Measurement of the differential $\gamma +2b$-jet cross section and the ratio $\sigma$($\gamma +2b$-jets)/$\sigma$($\gamma +b$-jet) in $p\bar{p}$ collisions at $\sqrt{s}$=1.96 TeV

We present the first measurements of the differential cross section $d\sigma \mathrm{/}d{p}_T^{\gamma }$ for the production of an isolated photon in association with at least two $b$-quark jets. The measurements consider photons with rapidities $\mathrm{\mid }{y}^{\gamma }\mathrm{\mid }<1.0$ and transverse momenta $30 < p_{T}^{\gamma} < 200$\text{GeV}\mathrm{.}The$b$-quarkjetsarerequiredtohave$p_T^{jet}>15$GeVand$| y^{jet}| < 1.5$\mathrm{.}Theratioofdifferentialproductioncrosssectionsfor$\gamma+2~b$-jetsto$\gamma+b$-jetasafunctionof$p_{T}^{\gamma}$ is also presented. The results are based on the proton-antiproton collision data at $\sqrt{s}=$1.96~\TeV collected with the D0 detector at the Fermilab Tevatron Collider. The measured cross sections and their ratios are compared to the next-to-leading order perturbative QCD calculations as well as predictions based on the $k_T$-factorization approach and those from the SHERPA and PYTHIA Monte Carlo event generators.