Open charm spectroscopy at LHCb

Mark Whitehead111Work supported by the European Research Council.

Department of Physics
University of Warwick, Coventry, CV4 7AL, UK

> Recent charm spectroscopy results from Dalitz plot analyses of $B$ decays to
> open charm final states at LHCb are presented. The decay modes used are
> $B^{+}\to D^{-}K^{+}\pi^{+}$, $B^{0}\to\overline{D}{}^{0}\pi^{+}\pi^{-}$ and
> $B^{0}\to\overline{D}{}^{0}K^{+}\pi^{-}$.

> PRESENTED AT
>
>
>
>
> The 7th International Workshop on Charm Physics (CHARM 2015)
> Detroit, MI, 18-22 May, 2015

##  1 Introduction

The family of charm mesons are predicted by heavy quark effective theory [1]
and lattice QCD [2]. The 1P states have been well measured by the
$B$-factories and LHCb [3, 4, 5, 6]. Evidence for higher mass $D(2600)$ and
$D(2760)$ states has been seen [5, 6]. Only natural spin-parity resonances
($J^{P}=$ $0^{+}$, $1^{-}$, $2^{+}$,…) contribute in $B\to D_{(s)}hh^{\prime}$
decays where $h$ and $h^{\prime}$ are kaons and pions. In 2014 LHCb published
results from a Dalitz plot analysis of
$B^{0}_{s}\to\overline{D}{}^{0}K^{-}\pi^{+}$ decays, which included the first
observation of the $D_{s1}(2860)^{-}$ and $D_{s3}(2860)^{-}$ mesons [7, 8].
These states are thought to be members of the $D_{s}$ 1D family [9, 10]. It is
therefore interesting to explore $D$ meson spectroscopy to find and identify
new states to compare their properties with the theory predictions. Three
analyses are presented, using $B^{+}\to D^{-}K^{+}\pi^{+}$ [11],
$B^{0}\to\overline{D}{}^{0}\pi^{+}\pi^{-}$ [12] and
$B^{0}\to\overline{D}{}^{0}K^{+}\pi^{-}$ decays [13].

##  2 Dalitz plot analysis of $B^{+}\to D^{-}K^{+}\pi^{+}$ decays

The first observation of the decay $B^{+}\to D^{-}K^{+}\pi^{+}$, with
$D^{-}\to K^{+}\pi^{-}\pi^{-}$, is made using the topologically similar decay
$B^{+}\to D^{-}\pi^{+}\pi^{+}$ as a normalisation channel [11]. Event
selection is based on a neural network used to reduce combinatorial
background. Candidates in the signal and normalisation channels are shown in
Fig. 1, with fits used to extract the signal and normalisation channel yields
overlaid. Accounting for the selection efficiencies gives the branching
fraction ratio

$\frac{\mathcal{B}(B^{+}\to D^{-}K^{+}\pi^{+})}{\mathcal{B}(B^{+}\to
D^{-}\pi^{+}\pi^{+})}=0.0720\pm 0.0019\pm 0.0021\,,$

where the uncertainties are statistical and systematic, respectively. Using
the known value of $\mathcal{B}(B^{+}\to D^{-}\pi^{+}\pi^{+})=(1.01\pm
0.05)\times 10^{-3}$ [14] gives

$\mathcal{B}(B^{+}\to D^{-}K^{+}\pi^{+})=(7.31\pm 0.19\pm 0.22\pm 0.39)\times
10^{-5}\,,$

where the third uncertainty is from $\mathcal{B}(B^{+}\to
D^{-}\pi^{+}\pi^{+})$.

Figure 1: Fits to the $B$ candidate invariant mass distribution for (left)
$B^{+}\to D^{-}\pi^{+}\pi^{+}$ and (right) $B^{+}\to D^{-}K^{+}\pi^{+}$
candidates. Components are described in the legend.

The Dalitz plot analysis is performed on candidates in the $B$ mass window
$5239.4$–$5317.1$ MeV (natural units are used throughout), with about $2000$
signal candidates and a purity of approximately $93\,\%$. In $B^{+}\to
D^{-}K^{+}\pi^{+}$ decays, resonances are only expected to appear in
$m(D\pi)$, allowing angular moments from the Legendre polynomials to be used
to guide the amplitude model. The moments study showed no evidence of
structures above spin 2. The components included in the amplitude model are
shown in Table 1.

Resonance | Spin | DP axis | Model | Parameters
---|---|---|---|---
$D^{*}_{0}(2400)^{0}$ | 0 | $m^{2}(D\pi)$ | RBW |  $m=2318\pm 29{\rm MeV}$, $\Gamma=267\pm 40{\rm MeV}$
$D^{*}_{2}(2460)^{0}$ | 2 | $m^{2}(D\pi)$ | RBW | Determined from data
$D^{*}_{J}(2760)^{0}$ | 1 | $m^{2}(D\pi)$ | RBW | Determined from data
Nonresonant | 0 | $m^{2}(D\pi)$ | EFF | Determined from data
Nonresonant | 1 | $m^{2}(D\pi)$ | EFF | Determined from data
$D^{*}_{v}(2007)^{0}$ | 1 | $m^{2}(D\pi)$ | RBW |  $m=2006.98\pm 0.15{\rm MeV}$, $\Gamma=2.1{\rm MeV}$
$B^{*0}_{v}$ | 1 | $m^{2}(DK)$ | RBW |  $m=5325.2\pm 0.4{\rm MeV}$, $\Gamma=0.0{\rm MeV}$
Table 1: Components of the $B^{+}\to D^{-}K^{+}\pi^{+}$ amplitude fit model.
RBW and EFF are the relativistic Breit-Wigner function and exponential form
factor, respectively. Terms with subscript $v$ are virtual components, where
the resonant pole mass is outside of the Dalitz plot boundary.

The amplitude fit is performed with the Laura++ package [15] using the isobar
formalism [16, 17, 18], with histograms to describe backgrounds and signal
efficiency. For the full fit results see Ref. [11]. Figure 2 shows the fit
projection in $m(D\pi)$. Significant contributions are seen from the
$D^{*}_{0}(2400)^{0}$, $D^{*}_{2}(2460)^{0}$ and $D^{*}_{J}(2760)^{0}$ states,
where the spin of the latter is determined to be 1 for the first time. Other
spin hypotheses are rejected with high significance ($>6\sigma$). The mass and
width for the $D^{*}_{1}(2760)^{0}$ and $D^{*}_{2}(2460)^{0}$ resonances are
found to be

$\displaystyle m(D^{*}_{2}(2460)^{0})$ $\displaystyle=$
$\displaystyle(2464.0\pm 1.4\pm 0.5\pm 0.2)\,{\rm MeV}\,,$
$\displaystyle\Gamma(D^{*}_{2}(2460)^{0})$ $\displaystyle=$
$\displaystyle\phantom{24}(43.8\pm 2.9\pm 1.7\pm 0.6)\,{\rm MeV}\,,$
$\displaystyle m(D^{*}_{1}(2760)^{0})$ $\displaystyle=$
$\displaystyle\phantom{.0}(2781\pm\phantom{.}18\pm\phantom{.}11\pm\phantom{.0}6)\,{\rm
MeV}\,,$ $\displaystyle\Gamma(D^{*}_{1}(2760)^{0})$ $\displaystyle=$
$\displaystyle\phantom{.02}(177\pm\phantom{.}32\pm\phantom{.}20\pm\phantom{.0}7)\,{\rm
MeV}\,,$

where the uncertainties are statistical, experimental systematic and model
dependent systematic, respectively.

Figure 2: Projection of the amplitude fit in $m(D\pi)$ for $B^{+}\to
D^{-}K^{+}\pi^{+}$ candidates. Components are as described in the legend.

##  3 Dalitz plot analysis of $B^{0}\to\overline{D}{}^{0}\pi^{+}\pi^{-}$
decays

The amplitude analysis of the $B^{0}\to\overline{D}{}^{0}\pi^{+}\pi^{-}$ final
state is performed using the $\overline{D}{}^{0}\to K^{+}\pi^{-}$ decay [12].
With larger data samples this channel can be used to measure $\cos(2\beta)$
and $\sin(2\beta)$ [19, 20], where $\beta$ is an angle of the unitarity
triangle. Resonant structures are expected in both $m(D\pi)$ and $m(\pi\pi)$.
Combinatorial background is removed using a Fisher discriminant multivariate
selection. Figure 3 shows the $B$ candidate invariant mass distribution of
selected candidates. The signal window used in the amplitude analysis is
$5250$–$5310$ MeV. It contains about $10000$ signal candidates with a signal
purity of around $98\,\%$.

Figure 3: Fit to the $B$ candidate invariant mass distribution for
$B^{0}\to\overline{D}{}^{0}\pi^{+}\pi^{-}$ decays. The data are black points
and the fit and backgrounds are shown in red and green, respectively.

Two amplitude fits are performed, using the isobar model and a K-matrix
approach [21, 22] for the $\pi\pi$ S-wave contribution. The resonances
included in the models are shown in Table 2. Projections of the isobar model
fit are shown in Fig 4, see Ref. [12] for the K-matrix results. The charm
resonances $D^{*}_{0}(2400)^{-}$, $D^{*}_{2}(2460)^{-}$ and
$D^{*}_{J}(2760)^{-}$ are found to be significant and the
$D^{*}_{J}(2760)^{-}$ state is determined, with high significance, to be spin
3 for the first time. It is interesting to note that in the $B^{+}\to
D^{-}K^{+}\pi^{+}$ analysis the $D^{*}_{J}(2760)^{0}$ was found to be spin 1.
This suggests that there could be two overlapping states, as was seen in the
$D_{s}$ meson family in $B^{0}_{s}\to\overline{D}{}^{0}K^{-}\pi^{+}$ decays
[7, 8]. The masses and widths of the charm resonances from the isobar model
fit are

$\displaystyle m(D^{*}_{0}(2400)^{-})$ $\displaystyle=$
$\displaystyle\phantom{.6}(2349\pm\phantom{.6}6\pm\phantom{.0}1\pm\phantom{.0}4)\,{\rm
MeV}\,,$ $\displaystyle\Gamma(D^{*}_{0}(2400)^{-})$ $\displaystyle=$
$\displaystyle\phantom{2.6}(217\pm\phantom{.}13\pm\phantom{.0}5\pm\phantom{.}12)\,{\rm
MeV}\,,$ $\displaystyle m(D^{*}_{2}(2460)^{-})$ $\displaystyle=$
$\displaystyle(2468.6\pm 0.6\pm 0.0\pm 0.3)\,{\rm MeV}\,,$
$\displaystyle\Gamma(D^{*}_{2}(2460)^{-})$ $\displaystyle=$
$\displaystyle\phantom{24}(47.3\pm 1.5\pm 0.3\pm 0.6)\,{\rm MeV}\,,$
$\displaystyle m(D^{*}_{3}(2760)^{-})$ $\displaystyle=$
$\displaystyle\phantom{.0}(2798\pm\phantom{.6}7\pm\phantom{.0}1\pm\phantom{.0}7)\,{\rm
MeV}\,,$ $\displaystyle\Gamma(D^{*}_{3}(2760)^{-})$ $\displaystyle=$
$\displaystyle\phantom{.02}(105\pm\phantom{.}18\pm\phantom{.0}6\pm\phantom{.}23)\,{\rm
MeV}\,,$

where the uncertainties are statistical, experimental systematic and model
dependent systematic, respectively. Good agreement is seen between the isobar
model and K-matrix fit results.

Resonance | Spin | Model |  $m_{r}$ (MeV) |  $\Gamma_{0}$ (MeV)
---|---|---|---|---
$\overline{D}{}^{0}\pi^{-}$ P-wave | 1 |  [12] | Floated
$D_{0}^{*}(2400)^{-}$ | 0 | RBW | Floated
$D_{2}^{*}(2460)^{-}$ | 2 | RBW | Floated
$D_{J}^{*}(2760)^{-}$ | 3 | RBW | Floated
$\rho(770)$ | 1 | GS | $775.02\pm 0.35$ | $149.59\pm 0.67$
$\omega(782)$ | 1 |  [12] | $781.91\pm 0.24$ | $8.13\pm 0.45$
$\rho(1450)$ | 1 | GS | $1493\pm 15$ | $427\pm 31$
$\rho(1700)$ | 1 | GS | $1861\pm 17$ | $316\pm 26$
$f_{2}(1270)$ | 2 | RBW | $1275.1\pm 1.2\phantom{0}$ | $185.1^{+2.9}_{-2.4}$
$\pi\pi$ S-wave | 0 | K-matrix |  [12]
$f_{0}(500)$ | 0 |  [12] |  [12]
$f_{0}(980)$ | 0 | FLT |  [12]
$f_{0}(2020)$ | 0 | RBW | $1992\pm 16$ | $442\pm 60$
Nonresonant | 0 |  [12] |  [12]
Table 2: Components of the isobar and K-matrix amplitude fit models to
$B^{0}\to\overline{D}{}^{0}\pi^{+}\pi^{-}$ decays. GS is the Gounaris-Sakurai
function and FLT is the Flatté shape. See Ref. [12] for more details.

Figure 4: Projection of the isobar model fit in (left) $m(\pi\pi)$ and (right)
$m(D\pi)$ for $B^{0}\to\overline{D}{}^{0}\pi^{+}\pi^{-}$ candidates. The
components are (black) data, (blue) isobar fit, (green) $\pi^{+}\pi^{-}$ P-
and D-wave, (pink) $D\pi$ contributions, (red) $\pi^{+}\pi^{-}$ S-wave and
(grey) background.

##  4 Dalitz plot analysis of $B^{0}\to\overline{D}{}^{0}K^{+}\pi^{-}$ decays

An amplitude analysis of $B^{0}\to\overline{D}{}^{0}K^{+}\pi^{-}$ decays with
$\overline{D}{}^{0}\to K^{+}\pi^{-}$ is presented [13]. The goal of studying
$B^{0}\to{D}K^{+}\pi^{-}$ decays is to measure the unitarity triangle angle
$\gamma$, as outlined in Refs. [23, 24]. It can also be used to access the
same charm resonances as $B^{0}\to\overline{D}{}^{0}\pi^{+}\pi^{-}$ decays,
although the available statistics are smaller. Contributions also appear in
the $m^{2}(K\pi)$ axis of the Dalitz plot.

The event selection is based on a neural network to distinguish between signal
and combinatorial background. The $B$ candidate mass distribution of selected
events is shown in Fig. 5, overlaid with the fit used to determine the signal
and background yields. Events in the signal region, defined as
$5248.6$–$5309.1$ MeV, are selected for the Dalitz plot fit. There are
approximately $2500$ signal candidates with a purity of around $75\,\%$ in
this window.

Figure 5: Fit to the $B$ candidate invariant mass distribution for
$B^{0}\to\overline{D}{}^{0}K^{+}\pi^{-}$ candidates with (left) linear and
(right) log $y$-axis scales. Components are described in the legend.

The amplitude fit contains contributions from the terms shown in Table 3 and
is performed using the Laura++ package [15] with the isobar formalism.
Backgrounds and efficiency corrections are both accounted for in the fit. For
the full results of the amplitude fit see Ref. [13]. The projections of the
amplitude fit in $m(D\pi)$ and $m(K\pi)$ are shown in Fig. 6 (left) and
(right), respectively.

Resonance | Spin | DP axis | Model | Parameters (MeV)
---|---|---|---|---
$K^{*}(892)^{0}$ | 1 | $m^{2}(K\pi)$ | RBW |  $m_{0}=895.81\pm 0.19$, $\Gamma_{0}=47.4\pm 0.6$
$K^{*}(1410)^{0}$ | 1 | $m^{2}(K\pi)$ | RBW |  $m_{0}=1414\pm 15$, $\Gamma_{0}=232\pm 21$
$K^{*}_{0}(1430)^{0}$ | 0 | $m^{2}(K\pi)$ | LASS | Determined from data
$K^{*}_{2}(1430)^{0}$ | 2 | $m^{2}(K\pi)$ | RBW |  $m_{0}=1432.4\pm 1.3$, $\Gamma_{0}=109\pm 5$
$D^{*}_{0}(2400)^{-}$ | 0 | $m^{2}(D\pi)$ | RBW | Determined from data
$D^{*}_{2}(2460)^{-}$ | 2 | $m^{2}(D\pi)$ | RBW | Determined from data
Nonresonant | 0 | $m^{2}(D\pi)$ | dabba | Fixed
Nonresonant | 1 | $m^{2}(D\pi)$ | EFF | Determined from data
Table 3: Components included in the $B^{0}\to\overline{D}{}^{0}K^{+}\pi^{-}$
amplitude fit model. More details on the dabba and LASS models can be found in
Ref. [13].

Figure 6: Projection of the amplitude fit in (left) $m(D\pi)$ and (right)
$m(K\pi)$ for $B^{0}\to\overline{D}{}^{0}K^{+}\pi^{-}$ candidates. Components
are described in the legend. The dip in the right plot is due to a veto at
$m(D^{0})$.

The charm resonance results are in agreement with the
$B^{0}\to\overline{D}{}^{0}\pi^{+}\pi^{-}$ analysis. Due to the lower
statistics available no contribution is seen at $m(D\pi)\approx 2760$ MeV. The
masses and widths of the states $D^{*}_{0}(2400)^{-}$ and
$D^{*}_{2}(2460)^{-}$ are reported to be

$\displaystyle m(D^{*}_{0}(2400)^{-})$ $\displaystyle=$
$\displaystyle\phantom{.0}(2360\pm\phantom{.}15\pm\phantom{.}12\pm\phantom{.}28)\,{\rm
MeV},$ $\displaystyle\Gamma(D^{*}_{0}(2400)^{-})$ $\displaystyle=$
$\displaystyle\phantom{.00}(255\pm\phantom{.}26\pm\phantom{.}20\pm\phantom{.}47)\,{\rm
MeV},$ $\displaystyle m(D^{*}_{2}(2460)^{-})$ $\displaystyle=$
$\displaystyle(2465.6\pm 1.8\pm 0.5\pm 1.2)\,{\rm MeV},$
$\displaystyle\Gamma(D^{*}_{2}(2460)^{-})$ $\displaystyle=$
$\displaystyle\phantom{00}(46.0\pm 3.4\pm 1.4\pm 2.9)\,{\rm MeV},$

where the uncertainties are statistical, experimental systematic and model
dependent systematic, respectively. These results are in agreement with those
from the $B^{0}\to\overline{D}{}^{0}\pi^{+}\pi^{-}$ analysis but are less
precise.

##  5 Summary

The latest results on charm spectroscopy from Dalitz plot analyses of $B$
meson decays at LHCb are presented. First observations are made of the
$D^{*}_{1}(2760)^{0}$ and $D^{*}_{3}(2760)^{-}$ mesons. Larger data samples
are needed to determine whether or not the isospin partners of these states
can be seen.

ACKNOWLEDGEMENTS

I thank the members of the LHCb collaboration for their help in preparing the
talk and this document. Work supported by the European Research Council under
FP7.

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