Measurement of the relative <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>c</mml:mi><mml:mo>±</mml:mo></mml:msubsup><mml:mo stretchy="false">/</mml:mo><mml:msup><mml:mi>B</mml:mi><mml:mo>±</mml:mo></mml:msup></mml:math> production cross section with the ATLAS detector at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>8</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>TeV</mml:mi></mml:math>

The total cross section and differential cross sections for the production of ${B}_{c}^{\ifmmode\pm\else\textpm\fi{}}$ mesons, times their branching fraction to $J/\ensuremath{\psi}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$, are measured relative to those for the production of ${B}^{\ifmmode\pm\else\textpm\fi{}}$ mesons, times their branching fraction to $J/\ensuremath{\psi}{K}^{\ifmmode\pm\else\textpm\fi{}}$. The data used for this study correspond to an integrated luminosity of $20.3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of $pp$ collisions recorded by the ATLAS detector at the Large Hadron Collider in 2012 at a center-of-mass energy of $\sqrt{s}=8\text{ }\text{ }\mathrm{TeV}$. The measurement is performed differentially in bins of transverse momentum ${p}_{\mathrm{T}}$ for $13\text{ }\text{ }\mathrm{GeV}<{p}_{\mathrm{T}}({B}_{c}^{\ifmmode\pm\else\textpm\fi{}})<22\text{ }\text{ }\mathrm{GeV}$ and ${p}_{\mathrm{T}}({B}_{c}^{\ifmmode\pm\else\textpm\fi{}})>22\text{ }\text{ }\mathrm{GeV}$ and in bins of rapidity $y$ for $|y|<0.75$ and $0.75<|y|<2.3$. The relative cross section times branching fraction for the full range ${p}_{\mathrm{T}}>13\text{ }\text{ }\mathrm{GeV}$ and $|y|<2.3$ is $(0.34\ifmmode\pm\else\textpm\fi{}0.0{4}_{\mathrm{stat}}{{\text{ }}_{\ensuremath{-}0.02}^{+0.06}}_{\mathrm{sys}}\ifmmode\pm\else\textpm\fi{}0.0{1}_{\text{lifetime}})%$. The differential measurements suggest that the production cross section of the ${B}_{c}^{\ifmmode\pm\else\textpm\fi{}}$ decreases faster with ${p}_{\mathrm{T}}$ than the production cross section of the ${B}^{\ifmmode\pm\else\textpm\fi{}}$, while no significant dependence on rapidity is observed.

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