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The differential charged jet cross sections, jet fragmentation distributions, and jet shapes are measured in minimum bias proton-proton collisions at centre-of-mass energy s√=7 TeV using the ALICE detector at the LHC. Jets are reconstructed from charged particle momenta in the mid-rapidity region using the sequential recombination kT and anti-kT as well as the SISCone jet finding algorithms with several resolution parameters in the range R=0.2 to 0.6. Differential jet production cross sections measured with the three jet finders are in agreement in the transverse momentum (pT) interval 20<pjet,chT<100 GeV/c. They are also consistent with prior measurements carried out at the LHC by the ATLAS collaboration. The jet charged particle multiplicity rises monotonically with increasing jet pT, in qualitative agreement with prior observations at lower energies. The transverse profiles of leading jets are investigated using radial momentum density distributions as well as distributions of the average radius containing 80% (⟨R80⟩) of the reconstructed jet pT. The fragmentation of leading jets with R=0.4 using scaled pT spectra of the jet constituents is studied. The measurements are compared to model calculations from event generators (PYTHIA, PHOJET, HERWIG). The measured radial density distributions and ⟨R80⟩ distributions are well described by the PYTHIA model (tune Perugia-2011). The fragmentation distributions are better described by HERWIG.
Affine Bruhat--Tits buildings are geometric spaces extracting the combinatorics of algebraic groups. The building of PGL parametrizes flags of subspaces/lattices in or, equivalently, norms on a fixed finite-dimensional vector space, up to homothety. It has first been studied by Goldman and Iwahori as a piecewise-linear analogue of symmetric spaces. The space of seminorms compactifies the space of norms and admits a natural surjective restriction map from the Berkovich analytification of projective space that factors the natural tropicalization map. Inspired by Payne's result that the analytification is the limit of all tropicalizations, we show that the space of seminorms is the limit of all tropicalized linear embeddings ι:Pr↪Pn and prove a faithful tropicalization result for compactified linear spaces. The space of seminorms is in fact the tropical linear space associated to the universal realizable valuated matroid.