On the Determination of the Polarized Sea Distributions of the Nucleon

The possibilities to determine the flavor structure of the polarized sea (antiquark) distributions of the nucleon via vector boson $(\gamma^*, W^{\pm}, Z^0)$ production at high energy polarized hadron--hadron colliders, such as the Relativistic Heavy--Ion Collider (RHIC), are studied in detail. In particular the perturbative stability of the expected asymmetries in two representative models for the (un)broken flavor structure are investigated by confronting perturbative QCD leading order predictions of the expected asymmetries with their next--to--leading order counterparts.Comment: 28 pages, LaTe

Spin-Dependent Structure Functions of Real and Virtual Photons

The implications of the positivity constraint, $|g_1^{\gamma(P^2)}(x,Q^2)| \leq F_1^{\gamma(P^2)}(x,Q^2)$, on the presently unknown spin--dependent structure function $g_1^{\gamma(P^2)}(x,Q^2)$ of real and virtual photons are studied at scales $Q^2\gg P^2$ where longitudinally polarized photons dominate physically relevant cross sections. In particular it is shown how to implement the physical constraints of positivity and continuity at $P^2=0$ in NLO calculations which afford a nontrivial choice of suitable (DIS) factorization schemes related to $g_1^{\gamma}$ and $F_1^{\gamma}$ and appropriate boundary conditions for the polarized parton distributions of real and virtual photons. The predictions of two extreme `maximal' and `minimal' saturation scenarios are presented and compared with results obtained within the framework of a simple quark `box' calculation expected to yield reasonable estimates in the not too small regions of $x$ and $P^2$.Comment: 33 pages, LaTeX, 12 figure

The Kinetic Interpretation of the DGLAP Equation, its Kramers-Moyal Expansion and Positivity of Helicity Distributions

According to a rederivation - due to Collins and Qiu - the DGLAP equation can be reinterpreted (in leading order) in a probabilistic way. This form of the equation has been used indirectly to prove the bound $|\Delta f(x,Q)| < f(x,Q)$ between polarized and unpolarized distributions, or positivity of the helicity distributions, for any $Q$. We reanalize this issue by performing a detailed numerical study of the positivity bounds of the helicity distributions. To obtain the numerical solution we implement an x-space based algorithm for polarized and unpolarized distributions to next-to-leading order in $\alpha_s$, which we illustrate. We also elaborate on some of the formal properties of the Collins-Qiu form and comment on the underlying regularization, introduce a Kramers-Moyal expansion of the equation and briefly analize its Fokker-Planck approximation. These follow quite naturally once the master version is given. We illustrate this expansion both for the valence quark distribution $q_V$ and for the transverse spin distribution $h_1$.Comment: 38 pages, 27 figures, Dedicated to Prof. Pierre Ramond for his 60th birthda

Mesonic Parton Densities Derived From Constituent Quark Model Constraints

Using constituent quark model constraints we calculate the gluon and sea content of pions solely in terms of their valence density and the known sea and gluon densities of the nucleon. The resulting small-x predictions for g^{pi}(x,Q^2) and \bar{q}^{pi}(x,Q^2) are unique and parameter free, being entirely due to QCD dynamics. Similar ideas are applied for calculating the gluon and sea content of kaons which, for our suggested choice of the kaon's valence densities, turn out to be identical to the ones of the pion.Comment: 16 pages, LaTeX, 6 figures, uses epsfig and amssymb style

Pionic Parton Distributions Revisited

Using constituent quark model constraints we calculate the gluon and sea-quark content of pions solely in terms of their valence density (fixed by \pi N Drell-Yan data) and the known sea and gluon distributions of the nucleon, using the most recent updated valence-like input parton densities of the nucleon. The resulting small-x dynamical QCD predictions for g^{\pi}(x,Q^2) and \bar{q}^{\pi}(x,Q^2) are unique and parameter free. Simple analytic parametrizations of the resulting parton distributions of the pion are presented in LO and NLO. These results and parametrizations will be important, among other things, for updated formulations of the parton distributions of real and virtual photons.Comment: 14 pages incl. 3 figures, LaTe

Bloom-Gilman duality of the nucleon structure function and the elastic peak contribution

The occurrence of the Bloom-Gilman duality in the nucleon structure function is investigated by analyzing the Q**2-behavior of low-order moments, both including and excluding the contribution arising from the nucleon elastic peak. The Natchmann definition of the moments has been adopted in order to cancel out target-mass effects. It is shown that the onset of the Bloom-Gilman duality occurs around Q**2 ~ 2 (GeV/c)**2 if only the inelastic part of the nucleon structure function is considered, whereas the inclusion of the nucleon elastic peak contribution leads to remarkable violations of the Bloom-Gilman duality.Comment: in Proc. of the XVI European Conference on Few-body Problems in Physics, Autrans (France), July 199

A Conversation with Justice Ruth Bader Ginsburg

Professor Gillian Metzger: Katherine, thank you for that wonderful overview of all that the Justice has achieved and the history of Columbia Law School. And I want to apologize for those to whom I am showing my back, but this will allow us to have more of a conversation with the Justice. Justice, thank you so much for being with us today. It is a real privilege for us to get to talk to you this way, and we know for the entire audience. You have had – as you have now heard (LAUGHS) – an amazing and just tremendously varied career, spanning so many different roles of academic, public interest advocate, judge, now Justice. We can\u27t possibly cover all of this in the time we have this morning, but what we are hoping to do is talk a little bit about each of these roles, how each step you took influenced the rest, and then we will be throwing it open after our conversation for questions from the audience