Study of the $D_{sJ}^{*}(2317{)}^{+}$ and $D_{sJ}(2460{)}^{+}$ mesons in inclusive $c\overline{c}$ production near $\sqrt{s}=10.6\mathrm{GeV}$

A study of the $D_{sJ}^{*}(2317{)}^{+}$ and $D_{sJ}(2460{)}^{+}$ mesons in inclusive $c\overline{c}$ production is presented using $232{\mathrm{fb}}^{-1}$ of data collected by the BABAR experiment near $\sqrt{s}=10.6\mathrm{GeV}$. Final states consisting of a $D_s^{+}$ meson along with one or more ${\pi }^0$, ${\pi }^{\pm }$, or $\gamma$ particles are considered. Estimates of the mass and limits on the width are provided for both mesons and for the $D_{s1}(2536{)}^{+}$ meson. A search is also performed for neutral and doubly charged partners of the $D_{sJ}^{*}(2317{)}^{+}$ meson.

Figure 1

The $c\overline{s}$ meson spectrum, as predicted by Godfrey and Isgur [5] (solid lines) and Di Pierro and Eichten [8] (dashed lines) and as observed by experiment (points). The $DK$ and $D^{*}K$ mass thresholds are indicated by the horizontal lines spanning the width of the plot.

Figure 2

(a) The invariant mass spectrum of $D_s^{+}$ candidates before (top histogram) and after (bottom points) applying subresonant $\varphi {\pi }^{+}$ and ${\overline{K}}^{*}{K}^{+}$ selection. The light (dark) areas indicate the signal (sideband) regions. (b) The invariant $\gamma \gamma$ mass of ${\pi }^0$ candidates before (top histogram) and after (bottom points) applying the ${\pi }^0$ veto described in the text. The light histogram indicates those candidates that pass the ${\chi }^2$ requirement. The curve in (a) is the ${\chi }^2$ fit described in the text.

Figure 3

An illustration of the $D_s^{+}$ subresonant selection requirements. The light shaded area is the kinematic range for $D_s^{+}\to K^{+}{K}^{-}{\pi }^{+}$ decay. The vertical line with an arrow represents the selection requirement used to remove $D^0\to K^{+}{K}^{-}$ decay. The four dark regions indicate those portions of the $D_s^{+}$ phase space used for final candidate selection, corresponding to $D_s^{+}\to \varphi {\pi }^{+}$ and $D_s^{+}\to {\overline{K}}^{*}{K}^{+}$ decay.

Figure 4

The sideband subtracted $p^{*}$ spectrum for $D_s^{+}$ candidates after all selection requirements are met.

Figure 5

The $D_s^{+}$-sideband subtracted $p^{*}$ spectrum for associated (a) ${\pi }^{\pm }$, (b) ${\pi }^0$, and (c) $\gamma$, after the selection requirements described in the text are fulfilled.

Figure 6

The $D_s^{+}$-sideband subtracted $K^{+}{K}^{-}$ invariant mass spectrum near the $\varphi$ mass for the $D_s^{+}$ sample obtained before applying the $\varphi {\pi }^{+}$ and ${\overline{K}}^{*}{K}^{+}$ selection requirements. The curve is the fit described in the text. The dashed line is the portion of the fit attributed to contributions from other than $\varphi$ decay. The vertical lines indicate the $\varphi$ mass selection window.

Figure 7

The invariant mass distribution for (solid points) $D_s^{+}{\pi }^0$ candidates and (open points) the equivalent using the $D_s^{+}$ sidebands. The curve represents the likelihood fit described in the text. Included in this fit is (light shade) a contribution from combinatorial background and (dark shade) the reflection from $D_{sJ}(2460{)}^{+}\to D_s^{*}(2112{)}^{+}{\pi }^0$ decay. The inset highlights the details near the $D_{sJ}^{*}(2317{)}^{+}$ mass.

Figure 8

The reconstructed $D_s^{+}{\pi }^0$ invariant mass spectrum from (a) $D_{sJ}^{*}(2317{)}^{+}$ and (b) $D_{sJ}(2460{)}^{+}$ MC samples. The fit function of Eq. (9) is overlaid. (c) The projection of $D_s^{+}{\pi }^0$ mass for subresonant $D_{sJ}(2460{)}^{+}$ decay through the $D_s^{*}(2112{)}^{+}$ meson is restricted to a narrow range centered around $2313.4\mathrm{MeV}/c^2$. (d) The reconstructed $D_s^{+}{\pi }^0$ invariant mass spectrum for the $D_{sJ}(2460{)}^{+}$ reflection from MC simulation. The solid curve is the fit function. The dashed curve is the same fit function with the Gaussian smearing removed.

Figure 9

Fit results near the $D_{sJ}^{*}(2317{)}^{+}$ peak for the $D_s^{+}{\pi }^0$ sample divided into combinations (a) with and (b) without a $D_s^{+}$ consistent with $D_s^{*}(2112{)}^{+}\to D_s^{+}\gamma$ decay. The curves and shaded regions, as described in Fig. 7, represent the result of a likelihood fit.

Figure 10

Corrected $D_{sJ}^{*}(2317{)}^{+}\to D_s^{+}{\pi }^0$ yield as a function of $p^{*}$.

Figure 11

Likelihood fit results for a $D_{sJ}^{*}(2317{)}^{+}$ meson of instrinsic width (dashed line) $\Gamma =0$ and (solid line) $\Gamma =3.8\mathrm{MeV}$. Shown in comparison is the mass distribution (solid points) for the $D_s^{+}{\pi }^0$ candidates.

Figure 12

The invariant $D_s^{+}\gamma$ mass distribution using $\gamma$ candidates with loose (150 MeV) and final (500 MeV) energy requirements. The insert focuses on the region of the $D_s^{*}(2112{)}^{+}$ meson using the loose energy requirement. The curve represents the fit described in the text.

Figure 13

The reconstructed $D_s^{+}\gamma$ invariant mass spectrum from MC samples for (a) $D_{sJ}^{*}(2317{)}^{+}$ and (b) $D_{sJ}(2460{)}^{+}$ decay and (c) $D_{sJ}^{*}(2317{)}^{+}\to D_s^{+}{\pi }^0$ and (d) $D_{sJ}(2460{)}^{+}\to D_s^{*}(2112{)}^{+}{\pi }^0$ reflections. The curves are the fit functions described in the text. The $D_{sJ}^{*}(2317{)}^{+}$ signal shapes from (a) and (b) are shown for comparison in (c) and (d) in gray.

Figure 14

An example likelihood fit to the $D_s^{+}\gamma$ invariant mass distribution. The solid points in the top plot are the mass distribution. The open points are the $D_s^{+}$ sidebands, scaled appropriately. The bottom plot shows the same data after subtracting the background curve from the fit. Various contributions to the likelihood fit are also shown.

Figure 15

Corrected $D_{sJ}(2460{)}^{+}\to D_s^{+}\gamma$ yield as a function of $p^{*}$.

Figure 16

(a) The sample of $D_s^{+}{\pi }^0\gamma$ candidates shown in solid points. The fit described in the text is overlaid. The open points are those candidates which fall in a restricted $D_s^{+}\gamma$ mass range. (b) The reconstructed $D_s^{+}{\pi }^0\gamma$ invariant mass spectrum from a $D_{sJ}(2460{)}^{+}\to D_s^{*}(2112{)}^{+}{\pi }^0$ MC sample. The fit function of Eq. (15) is overlaid.

Figure 17

The light gray region indicates the range of $D_s^{+}{\pi }^0$ and $D_s^{+}\gamma$ mass that is kinematically allowed in the decay of an object of mass $2458.0\mathrm{MeV}/c^2$ to $D_s^{+}{\pi }^0\gamma$. The lines mark the kinematic space associated with decays which proceed through an intermediate $D_s^{*}(2112{)}^{+}$ or $D_{sJ}^{*}(2317{)}^{+}$ meson.

Figure 18

The combined $D_s^{+}{\pi }^0\gamma$ invariant mass distribution (solid points) as obtained from MC samples for the combination of the $D_{sJ}^{*}(2317{)}^{+}$ reflection and $D_{sJ}(2460{)}^{+}\to D_s^{*}(2112{)}^{+}{\pi }^0$ decays in which the incorrect $\gamma$ is chosen. The $D_{sJ}(2460{)}^{+}$ contribution alone is shown in open points. Shown are the (a) upper, (b) signal, and (c) lower $D_s^{+}\gamma$ mass selection windows. The curves are fits to Gaussian distributions.

Figure 19

The invariant mass distribution of $D_s^{+}{\pi }^0\gamma$ candidates in the (a) upper, (b) signal, and (c) lower $D_s^{+}\gamma$ mass selection windows for (solid points) the $D_s^{+}$ signal and (open points) $D_s^{+}$ sideband samples. The curves represent the fits described in the text. The dark gray (light gray) region corresponds to the predicted contribution from the $D_{sJ}^{*}(2317{)}^{+}$ [$D_s^{*}(2112{)}^{+}$] reflection.

Figure 20

Corrected $D_{sJ}(2460{)}^{+}\to D_s^{+}{\pi }^0\gamma$ yield as a function of $p^{*}$.

Figure 21

The reconstructed (a) $D_s^{+}{\pi }^0$ and (b) $D_s^{+}\gamma$ invariant mass distributions for the two possible $D_{sJ}(2460{)}^{+}$ subresonant decay modes. The distributions from a $D_{sJ}(2460{)}^{+}\to D_s^{*}(2112{)}^{+}{\pi }^0$ MC sample are shown in points. The curves are the fits described in the text. The shaded regions are the shapes assumed for $D_{sJ}(2460{)}^{+}\to D_{sJ}^{*}(2317{)}^{+}\gamma$ decay.

Figure 22

The $D_s^{+}\gamma$ versus $D_s^{+}{\pi }^0$ mass distributions for the $D_s^{+}{\pi }^0\gamma$ candidates. The horizontal (vertical) band corresponds to background from $D_s^{*}(2112{)}^{+}\to D_s^{+}\gamma$ [$D_{sJ}^{*}(2317{)}^{+}\to D_s^{+}{\pi }^0$] decay. The excess of candidates near the crossing of these two bands is the $D_{sJ}(2460{)}^{+}$ signal. The curve indicates the region of phase space in which the $D_{sJ}(2460{)}^{+}$ decay is kinematically restricted. The grid identifies the subsample of candidates used in the likelihood fit shown in Fig. 23.

Figure 23

The $D_s^{+}{\pi }^0$ and $D_s^{+}\gamma$ invariant mass distributions for $D_s^{+}{\pi }^0\gamma$ candidates that fall within the indicated portions of the grid shown in Fig. 22. The histograms represent the results of a likelihood fit. The light gray region corresponds to combinatorial background. The medium gray (dark gray) region represents the fitted fraction of $D_{sJ}(2460{)}^{+}\to D_s^{*}(2112{)}^{+}{\pi }^0$ [$D_{sJ}(2460{)}^{+}\to D_{sJ}^{*}(2317{)}^{+}\gamma$].

Figure 24

Efficiency-corrected yields in five $\cos {\vartheta }_h$ bins for the decay $D_{sJ}(2460{)}^{+}\to D_s^{*}(2112{)}^{+}{\pi }^0$. The solid histogram is the result of a fit to the function described in the text. The dashed histogram is a similar fit with the $a_2$ parameter fixed to zero.

Figure 25

The Dalitz phase space available to (a) the $D_{sJ}^{*}(2317{)}^{+}$ and (b) the $D_{sJ}(2460{)}^{+}$ mesons in the $D_s^{+}{\pi }^0{\pi }^0$ final state. The dashed horizontal line corresponds to the $D_s^{*}(2112{)}^{+}$ mass. The dark shaded regions are those parts of the phase space removed by the requirement $m(D_s^{+}{\pi }^0)>2117.4\mathrm{MeV}/c^2$. The dotted curve in (b) is the $D_{sJ}^{*}(2317{)}^{+}$ phase space drawn for comparison.

Figure 26

The invariant mass distribution for (solid points) $D_s^{+}{\pi }^0{\pi }^0$ candidates and (open points) the equivalent using the $D_s^{+}$ sidebands. The curve represents the likelihood fit described in the text. The inset focuses on the low mass region. The dotted line in the inset indicates the $D_{sJ}^{*}(2317{)}^{+}$ mass.

Figure 27

The Dalitz phase space corresponding to the $D_s^{+}\gamma \gamma$ samples for (a) $D_{sJ}^{*}(2317{)}^{+}$ and (b) $D_{sJ}(2460{)}^{+}$ mesons. The dark shaded and light shaded regions correspond to the $D_s^{*}(2112{)}^{+}$ and nonresonant samples, respectively. The horizontal (vertical) dashed line indicates the $D_s^{*}(2112{)}^{+}$ (${\pi }^0$) mass.

Figure 28

The $D_s^{+}\gamma \gamma$ invariant mass distribution (solid points) for candidates in (a) the $D_s^{*}(2112{)}^{+}$ sample, (b) the nonresonant sample, and (c) either sample. The open points are the corresponding distributions for the $D_s^{+}$ sideband. The vertical dashed lines indicate the $D_{sJ}^{*}(2317{)}^{+}$ and $D_{sJ}(2460{)}^{+}$ meson masses.

Figure 29

(a) Shown on top as a function of $D_s^{+}\gamma$ and $D_s^{+}\gamma \gamma$ masses are the bands corresponding to the $D_s^{*}(2112{)}^{+}$ sample requirement [$D_s^{+}\gamma$ mass within $15\mathrm{MeV}/c^2$ of the $D_s^{*}(2112{)}^{+}$ mass] and the effect of this requirement on the other $\gamma$ candidate. The overlap of the two bands produces the shape shown below. (b) The $D_s^{+}\gamma \gamma$ mass distribution of the $D_{sJ}(2460{)}^{+}\to D_s^{*}(2112{)}^{+}{\pi }^0$ reflection from a MC sample. The curve is the fit described in the text.

Figure 30

The $D_s^{+}\gamma \gamma$ invariant mass distribution for the $D_s^{*}(2112{)}^{+}$ sample is shown on top. The thick curve is the result of the likelihood fit. The mass distribution after subtracting the portion assigned by the fit to combinatorial background is shown on bottom.

Figure 31

The $D_s^{+}\gamma \gamma$ invariant mass distribution for the nonresonant sample is shown on top. The thick curve is the result of the likelihood fit. The mass distribution after subtracting the portion assigned by the fit to combinatorial background is shown on bottom.

Figure 32

The invariant mass distributions (solids points) of (a) $D_s^{+}{\pi }^{-}$ and (b) $D_s^{+}{\pi }^{+}$ candidates and (open points) the equivalent for the $D_s^{+}$ sidebands. The shaded regions indicate the range of assumed $D_{sJ}^{*}(2317{)}^{++}$ and $D_{sJ}^{*}(2317{)}^0$ masses. The vertical dotted line marks the $D_{sJ}(2460{)}^{+}$ mass. The curves are the fits described in the text that produce the largest yield within the shaded region.

Figure 33

The invariant mass distribution of (solid points) $D_s^{+}{\pi }^{+}{\pi }^{-}$ candidates and (open points) the equivalent using the $D_s^{+}$ sidebands. The curve is the fit described in the text. The inset focuses on the low mass region. The dotted line in the inset indicates the $D_{sJ}^{*}(2317{)}^{+}$ mass.

Figure 34

The invariant mass distributions of MC samples of (a) $D_{sJ}(2460{)}^{+}$ and (b) $D_{s1}(2536{)}^{+}$ decay to $D_s^{+}{\pi }^{+}{\pi }^{-}$. The curves are the functions described in the text.