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Front. Phys. 12(5), 121301 (2017) DOI 10.1007/s11467-017-0691-9 Perspective

Prospects for rare and forbidden decays at BESIII

Hai-Bo Li1,2,†

1Institute of High Energy , Beijing 100049, China 2University of Chinese Academy of , Beijing 100049, China Corresponding author. E-mail: †[email protected] Received April 17, 2017; accepted May 8, 2017

The study of hyperon decays at the Beijing Spectrometer III (BESIII) is proposed to inves- tigate the events of J/ψ decay into hyperon pairs, which provide a pristine experimental environment at the Beijing Electron– Collider II. About 106–108 , i.e., Λ, Σ, Ξ, and Ω, will be produced in the J/ψ and ψ(2S) decays with the proposed data samples at BESIII. Based on these samples, the measurement sensitivity of the branching fractions of the hyperon decays is in the range of 10−5–10−8. In addition, with the known center-of- energy and “tag technique”, rare decays and decays with invisible final states can be probed.

Keywords BESIII, J/ψ decay, hyperon, rare decay, FCNC, flavor violation

PACS numbers 13.30.Ce, 14.20.Jn, 11.30.Hv

Contents can be collected with a running period of one year. The inclusive hyperon production rate can reach a few per- 1 Introduction 1 2 Status of BESIII 1 cent in the J/ψ decays, while the hyperon-pair produc- ∼ −3 3 Semileptonic hyperon decays 2 tion rate is 10 . With these data, the decay properties 4 Radiative hyperon decays 3 of the -1/2 octet can be revisited and the de- 5 Rare and forbidden hyperon decays 4 cay parameters with the coherent production of hyperon → ¯ 5.1 B → B l+l− dilepton decays 4 pairs in J/ψ BB decays (where the spin-1/2 hyperon i f pairs are in the 1−− state) can be probed. This survey 5.2 Bi → Bf νν¯ decays via a Z-type penguin 4 5.3 Lepton-number-violating decays with will focus on hyperon decays that can be studied at BE- ∆L = 2 5 SIII and rare decays, for which the search has not yet 5.4 Other decays violating lepton number and begun. 6 6 Summary 6 2 Status of BESIII Acknowledgements 7 References and notes 7 The BESIII detector consists mainly of a cylindrical main draft chamber (MDC) with momentum resolu- tion σ /p ∼0.5% for charged with momen- 1 Introduction pt t tum at 1.0 GeV, a -of-flight (TOF) system with two layers of plastic scintillator counters located out- In this paper, the hyperon physics program at the side of the MDC, and a highly hermetic electromag- Beijing Electron Spectrometer III/Beijing Electron– netic calorimeter√ (EMC) with an energy resolution of Positron Collider II (BESIII/BEPCII) and prospects of σ /E = 2.5%/ E(GeV) [1]. The MDC has its first its upgradation were surveyed. Even with the designed E sensitive layer at a radius of 6.0 cm from the interaction luminosity of the BEPCII, ∼1010 J/ψ and ψ(2S) events point (IP), and the MDC combined with a magnetic field of 1.0 T provides precise momentum measurements of *arXiv: 1612.01775. charged particles with transverse momentum >50 MeV.

© The Author(s) 2017. This article is published with open access at www.springer.com/11467 and journal.hep.com.cn/fop Perspective

BESIII has so far acquired ∼5 × 108 and ∼13 × 108 Table 3 Hyperon production from the J/ψ three-body events on the ψ(2S) and J/ψ peaks, respectively. In the decays with 1010 events on the J/ψ peak and 3×109 events on 10 next few years, by the end of 2018, ∼10 events on the the ψ(2S) peak. NB is the number of the expected hyperon J/ψ peak are going to be collected, and subsequently events. Data are from PDG2016 [3]. ∼3 × 109 events on the ψ(2S) peak will be taken. The B × −4 × 6 expected data samples collected at BESIII/BEPCII per Decay mode ( 10 ) NB ( 10 ) year are summarized in Table 1 [2]. In this paper, the J/ψ → pK−Λ¯ 8.9  1.6 8.9  1.6 −1 sensitivity studies are based on 5 fb luminosity at the J/ψ → ΛΛπ¯ +π− 43  10 43  10 J/ψ or ψ(2S) peaks for probing hyperon decays. − J/ψ → pK Σ¯0 2.9  0.8 2.9  0.8 As indicated in Table 2, the branching fractions for → ¯− +   the J/ψ decays into hyperon pairs are on the order of J/ψ ΛΣ π (or c.c.) 8.3 0.7 8.3 0.7 −∗ 10−3, and ∼107 hyperon pairs can be produced in the J/ψ → ΛΣ¯+π (or c.c.) 8.3  0.7 8.3  0.7 − J/ψ decays per year. The Ω can be only produced J/ψ → pK−Σ¯(1385)0 5.1  3.2 5.1  3.2 in the ψ(2S) decays owing to the allowed phase space, ∗Estimated from . and ∼104–105 Ω−Ω¯+ pairs will be produced per year at BESIII. Since there is always a or a produced from the Σ− hadronic decays or semileptonic decays, one has to use a “tag technique” to look for the − 3 Semileptonic hyperon decays Σ decays. In Table 3, the three-body decays of J/ψ → ΛΣ¯ −π+ + c.c. can be used to study the Σ− decays by ¯ + The Cabibbo–Kobayashi–Maskawa matrix elements looking at the recoiling mass of the Λπ . − |Vud| and |Vus| characterize mixings in d → ue ν¯e − and s → ue ν¯e processes [4, 5] in the (SM). So far the most precise determinations of |Vud| Table 1 τ- production at BEPCII in one-year run | | (107 s). and Vus have been obtained, respectively, from super- allowed Fermi transitions together with decays and Data sample Central-of-mass (MeV) #Events per year from leptonic and semileptonic decays [6–8]. How- ever, hyperon semileptonic decays can also provide inde- J/ψ 3097 10 × 109 pendent constraints on |V | and |V | [9, 10]. + − × 6 ud us τ τ 3670 12 10 In addition one can test the V –A structure [11] of × 9 ψ(2S) 3686 3.0 10 the charged currents in the semileptonic hyperon de- D0D¯ 0 3770 18 × 106 cays [10, 12]. The semileptonic hyperon decays provide D+D− 3770 14 × 106 essential information on the structures of the + − 6 Ds Ds 4030 1.0 × 10 and low-lying hyperons. The data for the semileptonic + − 6 Ds Ds 4170 2.0 × 10 hyperon decays reveal experimentally the pattern of fla- vor SU(3) symmetry breaking [13]. In exact flavor SU(3) symmetry, the ratios of the axial-vector and vector con- Table 2 Hyperon production from the J/ψ or ψ(2S) two- stants g1/f1 are expressed only by the two constants F body decays with 1010 events on the J/ψ peak and 3 × 109 and D. Similarly, those of the vector constants f2/f1 are events on the ψ(2S) peak. NB is the number of the expected written in terms of the anomalous magnetic moments of hyperon events. Data are from the Data the and the neutron with flavor SU(3) symmetry (PDG2016) [3]. assumed [9]. Details of the semileptonic hyperon decay constants can be found in a review paper [9], and recent Decay mode B(×10−3) N (×106) B developments are described elsewhere [14–18]. However, → ¯   J/ψ ΛΛ 1.61 0.15 16.1 1.5 the experimental data for the semileptonic hyperon de- 0 ¯0 J/ψ → Σ Σ 1.29  0.09 12.9  0.9 cays show that the flavor SU(3) symmetry may be mani- − J/ψ → Σ+Σ¯ 1.50  0.24 15.0  2.4 festly broken [14], and further precision data are needed, J/ψ → Σ(1385)−Σ¯+ (or c.c.) 0.31  0.05 3.1  0.5 especially for the decays of Ξ0, Ξ−, and Ω− as listed J/ψ → Σ(1385)−Σ¯(1385)+ (or c.c.) 1.10  0.12 11.0  1.2 in Table 4. The current measured values for the form- J/ψ → Ξ0Ξ¯0 1.20  0.24 12.0  2.4 factor ratio g1(0)/f1(0) in the Cabibbo model [19] are J/ψ → Ξ−Ξ¯+ 0.86  0.11 8.6  1.0 also listed in Table 4. − → 0 − − → 0 − J/ψ → Ξ(1530)0Ξ¯0 0.32  0.14 3.2  1.4 The decays of Σ Σ e ν¯e and Ξ Ξ e ν¯e have not been observed yet. As the lepton pairs (e−ν¯ ) are J/ψ → Ξ(1530)−Ξ¯+ 0.59  0.15 5.9  1.5 e too soft to be detected by the BESIII detector, to study − ¯+ ψ(2S) → Ω Ω 0.05  0.01 0.15  0.03 − 0 − − + + Σ → Σ e ν¯e in the J/ψ → ΛΣ¯ π decay, Λπ¯ can

Hai-Bo Li, Front. Phys. 12(5), 121301 (2017) 121301-2 Perspective

→ Table 4 Allowed baryon transitions Bi Bf eν between were from experiments conducted nearly forty years ago. P 1 + members of the J = 2 SU(3) baryon octet. The present Most of these upper limits can be improved with data status of branching fractions for the semileptonic hyperon from BESIII, and the expected sensitivity ranges from decays from PDG2016 [3] and data for the form-factor ratio 10−6 to 10−5 on these branching fraction measurements. g1(0)/f1(0) in the Cabibbo model [19] are also shown. “−” indicates “not available”.

−4 4 Radiative hyperon decays Decay mode B (×10 ) |∆S| g1(0)/f1(0) Λ → pe−ν¯ 8.32  0.14 1 0.718  0.015 e Since the discovery of hyperons, the nature of (weak) + → +  Σ Λe νe 0.20 0.05 0 – radiative decays still remains an open question [20, 21]. − → −  −  Σ ne ν¯e 10.17 0.34 1 0.340 0.017 Study of weak radiative hyperon decays provides an im- − → −  Σ Λe ν¯e 0.573 0.027 0 – portant tool for investigating the interplay of the elec- − 0 − Σ → Σ e ν¯e – 0 – tromagnetic, weak, and strong interactions. The descrip- 0 + − Ξ → Σ e ν¯e 2.52  0.08 1 1.210  0.050 tion of these processes in terms of well-understood elec- − − Ξ → Λe ν¯e 5.63  0.31 1 0.250  0.050 troweak is complicated by the presence of strong − 0 − interactions [22, 23]. The hyperons in the baryon octet Ξ → Σ e ν¯e 0.87  0.17 1 – − 0 − provide us with multiple reactions of this class with vary- Ξ → Ξ e ν¯e < 23 (90% C.L.) 0 – ing quark content of the initial and final state . Ω− → Ξ0e−ν¯ 56  28 1 – e These decays are listed in Table 6. The transition matrix element T for a general radiative decay of a hyperon Bi of momentum p to a baryon Bf be fully reconstructed as the “tag side”, following an ex- of momentum p′ and a momentum q, amination of the recoiling mass of the Λπ¯ + to clearly − ′ define the Σ signal region; therefore, one can finally Bi(p) → Bf (p ) + γ(q), (1) reconstruct a Σ0 in the rest of the event to represent the − 0 − Σ → Σ e ν¯e signal; namely, the lepton pairs can be is given by [24] missed and reconstructed by examining the tagged sig- − → 0 − → − ¯+ e ′ nals. To study Ξ Ξ e ν¯e in J/ψ Ξ Ξ decay, T = GF √ ϵν u¯(p )(A + Bγ5)σµν qµu(p), (2) one can reconstruct the Ξ¯+ with Ξ¯+ → Λπ¯ + decay as a 4π “tag”, then look at the Ξ− signal on the recoiling mass where u¯(p′) and u(p) are the wave functions of the of the fully reconstructed Ξ¯+, and finally reconstruct a baryon and hyperon, respectively, ϵ is the polarization Ξ0 (with a Ξ0 → Λπ0 mode) to represent the signals. ν vector of the photon, A and B are the -conserving All these analyses will be benefit from the well-known − (M1) and parity-violating (E1) amplitudes, σ and γ center-of-mass energy of the initial e+e collision at BE- µν 5 are the combinations of the Dirac , G SIII/BEPCII. The expected sensitivity on the branching F − − is the Fermi constant, and e is the electron . The fractions will be in the range of 10 5–10 6. For the rare and forbidden semileptonic hyperon de- − cays with ∆S = ∆Q or ∆S = 2, examples are listed Table 6 Present status of branching fractions (B) and in Table 5, with available data from the PDG [3], which parameters (αγ ) for the radiative hyperon decays from PDG2016 [3]. Neither the branching fraction nor the asymmetry parameter for Σ0 → nγ has been measured owing Table 5 Present status of branching fractions (B) for the to its huge electromagnetic partial width. “−” indicates “not ∆S = −∆Q or ∆S = 2 rare semileptonic hyperon decays available”. from PDG2016 [3]. “−” indicates “not available”. −3 Bi → Bf γ B (×10 ) αγ Decay mode B (×10−6)@90% C.L. ∆S Λ → nγ 1.75  0.15 – + + ∗ Σ → ne νe < 5 1 Σ+ → pγ 1.23  0.05 −0.76  0.08 0 − + ∗ Ξ → Σ e νe < 900 1 Σ0 → nγ – – 0 − Ξ → pe ν¯e < 1300 2 0 →  −  − − Ξ Λγ 1.17 0.07 0.70 0.07 Ξ → ne ν¯e < 3200 2 0 0 − − Ξ → Σ γ 3.33  0.10 −0.69  0.06 Ω → Λe ν¯e – 2 − − − 0 − Ξ → Σ γ 1.27  0.23 1.0  1.3 Ω → Σ e ν¯e – 2 Ω− → Ξ−γ < 0.46 (90% C.L.) – ∗∆S = −∆Q process.

Hai-Bo Li, Front. Phys. 12(5), 121301 (2017) 121301-3 Perspective asymmetry parameter is [25] 5 Rare and forbidden hyperon decays 2Re(A∗B) αγ = 2 2 . (3) |A| + |B| + − 5.1 Bi → Bf l l dilepton decays One needs both nonzero A and B amplitudes to get nonzero asymmetry. In the Type A region as listed in Table 7, the decays → + − For a polarized spin-1/2 hyperon decaying radiatively Bi Bf l l (where l = e, µ; i.e., Dalitz decay) can via a ∆Q = 0, ∆S = 1 transition, which is a flavor- be described as proceeding through both short-distance changing-neutral-current (FCNC) process, the angular and long-distance contributions. In the SM, the leading distribution of the direction pˆ of the final spin-1/2 baryon short-distance contribution comes from an FCNC inter- in the hyperon rest frame is action, which is allowed only at loop level [35]. As dis- cussed in Section 4, the decays of B → B e+e− play 0 i f dN N an important role in helping us to understand the dy- = (1 + αγ Pi · pˆ), (4) dΩ 4π namics of radiative hyperon decays, and the decay rates where Pi is the polarization of the decaying hyperon. If are suppressed by two orders of magnitudes if we assume the decaying hyperon is unpolarized, the decay baryon an inner bremsstrahlung-like mechanism producing the + − + − has a longitudinal polarization given by Pf = −αγ [26]. e e pairs [34]. For the decay Bi → Bf µ µ , the pro- There is an old theorem by Hara [27–30] regarding the cess is dominated by long-distance contributions, which ∗ ∗ vanishing of the parity-violating B amplitudes for weak are from the Bi → Bf γ and Bi → Bf V (where V could radiative hyperon decays. According to Hara’s theorem, be ρ/ω vector ) processes, namely, the so-called the relevant parity-violating amplitude should vanish in vector dominant model mechanism [24]. For example, the SU(3) limit. For broken SU(3), according to the the branching fraction of Σ+ → pµ+µ− is predicted to size of -level SU(3)-breaking effects elsewhere, be B(Σ+ → pµ+µ−) ∈ [1.6, 9.0] × 10−8 [35] by consid- one would expect this asymmetry to be of the order of ering the long-distance contributions, while the short- 0.2 [24], and not of the order of −1 as indicated in Ta- distance SM contributions are suppressed at a branch- ble 6. The situation was further confounded by a number ing fraction of ∼10−12. Dalitz decays of hyperons are of theoretical calculations that violated Hara’s theorem of particular interest, as they also allow a direct search (even) in the SU(3) limit [21]. In particular, the large for a new or vector particle, which could lead to asymmetry observed in the decay Σ+ → pγ has been fu- an s → d transition at the tree level [36]. Recently, eling numerous discussions over many years and remains the beauty experiment (LHCb) poorly understood at the parton level [21]. searched for Σ+ → pµ+µ− decay and observed an excess As listed in Table 6, the uncertainty on the asymme- of events with respect to the background expectations try parameter in the Ξ− → Σ−γ decay is still very large with a signal significance of 4.0 standard deviations. No and can be improved, and there is no measurement of significant structure is observed in the dimuon invariant the decay parameter for the Λ → nγ decay yet. The cur- mass distribution. Owing to the difficulty of normaliza- rent data were all from the fixed target experiments more tion in the absence of signal, only an upper limit on the than a few decades ago, and improved or cross-checked branching fraction is set to be 6.3×10−8 at 95% C.L. [37], measurements should be done in the future. BESIII will which agrees with the SM [35], whereas the + − collect ∼10 billion J/ψ events, and the numbers of hy- sensitivities for the decays Bi → Bf l l are estimated peron events from the J/ψ decays are estimated in Ta- to be 10−6–10−7 as listed in Table 7 (Type A) with the bles 2 and 3. BESIII data. In addition to the two-body radiative decays, weak hyperon dilepton decays will provide additional infor- 5.2 Bi → Bf νν¯ decays via a Z-type penguin mation on the radiative transitions [31, 32]. Accord- ing to PDG2016, the only observed hyperon dilepton Analogous to the rare K → πνν¯ decays [38], the rare 0 + − decay is the Ξ → Λe e decay, which is measured Bi → Bf νν¯ decays are important tools for testing the to be B(Ξ0 → Λe+e−) = (7.6  0.6) × 10−6 [33], SM and for searching for possible new physics. As they which is consistent with an inner bremsstrahlung-like proceed through an FCNC process, though they are very production mechanism for the e+e− pair. The consis- suppressed in the SM, they show an exceptional sen- tency is further supported by the e+e− invariance mass sitivity to short-distance physics that is similar to the spectrum. The decay parameter was determined to be K → πνν¯ decays [39, 40]. There are many discussions αΞΛee = −0.8  0.2 [33], which is consistent with that on the new physics models that may contribute to the measured for the Ξ0 → Λγ decay as listed in Table 6. s → dνν¯ transition at the loop or even tree level; for a re- A detailed discussion of radiative dilepton decays is pre- cent review, see Ref. [41]. Unfortunately, no Bi → Bf νν¯ sented in the next section. decays have been searched for experimentally so far. As

Hai-Bo Li, Front. Phys. 12(5), 121301 (2017) 121301-4 Perspective

Γ (K+ → π+νν¯) Γ (Σ+ → pνν¯) Table 7 Rare and forbidden hyperon decays and expected ≈ . (5) sensitivities with 1010 events on the J/ψ peak and 3 × 109 Γ (K+ → π0e+ν) Γ (Σ− → ne+ν) events on the ψ(2S) peak. Type A decay modes are through a photon–penguin-like weak ; Type B decay Thus, in the SM, one can estimate the branching frac- modes are through a Z–penguin-like weak neutral current; tion to be B(Σ+ → pνν¯) ∼ 5 × 10−13 by considering the Type C decay modes are neutrinoless double β decays, which lifetime difference between Σ+ and Σ− and isospin rota- violate lepton number. The current data are from the world tion [42]. Obviously, BESIII cannot reach a sensitivity average in PDG2016 [3]. “−” indicates “not available”. of 10−13. Since the in the final states are “invisible” Current data Sensitivity Decay mode B (×10−6) B (90% C.L.) (×10−6) Type in the detector and, at BESIII, the initial energy and momentum of electron and positron are known, one can Λ → ne+e− – < 0.8 use the “tag technique” to fully reconstruct one of the Σ+ → pe+e− < 7 < 0.4 hyperons and look at the recoil side in the ψ decay into hyperon pairs. It would be interesting to make a first 0 → + −  Ξ Λe e 7.6 0.6 < 1.2 study of the Σ+ → pνν¯ decay, and one should obtain Ξ0 → Σ0e+e− – < 1.3 a sensitivity of 10−8 with 1010 J/ψ decay events. More Type A Ξ− → Σ−e+e− – < 1.0 examples of these decays are listed in Table 7 (Type B), which will be unique accomplishments of the BESIII ex- − → − + − Ω Ξ e e – < 26.0 periment. + → + − +0.09 Σ pµ µ (0.09−0.08) < 0.4 Ω− → Ξ−µ+µ− – < 30.0 5.3 Lepton-number-violating decays with ∆L = 2

Λ → nνν¯ – < 0.3 Nonzero neutrino mass is now well established [43–56]; Σ+ → pνν¯ – < 0.4 therefore, it is crucially important to study the prop- erties of these nonzero-mass neutrinos. One interesting 0 Ξ → Λνν¯ – < 0.8 question is whether neutrinos are Majorana or Dirac neu- Type B Ξ0 → Σ0νν¯ – < 0.9 trinos [57, 58]. Lepton-number-violating (LNV) interac- − − ∗ tions with ∆L = 2 are widely viewed as the most robust Ξ → Σ νν¯ – – test of the Majorana nature of massive neutrinos [57, 58]. − − Ω → Ξ νν¯ – < 26.0 Currently, neutrinoless double β (0νββ) decays of heavy Σ− → Σ+e−e− – < 1.0 nuclei [59] have become the most sensitive way to search for the effects of very light Majorana neutrinos. However, Σ− → pe−e− – < 0.6 theoretical analysis of these processes is complicated by − − − Ξ → pe e – < 0.4 the nuclear matrix elements, which are very difficult to Ξ− → Σ+e−e− – < 0.7 calculate reliably. Here we focus on the ∆L = 2 transi- tions between spin-1/2 hyperons, B− → B+l−l′− (where Ω− → Σ+e−e− – < 15.0 i f l, l′ = e or µ). Examples of these decays are listed in Σ− → pµ−µ− – < 1.1 Table 7 (Type C). Type C Ξ− → pµ−µ− < 0.04 < 0.5 Only one experimental upper limit for the channels listed in Table 7 (Type C) has been reported so far, Ω− → Σ+µ−µ− – < 17.0 namely, B(Ξ− → pµ−µ−) < 4.0 × 10−8. In the case Σ− → pe−µ− – < 0.8 of the decays listed in Table 7 (Type C), two down-type Ξ− → pe−µ− – < 0.5 (d or s) quarks convert into two up-, changing the charge of hyperons according to the ∆Q = ∆L = +2 − → + − − Ξ Σ e µ – < 0.8 rule. These quark transitions are assumed to occur at Ω− → Σ+e−µ− – < 17.0 the same space-time location and, therefore, they are driven by local four-quark operators [60–62]. Thus the ∗ − − − It is hard to reconstruct the Ξ → Σ νν¯ decay since the Σ de- study of the relatively simpler case provided by 0νββ cays into final states including neutron. Thus both neutron and neutrinos can not be detected at BESIII, and the “tag technique” hyperons decays may shed some light on the approxi- will not work. mations used to evaluate the hadronic matrix elements relevant for similar nuclear decays [60–62]. In Ref. [61], based on the model where Σ− → pe−e− decay is induced an example, assuming that the decay Σ+ → pνν¯ is dom- by a loop of baryons and light Majorana neutrinos, the inated by the short-distance contribution, one can make predicted branching fraction for Σ− → pe−e− decay, as an estimation based on the following relation [38, 42]: an example, is <10−33, whereas, in Ref. [62], based on a

Hai-Bo Li, Front. Phys. 12(5), 121301 (2017) 121301-5 Perspective

model with four-quark operators, the predicted branch- Table 8 Lepton- or baryon-number-violating hyperon de- ing fraction is <10−23, which is still too small to be ob- cays and expected sensitivities with 1010 events on the J/ψ served in any future high-intensity experiment. Thus, peak and 3×109 events on the ψ(2S) peak. The current data any observable rates for these decays must indicate a are from CLAS [68] as listed in PDG2016 [3]. “−” indicates “not available,” l = e or µ, and M  refers to the charged sta- new interaction beyond the SM.    It will be very interesting to search for the B− → ble mesons (M = π or K ). Each reaction shows evidence i of ∆L = 1 or/and ∆B ≠ 0, and each reaction conserves B+e−e− decays at BESIII with 1010 J/ψ decay into f and angular momentum. hyperon–antihyperon final states, which will produce 107–108 hyperons. Therefore, the sensitivities will be −7 Current data Sensitivity on the order of 10 with clean backgrounds. Note that Decay mode B (×10−6) (90% C.L.) B (×10−6) ∆L ∆B the decays of B− → B+µ−µ− can be also searched for i f − at LHCb with higher sensitivities owing to the huge pro- Λ → pl – < 0.05 +1 0 duction cross section there. Σ+ → nl+ – < 0.5 −1 0 Σ0 → pl− – < 0.03 +1 0 5.4 Other decays violating lepton number and baryon − → − number Σ nl – < 1.0 +1 0 Ξ0 → pl− – < 0.1 +1 0 The SM has been proved to be extremely successful. As 0 → + − we discussed in Section 5.3, the nonzero neutrino mass Ξ Σ l – < 0.3 +1 0 indicates that the lepton number (L) may be violated. Ξ0 → Σ−l+ – < 1.0 −1 0 There are also a number of reasons to consider baryon Ξ− → Λl− – < 0.2 +1 0 number violation: (i) there is a suggestion originally Ξ− → Σ0l− – < 0.5 +1 0 from Sakharov theory that CP violation combined with a − → − baryon-number-violating (BNV) interaction can explain Ω Λl – < 13 +1 0 the baryon asymmetry of the universe [63]; (ii) many Ω− → Σ0l− – < 14 +1 0 grand unified theories allow the proton to decay [64–66]; Ω− → Ξ0l− – < 16 +1 0 (iii) B–L is an important symmetry and, therefore, if Λ → M +l− < 0.4–3.0 [68] < 0.1 +1 −1 ∆L exists, there is also a ∆B interaction. In particu- − lar, in the SM, in the electroweak phase transition, there Λ → M l+ < 0.4–3.0 [68] < 0.1 −1 −1 is a possibility of a ∆B, ∆L transition that conserves Λ → KS ν < 20 [68] < 0.6 +1 −1 B–L, an essential component of theories of + + Σ → KS l – < 0.2 −1 −1 [67]. Recently, searches for the BNV and LNV decays Σ− → K l− – < 1.0 +1 −1 of Λ were performed by the CLAS experiment [68] by S − → − − using a data set for photoproduction off of the proton Ξ KS l – < 0.2 +1 1 collected with the CLAS detector at Jefferson Labora- Ξ0 → M +l− – < 0.1 +1 −1 ∼ × 6 → + tory containing 1.8 10 reconstructed γp K Λ Ξ0 → M −l+ – < 0.1 −1 −1 events. The sensitivities on the branching fraction for 0 → − each of the processes studied ranged from 7 × 10−7 to Ξ KS ν – < 2.0 +1 1 2 × 10−5 [68]. All BNV and LNV decays can be further studied with data from J/ψ decay into hyperon pairs as listed in Table 8. Some of them (Σ and Ξ hyperon de- cays) were never searched for, and the sensitivities will 6 Summary be 10−7 or better. In addition, baryon-number viola- tion with ∆B = 2 processes can be searched for in the Ever since the discovery of hyperons and of their weak Λ → pπ¯ + decays that were also presented by the CLAS decays it has been a challenge to measure with precision experiment [68] for the first time. At BESIII, possible the properties of their decays and to test the SM and be- baryon-number-violation can be probed in J/ψ → ΛΛ¯ yond. Hyperon semileptonic and radiative decay are still decay with better sensitivity than that of CLAS. Fur- a challenge on both experimental and theoretical fronts. thermore, Λ–Λ¯ oscillations can be investigated by using The rare and forbidden hyperon decays will play impor- coherent productions of Λ pairs in J/ψ → ΛΛ¯ decay; for tant role in the search for new physics [3, 71–82]. In details, see Refs. [69, 70]. this paper, we propose studying hyperon decays at BE- In conclusion, the search for baryon and lepton num- SIII with events in the J/ψ or ψ(2S) decay into hyperon ber nonconservation represents an important probe of pairs. We learned that the two-body decays of the J/ψ physics beyond the SM and particularly new physics at and ψ(2S) will provide a pristine experimental environ- a very high mass scale. ment; especially, rare decays and decays with invisible

Hai-Bo Li, Front. Phys. 12(5), 121301 (2017) 121301-6 Perspective

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