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| CMS-PAS-BPH-22-007 | ||
| Measurement of double-differential and total charm-production cross sections at 7 TeV | ||
| CMS Collaboration | ||
| 23 July 2024 | ||
| Abstract: The production cross section of D$ ^{*\pm} $ mesons in proton-proton collisions is measured at a center-of-mass energy of 7 TeV with the CMS detector. Special low-$ p_T $ tracking and low-pileup data are used, corresponding to an integrated luminosity of 3.0 nb$^{-1}$. A double-differential cross-section measurement is performed covering D$ ^{*\pm} $ transverse momentum $ p_{\rm T} $ down to 1 GeV and a rapidity range of $ |y| < $ 2.5. The total charm-quark pair cross section, $ \sigma_{{\rm c\bar c},{\rm tot}}$(7 TeV) $ = $ 9.39 $ ^{+1.35}_{-1.49} $ mb is extracted from the D$ ^{*\pm} $-meson cross section. For this purpose, the results are combined with published measurements by the LHCb Collaboration covering rapidities larger than 2.5, and then extrapolated to the full kinematical phase space by means of a new data-driven procedure that includes a complete treatment of charm-fragmentation nonuniversality. This combination probes the largest phase space for charm production ever explored at LHC, resulting in the smallest extrapolation factor, which minimizes the impact of theoretical uncertainties. The resulting cross sections are compared to NLO+NLL and NNLO-QCD predictions and to the results from other experiments. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures & Tables | Summary | Additional Figures | References | CMS Publications |
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| Figures | |
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Figure 1:
Actual phase space in transverse momentum $ p_T $ and rapidity $ |y| $ for prompt-$ \mathrm{D}^{*} $ production cross sections covered by ALICE [8,9,10], LHCb [14], and CMS (this analysis) at 7 TeV. The measurements in the overlapping regions between CMS and ALICE, as well as CMS and LHCb, are compared in order to demonstrate consistency. The combination of the CMS and LHCb measurements covers most of the phase space and is used in the total charm cross-section determination. The measurement is extrapolated for the small remaining uncovered regions. |
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Figure 2:
$ \Delta M = M_{{\rm D}^{*+}} - M_{{\rm D}^0} $ distributions in data for the lower (higher) $ p_{\mathrm{T}} $ category on the left (right). Shown are the right-charge data (blue points) and the wrong-charge data (red histograms), normalized to the right-charge data in the gray shaded side band regions. Corresponding fits (solid lines) are also shown to guide the eye. The ``background only'' dashed line refers to the background-only part of the full right-charge fit. The mass region used for the final signal extraction is indicated by the pink band. |
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Figure 2-a:
$ \Delta M = M_{{\rm D}^{*+}} - M_{{\rm D}^0} $ distributions in data for the lower (higher) $ p_{\mathrm{T}} $ category on the left (right). Shown are the right-charge data (blue points) and the wrong-charge data (red histograms), normalized to the right-charge data in the gray shaded side band regions. Corresponding fits (solid lines) are also shown to guide the eye. The ``background only'' dashed line refers to the background-only part of the full right-charge fit. The mass region used for the final signal extraction is indicated by the pink band. |
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Figure 2-b:
$ \Delta M = M_{{\rm D}^{*+}} - M_{{\rm D}^0} $ distributions in data for the lower (higher) $ p_{\mathrm{T}} $ category on the left (right). Shown are the right-charge data (blue points) and the wrong-charge data (red histograms), normalized to the right-charge data in the gray shaded side band regions. Corresponding fits (solid lines) are also shown to guide the eye. The ``background only'' dashed line refers to the background-only part of the full right-charge fit. The mass region used for the final signal extraction is indicated by the pink band. |
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Figure 3:
The ratio of nonprompt to prompt $ \mathrm{D}^{*} $-meson cross sections. With the assigned uncertainty of 30%, the PYTHIA prediction after correction describes well the ratio of the nonprompt 5 TeV CMS measurement [25], converted to 7 TeV, to the prompt 7 TeV measurement (this work). The central FONLL prediction is only shown as a consistency check and not used. |
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Figure 4:
Double-differential prompt-$ \mathrm{D}^{*} $ cross section as a function of $ p_{\mathrm{T}} $ in $ |y| $ bins for data (points) and predictions (lines). The last bin in each panel is the overflow bin. Statistical (vertical bars) and systematic uncertainties (boxes) are shown separately. Lower vertical bars that would extend to log(zero) (long-dashed) have been truncated for clarity. The points from ALICE and LHCb have been slightly offset horizontally for clarity. The bottom panels show the ratios to the PYTHIA predictions in linear scale. |
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Figure 4-a:
Double-differential prompt-$ \mathrm{D}^{*} $ cross section as a function of $ p_{\mathrm{T}} $ in $ |y| $ bins for data (points) and predictions (lines). The last bin in each panel is the overflow bin. Statistical (vertical bars) and systematic uncertainties (boxes) are shown separately. Lower vertical bars that would extend to log(zero) (long-dashed) have been truncated for clarity. The points from ALICE and LHCb have been slightly offset horizontally for clarity. The bottom panels show the ratios to the PYTHIA predictions in linear scale. |
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Figure 4-b:
Double-differential prompt-$ \mathrm{D}^{*} $ cross section as a function of $ p_{\mathrm{T}} $ in $ |y| $ bins for data (points) and predictions (lines). The last bin in each panel is the overflow bin. Statistical (vertical bars) and systematic uncertainties (boxes) are shown separately. Lower vertical bars that would extend to log(zero) (long-dashed) have been truncated for clarity. The points from ALICE and LHCb have been slightly offset horizontally for clarity. The bottom panels show the ratios to the PYTHIA predictions in linear scale. |
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Figure 4-c:
Double-differential prompt-$ \mathrm{D}^{*} $ cross section as a function of $ p_{\mathrm{T}} $ in $ |y| $ bins for data (points) and predictions (lines). The last bin in each panel is the overflow bin. Statistical (vertical bars) and systematic uncertainties (boxes) are shown separately. Lower vertical bars that would extend to log(zero) (long-dashed) have been truncated for clarity. The points from ALICE and LHCb have been slightly offset horizontally for clarity. The bottom panels show the ratios to the PYTHIA predictions in linear scale. |
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Figure 4-d:
Double-differential prompt-$ \mathrm{D}^{*} $ cross section as a function of $ p_{\mathrm{T}} $ in $ |y| $ bins for data (points) and predictions (lines). The last bin in each panel is the overflow bin. Statistical (vertical bars) and systematic uncertainties (boxes) are shown separately. Lower vertical bars that would extend to log(zero) (long-dashed) have been truncated for clarity. The points from ALICE and LHCb have been slightly offset horizontally for clarity. The bottom panels show the ratios to the PYTHIA predictions in linear scale. |
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Figure 4-e:
Double-differential prompt-$ \mathrm{D}^{*} $ cross section as a function of $ p_{\mathrm{T}} $ in $ |y| $ bins for data (points) and predictions (lines). The last bin in each panel is the overflow bin. Statistical (vertical bars) and systematic uncertainties (boxes) are shown separately. Lower vertical bars that would extend to log(zero) (long-dashed) have been truncated for clarity. The points from ALICE and LHCb have been slightly offset horizontally for clarity. The bottom panels show the ratios to the PYTHIA predictions in linear scale. |
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Figure 5:
$ \mathrm{D}^{*+}+\mathrm{D}^{*-} $ cross sections as a function $ |y| $ in bins of $ p_{\mathrm{T}} $. The symbols for the data are the same as in Fig. 4. The red bands are the data driven FONLL (ddFONLL), which describe the data (black points/grey boxes) well in the full phase space. The total uncertainty in the band includes the PDF uncertanties [47], the uncertainty in $ \tilde f $, as well as the $ \chi^2 $ scan uncertainties in the QCD parameters. The LHCb data are the double-differential version of those in Table 6. |
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Figure 5-a:
$ \mathrm{D}^{*+}+\mathrm{D}^{*-} $ cross sections as a function $ |y| $ in bins of $ p_{\mathrm{T}} $. The symbols for the data are the same as in Fig. 4. The red bands are the data driven FONLL (ddFONLL), which describe the data (black points/grey boxes) well in the full phase space. The total uncertainty in the band includes the PDF uncertanties [47], the uncertainty in $ \tilde f $, as well as the $ \chi^2 $ scan uncertainties in the QCD parameters. The LHCb data are the double-differential version of those in Table 6. |
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Figure 5-b:
$ \mathrm{D}^{*+}+\mathrm{D}^{*-} $ cross sections as a function $ |y| $ in bins of $ p_{\mathrm{T}} $. The symbols for the data are the same as in Fig. 4. The red bands are the data driven FONLL (ddFONLL), which describe the data (black points/grey boxes) well in the full phase space. The total uncertainty in the band includes the PDF uncertanties [47], the uncertainty in $ \tilde f $, as well as the $ \chi^2 $ scan uncertainties in the QCD parameters. The LHCb data are the double-differential version of those in Table 6. |
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Figure 5-c:
$ \mathrm{D}^{*+}+\mathrm{D}^{*-} $ cross sections as a function $ |y| $ in bins of $ p_{\mathrm{T}} $. The symbols for the data are the same as in Fig. 4. The red bands are the data driven FONLL (ddFONLL), which describe the data (black points/grey boxes) well in the full phase space. The total uncertainty in the band includes the PDF uncertanties [47], the uncertainty in $ \tilde f $, as well as the $ \chi^2 $ scan uncertainties in the QCD parameters. The LHCb data are the double-differential version of those in Table 6. |
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Figure 5-d:
$ \mathrm{D}^{*+}+\mathrm{D}^{*-} $ cross sections as a function $ |y| $ in bins of $ p_{\mathrm{T}} $. The symbols for the data are the same as in Fig. 4. The red bands are the data driven FONLL (ddFONLL), which describe the data (black points/grey boxes) well in the full phase space. The total uncertainty in the band includes the PDF uncertanties [47], the uncertainty in $ \tilde f $, as well as the $ \chi^2 $ scan uncertainties in the QCD parameters. The LHCb data are the double-differential version of those in Table 6. |
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Figure 5-e:
$ \mathrm{D}^{*+}+\mathrm{D}^{*-} $ cross sections as a function $ |y| $ in bins of $ p_{\mathrm{T}} $. The symbols for the data are the same as in Fig. 4. The red bands are the data driven FONLL (ddFONLL), which describe the data (black points/grey boxes) well in the full phase space. The total uncertainty in the band includes the PDF uncertanties [47], the uncertainty in $ \tilde f $, as well as the $ \chi^2 $ scan uncertainties in the QCD parameters. The LHCb data are the double-differential version of those in Table 6. |
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Figure 5-f:
$ \mathrm{D}^{*+}+\mathrm{D}^{*-} $ cross sections as a function $ |y| $ in bins of $ p_{\mathrm{T}} $. The symbols for the data are the same as in Fig. 4. The red bands are the data driven FONLL (ddFONLL), which describe the data (black points/grey boxes) well in the full phase space. The total uncertainty in the band includes the PDF uncertanties [47], the uncertainty in $ \tilde f $, as well as the $ \chi^2 $ scan uncertainties in the QCD parameters. The LHCb data are the double-differential version of those in Table 6. |
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Figure 5-g:
$ \mathrm{D}^{*+}+\mathrm{D}^{*-} $ cross sections as a function $ |y| $ in bins of $ p_{\mathrm{T}} $. The symbols for the data are the same as in Fig. 4. The red bands are the data driven FONLL (ddFONLL), which describe the data (black points/grey boxes) well in the full phase space. The total uncertainty in the band includes the PDF uncertanties [47], the uncertainty in $ \tilde f $, as well as the $ \chi^2 $ scan uncertainties in the QCD parameters. The LHCb data are the double-differential version of those in Table 6. |
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Figure 5-h:
$ \mathrm{D}^{*+}+\mathrm{D}^{*-} $ cross sections as a function $ |y| $ in bins of $ p_{\mathrm{T}} $. The symbols for the data are the same as in Fig. 4. The red bands are the data driven FONLL (ddFONLL), which describe the data (black points/grey boxes) well in the full phase space. The total uncertainty in the band includes the PDF uncertanties [47], the uncertainty in $ \tilde f $, as well as the $ \chi^2 $ scan uncertainties in the QCD parameters. The LHCb data are the double-differential version of those in Table 6. |
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Figure 5-i:
$ \mathrm{D}^{*+}+\mathrm{D}^{*-} $ cross sections as a function $ |y| $ in bins of $ p_{\mathrm{T}} $. The symbols for the data are the same as in Fig. 4. The red bands are the data driven FONLL (ddFONLL), which describe the data (black points/grey boxes) well in the full phase space. The total uncertainty in the band includes the PDF uncertanties [47], the uncertainty in $ \tilde f $, as well as the $ \chi^2 $ scan uncertainties in the QCD parameters. The LHCb data are the double-differential version of those in Table 6. |
png pdf |
Figure 5-j:
$ \mathrm{D}^{*+}+\mathrm{D}^{*-} $ cross sections as a function $ |y| $ in bins of $ p_{\mathrm{T}} $. The symbols for the data are the same as in Fig. 4. The red bands are the data driven FONLL (ddFONLL), which describe the data (black points/grey boxes) well in the full phase space. The total uncertainty in the band includes the PDF uncertanties [47], the uncertainty in $ \tilde f $, as well as the $ \chi^2 $ scan uncertainties in the QCD parameters. The LHCb data are the double-differential version of those in Table 6. |
png pdf |
Figure 5-k:
$ \mathrm{D}^{*+}+\mathrm{D}^{*-} $ cross sections as a function $ |y| $ in bins of $ p_{\mathrm{T}} $. The symbols for the data are the same as in Fig. 4. The red bands are the data driven FONLL (ddFONLL), which describe the data (black points/grey boxes) well in the full phase space. The total uncertainty in the band includes the PDF uncertanties [47], the uncertainty in $ \tilde f $, as well as the $ \chi^2 $ scan uncertainties in the QCD parameters. The LHCb data are the double-differential version of those in Table 6. |
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Figure 6:
The measured total charm-quark pair cross section at 7 TeV (bands) is compared with NNLO-QCD theory for different PDF sets, as indicated in the legend (points with uncertainties, from scale variations at NNLO and PDFs, shown separately). The figure is adapted from Ref. [20] and the result from this work was added with its total uncertainty (red band). The violet band is the result obtained with extrapolation of LHCb [14] and ALICE [10] data based on fragmentation universality [20], which is superseded by the result of this work, with smaller extrapolation from CMS (this work) + LHCb [14] data and full nonuniversality treatment. |
| Tables | |
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Table 1:
$ \mathrm{D}^{*} $ preselection. |
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Table 2:
Additional $ \mathrm{D}^{*} $ candidate selection for each $ p_{\mathrm{T}} $ range category. |
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Table 3:
Number of extracted $ \mathrm{D}^{*} $-signal events at reconstruction level for each phase-space bin. The majority of the phase-space bins exhibit a significant signal yield, except for a few regions in the highest $ |y| $ or lowest $ p_{\mathrm{T}} $ bins, where the signal efficiency is decreasing while the background is rising, as expected. Only statistical uncertainties are reported here. Low-significance bins are kept, because phase-space coverage is crucial for the total cross-section extraction. The value in parentheses corresponds to the only bin in which the expected event yield essentially vanishes: that bin is then excluded from further processing. |
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Table 4:
Summary of systematic uncertainties. A single number refers to the same number applied to all bins. A range indicates typical values for well-measured bins. |
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Table 5:
The $ \mathrm{D}^{*+}+\mathrm{D}^{*-} $ cross sections measured in this work. The last column of each row shows the fiducial cross section in the kinematical ranges listed, integrated over $ p_{\mathrm{T}} $. |
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Table 6:
The $ \mathrm{D}^{*+}+\mathrm{D}^{*-} $ cross sections measured from LHCb [14]. The last column of each row shows the fiducial cross section in the kinematical ranges listed, integrated over $ p_{\mathrm{T}} $. The LHCb measurements, originally for positive rapidity only, have been symmetrized in $ y $. The row in parentheses is excluded from the LHCb total used here because it overlaps with the CMS measurements. |
| Summary |
|
Double-differential cross sections for the production of prompt D$ ^* $ mesons in pp collisions at 7 TeV were measured in the kinematical range of transverse momentum $ p_{\mathrm{T}} > $ 1 GeV and rapidity $ |y| < $ 2.5, from data with an effective luminosity of 3.0 mb$^{-1}$, taken in 2010. These data include events from zero-bias (beam crossing) and minimum-bias (minimal detector signal) triggers, as well as `next-to-minimum-bias' collisions obtained from pileup collisions in events from other triggers, thereby using pileup as a physics resource. Access to the lowest transverse momenta is facilitated by the special low-$ p_{\mathrm{T}} $ tracking applied to the 2010 data reconstruction. All the input data sets used are also available in the form of CMS Open Data. Good agreement with NLO+NLL (FONLL) QCD predictions still relying on charm-fragmentation universality is observed for the D$ ^* $ cross section, with the measurements preferring the upper edge of the theory band. This confirms the trend also found in previous measurements in different regions of phase space, e.g., the CMS single differential measurements at 13 and 5 TeV. The charm-nonuniversality effects for $ \mathrm{D}^{*} $ mesons (in contrast to charm baryons) can thus be concluded to be smaller than the very large NLO-QCD scale uncertainties for perturbative higher-order QCD corrections. The measured double-differential cross sections are in agreement and competitive with the ones obtained by ALICE in the rapidity range $ |y| < $ 0.5, and by LHCb in the rapidity range 2 $ < |y| < $ 2.5. The region 0.5 $ < |y| < $ 2.0 is covered double-differentially for the first time, and was never measured at all at 7 TeV for $ p_{\mathrm{T}} < $ 3.5 GeV. From CMS measurements only, the integrated fiducial cross section for $ {\mathrm{D}^{\ast}(2010)^{\pm}} $ production with $ p_{\mathrm{T}} > $ 1 GeV and $ |y| < $ 2.5, excluding the region $ p_{\mathrm{T}} < $ 2 GeV and $ |y| > $ 2, was determined to be $ \sigma_{\text{CMS}} = $ 1.28 $ \pm $ 0.22 mb. The almost full phase-space coverage for charm production of this measurement, when taken in conjunction with the published measurements by LHCb, allows an extrapolation to the total cross section for charm-pair production at 7 TeV using a data-constrained effective theory, with relatively small theoretical extrapolation uncertainty. This is important, e.g., for the comparison to available NNLO-QCD predictions, which do not depend on fragmentation for this quantity. The related extrapolation factor of only 1.4 is the smallest ever achieved for a total charm-pair cross-section measurement at the LHC. Following Ref. [21] this is done accounting for the latest experimental results on charm-fragmentation nonuniversality, including full coverage of the related uncertainties. It is the first such result at 7 TeV, therefore superseding all previous 7 TeV total charm-pair cross-section determinations. In particular, the data-constrained effective theory (ddFONLL) used for the extrapolation is also able to successfully describe charm-baryon production (as measured elsewhere) with the same parameters, within uncertainties. The cross section obtained, |
| Additional Figures | |
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Additional Figure 1:
Double-differential prompt-$ \mathrm{D}^{*} $ cross section as a function of $ p_{\mathrm{T}} $ in $ |y| $ bins. The last bin is the overflow bin. m refers to the power (offset) indicated on the vertical axis label. Vertical bars indicate statistical and systematic uncertainties added in quadrature. Lower vertical bars that would extend to log(zero) (short-dashed) have been truncated for clarity. The points from ALICE and LHCb have been slightly offset horizontally for clarity. |
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