Factorization of e+e− → H X cross section, differential in zh, PT and thrust, in the 2-jet limit

Factorizing the cross section for single hadron production in e+e− annihilations is a highly non trivial task when the transverse momentum of the outgoing hadron with respect to the thrust axis is taken into account. We work in a scheme that allows to factorize the e+e−→ H X cross section as a convolution of a calculable hard coefficient and a Transverse Momentum Dependent (TMD) fragmentation function. The result, differential in zh, PT and thrust, will be given to all orders in perturbation theory and explicitly computed to Next to Leading Order (NLO) and Next to Leading Log (NLL) accuracy. The predictions obtained from our computation, applying the simplest and most natural ansatz to model the non-perturbative part of the TMD, are in exceptional agreement with the experimental measurements of the BELLE Collaboration. The factorization scheme we propose relates the TMD parton densities defined in 1-hadron and 2-hadron processes, restoring the possi- bility to perform global phenomenological studies of TMD physics including experimental data from semi-inclusive deep inelastic scattering, Drell-Yan processes, e+e−→ H1H2X and e+e−→ H X annihilations.

Shape measurements of live pigs using 3-D image capture

A photogrammetric stereo imaging system was used to capture 3-D models of live pigs, and quantitative shape measurements were extracted from cross sections of the models. Stereo images were captured of 32 pigs, divided into high-lysine and low-lysine diet groups, and 3-D models were built from the images. Each pig was imaged once per week for 14 weeks. After slaughter, 10 of the pigs were dissected for muscle and fat measurements. A sequence of algorithms was applied to the 3-D models: differential geometry to reveal surface curvature features and detect the spine; manual landmark placement; fitting a curve to the spine; determining the vertical axis of the body; placing a slice plane across the abdomen close to the P2 position; extracting a cross section; and fitting a shape model to the cross section. Differential geometry revealed many qualitative features of the musculature. The spine was a line of minimum curvature along the back. The high-lysine pigs had higher height-to-width ratios and flatter backs than the low-lysine pigs. The dissected total muscle mass had a -0·66 correlation with the flatness-of-back shape parameter, and a 0·64 correlation with weight.

A quantitative approach to inner shell losses

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

Second Born approximation to the Bremsstrahlung differential cross-section

In this paper we calculate the second Born approximation contribution to the Bremsstrahlung cross-section differential in both the photon and electron angles. This is divergent if a Coulomb potential is considered, but it is found, on following the idea of Dalitz (1951), that all observable quantities turn out to be finite when we perform the calculation for a Yukawa potential and take the limit of zero screening. It is shown that this is true to order Z 3 in the differential cross-section before it is averaged over spins, and the cross-section is calculated explicitly for the case of an unpolarized beam when the final states of polarization are not observed. Further, it is pointed out that the same methods can be applied satisfactorily in the case of pair production.