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Correlation at Low Temperature: II. Asymptotics

2004

The present paper is a continuation of ref. 4, where the truncated two-point correlation function for a class of lattice spin systems was proved to have exponential decay at low temperature, under a weak coupling assumption. In this paper we compute the asymptotics of the correlation function as the temperature goes to zero. This paper thus extends ref. 3 in two directions: The Hamiltonian function is allowed to have several local minima other than a unique global minimum, and we do not require translation invariance of the Hamiltonian function. We are in particular able to handle spin systems on a general lattice.

Hamiltonian mechanicsMathematical analysisCrystal systemStatistical and Nonlinear PhysicsCorrelationMaxima and minimaContinuationsymbols.namesakeLattice (order)symbolsExponential decayLaplace operatorMathematical PhysicsMathematicsMathematical physicsJournal of Statistical Physics
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"Table 22" of "Test of CP invariance in vector-boson fusion production of the Higgs boson in the H → ττ channel in proton–proton collisions at s=13Te…

2020

Post-fit BDT distributions in the $Z\to \ell\ell$ CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ SF analysis channel. The size of the combined statistical, experimental, and theoretical uncertainties is given. The exact value of the $p_{\mathrm{T}}$ cut on the leptons depends on the trigger.

Higgs Production13000.0Proton-Proton ScatteringBDT ScoreHigh Energy Physics::PhenomenologyTau-Tau DecayHigh Energy Physics::ExperimentP P -> H + X
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"Table 20" of "Test of CP invariance in vector-boson fusion production of the Higgs boson in the H → ττ channel in proton–proton collisions at s=13Te…

2020

Post-fit BDT distributions in the top-quark CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ SF channel. The size of the combined statistical, experimental, and theoretical uncertainties is given. The exact value of the $p_{\mathrm{T}}$ cut on the leptons depends on the trigger.

Higgs Production13000.0Proton-Proton ScatteringBDT ScoreHigh Energy Physics::PhenomenologyTau-Tau DecayHigh Energy Physics::ExperimentP P -> H + X
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"Table 21" of "Test of CP invariance in vector-boson fusion production of the Higgs boson in the H → ττ channel in proton–proton collisions at s=13Te…

2020

Post-fit BDT distributions in the top-quark CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ DF channel. The size of the combined statistical, experimental, and theoretical uncertainties is given.

Higgs Production13000.0Proton-Proton ScatteringBDT ScoreHigh Energy Physics::PhenomenologyTau-Tau DecayHigh Energy Physics::ExperimentP P -> H + X
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"Table 3" of "Test of CP invariance in vector-boson fusion production of the Higgs boson in the H → ττ channel in proton–proton collisions at s=13TeV…

2020

Post-fit BDT distributions after the VBF event selection for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ analysis channel. The VBF signal is shown for $\mu = 0.73$ and $\tilde d = -0.01$. ''Other bkg'' denotes all background contributions not listed explicitly in the legend. The size of the combined statistical, experimental, and theoretical uncertainties is given. The exact value of the $p_{\mathrm{T}}$ cut on the leading lepton depends on the trigger.

Higgs Production13000.0Proton-Proton ScatteringBDT ScoreTau-Tau DecayHigh Energy Physics::ExperimentP P -> H + X
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"Table 2" of "Test of CP invariance in vector-boson fusion production of the Higgs boson in the H → ττ channel in proton–proton collisions at s=13TeV…

2020

Post-fit BDT distributions after the VBF event selection for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ DF analysis channel. The VBF signal is shown for $\mu = 0.73$ and $\tilde d = -0.01$. ''Other bkg'' denotes all background contributions not listed explicitly in the legend. The size of the combined statistical, experimental, and theoretical uncertainties is given.

Higgs Production13000.0Proton-Proton ScatteringBDT ScoreTau-Tau DecayHigh Energy Physics::ExperimentP P -> H + X
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"Table 1" of "Test of CP invariance in vector-boson fusion production of the Higgs boson in the H → ττ channel in proton–proton collisions at s=13TeV…

2020

Post-fit BDT distributions after the VBF event selection for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ SF analysis channel. The VBF signal is shown for $\mu = 0.73$ and $\tilde d = -0.01$. ''Other bkg'' denotes all background contributions not listed explicitly in the legend. The size of the combined statistical, experimental, and theoretical uncertainties is given. The exact value of the $p_{\mathrm{T}}$ cut on the leptons depends on the trigger.

Higgs Production13000.0Proton-Proton ScatteringBDT ScoreTau-Tau DecayHigh Energy Physics::ExperimentP P -> H + X
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"Table 4" of "Test of CP invariance in vector-boson fusion production of the Higgs boson in the H → ττ channel in proton–proton collisions at s=13TeV…

2020

Post-fit BDT distributions after the VBF event selection for the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ analysis channel. The VBF signal is shown for $\mu = 0.73$ and $\tilde d = -0.01$. ''Other bkg'' denotes all background contributions not listed explicitly in the legend. The size of the combined statistical, experimental, and theoretical uncertainties is given.

Higgs Production13000.0Proton-Proton ScatteringBDT ScoreTau-Tau DecayP P -> H + X
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"Table 5" of "Test of CP invariance in vector-boson fusion production of the Higgs boson in the H → ττ channel in proton–proton collisions at s=13TeV…

2020

Post-fit $m_{\tau\tau}^{\mathrm{MMC}}$ distributions in the low BDT score CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ SF analysis channel. ''Other bkg'' denotes all background contributions not listed explicitly in the legend. The size of the combined statistical, experimental, and theoretical uncertainties is given. The exact value of the $p_{\mathrm{T}}$ cut on the leptons depends on the trigger.

Higgs Production13000.0Proton-Proton ScatteringHigh Energy Physics::PhenomenologyTau-Tau DecayHigh Energy Physics::ExperimentP P -> H + XMMC
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"Table 9" of "Test of CP invariance in vector-boson fusion production of the Higgs boson in the H → ττ channel in proton–proton collisions at s=13TeV…

2020

Post-fit Optimal Observable distributions in the low BDT score CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ SF analysis channel. ''Other bkg'' denotes all background contributions not listed explicitly in the legend. The size of the combined statistical, experimental, and theoretical uncertainties is given. The exact value of the $p_{\mathrm{T}}$ cut on the leptons depends on the trigger.

Higgs Production13000.0Proton-Proton ScatteringHigh Energy Physics::PhenomenologyTau-Tau DecayOptimal ObservableHigh Energy Physics::ExperimentP P -> H + X
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