Prospects for time-dependent mixing and CP-violation measurements at Belle II

TL;DR

The paper discusses the potential of the Belle II experiment to measure time-dependent mixing and CP violation in charm meson decays with a significantly larger data sample than previous experiments.

Contribution

It presents the expected sensitivity of Belle II for key measurements of D0-D0bar mixing and CP violation in specific decay channels.

Findings

Projected sensitivity for D0-D0bar mixing parameters

Expected improvements in CP violation measurements

Large data sample enhances measurement precision

Abstract

The Belle II experiment is under construction at the KEK laboratory in Japan. Belle II will study e+e- collisions at or near the Upsilon(4S) resonance with the goal of collecting 50 ab-1 of data, which is a large increase over that recorded by the Belle and BaBar experiments. This data will provide a large sample of charm meson decays. In this report we present the expected sensitivity of Belle II for measuring time-dependent mixing and CP violation in the D0-D0bar system. We focus on measurements of D0-> K+ pi-, D0-> K+ pi- pi0, and D0-> K0_S pi+ pi- decays.

Tables

Table 1. Table 1: Layers and segmentation of the Belle II vertex detector.

Layer	Type	Distance from IP	Size or pitch	Number of pixels
		(mm)	($\mu$m)	or strips
1	pixels	14	$(55,60)\times 50$	$\mathrm{3\hspace{0.17em}072\hspace{0.17em}000}$
2	pixels	22	$(70,85)\times 50$	$\mathrm{4\hspace{0.17em}608\hspace{0.17em}000}$
3	strips	38	$50\left(\varphi \right),\mathrm{\hspace{0.17em}160}\left(z\right)$	$768\left(\varphi \right),\mathrm{\hspace{0.17em}768}\left(z\right)$
4	strips	80	$50,75\left(\varphi \right),\mathrm{\hspace{0.17em}240}\left(z\right)$	$768\left(\varphi \right),\mathrm{\hspace{0.17em}512}\left(z\right)$
5	strips	104	$50,75\left(\varphi \right),\mathrm{\hspace{0.17em}240}\left(z\right)$	$768\left(\varphi \right),\mathrm{\hspace{0.17em}512}\left(z\right)$
6	strips	135	$50,75\left(\varphi \right),\mathrm{\hspace{0.17em}240}\left(z\right)$	$768\left(\varphi \right),\mathrm{\hspace{0.17em}512}\left(z\right)$

Table 2. Table 2: Preliminary results of a toy MC study of D 0 → K + ​ π − → superscript 𝐷 0 superscript 𝐾 superscript 𝜋 D^{0}\!\rightarrow\!K^{+}\pi^{-} decays: uncertainty on “rotated” mixing parameters x ′ superscript 𝑥 ′ x^{\prime} and y ′ superscript 𝑦 ′ y^{\prime} , and on C ​ P 𝐶 𝑃 CP -violating parameters | q / p | 𝑞 𝑝 |q/p| and ϕ italic-ϕ \phi , for three values of integrated luminosity.

Parameter	5 ab-1	20 ab-1	50 ab-1
$\delta x^{\prime }$ (%)	0.37	0.23	0.15
$\delta y^{\prime }$ (%)	0.26	0.17	0.10
$\delta \left|q/p\right|$ (%)	0.20	0.09	0.05
$\delta \varphi$ (∘)	16	9.2	5.7

Table 3. Table 3: Precision obtained for x 𝑥 x , y 𝑦 y , | q / p | 𝑞 𝑝 |q/p| , and ϕ italic-ϕ \phi from a Belle analysis of D 0 → K S 0 ​ π + ​ π − → superscript 𝐷 0 subscript superscript 𝐾 0 𝑆 superscript 𝜋 superscript 𝜋 D^{0}\!\rightarrow\!K^{0}_{S}\pi^{+}\pi^{-} decays  [ 11 ] , and the precision expected for Belle II as obtained by scaling the Belle errors (see text).

	$\sigma \left(x\right)$	$\sigma \left(y\right)$	$\sigma \left|\frac{q}{p}\right|$	$\sigma \left(\varphi \right)$
	(${10}^{-2}$)	(${10}^{-2}$)		(∘)
Belle ${\sigma }_{\mathrm{stat}}$	0.19	0.15	0.155	10.7
Belle ${\sigma }_{\mathrm{syst}}$	0.06	0.06	0.054	4.5
Belle ${\sigma }_{\mathrm{irred}}$	0.11	0.04	0.069	3.8
Belle II ${\sigma }_{\mathrm{tot}}$	0.11	0.05	0.073	4.1

Equations

$$\frac{dN}{dt}(D^0)$$

$$\frac{dN}{dt}(\overline{D}{}^0)$$

$$\frac{dN}{dt}(D^0)$$

$$\frac{dN}{dt}(\overline{D}{}^0)$$

Full text

1 Introduction

The Belle experiment at the KEK laboratory in Japan is now being upgraded to the Belle II experiment. The goal of Belle II is to collect a data set corresponding to 50 times what Belle obtained. The experiment is designed to search for new physics in $B$ and $D$ meson decays, and in $\tau$ lepton decays. Within this broad physics program, measuring mixing and $CP$ violation in the neutral charm system is an important goal. The first evidence for $D^{0}$-$\overline{D}{}^{\,0}$ mixing was obtained in 2007 by the Belle [1] and BaBar [2] experiments, with subsequent observations made by LHCb [3] and CDF [4]. However, the current precision on the mixing parameters $x=\Delta m/\Gamma$ and $y=\Delta\Gamma/(2\Gamma)$, where $\Delta m$ and $\Delta\Gamma$ are the differences in masses and decay widths between the two mass eigenstates and $\Gamma$ is the mean decay width, is insufficient to determine whether $y>x$ or even whether $x\neq 0$ [5]. To establish this, higher statistics measurements are needed. $CP$ violation in the $D^{0}$-$\overline{D}{}^{\,0}$ system has not yet been observed. The predicted rate within the Standard Model (SM) is very small, and an observation of $CP$ violation by Belle II could indicate new physics.

There are several advantages of performing these measurements at an $e^{+}e^{-}$ experiment such as Belle II rather than at a hadron machine: lower backgrounds, higher trigger efficiency, excellent $\gamma$ and $\pi^{0}$ reconstruction (and thus $\eta$, $\eta^{\prime}$, and $\rho^{+}$ reconstruction), high flavor-tagging efficiency with low dilution, and numerous control samples with which to study systematics. In this report we present Belle II prospects for measuring the mixing parameters $x$ and $y$, and $CP$-violating parameters $|q/p|$ and ${\rm Arg}(q/p)=\phi$, where $q$ and $p$ are the complex coefficients relating the $D^{0}$-$\overline{D}{}^{\,0}$ flavor eigenstates with the mass eigenstates. We focus on three benchmark decay modes: $D^{0}\!\rightarrow\!K^{+}\pi^{-}$, $D^{0}\!\rightarrow\!K^{+}\pi^{-}\pi^{0}$, and $D^{0}\!\rightarrow\!K^{0}_{S}\pi^{+}\pi^{-}$ [6]. In all cases the flavor of the neutral $D$ is determined by requiring that it originate from a $D^{*+}\!\rightarrow\!D^{0}\pi^{+}$ or $D^{*-}\!\rightarrow\!\overline{D}{}^{\,0}\pi^{-}$ decay; the charge of the $\pi^{\pm}$ identifies the $D^{0}$ or $\overline{D}{}^{\,0}$ flavor. All results given are preliminary.

2 Decay-time resolution

Measurements of time-dependent mixing and $CP$ violation depend on measuring decay times precisely. Due to an improved vertex detector, the decay time resolution of Belle II should be superior to that of Belle and BaBar. Whereas Belle used a four-layer silicon-strip detector, Belle II will use four layers of silicon strips plus two layers of silicon pixels, as shown in Fig. 1. Some parameters of the vertex detector are listed in Table 1. The pixel layers will lie only 14 mm and 22 mm from the interaction point (IP), and the smallest pixel size will be $55\times 50$ $\mu$m2.

Figure 2 (left) shows the resolution on the impact parameter of tracks with respect to the IP as a function of track momentum, as obtained from Monte Carlo (MC) simulation. Also shown are corresponding results from BaBar. The figure indicates that the Belle II resolution will be approximately half that of BaBar. Figure 2 (right) plots the residuals of decay time for a large sample of MC $D^{*+}\!\rightarrow\!D^{0}\pi^{+},\ D^{0}\!\rightarrow\!K^{+}K^{-}$ decays. The RMS of this distribution is 140 fs, which is almost half the decay time resolution of BaBar (270 fs). Similar results have been obtained for prompt $D^{0}\!\rightarrow\!K^{+}K^{-}$ decays, and also for $D^{0}\!\rightarrow\!\pi^{+}\pi^{-}$ decays.

3 Mixing and $\boldsymbol{CP}$ violation in $\boldsymbol{D^{0}\!\rightarrow\!K^{+}\pi^{-}}$

To study the sensitivity of Belle II to parameters $x$, $y$, $|q/p|$, and $\phi$ in “wrong-sign” $D^{0}\!\rightarrow\!K^{+}\pi^{-}$ decays, we perform a “toy” MC study as follows. We generate an ensemble of 1000 MC experiments, with each experiment consisting of a sample of $D^{0}$ decays and a separate sample of $\overline{D}{}^{\,0}$ decays. The number of events in each sample corresponds to 5 ab*-1*, 20 ab*-1*, and 50 ab*-1* of data. For the full dataset (50 ab*-1*), there are a total of 438600 $D\!\rightarrow\!K^{\pm}\pi^{\mp}$ decays. The decay times are obtained by sampling from the following probability density functions (PDFs):

[TABLE]

where $x^{\prime}=x\cos\delta+y\sin\delta$, $y^{\prime}=-x\sin\delta+y\cos\delta$, and $\delta$ is the strong phase difference between $D^{0}\!\rightarrow\!K^{-}\pi^{+}$ and $\overline{D}{}^{\,0}\!\rightarrow\!K^{-}\pi^{+}$ amplitudes. This strong phase difference can be measured at BESIII using $CP$-tagged $D_{CP}\!\rightarrow\!K^{-}\pi^{+}$ decays [7]. The parameter $R_{D}$ ($\overline{R}_{D}$) is the ratio of amplitudes squared $|{\cal A}(D^{0}\!\rightarrow\!K^{+}\pi^{-})/{\cal A}(D^{0}\!\rightarrow\!K^{-}\pi^{+})|^{2}$ ($|{\cal A}(\overline{D}{}^{\,0}\!\rightarrow\!K^{-}\pi^{+})/{\cal A}(\overline{D}{}^{\,0}\!\rightarrow\!K^{+}\pi^{-})|^{2}$).

After generation, the decay times are smeared by the expected decay time resolution of 140 fs, and the resulting $D^{0}$ and $\overline{D}{}^{\,0}$ time distributions are simultaneously fitted. Backgrounds are not yet included in this study; a first look at backgrounds indicates that when they are included, the fitted errors increase by only a small amount. The PDFs used for the fit are the convolution of Eqs. (1) and (2) with a Gaussian resolution function; this results in products of exponential functions and Error functions. The preliminary results are listed in Table 2. The final Belle II sensitivity for $|q/p|$ is $<0.1\%$, and that for $\phi$ is $6^{\circ}$. This precision is a significant improvement over that which Belle and BaBar achieved.

4 Mixing in $\boldsymbol{D^{0}\!\rightarrow\!K^{+}\pi^{-}\pi^{0}}$

We study mixing in $D^{0}\!\rightarrow\!K^{+}\pi^{-}\pi^{0}$ decays using an MC simulation based on EVTGEN [8]. For this study we generate an ensemble of 10 experiments, with each experiment consisting of 225000 $D^{0}\!\rightarrow\!K^{+}\pi^{-}\pi^{0}$ decays corresponding to 50 ab*-1* of Belle II data. The generated decay times are smeared by a resolution of 140 fs, and the decay model used to generate and fit the Dalitz plot is the isobar model used by BaBar [9]. Possible $CP$ violation and backgrounds are neglected in this phase of the study. More details are given in Ref. [10].

The mixing parameters are $x^{\prime\prime}=x\cos\delta_{K\pi\pi}+y\sin\delta_{K\pi\pi}$ and $y^{\prime\prime}=-x\sin\delta_{K\pi\pi}+y\cos\delta_{K\pi\pi}$, where $\delta_{K\pi\pi}$ is the strong phase difference between $D^{0}\!\rightarrow\!K^{-}\pi^{+}\pi^{0}$ and $\overline{D}{}^{\,0}\!\rightarrow\!K^{-}\pi^{+}\pi^{0}$ amplitudes evaluated at $m_{\pi\pi}=M_{\rho}$. For this study the strong phase $\delta_{K\pi\pi}$ is fixed to $10^{\circ}$, and the fitted parameters are $x$ and $y$. The results are shown in Fig. 3. The input values are $x=0.0258$ and $y=0.0039$, and the RMS of the distributions of residuals are $\delta x=0.057\%$ and $\delta y=0.049\%$. This precision is approximately one order of magnitude better than that achieved by BaBar [9]. The projections of a typical fit (one experiment in the ensemble) are shown in Fig. 4. In practice, to extract values for $x$ and $y$ requires knowledge of the strong phase $\delta_{K\pi\pi}$; this can in principle be measured at BESIII using $CP$-tagged $D_{CP}\!\rightarrow\!K^{-}\pi^{+}\pi^{0}$ decays.

5 Mixing and $\boldsymbol{CP}$ violation in $\boldsymbol{D^{0}\!\rightarrow\!K^{0}_{S}\pi^{+}\pi^{-}}$

Another method for measuring mixing and $CP$ violation is by fitting the time-dependent Dalitz plot for $D^{0}\!\rightarrow\!K^{0}_{S}\pi^{+}\pi^{-}$ decays. One calculates the observables $m_{+}\equiv(P^{0}_{K_{S}}+P_{\pi^{+}})^{2}$ and $m_{-}\equiv(P^{0}_{K_{S}}+P_{\pi^{-}})^{2}$ and performs an unbinned maximum likelihood fit to $m_{+}$, $m_{-}$, and the decay time $t$. To fit for $CP$-violating parameters $|q/p|$ and $\phi$ (in addition to $x$ and $y$) requires dividing the data sample into $D^{0}$ and $\overline{D}{}^{\,0}$ decays and fitting the two subsamples simultaneously.

The time-dependent PDFs are

[TABLE]

where ${\cal A}_{f}$ ($\overline{\cal A}_{f}$) is the decay amplitude for $D^{0}\!\rightarrow\!f$ ($\overline{D}{}^{\,0}\!\rightarrow\!f$) decays. These amplitudes must be modeled, and the parameters of the model must also be fitted or else taken from a previous measurement. For a Belle analysis of $D^{0}\!\rightarrow\!K^{0}_{S}\pi^{+}\pi^{-}$ decays using 976 fb*-1* of data [11], the decay model used consisted of 14 intermediate resonances modeled by isobars, plus $K\pi$ and $\pi\pi$ $S$-waves. The magnitudes and phases of the isobars, and parameters of the $S$-waves, were obtained from a separate time-independent fit to the data.

An important advantage of this measurement is that the fitted PDFs (Eqs. 3 and 4) depend on $x$ and $y$ without being “rotated” by an unknown strong phase difference. The results obtained by Belle [11] are listed in Table 3 along with the precision estimated for Belle II. This precision is obtained as follows. The statistical errors of the Belle measurement ($\sigma_{\rm stat}$) are scaled by the square root of the ratio of luminosities. The systematic errors are divided into two categories: “reducible” errors ($\sigma_{\rm syst}$) that should decrease with luminosity such as errors due to background modeling as determined from control samples; and “irreducible” errors ($\sigma_{\rm irred}$) that do not decrease with more data such as uncertainty in decay time resolution due to detector misalignment. The total error is calculated as $\sigma_{\rm Belle\ II}=\sqrt{(\sigma^{2}_{\rm stat}+\sigma^{2}_{\rm syst})\cdot({\cal L}_{\rm Belle}/50{\rm\ ab}^{-1})+\sigma^{2}_{\rm irred}}$. These errors are conservative, as the simple scaling used does not account for the improved decay time resolution of the Belle II vertex detector as compared to that of Belle (see Section 2).

Acknowledgements

The authors thank the CKM 2016 organizers for a well-run workshop and excellent hospitality. This research is supported by the U.S. Department of Energy.