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

A QCD analysis of diffractive deep-inelastic scattering data

We perform a novel type of analysis of diffractive deep-inelastic scattering data, in which the input parton distributions of the Pomeron are parameterised using the perturbative QCD expressions. In particular, we treat individually the components of the Pomeron of different size. We are able to describe simultaneously both the recent ZEUS and H1 diffractive data. In addition to the usual two-gluon model for the perturbative Pomeron, we allow for the possibility that it may be made from two sea quarks.Comment: 13 pages, 5 figures. Version published in Eur. Phys. J.

Initial conditions and charged multiplicities in ultra-relativistic heavy-ion collisions

At ultra-relativistic energies the minijet production in heavy-ion collisions becomes sensitive to semi-hard parton rescatterings in the initial stages of the process. As a result global characteristics of the event, like the initial minijet density, become rather insensitive on the infrared cutoff that separates hard and soft interactions. This allows to define a nearly parameter-free {\it saturation cutoff} at which the initial conditions may be computed. As an application we study the centrality dependence of the charged particle multiplicity, which is compared with present RHIC data and predicted at higher energies.Comment: 10 pages, 3 figure

An Alternative Method to Obtain the Quark Polarization of the Nucleon

An alternate method is described to extract the quark contribution to the spin of the nucleon directly from the first moment of the deuteron structure function, $g^d_1$. It is obtained without recourse to the use of input on the nucleon wave function from hyperon decays involving the flavor symmetry parameters, F and D. The result for the quark polarization of the nucleon, $\Delta\Sigma_ N,$ is in good agreement with the values of the singlet axial current matrix element, $a_0$, obtained from recent next-to-leading order analyses of current proton, neutron and deuteron data.Comment: 7 pages, 1 figur

Next-to-leading order QCD corrections to one hadron-production in polarized pp collisions at RHIC

We calculate the next-to-leading order QCD corrections to the spin-dependent cross section for single-inclusive hadron production in hadronic collisions. This process will be soon studied experimentally at RHIC, providing a tool to unveil the polarized gluon distribution $\Delta g$. We observe a considerably improvement in the perturbative stability for both unpolarized and polarized cross sections. The NLO corrections are found to be non-trivial, resulting in a reduction of the asymmetry.Comment: 8 pages, RevTeX4, 9 figures include

Families of N=2 Strings

In a given 4d spacetime bakcground, one can often construct not one but a family of distinct N=2 string theories. This is due to the multiple ways N=2 superconformal algebra can be embedded in a given worldsheet theory. We formulate the principle of obtaining different physical theories by gauging different embeddings of the same symmetry algebra in the same ``pre-theory.'' We then apply it to N=2 strings and formulate the recipe for finding the associated parameter spaces of gauging. Flat and curved target spaces of both (4,0) and (2,2) signatures are considered. We broadly divide the gauging choices into two classes, denoted by alpha and beta, and show them to be related by T-duality. The distinction between them is formulated topologically and hinges on some unique properties of 4d manifolds. We determine what their parameter spaces of gauging are under certain simplicity ansatz for generic flat spaces (R^4 and its toroidal compactifications) as well as some curved spaces. We briefly discuss the spectra of D-branes for both alpha and beta families.Comment: 66+1 pages, 2 tables, latex 2e, hyperref. ver2: typos corrected, reference adde

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.

Small representations of finite classical groups

Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of representations of the group. In particular, the representations of small dimensions tend to contribute the largest terms to these sums, so a systematic knowledge of these small representations could lead to proofs of important conjectures which are currently out of reach. Despite the classification by Lusztig of the irreducible representations of finite groups of Lie type, it seems that this aspect remains obscure. In this note we develop a language which seems to be adequate for the description of the "small" representations of finite classical groups and puts in the forefront the notion of rank of a representation. We describe a method, the "eta correspondence", to construct small representations, and we conjecture that our construction is exhaustive. We also give a strong estimate on the dimension of small representations in terms of their rank. For the sake of clarity, in this note we describe in detail only the case of the finite symplectic groups.Comment: 18 pages, 9 figures, accepted for publications in the proceedings of the conference on the occasion of Roger Howe's 70th birthday (1-5 June 2015, Yale University, New Haven, CT