Quark and Gluon Momentum Fractions in the Pion from N_{f}=2+1+1 Lattice QCD.

We perform the first full decomposition of the pion momentum into its gluon and quark contributions. We employ an ensemble generated by the Extended Twisted Mass Collaboration with N_{f}=2+1+1 Wilson twisted mass clover fermions at maximal twist tuned to reproduce the physical pion mass. We present our results in the MS[over ¯] scheme at 2 GeV.

Reduced forms of the Wigner distribution function for the numerical analysis of rotationally symmetric synchrotron radiation.

In an effort to provide a computationally convenient approach to the characterization of partially coherent synchrotron radiation in phase space, a thorough discussion of the minimum dimensionality of the Wigner distribution function for rotationally symmetric sources of arbitrary degrees of coherence is presented. It is found that perfectly coherent, perfectly incoherent and partially coherent sources may all be characterized by a three-dimensional reduced Wigner distribution function, and some special cases are discussed in which a two-dimensional reduced Wigner distribution function suffices. An application of the dimension-reducing formalism to the case of partially coherent radiation from a planar undulator and a circularly symmetric electron beam as can be found in linear accelerators is demonstrated.