NLL QCD contribution of the electromagnetic dipole operator to B -> Xs gamma gamma with a massive strange quark

We calculate the O(αs) corrections to the double differential decay width dΓ77/(ds1ds2) for the process B¯→Xsγγ, originating from diagrams involving the electromagnetic dipole operator O7. The kinematical variables s1 and s2 are defined as si=(pb−qi)2/m2b, where pb, q1, q2 are the momenta of the b quark and two photons. We introduce a nonzero mass ms for the strange quark to regulate configurations where the gluon or one of the photons become collinear with the strange quark and retain terms which are logarithmic in ms, while discarding terms which go to zero in the limit ms→0. When combining virtual and bremsstrahlung corrections, the infrared and collinear singularities induced by soft and/or collinear gluons drop out. By our cuts the photons do not become soft, but one of them can become collinear with the strange quark. This implies that in the final result a single logarithm of ms survives. In principle, the configurations with collinear photon emission could be treated using fragmentation functions. In a related work we find that similar results can be obtained when simply interpreting ms appearing in the final result as a constituent mass. We do so in the present paper and vary ms between 400 and 600 MeV in the numerics. This work extends a previous paper by us, where only the leading power terms with respect to the (normalized) hadronic mass s3=(pb−q1−q2)2/m2b were taken into account in the underlying triple differential decay width dΓ77/(ds1ds2ds3).

Remarks on higher-order hadronic corrections to the muon g-2

Recently, it was shown that insertions of hadronic vacuum polarization at O(α4) generate non-negligible effects in the calculation of the anomalous magnetic moment of the muon. This result raises the question if other hadronic diagrams at this order might become relevant for the next round of g−2 measurements as well. In this note we show that a potentially enhanced such contribution, hadronic light-by-light scattering in combination with electron vacuum polarization, is already sufficiently suppressed.

Bipartite graphs and quasipositive surfaces

We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links. We then introduce a combinatorial notion of adjacency for bipartite graph links and discuss its potential relation with the adjacency problem for plane curve singularities.

Positive braids of maximal signature

We characterise positive braid links with positive Seifert form via a finite number of forbidden minors. From this we deduce a one-to-one correspondence between prime positive braid links with positive Seifert form and simply laced Dynkin diagrams, as well as a simple classification of alternating positive braid knots.

XMapTools: a MATLAB©-based program for electron microprobe X-ray image processing and geothermobarometry

XMapTools is a MATLAB©-based graphical user interface program for electron microprobe X-ray image processing, which can be used to estimate the pressure–temperature conditions of crystallization of minerals in metamorphic rocks. This program (available online at http://www.xmaptools.com) provides a method to standardize raw electron microprobe data and includes functions to calculate the oxide weight percent compositions for various minerals. A set of external functions is provided to calculate structural formulae from the standardized analyses as well as to estimate pressure–temperature conditions of crystallization, using empirical and semi-empirical thermobarometers from the literature. Two graphical user interface modules, Chem2D and Triplot3D, are used to plot mineral compositions into binary and ternary diagrams. As an example, the software is used to study a high-pressure Himalayan eclogite sample from the Stak massif in Pakistan. The high-pressure paragenesis consisting of omphacite and garnet has been retrogressed to a symplectitic assemblage of amphibole, plagioclase and clinopyroxene. Mineral compositions corresponding to ~165,000 analyses yield estimates for the eclogitic pressure–temperature retrograde path from 25 kbar to 9 kbar. Corresponding pressure–temperature maps were plotted and used to interpret the link between the equilibrium conditions of crystallization and the symplectitic microstructures. This example illustrates the usefulness of XMapTools for studying variations of the chemical composition of minerals and for retrieving information on metamorphic conditions on a microscale, towards computation of continuous pressure–temperature-and relative time path in zoned metamorphic minerals not affected by post-crystallization diffusion.

Daily and seasonal thermal stresses in tilings: a field survey combined with numeric modeling

This study investigates thermally induced tensile stresses in ceramic tilings. Daily and seasonal thermal cycles, as well as, rare but extreme events, such as a hail-storm striking a heated terrace tiling, were studied in the field and by numerical modeling investigations. The field surveys delivered temperature– time diagrams and temperature profiles across tiling systems. These data were taken as input parameters for modeling the stress distribution in the tiling system in order to detect potential sites for material failure. Dependent on the thermal scenario (e.g., slow heating of the entire structure during morning and afternoon, or a rapid cooling of the tiles by a rain storm) the modeling indicates specific locations with high tensile stresses. Typically regions along the rim of the tiling field showed stresses, which can become critical with respect to the adhesion strength. Over the years, ongoing cycles of thermal expansion–contraction result in material fatigue promoting the propagation of cracks. However, the installation of flexible waterproofing membranes (applied between substrate and tile adhesive) represents an efficient technical innovation to reduce such crack propagation as confirmed by both numerical modeling results and microstructural studies on real systems.