QCD coherence and jet rates in small x deep inelastic scattering

The contributions to the deep inelastic scattering structure function which arise from emission of zero, one, two or three resolvable gluons and any number of unresolvable ones are computed to order ${\bar \alpha}_{S}^{3}$. Coherence effects are taken into account via angular ordering and are demonstrated to yield (at the leading logarithm level) the identical results to those obtained assuming the multi-Regge kinematics of BFKL.Comment: 14 pages. Extensively rewritten. To be published in Physics Letters

Cluster and field elliptical galaxies at z~1.3. The marginal role of the environment and the relevance of the galaxy central regions

We compared the properties of 56 elliptical galaxies selected from three clusters at $1.2<z<1.4$ with those of field galaxies in the GOODS-S (~30), COSMOS (~180) and CANDELS (~220) fields. We studied the relationships among effective radius, surface brightness, stellar mass, stellar mass density $\Sigma_{Re}$ and central mass density $\Sigma_{1kpc}$ within 1 kpc radius. We find that cluster ellipticals do not differ from field ellipticals: they share the same structural parameters at fixed mass and the same scaling relations. On the other hand, the population of field ellipticals at $z\sim1.3$ shows a significant lack of massive ($M_*> 2\times 10^{11}$ M$_\odot$) and large (R$_e > 4-5$ kpc) ellipticals with respect to the cluster. Nonetheless, at $M*<2\times 10^{11}$ M$_\odot$, the two populations are similar. The size-mass relation of ellipticals at z~1.3 defines two different regimes, above and below a transition mass $m_t\sim 2-3\times10^{10}$ M$_\odot$: at lower masses the relation is nearly flat (R$_e\propto M_*^{-0.1\pm 0.2}$), the mean radius is constant at ~1 kpc and $\Sigma_{Re}\sim \Sigma_{1kpc}$ while, at larger masses, the relation is R$_e\propto M*^{0.64\pm0.09}$. The transition mass marks the mass at which galaxies reach the maximum $\Sigma_{Re}$. Also the $\Sigma_{1kpc}$-mass relation follows two different regimes, $\Sigma_{1kpc}\propto M*^{0.64\ >m_t}_{1.07\ <m_t}$, defining a transition mass density $\Sigma_{1kpc}\sim 2-3\times10^3$ M$_\odot$ pc$^{-2}$. The mass density $\Sigma_{Re}$ does not correlate with mass, dense/compact galaxies can be assembled over a wide mass regime, independently of the environment. The central mass density, $\Sigma_{1kpc}$, besides to be correlated with the mass, is correlated to the age of the stellar population: the higher the central stellar mass density, the higher the mass, the older the age of the stellar population. [Abridged]Comment: Accepted for publication in A&A; 20 pages, 13 figures (replaced to match the A&A version

QCD analysis of D-parameter in near-to-planar three-jet events

We present the QCD analysis of D-parameter distribution in near-to-planar 3-jet e+e- annihilation events. We derive the all-order resummed perturbative prediction and the leading power suppressed non-perturbative corrections both to the mean value and the distribution. Here non-perturbative corrections are larger than in 2-jet shape observables, so that higher order non-perturbative effects could be relevant. Experimental data (not yet available) are needed in order to cast light on this important point. The technique we develop aims at improving the accuracy of the theoretical description of multi-jet ensembles, in particular in hadron-hadron collisions.Comment: 26 pages, 6 figures, JHEP class include

QCD analysis of near-to-planar 3-jet events

Perturbative QCD analysis is presented of the cumulative out-of-plane momentum distribution in the near-to-planar e+e- annihilation events, K_out << Q. In this kinematical region multiple gluon radiation effects become essential. They are resummed with the single-logarithmic accuracy, which programme includes the 2-loop treatment of the basic radiation and matching with the exact O(alpha_s^2) result. Dedicated experimental analyses of 3-jet event characteristics are of special interest for the study of the non-perturbative confinement effects.Comment: 32 pages, 1 figure, JHEP class include

Non-perturbative QCD analysis of near-to-planar three-jet events

We present the analysis of the 1/Q-suppressed non-perturbative (NP) contribution to the cumulative out-of-event-plane momentum distribution in e+e- annihilation in the near-to-planar three-jet region. It complements our previous study of the perturbative (PT) distributions resummed to single logarithmic accuracy. Due to inter-jet soft gluon radiation, the NP contributions (as well as the PT distributions) are sensitive to the geometry (the angles between jets) and the colour structure of the underlying hard process (topology of the three-prong parton antenna). The results and techniques presented here could be extended to other multi-jet processes and, in particular, to hadron-hadron collisions.Comment: 53 pages, 4 figures, JHEP class include

Moduli Spaces of Curves with Homology Chains and c=1 Matrix Models

We show that introducing a periodic time coordinate in the models of Penner-Kontsevich type generalizes the corresponding constructions to the case of the moduli space ${\cal S}_{gn}^k$ of curves $C$ with homology chains \gamma\in H_1(C,\zet_k). We make a minimal extension of the resulting models by adding a kinetic term, and we get a new matrix model which realizes a simple dynamics of \zet_k-chains on surfaces. This gives a representation of $c=1$ matter coupled to two-dimensional quantum gravity with the target space being a circle of finite radius, as studied by Gross and Klebanov.Comment: IFUM 459/FT (LaTeX, 9 pages; a few misprints have been corrected and the introduction has been slightly modified

Infrared safe definition of jet flavour

It is common, in both theoretical and experimental studies, to separately discuss quark and gluon jets. However, even at parton level, widely-used jet algorithms fail to provide an infrared safe way of making this distinction. We examine the origin of the problem, and propose a solution in terms of a new "flavour-kt" algorithm. As well as being of conceptual interest this can be a powerful tool when combining fixed-order calculations with multi-jet resummations and parton showers. It also has applications to studies of heavy-quark jets.Comment: 22 pages, 7 figure