Forks, Noodles and the Burau representation for n=4n=4

\begin{abstract} The reduced Burau representation is a natural action of the braid group $B_n$ on the first homology group $H_1({\tilde{D}}_n;\mathbb{Z})$ of a suitable infinite cyclic covering space ${\tilde{D}}_n$ of the $n$--punctured disc $D_n$. It is known that the Burau representation is faithful for $n\le 3$ and that it is not faithful for $n\ge 5$. We use forks and noodles homological techniques and Bokut--Vesnin generators to analyze the problem for $n=4$. We present a Conjecture implying faithfulness and a Lemma explaining the implication. We give some arguments suggesting why we expect the Conjecture to be true. Also, we give some geometrically calculated examples and information about data gathered using a C\texttt{++} program.Comment: 24 pages, 21 figure

Knots and algebras

This paper gives a skein-theoretic construction of the Hecke algebras based on oriented tangles and the Homfly relations. A similar approach with unoriented tangles and Kauffman's Dubrovnik relations then gives a construction of the Birman-Wenzl algebra

Two Graviton Production at e+e−e^+e^- and Hadron Hadron Colliders in the Randall-Sundrum Model

We compute the pair production cross section of two Kaluza Klein modes in the Randall-Sundrum model at $e^+e^-$ and hadron hadron colliders. These processes are interesting because they get dominant contribution from the graviton interaction at next to leading order. Hence they provide a nontrivial test of the low scale gravity models. All the Feynman rules at next to leading order are also presented. These rules may be useful for many phenomenological applications including the computation of higher order loop corrections.Comment: 24 pages, 11 figures, some typos correcte

Charged particle multiplicities in pp interactions at √s = 0.9, 2.36, and 7 TeV

Measurements of primary charged hadron multiplicity distributions are presented for non-single-diractive events in proton-proton collisions at centre-of-mass energies of √s = 0.9, 2.36, and 7 TeV, in five pseudorapidity ranges from |η| < 0.5 to |η| < 2.4. The data were collected with the minimum-bias trigger of the CMS experiment during the LHC commissioning runs in 2009 and the 7 TeV run in 2010. The multiplicity distribution at √s = 0.9 TeV is in agreement with previous measurements. At higher energies the increase of the mean multiplicity with √s is underestimated by most event generators. The average transverse momentum as a function of the multiplicity is also presented. The measurement of higher-order moments of the multiplicity distribution confirms the violation of Koba-Nielsen-Olesen scaling that has been observed at lower energies

Measurements of inclusive W and Z cross sections in pp collisions at √s=7 TeV

Measurements of inclusive W and Z boson production cross sections in pp collisions at √s = 7 TeV are presented, based on 2.9 pb^(-1) of data recorded by the CMS detector at the LHC. The measurements, performed in the electron and muon decay channels, are combined to give σ(pp → WX) x B (W → lv) = 9.95 ± 0.07 (stat.) ± 0.28 (syst.) ± 1.09 (lumi.) nb and σ(pp → ZX) x B (Z → ℓ+ℓ-) = 0.931 ± 0.026 (stat.) ± 0.023 (syst.) ± 0.102 (lumi.) nb, where ℓ stands for either e or µ. Theoretical predictions, calculated at the next-to-next-to-leading order in QCD using recent parton distribution functions, are in agreement with the measured cross sections. Ratios of cross sections, which incur an experimental systematic uncertainty of less than 4%, are also reported

Search for physics beyond the standard model using multilepton signatures in pp collisions at √s=7 TeV

A search for physics beyond the standard model in events with at least three leptons and any number of jets is presented. The data sample corresponds to 35 pb^(−1) of integrated luminosity in pp collisions at √s=7 TeV collected by the CMS experiment at the LHC. A number of exclusive multileptonic channels are investigated and standard model backgrounds are suppressed by requiring sufficient missing transverse energy, invariant mass inconsistent with that of the Z boson, or high jet activity. Control samples in data are used to ascertain the robustness of background evaluation techniques and to minimise the reliance on simulation. The observations are consistent with background expectations. These results constrain previously unexplored regions of supersymmetric parameter space