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| CMS-HIN-21-014 ; CERN-EP-2024-176 | ||
| Bottom quark energy loss and hadronization with $ {\mathrm{B}^{+}} $ and $ \mathrm{B}_{\mathrm{s}}^{0} $ nuclear modification factors using pp and PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV | ||
| CMS Collaboration | ||
| 11 September 2024 | ||
| Submitted to J. High Energy Phys. | ||
| Abstract: The production cross sections of $ \mathrm{B}_{\mathrm{s}}^{0} $ and $ {\mathrm{B}^{+}} $ mesons are reported in proton-proton (pp) collisions recorded by the CMS experiment at the CERN LHC with a center-of-mass energy of 5.02 TeV. The data sample corresponds to an integrated luminosity of 302 pb$^{-1}$. The cross sections are based on measurements of the $ \mathrm{B}_{\mathrm{s}}^{0} \to \mathrm{J}/\psi (\mu^{+}\mu^{-})\,\phi(1020) (\mathrm{K^+} \mathrm{K^-}) $ and $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi (\mu^{+}\mu^{-})\,\mathrm{K^+} $ decay channels. Results are presented in the transverse momentum ($ p_{\mathrm{T}} $) range 7-50 GeV/$c$ and the rapidity interval $ |y| < $ 2.4 for the $ {\mathrm{B}} $ mesons. The measured $ p_{\mathrm{T}} $-differential cross sections of $ {\mathrm{B}^{+}} $ and $ \mathrm{B}_{\mathrm{s}}^{0} $ in pp collisions are well described by fixed-order plus next-to-leading logarithm perturbative quantum chromodynamics calculations. Using previous PbPb collision measurements at the same nucleon-nucleon center-of-mass energy, the nuclear modification factors, $ R_{\mathrm{AA}} $, of the $ {\mathrm{B}} $ mesons are determined. For $ p_{\mathrm{T}} > $ 10 GeV/$c$, both mesons are found to be suppressed in PbPb collisions (with $ R_{\mathrm{AA}} $ values significantly below unity), with less suppression observed for the $ \mathrm{B}_{\mathrm{s}}^{0} $ mesons. In this $ p_{\mathrm{T}} $ range, the $ R_{\mathrm{AA}} $ values for the $ {\mathrm{B}^{+}} $ mesons are consistent with those for inclusive charged hadrons and $ \mathrm{D^0} $ mesons. Below 10 GeV/$c$, both $ {\mathrm{B}^{+}} $ and $ \mathrm{B}_{\mathrm{s}}^{0} $ are found to be less suppressed than either inclusive charged hadrons or $ \mathrm{D^0} $ mesons, with the $ \mathrm{B}_{\mathrm{s}}^{0} R_{\mathrm{AA}} $ value consistent with unity. The $ R_{\mathrm{AA}} $ values found for the $ {\mathrm{B}^{+}} $ and $ \mathrm{B}_{\mathrm{s}}^{0} $ are compared to theoretical calculations, providing constraints on the mechanism of bottom quark energy loss and hadronization in the quark-gluon plasma, the hot and dense matter created in ultrarelativistic heavy ion collisions. | ||
| Links: e-print arXiv:2409.07258 [hep-ex] (PDF) ; CDS record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Invariant mass distributions of $ {\mathrm{B}^{+}} $ (left) and $ \mathrm{B}_{\mathrm{s}}^{0} $ (right) candidates, for the lowest (upper) and highest (lower) $ p_{\mathrm{T}} $ ranges in pp collisions at $ \sqrt{s}= $ 5.02 TeV. The bottom section in each panel shows the pulls, calculated as the difference between the data points and the fit results, divided by the uncertainty in data. |
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Figure 1-a:
Invariant mass distributions of $ {\mathrm{B}^{+}} $ (left) and $ \mathrm{B}_{\mathrm{s}}^{0} $ (right) candidates, for the lowest (upper) and highest (lower) $ p_{\mathrm{T}} $ ranges in pp collisions at $ \sqrt{s}= $ 5.02 TeV. The bottom section in each panel shows the pulls, calculated as the difference between the data points and the fit results, divided by the uncertainty in data. |
png pdf |
Figure 1-b:
Invariant mass distributions of $ {\mathrm{B}^{+}} $ (left) and $ \mathrm{B}_{\mathrm{s}}^{0} $ (right) candidates, for the lowest (upper) and highest (lower) $ p_{\mathrm{T}} $ ranges in pp collisions at $ \sqrt{s}= $ 5.02 TeV. The bottom section in each panel shows the pulls, calculated as the difference between the data points and the fit results, divided by the uncertainty in data. |
png pdf |
Figure 1-c:
Invariant mass distributions of $ {\mathrm{B}^{+}} $ (left) and $ \mathrm{B}_{\mathrm{s}}^{0} $ (right) candidates, for the lowest (upper) and highest (lower) $ p_{\mathrm{T}} $ ranges in pp collisions at $ \sqrt{s}= $ 5.02 TeV. The bottom section in each panel shows the pulls, calculated as the difference between the data points and the fit results, divided by the uncertainty in data. |
png pdf |
Figure 1-d:
Invariant mass distributions of $ {\mathrm{B}^{+}} $ (left) and $ \mathrm{B}_{\mathrm{s}}^{0} $ (right) candidates, for the lowest (upper) and highest (lower) $ p_{\mathrm{T}} $ ranges in pp collisions at $ \sqrt{s}= $ 5.02 TeV. The bottom section in each panel shows the pulls, calculated as the difference between the data points and the fit results, divided by the uncertainty in data. |
png pdf |
Figure 2:
The $ p_{\mathrm{T}} $-differential cross sections of $ {\mathrm{B}^{+}} $ (left) and $ \mathrm{B}_{\mathrm{s}}^{0} $ (right) mesons in pp collisions at $ \sqrt{s}= $ 5.02 TeV. The vertical bars (shaded boxes) correspond to statistical (systematic) uncertainties. The horizontal bars reflect the bin widths. The global systematic uncertainty includes uncertainties in the integrated luminosity and the external branching fractions. The comparison with the calculation from FONLL (open boxes) is also shown. The lower panels show that the measured cross sections deviate from the FONLL calculations by less than 20%, and the two are consistent within uncertainty. |
png pdf |
Figure 2-a:
The $ p_{\mathrm{T}} $-differential cross sections of $ {\mathrm{B}^{+}} $ (left) and $ \mathrm{B}_{\mathrm{s}}^{0} $ (right) mesons in pp collisions at $ \sqrt{s}= $ 5.02 TeV. The vertical bars (shaded boxes) correspond to statistical (systematic) uncertainties. The horizontal bars reflect the bin widths. The global systematic uncertainty includes uncertainties in the integrated luminosity and the external branching fractions. The comparison with the calculation from FONLL (open boxes) is also shown. The lower panels show that the measured cross sections deviate from the FONLL calculations by less than 20%, and the two are consistent within uncertainty. |
png pdf |
Figure 2-b:
The $ p_{\mathrm{T}} $-differential cross sections of $ {\mathrm{B}^{+}} $ (left) and $ \mathrm{B}_{\mathrm{s}}^{0} $ (right) mesons in pp collisions at $ \sqrt{s}= $ 5.02 TeV. The vertical bars (shaded boxes) correspond to statistical (systematic) uncertainties. The horizontal bars reflect the bin widths. The global systematic uncertainty includes uncertainties in the integrated luminosity and the external branching fractions. The comparison with the calculation from FONLL (open boxes) is also shown. The lower panels show that the measured cross sections deviate from the FONLL calculations by less than 20%, and the two are consistent within uncertainty. |
png pdf |
Figure 3:
The $ p_{\mathrm{T}} $ dependence of the nuclear modification factor of $ {\mathrm{B}^{+}} $ (left) and $ \mathrm{B}_{\mathrm{s}}^{0} $ (right) mesons using PbPb and pp collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV. The vertical bars (boxes) correspond to statistical (systematic) uncertainties. The horizontal bars reflect the bin widths and not uncertainties.The global systematic uncertainty includes the uncertainties in the integrated luminosity, $ T_{\mathrm{AA}} $, and the number of minimum bias events [52]. For the $ {\mathrm{B}^{+}} $ meson, four theoretical calculations are also shown for comparison: TAMU [76,24], DREENA-A [77,78], CUJET3.0 [79,80,81], and AdS/CFT HH [82,83] with the diffusion coefficient either dependent or independent of the quark momentum. For the $ \mathrm{B}_{\mathrm{s}}^{0} $ meson, three theoretical calculations are shown for comparison: TAMU [76,24], DREENA-A [77,78], and CUJET3.0 [79,80,81]. The line width of the theoretical calculation from Refs. [76,24] indicates the uncertainty in the total b quark coalescence probability (no shadowing is applied). The rapidity range is $ |y| < $ 2.4 for all the theoretical predictions and, therefore, these predictions can only be compared to the measurements in the range of $ p_{\mathrm{T}} > $ 10 GeV/$c$. |
png pdf |
Figure 3-a:
The $ p_{\mathrm{T}} $ dependence of the nuclear modification factor of $ {\mathrm{B}^{+}} $ (left) and $ \mathrm{B}_{\mathrm{s}}^{0} $ (right) mesons using PbPb and pp collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV. The vertical bars (boxes) correspond to statistical (systematic) uncertainties. The horizontal bars reflect the bin widths and not uncertainties.The global systematic uncertainty includes the uncertainties in the integrated luminosity, $ T_{\mathrm{AA}} $, and the number of minimum bias events [52]. For the $ {\mathrm{B}^{+}} $ meson, four theoretical calculations are also shown for comparison: TAMU [76,24], DREENA-A [77,78], CUJET3.0 [79,80,81], and AdS/CFT HH [82,83] with the diffusion coefficient either dependent or independent of the quark momentum. For the $ \mathrm{B}_{\mathrm{s}}^{0} $ meson, three theoretical calculations are shown for comparison: TAMU [76,24], DREENA-A [77,78], and CUJET3.0 [79,80,81]. The line width of the theoretical calculation from Refs. [76,24] indicates the uncertainty in the total b quark coalescence probability (no shadowing is applied). The rapidity range is $ |y| < $ 2.4 for all the theoretical predictions and, therefore, these predictions can only be compared to the measurements in the range of $ p_{\mathrm{T}} > $ 10 GeV/$c$. |
png pdf |
Figure 3-b:
The $ p_{\mathrm{T}} $ dependence of the nuclear modification factor of $ {\mathrm{B}^{+}} $ (left) and $ \mathrm{B}_{\mathrm{s}}^{0} $ (right) mesons using PbPb and pp collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV. The vertical bars (boxes) correspond to statistical (systematic) uncertainties. The horizontal bars reflect the bin widths and not uncertainties.The global systematic uncertainty includes the uncertainties in the integrated luminosity, $ T_{\mathrm{AA}} $, and the number of minimum bias events [52]. For the $ {\mathrm{B}^{+}} $ meson, four theoretical calculations are also shown for comparison: TAMU [76,24], DREENA-A [77,78], CUJET3.0 [79,80,81], and AdS/CFT HH [82,83] with the diffusion coefficient either dependent or independent of the quark momentum. For the $ \mathrm{B}_{\mathrm{s}}^{0} $ meson, three theoretical calculations are shown for comparison: TAMU [76,24], DREENA-A [77,78], and CUJET3.0 [79,80,81]. The line width of the theoretical calculation from Refs. [76,24] indicates the uncertainty in the total b quark coalescence probability (no shadowing is applied). The rapidity range is $ |y| < $ 2.4 for all the theoretical predictions and, therefore, these predictions can only be compared to the measurements in the range of $ p_{\mathrm{T}} > $ 10 GeV/$c$. |
png pdf |
Figure 4:
Comparison of the nuclear modification factor as a function of $ p_{\mathrm{T}} $ of $ {\mathrm{B}^{+}} $ and $ \mathrm{B}_{\mathrm{s}}^{0} $ mesons with $ \mathrm{B}_{c} $ mesons [27] (left) as well as with $ \mathrm{D^0} $ mesons [86] and inclusive charged hadrons [60] (right) in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV. The vertical bars (boxes) correspond to statistical (systematic) uncertainties. The horizontal bars reflect the bin widths. The global systematic uncertainties, written in text on the left plot and depicted in shaded boxes around $ R_{\mathrm{AA}}= $ 1 on the right plot, comprise the uncertainties in $ T_{\mathrm{AA}} $, the number of minimum-bias events, and the luminosity in pp collisions. The dashed lines and the open boxes in the $ \mathrm{B}_{c} $ data (left plot) represent bin-to-bin-uncorrelated and total uncertainties, respectively. |
png pdf |
Figure 4-a:
Comparison of the nuclear modification factor as a function of $ p_{\mathrm{T}} $ of $ {\mathrm{B}^{+}} $ and $ \mathrm{B}_{\mathrm{s}}^{0} $ mesons with $ \mathrm{B}_{c} $ mesons [27] (left) as well as with $ \mathrm{D^0} $ mesons [86] and inclusive charged hadrons [60] (right) in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV. The vertical bars (boxes) correspond to statistical (systematic) uncertainties. The horizontal bars reflect the bin widths. The global systematic uncertainties, written in text on the left plot and depicted in shaded boxes around $ R_{\mathrm{AA}}= $ 1 on the right plot, comprise the uncertainties in $ T_{\mathrm{AA}} $, the number of minimum-bias events, and the luminosity in pp collisions. The dashed lines and the open boxes in the $ \mathrm{B}_{c} $ data (left plot) represent bin-to-bin-uncorrelated and total uncertainties, respectively. |
png pdf |
Figure 4-b:
Comparison of the nuclear modification factor as a function of $ p_{\mathrm{T}} $ of $ {\mathrm{B}^{+}} $ and $ \mathrm{B}_{\mathrm{s}}^{0} $ mesons with $ \mathrm{B}_{c} $ mesons [27] (left) as well as with $ \mathrm{D^0} $ mesons [86] and inclusive charged hadrons [60] (right) in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV. The vertical bars (boxes) correspond to statistical (systematic) uncertainties. The horizontal bars reflect the bin widths. The global systematic uncertainties, written in text on the left plot and depicted in shaded boxes around $ R_{\mathrm{AA}}= $ 1 on the right plot, comprise the uncertainties in $ T_{\mathrm{AA}} $, the number of minimum-bias events, and the luminosity in pp collisions. The dashed lines and the open boxes in the $ \mathrm{B}_{c} $ data (left plot) represent bin-to-bin-uncorrelated and total uncertainties, respectively. |
| Tables | |
png pdf |
Table 1:
Summary of systematic uncertainties (in %) for the $ {\mathrm{B}^{+}} $ (upper table) and $ \mathrm{B}_{\mathrm{s}}^{0} $ (lower one) meson cross section as a function of $ p_{\mathrm{T}} $. The systematic uncertainties in luminosity and branching fractions are global uncertainties that are applied equally to all $ p_{\mathrm{T}} $ ranges. |
| Summary |
| In summary, the differential cross sections of $ {\mathrm{B}^{+}} $ and $ \mathrm{B}_{\mathrm{s}}^{0} $ mesons as functions of transverse momentum ($ p_{\mathrm{T}} $) in proton-proton (pp) collisions at a center-of-mass energy of 5.02 TeV have been measured with the CMS detector at the LHC. The mesons were reconstructed via the exclusive decay channels $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi (\mu^{+}\mu^{-})\,\mathrm{K^+} $ and $ \mathrm{B}_{\mathrm{s}}^{0} \to \mathrm{J}/\psi (\mu^{+}\mu^{-})\,\phi(1020) (\mathrm{K^+} \mathrm{K^-}) $ in the $ p_{\mathrm{T}} $ intervals of 5-60 and 7-50 GeV/$c$ for $ {\mathrm{B}^{+}} $ and $ \mathrm{B}_{\mathrm{s}}^{0} $, respectively. The measured $ p_{\mathrm{T}} $-differential cross sections of $ {\mathrm{B}^{+}} $ and $ \mathrm{B}_{\mathrm{s}}^{0} $ mesons in pp collisions are well-described by fixed-order plus next-to-leading logarithm calculations. The nuclear modification factors ($ R_{\mathrm{AA}} $) are obtained from these differential cross sections and the corresponding measurements in lead-lead collisions. The $ R_{\mathrm{AA}} $ of $ \mathrm{B}_{\mathrm{s}}^{0} $ and $ {\mathrm{B}^{+}} $ mesons are significantly lower than unity for $ p_{\mathrm{T}} > $ 10 GeV/$c$, while at lower $ p_{\mathrm{T}} $ the $ \mathrm{B}_{\mathrm{s}}^{0} $ meson results hint at having larger $ R_{\mathrm{AA}} $ values than found for $ {\mathrm{B}^{+}} $ mesons. The $ R_{\mathrm{AA}} $ data for $ {\mathrm{B}^{+}} $ and $ \mathrm{B}_{\mathrm{s}}^{0} $ mesons are compared to theoretical calculations, providing constraints for the mechanisms of bottom quark energy loss and hadronization in the quark-gluon plasma. The results are also compared to experimental $ R_{\mathrm{AA}} $ values for charm and light-flavor hadrons. The $ {\mathrm{B}^{+}} $ meson $ R_{\mathrm{AA}} $ values are compatible with those found for generic charged hadrons and $ \mathrm{D^0} $ mesons in the $ p_{\mathrm{T}} $ range from 10 to 30 GeV/$c$, while the $ R_{\mathrm{AA}} $ values from 7 to 10 GeV/$c$ are consistent with expectations based on the quark mass dependence of parton energy loss. |
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