Measurement of mass and width of the excited charmed meson states $D_1^0$ and $D_2^{*0}$ at CDF

We report on precision measurements of the masses and widths of the narrow, orbitally excited states $D_1^0$ and $D_2^{*0}$ using the CDF II detector at the Fermilab Tevatron. Both states (collectively called $D^{**}$) are reconstructed in the decay channel $D^{**}\to D^{*+}{\pi }^{-}$. The $D_2^{*0}$ is also reconstructed in the $D^{**}\to D^{+}{\pi }^{-}$ channel. Using a data set with an integrated luminosity of $210{\mathrm{pb}}^{-1}$, the measured masses and widths for the $D_1^0$ are $2421.7\pm 0.7\pm 0.6\mathrm{MeV}/c^2$ and $20.0\pm 1.7\pm 1.3\mathrm{MeV}/c^2$ respectively, while for the $D_2^{*0}$ they are $2463.3\pm 0.6\pm 0.8\mathrm{MeV}/c^2$ and $49.2\pm 2.3\pm 1.2\mathrm{MeV}/c^2$. These values are currently the single best measurements available.

Figure 1

The mass ordering of the $L=0$ and $L=1$ $D$-meson system. The arrows show the hyperfine splitting of the $P$-wave $j_q=1/2$ and $j_q=3/2$ states. Properties of the broad $P$-wave $j_q=1/2$ states are not well established.

Figure 2

(a) The $J/\psi$ mass as a function of $p_T$, before (dashed) and after (solid) tracking calibration. The slope is reduced from $0.50\pm 0.03$ to $0.006\pm 0.010\mathrm{MeV}/c^2$ per $\mathrm{GeV}/c$. (b) The $D^0$ mass as a function of $p_T$, after calibration. The dashed lines indicate the world average $1\sigma$ error band of $\sim 1\mathrm{MeV}/c^2$.

Figure 3

Invariant mass difference between $D^{*}\pi$ system and the $D^{*}$. The points represent the data, and lines represent the projection of the fit results for the individual components described in the text.

Figure 4

Invariant mass difference between the $D^{+}{\pi }^{-}$ system and the $D^{+}$, with the same definitions as Fig. 3.

Figure 5

$D_1^0$ (solid) and $D_2^{*0}$ (open) mass comparison with theoretical expectations (triangles) and previous measurements and current world average (circles). Errors for theory predictions are not readily available.