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  1. Modern practice for training classification deepnets involves a terminal phase of training (TPT), which begins at the epoch where training error first vanishes. During TPT, the training error stays effectively zero, while training loss is pushed toward zero. Direct measurements of TPT, for three prototypical deepnet architectures and across seven canonical classification datasets, expose a pervasive inductive bias we call neural collapse (NC), involving four deeply interconnected phenomena. (NC1) Cross-example within-class variability of last-layer training activations collapses to zero, as the individual activations themselves collapse to their class means. (NC2) The class means collapse to the vertices of a simplexmore »equiangular tight frame (ETF). (NC3) Up to rescaling, the last-layer classifiers collapse to the class means or in other words, to the simplex ETF (i.e., to a self-dual configuration). (NC4) For a given activation, the classifier’s decision collapses to simply choosing whichever class has the closest train class mean (i.e., the nearest class center [NCC] decision rule). The symmetric and very simple geometry induced by the TPT confers important benefits, including better generalization performance, better robustness, and better interpretability.« less
  2. Abstract Quantum chromodynamics, the theory of the strong force, describes interactions of coloured quarks and gluons and the formation of hadronic matter. Conventional hadronic matter consists of baryons and mesons made of three quarks and quark-antiquark pairs, respectively. Particles with an alternative quark content are known as exotic states. Here a study is reported of an exotic narrow state in the D 0 D 0 π + mass spectrum just below the D *+ D 0 mass threshold produced in proton-proton collisions collected with the LHCb detector at the Large Hadron Collider. The state is consistent with the ground isoscalarmore »$${{{{{{\rm{T}}}}}}}_{{{{{{\rm{c}}}}}}{{{{{\rm{c}}}}}}}^{+}$$ T c c + tetraquark with a quark content of $${{{{{\rm{c}}}}}}{{{{{\rm{c}}}}}}\overline{{{{{{\rm{u}}}}}}}\overline{{{{{{\rm{d}}}}}}}$$ c c u ¯ d ¯ and spin-parity quantum numbers J P  = 1 + . Study of the DD mass spectra disfavours interpretation of the resonance as the isovector state. The decay structure via intermediate off-shell D *+ mesons is consistent with the observed D 0 π + mass distribution. To analyse the mass of the resonance and its coupling to the D * D system, a dedicated model is developed under the assumption of an isoscalar axial-vector $${{{{{{\rm{T}}}}}}}_{{{{{{\rm{c}}}}}}{{{{{\rm{c}}}}}}}^{+}$$ T c c + state decaying to the D * D channel. Using this model, resonance parameters including the pole position, scattering length, effective range and compositeness are determined to reveal important information about the nature of the $${{{{{{\rm{T}}}}}}}_{{{{{{\rm{c}}}}}}{{{{{\rm{c}}}}}}}^{+}$$ T c c + state. In addition, an unexpected dependence of the production rate on track multiplicity is observed.« less
    Free, publicly-accessible full text available December 1, 2023
  3. Abstract Conventional, hadronic matter consists of baryons and mesons made of three quarks and a quark–antiquark pair, respectively 1,2 . Here, we report the observation of a hadronic state containing four quarks in the Large Hadron Collider beauty experiment. This so-called tetraquark contains two charm quarks, a $$\overline{{{{{u}}}}}$$ u ¯ and a $$\overline{{{{{d}}}}}$$ d ¯ quark. This exotic state has a mass of approximately 3,875 MeV and manifests as a narrow peak in the mass spectrum of D 0 D 0 π + mesons just below the D *+ D 0 mass threshold. The near-threshold mass together with the narrow widthmore »reveals the resonance nature of the state.« less
    Free, publicly-accessible full text available July 1, 2023
  4. A bstract A precision measurement of the Z boson production cross-section at $$ \sqrt{\mathrm{s}} $$ s = 13 TeV in the forward region is presented, using pp collision data collected by the LHCb detector, corresponding to an integrated luminosity of 5.1 fb − 1 . The production cross-section is measured using Z → μ + μ − events within the fiducial region defined as pseudorapidity 2 . 0 < η < 4 . 5 and transverse momentum p T > 20 GeV /c for both muons and dimuon invariant mass 60 < M μμ < 120 GeV /c 2 .more »The integrated cross-section is determined to be $$ \sigma \left(Z\to {\mu}^{+}{\mu}^{-}\right)=196.4\pm 0.2\pm 1.6\pm 3.9\ \mathrm{pb}, $$ σ Z → μ + μ − = 196.4 ± 0.2 ± 1.6 ± 3.9 pb , where the first uncertainty is statistical, the second is systematic, and the third is due to the luminosity determination. The measured results are in agreement with theoretical predictions within uncertainties.« less
    Free, publicly-accessible full text available July 1, 2023
  5. A bstract Coherent production of J/ψ mesons is studied in ultraperipheral lead-lead collisions at a nucleon-nucleon centre-of-mass energy of 5 TeV, using a data sample collected by the LHCb experiment corresponding to an integrated luminosity of about 10 μb −1 . The J/ψ mesons are reconstructed in the dimuon final state and are required to have transverse momentum below 1 GeV. The cross-section within the rapidity range of 2 . 0 < y < 4 . 5 is measured to be 4 . 45 ± 0 . 24 ± 0 . 18 ± 0 . 58 mb, where the firstmore »uncertainty is statistical, the second systematic and the third originates from the luminosity determination. The cross-section is also measured in J/ψ rapidity intervals. The results are compared to predictions from phenomenological models.« less
    Free, publicly-accessible full text available July 1, 2023