# Precision measurement of $D$ meson mass differences

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## Abstract

Using three- and four-body decays of $D$ mesons produced in semileptonic $b$-hadron decays, precision measurements of $D$ meson mass differences are made together with a measurement of the $D^{0}$ mass. The measurements are based on a dataset corresponding to an integrated luminosity of $1.0 fb^{-1}$ collected in $pp$ collisions at 7 TeV. Using the decay $D^0 \rightarrow K^{+} K^{-} K^{-} \pi^{+}$, the $D^0$ mass is measured to be $M(D^0) &=& 1864.75 \pm 0.15 ({\rm stat}) \pm 0.11 ({\rm syst}) \textrm{MeV/c^2}$. The mass differences $M(D^{+}) - M(D^{0}) = 4.76 \pm 0.12 ({\rm stat}) \pm 0.07 ({\rm syst}) \textrm{MeV/c^2}$ and $M(D^{+}_s) - M(D^{+}) = 98.68 \pm 0.03 ({\rm stat}) \pm 0.04 ({\rm syst}) \textrm{MeV/c^2}$ are measured using the $D^0 \rightarrow K^{+} K^{-} \pi^{+} \pi^{-}$ and $D^{+}_{(s)} \rightarrow K^{+}K^{-} \pi^{+}$ modes.

## Figures and captions

 Invariant mass distributions for the (a) $K^{+} K^{-} \pi^{+} \pi^{-}$ and (b) $K^{+} K^{-} K^{-} \pi^{+}$ final states. In each case the result of the fit described in the text is superimposed (solid line) together with the background component (dotted line). The pull, i.e. the difference between the fitted and measured value divided by the uncertainty on the measured value, is shown below each plot. pretty[..].pdf [13 KiB] HiDef png [230 KiB] Thumbnail [198 KiB] *.C file pretty[..].pdf [13 KiB] HiDef png [231 KiB] Thumbnail [199 KiB] *.C file Invariant mass distribution for the $K^{+} K^{-} \pi^{+}$ final state. The result of the fit described in the text is superimposed (solid line) together with the background component (dotted line). The pull, i.e. the difference between the fitted value and the measured value divided by the uncertainty, is shown below the plot. pretty[..].pdf [22 KiB] HiDef png [238 KiB] Thumbnail [204 KiB] *.C file Measured $D^0$ mass versus $f$ as defined in Eq. 2. The (yellow) shaded area corresponds to a systematic uncertainty on the momentum scale of $0.03 \%$ centred on the result for the $D^0 \rightarrow K^{+} K^{-} K^{-} \pi^{+}$ mode (horizontal dashed line). Only the $D^0 \rightarrow K^{+} K^{-} K^{-} \pi^{+}$ mode, where the systematic uncertainty is lowest, is used to determine the $D^0$ mass. dmasssyst.pdf [4 KiB] HiDef png [125 KiB] Thumbnail [101 KiB] *.C file Animated gif made out of all figures. PAPER-2013-011.gif Thumbnail

## Tables and captions

 Signal yields, mass values, resolution scale factors and binned $\chi^2$/ndf (using 100 bins) obtained from the fits shown in Fig. 1 and Fig. 2 together with the values corrected for the effect of QED radiative corrections as described in the text. Table_1.pdf [54 KiB] HiDef png [58 KiB] Thumbnail [25 KiB] tex code Systematic uncertainties (in ${\mathrm{ Me V /}c^2}$ ) on the mass measurements and on their differences. Table_2.pdf [51 KiB] HiDef png [57 KiB] Thumbnail [26 KiB] tex code LHCb measurements, compared to the best previous measurements and to the results of a global fit to available open charm mass data. The quoted uncertainties are the quadratic sums of the statistical and systematic contributions. All values are in ${\mathrm{ Me V /}c^2}$ . Table_3.pdf [46 KiB] HiDef png [47 KiB] Thumbnail [23 KiB] tex code

## Supplementary Material [file]

 This ZIP file contains supplemetary material for the publication LHCb-PAPER-2013-013. The files are: Fig1.* D0 mass comparision Fig2.* D+ - D0 mass difference comparision Fig3.* Ds+ - D+ mass difference comparision Supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps : The figures in variuous formats Fig1.pdf [3 KiB] HiDef png [143 KiB] Thumbnail [125 KiB] *C file Fig3.pdf [4 KiB] HiDef png [145 KiB] Thumbnail [138 KiB] *C file supple[..].pdf [81 KiB] HiDef png [247 KiB] Thumbnail [144 KiB] *C file

Created on 20 February 2021.