Measurement of the Prompt Double J/psi Production Cross Section in pp Collisions at sqrt(s) = 7 TeV

The cross section for the simultaneous production of two$~\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi~$mesons in proton-proton collisions at $\sqrt{s}$ = 7$~\mbox{TeV}~$at the LHC from a sample corresponding to an integrated luminosity of $4.73 \pm 0.12~\mbox{fb}^{-1}~$has been measured with the CMS detector. The two$~\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi~$mesons are fully reconstructed via their decays into $\mu^+ \mu^-$, and the signal yield is extracted with an extended maximum-likelihood fit. The acceptance region is defined by the individual$~\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi~$transverse momentum ($p_\mathrm{T}^{\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi}$) and rapidity ($|y^{\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi}|$): $p_\mathrm{T}^{\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi}>6.5~\mbox{GeV}/c~$for $|y^{\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi}|<1.2$, $p_\mathrm{T}^{\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi}>6.5 \rightarrow 4.5~\mbox{GeV}/c~$(where the $p_\mathrm{T}~$threshold scales linearly from 6.5 to 4.5$~\mbox{GeV}/c$) in the region $1.2<|y^{\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi}|<1.43$, and $p_\mathrm{T}^{\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi}>4.5~\mbox{GeV}/c~$for $1.43<|y^{\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi}|<2.2$. The total cross section assuming unpolarized prompt double$~\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi~$production is found to be $\sigma = 1.49 \pm 0.07 \pm 0.14~\mbox{nb}$, where the first uncertainty is statistical and the second is systematic. Different extreme assumptions about the$~\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi~$polarization can increase the cross section by as much as 27$\%$ or decrease it by as much as $31\%$. The differential cross section is measured in bins of the double$~\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi~$invariant mass, the absolute difference in rapidity of the two$~\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi~$mesons, and the transverse momentum of the double$~\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi~$system. The double$~\mathrm{J}\hspace{-.08em}/\hspace{-.14em}\psi~$invariant mass distribution is examined for possible contributions from $\eta_b$ production.