Significance of Strangeness Conservation/Violation Studies at BESIII

Home , Strange particle

Proceedings of the Pakistan Academy of Sciences: Pakistan Academy of Sciences A. Physical and Computational Sciences 55 (2): 1–11 (2018) Copyright © Pakistan Academy of Sciences ISSN: 2518-4245 (print), 2518-4253 (online) Review Article

Aneela Amin1 , Khadija Saeed1, Farzana Younas1, and Ghalib ul Islam2 ∗ 1Centre for High Energy Physics, University of the Punjab, Lahore (54590), Pakistan 2Department of Physics, The University of Lahore, Lahore (53700), Pakistan

Abstract Strangeness violation and conservation have been studied in Charmonia and its higher state decays. The data of some prominent decay modes has been collected from BESIII laboratory from the years 2009 to date. The strangeness violating decays play an important role in the study of weak interactions. On the other hand, strangeness conserving decays describe the strong interactions. An overview of strangeness conserving decays and strangeness violating decays has been given and the decay modes are presented in tabular form. The study reveals that associated production occurs only in strangeness conserving decays rather than strangeness violating decays. Experimental and theoretical results are presented in order to arrange phenomenological developments and queries may search new domains in Experimental High Energy Physics, and will explore new prospects of strangeness, a basic quantum number of hadrons and its associated production.

Keywords: Strangeness, Charmonia, Strangeness conserving decays, Strangeness violating decays, Standard model

1. INTRODUCTION described the interactions among these particles known as Standard Model. According to The study of particles and the interaction between Standard Model, three types of interactions exist them shows that quarks and leptons are the basic among these particles i.e. electromagnetic, strong constituents of matter [1]. These quarks exist in and weak interaction [4-5]. bound states. There are six type of quarks, named as, up , down , strange , charm , In this paper, all those decay processes have bottom , top quark. Similarly, there are six been studied in which strangeness exists. These type of leptons , electron , muon and tau processes involve strange baryons and strange alongwith their neutrinos electron neutrinos , mesons and the list of these strange mesons and muon neutrino and tau neutrino [2]. baryons are listed in Table 1 and Table 2

respectively. The data involving strangeness has

According to the quark model, these quarks been collected from BESIII Laboratory for the are combined together to form hadrons. Hadrons period 2009 to 2017. It was observed that some are strongly interacting particles and are divided decay processes are those in which law of into two categories, named as, Baryons and conservation of strangeness holds. This fact is Mesons [3]. In 1960, these particles are arranged according to the theory of Standard Model. On the in Eightfold way-classification according to their other hand, some strangeness violating reactions quantum numbers. Baryons consist of three quarks have also been observed in BESIII, which show or three anti-quarks. Mesons consist of a quark that evidences for the strangeness violations are and anti-quark. The baryons and mesons are increasing day by day. Such kind of decays, arranged into octets and decuplets according to showing weak interactions are discussed and their spin, charge and strange quantum numbers. highlighted in many decay modes in BESIII and This classification of baryon and meson is shown their branching fractions have also been reported. in the Fig. 1 to Fig. 4. An important property of strangeness, called associated production, has also been introduced In 1970, a new theory was predicted which which is very prominent in the strangeness

———————————————— Received, December 2017; Accepted, June 2018 * Corresponding Author: Aneela Amin; [email protected] 2 Aneela Amin et al

conserving decays of Charmonia. The decays modes showing associated production are listed in the Table 3(a) to 3(d). These decay modes are governed by strong interactions only [2].

Here is the baryon with mass The data consisting of strangeness conserving [6] . Since baryon is very unstable decays and strangeness violating decays along particle, so it decays further into some other with their branching fractions have been arranged particles as shown in the following reaction; in the Table 3(a) to 3(d) and Table 4(a) to 4(e).

2. Strangeness Baryon number is conserved in this reaction,

Strangeness „S‟ [6] is a quantity associated with all therefore should decay via strong interaction hadrons. Strangeness is basically an additive and its life time should be of the order quantum number. Like baryon number, lepton of . But it has been observed that number, this quantum number is assigned to all its decay time is of the order of hadrons named as strangeness quantum number. It which is approximately equal to the life time of became necessary to introduce this quantum weak decays. So baryon deca ys via weak number for the study of properties of particles. interaction and it shows strange behavior [6]. The reasons for introducing this quantity are few reactions which are quite different in nature from A similar strange behavior has been observed the other decay processes. For example, in the in the decay of kaon meson. This reaction is also following reaction, a proton and pion interacts given below; very strongly to produce a baryon.

Figure 1. The spin ½ baryons arranged in baryon octet Figure 2. The spin 3⁄2 baryons arranged in baryon decu- [4-5] plets [4-5].

Figure 3. The meson nonet with spin 0 [4-5] Figure 4. The meson nonet with spin 1 [4-5] Study of Strangeness at BESIII 3

This decay has baryon number . So it the section below. must be carried out via strong interaction. But this does not happen. Its life time is again observed to 3. Associated Production and its Significance be rather than which shows In 1952, Abraham Pais observed some neutral that it is a weak decay. Again, this is the Strange 0 particles (V ‟s) produced in cloud chamber with Behavior [6]. Strangeness [6] leads to a new -27 2 conservation law. This law is known as Law of larger cross section (~ 10 cm ) and these particles decayed through smaller cross section (~ Conservation of Strangeness. -40 2 10 cm ) [6]. This phenomenon happened in Strangeness values could be 0, 1, -1. The strange particles as strange particles are produced abundantly having life time of 10-23 seconds but strangeness quantum number violates in those -10 reactions which do not decay via strong interaction their decay time is relatively slow about 10 but this quantum number is conserved in strong seconds. This shows that their production interactions. The results of three reactions mechanism is different from their disintegration indicating the strangeness conservation and mechanism. So one can say that strong force strangeness violation as under; governs the production of strange particles whereas weak force is responsible for their decay. So if a strange particle is produced in strong (decays via strong interaction) interaction, they are always produced in pairs of particles of opposite strangeness so as to conserve (decays via weak intercation) the total strangeness. This phenomenon is called (decays via weak interaction) Associated Production [6].

It has been observed from the above three Some strange mesons have been listed in the reactions that law of strangeness is violated in the Table 1 along with their quark contents and processes which decay through weak interactions strangeness, . Similarly, some strange and it is conserved in strong decays [6]. The baryons having strangeness are conservation of strangeness via strong interaction listed in the Table 2 [7]. In next section, a brief is discussed in terms of associated production in description of BESIII experimental setup is given.

Table 1. List of Strange Mesons with [7] Mesons Quark Contents Strangeness

̅ ( ⃰ )

̅ ̅ ( ̅ ̅) ⁄ √ ( ⃰ )

( ̅ ̅) ⁄ √

Charmed+ Strange Mesons Quark Content ̅ s Strangeness ̅

Bottom +Strange Mesons Quark Content ̅ s Strangeness

̅ ̅ ̅

4 Aneela Amin et al

4. BESIII Experimental Setup (GDML). BOSS provides many services to meet the requirement of analysis such as navigation and This paper is about the theoretical study of reconstruction of MC tracks. This Data processing strangeness conservations and violation of and physics analysis software system has three Charmonia, based on the data collected from main functions i.e. Simulation, Reconstruction and BESIII detector. BESIII detector uses the BESIII Calibration. BESIII detector simulation is based offline software system (BOSS), CLHEP libraries upon GEANT4 package which gives information and Root software to study the charmonium about the detector, particle tracking and their spectroscopy [8-9]. interaction with the detector [9].

The upgraded version of BES is BESIII that 6. CHARMONIUM SPECTROSCOPY consists of BEPCII collider and BESIII detector. BESIII detector is specifically used to In 1974, the discovery of charmonium meson study the Tau-Charm P hysics within energy range at BNL (Brookhaven National Laboratory) and of 2 to 5 GeV. BESIII detector became SLAC (Stanford Linear Accelerator Center) has operational from 2009 [8]. BESIII detector has opened up a new horizon in the field of research. four main components named as Main Drift After that, some other states of charmonium were Chamber (MDC), Electromagnetic Calorimeter discovered at some higher energies named as , (EMC), Time of Flight System (TOF) and Muon , , , and states. The decays of Chamber System (MUC). These parts of detector these charmonium and its higher states were detect various particles and their specific mainly studied at BES (Beijing Electron properties such as their momentum, energy, Spectrometer) Lab [8-10]. energy losses, position and time etc. within certain energy range of Charmonia. For more detail, for The charmonium and its higher energy states example, MDC used to measure the momentum being discussed here, contain charm quark as one and energy loss information of charged particles. of its quark content. The decays of these Electromagnetic Calorimeter (EMC) is used to charmonium states are categorized as the measure the energy and position of electron and strangeness conserving and strangeness violating photons only. Time of Flight System (TOF) is decays. These decays are listed in Table 3 (a) to used to measure the time of flight of charged 3(d) and Table 4(a) to 4(e). particles from the point of interaction to the detector. Since most of the collisions processes 7. DISCUSSIONS AND CONCLUSION decays into muons, so Muon Chamber (MUC) is used to detect the paths and positions of muons Strangeness has been observed in , , , produced during the e- e+ or collisions [8-9]. , and -decays. The data of these

All the parts and efficiencies of BESIII decays has been collected from BESIII experimental setup are related ̅ and much Laboratory. The branching fractions of strangeness dependent on BOSS (BESIII Offline Software conserving and strangeness violating decays have System) [9]. A brief introduction to BESIII Offline been studied from the years 2009 to 2017. In Table Software (BOSS) is given in next section. 3(a), the decays of , in which strangeness conservation occurs, are given [11-16]. Table 3(b) 5. BESIII Offline Software (BOSS) consists of decays containing strange baryon anti-baryon pair along with single non-strange BESIII Offline Software System (BOSS) uses the meson to conserve the strangeness [14-22]. Table C++ language and object oriented programming 3(c) shows only 2-body strangeness conserving and works on Scientific Linux Operating System. decays of strange baryon-anti-baryon pair or BESIII Offline System is based upon Gaudi strange meson-anti-meson pair [13, 23-24]. In the Framework which provides interfaces and its same way, 2-body, 3-body and 4-body strangeness utilities for simulating the data and physics conserving decays of are listed in table 3(d) analysis. Software Configuration is managed by [18, 25-28]. From this data, it is clear that configuration management tool (CMT). It provides associated production takes place in strangeness different packages, libraries and their utilities. conserving decays. These decays are the Information and specification of detector is stored manifestation of strong interactions. in Geometrical Description Markup Language Study of Strangeness at BESIII 5

Table 2. List of Strange Baryons [7] Strange Baryons Quark Contents Strangeness

Sigma Strange Baryons Quark Contents Strangeness ̅ ̅̅ ̅̅ ̅

Xi Strange Baryons Quark Contents Strangeness

Omega Strange Baryons Quark Contents Strangeness

6 Aneela Amin et al

Table 3 (a). Strangeness Conserving Decays of States Studied at BESIII

Decay Channel No. of Events Branching Fraction Year 2009

̅ [11 ] ̅ [12] 2009 ̅

̅ 2012

̅ [13]

̅ 2016

[14] ̅ 2016

̅ [15] 2017 [16 ] ̅

̅ Table 3 (b). Strangeness Conserving Decays of Studied at BESIII

Decay Channel No. of Events Branching Fraction year [17] 2012

[18 ] 2013

̅ [19] 2013

̅ [20] at C.L 2013 at C.L ̅ at C.L ̅ at C.L ̅ at C.L ̅ at C.L

̅ at C.L

at C.L ̅

̅ [21] 2013 ̅

̅ [22 ] 2014 ̅ 2016 [14]

2016 ̅ [15]

2017

[16] ̅

̅ Study of Strangeness at BESIII 7

Table 3 (c). Strangeness Conserving Decays of Studied at BESIII

Decay Channel No. of Events Branching Fraction year [23] at C.L 2011 [13 ] 2012 ̅ [24] 2013

̅ ̅ [24]

̅ Table 3 (d). Strangeness Conserving Decays of Studied at BESIII

Decay Channel No. of Events Branching Fraction year 2011

̅ [25]

2012 ̅ ̅

̅ [26]

2013 ̅ ̅

[27] ̅

̅ 2013

[18 ]

2017 ̅

̅[28]

̅ Table 4 (a). Strangeness Violating Decays of Studied at BESIII

Decay Channel Branching Fraction year at C.L 2014 [29 ] at C.L

2017 ̅ ̅ [30] at C.L

8 Aneela Amin et al

Table 4 (b). Strangeness Violating Decays of Studied at BESIII

Decay Channel Branching Fraction year

[31] 2013

[32] 2015

̅ Table 4(c). Strangeness Violating Decays of D-meson Studied at BESIII

Decay Channel Branching Fraction year

[33] 2015

[34] 2016

[35 ] 2016

̅ 2016

[36 ]

2016

[37]

[38] 2017

2017

[39 ]

Table 4 (d). Strangeness Violating Decays of Studied at BESIII

Decay Channel Branching Fraction year

[40] 2015

[41] 2016

[42] 2017

[43 ] 2017

Table 4 (e). Strangeness Violating Decays of Studied at BESIII

Decay Channel Branching Fraction year 2013

[44]

Study of Strangeness at BESIII 9

Recently, it was observed that when ideas of existing impressions but from any decays into neutral strange meson pairs such as struggle, a new episode of experimental High and , strangeness always violate as Energy physics may be released from studying given in Table 4(a) [29-30]. In Table 4(b), 3-body “significance of strangeness conservation- and 7-body strangeness violating decays are violation decays of strange mesons”. presented alongwith their branching fractions [31- 32]. The table 4(c) contains higher state of 9. ACKNOWLEDGEMENTS charmonia named as D-meson. In years 2016 and 2017, a lot of work has been done on the D-meson We pay our gratitude to Higher Education Commission of Pakistan for their financial support under decays and these are all strangeness violating Indigenous PhD Fellowship Program, Phase VI. We because D meson is the lightest meson with mass 2 are highly indebted to Prof. Dr. Haris Rashid, Dr. 1.864 GeV/c having single charm quark. It is Talab Hussain and Dr. Abrar Ahmad Zafar for their necessary for the decay of D meson, one of its valuable guidance and moral support. charm quark transform into some other quark. This transformation occurs via weak interaction and 10. REFERENCES this decay is always mediated by W boson [33- 39]. The 3-body and 4-body decay modes of , 1. Halzen, F. & A.D. Martin. Quarks and leptons: an given in Table 4(d) shows the strangeness introductory course in modern particle physics. violating decay modes [40-43]. In Table 4(e), the John Wiley and Sons, Inc., America (1984). 2. Perkins, D. H.. Introduction to High Energy strangeness violating decays of are shown and Physics. Addison-Wesley Publishing Company, their branching fractions are also mentioned [44]. Inc. Third Edition, United Kingdom (1987). From this study of strangeness violating decays, it 3. Mandl, F. & G. Shaw. Quantum Field Theory. John can be concluded that associated production Wiley and Sons, Inc., Manchester, United doesn‟t take place in strangeness violating decays Kingdom (1988). and these decays corresponds to the weak 4. Lakhina, O. Study of meson properties in quark interactions. models. PhD Thesis. Physics Department, University of Pittsburgh (2006). 8. SUMMARY 5. Blundell, H. G. Meson Properties in the Quark Model: A Look at Some Outstanding Problems. This was a review of experimental results of BES- PhD Thesis. Corletaton University, Canada III experiment for studying significance of (1996). 6. Kovacs, J.S. & C.L. William. Conservation Laws strangeness conservation-violation results of for Elementary Particle Reactions. Michigan State hadrons. Although no ﬁnal explanation have been University, Peter Signell for Project PHYSNET, given in experimental results and theoretical Physics-Astronomy Bldg., E. Lansing, MI 48824 exertions, but some positive concepts have been 517: 355-3784 (2001). introduced. A detailed list of strange mesons and 7. Patrignani, C., M. Antonelli, K. Agashe, G. baryons is given along with their quark contents Aielli, et al. Review of Particle Physics, Particle and strangeness values. Strangeness conserving Data Group. Chinese Physics C 40: 100001- and strangeness violating decay modes of J/ψ, ψ′, 101810 (2016). , , , and D-mesons have been 8. Ablikim, M., Z.H. An, J.Z. Bai, X.Y. Ma, H.X. Yang, et al. Design and Construction of the BESIII presented in tabular form with proper details of Detector. Nuclear Instruments and Methods in

number of events, Branching Fractions and the Physics Research Section A: Accelerators, year in which that specific phenomenon was Spectrometers, Detectors and Associated observed. The understanding of such kinds of Equipment 614: 345-399 (2010). complex decay modes is very important for the 9. Deng, Z., H. Liu, Y. Yuan, M. He, Y. Liang, G. scientists to learn about the universe at its most Cao & Z. You. BESIII Simulation fundamental level. Experimental and theoretical Software. Proceedings of Science 043: 1-7 (2007). results shed light on new phenomenology and may 10. Nakamura, K., K. Hagiwara, K. Hikasa, H. explore new worlds in High Energy Physics, Murayama, M. Tanabashi,et al. Review of Particle Physics. Journal of Physics G: Nuclear and although systematic efforts are difficult to carry Particle Physics 37: 075021-075024 (2010). out for charmonium systems. This study concludes 11. Wei, D.H. The SU(3) symmetry breaking in J/ψ that experimental trials will be more effective decays. Journal of Physics G: Nuclear and Particle rather than comparing theoretical perceptions. Physics 36: 115006-115012 (2009). Although, we may not reach up to revolutionary 10 Aneela Amin et al

12. Ablikim, M., Y. Bai, Y. Ban, X. Cai, H. F. Chen, into and final states. BESIII + − − + J. C. Chen, et al. J/ψ decays into Σ Σ and Ξ Ξ . Collabora tion. Physical Review D 87: 012003- BES Collaboration. Physical Review D 78: 092005 012012 (2013). ̅ ̅ -092012 (2008). 25. Ablikim, M., M.N. Achasov, L. An, M. L. Chen, C. 13. Ablikim, M.,M. N. Achasov, A. Calcaterra, O. D. Fu, et al. Observation of decaying into Bondarenko, N. Berger, M. Bertani, E. Boger, et final state. BESIII Collaboration. al. First observation of the isospin violating decay Physical Review D 83: 112009-112018 (2011). . BESIII Collaboration. Physical 26. Ablikim, ̅ M., M.N. Achasov, L. B. Guo, K. Review D 86 : 032008-032018 (2012). Goetzen, W. X. Gong, et al. Observation of 14. Ablikim, ̅M., M. N. Achasov, X. C. Ai, S. decays to . BESIII Collaboration. Ahmed, et al. Study of Physical Review D 86 : 052004-052012 (2012). and . BESIII 27. Ablikim, M., M.N. ̅ Achasov, J. Z. Bai, G. F. Cao, Collaboration. Physics Letter B 770: 217 -225 S. A. Cetin, X. Cai, et al. Measurements of Baryon ̅ ̅ (2016). . Pair Decays of Mesons. BESIII Collaboration. 15. Ablikim, M., M.N. Achasov, X. C. Ai, O. Physical Review D 87: 032007-032016 (2013).

Albayrak, M. Albrecht, D. J. Ambrose, et al. Study 28. Ablikim, M., M.N. Achasov, S. Ahmed, S. of decays to the and Fegan, D. Dedovich, A. Denig, et al. Improved final states. BESIII Collaboration. Physical Review measurements of and decays. D 93: 072003- 072013 ̅ (2016). ̅ BESIII Collaboration. Physical Review D 97:

16. Ablikim, M., M.N. Achasov, S. A. N. Ahmed, M. 052011-052020 (2018). ̅ ̅ Albrecht, Z Ning, et al. Study of J/ψ and ψ(3686) 0 − + 29. Ablikim, M., M.N. Achasov, S. Braun, J. P. Dai, → Σ (1385) (1385) and ΞΞ . BESIII W. G. Li, K. L. He, et al. Search for the rare Collaboration. Physics Letter B 770: 217-225 decays and . BESIII ̅ ̅̅ (2017). Collaboration. Physical Review D 89∗: 071101-

17. Ablikim, M., M.N. Achasov, O. Albayrak, D. J. 071109 (2014). ̅ ̅ Ambrose, F. F. An, Q. An, et al. Experimental 30. Ablikim, M., M.N. Achasov, A. Amoroso, J. Z. Study of decays to and . Bai, D. W. Bennett, et al. Branching fraction BESIII Collaboration. Physical Review D 86: measurement of and search for

072011- 072024 (2012). . BESIII Collaboration. Physical

18. Ablikim, M., M.N. Achasov, O. Albayrak, D. J. Review D 96: 112001 -112008 (2017) .

Ambrose, F. F. An, et al. Measurements of 31. Abl ikim, M., M.N. Achasov, O. Albayrak, D. J. and . BESIII Ambrose, T. Hu, F. A. Harris, et al. Evidence for Collaboration. Physical Review D 87: 012007- in . BESIII ̅ ̅ 012017 (2013). Collaboration. Physical Review D 87 : 052005-

19. Ablikim, M., M. N. Achasov, J. Becker, M. 052013 (2013). Bertani, et al. Study of 32. Ablikim, M., M.N. Achasov, X. C. Ai, O. decays. BESIII Collaboration. Physical Reviews - Albayrak, J. M. Bian, et al. Measurements of ̅ 092017 (2013). . BESIII 20. Ablikim, M., M.N. Achasov, R. A. Briere, X. Collaboration. Physical Review D 91: 092006- Cai, H. L. Dai, et al. Search for Baryonic Decays 092017 (2015). ̅ of and . BESIII Collaboration. 33. Ablikim, M.,M.N. Achasov, J. Z. Bai, C. Hu, L. Y. Physical Review D 87: 112011-112021 (2013). Dong, G. Cibinetto, et al. Study of decay dynamics

21. Ablikim, M., M.N. Achasov, X. C. Ai, O. and CP asymmetry in decay. Albayrak, D. J. Ambrose, et al. Observation of the BESIII Collaboration. Physical Review D 92:

decay ψ(3686) → . BESIII 112008-112023 (2015). Collaboration. Physical Review D 88: 112007- ̅ 34. Ablikim, M., M.N. Achasov, A. Calcaterra, G. 112016 (2013). Chelkov, R. Kliemt, H. Loehner, et al. Study of 22. Ablikim, M.,M.N. Achasov, X. C. Ai, F. F. An, . BESIII J. Z. Bai, et al. Measurement of the branching Collaboration. Physical Review D 94: 032001-

fraction for . BESIII 032018 (2016). Collaboration. Physical Review D 89 : 112006- 35. Ablikim, M., M.N. Achasov, X. Chen, C. Dong, 112014 (2014). D. Dedovich, et al. Improved measurement of the 23. Ablikim, M., M.N. Achasov, J. Becker, N. absolute branching fraction of Berger, J. Z. Bai, et al. Search for decays into decay. European Physical Journal C 76:369 -379 vector meson pairs. BESIII Collaboration. ̅ (2016).

Physical Review D 84: 091102--091109 (2011). 36. Ablikim, M., M.N. Achasov, X. C. Ai, F. F. 24. Ablikim, M.,, M.N. Achasov, J. Z. Bai, J. C. An, J. V. Bennett, et al. Measurement of the Chen, M. Y. Dong, et al. Observation of decay absolute branching fractions for and

Study of Strangeness at BESIII 11

. BESIII Collaboration. Physical 41. Ablikim, M., M. N. Achasov, X. C. Ai, O. Review D 94 : 112003-112010 (2016). Albayrak, J. Dong, et al. Measurements of

37. Abl ikim, M., M.N. Achasov, R. A. Briere, G. absolute hadronic branching fractions of Chelkov, J. C. Chen, et al. Measurements of the baryon. BESIII Collaboration. Physical Review

branching fractions for Letter 116: 052001-052008 (2016). and , . BESIII Collaboration. 42. Ablikim, M., M. N. Achasov, S. Ahmed, M.

Physics Letter B 765: 231 -237 (2017). Albrecht, et al. Observation of the decay

38. Ablikim, M., M.N. Achasov, S. Ahmed, Y. Ban, c . BESIII Collaboration. Physics Letters

J. F. Chang, et al. Analysis of and B 772: 388 -397 (2017). Semileptonic Decays . BESIII 43. Abl ikim, M., M. N. Achasov, A. Amoroso, S.

Collaboration. Physical Review D 96 ̅: 012002 - Ahmed, J. Z. Bai, et al. Observation of

012017 (2017). BESIII Collaboration. Physical Review

39. Ablikim, M., M.N. Achasov, M. Albrecht, A. Letter s 118: 112001-112008 (2017).

Dbeyssi, , S. L. Niu, et al. Measurements of the 44. Abl ikim, M., M.N. Achasov, D. J. Ambrose, F. F. branching fractions for the semi-leptonic decays An, et al. Search for hadronic transition , , . BESIII and observation of . Collaboration. Physical Review D 97: 012006- BESIII Collaboration. Physical Review D 87 :

012015 (2018). 012002 -012015 (2013). ̅ 40. Ablikim, M., M. N. Achasov, J. Z. Bai, Q. An, et al. Measurement of the absolute branching fraction for . BESIII Collaboration. Physical Review Letters 115: 221805-221812 (2015).