Introduction to supergeometry

These notes are based on a series of lectures given by the first author at the school of `Poisson 2010', held at IMPA, Rio de Janeiro. They contain an exposition of the theory of super- and graded manifolds, cohomological vector fields, graded symplectic structures, reduction and the AKSZ-formalism.Comment: Lecture notes of a course held at the school Poisson 2010 at IMPA, July 2010; 21 pages; references improve

Resurrection of the genus Staphisagria J. Hill, sister to all the other Delphinieae (Ranunculaceae)

Molecular sequence data show that the three species of Delphinium subg. Staphisagria (J. Hill) Peterm. form the sister clade to Aconitum L., Aconitella Spach, Consolida (DC.) S.F. Gray, and all remaining species of Delphinium L. To account for this finding we resurrect Staphisagria J. Hill (1756). Names in Staphisagria are available for two of the species. We here make the required new combination for the third species, Staphisagria picta (Willd.) F. Jabbour, provide a key to the species, and illustrate one of them

On Kaon production in e+e- and Semi-inclusive DIS reactions

We consider semi-inclusive unpolarized DIS for the production of charged kaons and the different possibilities to test the conventionally used assumptions s-\bar=0 and D_d^{K^+-K^-}=0. The considered tests have the advantage that they do not require any knowledge of the fragmentation functions. We also show that measurements of both charged and neutral kaons would allow the determination of the kaon FFs D_q^{K^++K^-} solely from SIDIS measurements, and discuss the comparison of (D_u-D_d)^{K^+-K^-} obtained independently in SIDIS and e+e- reactions. All analysis are performed in LO and NLO in QCD. The feasibility of the tests to HERMES SIDIS data is considered.Comment: 7 pages, NLO analysis for all presented tests and feasibility to HERMES data adde

Sea quark polarization and semi-inclusive DIS data

We investigate the potential impact of forthcoming Jefferson Lab semi-inclusive polarized deep inelastic scattering proton measurements in the determination of the sea quark polarization in the nucleon by means of a next to leading order global QCD analysis. Specifically, we estimate the resulting improvement in the constraints on polarized parton densities for the different flavors, which is found to be significant for up and strange quarks, and the correlation between remaining uncertainty ranges for each of the parton species.Comment: 7 pages, 4 figures. Version to be published in the European Physical Journal

Universality of non-leading logarithmic contributions in transverse-momentum distributions

We consider the resummation of the logarithmic contributions to the region of small transverse momenta in the distributions of high-mass systems (lepton pairs, vector bosons, Higgs particles, ....) produced in hadron collisions. We point out that the resummation formulae that are usually used to compute the distributions in perturbative QCD involve process-dependent form factors and coefficient functions. We present a new universal form of the resummed distribution, in which the dependence on the process is embodied in a single perturbative factor. The new form simplifies the calculation of non-leading logarithms at higher perturbative orders. It can also be useful to systematically implement process-independent non-perturbative effects in transverse-momentum distributions. We also comment on the dependence of these distributions on the factorization and renormalization scales.Comment: misprints corrected in Eqs. (6), (7) and (12), results unchange

Direct Higgs production and jet veto at hadron colliders

We consider Higgs boson production through gluon--gluon fusion in hadron collisions, when a veto is applied on the transverse momenta of the accompanying hard jets. We compute the QCD corrections to this process at NLO and NNLO, and present numerical results at the Tevatron and the LHC.Comment: 5 pages, 4 ps figures, presented at the XXXVIIth Rencontres de Moriond, QCD and Hadronic interactions, Les Arc1800, Franc

Higgs production in hadron collisions: soft and virtual QCD corrections at NNLO

We consider QCD corrections to Higgs boson production through gluon-gluon fusion in hadron collisions. Using the recently evaluated two-loop amplitude for this process and the corresponding factorization formulae for soft-gluon bremsstrahlung at O(alpha_s^2), we compute the soft and virtual contributions to the NNLO cross section. We also discuss soft-gluon resummation at next-to-next-to-leading logarithmic accuracy. Numerical results for Higgs boson production at the LHC are presented.Comment: 17 pages, 4 figures included. One note and one reference adde

Higgs production at hadron colliders in (almost) NNLO QCD

We compute the soft and virtual NNLO QCD corrections to Higgs production through gluon-gluon fusion at hadron colliders. We present numerical results obtained at the LHC and at the Tevatron Run II.Comment: latex, 5 pages, presented at the XXXVIth Rencontres de Moriond, QCD and Hadronic interactions, Les Arc1800, France and at the 9th International Workshop on Deep Inelastic Scattering DIS2001, Bologna, Ital

Graph Saturation in Multipartite Graphs

Let $G$ be a fixed graph and let ${\mathcal F}$ be a family of graphs. A subgraph $J$ of $G$ is ${\mathcal F}$-saturated if no member of ${\mathcal F}$ is a subgraph of $J$, but for any edge $e$ in $E(G)-E(J)$, some element of ${\mathcal F}$ is a subgraph of $J+e$. We let $\text{ex}({\mathcal F},G)$ and $\text{sat}({\mathcal F},G)$ denote the maximum and minimum size of an ${\mathcal F}$-saturated subgraph of $G$, respectively. If no element of ${\mathcal F}$ is a subgraph of $G$, then $\text{sat}({\mathcal F},G) = \text{ex}({\mathcal F}, G) = |E(G)|$. In this paper, for $k\ge 3$ and $n\ge 100$ we determine $\text{sat}(K_3,K_k^n)$, where $K_k^n$ is the complete balanced $k$-partite graph with partite sets of size $n$. We also give several families of constructions of $K_t$-saturated subgraphs of $K_k^n$ for $t\ge 4$. Our results and constructions provide an informative contrast to recent results on the edge-density version of $\text{ex}(K_t,K_k^n)$ from [A. Bondy, J. Shen, S. Thomass\'e, and C. Thomassen, Density conditions for triangles in multipartite graphs, Combinatorica 26 (2006), 121--131] and [F. Pfender, Complete subgraphs in multipartite graphs, Combinatorica 32 (2012), no. 4, 483--495].Comment: 16 pages, 4 figure

Quantum nondemolition measurement of mechanical motion quanta

The fields of opto- and electromechanics have facilitated numerous advances in the areas of precision measurement and sensing, ultimately driving the studies of mechanical systems into the quantum regime. To date, however, the quantization of the mechanical motion and the associated quantum jumps between phonon states remains elusive. For optomechanical systems, the coupling to the environment was shown to preclude the detection of the mechanical mode occupation, unless strong single photon optomechanical coupling is achieved. Here, we propose and analyse an electromechanical setup, which allows to overcome this limitation and resolve the energy levels of a mechanical oscillator. We find that the heating of the membrane, caused by the interaction with the environment and unwanted couplings, can be suppressed for carefully designed electromechanical systems. The results suggest that phonon number measurement is within reach for modern electromechanical setups.Comment: 8 pages, 5 figures plus 24 pages, 11 figures supplemental materia