Inclusive production of the $X(4140)$ state in $p \overline p $ collisions at D0

We present a study of the inclusive production of the $X(4140)$ with the decay to the $J/\psi \phi$ final state in hadronic collisions. Based on $10.4~\rm{fb^{-1}}$ of $p \overline p $ collision data collected by the D0 experiment at the Fermilab Tevatron collider, we report the first evidence for the prompt production of $X(4140)$ and find the fraction of $X(4140)$ events originating from $b$ hadrons to be $f_b=0.39\pm 0.07 {\rm \thinspace (stat)} \pm 0.10 {\rm \thinspace (syst)} $. The ratio of the non-prompt $X(4140)$ production rate to the $B_s^0$ yield in the same channel is $R=0.19 \pm 0.05 {\rm \thinspace (stat)} \pm 0.07 {\rm \thinspace (syst)}$. The values of the mass $M=4152.5 \pm 1.7 (\rm {stat}) ^{+6.2}_{-5.4} {\rm \thinspace (syst)}$~MeV and width $\Gamma=16.3 \pm 5.6 {\rm \thinspace (stat)} \pm 11.4 {\rm \thinspace (syst)}$~MeV are consistent with previous measurements. 8 pages, 2 figues