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CMS-PAS-BPH-19-001
Relative cross sections of the ${\rm B_c^+(2S)}$ and ${\rm B_c^{*+}(2S)}$ states with respect to the ${\rm B_c^+}$ state in proton-proton collisions at $\sqrt{s} = $ 13 TeV
Abstract: The ${\rm B_c^+(2S)}$ to ${\rm B_c^+}$ and ${\rm B_c^{*+}(2S)}$ to ${\rm B_c^+}$ cross section ratios, as well as the ${\rm B_c^{*+}(2S)}$ to ${\rm B_c^+(2S)}$ cross section ratio, are measured in proton-proton collisions at $\sqrt{s} = $ 13 TeV, using a data sample collected by the CMS experiment, corresponding to an integrated luminosity of 143 fb$^{-1}$. The three measurements are made in the ${\rm B_c^+}$ phase space window defined by transverse momentum $p_{\rm T} > $ 15 GeV and absolute rapidity $|y| < $ 2.4, with the excited ${\rm B_c^{(*)+}(2S)}$ states reconstructed in their ${\rm B_c^+} \pi^+ \pi^-$ decay. The ${\rm B_c^+(2S)}$ to ${\rm B_c^+}$, ${\rm B_c^{*+}(2S)}$ to ${\rm B_c^+}$, and ${\rm B_c^{*+}(2S)}$ to ${\rm B_c^+(2S)}$ cross section ratios, including the (unknown) ${\rm B_c^{(*)+}(2S) \to B_c^+}\pi^+\pi^-$ branching fractions, are (3.57 $\pm$ 0.69 (stat) $\pm$ 0.32 (syst) )%, (4.91 $\pm$ 0.69 (stat) $\pm$ 0.57 (syst) )%, and 1.39 $\pm$ 0.35 (stat) $\pm$ 0.09 (syst), respectively, where the first uncertainty is statistical and the second is systematic. None of these ratios shows a significant dependence on the $p_{\rm T}$ or $|y|$ of the ${\rm B_c^+}$. The shape of the invariant mass distribution of the dipions emitted in the ${\rm B_c^{(*)+}(2S) \to B_c^+}\pi^+\pi^-$ decays is also reported.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Invariant mass distribution of the ${\mathrm{B_c}^{+} \to \mathrm{J}/\psi \pi^{+}}$ candidates, after applying all event selection criteria. The fitted contributions are shown by the stacked distributions, the solid line representing their sum. Taken from Ref. [1].

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Figure 2:
Invariant mass distribution of the ${{{\mathrm{B_c}^{(*)+}} (\text{2S})} \to {\mathrm{B_c}^{+}} \pi^{+}\pi^{-}} $ candidates, the ${{{\mathrm{B_c}^{(*)+}} (\text{2S})}} $ being the lower-mass peak. The fitted contributions are shown by the stacked distributions, the solid line representing their sum. Taken from Ref. [1].

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Figure 3:
The $R^{+}$, $R^{*+}$, and $R^{*+} / R^{+}$ cross section ratios as a function of the ${\mathrm{B_c}^{+}}$ ${p_{\mathrm {T}}}$ (left) and the ${\mathrm{B_c}^{+}}$ $ {|y|}$ (right). The markers are shown at the average ${\mathrm{B_c}^{+}}$ $ {p_{\mathrm {T}}} $ or $ {|y|}$ values of the events contributing to each bin.

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Figure 3-a:
The $R^{+}$, $R^{*+}$, and $R^{*+} / R^{+}$ cross section ratios as a function of the ${\mathrm{B_c}^{+}}$ ${p_{\mathrm {T}}}$ (left) and the ${\mathrm{B_c}^{+}}$ $ {|y|}$ (right). The markers are shown at the average ${\mathrm{B_c}^{+}}$ $ {p_{\mathrm {T}}} $ or $ {|y|}$ values of the events contributing to each bin.

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Figure 3-b:
The $R^{+}$, $R^{*+}$, and $R^{*+} / R^{+}$ cross section ratios as a function of the ${\mathrm{B_c}^{+}}$ ${p_{\mathrm {T}}}$ (left) and the ${\mathrm{B_c}^{+}}$ $ {|y|}$ (right). The markers are shown at the average ${\mathrm{B_c}^{+}}$ $ {p_{\mathrm {T}}} $ or $ {|y|}$ values of the events contributing to each bin.

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Figure 4:
Normalized invariant mass distribution of the dipions emitted in the ${{{\mathrm{B_c}^{(*)+}} (\text{2S})} \to {\mathrm{B_c}^{+}} \pi^{+}\pi^{-}} $ decays, $M(\pi^{+}\pi^{-})$. Both the statistical (inner tick marks) and the total (outer tick marks) uncertainties are represented. The histograms represent the two corresponding phase space distributions.
Tables

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Table 1:
Ratios of the reconstruction efficiencies relevant for the determination of the $R^{+}$, $R^{*+}$, and $R^{*+} / R^{+}$ cross section ratios. The central values are followed by the several uncertainties mentioned in the text.

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Table 2:
Systematic uncertainties (in %) on the cross section ratios, corresponding to the sources described in the text. The total uncertainty is the sum in quadrature of the individual terms.
Summary
The ${{\mathrm{B_c}^{+}} (\text{2S})}$ to ${\mathrm{B_c}^{+}}$ and ${{\mathrm{B_c}^{*+}} (\text{2S})}$ to ${\mathrm{B_c}^{+}}$ cross section ratios, as well as the ${{\mathrm{B_c}^{*+}} (\text{2S})}$ to ${{\mathrm{B_c}^{+}} (\text{2S})}$ cross section ratio, have been measured in proton-proton collisions at $\sqrt{s} = $ 13 TeV. The measurement was made on the basis of a data sample collected by the CMS experiment in the Run 2 of the LHC (2015-2018), corresponding to an integrated luminosity of 143 fb$^{-1}$.

The ${{\mathrm{B_c}^{+}} (\text{2S})}$ to ${\mathrm{B_c}^{+}}$, ${{\mathrm{B_c}^{*+}} (\text{2S})}$ to ${\mathrm{B_c}^{+}}$, and ${{\mathrm{B_c}^{*+}} (\text{2S})}$ to ${{\mathrm{B_c}^{+}} (\text{2S})}$ cross section ratios, including the (unknown) ${{{\mathrm{B_c}^{(*)+}} (\text{2S})} \to {\mathrm{B_c}^{+}} \pi^{+}\pi^{-}} $ branching fractions, are
$R^{+} = $ 3.57 $\pm$ 0.69 (stat) $\pm$ 0.32 (syst) %
$R^{*+} = $ 4.91 $\pm$ 0.69 (stat) $\pm$ 0.57 (syst) %
$R^{*+} / R^{+} = $ 1.39 $\pm$ 0.35 (stat) $\pm$ 0.09 (syst)
where the first uncertainty is statistical and the second is systematic. No significant dependences on the $p_{\mathrm{T}}$ or $|y|$ of the $\mathrm{B_c}^{+}$ mesons have been observed for any of these three ratios. The shapes of the invariant mass distributions of the dipions emitted in the ${{{\mathrm{B_c}^{(*)+}} (\text{2S})} \to {\mathrm{B_c}^{+}} \pi^{+}\pi^{-}} $ decays have also been reported. These results, obtained in the phase space region defined by $\mathrm{B_c}^{+}$ transverse momentum $p_{\mathrm{T}}> $ 15 GeV and $\mathrm{B_c}^{+}$ absolute rapidity $|y| < $ 2.4, are expected to provide important experimental information to improve the theoretical understanding of the nature of the $\mathrm{\bar{b}c}$ heavy quarkonium states and of the processes behind their production.
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