The LPM effect in sequential bremsstrahlung 2: factorization

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. In this paper, we continue analysis of the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD), avoiding soft-gluon approximations. In particular, this paper analyzes the subtle problem of how to precisely separate overlapping double splitting (e.g.\ overlapping double bremsstrahlung) from the case of consecutive, independent bremsstrahlung (which is the case that would be implemented in a Monte Carlo simulation based solely on single splitting rates). As an example of the method, we consider the rate of real double gluon bremsstrahlung from an initial gluon with various simplifying assumptions (thick media; $\hat q$ approximation; large $N_c$; and neglect for the moment of processes involving 4-gluon vertices) and explicitly compute the correction $\Delta\,d\Gamma/dx\,dy$ due to overlapping formation times.Comment: 59 pages, 37 figures. The major changes from v1: new section I.A.4 added to give kinetic theory analogy to better explain the importance of the subtraction defining Delta[d(Gamma)/dx dy]; new appendix F added to compare/contrast with issues raised by Blaizot, Dominguez, Iancu, and Mehtar-Tani [22

The LPM effect in sequential bremsstrahlung: dimensional regularization

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. Of recent interest is the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD). In previous papers, we have developed methods for computing such corrections without making soft-gluon approximations. However, our methods require consistent treatment of canceling ultraviolet (UV) divergences associated with coincident emission times, even for processes with tree-level amplitudes. In this paper, we show how to use dimensional regularization to properly handle the UV contributions. We also present a simple diagnostic test that any consistent UV regularization method for this problem needs to pass.Comment: 59 pages, 8 figures [main change from v1: addition of the new appendix B summarizing more about use of the i*epsilon prescription in earlier work

On the multiplicity of non-iterated periodic billiard trajectories

We introduce the iteration theory for periodic billiard trajectories in a compact and convex domain of the Euclidean space, and we apply it to establish a multiplicity result for non-iterated trajectories.Comment: 21 pages, 2 figures; v3: final version, as publishe

A Modified Oil Refining Loss Method

In certain research studies involving the determination of the refining loss of vegetable oils, such as soybean, the 500-gram samples required by the official method may not be available. The chromatographic method, while giving consistent results on a given sample, does not give results which check the official method. A modification of the official cup method was developed using a cup of special design with a 50-gram sample. Good checks with the official method were obtained. It was found that variations in evaporation losses were more important than mixing speeds in affecting results

Looking for CP Violation in W Production and Decay

We describe CP violating observables in resonant $W^\pm$ and $W^\pm$ plus one jet production at the Tevatron. We present simple examples of CP violating effective operators, consistent with the symmetries of the Standard Model, which would give rise to these observables. We find that CP violating effects coming from new physics at the $TeV$ scale could in principle be observable at the Tevatron with $10^6$ $W^\pm$ decays.Comment: 15 pgs with standard LATEX, 7 ps figures embedded with eps

Spin Dependent Drell Yan in QCD to O(αs2)O(\alpha_s^2) (I). (The Non-Singlet Sector)

A study of the order $\alpha_s^2$ corrections to the Drell Yan (non-singlet) cross section for incoming states of arbitrary longitudinal helicities is presented. The study is performed in the case of the transverse momentum distributions, $(q_T)$, of the lepton pair and extends the calculation of Ellis Martinelli and Petronzio (EMP) to the polarized case. We use the $\bar{MS}$ scheme and the t'Hooft-Veltman regularization for the helicity projectors. From our results one can obtain the bulk of the totally inclusive NNLO cross section for the production of a Drell Yan pair in the non-singlet sector by a simple integration over the heavy photon momentum. We show that in the $\bar{MS}$ helicity is not conserved, unless a finite renormalization is done to reenter into a physical scheme ($\bar{MS}_p$). This aspect of the calculation follows the same trend as in polarized production of single and double photon to $O(\alpha_s^2)$. In the unpolarized limit we reproduce all the results of EMP.Comment: 39 pages, 7 figures (included