Charm physics at BESIII

TL;DR

This paper reports recent experimental results from BESIII on charm meson decays, including measurements of decay constants, branching fractions, and mixing parameters, providing valuable data for understanding charm quark physics.

Contribution

It presents new measurements of charm meson decay constants, branching fractions, and mixing parameters using BESIII data, advancing experimental knowledge in open charm physics.

Findings

Measured $f_{Ds} = (241 \, ext{MeV})$ with uncertainties.

Found preliminary evidence for $D_{s}^{+} o au^{+} u$ decay.

Measured $y_{CP} = (0.98 \, ext{±} \, 2.43)\%$ for $D^0$ mixing.

Abstract

The study of mesons and baryons which contain at least one charm quark is referred to as open charm physics. It offers the possibility to study up-type quark transitions. Since the $c$ quark can not be treated in any mass limit, theoretical predictions are difficult and experimental input is crucial. BESIII collected large data samples of $e^{+}e^{-}$ collisions at several charm thresholds. The at-threshold decay topology offers special opportunities to study open charm decays. We present a selection of recent BESIII results. Branching fractions and the $D_{s}^{+}$ decay constant are measured using the leptonic decays to $\mu^{+}\nu$ and $\tau^{+}\nu$. From a data sample of $0.482 fb^{-1}$ collected at the $D_{s}^{+}D_{s}^{-}$ threshold we measure $f_{Ds}=(241 \pm 16.3(stat.) \pm 6.6(sys.)) MeV$. BESIII recently found preliminary evidence of the decay $D_{s}^{+}\rightarrow\tau^{+}\nu$ and with a significance larger than $4 \sigma$ using $2.81 fb^{-1}$ of data at the $D^0\overline{D^0}$ threshold. Using the same data sample the decay $D^0\rightarrow K^0_{S/L} \pi^0(\pi^0)$ is analysed. The branching fractions are measured and using the $CP$ eigenstates $K_{S/L}^0\pi^0$ the $D^0$ mixing parameter $y_{CP} = (0.98 \pm 2.43)\%$ is measured.

Tables

Table 1. Table 1: Double tag yields and branching fractions of C ​ P 𝐶 𝑃 C\!P eigenstates K S / L 0 ​ π 0 ​ ( π 0 ) subscript superscript 𝐾 0 𝑆 𝐿 superscript 𝜋 0 superscript 𝜋 0 K^{0}_{\scriptscriptstyle S/L}\pi^{0}(\pi^{0}) . Uncertainties are statistical only.

Channel	$CP$	$N_{CF,CP\pm }$	${ℬ}_{CP\pm }$	R
$K_S^0$ ${\pi }^0$	$+$	$7141\pm 91.$	$1.230\pm 0.020$	$0.1077\pm 0.0125$
$K_L^0$ ${\pi }^0$	$-$	$6678\pm 118.$	$0.991\pm 0.019$
$K_S^0$ ${\pi }^0$ ${\pi }^0$	$+$	$2623\pm 60.$	$0.975\pm 0.024$	$-0.0929\pm 0.0209$
$K_L^0$ ${\pi }^0$ ${\pi }^0$	$-$	$2136\pm 69.$	$1.18\pm 0.04$

Equations

$$\Gamma (D_{s(d)}\to l^{+}{\nu }_l)=\frac{G_F^2}{8\pi }{f}_{D_{s(d)}}^2{m}_l^2{m}_{D_{s(d)}}{\left(1-\frac{m_l^2}{m_{D_{s(d)}}^2}\right)}^2\text{absolutevalue}{V_{cs(d)}}^2.$$

$$\mathcal{B}(D_{s(d)}\to l^{+}{\nu }_l)=\frac{N_{\text{sig,tag}}}{{ϵ}_{\text{sig,tag}}}\times \frac{{ϵ}_{\text{tag}}}{N_{\text{tag}}}.$$

$$M{M}^2=\frac{{\left(E_{\text{beam}}-E_{\mu }\right)}^2}{c^4}-\frac{{\left(-{\vec{p}}_{D_{s(d)}}-{\vec{p}}_{{\mu }^{+}}\right)}^2}{c^2}.$$

$$\mathcal{B}(D_s^{+}\to {\mu }^{+}{\nu }_{\mu })$$

$$\mathcal{B}(D_s^{+}\to {\tau }^{+}{\nu }_{\tau })$$

$$\displaystyle f_{D^{+}_{s}}=($241.0$\,\,\pm$16.3$\,\,\text{($\text{stat.}$)}\,\pm$6.5$\,\,\text{($\text{sys.}$)})\,$\mathrm{MeV}$.$$

$$\displaystyle{\mathcal{B}}(D^{+}\rightarrow\tau^{+}\nu_{\tau})=$1.20\pm 0.24\text{\,}\mathrm{\times 10}{-3}$.$$

$$\displaystyle R:=\frac{\Gamma(D^{+}\rightarrow\tau^{+}\nu_{\tau})}{\Gamma(D^{+}\rightarrow\mu^{+}\nu_{\mu})}=$3.21\pm 0.64$.$$

$$M^{\pm }=\frac{N_{CF,CP\pm }}{{ϵ}_{CF,CP\pm }}\frac{{ϵ}_{CF}}{N_{CF}}.$$

$${\mathcal{B}}_{CP\pm }=\frac{1}{1\mp C_f}{M}^{\pm },C_f=\frac{M^{-}-M^{+}}{M^{-}+M^{+}}.$$

$$R_{K^0{\pi }^0({\pi }^0)}=\frac{{\mathcal{B}}_{K_S^0{\pi }^0({\pi }^0)}-{\mathcal{B}}_{K_L^0{\pi }^0({\pi }^0)}}{{\mathcal{B}}_{K_S^0{\pi }^0({\pi }^0)}+{\mathcal{B}}_{K_L^0{\pi }^0({\pi }^0)}}.$$

$${\mathcal{B}}_{CP}\approx {\mathcal{B}}_{\text{flavour}}(1\mp y_{CP}).$$

$$y_{CP}=\frac{{\mathcal{B}}_{-;f}-{\mathcal{B}}_{+;f}}{{\mathcal{B}}_{-;f}+{\mathcal{B}}_{+;f}}.$$

$$\displaystyle y_{C\!P}=$0.98\pm 2.43\text{\,}\mathrm{\char 37\relax}$.$$

Full text

1 Introduction

The BESIII experiment is located at the Institute of High Energy Physics in Beijing. Symmetric $e^{+}e^{-}$ collisions from Beijing Electron-Positron Collider (BEPCII) in an energy range between $2.0\text{\,}\mathrm{GeV}$ and $4.6\text{\,}\mathrm{GeV}$ are analyzed. The maximum luminosity of BEPCII of $1\text{\times}{10}^{33}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$ at \sqrt{s}=$$3.773\text{\,}\mathrm{GeV} were surpassed in April 2016.

The detector measures charged track momenta with a relative precision of $0.5\text{\,}\mathrm{\char 37\relax}$ (@$1.0\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{c}$) using a multi-wire drift chamber in a $1\text{\,}\mathrm{T}$ magnetic field. Electromagnetic showers are measured in a caesium iodide calorimeter with a relative precision of $2.5\text{\,}\mathrm{\char 37\relax}$ (@$1.0\text{\,}\mathrm{GeV}$) and a good particle identification is achieved by combining information from energy loss in the drift chamber, from the time-of-flight system and from the calorimeter. Muons can be identified using 9 layers of resistive plate chambers integrated in the magnet return yoke. Details are provided elsewhere [1]. BESIII has collected large data samples in the tau-charm region. The interesting samples for the study of charmed hadrons are usually at a center-of-mass energy close to a threshold. The samples of interest for the analyses described in the following were recorded at the $D^{0}{\kern-1.60004pt\kern 1.99997pt\overline{\kern-1.99997ptD}\rule{0.0pt}{6.45831pt}^{0}}$/$D^{+}{\kern-1.60004ptD^{-}}$ threshold $(\sqrt{s}=$3.773\text{,}\mathrm{GeV}$)$ and at the $D^{+}_{s}{\kern-1.60004ptD^{-}_{s}}$ threshold $(\sqrt{s}=$4.009\text{,}\mathrm{GeV}$)$. Integrated luminosities of $2.81\text{\,}{\mathrm{fb}}^{-1}$ and $0.482\text{\,}{\mathrm{fb}}^{-1}$ were recorded, respectively.

The at-threshold decay topology at a center-of-mass energy of $3.773\text{\,}\mathrm{GeV}$ is illustrated in figure 1. A pair of mesons is produced and it is possible to conclude from the decay of one meson (so-called tag meson) properties of the second decay. For instance in case of neutral $D$ decays the flavour or the $C\!P$ quantum numbers of the signal decay can be measured, even if the signal final state does not provide this information. In case of charged $D$ decays the reconstruction of both decays is used to reduce the background and furthermore if undetected particles are involved in the signal decay the four momenta of those can be reconstructed. In particular the study of leptonic and semi-leptonic decays benefits from this. The reconstruction of both decays in each event is referred to as double tag technique.

In the following we present the measurements of the $D^{+}_{s}$ decay constant (section 2.1), first evidence of the decay $D^{+}\rightarrow\tau\nu_{\tau}$ (section 2.2) and the analysis of the decay $D^{0}\rightarrow K^{0}_{\scriptscriptstyle S/L}\pi^{0}(\pi^{0})$ (section 3).

2 Pure leptonic $D_{s(d)}^{+}$ decays

The pure leptonic decay of charged $D_{s(d)}$ mesons proceeds via the annihilation of $c$ and $\overline{s}$ ($\overline{d}$) to a virtual $W^{\pm}$ boson and its decay to $l^{+}\nu_{l}$. The decay rate can be parametrized as:

[TABLE]

With the Fermi constant $G_{F}$, the lepton mass $m_{l}$, the corresponding CKM matrix element $\absolutevalue{V_{cs(d)}}^{2}$, the $D_{s(d)}$ mass $m_{D_{s(d)}}$ and the decay constant $f_{D_{s(d)}}^{2}$. The decay constant parametrizes the $\mathrm{QCD}$ effects on the decay. From the measurement of the decay width $\Gamma(D_{s(d)}\rightarrow l^{+}\nu_{l})$ the decay constant $f_{D_{s(d)}}^{2}$ can be extracted.

The branching fraction can be measured via the previously described double tag technique. In each event the tag decay is reconstructed via numerous decay channels. The number of events that contain a tag candidate is denoted by $N_{\text{tag}}$. Among those events the signal decay is reconstructed and the number of events that contain a tag decay and a signal decay is denoted by $N_{\text{sig,tag}}$. The branching fraction is given by:

[TABLE]

The efficiencies for reconstruction and selection $\epsilon_{i}$ are obtained from simulation. Since the final state contains a neutrino which is not detected the signal yield is determined using the missing mass:

[TABLE]

The beam energy is denoted by $E_{\text{beam}}$ and the reconstructed momentum of the tag $D_{s(d)}$ decay candidate by $\vec{p}_{D_{s(d)}}$.

2.1 $D^{+}_{s}\rightarrow\mu^{+}\nu_{\mu}$ and $D^{+}_{s}\rightarrow\tau^{+}\nu_{\tau}$

The distribution of $MM^{2}$ of $D^{+}_{s}\rightarrow\mu^{+}\nu_{\mu}$ and $D^{+}_{s}\rightarrow\tau^{+}\nu_{\tau}$ is shown in figure 2. The $\tau^{+}$ is reconstructed via its decay to $\pi^{+}\overline{\nu}_{\tau}$. The yield is determined via a simultaneous fit to signal and sideband regions whereas the sideband regions are defined in the $\kern 1.99997pt\overline{\kern-1.99997ptD}^{+}_{s}$ mass spectrum of the tag candidate. The $\mu^{+}\nu_{\mu}$ signal is shown as red dotted curve and the $\tau^{+}\nu_{\tau}$ signal as black dot-dashed curve. Background from misreconstructed tag $D^{+}_{s}$ decays and background from non-$D^{+}_{s}{\kern-1.60004ptD^{-}_{s}}$ events is shown as green short dashed and violet long dashed curve, respectively. Within a sample of $15\,127\pm 321.$ events which contain a tag candidate we find $69.3\pm 9.3$ $D^{+}_{s}\rightarrow\mu^{+}\nu_{\mu}$ decays and $32.5\pm 4.3$ $D^{+}_{s}\rightarrow\tau^{+}\nu_{\tau}$ decays. In the fitting procedure the ratio of $D^{+}_{s}\rightarrow\mu^{+}\nu_{\mu}$ to $D^{+}_{s}\rightarrow\tau^{+}\nu_{\tau}$ was constraint to its Standard model prediction. The yields are corrected for radiative effects and we obtain:

[TABLE]

The branching fractions $\mathcal{B}$ ($D^{+}_{s}\rightarrow\mu^{+}\nu_{\mu}$) and $\mathcal{B}$ ($D^{+}_{s}\rightarrow\tau^{+}\nu_{\tau}$) are consistent with the world average within $1$ and $1.5$ standard deviations, respectively. Furthermore, the branching fractions are consistently determined using a fitting method which does not rely on the ratio of $D^{+}_{s}\rightarrow\mu^{+}\nu_{\mu}$ to $D^{+}_{s}\rightarrow\tau^{+}\nu_{\tau}$. For further details we refer to [2].

Using ${\mathcal{B}}(D^{+}_{s}\rightarrow\mu^{+}\nu_{\mu})$ the decay constant $f_{D^{+}_{s}}$ is determined using eq. 1:

[TABLE]

The CKM matrix element $\absolutevalue{V_{cd}}=$0.974,25\pm 0.000,22$$ [3] and the $D^{+}_{s}$ lifetime [3] is used. A good agreement with LQCD calculations is found. Result are published in [2]

2.2 $D^{+}\rightarrow\tau^{+}\nu_{\tau}$

The $MM^{2}$ distribution of $D^{+}\rightarrow\tau^{+}\nu_{\tau}$ is shown in figure 3. The most severe background to the signal channel is $\mu^{+}\nu_{\mu}$. To distinguish signal and background in a fitting procedure we use the difference in energy deposit of pions and muons in the electromagnetic calorimeter (EMC). We split the sample into events with an energy deposit larger and sample $300\text{\,}\mathrm{MeV}$. As shown in figure 3(b) above $300\text{\,}\mathrm{MeV}$ the number of $\mu^{+}\nu_{\mu}$ events is reduced compared to the number of $\tau^{+}\nu_{\tau}$ events.

We obtain a preliminary signal yield of $137\pm 27.\text{\,}\mathrm{e}$vents. The significance of the signal is larger than $4\text{\,}\mathrm{\sigma}$. The preliminary branching fraction is given by:

[TABLE]

Furthermore, we extract the ratio of $\tau^{+}\nu_{\tau}$ to $\mu^{+}\nu_{\mu}$ decays:

[TABLE]

The result is consistent with the Standard Model prediction.

3 Analysis of the decay $D^{0}\rightarrow K^{0}_{\scriptscriptstyle S/L}\pi^{0}(\pi^{0})$

We present preliminary results of the branching measurement of the decays $D^{0}\rightarrow K^{0}_{\scriptscriptstyle S/L}\pi^{0}$ and $D^{0}\rightarrow K^{0}_{\scriptscriptstyle S/L}\pi^{0}$. Furthermore we determine the $D^{0}$ mixing parameter $y_{C\!P}$ using the $C\!P$ eigenstates $K^{0}_{\scriptscriptstyle S}\pi^{0}$ and $K^{0}_{\scriptscriptstyle L}\pi^{0}$. The challenge in this channel is the reconstruction of the $K^{0}_{\scriptscriptstyle L}$ decay since its long decay time signals of its decay products in the drift chamber is very unlikely. We use the constraint kinematics at the $D^{0}{\kern-1.60004pt\kern 1.99997pt\overline{\kern-1.99997ptD}\rule{0.0pt}{6.45831pt}^{0}}$ threshold to predict the $K^{0}_{\scriptscriptstyle L}$ four-momentum and furthermore require a certain energy deposit in the electromagnetic calorimeter.

The branching fraction of a $C\!P$ eigenstate can be measured in a self-normalization way using Cabibbo favoured (CF) tag channels. We define:

[TABLE]

The yields of double of double and single tag events is denoted by $N_{CF,CP\pm}$ and $N_{CF}$ and the corresponding reconstruction efficiencies by $\epsilon_{CF,CP\pm}$ and $\epsilon_{CF}$. The branching fraction is given by:

[TABLE]

We use the flavour tag channels $K^{-}\pi^{+}$, $K^{-}\pi^{+}\pi^{-}\pi^{+}$ and $K^{-}\pi^{+}\pi^{0}$. The double tag yields and the preliminary branching fractions are listed in table 1. The branching fractions of the final states $K^{0}_{\scriptscriptstyle S/L}\pi^{0}$ and $K^{0}_{\scriptscriptstyle S}\pi^{0}\pi^{0}$ are consistent with the PDG average [3] and the branching fraction to $K^{0}_{\scriptscriptstyle S}\pi^{0}\pi^{0}$ is the first accurate measurement.

From the branching fractions we can calculate the asymmetry between the $C\!P$ eigenstates:

[TABLE]

The results are also listed in table 1.

3.1 Measurement of $y_{CP}$

Using the final states $K^{0}_{\scriptscriptstyle S}\pi^{0}$ and $K^{0}_{\scriptscriptstyle L}\pi^{0}$ we determine the $D^{0}$ mixing parameter $y_{C\!P}$. The branching ratio of a $C\!P$ eigenstate is connected to the branching ratio of a pure flavour eigenstate via:

[TABLE]

The parameter $y_{C\!P}$ is then given by the asymmetry of branching ratios of $C\!P$ even and odd states to pure flavour states f:

[TABLE]

The previously mentioned Cabibbo favoured final states are not pure flavour eigenstates. Therefore, we use the semi-leptonic decay to $K^{-}e^{+}\nu_{e}$. We obtain a preliminary value of:

[TABLE]

We quote statistical uncertainty only. The result is in agreement with a previous measurement of BESIII [4] as well as with the HFAG average [5]. Results are preliminary and we quote statistical uncertainties only.

4 Summary

The BESIII experiment has collected large data sample at charm-related thresholds. The constraint kinematics at those energies allow the reconstruction of (semi-) leptonic decays with low background. Furthermore, the quantum entanglement of $D^{0}{\kern-1.60004pt\kern 1.99997pt\overline{\kern-1.99997ptD}\rule{0.0pt}{6.45831pt}^{0}}$ at threshold provides a unique laboratory for the analysis of $C\!P$ eigenstates. We present the analysis of the leptonic decay of $D^{+}_{s}$ to $\mu^{+}\nu_{\mu}$ and $\tau^{+}\nu_{\tau}$ with the measurement of branching fractions of the derived $D^{+}_{s}$ form factor. Recently, BESIII has found preliminary evidence of the decay $D^{+}$ $\rightarrow$ $\tau^{+}$ $\nu_{\tau}$ with a statistical significance above $4\text{\,}\mathrm{\sigma}$. The analysis of the $D^{0}\rightarrow K^{0}_{\scriptscriptstyle S/L}\pi^{0}(\pi^{0})$ includes the measurement of the branching fractions and using the decays to $K^{0}_{\scriptscriptstyle S/L}\pi^{0}$ the measurement of the $D^{0}$ mixing parameter $y_{C\!P}$.