Search for rare decay $J/ \psi \to \phi e^+ e^-$

TL;DR

This study searches for the rare decay $J/\psi \to \phi e^+ e^-$ using a large dataset, finds no signal, and sets an upper limit on its branching fraction, which is still above Standard Model expectations.

Contribution

First search for the decay $J/\psi \to \phi e^+ e^-$ with a large dataset, establishing an upper limit on its branching fraction.

Findings

No signal observed for the decay.

Upper limit on branching fraction set at $1.2 \times 10^{-7}$.

Limit is about ten times higher than Standard Model prediction.

Abstract

Using a data sample of $448.1\times10^6$ $\psi(3686)$ events collected at $\sqrt{s}=$ 3.686 GeV with the BESIII detector at the BEPCII, we search for the rare decay $J/\psi \to \phi e^+ e^-$ via $\psi(3686) \to \pi^+\pi^- J/\psi $. No signal events are observed and the upper limit on the branching fraction is set to be $\mathcal{B}(J/\psi \to \phi e^+ e^-) < 1.2 \times 10^{-7}$ at the 90\% confidence level, which is still about one order of magnitude higher than the Standard Model prediction.

Tables

Table 1. Table 1: Summary of relative systematic uncertainties (in %).

Sources	Uncertainty
$N_{\psi \left(3686\right)}^{\mathrm{tot}}$	0.7
Tracking	6.0
PID	2.3
Kinematic fit	3.3
Signal region	1.8
Background estimation	1.5
MC statistics	0.4
MC modeling	5.4
$ℬ\left(\psi \left(3686\right)\to {\pi }^{+}{\pi }^{-}J/\psi \right)$	0.9
$ℬ\left(\varphi \to K^{+}{K}^{-}\right)$	1.0
Total	9.5

Table 2. Table 2: Input values used to obtain the upper limit on the branching fraction of J / ψ → ϕ ​ e + ​ e − → 𝐽 𝜓 italic-ϕ superscript 𝑒 superscript 𝑒 J/\psi\to\phi e^{+}e^{-} . N obs superscript 𝑁 obs N^{\rm obs} , N bkg superscript 𝑁 bkg N^{\rm bkg} and N up superscript 𝑁 up N^{\rm up} represent the number of observed events, background events, and the upper limit on the number of observed events, respectively.

Item	Value
$N_{\psi \left(3686\right)}^{\mathrm{tot}}$	$\left(448.1\pm 2.9\right)\times {10}^6$
$N^{\mathrm{obs}}$	$0$
$N^{\mathrm{bkg}}$	$1.6\pm 1.1$
$N^{\mathrm{up}}$(90% CL)	$1.31$
$ϵ$	$\left(15.13\pm 0.05\right)$%
$ℬ\left(\psi \left(3686\right)\to {\pi }^{+}{\pi }^{-}J/\psi \right)$	$\left(34.49\pm 0.30\right)$%
$ℬ\left(\varphi \to K^{+}{K}^{-}\right)$	$\left(48.9\pm 0.5\right)$%
${\Delta }_{\mathrm{sys}}$	9.5%
$ℬ\left(J/\psi \to \varphi e^{+}{e}^{-}\right)$

Equations

$$\mathcal{B}(J/\psi \to \varphi e^{+}{e}^{-})<\frac{N^{\mathrm{up}}\times (1+N^{\mathrm{up}}\times {\Delta }_{\mathrm{sys}}^2/2)}{N_{\psi (3686)}^{\mathrm{tot}}\times ϵ\times \prod {\mathcal{B}}_i},$$

$$\mathcal{B}(J/\psi \to \varphi e^{+}{e}^{-})<1.2\times 10^{-7}.$$

Full text

I INTRODUCTION

The BESIII experiment has accumulated $4.48\times 10^{8}$ $\psi(3686)$ events which is the largest $\psi(3686)$ data sample produced directly in $e^{+}e^{-}$ annihilation in the world currently. By tagging the two soft pions in the decay of $\psi(3686)\to\pi^{+}\pi^{-}J/\psi$, the final states from $J/\psi$ decay can be well distinguished. This provides an almost background free sample to investigate the rare $J/\psi$ decay, which may be sensitive to new physics. The rare decay $J/\psi\to\phi e^{+}e^{-}$ is one particulary interesting example guoxd . This decay channel occurs mainly through the three dynamic processes shown in Figs. 1(a)-(c). These include: (a) the leading-order electromagnetic (EM) process; (b) the EM and strong mixed loop process; and (c) the EM process proceeding through three virtual photons. In diagram (b), the non-perturbative strong loop can be treated as proceeding through intermediate mesons, as discussed in Ref. guoxd . Within the framework of the Standard Model (SM), the partial widths from the leading EM and mixed loop processes are predicted to be at a level of $10^{-6}$ and $10^{-9}$ keV, respectively, corresponding to branching fractions at the order of $10^{-8}$ and $10^{-11}$ guoxd . However, if there is a new particle involved in the intermediate process, such as a dark photon with a mass of several MeV/$c^{2}$ or a glueball with certain quantum numbers, contribution from Fig. 1(b) can be enhanced greatly. Thus, any deviations from the predictions guoxd would hint at the existence of new physics. Alternatively, if a positive result were obtained with a branching fraction in the expected range, this decay channel could be used to extract information of some interesting mesons such as $f_{0}(980)$ or $a_{0}(980)$ since their form factors are involved in the predictions.

Although BESIII has also available the currently world’s largest data sample of directly produced $J/\psi$, this is not used in the present analysis due to badly-controlled background contamination from QED processes. In this work, we report on search for the rare decay of $J/\psi\to\phi e^{+}e^{-}$ via $\psi(3686)\to\pi^{+}\pi^{-}J/\psi$.

II BESIII AND BEPCII

The BESIII detector bes3 at the BEPCII $e^{+}e^{-}$ collider is a major upgrade of the BESII experiment bes2 at the Beijing Electron-Positron Collider (BEPC) and is optimized to study physics in the $\tau$-charm energy region. The design peak luminosity of BEPCII, $1.0\times 10^{33}$ cm*-2s-1* at a center-of-mass energy of $3773$ MeV, was achieved in 2016. The BESIII detector, with a geometrical acceptance of $93$% of the full solid angle, consists of the following five main components. $(1)$ A small-celled multi-layer drift chamber (MDC) with $43$ layers is used for charged track reconstruction and measurement of ionization energy loss ($dE/dx$). The average single-wire resolution is $135$ $\mu$m, and the momentum resolution for $1.0$ GeV/$c$ charged particles in a $1$ T magnetic field is $0.5$%. The specific $dE/dx$ resolution is 6% for electrons from Bhabha scattering. $(2)$ A time-of-flight (TOF) system surrounds the MDC. This system is composed of a two-layer barrel, each layer consisting of $88$ pieces of $5$ cm thick and $2.4$ m long plastic scintillators, as well as two end caps each with $96$ fan-shaped, $5$ cm thick, plastic scintillators. The time resolution is $80$ ps in the barrel and $110$ ps in the end caps, providing a $K/\pi$ separation of more than $2\sigma$ for momenta up to $1.0$ GeV/$c$. $(3)$ An electromagnetic calorimeter (EMC) is used to measure photon energies and consists of $6240$ CsI(Tl) crystals in a cylindrically-shaped barrel and two end caps. For $1.0$ GeV photons, the energy resolution is $2.5$% in the barrel and $5$% in the end caps, and the position resolution is $6$ mm in the barrel and $9$ mm in the end caps. $(4)$ A superconducting solenoid magnet surrounding the EMC provides a 1 T magnetic field. $(5)$ The muon chamber system is made of resistive plate chambers with $9$ layers in the barrel and $8$ layers in the end caps and is incorporated into the return iron yoke of the superconducting magnet. The global position resolution is about $2$ cm.

Interactions within the BESIII detector are simulated by the GEANT4-based geant4 simulation software boost boost , which includes: geometric and material descriptions of the BESIII detector; detector response and digitization models; and a record of detector running conditions and performances. The production of the $\psi(3686)$ resonance is simulated by the Monte Carlo (MC) generator KKMC kkmc , which incorporates the effects of the energy spread of the beam and initial-state radiation. Known decays are generated by EVTGEN evtgen using the branching fractions quoted by the Particle Data Group (PDG) pdg18 , and the remaining unknown decays are generated with the LUNDCHARM model lundcharm .

In this analysis, the process $J/\psi\to\phi e^{+}e^{-}$ is studied via $\psi(3686)\to\pi^{+}\pi^{-}J/\psi$, and the $\phi$ meson is reconstructed using its decay to $K^{+}K^{-}$. The transition $\psi(3686)\to\pi^{+}\pi^{-}J/\psi$ is generated according to the results of an amplitude analysis as described in Ref. bes2jpsipipi . The process $J/\psi\to\phi e^{+}e^{-}$ is generated according to the amplitude given in Ref. guoxd , in which the leading-order EM process is expected to be the dominant contribution according to the SM prediction. The spin correlation of $J/\psi$ produced in the previous decay is considered as in Ref. lifengyun . The decay $\phi\to K^{+}K^{-}$ is generated using a $\sin^{2}\theta_{K}$ distribution, where $\theta_{K}$ is the helicity angle of the kaon in the center-of-mass system of the $\phi$ meson.

III Event Selection

Charged tracks are reconstructed with MDC hits within the range $|\cos\theta|<0.93$, where $\theta$ is the polar angle with respect to the electron beam direction. They are required to originate from the interaction region, defined as $R_{xy}<1$ cm and $R_{z}<10$ cm, where $R_{xy}$ and $R_{z}$ are the projections of the distances from the closest approach of the tracks to the interaction point in the $xy$-plane and in the $z$-direction, respectively.

Particle identification (PID) probabilities for good charged tracks are calculated with the $dE/dx$ and TOF measurements under the hypothesis that the track originated from a pion, kaon, proton or electron. For kaon candidates, we require that the probability for the kaon hypothesis is larger than the corresponding probability for the pion and proton hypotheses. For electron candidates, the probability for electron hypothesis is required to be larger than the probabilities for the pion and kaon hypotheses. To avoid contamination from pions, electron candidates must satisfy the additional requirement $E/p>0.8$, where $E$ and $p$ represent the energy deposited in the EMC and the momentum of the electron, respectively.

For the two pions, no PID selection criterion is required. All pairs of opposite charged tracks with momentum less than $0.45$ GeV/$c$ are assumed to be pions, and their recoil masses $M_{\pi^{+}\pi^{-}}^{\rm rec}$ are calculated and required to be within the range $(3.05,3.15)$ GeV/$c^{2}$.

To improve the mass resolution and suppress backgrounds, an energy-momentum constrained kinematic fit ($4$C) to the initial beam four momentum is imposed on the selected charged tracks. The resulting $\chi^{2}_{4\rm C}$ of the kinematic fit is required to be less than $40$. If more than one combination is found in an event, the combination with the least $\chi^{2}_{4\rm C}$ is retained for further analysis.

IV Analysis

The process $J/\psi\to\phi e^{+}e^{-}$ is studied by examining the two-dimensional distribution of the $M_{\pi^{+}\pi^{-}}^{\rm rec}$ versus the invariant mass of the $K^{+}K^{-}$ pair, $M_{K^{+}K^{-}}$. Figure 2(a) shows the distribution for the signal MC sample, where the signal region (shown as a red solid box) is defined as $|M_{K^{+}K^{-}}-M_{\phi}|<0.010$ GeV/$c^{2}$ and $|M^{\rm rec}_{\pi^{+}\pi^{-}}-M_{J/\psi}|<0.007$ GeV/$c^{2}$, where $M_{\phi}$ and $M_{J/\psi}$ are the nominal masses of $\phi$ and $J/\psi$ mesons in taken from PDG pdg18 , respectively. The five boxes with equal area around the signal region are selected as sideband regions, which are categorized into three types. The first type is used to estimate the background without a $J/\psi$ in the intermediate state; the second one is for the estimation of the background without a $\phi$ in the intermediate state. These first two are shown as the pink dashed boxes and the green dashed double dotted box, respectively. The third type is for the estimation of the background that includes neither a $J/\psi$ nor a $\phi$ in the intermediate state, and is shown as blue dashed dotted boxes. Figure 2(b) shows the corresponding plot for the $\psi(3686)$ data sample. No events are observed in the signal region and two events are observed in the $\phi$ sideband. The non-flat non-$\phi$ background, mainly due to the threshold effect, is estimated by $\psi(3686)\to\pi^{+}\pi^{-}J/\psi$ with $J/\psi\to\phi\pi^{+}\pi^{-}$ and $\phi\to K^{+}K^{-}$. The scale factor is determined to be $0.8$ for the background in the $\phi$ signal region to that in the $\phi$ sideband region. Therefore, the scaled background estimated by the sideband data is $1.6\pm 1.1$ events. The projections of Fig. 2(b) on $M^{\rm rec}_{\pi^{+}\pi^{-}}$ and $M_{K^{+}K^{-}}$ are shown in Figs. 3(a) and (b), respectively.

The backgrounds from $\psi(3686)$ decays are also studied with an inclusive MC sample of 506 million $\psi(3686)$ events. No events survive in the signal region, and only one event is found in the second type of sideband region. This event is from $\psi(3686)\to\pi^{+}\pi^{-}J/\psi,J/\psi\to K^{+}K^{-}\pi^{0},\pi^{0}\to\gamma e^{+}e^{-}$, which will not form a peak in $\phi$ signal region. In addition, the potential peaking backgrounds from $\psi(3686)\to\pi^{+}\pi^{-}J/\psi$ with $J/\psi\to\phi\eta/\pi^{0}$ and $\eta/\pi^{0}\to\gamma e^{+}e^{-}$ are studied through exclusive MC events generated with a size corresponding to more than 100 times of that of data. The contribution from these channels is negligible.

Possible background sources from continuum processes are estimated with $44$ pb*-1* of data collected at a center-of-mass energy $\sqrt{s}=3.65$ GeV condata , which is about one fifteenth of the integrated luminosity of the $\psi(3686)$ data. There are no events satisfying the above selection criteria, therefore we neglect the continuum background.

V Systematic Uncertainties

The systematic uncertainties originate mainly from the number of $\psi(3686)$ events, the tracking efficiency, the PID efficiency, the kinematic fit, the selection of the $J/\psi$ and $\phi$ signal regions, background estimation, MC statistics, and the branching fractions of intermediate decays. These are discussed in detail in the following, and are summarized in Table 1.

The uncertainty from the total number of $\psi(3686)$ events is estimated to be $0.7$% npsip .

The tracking efficiencies for $\pi^{\pm}$ mesons have been studied with the process $\psi(3686)\to\pi^{+}\pi^{-}J/\psi$, $J/\psi\to\ell^{+}\ell^{-}(\ell=e,\mu)$. The difference in the efficiencies between data and MC simulation is $1.0$% per pion ktrkpid . The tracking efficiencies for $K^{\pm}$ mesons as functions of transverse momentum have been studied with the process $J/\psi\to K_{S}^{0}K^{\pm}\pi^{\mp}$, $K_{S}^{0}\to\pi^{+}\pi^{-}$. The difference in the efficiencies between data and MC simulation is $1.0$% per kaon ktrkpid . The tracking efficiencies for $e^{\pm}$ are obtained with a control sample of radiative Bhabha scattering $e^{+}e^{-}\to\gamma e^{+}e^{-}$ (including $J/\psi\to\gamma e^{+}e^{-}$ ) at the $J/\psi$ resonance in Ref. etrk . The difference in tracking efficiencies between data and MC simulation is calculated bin-by-bin over the distribution of transverse momentum versus the polar angle of the lepton tracks. The uncertainty is determined to be $1.0$% per electron/positron. The systematic uncertainties arising from the different charged tracks are summed linearly to be $6.0$%.

High purity control samples of $e^{+}e^{-}\to\gamma e^{+}e^{-}$ and $J/\psi\to K^{+}K^{-}\pi^{0}$ have been selected to study the electron/positron and kaon PID uncertainty. The difference of PID efficiency between data and MC simulation is calculated in bins of momentum and cos$\theta$. Averaged systematic uncertainties for electron/positron and kaon identification are obtained by weighting the difference with the events in each bin of momentum and cos$\theta$ from the signal MC sample, and determined to be $0.4$% per electron/positron and $0.8$% per kaon. Adding these values linearly, the PID systematic uncertainty is determined to be $2.4$%.

The systematic uncertainty of the $4$C kinematic fit is studied using a control sample of $\psi(3686)\to\pi^{+}\pi^{-}J/\psi$ with $J/\psi\to\phi\pi^{+}\pi^{-}$, $\phi\to K^{+}K^{-}$. The efficiency difference between data and MC simulation with the $\chi^{2}_{\rm 4C}<40$ requirement is $3.3$%, which is assigned as the systematic uncertainty.

The uncertainty from the signal regions of $M_{K^{+}K^{-}}$ and $M^{\rm rec}_{\pi^{+}\pi^{-}}$, due to their resolution difference between data and MC simulation, is studied by means of the control sample $\psi(3686)\to\pi^{+}\pi^{-}J/\psi$, $J/\psi\to\phi\pi^{+}\pi^{-}$, $\phi\to K^{+}K^{-}$. The efficiency differences in the $M_{K^{+}K^{-}}$ and $M^{\rm rec}_{\pi^{+}\pi^{-}}$ signal regions between data and MC simulation are $0.2$% and $1.8$%, respectively. Adding them in quadrature yields $1.8$%, which is taken as the systematic uncertainty.

The uncertainty on the background estimation is studied by an alternative estimation of the scale factor ($0.74$), estimated using the inclusive MC sample instead of data. The difference between the resulting upper limits is taken as the systematic uncertainty, which is $1.5$%.

The uncertainty of the detection efficiency attributed to the limited size of the MC sample, $0.4$%, is taken as the systematic uncertainty from MC statistics.

To estimate the uncertainty from the model used to simulate the $J/\psi\to\phi e^{+}e^{-}$ decay, we generated a MC sample based on the phase-space assumption. The difference between the efficiencies determined from the MC sample described in Sec. II and the phase space MC sample is $10.7$%. We take half of the difference ($5.4$%) as the systematic uncertainty from MC modeling.

In the determination of the upper limit on the branching fraction of the process of interest, we have accounted for the branching fractions of $\psi(3686)\to\pi^{+}\pi^{-}J/\psi$ and $\phi\to K^{+}K^{-}$ by taking the values given by the PDG pdg18 . The uncertainties of these cited values are taken as a source of systematic uncertainty, which are $0.9$% and $1.0$%, respectively.

The total systematic uncertainty, $\Delta_{\rm sys}$, is calculated by adding the uncertainties from all sources in quadrature.

VI Result

Since no candidate events are observed in the signal region and $1.6\pm 1.1$ background events are estimated, the upper limit on the number of $\psi(3686)\to\pi^{+}\pi^{-}J/\psi$ events with $J/\psi\to\phi e^{+}e^{-}$ is set to be $1.31$ at the $90$% confidence level (CL) using the Feldman-Cousins feldman method with the assumption of a Poisson process.

After taking into account the systematic uncertainty cousins , the upper limit of the branching fraction of $J/\psi\to\phi e^{+}e^{-}$ is calculated with

[TABLE]

where $N^{\rm tot}_{\psi(3686)}$ is the number of $\psi(3686)$ events, $\prod\mathcal{B}_{i}$ represents the branching fraction product $\mathcal{B}(\psi(3686)\to\pi^{+}\pi^{-}J/\psi)\times\mathcal{B}(\phi\to K^{+}K^{-})$ and $\epsilon$ is the detection efficiency, which is $(14.31\pm 0.05)$% determined by MC simulations as described in Sec. II. Table 2 summarizes the various values that were used as input to Eq. (1). We find an upper limit on the branching fraction of the $J/\psi\to\phi e^{+}e^{-}$ process at the 90% CL of

[TABLE]

VII Summary

Using the $448.1\times 10^{6}$ $\psi(3686)$ events collected with the BESIII detector, we report a search for the rare decay $J/\psi\to\phi e^{+}e^{-}$ via $\psi(3686)\to\pi^{+}\pi^{-}J/\psi$. No signal events are observed and the upper limit of the branching fraction for this decay is calculated to be $\mathcal{B}(J/\psi\to\phi e^{+}e^{-})<1.2\times 10^{-7}$ by the Feldman-Cousins method at the $90$% CL, which is one order of magnitude higher than the prediction in Ref. guoxd . Our result shows that, even if there are new particles involved in the Fig. 1(b) process, their contributions will not be too large, and the masses of the possible existing new particles or their coupling information to vector mesons ($J/\psi$ and $\phi$) can also be constrained.

VIII Acknowledgements

The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National Key Basic Research Program of China under Contract No. 2015CB856700; National Natural Science Foundation of China (NSFC) under Contracts Nos. 11575077, 11475090, 11235011, 11335008, 11425524, 11625523, 11635010, 11735014, 11835012; the Outstanding Youth project of Natural Science Foundation of Hunan Province; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; Joint Large-Scale Scientific Facility Funds of the NSFC and CAS under Contracts Nos. U1532257, U1532258, U1732263, U1832207; CAS Key Research Program of Frontier Sciences under Contracts Nos. QYZDJ-SSW-SLH003, QYZDJ-SSW-SLH040; 100 Talents Program of CAS; INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG under Contract No. Collaborative Research Center CRC 1044; Istituto Nazionale di Fisica Nucleare, Italy; Koninklijke Nederlandse Akademie van Wetenschappen (KNAW) under Contract No. 530-4CDP03; Ministry of Development of Turkey under Contract No. DPT2006K-120470; National Science and Technology fund; The Knut and Alice Wallenberg Foundation (Sweden) under Contract No. 2016.0157; The Swedish Research Council; U. S. Department of Energy under Contracts Nos. DE-FG02-05ER41374, DE-SC-0010118, DE-SC-0012069; University of Groningen (RuG) and the Helmholtzzentrum für Schwerionenforschung GmbH (GSI), Darmstadt.