New Physics Searches at the BESIII Experiment

Flavor changing neutral current (FCNC) processes transform an up-type ($u,c,t$) or down-type ($d,s,b$) quark into another quark of the same type but with a different flavor. In the SM, these processes are mediated by the $Z$ boson and are known as neutral currents. However, they are strongly suppressed by the Glashow–Iliopoulos–Maiani (GIM) cancellation Glashow et al. (1970) and only occur as second-order loop processes. In many extensions of the SM, virtual TeV-scale particles can contribute competing processes that lead to measurable deviations from SM-inferred transition rates or other properties. Hence studies of rare FCNC processes are suitable probes for new physics.

Recently, hints of discrepancies have been observed in the semi-leptonic FCNC processes of the $b$-quark, $b\to s\ell^{+}\ell^{-}$ ($\ell=e,\mu$) by the LHCb experiment Capriotti (2019): (1) The differential branching fractions measured as a function of the squared four-momentum transferred to the two leptons, $Q^{2}$, for several $B$-meson decay modes are below the theoretical predictions Aaij et al. (2014a, 2015a, 2016a, 2015b); Detmold and Meinel (2016). The largest local discrepancy is a $3.3\sigma$ difference in the rate for $B_{s}^{0}\to\phi\mu^{+}\mu^{-}$ decay from its SM-predicted value. (2) The ratios of branching fractions for decays involving muons and electrons, defined as $R_{K}=\frac{\mathcal{B}(B^{+}\to K^{+}\mu^{+}\mu^{-})}{\mathcal{B}(B^{+}\to K^{+}e^{+}e^{-})}$ and $R_{K^{*}}=\frac{\mathcal{B}(B^{+}\to K^{*+}\mu^{+}\mu^{-})}{\mathcal{B}(B^{+}\to K^{*+}e^{+}e^{-})}$, which are unity in the SM (i.e. lepton-flavor universality), were measured to be Aaij et al. (2014b, 2017)

where the levels of deviations from the SM predictions are indicated. (3) Measurements of the quantity $P^{\prime}_{5}$, which is the chiral asymmetry produced by the interference between the transversely and longitudinally polarized amplitudes in the decay $B\to K^{*+}\ell^{+}\ell^{-}$, are $2.8\sigma$ and $3.0\sigma$ lower than the SM prediction in two $Q^{2}$ intervals below the $J/\psi$ resonance mass Aaij et al. (2016b). Since these discrepancies could be evidence for new particles that would extend the SM, it is important to check if there are similar deviations in the charm sector.

While SM rates for FCNC transitions in the down-type $b$- or $s$-quark sectors are relatively frequent because of the large mass of the top quark contribution to the loop, those in the up-type $c$-quark sector are especially rare due to the small masses of the intermediate down-like quarks in the loop that result in a strong GIM cancellation. For $c\to u$ transition rates for charmed and charmonia particles that proceed via the SM loop contribution, dubbed as short distance (SD) effects, the expected branching fractions are typically between $<10^{-8}$ Greub et al. (1996); Fajfer et al. (2001a); Burdman et al. (2002); Fajfer et al. (2001b); Paul et al. (2011); Cappiello et al. (2013) and $10^{-10}$-$10^{-14}$ Sanchis-Lozano (1994); Wang et al. (2008), respectively. For FCNC decays of charmed mesons, the measured rates are enhanced by a few orders of magnitude by SM contributions from long distance (LD) effects that proceed via di-lepton decays of ordinary $\rho$, $\omega$ and $\phi$ vector mesons Paul et al. (2011); Cappiello et al. (2013). However, some extensions to the SM further enhance these FCNC processes, sometimes by orders of magnitude Prelovsek and Wyler (2001); Paul et al. (2010); Fajfer et al. (2001b); Hill (1995); Aulakh and Mohapatra (1982); Glashow and Weinberg (1977).

The BESIII experiment has searched for $c$-quark FCNC processes in both charmed meson and charmonium decays. No significant signals for new physics are found in any of the investigated decay modes, and the inferred 90% confidence level (CL) upper limits on the branching fractions are summarized in Table 1.

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  For the $D^{0}\to\gamma\gamma$ mode, the upper limit is consistent with that previously set by the BaBar experiment Lees et al. (2012a). The BESIII result is the first experimental study of this decay that uses $D^{0}$ mesons produced at the open-charm threshold.

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  For the rare decays $D\to h(h^{(^{\prime})})e^{+}e^{-}$, where $h$=light meson(s), searches for four-body decays of $D^{+}$ mesons are performed for the first time, and the upper limits for $D^{0}$ meson decays are, in general, one order of magnitude better than previous measurements Patrignani et al. (2016).

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  Searches for the FCNC decays $\psi(2S)\to D^{0}e^{+}e^{-}$ and $\psi(2S)\to\Lambda_{c}^{+}\bar{p}e^{+}e^{-}$ are performed for the first time. The upper limit on $J/\psi\to D^{0}e^{+}e^{-}$ is two orders of magnitude more stringent than the best previous result, which was set by the BESII collaboration Ablikim et al. (2006a).

The BESIII FCNC search results mentioned above are based on data collected in 2009-2012, which included 1.31B $J/\psi$ and 448M $\psi(2S)$ event samples and a 2.93 fb^-1 data sample that was accumulated at $E_{\rm CM}=3.773$ GeV, the peak energy of the $\psi(3770)\rightarrow D\bar{D}$ resonance. BESIII has recently increased the $J/\psi$ data sample to 10B events and will eventually increase the $\psi(2S)$ sample to 3B events, and the $\psi(3770)\rightarrow D\bar{D}$ data to 20 fb^-1 (see Table 7.1 in ref. Ablikim et al. (2020a)). Since the results listed in Table 1 are mainly limited by statistics, when the full data are available and analyzed, the sensitivity levels of FCNC searches should improve, in most cases, by factors of $\sim 7$, and decay branching fractions will be probed at the $10^{-6}$-$10^{-8}$ levels. If no interesting signals are found, more stringent upper limits would be established that should further constrain the parameter spaces of a number of new physics models.

In contrast to FCNC processes, charged-current weak decays of charmonium states are allowed, but are expected to occur as very rare processes; the SM-predicted branching fractions are of the order $10^{-10}$-$10^{-8}$ Sanchis-Lozano (1994), which means they would be difficult to detect at BESIII, even with the full 10B event $J/\psi$ data sample. However, some BSM calculations based on a two-Higgs-doublet model predict that the branching ratios of charmonium weak decays could be enhanced to be as large as $10^{-5}$ Datta et al. (1999). BESIII searched for several Cabibbo-favored weak decays, such as the hadronic processes $J/\psi\to D_{s}^{-}\rho^{+}$ and $J/\psi\to\bar{D}^{0}\bar{K}^{*0}$ Ablikim et al. (2014a), and the semi-leptonic process $J/\psi\to D_{s}^{(*)-}e^{+}\nu_{e}$ Ablikim et al. (2014b), and established 90% CL branching fraction upper limits in the $\sim 10^{-5}$-$10^{-6}$ range. Searches for some Cabibbo-suppressed weak decays of the $J/\psi$ are currently underway at BESIII, with expected branching fraction sensitivity levels of about $10^{-7}$.

The equality of the electron and muon couplings, $g_{e}$ and $g_{\mu}$, has been established at the ${\mathcal{O}}(0.2\%)$ level, i.e. $(g_{e}/g_{\mu}-1)=0.002\pm 0.002$, by a comparison between the $K^{+}\rightarrow e^{+}\nu_{e}$ and $K^{+}\rightarrow\mu^{+}\nu_{\mu}$ partial decay widths measured by the NA62 experiment Lazzeroni et al. (2013) together with PDG values for the $K^{+}$ lifetime and the electron & muon masses Tanabashi et al. (2018). The best test of the equality of the $\tau$-lepton coupling and muon couplings, $(g_{\tau}/g_{\mu}-1)=0.0008\pm 0.0021$, has similar precision and is from a BESIII measurement of the tau mass Ablikim et al. (2014c) together with with PDG values of the tau-lepton’s lifetime and leptonic decay branching fractions.

The possibility of LFU violation has attracted considerable recent attention because of measurements from BaBar Lees et al. (2012b), Belle Abdesselam et al. (2019) and LHCb Aaij et al. (2018) of the relative decay rates for the semileptonic processes $\bar{B}\rightarrow D^{(*)}\tau^{-}\nu$ and $\bar{B}\rightarrow D^{(*)}\ell^{-}\nu$ ($\ell^{-}=\mu^{-}\ {\rm or}\ e^{-})$ that seem to violate SM expectations. Specifically, the HFLAV Group’s recent averages of experimental measurements are Amhis et al. (2019):

Here the discrepancies with LFU, if they are real and not just statistical fluctuations, are of order 10%, and motivate more careful checks of LFU in semileptonic and purely leptonic charmed particle decays with BESIII data.

The CKM matrix (see Fig. 1a) is the DNA of flavor physics; its elements characterize all of the SM weak charged current interactions of quarks. It defines a rotation in three-dimensions of flavor-space and, in the SM where there are three quark generations, it must be exactly unitary; any deviation from this would be a clear signal for new physics.

The unitarity condition for the top row of the CKM matrix is: $|V_{ud}|^{2}+|V_{us}|^{2}+|V_{ub}|^{2}=1$. Experimentally, a high precision value of $|V_{ud}|$ comes from an analysis of eight superallowed $0^{+}\rightarrow 0^{+}$ nuclear $\beta$-decays Hardy and Towner (2016) corrected for electroweak effects. The latest result is $|V_{ud}|=0.97370(4)$ Seng et al. (2018). A precise value of the ratio $|V_{us}|/|V_{ud}|=0.2313(5)$ ratio is determined from a KLOE measurement of ${\mathcal{B}}(K^{+}\rightarrow\mu^{+}\nu)$ Ambrosino et al. (2006), the PDG 2018 world average for ${\mathcal{B}}(\pi^{+}\rightarrow\mu^{+}\nu)$ Tanabashi et al. (2018) and a FLAG average of LQCD evaluations of the pseudoscalar form-factor ratio $f_{K^{+}}/f_{\pi^{+}}$ Aoki et al. (2020). The value of $|V_{ub}|^{2}$, determined from $B$-meson decays, is $\sim{\mathcal{O}}(10^{-5})$ and is a negligible contributor to the unitarity condition Tanabashi et al. (2018). The combination of these results Seng et al. (2018),

indicates a nominal $\sim 3.5\sigma$ deviation from unitarity that, if taken at face value, is strong evidence for a SM violation.

Since deviations from CKM unitarity would be a clear sign of new physics, the eqn. 2 result inspired further investigations. These included: independent determinations of $|V_{ud}|$ based on the neutron lifetime Czarnecki et al. (2019); Seng et al. (2020) that returned consistent results, albeit with a slightly larger error; an independent evaluation of $|V_{us}|/|V_{ud}|$ using ${\mathcal{B}}(K_{L}\rightarrow\pi\ell\nu)$ and ${\mathcal{B}}(\pi^{+}\rightarrow\pi^{0}e^{+}\nu)$ Bazavov et al. (2019) that found an even larger deviation from unitarity, but with a corresondingly larger error; and reexaminations of the nuclear physics corrections used in the nuclear $\beta$-decay analyses for $|V_{ud}|$ Seng et al. (2019); Gorchtein (2019) that did not change the central value, but indicated that the previous error that was assigned to these effects may have been somewhat underestimated. The current state of affairs is that the best current analyses of the existing data find an ${\mathcal{O}}(0.1\%)$ deviation from unitarity for the top row of the CKM matrix with a significance level that is somewhere in the $2\sigma\sim 5\sigma$ range.

The strong generational hierarchy of the CKM quark-flavor mixing matrix is illustrated in Fig. 1a, where the Wolfenstein parameterization Wolfenstein (1983) is shown with shaded rectangles with areas that are proportional to $|V_{i,j}|$. Transitions between different generations (i.e., further off-diagonal elements) are successively suppressed by additional factors of $\lambda=\sin\theta_{C}\simeq 0.225$, where $\theta_{C}$ is the Cabibbo angle. A striking feature of the Wolfenstein formulation, and a characteristic of the SM, is that, to ${\mathcal{O}}(\lambda^{6})\sim 10^{-4}$, the four entries in the upper-left corner of the matrix, i.e., all transitions involving ($u,d$) & ($c,s$) quarks, are well characterized by the single parameter, $\sin\theta_{C}$. The authors of ref. Grossman et al. (2019) argue that comparing the $\sin\theta_{C}$ values derived from different $q_{i}\leftrightarrow q_{j}$ ($i=u,c;~{}j=d,s$) subprocesses is a more sensitive test for new physics than tests of the CKM matrix unitarity, and provide, in support of this claim, an example of a toy model that has a heavy gauge boson with different $d$- and $s$-quark couplings that demonstrates this. In Fig. 1b, values of $\sin\theta_{C}$ derived from the nuclear $\beta$-decay ($u\leftrightarrow d$) and $K_{\ell 2}~{}\&~{}K_{\ell 3}$ decays ($u\leftrightarrow s$) transitions discussed in the previous paragraph are shown. The apparent discrepancy from a single, universal value is referred to as the Cabibbo angle anomaly.

Studies of $c\rightarrow d$ transitions provide independent $\sin\theta_{C}$ determinations. In the SM, $|V_{cd}|=|V_{us}|=\sin\theta_{C}$; a deviation between the $\sin\theta_{C}$ value inferred from $c\rightarrow d$ decays with the one evaluated from $K_{\ell 2}~{}\&~{}K_{\ell 3}$ decays would be another clear indication of new physics. To date, this relation has not been strenuously tested. The PDG 2018 world-average value, $|V_{us}|=0.2243\pm 0.0005$, differs from that for $|V_{cd}|=0.218\pm 0.004$ by $1.5\sigma$, where the uncertainty of the latter is nearly an order of magnitude poorer Tanabashi et al. (2018). The best determinations of $|V_{cd}|$ to date are from statistically limited BESIII measurements of ${\mathcal{B}}(D^{+}\rightarrow\mu^{+}\nu)$ Ablikim et al. (2014d) and the ratio ${\mathcal{B}}(D^{0}\rightarrow\pi^{-}e^{+}\nu)/{\mathcal{B}}(D^{0}\rightarrow K^{-}e^{+}\nu)$ Ablikim et al. (2015b), both of which are based on analyses of BESIII’s 2.97 fb^-1 sample of $\psi(3770)\rightarrow D\bar{D}$ events that are discussed elsewere in this volume Li and Lyu (2020). The average value of the two $|V_{cd}|$ measurements is plotted in Fig. 1b.

With the full 20 fb^-1 $\psi(3770)$ data sample, the BESIII precision on $|V_{cd}|$ should be improved by at least a factor of 2.5; if the result is the same as the current central value, the significance of the discrepancy would increase to about the $4\sigma$ level.

Parity violation in the weak interactions was discovered in 1957 Lee and Yang (1956); Wu et al. (1957). Immediately thereafter there was considerable interest is studying parity violations in strange hyperon decays that were predicted by Lee and Yang Lee and Yang (1957). For the $Y\rightarrow B\pi$ weak decay process, where $Y$ is one of the spin $=1/2$ strange hyperons and $B$ is an octet baryon, parity violation allows for both $S$- and $P$-wave transitions, and the final states are characterized by the Lee-Yang parameters:

where $\alpha^{2}+\beta^{2}+\gamma^{2}=1$. If the initial-state $Y$ has a non-zero polarization $\vec{\mathcal{P}}_{Y}$, the $B$ flight direction in the $Y$ rest frame relative to the polarization direction, $\theta$, is distributed as $dN/d\cos\theta\propto 1+\alpha|\vec{\mathcal{P}}_{Y}|\cos\theta$ and, if $\alpha$ is also non-zero, has an explicit parity-violating up-down asymmetry. The polarization of the daughter baryon, $\vec{\mathcal{P}}_{B}$, depends on ${\mathcal{P}}_{Y}$, $\theta$, and the $\alpha,\ \beta,\ \gamma$ parameters as illustrated in Fig. 2a. If $CP$ is conserved, the decay parameters for $Y$ and $\bar{Y}$ are equal in magnitude but opposite in sign. (The parameters for $\bar{Y}$ are denoted by $\bar{\alpha}$ & $\bar{\beta}$.) Violations of $CP$ symmetry would result in non-zero values for the parameters $A_{CP}$ and $B_{CP}$, defined as

Measuring $\alpha_{\Lambda}$ for $\Lambda\rightarrow p\pi^{-}$ decay is not straight forward. Measurements of the up-down parity-violating asymmetry in $\Lambda\rightarrow p\pi^{-}$ determine the product $\alpha_{\Lambda}{\mathcal{P}}_{\Lambda}$, where ${\mathcal{P}}_{\Lambda}$ is generally unknown. To extract $\alpha_{\Lambda}$, the polarization of the final-state proton must be measured. This was done in a series of pre-1975 experiments by scattering the final-state proton on carbon, with a world-average result of $\alpha_{\Lambda}=0.642\pm 0.013$ Bricman et al. (1978); this was the PDG value for 43 years, from 1976 until 2019.

BESIII measured $\alpha_{\Lambda}$ and $\bar{\alpha}_{\Lambda}$ with fully reconstructed $e^{+}e^{-}\rightarrow J/\psi\rightarrow(\Lambda\rightarrow p\pi^{-})(\bar{\Lambda}\rightarrow\bar{p}\pi^{+})$ events. For this reaction, the joint angular distribution can be expressed as Fäldt and Kupsc (2017)

where: $\theta_{\Lambda}$ is the $\Lambda$ production angle relative to the $e^{+}$-beam direction (the $\cos\theta_{\Lambda}$ distribution is $1+\alpha_{\psi}\cos^{2}\theta_{\Lambda}$); $\Delta\Phi$ is the complex phase difference between the $A_{+,+}$ and $A_{+,-}$ helicity amplitudes; and $\xi$ denotes $(\theta_{\Lambda},\theta_{-},\phi_{-}\theta_{+},\phi_{+})$, where $\theta_{-},\phi_{-}$ ( $\theta_{+},\phi_{+}$) are the $\Lambda$ ($\bar{\Lambda}$) decay angles (see Fig. 2b). The $\cos\theta_{\Lambda}$-dependent $\Lambda$ (and $\bar{\Lambda}$) polarization is given by

The $\Lambda$ polarization is zero if the $A_{+,+}$ and $A_{+,-}$ helicity amplitudes are relatively real (i.e., $\Delta\Phi=0$), in which case it is apparent from eqn. 5 that only the product $\alpha_{\Lambda}\bar{\alpha}_{\Lambda}$ can be measured and individual determinations of $\alpha_{\Lambda}$ and $\bar{\alpha}_{\Lambda}$ cannot be extracted from the data. (Expressions for ${\mathcal{F}}_{1}(\xi)$ and ${\mathcal{F}}_{2}(\xi)$ are provided in ref. Fäldt and Kupsc (2017).)

When BESIII was being planned, it was generally thought that ${\mathcal{P}}_{\Lambda}\approx 0$ and that $J/\psi\rightarrow\Lambda\bar{\Lambda}$ events would not be useful for $CP$ tests. It was somewhat of a surprise when BESIII subsequently discovered that, in fact, the polarization of $\Lambda$ and $\bar{\Lambda}$ hyperons produced in $J/\psi$ decays is substantial Ablikim et al. (2019d), as shown in Fig. 3a. With a sample of 420K fully reconstructed $J/\psi\rightarrow(\Lambda\rightarrow p\pi^{-})(\bar{\Lambda}\rightarrow\bar{p}\pi^{+})$ events in a 1.31B $J/\psi$ event sample, BESIII measured $A_{CP}^{\Lambda}=-0.006\pm 0.012\ \pm 0.007$. This null result improved on the precision of the best previous measurement, $A_{CP}^{\Lambda}=+0.013\pm 0.022$ Barnes et al. (1996), that was based on 96K $p\bar{p}\rightarrow\Lambda\bar{\Lambda}$ events, by a factor of two. As a by-product of this measurement, BESIII made the world’s most precise measurement of $\alpha_{\Lambda}=0.750\pm 0.010$, a result that is more than five standard deviations higher than the previous PDG average value. It is likely that all previous measurements were biased by a common systematic problem, probably related to the spin analyzing properties of carbon; the PDG 2019 value for $\alpha_{\Lambda}$ is solely based on the BESIII value Tanabashi et al. (2018).

The BESIII values for $A_{CP}^{\Lambda}$ and $\alpha_{\Lambda}$ mentioned in the previous paragraph were realized by an analysis of 1.3 B $J/\psi$ decays, which is a small subset of BESIII’s total 10B $J/\psi$ event sample. The analysis of the full data set is currently underway that, when done, will provide a factor-of-three improvement in sensitivity.

BESIII is currently applying a similar analysis to $J/\psi\to(\Xi^{-}\rightarrow\Lambda\pi^{-})(\bar{\Xi}^{+}\rightarrow\bar{\Lambda}\pi^{+})$ hyperon pairs, where preliminary results demonstrate that there is substantial transverse $\Xi$ polarization (see Fig. 3b). In $\Xi^{-}\bar{\Xi}^{+}$ events, the $\alpha_{\Xi}$ decay parameter influences both the up-down decay asymmetry in the primary $\Xi\rightarrow\Lambda\pi$ process, and the polarization of the daughter $\Lambda$ hyperons (see Fig. 3a) that can be determined from the decay asymmetry in the secondary $\Lambda\rightarrow p\pi^{-}$ decay. For a given sample of $J/\psi$ decays, the number of fully reconstructed $\Xi^{-}\bar{\Xi}^{+}$ events in which $\Lambda\rightarrow p\pi^{-}$ and $\bar{\Lambda}\rightarrow\bar{p}\pi^{+}$ are only about one quarter of the number of reconstructed $J/\psi\rightarrow\Lambda\bar{\Lambda}$ events because of the smaller $J/\psi\rightarrow\Xi^{-}\bar{\Xi}^{+}$ branching fraction and a lower detection efficiency. Nevertheless, this lower event number is compensated by the added information from the daughter $\Lambda$ decays. As a result, the sensitivity per event for the $\Xi^{-}$ decay parameters is higher than that for $\Lambda$ parameters with $J/\psi\rightarrow\Lambda\bar{\Lambda}$ events, and simulations show comparable precisions for $\alpha_{\Xi^{-}}$ and $\alpha_{\Lambda}$ Adlarson and Kupsc (2019). In contrast to $\Lambda\rightarrow p\pi$, where measuring the daughter proton’s polarization is impractical, in $\Xi\rightarrow\Lambda\pi$ decays the daughter $\Lambda$ polarization is measured and $B_{CP}^{\Xi^{-}}$ can be determined; $B_{CP}^{\Xi^{-}}$ is potentially more sensitive to new physics than $A_{CP}^{\Xi^{-}}$ Gonzalez and Illana (1994).

In addition to the $\Lambda$ hyperons produced by $J/\psi\rightarrow\Lambda\bar{\Lambda}$, those produced as daughters in $J/\psi\to(\Xi^{-}\rightarrow\Lambda\pi^{-})(\bar{\Xi}^{+}\rightarrow\bar{\Lambda}\pi^{+})$ events are also useful for $A_{CP}^{\Lambda}$ measurements. The rms polarization of $\Lambda$ hyperons produced via $J/\psi\rightarrow\Lambda\bar{\Lambda}$ (see Fig. 3a) is $\langle{\mathcal{P}}_{J/\psi,\Lambda}\rangle_{\rm rms}\approx 0.13$. In contrast, the rms polarization for $\Lambda$ hyperons produced as a daughter particle in $\Xi^{-}\rightarrow\Lambda\pi^{-}$ decay is $\langle{\mathcal{P}}_{\Xi^{-},\Lambda}\rangle_{\rm rms}\approx|\alpha_{\Xi^{-}}|=0.39\pm 0.01$ (see Fig. 2a). Thus, $\langle{\mathcal{P}}_{\Xi^{-},\Lambda}\rangle_{\rm rms}\approx 3\langle{\mathcal{P}}_{J/\psi,\Lambda}\rangle_{\rm rms}$ and, since the $A_{CP}^{\Lambda}$ sensitivity is proportional to $\sqrt{n_{\rm evts}}$ but linear in $\langle{\mathcal{P}}_{\Lambda}\rangle_{\rm rms}$, a $\Lambda$ from $\Xi^{-}\rightarrow\Lambda\pi^{-}$ decay has nine times the equivalent statistical power of a $\Lambda$ from $J/\psi\rightarrow\Lambda\bar{\Lambda}$. Detailed estimates of BESIII’s ultimate statistical error for $A_{CP}$ with the existing 10B $J/\psi$ event sample, including $\Lambda$ hyperons from $\Xi\rightarrow\Lambda\pi$ decays, are reported in ref. Adlarson and Kupsc (2019) and summarized here in Table 3. The projected ultimate $A_{CP}^{\Lambda}$ sensitivity is ${\mathcal{O}}(2\times 10^{-3})$, which is an order of magnitude improvement on the pre-BESIII result Barnes et al. (1996).

The Landau-Yang theorem states that a massive spin 1 meson cannot decay to two photons Landau (1948); Yang (1950). As a consequence, the $J/\psi\rightarrow\gamma\gamma$ decay mode is strictly forbidden. An unambiguous signal for $J/\psi\rightarrow\gamma\gamma$ would signal a breakdown of the spin-symmetry theorem of QFT, the underlying framework of the SM and its many proposed new physics extensions. (For a discussion of how QFT might be modified to accommodate a Landau-Yang theorem violation see ref. Gninenko et al. (2011).)

The PDG 2018 upper limit, ${\mathcal{B}}(J/\psi\rightarrow\gamma\gamma)<1.6\times 10^{-7}$ Tanabashi et al. (2018), is entirely based on a BESIII measurement that uses tagged $J/\psi$ mesons that recoil from the $\pi^{+}\pi^{-}$ system in $\psi(2S)\rightarrow\pi^{+}\pi^{-}J/\psi$ decays Ablikim et al. (2014e), and is a factor of 20 times more sensitive than previous measurements. In a data sample containing 106M $\psi(2S)$ decays, events with two oppositely charged tracks and two $\gamma$-rays that satisfy a four-constraint energy-momentum kinematic fit to the $\pi^{+}\pi^{-}\gamma\gamma$ hypothesis were selected. Figure 4a shows the mass recoiling against the $\pi^{+}\pi^{-}$ tracks where there is a $29\pm 7$ event peak at the $J/\psi$ mass that is consistent with being entirely due to the expected background from roughly equal numbers of $J/\psi\rightarrow\gamma\pi^{0}$ and $\gamma\eta$ events in which the $\pi^{0}$ and $\eta$ decay to a pair of $\gamma$-rays with a large energy asymmetry and the low energy $\gamma$ is undetected either because its energy is below the detection threshold or it outside of the fiducial acceptance region of the detector ($|\cos\theta_{\gamma}|>0.92$).

The discovery of neutrino oscillations Fukuda et al. (1998) provided clear evidence for violations of lepton flavor conservation (LFV) in the neutrino sector. However, the SM translation of the neutrino results to the charged-lepton sector predicts LFV effects that are proportional to powers of the neutrino masses with branching fractions that are immeasurably small ($<10^{-51}$). Thus, any observation of LFV at levels much higher than this would be clear evidence for new physics, such as grand unified (GUT) theories or the presence of extra dimensions. Although most attention is given to LFV searches in muon decay, tau decay and $\mu\rightarrow e$ conversion experiments, in some theories LFV quarkonium decays, including $V\rightarrow\ell^{-}_{i}\ell^{+}_{j}$ decays, where $i\neq j$, are promising reactions Bordes et al. (2001). BESIII searched for the LFV decay $J/\psi\rightarrow e^{-}\mu^{+}$.

The best previous limit was a 2003 BESII result, ${\mathcal{B}}(J/\psi\rightarrow e^{-}\mu^{-})<1.1\times 10^{-6}$ Bai et al. (2003), that was based on an analysis of a sample of $58$M $J/\psi$ events. This was improved by a 2013 BESIII result that used a sample of 230M $J/\psi$ events. In this analysis, the variables $|\sum\vec{p}|/\sqrt{s}$ and $E_{\rm vis}/\sqrt{s}$ are examined for events with two back-to-back and oppositely charged tracks, with one track positively identified as an electron and the other as muon. Events with detected $\gamma$-rays or additional tracks are rejected, and selected events are required to satisfy a four-constraint energy-momentum kinematic fit. The main background is expected to be from $J/\psi\rightarrow\mu^{+}\mu^{-}$ events in which one of the muons passes the electron identification requirements. Figure 5a shows a scatterplot of $|\sum\vec{p}|/\sqrt{s}$ vs. $E_{\rm vis}/\sqrt{s}$ for selected events, where the four events in the signal box are consistent with the $4.75\pm 1.09$ background events that are expected. (This background level corresponds to a muon to electron misidentification probability of $\sim 10^{-7}$.) The 90% CL upper limit of ${\mathcal{B}}(J/\psi\rightarrow e^{-}\mu^{+})<1.6\times 10^{-7}$ that is established Ablikim et al. (2013a) is a factor of seven more stringent than the previous result.