of phenomenological application

On the need for a global engineering initiative to mitigate climate change

There is growing scientific evidence that the continued emission of greenhouse gases will eventually lead to catastrophic irreversible climate change and that, therefore, a global effort needs to be started to transition to a fully renewable economy. In this article, the engineering challenges of converting to emission-free power generation are reviewed and the feasibility of two proposed solutions, i.e. the ‘wind–water–solar’ and the ‘energy ship’ proposals, are discussed. It is concluded that a well-conceived and executed engineering effort needs to be initiated and guided by a Global Engineering Council for the purpose of examining and ranking various proposals and making specific recommendations

Identification of γ-ray emission from 3C 345 and NRAO 512

For more than 15 years, since the days of the Energetic Gamma-Ray Experiment Telescope (EGRET) on board the Compton Gamma-Ray Observatory (CGRO; 1991−2000), it has remained an open question why the prominent blazar 3C 345 was not reliably detected at γ-ray energies ≥ 20 MeV. Recently a bright γ-ray source (0FGL J1641.4+3939/1FGL J1642.5+3947), potentially associated with 3C 345, was detected by the Large Area Telescope (LAT) on Fermi. Multiwavelength observations from radio bands to X-rays (mainly GASP-WEBT and Swift) of possible counterparts (3C 345, NRAO 512, B3 1640 + 396) were combined with 20 months of Fermi-LAT monitoring data (August 2008 − April 2010) to associate and identify the dominating γ-ray emitting counterpart of 1FGL J1642.5+3947. The source 3C 345 is identified as the main contributor for this γ-ray emitting region. However, after November 2009 (15 months), a significant excess of photons from the nearby quasar NRAO 512 started to contribute and thereafter was detected with increasing γ-ray activity, possibly adding flux to 1FGL J1642.5+3947. For the same time period and during the summer of 2010, an increase of radio, optical and X-ray activity of NRAO 512 was observed. No γ-ray emission from B3   1640 + 396 was detected