Uniqueness of Nash equilibria in quantum Cournot duopoly game

A quantum Cournot game of which classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties, (i) if the measurement of entanglement between strategic variables chosen by the competing firms is sufficiently large, the multiplicity of equilibria vanishes, and, (ii) the more strongly the strategic variables are entangled, the more closely the unique equilibrium approaches to the optimal one.Comment: 7 pages, 2 figure

A Novel Clustering Algorithm Based on Quantum Games

Enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum game with the problem of data clustering, and then develop a quantum-game-based clustering algorithm, in which data points in a dataset are considered as players who can make decisions and implement quantum strategies in quantum games. After each round of a quantum game, each player's expected payoff is calculated. Later, he uses a link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them in order to maximize his payoff. Further, algorithms are discussed and analyzed in two cases of strategies, two payoff matrixes and two LRR functions. Consequently, the simulation results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms have fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.Comment: 19 pages, 5 figures, 5 table

Measurements of ψ(2S)\psi(2S) decays into Vector- Tensor final states

Decays of the $\psi(2S)$ into vector plus tensor meson final states have been studied with 14 million $\psi(2S)$ events collected with the BESII detector. Branching fractions of \psi(2S) \rt \omega f_{2}(1270), $\rho a_2(1320)$, $K^*(892)^0\bar{K}^*_2(1430)^0+c.c.$ and $\phi f_2^{\prime}(1525)$ are determined. They improve upon previous BESI results and confirm the violation of the "12%" rule for $\psi(2S)$ decays to VT channels with higher precision.Comment: 7 pages, 7 figures and 2 table

\psi(2S) Decays into \J plus Two Photons

Using \gamma \gamma J/\psi, J/\psi \ra e^+ e^- and $\mu^+ \mu^-$ events from a sample of $14.0\times 10^6$ \psip decays collected with the BESII detector, the branching fractions for \psip\ra \pi^0\J, \eta\J, and \psi(2S)\ar\gamma\chi_{c1},\gamma\chi_{c2}\ar\gamma\gamma\jpsi are measured to be B(\psip\ra \pi^0\J) = (1.43\pm0.14\pm0.13)\times 10^{-3}, B(\psip\ra \eta\J) = (2.98\pm0.09\pm0.23)%, B(\psi(2S)\ar\gamma\chi_{c1}\ar\gamma\gamma\jpsi) = (2.81\pm0.05\pm 0.23)%, and B(\psi(2S)\ar\gamma\chi_{c2}\ar\gamma\gamma\jpsi) = (1.62\pm0.04\pm 0.12)%.Comment: 7 pages, 6 figures. submitted to Phys. Rev.

Observation and study of the decay J/ψ→ϕηη′J/\psi\rightarrow\phi\eta\eta'

We report the observation and study of the decay $J/\psi\rightarrow\phi\eta\eta'$ using $1.3\times{10^9}$ $J/\psi$ events collected with the BESIII detector. Its branching fraction, including all possible intermediate states, is measured to be $(2.32\pm0.06\pm0.16)\times{10^{-4}}$. We also report evidence for a structure, denoted as $X$, in the $\phi\eta'$ mass spectrum in the $2.0-2.1$ GeV/$c^2$ region. Using two decay modes of the $\eta'$ meson ($\gamma\pi^+\pi^-$ and $\eta\pi^+\pi^-$), a simultaneous fit to the $\phi\eta'$ mass spectra is performed. Assuming the quantum numbers of the $X$ to be $J^P = 1^-$, its significance is found to be 4.4$\sigma$, with a mass and width of $(2002.1 \pm 27.5 \pm 21.4)$ MeV/$c^2$ and $(129 \pm 17 \pm 9)$ MeV, respectively, and a product branching fraction $\mathcal{B}(J/\psi\rightarrow\eta{}X)\times{}\mathcal{B}(X\rightarrow\phi\eta')=(9.8 \pm 1.2 \pm 1.7)\times10^{-5}$. Alternatively, assuming $J^P = 1^+$, the significance is 3.8$\sigma$, with a mass and width of $(2062.8 \pm 13.1 \pm 7.2)$ MeV/$c^2$ and $(177 \pm 36 \pm 35)$ MeV, respectively, and a product branching fraction $\mathcal{B}(J/\psi\rightarrow\eta{}X)\times{}\mathcal{B}(X\rightarrow\phi\eta')=(9.6 \pm 1.4 \pm 2.0)\times10^{-5}$. The angular distribution of $J/\psi\rightarrow\eta{}X$ is studied and the two $J^P$ assumptions of the $X$ cannot be clearly distinguished due to the limited statistics. In all measurements the first uncertainties are statistical and the second systematic.Comment: 10 pages, 6 figures and 4 table

Observation of ηc→ωω\eta_c\to\omega\omega in J/ψ→γωωJ/\psi\to\gamma\omega\omega

Using a sample of $(1310.6\pm7.0)\times10^6$ $J/\psi$ events recorded with the BESIII detector at the symmetric electron positron collider BEPCII, we report the observation of the decay of the $(1^1 S_0)$ charmonium state $\eta_c$ into a pair of $\omega$ mesons in the process $J/\psi\to\gamma\omega\omega$. The branching fraction is measured for the first time to be $\mathcal{B}(\eta_c\to\omega\omega)= (2.88\pm0.10\pm0.46\pm0.68)\times10^{-3}$, where the first uncertainty is statistical, the second systematic and the third is from the uncertainty of $\mathcal{B}(J/\psi\to\gamma\eta_c)$. The mass and width of the $\eta_c$ are determined as $M=(2985.9\pm0.7\pm2.1)\,$MeV/$c^2$ and $\Gamma=(33.8\pm1.6\pm4.1)\,$MeV.Comment: 13 pages, 6 figure

Observation of Ds+→pnˉD^+_s\rightarrow p\bar{n} and confirmation of its large branching fraction

The baryonic decay $D^+_s\rightarrow p\bar{n}$ is observed, and the corresponding branching fraction is measured to be $(1.21\pm0.10\pm0.05)\times10^{-3}$, where the first uncertainty is statistical and second systematic. The data sample used in this analysis was collected with the BESIII detector operating at the BEPCII $e^+e^-$ double-ring collider with a center-of-mass energy of 4.178~GeV and an integrated luminosity of 3.19~fb$^{-1}$. The result confirms the previous measurement by the CLEO Collaboration and is of greatly improved precision, which may deepen our understanding of the dynamical enhancement of the W-annihilation topology in the charmed meson decays

Measurement of proton electromagnetic form factors in e+e−→ppˉe^+e^- \to p\bar{p} in the energy region 2.00-3.08 GeV

The process of $e^+e^- \rightarrow p\bar{p}$ is studied at 22 center-of-mass energy points ($\sqrt{s}$) from 2.00 to 3.08 GeV, exploiting 688.5~pb$^{-1}$ of data collected with the BESIII detector operating at the BEPCII collider. The Born cross section~($\sigma_{p\bar{p}}$) of $e^+e^- \rightarrow p\bar{p}$ is measured with the energy-scan technique and it is found to be consistent with previously published data, but with much improved accuracy. In addition, the electromagnetic form-factor ratio ($|G_{E}/G_{M}|$) and the value of the effective ($|G_{\rm{eff}}|$), electric ($|G_E|$) and magnetic ($|G_M|$) form factors are measured by studying the helicity angle of the proton at 16 center-of-mass energy points. $|G_{E}/G_{M}|$ and $|G_M|$ are determined with high accuracy, providing uncertainties comparable to data in the space-like region, and $|G_E|$ is measured for the first time. We reach unprecedented accuracy, and precision results in the time-like region provide information to improve our understanding of the proton inner structure and to test theoretical models which depend on non-perturbative Quantum Chromodynamics