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

Observation and studies of jet quenching in PbPb collisions at √sNN = 2.76 TeV

Jet production in PbPb collisions at a nucleon-nucleon center-of-mass energy of 2.76 TeV was studied with the Compact Muon Solenoid (CMS) detector at the LHC, using a data sample corresponding to an integrated luminosity of 6.7 μb^(−1). Jets are reconstructed using the energy deposited in the CMS calorimeters and studied as a function of collision centrality. With increasing collision centrality, a striking imbalance in dijet transverse momentum is observed, consistent with jet quenching. The observed effect extends from the lower cutoff used in this study (jet pT = 120 GeV/c) up to the statistical limit of the available data sample (jet pT ≈ 210 GeV/c). Correlations of charged particle tracks with jets indicate that the momentum imbalance is accompanied by a softening of the fragmentation pattern of the second most energetic, away-side jet. The dijet momentum balance is recovered when integrating low transverse momentum particles distributed over a wide angular range relative to the direction of the away-side jet

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