The cross section for the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ is measured precisely at center-of-mass energies from 3.77 to 4.60 GeV using $9{\mathrm{fb}}^{-1}$ of data collected with the BESIII detector operating at the BEPCII storage ring. Two resonant structures are observed in a fit to the cross section. The first resonance has a mass of $(4222.0\pm 3.1\pm 1.4)\mathrm{MeV}/c^2$ and a width of $(44.1\pm 4.3\pm 2.0)\mathrm{MeV}$, while the second one has a mass of $(4320.0\pm 10.4\pm 7.0)\mathrm{MeV}/c^2$ and a width of $(101.4_{-19.7}^{+25.3}\pm 10.2)\mathrm{MeV}$, where the first errors are statistical and second ones are systematic. The first resonance agrees with the $Y(4260)$ resonance reported by previous experiments. The precision of its resonant parameters is improved significantly. The second resonance is observed in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ for the first time. The statistical significance of this resonance is estimated to be larger than $7.6\sigma$. The mass and width of the second resonance agree with the $Y(4360)$ resonance reported by the BABAR and Belle experiments within errors. Finally, the $Y(4008)$ resonance previously observed by the Belle experiment is not confirmed in the description of the BESIII data.

Einstein Telescope (ET) is the European project for a gravitational-wave (GW) observatory of third-generation. In this paper we present a comprehensive discussion of its science objectives, providing state-of-the-art predictions for the capabilities of ET in both geometries currently under consideration, a single-site triangular configuration or two L-shaped detectors. We discuss the impact that ET will have on domains as broad and diverse as fundamental physics, cosmology, early Universe, astrophysics of compact objects, physics of matter in extreme conditions, and dynamics of stellar collapse. We discuss how the study of extreme astrophysical events will be enhanced by multi-messenger observations. We highlight the ET synergies with ground-based and space-borne GW observatories, including multi-band investigations of the same sources, improved parameter estimation, and complementary information on astrophysical or cosmological mechanisms obtained combining observations from different frequency bands. We present advancements in waveform modeling dedicated to third-generation observatories, along with open tools developed within the ET Collaboration for assessing the scientific potentials of different detector configurations. We finally discuss the data analysis challenges posed by third-generation observatories, which will enable access to large populations of sources and provide unprecedented precision.

The cross sections of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c$ at center-of-mass energies from 3.896 to 4.600 GeV are measured using data samples collected with the BESIII detector operating at the Beijing Electron Positron Collider. The cross sections are found to be of the same order of magnitude as those of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ and $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\psi (2S)$, but the line shape is inconsistent with the $Y$ states observed in the latter two modes. Two structures are observed in the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c$ cross sections around 4.22 and $4.39\mathrm{GeV}/c^2$, which we call $Y(4220)$ and $Y(4390)$, respectively. A fit with a coherent sum of two Breit-Wigner functions results in a mass of $(4218.4_{-4.5}^{+5.5}\pm 0.9)\mathrm{MeV}/c^2$ and a width of $(66.0_{-8.3}^{+12.3}\pm 0.4)\mathrm{MeV}$ for the $Y(4220)$, and a mass of $(4391.5_{-6.8}^{+6.3}\pm 1.0)\mathrm{MeV}/c^2$ and a width of $(139.5_{-20.6}^{+16.2}\pm 0.6)\mathrm{MeV}$ for the $Y(4390)$, where the first uncertainties are statistical and the second ones systematic. The statistical significance of $Y(4220)$ and $Y(4390)$ is $10\sigma$ over one structure assumption.

The cross section of the $e^{+}{e}^{-}\to {\mathrm{\Lambda }}_c^{+}{\overline{\mathrm{\Lambda }}}_c^{-}$ process is measured with unprecedented precision using data collected with the BESIII detector at $\sqrt{s}=4574.5$, 4580.0, 4590.0 and 4599.5 MeV. The nonzero cross section near the ${\mathrm{\Lambda }}_c^{+}{\overline{\mathrm{\Lambda }}}_c^{-}$ production threshold is cleared. At center-of-mass energies $\sqrt{s}=4574.5$ and 4599.5 MeV, the higher statistics data enable us to measure the ${\mathrm{\Lambda }}_c$ polar angle distributions. From these, the ${\mathrm{\Lambda }}_c$ electric over magnetic form-factor ratios ($|G_E/G_M|$) are measured for the first time. They are found to be $1.14\pm 0.14\pm 0.07$ and $1.23\pm 0.05\pm 0.03$, respectively, where the first uncertainties are statistical and the second are systematic.

We study the $e^{+}{e}^{-}\to \gamma \omega J/\psi$ process using $11.6{\mathrm{fb}}^{-1}$ $e^{+}{e}^{-}$ annihilation data taken at center-of-mass energies from $\sqrt{s}=4.008\mathrm{GeV}$ to 4.600 GeV with the BESIII detector at the BEPCII storage ring. The $X(3872)$ resonance is observed for the first time in the $\omega J/\psi$ system with a significance of more than $5\sigma$. The relative decay ratio of $X(3872)\to \omega J/\psi$ and ${\pi }^{+}{\pi }^{-}J/\psi$ is measured to be $\mathcal{R}={1.6}_{-0.3}^{+0.4}\pm 0.2$, where the first uncertainty is statistical and the second systematic (the same hereafter). The $\sqrt{s}$-dependent cross section of $e^{+}{e}^{-}\to \gamma X(3872)$ is also measured and investigated, and it can be described by a single Breit-Wigner resonance, referred to as the $Y(4200)$, with a mass of ${4200.6}_{-13.3}^{+7.9}\pm 3.0\mathrm{MeV}/c^2$ and a width of ${115}_{-26}^{+38}\pm 12\mathrm{MeV}$. In addition, to describe the $\omega J/\psi$ mass distribution above $3.9\mathrm{GeV}/c^2$, we need at least one additional Breit-Wigner resonance, labeled as $X(3915)$, in the fit. The mass and width of the $X(3915)$ are determined. The resonant parameters of the $X(3915)$ agree with those of the $Y(3940)$ in $B\to K\omega J/\psi$ and of the $X(3915)$ in $\gamma \gamma \to \omega J/\psi$ observed by the Belle and BABAR experiments within errors.

The cross section of the process $e^{+}{e}^{-}\to {\pi }^{+}{D}^0{D}^{*-}$ for center-of-mass energies from 4.05 to 4.60 GeV is measured precisely using data samples collected with the BESIII detector operating at the BEPCII storage ring. Two enhancements are clearly visible in the cross section around 4.23 and 4.40 GeV. Using several models to describe the dressed cross section yields stable parameters for the first enhancement, which has a mass of $4228.6\pm 4.1\pm 6.3\mathrm{MeV}/c^2$ and a width of $77.0\pm 6.8\pm 6.3\mathrm{MeV}$, where the first uncertainties are statistical and the second ones are systematic. Our resonant mass is consistent with previous observations of the $Y(4220)$ state and the theoretical prediction of a $D{\overline{D}}_1(2420)$ molecule. This result is the first observation of $Y(4220)$ associated with an open-charm final state. Fits with three resonance functions with additional $Y(4260)$, $Y(4320)$, $Y(4360)$, $\psi (4415)$, or a new resonance do not show significant contributions from either of these resonances. The second enhancement is not from a single known resonance. It could contain contributions from $\psi (4415)$ and other resonances, and a detailed amplitude analysis is required to better understand this enhancement.