We compute the QCD×QED (O(α s α)) mixed and QED 2 (O(α 2 )) corrections to the production of an on-shell Z boson in hadronic collisions. We obtain them by profiting from the calculation of the pure QCD terms after taking the corresponding abelian limits. Therefore, we extend the available knowledge up to complete next-to-next-to leading order precision in QCD⊕QED.We present explicit results for the perturbative coefficients and perform the phenomenological analysis at different collider energies with particular emphasis on the mixed corrections. We study the contribution from the different channels and discuss the scale dependence stabilisation effect. We consider a factorisation approximation for the mixed order terms and show that it fails to reproduce the exact result. We find that the contributions are small, typically at the few per mille level, but that under some kinematical conditions they can compete with the pure QCD NNLO ones. *

The projectile beam coherence effects occurring in ion-atom collisions are analyzed on the basis of the recent theory of Karlovets et al. [Phys. Rev. A 92, 052703 (2015)] developed for the elastic scattering of wave packets of particles off a potential field. This theory is generalized to estimate the loss of coherence for inelastically scattered projectiles in ionizing collisions. The results obtained by the suggested model are compared with experimental data for the ionization of hydrogen atoms and molecules by 75-keV proton impact. Significantly improved agreement is observed between the theory and experiment. DOI: 10.1103/PhysRevA.93.032702 In a recent work Karlovets et al.[1] investigated theoretically the scattering of wave packets of nonrelativistic particles off a potential field. The authors derived a simple general expression that determines the number of scattering events for the case when the incident particle beam is a wave packet of arbitrary form but with its mean momentum strongly centered at a given value p i . Furthermore, they considered the example when the wave packet is scattered off randomly distributed potential centers. By averaging the number of events over the impact parameter between the potential center and the wave packet axis, they derived a formula for the effective cross section that reproduces the one obtained by previous authors (see, e.g., [2,3]where dσ /d | q i →q f is the differential cross section for the elastic scattering in an angle θ = arccos(q i ·q f ). Furthermore, by writing (k) = ⊥ (k ⊥ ) (k ), with strongly centered on p i , they obtainedKarlovets et al. carried out sample calculations for the case of electron impact, applying the Born approximation. They considered the collisions of a Gaussian wave packeton a Gaussian potential as well as on the hydrogen atom. Here σ ⊥ is the averaged transverse size of the wave packet. As a remarkable result, they found that the angular distributions of the effective cross section broaden with the decrease of σ ⊥ . [4] could control the coherence properties of the ion beam and thereby demonstrate the effect of the projectile coherence on the angular distribution of the scattered protons. The principle of the experiment is based on the van Cittert-Zernike theorem according to which the transverse coherence length r (the diameter of the area of coherence) of a source of waves at a distance L is of the order of λ/kα, where λ is the wavelength, α is the angular diameter of the source, and k is a dimensionless constant.Egodapitiya et al. used a well-collimated nearly monochromatic [< 1 eV full width at half maximum (FWHM)] proton beam that crossed a molecular hydrogen beam. The measured quantity was the doubly differential cross section (DDCS) for the ionization as a function of the scattering angle θ and the energy loss of the protons. The measurements were made at two coherence length values corresponding to two values of the distance between the target and the last aperture of the collimator, L = 6.5 and 50 cm. The diameter of t...