Convergence to global equilibrium for Fokker-Planck equations on a graph and Talagrand-type inequalities

In recent work, Chow, Huang, Li and Zhou introduced the study of Fokker-Planck equations for a free energy function defined on a finite graph. When $N\ge 2$ is the number of vertices of the graph, they show that the corresponding Fokker-Planck equation is a system of $N$ nonlinear ordinary differential equations defined on a Riemannian manifold of probability distributions. The different choices for inner products on the space of probability distributions result in different Fokker-Planck equations for the same process. Each of these Fokker-Planck equations has a unique global equilibrium, which is a Gibbs distribution. In this paper we study the {\em speed of convergence} towards global equilibrium for the solution of these Fokker-Planck equations on a graph, and prove that the convergence is indeed exponential. The rate as measured by the decay of the $L_2$ norm can be bound in terms of the spectral gap of the Laplacian of the graph, and as measured by the decay of (relative) entropy be bound using the modified logarithmic Sobolev constant of the graph. With the convergence result, we also prove two Talagrand-type inequalities relating relative entropy and Wasserstein metric, based on two different metrics introduced in [CHLZ] The first one is a local inequality, while the second is a global inequality with respect to the "lower bound metric" from [CHLZ]

Measurements of the branching fractions of the inclusive decays D0(D+)→π+π+π−X

Using eþe− annihilation data corresponding to an integrated luminosity of 2.93 fb−1 taken at a center-of mass energy of 3.773 GeV with the BESIII detector, we report the first measurements of the branching fractions of the inclusive decays D0 → πþπþπ−X and Dþ → πþπþπ−X, where pions from K0 S decays have been excluded from the πþπþπ− system and X denotes any possible particle combination. The branching fractions of D0ðDþÞ → πþπþπ−X are determined to be BðD0 → πþπþπ−XÞ¼ð17.60 0.11 0.22Þ% and BðDþ → πþπþπ−XÞ¼ð15.25 0.09 0.18Þ%, where the first uncertainties are statistical and the second systematic

Measurement of Λ\Lambda transverse polarization in e+e−e^{+}e^{-} collisions at s=3.68−3.71\sqrt{s}= 3.68-3.71 GeV

With data samples collected with the BESIII detector at seven energy points at $\sqrt{s}= 3.68 - 3.71$ GeV, corresponding to an integrated luminosity of 333 pb$^{-1}$, we present a study of the $\Lambda$ transverse polarization in the $e^+e^-\to\Lambda\bar\Lambda$ reaction. The significance of polarization by combining the seven energy points is found to be 2.6$\sigma$ including the systematic uncertainty, which implies a non-zero phase between the transition amplitudes of the $\Lambda\bar\Lambda$ helicity states. The modulus ratio and the relative phase of EM-$psionic$ form factors combined with all energy points are measured to be $R^{\Psi} =$ 0.71$^{+0.10}_{-0.10}$ $\pm$ 0.03 and $\Delta\Phi^{\Psi}$ = (23$^{+8.8}_{-8.0}$ $\pm$ 1.6$)^\circ$, where the first uncertainties are statistical and the second systematic.Comment: 19 pages, 4 figures, 3 tables, consistent with the publication in JHEP10(2023)08

Topological cell clustering in the ATLAS calorimeters and its performance in LHC Run 1

The reconstruction of the signal from hadrons and jets emerging from the proton–proton collisions at the Large Hadron Collider (LHC) and entering the ATLAS calorimeters is based on a three-dimensional topological clustering of individual calorimeter cell signals. The cluster formation follows cell signal-significance patterns generated by electromagnetic and hadronic showers. In this, the clustering algorithm implicitly performs a topological noise suppression by removing cells with insignificant signals which are not in close proximity to cells with significant signals. The resulting topological cell clusters have shape and location information, which is exploited to apply a local energy calibration and corrections depending on the nature of the cluster. Topological cell clustering is established as a well-performing calorimeter signal definition for jet and missing transverse momentum reconstruction in ATLAS

Search for hidden-charm tetraquark with strangeness in e+e−→K+Ds∗−D∗0+c.c.e^{+}e^{-}\rightarrow K^+ D_{s}^{*-} D^{*0}+c.c.

We report a search for a heavier partner of the recently observed $Z_{cs}(3985)^{-}$ state, denoted as $Z_{cs}^{\prime -}$, in the process $e^{+} e^{-}\rightarrow K^{+}D_{s}^{*-}D^{* 0}+c.c.$, based on $e^+e^-$ collision data collected at the center-of-mass energies of $\sqrt{s}=4.661$, 4.682 and 4.699 GeV with the BESIII detector. The $Z_{cs}^{\prime -}$ is of interest as it is expected to be a candidate for a hidden-charm and open-strange tetraquark. A partial-reconstruction technique is used to isolate $K^+$ recoil-mass spectra, which are probed for a potential contribution from $Z_{cs}^{\prime -}\to D_{s}^{*-}D^{* 0}$ ($c.c.$). We find an excess of $Z_{cs}^{\prime -}\rightarrow D_{s}^{*-}D^{*0}$ ($c.c.$) candidates with a significance of $2.9\sigma$, after considering systematic uncertainties, at a mass of $(4123.5 \pm 0.7_{\mathrm{stat.}} \pm 1.1_{\mathrm{syst.}}) \mathrm{MeV}/c^{2}$. As the data set is limited in size, the upper limits are evaluated at the 90% confidence level on the product of the Born cross section and the branching fraction of $Z_{cs}^{\prime-}\rightarrow D_{s}^{*-}D^{* 0}$, $\sigma^{\rm Born}\cdot\mathcal{B}$ at the three energy points, under different assumptions of the $Z_{cs}^{\prime -}$ mass from 4.120 to 4.140 MeV and of the width from 10 to 50 MeV. Under various mass and width assumptions, the upper limits of $\sigma^{\rm Born}\cdot\mathcal{B}$ are found to lie in the range of $2\sim6$, $3\sim7$ and $3\sim6$ pb at $\sqrt{s}=4.661$, 4.682 and 4.699 GeV, respectively. The larger data samples that will be collected in the coming years will allow a clearer picture to emerge concerning the existence and nature of the $Z_{cs}^{\prime -}$ state.Comment: 17 pages, 7 figure

Production of doubly-charged Δ\Delta baryon in e+e−e^{+}e^{-} annihilation at energies from 2.3094 to 2.6464 GeV

The processes $e^{+}e^{-} \to \Delta^{++}\bar{\Delta}^{--}$ and $e^{+}e^{-}\to \Delta^{++} \bar{p} \pi^{-} + c.c.$ are studied for the first time with $179~{\rm pb}^{-1}$ of $e^{+}e^{-}$ annihilation data collected with the BESIII detector at center-of-mass energies from $2.3094$ GeV to $2.6464$ GeV. No significant signal for the $e^{+}e^{-}\to \Delta^{++}\bar{\Delta}^{--}$ process is observed and the upper limit of the Born cross section is estimated at each energy point. For the process $e^{+}e^{-} \to \Delta^{++} \bar{p} \pi^{-} + c.c.$, a significant signal is observed at center-of-mass energies near 2.6454 GeV and the corresponding Born cross section is reported.Comment: 10 pages, 4 figure

Search for a scalar partner of the X(3872)X(3872) via ψ(3770)\psi(3770) decays into γηη′\gamma\eta\eta' and γπ+π−J/ψ\gamma\pi^{+}\pi^{-}J/\psi

Using a data sample corresponding to an integrated luminosity of 2.93 fb$^{-1}$ collected at a center-of-mass energy of 3.773~GeV with the BESIII detector at the BEPCII collider, we search for a scalar partner of the $X(3872)$, denoted as $X(3700)$, via $\psi(3770)\to \gamma\eta\eta'$ and $\gamma\pi^{+}\pi^{-}J/\psi$ processes. No significant signals are observed and the upper limits of the product branching fractions ${\cal B}(\psi(3770)\to\gamma X(3700))\cdot {\cal B}(X(3700)\to \eta\eta')$ and ${\cal B}(\psi(3770)\to\gamma X(3700))\cdot {\cal B}(X(3700)\to\pi^{+}\pi^{-}J/\psi)$ are determined at the 90\% confidence level, for the narrow $X(3700)$ with a mass ranging from 3710 to 3740 MeV/$c^2$, which are from 0.8 to 1.8 $(\times 10^{-5})$ and 0.9 to 3.4 $(\times 10^{-5})$, respectively

Measurement of branching fractions of Λc+\Lambda_{c}^{+} decays to Σ+K+K−\Sigma^{+} K^{+} K^{-}, Σ+ϕ\Sigma^{+}\phi and Σ+K+π−(π0)\Sigma^{+} K^{+} \pi^{-}(\pi^{0})

Based on 4.5 fb$^{-1}$ data taken at seven center-of-mass energies ranging from 4.600 to 4.699 GeV with the BESIII detector at the BEPCII collider, we measure the branching fractions of $\Lambda_{c}^{+}\rightarrow\Sigma^{+}+hadrons$ relative to $\Lambda_{c}^{+}\rightarrow \Sigma^+ \pi^+ \pi^-$. Combining with the world average branching fraction of $\Lambda_{c}^{+}\rightarrow \Sigma^+ \pi^+ \pi^-$, their branching fractions are measured to be $(0.377\pm0.042\pm0.018\pm0.021)\%$ for $\Lambda_{c}^{+}\rightarrow\Sigma^{+} K^{+} K^{-}$, $(0.200\pm0.023\pm0.010\pm0.011)\%$ for $\Lambda_{c}^{+}\rightarrow\Sigma^{+} K^{+} \pi^{-}$, $(0.414\pm0.080\pm0.029\pm0.023)\%$ for $\Lambda_{c}^{+}\rightarrow\Sigma^{+}\phi$ and $(0.197\pm0.036\pm0.008\pm0.011)\%$ for $\Lambda_{c}^{+}\rightarrow\Sigma^{+}K^{+} K^{-}$(non-$\phi$). In all the above results, the first uncertainties are statistical, the second are systematic and the third are from external input of the branching fraction of $\Lambda_{c}^{+}\rightarrow \Sigma^+ \pi^+ \pi^-$. Since no signal for $\Lambda_{c}^{+}\rightarrow\Sigma^{+} K^{+} \pi^{-}\pi^{0}$ is observed, the upper limit of its branching fraction is determined to be 0.11\% at the 90$\%$ confidence level