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

Interaction of small size wave packet with hadron target

We calculate in QCD the cross section for the scattering of an energetic small-size wave packet off a hadron target. We use our results to study the small-$\sigma$ behaviour of $P_{\pi}(\sigma)$, the distribution over cross section for the pion, in the leading $\alpha_{s}$-order.Comment: Revised version of the report CEBAF-TH-96-0

Shadowing Effects on the Nuclear Suppression Factor, R_dAu, in d+Au Interactions

We explore how nuclear modifications to the nucleon parton distributions affect production of high transverse momentum hadrons in deuteron-nucleus collisions. We calculate the charged hadron spectra to leading order using standard fragmentation functions and shadowing parameterizations. We obtain the d+Au to pp ratio both in minimum bias collisions and as a function of centrality. The minimum bias results agree reasonably well with the BRAHMS data while the calculated centrality dependence underestimates the data and is a stronger function of p_T than the data indicate.Comment: 18 pages, 3 figures, final version, Phys. Rev. C in pres

Open and Hidden Charm Production in Heavy Ion Collisions at Ultrarelativistic Energies

We consider the production of the open charm and J/psi mesons in heavy ion collisions at BNL RHIC. We discuss several recently developed pictures for J/psi production and argue that a measurement at RHIC energies is crucial for disentangling these different descriptions.Comment: 19 pages, Latex, 5 PS-figures. v3: Fig.6 is adde

Prompt photons at RHIC

We calculate the inclusive cross section for prompt photon production in heavy-ion collisions at RHIC energies ($\sqrt{s}=130$ GeV and $\sqrt{s}=200$ GeV) in the central rapidity region including next-to-leading order, $O(\alpha_{em}\alpha_s^2)$, radiative corrections, initial state nuclear shadowing and parton energy loss effects. We show that there is a significant suppression of the nuclear cross section, up to $\sim 30$ at $\sqrt{s}=200$ GeV, due to shadowing and medium induced parton energy loss effects. We find that the next-to-leading order contributions are large and have a strong $p_t$ dependence.Comment: 9 pages, 5 figures, expanded discussion of the K facto

The Non-Trapping Degree of Scattering

We consider classical potential scattering. If no orbit is trapped at energy E, the Hamiltonian dynamics defines an integer-valued topological degree. This can be calculated explicitly and be used for symbolic dynamics of multi-obstacle scattering. If the potential is bounded, then in the non-trapping case the boundary of Hill's Region is empty or homeomorphic to a sphere. We consider classical potential scattering. If at energy E no orbit is trapped, the Hamiltonian dynamics defines an integer-valued topological degree deg(E) < 2. This is calculated explicitly for all potentials, and exactly the integers < 2 are shown to occur for suitable potentials. The non-trapping condition is restrictive in the sense that for a bounded potential it is shown to imply that the boundary of Hill's Region in configuration space is either empty or homeomorphic to a sphere. However, in many situations one can decompose a potential into a sum of non-trapping potentials with non-trivial degree and embed symbolic dynamics of multi-obstacle scattering. This comprises a large number of earlier results, obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more detailed proofs and remark

A Belmont Report for Animals?

Human and animal research both operate within established standards. In the United States, criticism of the human research environment and recorded abuses of human research subjects served as the impetus for the establishment of the National Commission for the Protection of Human Subjects of Biomedical and Behavioral Research, and the resulting Belmont Report. The Belmont Report established key ethical principles to which human research should adhere: respect for autonomy, obligations to beneficence and justice, and special protections for vulnerable individuals and populations. While current guidelines appropriately aim to protect the individual interests of human participants in research, no similar, comprehensive, and principled effort has addressed the use of (nonhuman) animals in research. Although published policies regarding animal research provide relevant regulatory guidance, the lack of a fundamental effort to explore the ethical issues and principles that should guide decisions about the potential use of animals in research has led to unclear and disparate policies. Here, we explore how the ethical principles outlined in the Belmont Report could be applied consistently to animals. We describe how concepts such as respect for autonomy and obligations to beneficence and justice could be applied to animals, as well as how animals are entitled to special protections as a result of their vulnerability

Asymptotics and local constancy of characters of p-adic groups

In this paper we study quantitative aspects of trace characters $\Theta_\pi$ of reductive $p$-adic groups when the representation $\pi$ varies. Our approach is based on the local constancy of characters and we survey some other related results. We formulate a conjecture on the behavior of $\Theta_\pi$ relative to the formal degree of $\pi$, which we are able to prove in the case where $\pi$ is a tame supercuspidal. The proof builds on J.-K.~Yu's construction and the structure of Moy-Prasad subgroups.Comment: Proceedings of Simons symposium on the trace formul

Nuclear Effects in Charmonium Production in QCD

It is shown that the nuclear shadowing of charmonium due to the modification of the nuclear parton distribution is similar in the factorization approach based on non relativistic QCD and in the color evaporation model. In the first model, a separate study of the color octet and color singlet contributions to the yields of the various charmonium states as well as the contributions of these states to the total $J/\Psi$ production is performed. It is found a clear $x_F$ dependence of these contributions which can reproduce experimental data for moderate $x_F$.Comment: 11 pages, 5 Postscript figure

Recalculation of Proton Compton Scattering in Perturbative QCD

At very high energy and wide angles, Compton scattering on the proton (gamma p -> gamma p) is described by perturbative QCD. The perturbative QCD calculation has been performed several times previously, at leading twist and at leading order in alpha_s, with mutually inconsistent results, even when the same light-cone distribution amplitudes have been employed. We have recalculated the helicity amplitudes for this process, using contour deformations to evaluate the singular integrals over the light-cone momentum fractions. We do not obtain complete agreement with any previous result. Our results are closest to those of the most recent previous computation, differing significantly for just one of the three independent helicity amplitudes, and only for backward scattering angles. We present results for the unpolarized cross section, and for three different polarization asymmetries. We compare the perturbative QCD predictions for these observables with those of the handbag and diquark models. In order to reduce uncertainties associated with alpha_s and the three-quark wave function normalization, we have normalized the Compton cross section using the proton elastic form factor. The theoretical predictions for this ratio are about an order of magnitude below existing experimental data.Comment: Latex, 23 pages, 13 figures. Checked numerical integration one more way; added results for one more proton distribution amplitude; a few other minor changes. Version to appear in Phys. Rev.