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Evidence is reported for a narrow structure near the $J/\psi\phi$ thresholdin exclusive $B^+\to J/\psi\phi K^+$ decays produced in $\bar{p} p $ collisionsat $\sqrt{s}=1.96 \TeV$. A signal of $14\pm5$ events, with statisticalsignificance in excess of 3.8 standard deviations, is observed in a data samplecorresponding to an integrated luminosity of $2.7 \ifb$, collected by the CDFII detector. The mass and natural width of the structure are measured to be$4143.0\pm2.9(\mathrm{stat})\pm1.2(\mathrm{syst}) \MeVcc$ and$11.7^{+8.3}_{-5.0}(\mathrm{stat})\pm3.7(\mathrm{syst}) \MeVcc$.

Evidence for a Narrow Near-Threshold Structure in the $J/\psi\phi$ Mass Spectrum in $B^+\to J/\psi\phi K^+$ Decays