Automatic Numerical Analysis Based on Infinite-Precision Arithmetic

Abstract—Numerical analysis is an important process for cre-ating reliable numerical software. However, traditional analysis methods rely on manual estimation by numerical analysts, which is restricted by the problem size. Although some state-of-art software packages can check whether a program is numerical unstable, they cannot tell whether it is caused by ill-posed problem itself or by some improper implementation practices, while these packages work on the floating point values in the program. In this paper, we introduce an automatic framework that utilizes infinite-precision arithmetic to analyze large-scale numerical problems by computer. To eliminate rounding errors, the computing process iterates itself to increase intermediate precision until the calculation reaches the desired final precision. Then the framework perturbs the inputs and intermediate values of a certain numerical problem. By checking the gaps among different program outputs, the framework helps us understand whether the problem is well-conditioned or ill-conditioned. The framework also compares the infinite-precision arithmetic with fixed-precision arithmetic. The evaluation of a bunch of classical problems shows that our framework is able to detect the ill-conditioning in large-scale problems effectively

Search for high-mass resonances decaying to a jet and a Lorentz-boosted resonance in proton-proton collisions at $\sqrt{s}=13\text{ }\text{ }\mathrm{TeV}

Physics letters / B 832, 137263 (2022). doi:10.1016/j.physletb.2022.137263 Published by North-Holland Publ., Amsterda

Two-particle Bose-Einstein correlations and their Lévy parameters in PbPb collisions at sNN\sqrt{s_\mathrm{NN}} = 5.02 TeV

Two-particle Bose-Einstein momentum correlation functions are studied for charged-hadron pairs in lead-lead collisions at a center-of-mass energy per nucleon pair of $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV. The data sample, containing 4.27$\times10^{9}$ minimum bias events corresponding to an integrated luminosity of 0.607 nb$^{-1}$, was collected by the CMS experiment in 2018. The experimental results are discussed in terms of a L\'evy-type source distribution. The parameters of this distribution are extracted as functions of particle pair average transverse mass and collision centrality. These parameters include the L\'evy index or shape parameter ($\alpha$), the L\'evy scale parameter ($R$), and the correlation strength parameter ($\lambda$). The source shape, characterized by $\alpha$, is found to be neither Cauchy nor Gaussian, implying the need for a full L\'evy analysis. Similarly to what was previously found for systems characterized by Gaussian source radii, a hydrodynamical scaling is observed for the L\'evy $R$ parameter. The $\lambda$ parameter is studied in terms of the core-halo model.Comment: Submitted to Physical Review C. All figures and tables can be found at http://cms-results.web.cern.ch/cms-results/public-results/publications/HIN-21-011 (CMS Public Pages

{Search for direct production of GeV-scale resonances decaying to a pair of muons in proton-proton collisions at s \sqrt{s} = 13 TeV}

A search for direct production of low-mass dimuon resonances is performed using = 13 TeV proton-proton collision data collected by the CMS experiment during the 2017–2018 operation of the CERN LHC with an integrated luminosity of 96.6 fb−1. The search exploits a dedicated high-rate trigger stream that records events with two muons with transverse momenta as low as 3 GeV but does not include the full event information. The search is performed by looking for narrow peaks in the dimuon mass spectrum in the ranges of 1.1–2.6 GeV and 4.2–7.9 GeV. No significant excess of events above the expectation from the standard model background is observed. Model-independent limits on production rates of dimuon resonances within the experimental fiducial acceptance are set. Competitive or world’s best limits are set at 90% confidence level for a minimal dark photon model and for a scenario with two Higgs doublets and an extra complex scalar singlet (2HDM+S). Values of the squared kinetic mixing coefficient ε2 in the dark photon model above 10−6 are excluded over most of the mass range of the search. In the 2HDM+S, values of the mixing angle sin(θH) above 0.08 are excluded over most of the mass range of the search with a fixed ratio of the Higgs doublets vacuum expectation tan β = 0.5