A simple shower and matching algorithm

We present a simple formalism for parton-shower Markov chains. As a first step towards more complete uncertainty bands, we incorporate a comprehensive exploration of the ambiguities inherent in such calculations. To reduce this uncertainty, we then introduce a matching formalism which allows a generated event sample to simultaneously reproduce any infrared safe distribution calculated at leading or next-to-leading order in perturbation theory, up to sub-leading corrections. To enable a more universal definition of perturbative calculations, we also propose a more general definition of the hadronization cutoff. Finally, we present an implementation of some of these ideas for final-state gluon showers, in a code dubbed VINCIA.Comment: 32 pages, 6 figure

Bloch-Nordsieck violating electroweak corrections to inclusive TeV scale hard processes

We point out that, since the colliders initial states (e+ e-,p p, p pbar, ... ) carry a definite nonabelian flavor, electroweak radiative corrections to inclusive hard cross sections at the TeV scale are affected by peculiar Bloch-Nordsieck violating double logs. We recall the setup of soft cancellation theorems, and we analyze the magnitude of the noncancelling terms in the example of electron - positron annihilation into hadrons.Comment: Minor typos corrected, references added. Final version to appear on Phys. Rev. Let

The role of universal and non universal Sudakov logarithms in four fermion processes at TeV energies: the one-loop approximation revisited

We consider the separate effects on four fermion processes, in the TeV energy range, produced at one loop by Sudakov logarithms of universal and not universal kind, working in the 't Hooft xi=1 gauge. Summing the various vertex and box contributions allows to isolate two quite different terms.The first one is a combination of vertex and box quadratic and linear logarithms that are partially universal and partially not universal and independent of the scattering angle theta. The second one is theta-dependent, not universal, linearly logarithmic and only produced by weak boxes. We show that for several observables, measurable at future linear e+e- colliders (LC, CLIC), the role of the latter term is dominant and we discuss the implications of this fact for what concerns the reliability of a one-loop approximation.Comment: 22 pages and 13 figures; version to appear in Phys.Rev.D. e-mail: [email protected]

Top Quark Production at TeV Energies as a Potential SUSY Detector

We consider the process of top-antitop production from electron-positron annihilation, for c. m. energies in the few TeV regime, in the MSSM theoretical framework. We show that, at the one loop level, the \underline{slopes} of a number of observable quantities in an energy region around 3 TeV are only dependent on $\tan\beta$. Under optimal experimental conditions, a combined measurement of slopes might identify $\tan\beta$ values in a range $\tan\beta< 2$, $\tan\beta>20$ with acceptable precision.Comment: 14 pages, 6 Encapsulated PostScript figure

Top quark production at future lepton colliders in the asymptotic regime

The production of a tt(bar) pair from lepton-antilepton annihilation is considered for values of the center of mass energy much larger than the top mass, typically of the few TeV size. In this regime a number of simplifications occurs that allows to derive the leading asymptotic terms of various observables using the same theoretical description that was used for light quark production. Explicit examples are shown for the Standard Model and the Minimal Supersymmetric Standard Model cases.Comment: 20 pages and 13 figures. e-mail: [email protected]

Maximum union-free subfamilies

An old problem of Moser asks: how large of a union-free subfamily does every family of m sets have? A family of sets is called union-free if there are no three distinct sets in the family such that the union of two of the sets is equal to the third set. We show that every family of m sets contains a union-free subfamily of size at least \lfloor \sqrt{4m+1}\rfloor - 1 and that this bound is tight. This solves Moser's problem and proves a conjecture of Erd\H{o}s and Shelah from 1972. More generally, a family of sets is a-union-free if there are no a+1 distinct sets in the family such that one of them is equal to the union of a others. We determine up to an absolute multiplicative constant factor the size of the largest guaranteed a-union-free subfamily of a family of m sets. Our result verifies in a strong form a conjecture of Barat, F\"{u}redi, Kantor, Kim and Patkos.Comment: 10 page

Logarithmic SUSY electroweak effects on four-fermion processes at TeV energies

We compute the MSSM one-loop contributions to the asymptotic energy behaviour of fermion-antifermion pair production at future lepton-antilepton colliders. Besides the conventional logarithms of Renormalization Group origin, extra SUSY linear logarithmic terms appear of "Sudakov-type". In the TeV range their overall effect on a variety of observables can be quite relevant and drastically different from that obtained in the SM case.Comment: 19 pages and 14 figures, corrected version. e-mail: [email protected]

The early evolution of the H-free process

The H-free process, for some fixed graph H, is the random graph process defined by starting with an empty graph on n vertices and then adding edges one at a time, chosen uniformly at random subject to the constraint that no H subgraph is formed. Let G be the random maximal H-free graph obtained at the end of the process. When H is strictly 2-balanced, we show that for some c>0, with high probability as $n \to \infty$, the minimum degree in G is at least $cn^{1-(v_H-2)/(e_H-1)}(\log n)^{1/(e_H-1)}$. This gives new lower bounds for the Tur\'an numbers of certain bipartite graphs, such as the complete bipartite graphs $K_{r,r}$ with $r \ge 5$. When H is a complete graph $K_s$ with $s \ge 5$ we show that for some C>0, with high probability the independence number of G is at most $Cn^{2/(s+1)}(\log n)^{1-1/(e_H-1)}$. This gives new lower bounds for Ramsey numbers R(s,t) for fixed $s \ge 5$ and t large. We also obtain new bounds for the independence number of G for other graphs H, including the case when H is a cycle. Our proofs use the differential equations method for random graph processes to analyse the evolution of the process, and give further information about the structure of the graphs obtained, including asymptotic formulae for a broad class of subgraph extension variables.Comment: 36 page

The central limit problem for random vectors with symmetries

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein's method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry and we give a brief introduction to the classical method. The spherically symmetric case is treated by a variation of Stein's method which is adapted for continuous symmetries.Comment: AMS-LaTeX, uses xy-pic, 23 pages; v3: added new corollary to Theorem

High energy behaviour of gamma gamma to f f(bar) processes in SM and MSSM

We compute the leading logarithms electroweak contributions to gamma gamma to f f(bar) processes in SM and MSSM. Several interesting properties are pointed out, such as the importance of the angular dependent terms, of the Yukawa terms, and especially of the $\tan^2\beta$ dependence in the SUSY contributions. These properties are complementary to those found in e+e- to f f(bar). These radiative correction effects should be largely observable at future high energy gamma gamma colliders. Polarized beams would bring interesting checks of the structure of the one loop corrections. We finally discuss the need for two-loop calculations and resummation.Comment: 22 pages and 12 figures. e-mail: [email protected]