90 research outputs found

    Self-intersection local times of random walks: Exponential moments in subcritical dimensions

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    Fix p>1p>1, not necessarily integer, with p(d2)<dp(d-2)<d. We study the pp-fold self-intersection local time of a simple random walk on the lattice Zd\Z^d up to time tt. This is the pp-norm of the vector of the walker's local times, t\ell_t. We derive precise logarithmic asymptotics of the expectation of exp{θttp}\exp\{\theta_t \|\ell_t\|_p\} for scales θt>0\theta_t>0 that are bounded from above, possibly tending to zero. The speed is identified in terms of mixed powers of tt and θt\theta_t, and the precise rate is characterized in terms of a variational formula, which is in close connection to the {\it Gagliardo-Nirenberg inequality}. As a corollary, we obtain a large-deviation principle for tp/(trt)\|\ell_t\|_p/(t r_t) for deviation functions rtr_t satisfying t r_t\gg\E[\|\ell_t\|_p]. Informally, it turns out that the random walk homogeneously squeezes in a tt-dependent box with diameter of order t1/d\ll t^{1/d} to produce the required amount of self-intersections. Our main tool is an upper bound for the joint density of the local times of the walk.Comment: 15 pages. To appear in Probability Theory and Related Fields. The final publication is available at springerlink.co

    Search for light pseudoscalar boson pairs produced from decays of the 125 GeV Higgs boson in final states with two muons and two nearby tracks in pp collisions at √s = 13 TeV

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    Observation of nuclear modifications in W±^{±} boson production in pPb collisions at √S^{S}NN = 8.16 TeV

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    Measurement of prompt D0^{0} and D\overline{D}0^{0} meson azimuthal anisotropy and search for strong electric fields in PbPb collisions at root SNN\sqrt{S_{NN}} = 5.02 TeV

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    The strong Coulomb field created in ultrarelativistic heavy ion collisions is expected to produce a rapiditydependent difference (Av2) in the second Fourier coefficient of the azimuthal distribution (elliptic flow, v2) between D0 (uc) and D0 (uc) mesons. Motivated by the search for evidence of this field, the CMS detector at the LHC is used to perform the first measurement of Av2. The rapidity-averaged value is found to be (Av2) = 0.001 ? 0.001 (stat)? 0.003 (syst) in PbPb collisions at ?sNN = 5.02 TeV. In addition, the influence of the collision geometry is explored by measuring the D0 and D0mesons v2 and triangular flow coefficient (v3) as functions of rapidity, transverse momentum (pT), and event centrality (a measure of the overlap of the two Pb nuclei). A clear centrality dependence of prompt D0 meson v2 values is observed, while the v3 is largely independent of centrality. These trends are consistent with expectations of flow driven by the initial-state geometry. ? 2021 The Author. Published by Elsevier B.V. This is an open access article under the CC BY licens

    A search for pair production of new light bosons decaying into muons in proton-proton collisions at 13  TeV

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    A search for new light bosons decaying into muon pairs is presented using a data sample corresponding to an integrated luminosity of 35.9fb−1 of proton-proton collisions at a center-of-mass energy √s=13TeV, collected with the CMS detector at the CERN LHC. The search is model independent, only requiring the pair production of a new light boson and its subsequent decay to a pair of muons. No significant deviation from the predicted background is observed. A model independent limit is set on the product of the production cross section times branching fraction to dimuons squared times acceptance as a function of new light boson mass. This limit varies between 0.15 and 0.39 fb over a range of new light boson masses from 0.25 to 8.5 GeV. It is then interpreted in the context of the next-to-minimal supersymmetric standard model and a dark supersymmetry model that allows for nonnegligible light boson lifetimes. In both cases, there is significant improvement over previously published limits

    Measurement of the CP-violating phase ϕs_{s} in the B0^{0}s_{s}→J/ψ φ(1020) →μ⁺μ⁻K⁺K⁻ channel in proton-proton collisions at √s = 13 TeV

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    Production of Λ⁺c_{c} baryons in proton-proton and lead-lead collisions at √S^{S}NN = 5.02 TeV

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    Observation of electroweak production of Wγ with two jets in proton-proton collisions at √s = 13 TeV

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    A first observation is presented for the electroweak production of a W boson, a photon, and two jets in proton-proton collisions. The W boson decays are selected by requiring one identified electron or muon and an imbalance in transverse momentum. The two jets are required to have a high dijet mass and a large separation in pseudorapidity. The measurement is based on data collected with the CMS detector at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb1^{-1}. The observed (expected) significance for this process is 4.9 (4.6) standard deviations. After combining with previously reported CMS results at 8 TeV, the observed (expected) significance is 5.3 (4.8) standard deviations. The cross section for the electroweak Wγjj_{γjj} production in a restricted fiducial region is measured as 20.4 +/- 4.5 fb and the total cross section for Wγ_{γ} production in association with 2 jets in the same fiducial region is 108 +/- 16 fb. All results are in good agreement with recent theoretical predictions. Constraints are placed on anomalous quartic gauge couplings in terms of dimension-8 effective field theory operators

    Measurement of the azimuthal anisotropy of Y(1S) and Y(2S) mesons in PbPb collisions at √S^{S}NN = 5.02 TeV

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    The second-order Fourier coefficients (υ2_{2}) characterizing the azimuthal distributions of Υ(1S) and Υ(2S) mesons produced in PbPb collisions at sNN\sqrt{s_{NN}} = 5.02 TeV are studied. The Υmesons are reconstructed in their dimuon decay channel, as measured by the CMS detector. The collected data set corresponds to an integrated luminosity of 1.7 nb1^{-1}. The scalar product method is used to extract the υ2_{2} coefficients of the azimuthal distributions. Results are reported for the rapidity range |y| < 2.4, in the transverse momentum interval 0 < pT_{T} < 50 GeV/c, and in three centrality ranges of 10–30%, 30–50% and 50–90%. In contrast to the J/ψ mesons, the measured υ2_{2} values for the Υ mesons are found to be consistent with zero

    Search for MSSM Higgs bosons decaying to μ⁺μ⁻ in proton-proton collisions at √s = 13 TeV

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