Review of Particle Physics

S. Navas, C. Amsler, T. Gutsche, C. Hanhart, J. J. Hernández-Rey, C. Lourenço, A. Masoni, M. Mikhasenko, R. E. Mitchell, C. Patrignani, et al.

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To cite this version:

S. Navas, C. Amsler, T. Gutsche, C. Hanhart, J. J. Hernández-Rey, et al. Review of Particle Physics. Physical Review D, 2024, 110 (3), pp.030001. 10.1103/PhysRevD.110.030001. hal-04678727

HAL Id: hal-04678727

https://hal.science/hal-04678727v1

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Distributed under a Creative Commons Attribution 4.0 International License
# REVIEW OF PARTICLE PHYSICS*

## Particle Data Group

### Abstract

The *Review* summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,717 new measurements from 869 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Most of the 120 reviews are updated, including many that are heavily revised.

The *Review* is divided into two volumes. Volume 1 includes the Summary Tables and 97 review articles. Volume 2 consists of the Particle Listings and contains also 23 reviews that address specific aspects of the data presented in the Listings.

The complete *Review* (both volumes) is published online on the website of the Particle Data Group (pdg.lbl.gov) and in a journal. Volume 1 is available in print as the *PDG Book*. A *Particle Physics Booklet* with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print, as a web version optimized for use on phones, and as an Android app.

The 2024 edition of the *Review of Particle Physics* should be cited as:
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

DOI: 10.1103/PhysRevD.110.030001

For the online version see pdg.lbl.gov:

<figure><img src="image_3.png" /></figure>

© 2024

Except where otherwise noted, content of this work (the *Review of Particle Physics*) is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license.

<footnote>*The publication of the *Review of Particle Physics* is supported by the Director, Office of Science, Office of High Energy Physics of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231; by an implementing arrangement between the governments of Japan (MEXT: Ministry of Education, Culture, Sports, Science and Technology) and the United States (DOE) on cooperative research and development; by the Italian National Institute of Nuclear Physics (INFN); and by the European Laboratory for Particle Physics (CERN). Individual collaborators receive support for their PDG activities from their respective institutes or funding agencies.</footnote>
Particle Data Group

S. Navas*,¹ C. Amsler,² T. Gutsche,³ C. Hanhart,⁴ J.J. Hernández-Rey*,⁵ C. Lourenço,⁶ A. Masoni,⁷

M. Mikhasenko,⁸ R.E. Mitchell,⁹ C. Patrignani,¹⁰ C. Schwanda,¹¹ S. Spanier,¹² G. Venanzoni,¹³,¹⁴

C. Z. Yuan,¹⁵ K. Agashe,¹⁶ G. Aielli,¹⁷ B.C. Allanach,¹⁸ J. Alvarez-Muñiz,¹⁹ M. Antonelli,²⁰

E.C. Aschenauer,²¹ D.M. Asner,²¹ K. Assamagan,²¹ H. Baer,²² Sw. Banerjee,²³ R.M. Barnett,²⁴

L. Baudis,²⁵ C.W. Bauer,²⁴ J.J. Beatty,²⁶ J. Beringer,²⁴ A. Bettini,†,²⁷ O. Biebel,²⁸ K.M. Black,²⁹

E. Blucher,³⁰ R. Bonventre,²⁴ R.A. Briere,³¹ A. Buckley,³² V.D. Burkert,³³ M.A. Bychkov,³⁴

R.N. Cahn,²⁴ Z. Cao,¹⁵ M. Carena,³⁵,³⁰,³⁶ G. Casarosa,³⁷,¹⁴ A. Ceccucci,⁶ A. Cerri,³⁸,¹⁴,³⁹

R.S. Chivukula,⁴⁰ G. Cowan,⁴¹ K. Cranmer,²⁹ V. Crede,⁴² O. Cremonesi,⁴³ G. D'Ambrosio,⁴⁴

T. Damour,⁴⁵ D. de Florian,⁴⁶ A. de Gouvêa,⁴⁷ T. DeGrand,⁴⁸ S. Demers,⁴⁹ Z. Demiragli,⁵⁰

B.A. Dobrescu,³⁵ M. D'Onofrio,¹³ M. Doser,⁶ H.K. Dreiner,⁵¹ P. Eerola,⁵² U. Egede,⁵³

S. Eidelman,‡,⁵⁴ A.X. El-Khadra,⁵⁵ J. Ellis,⁵⁶,⁶ S.C. Eno,¹⁶ J. Erler,⁵⁷ V.V. Ezhela,⁵⁴ A. Fava,³⁵

W. Fetscher,⁵⁸ B.D. Fields,⁵⁹,⁵⁵ A. Freitas,⁶⁰ H. Gallagher,⁶¹ T. Gershon,⁶² Y. Gershtein,⁶³

T. Gherghetta,⁶⁴ M.C. Gonzalez-Garcia,⁶⁵,⁶⁶,⁶⁷ M. Goodman,⁶⁸ C. Grab,⁵⁸ A.V. Gritsan,⁶⁹

C. Grojean,⁷⁰,⁷¹ D.E. Groom,²⁴ M. Grünewald,⁷² A. Gurtu,⁶,⁷³ H.E. Haber,⁷⁴ M. Hamel,⁷⁵

S. Hashimoto,⁷⁶ Y. Hayato,⁷⁷,⁷⁸ A. Hebecker,⁷⁹ S. Heinemeyer,⁸⁰ K. Hikasa,⁸¹,⁸²,⁸³ J. Hisano,⁸⁴,⁸⁵

A. Höcker,⁶ J. Holder,⁸⁶,⁸⁷ L. Hsu,³⁵ J. Huston,⁸⁸ T. Hyodo,⁸⁹ Al. Ianni,⁹⁰ M. Kado,⁹¹ M. Karliner,⁹²

U.F. Katz,⁹³ M. Kenzie,⁹⁴ V.A. Khoze,⁹⁵ S.R. Klein,⁹⁶,⁹⁷ F. Krauss,⁹⁵ M. Kreps,⁶² P. Križan,⁹⁸,⁹⁹

B. Krusche‡,¹⁰⁰ Y. Kwon,¹⁰¹ O. Lahav,¹⁰² L.P. Lellouch,¹⁰³ J. Lesgourgues,¹⁰⁴ A.R. Liddle,¹⁰⁵

Z. Ligeti,²⁴ C.-J. Lin,²⁴ C. Lippmann,¹⁰⁶ T.M. Liss,¹⁰⁷ A. Lister,¹⁰⁸ L. Littenberg,²¹ K.S. Lugovsky,²⁴

S.B. Lugovsky,⁵⁴ A. Lusiani,¹⁰⁹,¹⁴ Y. Makida,⁷⁶ F. Maltoni,¹¹⁰,¹¹¹ A.V. Manohar,⁴⁰ W.J. Marciano,²¹

J. Matthews,¹¹² U.-G. Meißner,¹¹³,⁴ I.-A. Melzer-Pellmann,⁷⁰ P. Mertsch,¹⁰⁴ D.J. Miller,³²

D. Milstead,¹¹⁴ K. Mönig,¹¹⁵ P. Molaro,¹¹⁶,¹¹⁷ F. Moortgat,⁶,¹¹⁸ M. Moskovic,⁶ N. Nagata,¹¹⁹

K. Nakamura,⁷⁶,⁷⁸ M. Narain‡,¹²⁰ P. Nason,⁴³,¹²¹ A. Nelles,¹¹⁵,⁹³ M. Neubert,¹²² Y. Nir,¹²³

H.B. O'Connell,³⁵ C.A.J. O'Hare,¹²⁴ K.A. Olive,⁶⁴ J.A. Peacock,¹²⁵ E. Pianori,²⁴ A. Pich,⁵

A. Piepke,¹²⁶ F. Pietropaolo,⁶,¹²⁷ A. Pomarol,¹²⁸,¹²⁹ S. Pordes,³⁵ S. Profumo,⁷⁴ A. Quadt,¹³⁰

K. Rabbertz,¹³¹ J. Rademacker,¹³² G. Raffelt,⁹¹ M. Ramsey-Musolf,¹³³,¹³⁴,¹³⁵ P. Richardson,⁹⁵

A. Ringwald,⁷⁰ D.J. Robinson,²⁴ S. Roesler,⁶ S. Rolli,¹³⁶ A. Romaniouk,¹³⁷,⁵⁴ L.J. Rosenberg,¹³⁸

J.L. Rosner,³⁰ G. Rybka,¹³⁸ M.G. Ryskin,⁵⁴ R.A. Ryutin,⁵⁴ B. Safdi,⁹⁷ Y. Sakai,⁷⁶ S. Sarkar,¹³⁹

F. Sauli§,⁶ O. Schneider,¹⁴⁰ S. Schöert,¹⁴¹ K. Scholberg,¹⁴² A.J. Schwartz,¹⁴³ J. Schwiening,¹⁰⁶

D. Scott,¹⁰⁸ F. Sefkow,⁷⁰ U. Seljak,⁹⁷,²⁴ V. Sharma,⁴⁰ S.R. Sharpe,¹³⁸ V. Shiltsev¶,³⁵

G. Signorelli,³⁷,¹⁴ M. Silari, F. Simon,¹³¹ T. Sjöstrand,¹⁴⁴ P. Skands,⁵³ T. Skwarnicki,¹⁴⁵

G.F. Smoot,¹⁴⁶,⁹⁷,²⁴,¹⁴⁷,¹⁴⁸ A. Soffer,⁹² M.S. Sozzi,³⁷ C. Spiering,¹¹⁵ A. Stahl,¹⁴⁹ Y. Sumino,⁸³

F. Takahashi,⁸³ M. Tanabashi,⁸⁴,⁸⁵ J. Tanaka,¹⁵⁰ M. Taševský,¹⁵¹ K. Terao,¹⁵²,¹⁵³ K. Terashi,¹⁵⁰

J. Terning,¹⁵⁴ U. Thoma,¹¹³ R.S. Thorne,¹⁰² L. Tiator,⁵⁷ M. Titov,¹⁵⁵ D.R. Tovey,¹⁵⁶ K. Trabelsi,¹⁵⁷

P. Urquijo,¹⁵⁸ G. Valencia,⁵³ R. Van de Water,³⁵ N. Varelas,¹⁵⁹ L. Verde,⁶⁷,⁶⁶ I. Vivarelli,¹¹¹

P. Vogel,¹⁶⁰ W. Vogelsang,³ V. Vorobyev,⁵⁴ S.P. Wakely,³⁰,³⁶ W. Walkowiak,¹⁶¹ C.W. Walter,¹⁴²

D. Wands,¹⁶² D.H. Weinberg,¹⁶³ E.J. Weinberg,¹⁶⁴ N. Wermes,⁵¹ M. White,⁹⁷,²⁴ L.R. Wiencke,¹⁶⁵

S. Willocq,¹³⁵ C.L. Woody,²¹ R.L. Workman,¹⁶⁶ W.-M. Yao,²⁴ M. Yokoyama,¹¹⁹,⁷⁸ R. Yoshida,⁶⁸

G. Zanderighi,⁹¹,¹⁶⁷ G.P. Zeller,³⁵ R.-Y. Zhu,¹⁶⁸ S.-L. Zhu,¹⁶⁹ F. Zimmermann,⁶ P.A. Zyla,²⁴

Technical Associates: J. Anderson,²⁴ M. Kramer,²⁴ P. Schaffner,²⁴ W. Zheng,¹⁵

1. Universidad de Granada, Dpto. de Física Teórica y del Cosmos & C.A.F.P.E., Granada, Spain

2. Stefan Meyer Institute for Subatomic Physics, Austrian Academy of Sciences, Vienna, Austria

3. Universität Tübingen, Institut für Theoretische Physik, Tübingen, Germany

4. Forschungszentrum Jülich, Institute for Advanced Simulation, Jülich, Germany

5. IFIC — Instituto de Física Corpuscular, Universitat de València — C.S.I.C., Valencia, Spain

6. CERN, European Organization for Nuclear Research, Genève, Switzerland

7. INFN Sezione di Cagliari, Monserrato, Italy

8. Institut für Experimentalphysik 1, Ruhr-Universität Bochum, Bochum, Germany

9. Indiana University, Department of Physics, Bloomington, IN, USA

10. Università di Bologna and INFN, Dip. Scienze per la Qualità della Vita, Rimini, Italy

11. HEPHY, Vienna, Austria

12. University of Tennessee, Department of Physics and Astronomy, Knoxville, TN, USA

13. University of Liverpool, Department of Physics, Liverpool, UK

<footnote>*Support from Projects PID2021-124591NB-C41 and -C43, funded by MICIU/AEI/10.13039/501100011033 and FEDER, UE</footnote>

<footnote>†Coordination activities supported directly by INFN.</footnote>

<footnote>‡Deceased.</footnote>

<footnote>§Retired.</footnote>

<footnote>¶Supported by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with DOE.</footnote>
14. INFN Sezione di Pisa, Pisa, Italy

15. Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China

16. University of Maryland, Department of Physics, College Park, MD, USA

17. Università degli Studi di Roma "Tor Vergata", Rome, Italy

18. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

19. Instituto Galego de Física de Altas Enerxías (IGFAE) & Dept. Física de Partículas, Universidade de Santiago de Compostela, Santiago de Compostela, Spain

20. Lab. Nazionali di Frascati dell'INFN, Frascati, Italy

21. Brookhaven National Laboratory, Nuclear and Particle Physics Directorate, Upton, NY, USA

22. University of Oklahoma, Department of Physics and Astronomy, Norman, OK, USA

23. University of Louisville, Louisville, KY, USA

24. Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

25. Universität Zürich, Physik-Institut, Zürich, Switzerland

26. Ohio State University, Department of Physics, Columbus, OH, USA

27. INFN and Dipartimento di Fisica e Astronomia, Università di Padova, Padova, Italy

28. Ludwig-Maximilians-Universität, Fakultät für Physik, München, Germany

29. University of Wisconsin, Department of Physics, Madison, WI, USA

30. University of Chicago, Enrico Fermi Institute and Department of Physics, Chicago, IL, USA

31. Department of Physics, Carnegie Mellon University, Pittsburgh, PA, USA

32. University of Glasgow, School of Physics and Astronomy, Glasgow, UK

33. Jefferson Lab, Newport News, VA, USA

34. University of Virginia, Department of Physics, Charlottesville, VA, USA

35. Fermi National Accelerator Laboratory, Batavia, IL, USA

36. University of Chicago, Kavli Institute for Cosmological Physics, Chicago, IL, USA

37. University of Pisa, Pisa, Italy

38. Dipartimento Scienze fisiche, della Terra e dell'ambiente, Università degli Studi di Siena, Siena, Italy

39. Department of Physics and Astronomy, University of Sussex, Brighton, UK

40. Department of Physics, University of California at San Diego, La Jolla, CA, USA

41. Department of Physics, Royal Holloway, University of London, London, UK

42. Florida State University, Department of Physics, Tallahassee, FL, USA

43. INFN Sezione di Milano-Bicocca, Piazza della Scienza, Milano, Italy

44. INFN Sezione di Napoli, Napoli, Italy

45. Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France

46. UNSAM - Universidad Nacional de San Martin, International Center for Advanced Studies (ICAS) and Instituto de Ciencias Físicas (ICIFI), Buenos Aires, Argentina

47. Northwestern University, Department of Physics and Astronomy, Evanston, IL, USA

48. University of Colorado at Boulder, Department of Physics, Boulder, CO, USA

49. Yale University, New Haven, CT, USA

50. Boston University, Department of Physics, Boston, MA, USA

51. Universität Bonn, Physikalisches Institut, Bonn, Germany

52. Research Council of Finland, Helsinki, Finland

53. Monash University, School of Physics and Astronomy, Melbourne, Australia

54. Affiliation provided upon request

55. University of Illinois, Department of Physics, Urbana, IL, USA

56. King's College London, Department of Physics, London, UK

57. Institut für Kernphysik, Johannes Gutenberg University, Mainz, Germany

58. ETH Zurich, Institute for Particle Physics and Astrophysics, Zurich, Switzerland

59. University of Illinois, Department of Astronomy, Urbana, IL, USA

60. University of Pittsburgh, Department of Physics and Astronomy, Pittsburgh, PA, USA

61. Tufts University, Department of Physics and Astronomy, Medford, MA, USA

62. University of Warwick, Department of Physics, Coventry, UK

63. Department of Physics and Astronomy, Rutgers University, NJ, USA

64. University of Minnesota, School of Physics and Astronomy, Minneapolis, MN, USA

65. CN Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY, USA

66. Institució Catalana de Recerca i Estudis Avancats, Barcelona, Spain
67. Instituto de ciencias del Cosmos (ICC), University of Barcelona, Barcelona, Spain

68. Argonne National Laboratory, Argonne, IL, USA

69. Johns Hopkins University, Baltimore, MD, USA

70. Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany

71. Institut für Physik, Humboldt-Universität zu Berlin, Berlin, Germany

72. University College Dublin, School of Physics, Dublin, Ireland

73. TIFR, Mumbai, India

74. Santa Cruz Institute for Particle Physics, University of California, Santa Cruz, CA, USA

75. Université Paris-Saclay, CEA, LIST, F-91120 Palaiseau, France

76. KEK, High Energy Accelerator Research Organization, Tsukuba, Japan

77. Kamioka Observatory, ICRR, The University of Tokyo, Tokyo, Japan

78. The University of Tokyo, Kavli IPMU (WPI), The University of Tokyo Institutes for Advanced Study, Kashiwa, Japan

79. Heidelberg University, Institute for Theoretical Physics, Heidelberg, Germany

80. Instituto de Física Teórica (UAM/CSIC), Universidad Autónoma de Madrid, Madrid, Spain

81. Division for Interdisciplinary Advanced Research and Education, Tohoku University, Sendai, Japan

82. Institute of Liberal Arts and Sciences, Tohoku University, Sendai, Japan

83. Tohoku University, Department of Physics, Sendai, Japan

84. Department of Physics, Nagoya University, Nagoya, Japan

85. Nagoya University, Kobayashi-Maskawa Institute, Nagoya, Japan

86. University of Delaware, Department of Physics and Astronomy, Newark, DE, USA

87. University of Delaware, Bartol Research Institute, Newark, DE, USA

88. Michigan State University, Dept. of Physics and Astronomy, East Lansing, MI, USA

89. Department of Physics, Tokyo Metropolitan University, Tokyo, Japan

90. INFN - Laboratori Nazionali del Gran Sasso, Assergi, Italy

91. Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Garching, Germany

92. Department of Particle Physics, Tel-Aviv University, Tel Aviv, Israel

93. Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen Centre for Astroparticle Physics, Erlangen, Germany

94. University of Cambridge, Cambridge, UK

95. University of Durham, Institute for Particle Physics Phenomenology, Department of Physics, Durham, UK

96. Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

97. University of California, Department of Physics, Berkeley, CA, USA

98. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska, Slovenia

99. Jozef Stefan Institute, Ljubljana, Slovenia

100. University of Basel, Institute of Physics, Basel, Switzerland

101. Yonsei University, Department of Physics, Seoul, Republic of Korea

102. University College London, Department of Physics and Astronomy, London, UK

103. Aix-Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France

104. Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH, Aachen, Germany

105. Instituto de Astrofísica e Ciências do Espaço, Universidade de Lisboa, Lisbon, Portugal

106. GSI, Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany

107. The City College of New York, New York, NY, USA

108. University of British Columbia, Department of Physics and Astronomy, Vancouver, BC, Canada

109. Scuola Normale Superiore, Pisa, Italy

110. Université catholique de Louvain, Centre for Cosmology, Particle Physics and Phenomenology (CP3), Louvain-la-Neuve, Belgium

111. Università di Bologna and INFN, Dipartimento di Fisica e Astronomia, Bologna, Italy

112. Louisiana State University, Department of Physics and Astronomy, Baton Rouge, LA, USA

113. Universität Bonn, Helmholtz-Institut für Strahlen- und Kernphysik, Bonn, Germany

114. Stockholms Universitet, AlbaNova University Centre, Fysikum, Stockholm, Sweden

115. Deutsches Elektronen-Synchrotron DESY, Zeuthen, Germany

116. INAF-OATS, Trieste, Italy

117. Institute for Fundamental Physics of the Universe, Trieste, Italy

118. University of Ghent, Dept. of Physics and Astronomy, Ghent, Belgium

119. The University of Tokyo, Department of Physics, Tokyo, Japan
120. Brown University, Department of Physics, Providence, RI, USA

121. Dip. di Fisica "G. Occhialini", Università di Milano-Bicocca, Milano, Italy

122. Johannes Gutenberg University, PRISMA Cluster of Excellence and Mainz Institute for Theoretical Physics, Mainz, Germany

123. Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel

124. University of Sydney, Sydney, Australia

125. University of Edinburgh, Royal Observatory, Institute for Astronomy, Edinburgh, UK

126. University of Alabama, Department of Physics and Astronomy, Tuscaloosa, AL, USA

127. INFN Sezione di Padova, Padua, Italy

128. Universitat Autònoma de Barcelona, Departament de Física, Barcelona, Spain

129. IFAE, Universitat Autònoma de Barcelona, Barcelona, Spain

130. Georg-August-Universität Göttingen, II. Physikalisches Institut, Göttingen, Germany

131. Karlsruhe Institute of Technology, Karlsruhe, Germany

132. University of Bristol, HH Wills Physics Laboratory, Bristol, UK

133. Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China

134. Shanghai Jiao Tong University, Shanghai, China

135. University of Massachusetts, Department of Physics, Amherst, MA, USA

136. DOE, Washington, DC, USA

137. Universität Innsbruck, Department of Astro and Particle Physics, Innsbruck, Austria

138. University of Washington, Department of Physics, Seattle, WA, USA

139. University of Oxford, Rudolf Peierls Centre for Theoretical Physics, Oxford, UK

140. Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

141. Department of Physics, Technical University Munich, Munich, Germany

142. Duke University, Physics Department, Durham, NC, USA

143. University of Cincinnati, Department of Physics, Cincinnati, OH, USA

144. Lund University, Department of Astronomy and Theoretical Physics, Lund, Sweden

145. Syracuse University, Department of Physics, Syracuse, NY, USA

146. The Hong Kong University of Science and Technology, Kowloon, Hong Kong

147. Donostia International Physics Center (DIPC), Donostia-San Sebastián, Spain

148. Paris Centre for Cosmological Physics, APC (CNRS), Université de Paris, Paris, France

149. III. Physikalisches Institut, Physikzentrum, RWTH Aachen University, Aachen, Germany

150. International Center for Elementary Particle Physics (ICEPP), The University of Tokyo, Tokyo, Japan

151. Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic

152. SLAC National Accelerator Laboratory, Menlo Park, CA, USA

153. Stanford University, Stanford, CA, USA

154. Department of Physics, University of California, Davis, CA, USA

155. IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France

156. University of Sheffield, Department of Physics and Astronomy, Sheffield, UK

157. IJCLab, CNRS/IN2P3, Université Paris-Saclay, Orsay, France

158. University of Melbourne, School of Physics, Victoria, Australia

159. University of Illinois at Chicago, Chicago, IL, USA

160. California Institute of Technology, Kellogg Radiation Laboratory, Pasadena, CA, USA

161. Universität Siegen, Department für Physik, Siegen, Germany

162. University of Portsmouth, Institute of Cosmology and Gravitation, Portsmouth, UK

163. Ohio State University, Department of Astronomy and CCAPP, Columbus, OH, USA

164. Columbia University, Department of Physics, New York, NY, USA

165. Dept. of Physics, Colorado School of Mines, Golden, CO, USA

166. George Washington University, Department of Physics, Washington, D.C., USA

167. Technische Universität München, München, Germany

168. California Institute of Technology, High Energy Physics, Pasadena, CA, USA

169. School of Physics, Peking University, Beijing, China
HIGHLIGHTS OF THE 2024 EDITION OF THE REVIEW OF PARTICLE PHYSICS

All PDG data and review articles are available online at pdg.lbl.gov.

869 new papers with 2,717 new measurements

120 reviews (most are revised)

* 320 new measurements from LHC experiments (ATLAS, CMS and LHCb).

* Extensive Higgs boson coverage from 231 new papers and 557 measurements with latest results on mass, couplings, decay width and branching ratios, plus searches for other neutral and charged Higgs bosons.

* Supersymmetry: 36 new papers with 148 measurements with major exclusions.

* Top quark: 35 new papers provide latest results on mass, coupling, and the discovery of four top quark production at LHC.

* W mass: CDF published a new measurement of the W mass. It is more precise than the world average at the time, but the two results disagree. See comments in Particle Listings and our W mass review referencing the extensive studies done by the LHC TeV $M_W$ working group.

* c-, b-hadron physics: 161 papers and 597 measurements provide world-best data on lifetimes, mixing, CP violation, CKM angles, and constraints on new physics.

* Neutrino Physics: 10 new papers with measurements on neutrino mass, mixing, and CP-violation.

* Meson resonances: Substantial improvements, including new cross particle fits involving $J/\psi(1S)$, $\psi(2S)$ and $\eta_c(1S)$, merging of $\pi_1(1400)$ and $\pi_1(1600)$ with non-$q\bar{q}$ quantum numbers into same node, listing of complex pole positions when available, and inclusion of recently observed states. Several mesons now considered established added to Summary Tables.

* New naming scheme for the many recently discovered mesons and baryons with c or b quarks that are not compatible with conventional $q\bar{q}$ or $qqq$ structures. Listed in "Other mesons" and "Exotic baryons" sections.

* Major revision of *Higgs Physics* review summarizes latest LHC results and constraints on new physics.

* Major revision of *Cosmic rays* review, now covering all components of cosmic rays including neutrinos (which were previously discussed in Neutrino Telescopes in Particle Detectors for Non-Accelerator Physics).

* Major revision of *Large time-projection chambers for rare event detection* in Particle Detectors for Non-Accelerator Physics.

* Major revision of *Top Quark* review summarizes latest LHC results and constraints on new physics from top quark.

* Major revision of *Heavy Non-$q\bar{q}$ Mesons* review follows new naming scheme for states not compatible with $q\bar{q}$ or $qqq$ structures.

* Semiconductor detectors section of Particle Detectors at Accelerators review includes recent developments.

* New section on goodness-of-fit tests and expanded discussion of statistical tests in *Statistics* review.

* Updated EWK fit in *Electroweak Model and Constraints on New Physics* review.

* Semileptonic B Hadron Decays, Determination of $V_{cb}$ and $V_{ub}$ includes latest results and discusses long-standing issues with inclusive and exclusive measurements.

* Updated cross section results in the *Neutrino Cross Section Measurements* review.

* Updated $\tau$ decay parameters and branching ratio (BR) fits, including new treatment of $BR(a1(1260) \to \pi\gamma)$.
VOLUME 1: SUMMARY TABLES AND REVIEWS

<table><tr><td>Highlights</td><td>6</td></tr><tr><td>Introduction</td><td>11</td></tr><tr><td>History plots</td><td>19</td></tr><tr><td>Online particle physics information (rev.)</td><td>20</td></tr></table>

SUMMARY TABLES

<table><tr><td>Gauge and Higgs bosons</td><td>25</td></tr><tr><td>Leptons</td><td>28</td></tr><tr><td>Quarks</td><td>32</td></tr><tr><td>Mesons</td><td>33</td></tr><tr><td>Meson quick reference table</td><td>91</td></tr><tr><td>Baryon quick reference table</td><td>92</td></tr><tr><td>Baryons</td><td>93</td></tr><tr><td>Searches not in Other Sections</td><td>112</td></tr><tr><td>Tests of conservation laws</td><td>114</td></tr></table>

REVIEWS, TABLES, AND PLOTS

Constants, Units, Atomic and Nuclear Properties

<table><tr><td>1. Physical constants (rev.)</td><td>137</td></tr><tr><td>2. Astrophysical constants and parameters (rev.)</td><td>138</td></tr><tr><td>3. International system of units (SI)</td><td>140</td></tr><tr><td>4. Periodic table of the elements (rev.)</td><td>141</td></tr><tr><td>5. Electronic structure of the elements (rev.)</td><td>142</td></tr><tr><td>6. Atomic and nuclear properties of materials (rev.)</td><td>144</td></tr><tr><td>7. Electromagnetic relations</td><td>146</td></tr><tr><td>8. Naming scheme for hadrons (rev.)</td><td>148</td></tr></table>

Standard Model and Related Topics

<table><tr><td>9. Quantum chromodynamics (rev.)</td><td>153</td></tr><tr><td>10. Electroweak model and constraints on new physics (rev.)</td><td>185</td></tr><tr><td>11. Higgs boson physics, status of (rev.)</td><td>211</td></tr><tr><td>12. CKM quark-mixing matrix (rev.)</td><td>270</td></tr><tr><td>13. CP violation in the quark sector (rev.)</td><td>280</td></tr><tr><td>14. Neutrino masses, mixing, and oscillations (rev.)</td><td>295</td></tr><tr><td>15. Quark model (rev.)</td><td>322</td></tr><tr><td>16. Heavy-quark & soft-collinear effective theory (rev.)</td><td>341</td></tr><tr><td>17. Lattice quantum chromodynamics (rev.)</td><td>350</td></tr><tr><td>18. Structure functions (rev.)</td><td>367</td></tr><tr><td>19. Fragmentation functions in e<sup>+</sup>e<sup>-</sup>, ep and pp collisions (rev.)</td><td>389</td></tr><tr><td>20. High Energy Soft QCD and Diffraction (rev.)</td><td>406</td></tr></table>

Astrophysics and Cosmology

<table><tr><td>21. Experimental tests of gravitational theory (rev.)</td><td>431</td></tr><tr><td>22. Big-Bang cosmology (rev.)</td><td>444</td></tr><tr><td>23. Inflation (rev.)</td><td>457</td></tr><tr><td>24. Big-Bang nucleosynthesis (rev.)</td><td>474</td></tr><tr><td>25. Cosmological parameters (rev.)</td><td>482</td></tr><tr><td>26. Neutrinos in cosmology (rev.)</td><td>491</td></tr><tr><td>27. Dark matter (rev.)</td><td>499</td></tr><tr><td>28. Dark energy (rev.)</td><td>515</td></tr><tr><td>29. Cosmic microwave background (rev.)</td><td>524</td></tr><tr><td>30. Cosmic rays (rev.)</td><td>535</td></tr></table>

Experimental Methods and Colliders

<table><tr><td>31. Accelerator physics of colliders (rev.)</td><td>559</td></tr><tr><td>32. High-energy collider parameters (rev.)</td><td>569</td></tr><tr><td>33. Neutrino beam lines at high-energy proton synchrotrons (rev.)</td><td>574</td></tr><tr><td>34. Passage of particles through matter (rev.)</td><td>575</td></tr><tr><td>35. Particle detectors at accelerators (rev.)</td><td>591</td></tr><tr><td>36. Particle detectors for non-accelerator phys. (rev.)</td><td>649</td></tr><tr><td>37. Radioactivity and radiation protection (rev.)</td><td>679</td></tr><tr><td>38. Commonly used radioactive sources (rev.)</td><td>685</td></tr></table>

Mathematical Tools

<table><tr><td>39. Probability</td><td>689</td></tr><tr><td>40. Statistics (rev.)</td><td>694</td></tr><tr><td>41. Machine Learning</td><td>711</td></tr><tr><td>42. Monte Carlo techniques</td><td>748</td></tr><tr><td>43. Monte Carlo event generators (rev.)</td><td>752</td></tr><tr><td>44. Monte Carlo neutrino event generators</td><td>764</td></tr><tr><td>45. Monte Carlo particle numbering scheme (rev.)</td><td>768</td></tr><tr><td>46. Clebsch-Gordan coefficients, spherical harmonics, and d functions</td><td>772</td></tr><tr><td>47. SU(3) isoscalar factors and representation matrices</td><td>773</td></tr><tr><td>48. SU(n) multiplets and Young diagrams</td><td>774</td></tr></table>

Kinematics, Cross-Section Formulae, and Plots

<table><tr><td>49. Kinematics</td><td>777</td></tr><tr><td>50. Resonances (rev.)</td><td>781</td></tr><tr><td>51. Cross-section formulae for specific processes</td><td>792</td></tr><tr><td>52. Neutrino cross section measurements (rev.)</td><td>801</td></tr><tr><td>53. Plots of cross sections and related quantities (rev.)</td><td>807</td></tr></table>

Particle Properties

<table><tr><td>Gauge Bosons</td><td></td></tr><tr><td>54. Mass and width of the W boson (rev.)</td><td>815</td></tr><tr><td>55. Z boson</td><td>817</td></tr></table>

<table><tr><td>Charged Leptons</td><td></td></tr><tr><td>56. Muon anomalous magnetic moment (rev.)</td><td>822</td></tr><tr><td>57. Muon decay parameters (rev.)</td><td>826</td></tr><tr><td>58. τ branching fractions (rev.)</td><td>829</td></tr><tr><td>59. τ-lepton decay parameters (rev.)</td><td>832</td></tr></table>

<table><tr><td>Quarks</td><td></td></tr><tr><td>60. Quark masses (rev.)</td><td>834</td></tr><tr><td>61. Top quark (rev.)</td><td>844</td></tr></table>

(Continued on next page.)
## Mesons

62. Form factors for semileptonic kaon ($K_{\ell 3}$), radiative pion ($\pi_{\ell 2\gamma}$) & kaon ($K_{\ell 2\gamma}$) decays (rev.) 871

63. Spectroscopy of light meson resonances (rev.) 874

64. Scalar mesons below 1 GeV (rev.) 888

65. Rare kaon decays (rev.) 896

66. CPT invariance tests in neutral kaon decay (rev.) 902

67. $V_{ud}$, $V_{us}$, Cabibbo angle, and CKM unitarity (rev.) 904

68. CP-violation in $K_L$ decays (rev.) 908

69. Review of multibody charm analyses (rev.) 911

70. $D^0$-$\bar{D}^0$ mixing (rev.) 917

71. $D_s^+$ branching fractions 927

72. Leptonic decays of charged pseudoscalar mesons (rev.) 929

73. Production and decay of b-flavored hadrons (rev.) 940

74. Polarization in B decays (rev.) 951

75. $B^0$-$\bar{B}^0$ mixing (rev.) 955

76. Semileptonic B-hadron decays, $V_{cb}$ and $V_{ub}$ (rev.) 962

77. CKM angles from B hadrons, determination of (rev.) 980

78. Spectroscopy of mesons containing two heavy quarks (rev.) 985

79. Heavy non-$q\bar{q}$ mesons (rev.) 994

## Baryons

80. Baryon decay parameters 1001

81. N and $\Delta$ resonances 1002

82. $\Lambda$ and $\Sigma$ resonances 1007

83. Pole structure of the $\Lambda(1405)$ region 1010

84. Pentaquarks (rev.) 1012

## Hypothetical Particles and Concepts

85. Extra dimensions (rev.) 1021

86. $W'$-boson searches (rev.) 1029

87. $Z'$-boson searches (rev.) 1033

88. Supersymmetry: theory (rev.) 1038

89. Supersymmetry: experiment (rev.) 1058

90. Axions and other similar particles (rev.) 1079

91. Quark and lepton compositeness, searches for (rev.) 1098

92. Dynamical electroweak symmetry breaking: implications of the $H^0$ (rev.) 1104

93. Grand unified theories (rev.) 1119

94. Leptoquarks (rev.) 1134

95. Magnetic monopoles (rev.) 1138

## INDEX (Volumes 1 and 2 combined)

# VOLUME 2: PARTICLE LISTINGS

(available online only)

## Illustrative key and abbreviations

Illustrative key 1171

Abbreviations 1172

## Gauge and Higgs bosons

($\gamma$, gluon, graviton, W, Z, Higgs, Axions) 1185

## Leptons

(e, $\mu$, $\tau$, Heavy-charged lepton searches, Neutrino properties, Number of neutrino types, Double-$\beta$ decay, Neutrino mixing, Heavy-neutral lepton searches) 1297

## Quarks

(u, d, s, c, b, t, $b'$, $t'$ (4th gen.), Free quarks) 1371

## Mesons

Light unflavored ($\pi$, $\rho$, a, b) ($\eta$, $\omega$, f, $\phi$, h) 1411

Strange ($K$, $K^*$) 1538

Charmed ($D$, $D^*$) 1592

Charmed, strange ($D_s$, $D_s^*$, $D_{sJ}$) 1657

Bottom ($B$, $V_{cb}/V_{ub}$, $B^*$, $B_j^*$) 1681

Bottom, strange ($B_s$, $B_s^*$, $B_{sJ}^*$) 1865

Bottom, charmed ($B_c$) 1893

$c\bar{c}$ ($\eta_c$, $J/\psi(1S)$, $\chi_c$, $h_c$, $\psi$) 1898

$b\bar{b}$ ($\eta_b$, $\Upsilon$, $\chi_b$, $h_b$) 2023

Other mesons ($T_c$, $T_b$ tetraquarks) 2062

## Baryons

$N$ 2081

$\Delta$ 2137

$\Lambda$ 2161

$\Sigma$ 2187

$\Xi$ 2218

$\Omega$ 2231

Charmed ($\Lambda_c$, $\Sigma_c$, $\Xi_c$, $\Omega_c$) 2234

Doubly charmed ($\Xi_{cc}$) 2262

Bottom ($\Lambda_b$, $\Sigma_b$, $\Xi_b$, $\Omega_b$, b-baryon admixture) 2263

Exotic baryons ($P_c$ pentaquarks) 2285

## Searches not in Other Sections

Magnetic monopole searches 2289

Supersymmetric particle searches 2292

Technicolor 2347

Searches for quark and lepton compositeness 2348

Extra dimensions 2352

WIMP and dark matter searches 2359

Other particle searches 2374
## INTRODUCTION

<table><tr><td>1. Overview</td><td>11</td></tr><tr><td>2. Particle Listings responsibilities</td><td>11</td></tr><tr><td>3. Consultants</td><td>12</td></tr><tr><td>4. Naming scheme for hadrons</td><td>15</td></tr><tr><td>5. Procedures</td><td>15</td></tr><tr><td>5.1 Selection and treatment of data</td><td>15</td></tr><tr><td>5.2 Averages and fits</td><td>15</td></tr><tr><td>5.2.1 Treatment of errors</td><td>15</td></tr><tr><td>5.2.2 Unconstrained averaging</td><td>16</td></tr><tr><td>5.2.3 Constrained fits</td><td>16</td></tr><tr><td>5.3 Rounding</td><td>17</td></tr><tr><td>5.4 Discussion</td><td>17</td></tr><tr><td>History plots</td><td>19</td></tr></table>

## ONLINE PARTICLE PHYSICS INFORMATION

<table><tr><td>1. Introduction</td><td>20</td></tr><tr><td>2. Particle Data Group (PDG) resources</td><td>20</td></tr><tr><td>3. Particle physics information platform</td><td>20</td></tr><tr><td>4. Literature databases</td><td>20</td></tr><tr><td>5. Journals</td><td>21</td></tr><tr><td>6. Conference and seminars databases</td><td>21</td></tr><tr><td>7. Research institutions</td><td>21</td></tr><tr><td>8. People</td><td>21</td></tr><tr><td>9. Experiments</td><td>21</td></tr><tr><td>10. Jobs</td><td>21</td></tr><tr><td>11. Software packages and repositories</td><td>22</td></tr><tr><td>12. Data repositories and preservation</td><td>22</td></tr><tr><td>13. Particle physics education and outreach</td><td>22</td></tr><tr><td>14. Regional HEP efforts</td><td>22</td></tr></table>
<figure><img src="image_4.png" /></figure>
# Introduction

## 1 Overview

The Review of Particle Physics is a comprehensive review of the field of Particle Physics and of related areas in Cosmology. It is divided into two volumes. Volume 1 includes the “Summary Tables” and “Reviews, Tables, and Plots”. Volume 2 consists of the “Particle Listings”.

The Review is updated each year and made available on the PDG website (pdg.lbl.gov). In even-numbered years, the Review is also published in a journal and printed as the PDG Book together with an abridged Particle Physics Booklet containing Summary Tables and essential tables, figures, and equations from selected review articles. This edition is an updating through January 2024.

The Summary Tables give our best values and limits for particle properties such as masses, widths or lifetimes, and branching fractions, as well as an extensive summary of searches for hypothetical particles and a summary of experimental tests of conservation laws.

The 95 review articles in Reviews, Tables and Plots cover a wide variety of theoretical and experimental topics. Together with the Summary Tables they provide an exhaustive reference for the practicing particle physicist. Two more review articles, Online Particle Physics Information and Tests of Conservation Laws, can be found in the introduction and Summary Tables, respectively.

The Particle Listings are a compilation/evaluation of data on particle properties. They contain all the data used to get the values given in the Summary Tables. They also give information on unconfirmed particles and particle searches. In this edition, the Particle Listings include 2,717 new measurements from 869 papers, in addition to the 46,838 measurements from 12,909 papers that first appeared in previous editions [1]. 23 review articles are part of the Particle Listings and address specific aspects of the data presented in the Listings. Because of the large quantity of data, the Particle Listings are not an archive of all published data on particle properties. We refer interested readers to earlier editions for data now considered to be obsolete.

We organize the particles into six categories:

* Gauge and Higgs bosons

* Leptons

* Quarks

* Mesons

* Baryons

* Searches not in other sections

The last category only includes searches for particles that do not belong to the previous groups. For example, it includes searches for supersymmetric particles, compositeness and extra dimensions, while searches for heavy charged leptons are with the leptons.

In Sec. 2 of this Introduction, we list the main areas of responsibility of the authors of the Particle Listings. Our many consultants, without whom we would not have been able to produce this Review, are acknowledged in Sec. 3. In Sec. 4, we mention briefly the naming scheme for hadrons, and in Sec. 5, we discuss our procedures for choosing among measurements of particle properties and for obtaining best values of the properties from the measurements.

The accuracy and usefulness of this Review depend in large part on interaction between its users and the authors. We appreciate comments, criticisms, and suggestions for improvements of any kind. Please send them to pdg@lbl.gov from where they will be forwarded to the appropriate author according to the list of responsibilities in Sec. 2 below.

In addition to the online publication at pdg.lbl.gov, the Review is available in different formats:

* The printed PDG Book includes volume 1 only, i.e. it contains the Summary Tables and most review articles. Since the 2016 edition [2] the detailed tables from the Particle Listings are no longer printed.

* The Particle Physics Booklet includes the Summary Tables plus essential tables, figures, and equations from selected review articles.

Starting with the Booklets of the 2018 edition, we have excluded most text and explanations in order to revert back to a more pocket-sized format. The Booklet is available in print, as a web version optimized for use on phones, and as an Android app (see pdg.lbl.gov/booklet).

* pdgLive (pdgLive.lbl.gov) is a web application giving more interactive access to PDG data than the static web pages and PDF files that are also available.

* Files that can be downloaded from the PDG website include a table of masses, widths, and PDG Monte Carlo particle ID numbers; PDF files of volume 1 (PDG Book), volume 2 (Particle Listings) and Booklet; individual review articles; all figures; and an archive file containing the complete PDG website (except for pdgLive).

* Starting with the 2024 edition, the data published in the Review of Particle Physics is available in machine-readable format through a new PDG API (Application Programming Interface). See pdg.lbl.gov/api for details.

Copies of the PDG Book or the Particle Physics Booklet can be ordered from our website or directly at pdg.lbl.gov/order. For special requests only, please email pdg@lbl.gov in North and South America, Australia, and the Far East, and pdg-products@cern.ch in all other areas.

This Review is considered to be a single comprehensive review of particle physics and related areas. Therefore we prefer that it be cited as a whole, rather than citing e.g. an individual review article that is part of this Review. For the 2024 edition, the proper citation is:

S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).

If you wish to refer to a specific part of the Review, for example to the Higgs boson review article, the following form should be used:

Status of Higgs Boson Physics in S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).

## 2 Particle Listings responsibilities

* Asterisk indicates the people to contact with questions or comments about Particle Listings sections. Please contact them by e-mail to pdg@lbl.gov.

* Gauge and Higgs bosons

<table><tr><td>γ</td><td>A. Bettini, D.E. Groom*</td></tr><tr><td>Gluons</td><td>R.M. Barnett,* A.V. Manohar</td></tr><tr><td>Graviton</td><td>A. Bettini,* D.E. Groom</td></tr><tr><td>W, Z</td><td>M. Grünewald,* A. Gurtu*</td></tr><tr><td>Higgs bosons</td><td>S. Heinemeyer,* K. Hikasa, J. Tanaka</td></tr><tr><td>Heavy bosons</td><td>R. Bonventre,* K.A. Olive, M. Tanabashi</td></tr><tr><td>Axions</td><td>C. O'Hare, K.A. Olive, G. Raffelt,* F. Takahashi</td></tr></table>

* Leptons

<table><tr><td>Neutrinos</td><td>M. Goodman, C.-J. Lin,* K. Nakamura, K.A. Olive, A. Piepke</td></tr><tr><td>Double-β decay</td><td>A. Bettini*, A. Piepke</td></tr><tr><td>e, μ</td><td>A. Bettini,* C. Grab</td></tr><tr><td>τ</td><td>A. Lusiani, K. Mönig*</td></tr></table>

* Quarks

<table><tr><td>Quarks</td><td>R.M. Barnett,* A.V. Manohar</td></tr><tr><td>Top quark</td><td>Y. Sumino, W.-M. Yao*</td></tr><tr><td>b', t'</td><td>Y. Sumino, W.-M. Yao*</td></tr><tr><td>Free quark</td><td>A. Bettini,* C.-J. Lin</td></tr></table>

* Mesons

<table><tr><td>π, η</td><td>A. Bettini,* C. Grab</td></tr><tr><td>K (stable)</td><td>G. D'Ambrosio, C.-J. Lin*</td></tr><tr><td>D (stable)</td><td>G. Casarosa, J. Rademacker, D. Robinson*</td></tr><tr><td>B (stable)</td><td>A. Cerri,* P. Eerola, M. Kreps, Y. Kwon, W.-M. Yao*</td></tr></table>
Unstable mesons
C. Amsler,* T. Gutsche, C. Hanhart, J.J. Hernández-Rey, C. Lourenco, A. Masoni, M. Mikhasenko, R.E. Mitchell, S. Navas, C. Patrignani, C. Schwanda, S. Spanier, G. Venanzoni, C.Z. Yuan

### Baryons

Stable baryons C. Grab, D. Robinson*

Unstable baryons
V. Burkert, V. Crede, U. Thoma, L. Tiator, R.L. Workman*

Charmed baryons
G. Casarosa, J. Rademacker, D. Robinson*

Bottom baryons
A. Cerri,* P. Eerola, M. Kreps, Y. Kwon, W.-M. Yao*

### Miscellanoues searches

Monopole
A. Bettini,* D. Milstead

Supersymmetry
H.K. Dreiner,* A. de Gouvêa, I.-A. Melzer-Pellmann, K.A. Olive, I. Vivarelli

Technicolor
K. Agashe,* K.A. Olive, M. Tanabashi

Compositeness
M. Tanabashi, J. Terning*

Extra Dimensions
T. Gherghetta, K.A. Olive, D. Robinson*

WIMP, DM, Other
H. Baer, A. Bettini,* W.-M. Yao*

## 3 Consultants

The Particle Data Group benefits greatly from the assistance of hundreds of physicists who are asked to referee review articles and verify every piece of data entered into this *Review*. Of special value is the advice of the PDG Advisory Committee, which meets biennially and thoroughly reviews all aspects of our operation. The members of the 2022 committee are:

S. Demers (Yale)

D. d'Enterria (CERN)

J. Frieman (FNAL)

S. Gori (UCSC)

T. Nakada (EPFL)

M. Yokoyama (Tokyo)

We have especially relied on the expertise of the following people for advice on particular topics:

* I. Abt (MPP, Garching)

* R. Acciarri (FNAL)

* M. Albaladejo (IFIC, Valencia)

* S. Alderweireldt (Edinburgh U.)

* S. Alioli (INFN, Milano-Bicocca)

* A. Antognini (ETH Zurich)

* E. Aprile (Columbia U.)

* E. Armengaud (CEA Saclay, DSM/IRFU/SPP)

* M. Artuso (Syracuse U.)

* N. Asbah (CERN)

* P. Athron (Nanjing U.)

* G. Azuelos (U. de Montreal)

* P. Azzurri (INFN, Pisa)

* R. Battiston (Trento U.)

* R.A. Battye (Manchester U.)

* O. Behnke (DESY, Hamburg)

* G. Bell (Siegen U.)

* J. Bellido Caceres (Adelaide U.)

* V. Belyaev (ITEP)

* N.P. Berger (LAPP)

* F. Betti (Edinburgh U.)

* T. Biekotter (KIT)

* P. Blasi (GSSI)

* M. Bona (QMUL)

* C. Bonifazi (ICAS and ICIFI, UNSAM)

* D. Bose (Indian Inst. Tech., Kharagpur)

* E. Brost (BNL)

* R. Bruce (CERN)

* D.A. Bryman (TRIUMF)

* C. Buck (MPIK)

* M. Cadeddu (INFN, Cagliari)

* X. Calmet (Sussex U.)

* M. Calvi (INFN, Milano-Bicocca)

* J. Cao (IHEP Beijing)

* F. Capozzi (L'Aquila U.)

* L. Capriotti (INFN, Ferrara)

* T. Carli (CERN)

* B. Carlo (INFN, LNGS)

* N. Cartiglia (INFN, Torino)

* G. Cavoto (Rome U.; INFN, Rome)

* S. Cebrian Guajardo (U. de Zaragoza)

* F. Cerutti (LBNL)

* R. Cervantes (FNAL)

* M. Chan (EdUHK, Hong Kong)

* M. Charles (CNRS)

* C. Chen (CPPM Marseille)

* K. Chen (Taiwan National U. Physics Dep.)

* M. Chen (Queen's U.)

* Y. Chen (Taiwan National U. Physics Dep.)

* Y. Chenghui (IHEP Beijing)

* M. Chianese (INFN, Napoli; UNINA)

* Y. Chinone (KEK)

* V. Chobanova (CERN)

* J. Chou (Rutgers U.)

* C. Clement (Stockholm U.)

* G. Colangelo (Bern U.)

* P. Coloma (UAM/CSIC, U. Autónoma de Madrid)

* R. Contino (Rome U. Sapienza)

* A. Cortes Gonzalez (Physik, Humboldt U.)

* N. Crescini (Neel U.)

* M. Cruz (Honduras U.)

* A. Cukierman (Stanford U.; SLAC)

* C. Da Via (Manchester U.)

* C. Davies (Glasgow U.)

* F. de Almeida Dias (NIKHEF)

* A. De Angelis (INFN, Padova)

* J. De Blas (Granada U.)

* R. Della Monica (Salamanca U.)

* D. d'Enterria (CERN)

* A. Derbin (NRC Kurchatov Inst. PNPI)

* J. de Vries (CERN)

* A. de Wit (Zurich U.)

* A. Di Domenico (INFN, Rome)

* E. Di Marco (CERN)

* L. Dong (IHEP Beijing)

* G. Drexlin (KIT)

* J.J. Dudek (IReS)

* K. Dundas (Columbia U.)

* B. Dutta (TAMU)

* V. Dutta (UC Santa Barbara)

* A. Egorov (LPI Moscow)

* S.R. Elliott (LANL)

* R. Engel (KIT)
* A. Esposito (Rome U. Sapienza)

* T. Evans (Oxford U.)

* S. Fang (IHEP Beijing)

* Y. Farzan (IPM, Tehran)

* K. Ferguson (UC Los Angeles)

* A. Ferrari (CERN)

* A. Ferrari (Uppsala U.)

* C. Finley (Stockholm U.)

* W. Fischer (BNL)

* M. Flores (Wits U.; Philippines U., Quezon City)

* J. Flynn (Southampton U.)

* P. Fonte (LIP)

* J. Formaggio (MIT)

* D. Franco (Paris U.)

* K. Freese (Michigan U.; Nordita, Stockholm)

* T. Fujii (OMU Osaka)

* T. Fujita (Ochanomizu U.)

* R. Garisto (APS)

* C. Gatti (INFN, LNF)

* V. Gavrin (INR, Moscow)

* B. Geoffrey (Wits U.)

* A. Gilbert (Northwestern U.)

* V. Gligorov (CNRS)

* S.N. Gninenko (Russian Academy of Sciences)

* A. Godinho (CERN)

* J. Gomez Cadenas (DIPC)

* M. Goodsell (LPTHE, Paris)

* S. Gori (UC Santa Cruz)

* S.A. Gottlieb (Indiana U.)

* E. Goudzovski (Birmingham U.)

* L. Gouskos (CERN)

* P. Grabmayr (Tübingen U.)

* A. Greljo (Basel U.)

* A. Grohsjean (DESY, Hamburg)

* Y. Guo (Fudan U. Shanghai)

* P. Guzowski (Manchester U.)

* C. Ha (Northwestern U.)

* F. Halzen (Wisconsin U.)

* K. Harigaya (Chicago U.)

* F.A. Harris (Hawaii U.)

* F. Hartmann (KIT)

* A. Heijboen (NIKHEF)

* J. Heitger (WWU)

* S. Higashino (Kobe U.)

* A. Himmel (FNAL)

* A. Hinzmann (Hamburg U.)

* A. Hoang (HEPHY, Vienna)

* Y. Hochberg (Racah Inst. Hebrew U.)

* S. Hoof (INFN, Padua)

* X. Huang (PMO, Nanjing; USTC China)

* T. Huege (KIT)

* N. Huesken (JGU, Mainz)

* T. Humair (DESY, Hamburg)

* N. Huntemann (PTB, Braunschweig)

* N. Ilic (Toronto U.)

* K. Inoue (Osaka U.)

* K. Inoue (Tohoku U.)

* D. Jackson-Kimball (CSU Hayward)

* L. Jacob (LPSC, IN2P3)

* C. James (CIRA)

* P. Janot (CERN)

* B. Jayatilaka (FNAL)

* M. Jewell (Yale U.)

* C. Joram (CERN)

* A. Kalweit (CERN)

* M. Kamionkowski (Johns Hopkins U.)

* T. Kaneko (KEK)

* D. Kar (Wits U.)

* S. Karanth (UJ, Krakow)

* B. Ke (IHEP Beijing)

* E.T. Kearns (Boston U.)

* O. Kepka (CERN)

* J. Kieseler (Karlsruhe U.)

* Y. Kim (IBS, Daejeon)

* K. Kirch (ETH Zurich)

* E. Klempt (Bonn U.)

* J. Knolle (Ghent U.)

* A. Knue (Freiburg U.)

* B. Ko (IBS, Daejeon)

* K. Kohri (KEK; SOKENDAI; Kavli IPMU, UTIAS)

* E. Kou (LAL Orsay)

* D. Kovalskyi (MIT)

* G. Kramberger (Jozef Stefan Inst.)

* A. Kramida (NIST)

* S. Kraml (LPSC, Grenoble)

* G. Krintiras (CERN)

* W. Kuehn (Giessen U.)

* Y. L (IHEP Beijing)

* A. Lague (Toronto U.)

* H. Lee (IBS, Daejeon)

* A. Lenz (Siegen U.)

* O. Leroy (CPPM Marseille)

* J.D. Lewis (FNAL)

* H. Li (IHEP Beijing)

* P. Li (CERN)

* S. Li (IHEP Beijing)

* Z. Li (IHEP Beijing)

* Y. Liang (Guangxi U.)

* L. Liao (IHEP Beijing)

* J. Libby (Indian Inst. Tech., Madras)

* P. Lichard (Silesian U., Opava)

* Z. Ligeti (LBNL)

* C. Lin (Chicago U.)

* T. Linden (Stockholm U.)

* M. Lisanti (Princeton U.)

* E. Lisi (INFN, Bari)

* C. Liu (USTC China)

* G. Lucente (INFN, Bari)

* H. Ma (IHEP Beijing)

* Y. Ma (KwaZulu-Natal U.)

* F. Mahmoudi (IP2I, Lyon)

* S. Malde (Oxford U.)

* M. Maltoni (UAM/CSIC, U. Autónoma de Madrid)

* L. Manenti (NYU, Abu Dabi)

* C. Manzari (LBNL; UC Berkeley)

* R. Manzoni (ETH Zurich)

* M. Margoni (INFN, Padova)

* L. Mariscano (INFN, Genova)

* M. Martin (DESY, Hamburg)

* M. Masciovecchio (CERN)

* T. Masubuchi (UTokyo)

* M. Masuzawa (KEK)
* A. Mathad (ETH Zurich)

* S. Meinel (Arizona U.)

* C. Milardi (INFN, LNF)

* D. Mitzel (Heidelberg U.)

* R.N. Mohapatra (U. Maryland)

* P. Monni (CERN)

* J. Montejo (CERN)

* S. Moriyama (ICRR)

* H. Mu (CERN)

* S. Narison (Montpellier U.)

* K. Ni (UC San Diego)

* A. Nicholson (North Carolina U.)

* S. Nishida (KEK)

* A. Notari (ICC, U. of Barcelona)

* P.E. Onyisi (Texas U. Austin)

* L. Pagnanini (GSSI)

* T. Pajero (Phys. Dep. Oxford U.)

* N. Palanque-Delabrouille (LBNL)

* B. Pant (IIT, Jodhpur)

* I. Papaphilippou (CERN)

* J.R. Pelaez (UCM, Madrid)

* C. Pena (FNAL)

* S. Perazzini (CERN)

* D. Pereima (CERN)

* A. Pereiro (Santiago de Compostela U.)

* F. Petricca (MPP, Garching)

* F. Piccini (INFN, Pavia)

* P. Piminov (Budker Inst., Novosibirsk)

* J. Pinfold (Alberta U.)

* D. Pinna (Wisconsin U.)

* T. Poddar (TIFR Mumbai)

* S. Polikarpov (MEPhI Moscow)

* A. Pompili (INFN, Bari)

* N. Porayako (MPIK)

* W. Porod (Würzburg U.)

* R. Puthumanaillam (CERN)

* W. Qian (IHEP Beijing)

* R. Quagliani (CERN)

* M. Rama (CERN)

* A. Read (Oslo U.)

* F. Redi (CERN)

* A. Reimers (DESY, Hamburg)

* L. Reina (Florida State U.)

* F. Resnati (ETH Zurich)

* J. Richard (IP2I, Lyon)

* S. Rodrigues Sandner (IFIC, Valencia)

* D. Roenchen (FZ Jülich)

* K. Rogers (Toronto U.)

* C. Rovelli (INFN, Rome)

* G. Ruggiero (Lancaster U.)

* T. Saab (Florida State U.)

* W. Saenz-Arevalo (LPNHE Paris)

* R. Salerno (CNRS)

* J. Santiago (Granada U.)

* N. Saoulidou (Athens U.)

* P. Schmidt-Wellenburg (PSI)

* I. Schulthess (DESY, Hamburg)

* B. Schwingenheur (MPIK)

* S. Scorza (LPSC, Grenoble)

* Y.K. Semertzidis (IBS, Daejeon; KAIST)

* S. Seo (FNAL)

* S. Serednyakov (Budker Inst., Novosibirsk)

* A.G. Shamov (Budker Inst., Novosibirsk)

* D. Shemyakin (Novosibirsk U.)

* D. Sheng (USTC China)

* M. Shiozawa (ICRR)

* D. Shwartz (Budker Inst., Novosibirsk)

* C. Smarra (SISSA/INFN, Trieste)

* L. Soffi (INFN, Rome)

* P. Sommer (CERN)

* A.L. Spadafora (LBNL)

* E. Spadaro (INFN, Milano-Bicocca)

* S. Srinivasan (Manchester U.)

* J. Steggemann (ETH Zurich)

* I.W. Stewart (MIT)

* A. Suzuki (LBNL)

* O. Tajima (Kyoto U.)

* J. Terol Calvo (IAC)

* R. Tesarek (FNAL)

* M. Tobar (UWA, Perth)

* D. Tonelli (Trieste U.)

* E. Torrence (Oregon U.)

* N. Tran (FNAL)

* A. Tricoli (BNL)

* S.M. Turchikhin (CERN)

* Y. Unno (KEK)

* P.L. Vahle (William and Mary Coll.)

* K. Valerius (KIT)

* R.G. Van De Water (LANL)

* C. van Eldik (Erlangen U.)

* R. Van Kooten (Indiana U.)

* K. Van Tilburg (NYU, New York)

* T. Vazquez Schroeder (McGill U.)

* M. Viel (SISSA/INFN, Trieste)

* E. Vitagliano (Padova U.)

* M. Volpe (APC, Paris)

* K. von Sturm (INFN, Padova)

* K. Vos (Maastricht U.)

* M. Vos (IFIC, Valencia)

* A.P. Walker-Loud (LBNL)

* L. Wan (Boston U.)

* M. Wang (INFN, Milano-Bicocca)

* X. Wang (Adelaide U.)

* Z. Wang (NYU, New York)

* N. Wardle (Imperial Coll. Physics Dep.)

* A. Watson (Leeds U.)

* G. Watt (Durham U.)

* M. Weber (Bern U.)

* J. Wei (PMO, Nanjing)

* R. Wendell (Kyoto U.)

* L. Winslow (MIT)

* P. Winter (ANL)

* S. Witte (Phys. Dep. Oxford U.)

* C. Wittweg (Zurich U.)

* B. Yang (Seoul National U.)

* Y. Yang (MIT)

* J. Ye (Columbia U.)

* H. Yin (CERN)

* P. Yin (IHEP Beijing)

* J. Yoo (Seoul National U.)

* Z. You (Sun Yat-sen U.)

* Q. Yue (Tsinghua U.)
* D. Zerwas (LAL Orsay)

* X. Zhang (JGU, Mainz)

* Y. Zhang (Zhengzhou U.)

* M. Zhao (NKU)

* R. Zhao (UCAS, Beijing)

* L. Zhiqing (Shandong U.)

* G. Zsigmond (PSI)

# 4 Naming scheme for hadrons

We introduced in the 1986 edition [3] a new naming scheme for the hadrons. Changes from older terminology affected mainly the heavier mesons made of u, d, and s quarks. Otherwise, the only important change to known hadrons was that the $F^{\pm}$ became the $D_s^{\pm}$. None of the lightest pseudoscalar or vector mesons changed names, nor did the $c\bar{c}$ or $b\bar{b}$ mesons (we do, however, now use $\chi_c$ for the $c\bar{c}$ $\chi$ states), nor did any of the established baryons. The Summary Tables give both the new and old names whenever a change has occurred.

In the 2018 edition [4], the naming scheme was extended to address the naming of charmonium and bottomonium states that were commonly referred to as X, Y, or Z states in the literature. The further discovery of various exotic hadron states — including in particular tetraquarks and pentaquarks containing $qq\bar{q}q$ and $q\bar{q}qqq$ minimal quark content, respectively — has rendered the 2018 extension insufficient. In this edition, the naming scheme is revised and extended to cover all experimentally-known states. The current scheme is described in “Naming Scheme for Hadrons” (p. 1) of this Review. A table details the correspondence between the names newly adopted by the PDG and those that have previously appeared in the literature.

We give here our conventions on typesetting style. Particle symbols are italic (or slanted) characters: $e^{-}$, $p$, $\Lambda$, $\pi^{0}$, $K_{L}$, $D_{S}^{+}$, $b$. Charge is indicated by a superscript: $B^{-}$, $\Delta^{++}$. Charge is not normally indicated for $p$, $n$, or the quarks, and is optional for neutral isosinglets: $\eta$ or $\eta^{0}$. Antiparticles and particles are distinguished by charge for charged leptons and mesons: $\tau^{+}$, $K^{-}$. Otherwise, distinct antiparticles are indicated by a bar (overline): $\bar{\nu}_{\mu}$, $\bar{t}$, $\bar{p}$, $\bar{K}^{0}$, and $\bar{\Sigma}^{+}$ (the antiparticle of the $\Sigma^{-}$).

# 5 Procedures

## 5.1 Selection and treatment of data

The Particle Listings contain all relevant data known to us that are published in journals. With very few exceptions, we do not include results from preprints or conference reports. Nor do we include data that are of historical importance only (the Listings are not an archival record). We search every volume of 30 journals through our cutoff date for relevant data. We also include later published papers that are sent to us by the authors (or others).

In the Particle Listings, we clearly separate measurements that are used to calculate or estimate values given in the Summary Tables from measurements that are not used. We give explanatory comments in many such cases. Among the reasons a measurement might be excluded are the following:

* It is superseded by or included in later results.

* No error is given.

* It involves assumptions we question.

* It has a poor signal-to-noise ratio, low statistical significance, or is otherwise of poorer quality than other data available.

* It is clearly inconsistent with other results that appear to be more reliable. Usually we then state the criterion, which sometimes is quite subjective, for selecting “more reliable” data for averaging. See Sec. 5.4.

* It is not independent of other results.

* It is not the best limit (see below).

* It is quoted from a preprint or a conference report.

In some cases, none of the measurements is entirely reliable and no average is calculated. For example, the masses of many of the baryon resonances, obtained from partial-wave analyses, are quoted as estimated ranges thought to probably include the true

values, rather than as averages with errors. This is discussed in the Baryon Particle Listings.

For upper limits, we normally quote in the Summary Tables the strongest limit. We do not average or combine upper limits except in a very few cases where they may be re-expressed as measured numbers with Gaussian errors.

As is customary, we assume that particle and antiparticle share the same spin, mass, and mean life. The Tests of Conservation Laws table, following the Summary Tables, lists tests of CPT as well as other conservation laws.

We use the following indicators in the Particle Listings to tell how we get values from the tabulated measurements:

* OUR AVERAGE — From a weighted average of selected data.

* OUR FIT — From a constrained or overdetermined multiparameter fit of selected data.

* OUR EVALUATION — Not from a direct measurement, but evaluated from measurements of related quantities.

* OUR ESTIMATE — Based on the observed range of the data. Not from a formal statistical procedure.

* OUR LIMIT — For special cases where the limit is evaluated by us from measured ratios or other data. Not from a direct measurement.

An experimentalist who sees indications of new a particle will of course want to know what has been seen in that region in the past. Hence, we include in the Particle Listings all reported states that, in our opinion, have sufficient statistical merit and that have not been disproved by more reliable data. However, we promote to the Summary Tables only those states that we feel are well-established. This judgment is, of course, somewhat subjective and no precise criteria can be given. For more detailed discussions, see the reviews section on Particle Properties.

## 5.2 Averages and fits

We divide this discussion on obtaining averages and errors into three sections: (1) treatment of errors; (2) unconstrained averaging; (3) constrained fits.

### 5.2.1 Treatment of errors

In what follows, the “error” $\delta x$ means that the range $x \pm \delta x$ is intended to be a 68.3% confidence interval about the central value $x$. We treat this error as if it were Gaussian. Thus, when the error is Gaussian, $\delta x$ is the usual one standard deviation ($1\sigma$). Many experimenters now give statistical and systematic errors separately, in which case we usually quote both errors, with the statistical error first. For averages and fits, we then add the two errors in quadrature and use this combined error for $\delta x$.

When experimenters quote asymmetric errors ($\delta x)^{+}$ and ($\delta x)^{-}$ for a measurement $x$, the error that we use for that measurement in making an average or a fit with other measurements is a continuous function of these three quantities. When the resultant average or fit $\bar{x}$ is less than $x - (\delta x)^{-}$, we use $(\delta x)^{-}$; when it is greater than $x + (\delta x)^{+}$, we use $(\delta x)^{+}$. In between, the error we use is a linear function of $x$. Since the errors we use are functions of the result, we iterate to get the final result. Asymmetric output errors are determined from the input errors assuming a linear relation between the input and output quantities.

In fitting or averaging, we usually do not include correlations between different measurements, but we try to select data in such a way as to reduce correlations. Correlated errors are, however, treated explicitly when there are a number of results of the form $A_i \pm \sigma_i \pm \Delta$ that have identical systematic errors $\Delta$. In this case, one can first average the $A_i \pm \sigma_i$ and then combine the resulting statistical error with $\Delta$. One obtains, however, the same result by averaging $A_i \pm (\sigma_i^2 + \Delta_i^2)^{1/2}$, where $\Delta_i = \sigma_i \Delta[(\sum (1/\sigma_i^2))^{1/2}]$. This procedure has the advantage that, with the modified systematic errors $\Delta_i$, each measurement may be treated as independent and averaged in the usual way with other data. Therefore, when appropriate, we adopt this procedure. We tabulate $\Delta$ and invoke an automated procedure that computes $\Delta_i$ before averaging, and we include a note saying that there are common systematic errors.

Another common case of correlated errors occurs when experimenters measure two quantities and then quote the two and their
difference, e.g., $m_1, m_2$, and $\Delta = m_2 - m_1$. We cannot enter all of $m_1, m_2$ and $\Delta$ into a constrained fit because they are not independent. In some cases, it is a good approximation to ignore the quantity with the largest error and put the other two into the fit. However, in some cases correlations are such that the errors on $m_1, m_2$ and $\Delta$ are comparable and none of the three values can be ignored. In this case, we put all three values into the fit and invoke an automated procedure to increase the errors prior to fitting such that the three quantities can be treated as independent measurements in the constrained fit. We include a note saying that this has been done.

### 5.2.2 Unconstrained averaging

To average data, we use a standard weighted least-squares procedure and in some cases, discussed below, increase the errors with a “scale factor.” We begin by assuming that measurements of a given quantity are uncorrelated, and calculate a weighted average and error as

$$ \bar{x} \pm \delta\bar{x} = \frac{\sum_i w_i x_i}{\sum_i w_i} \pm \left( \sum_i w_i \right)^{-1/2}, \quad (1) $$

where

$$ w_i = 1/(\delta x_i)^2. $$

Here $x_i$ and $\delta x_i$ are the value and error reported by the ith experiment, and the sums run over the N experiments. We then calculate $\chi^2 = \sum w_i(\bar{x} - x_i)^2$ and compare it with $N-1$, which is the expectation value of $\chi^2$ if the measurements are from a Gaussian distribution.

If $\chi^2/(N-1)$ is less than or equal to 1, and there are no known problems with the data, we accept the results.

If $\chi^2/(N-1)$ is very large, we may choose not to use the average at all. Alternatively, we may quote the calculated average, but then make an educated guess of the error, a conservative estimate designed to take into account known problems with the data.

Finally, if $\chi^2/(N-1)$ is greater than 1, but not greatly so, we still average the data, but then also do the following:

(a) We increase our quoted error, $\delta\bar{x}$ in Eq. (1), by a scale factor $S$ defined as

$$ S = \left[ \frac{\chi^2}{N-1} \right]^{1/2}. \quad (2) $$

Our reasoning is as follows. The large value of the $\chi^2$ is likely to be due to underestimation of errors in at least one of the experiments. Not knowing which of the errors are underestimated, we assume they are all underestimated by the same factor $S$. If we scale up all the input errors by this factor, the $\chi^2$ becomes $N-1$, and of course the output error $\delta\bar{x}$ scales up by the same factor. See Ref. [5].

When combining data with widely varying errors, we modify this procedure slightly. We evaluate $S$ using only the experiments with smaller errors. Our cutoff or ceiling on $\delta x_i$ is arbitrarily chosen to be

$$ \delta_0 = 3N^{1/2} \delta\bar{x}, $$

where $\delta\bar{x}$ is the unscaled error of the mean of all the experiments. Our reasoning is that although the low-precision experiments have little influence on the values $\bar{x}$ and $\delta\bar{x}$, they can make significant contributions to the $\chi^2$, and the contribution of the high-precision experiments thus tends to be obscured. Note that if each experiment has the same error $\delta x_i$, then $\delta\bar{x} = \delta x_i/N^{1/2}$, so each $\delta x_i$ is well below the cutoff. (More often, however, we simply exclude measurements with relatively large errors from averages and fits: new, precise data chase out old, imprecise data.)

Our scaling procedure has the property that if there are two values with comparable errors separated by much more than their stated errors (with or without a number of other values of lower accuracy), the scaled-up error $\delta\bar{x}$ is approximately half the interval between the two discrepant values.

We emphasize that our scaling procedure for errors in no way affects central values. And if you wish to recover the unscaled error $\delta\bar{x}$, simply divide the quoted error by $S$.

(b) If the number $M$ of experiments with an error smaller than $\delta_0$ is at least three, and if $\chi^2/(M-1)$ is greater than 1.25,

we show in the Particle Listings an ideogram of the data. Figure 1 is an example. Sometimes one or two data points lie apart from the main body; other times the data split into two or more groups. We extract no numbers from these ideograms; they are simply visual aids, which the reader may use as he or she sees fit.

Each measurement in an ideogram is represented by a Gaussian with a central value $x_i$, error $\delta x_i$, and area proportional to $1/\delta x_i$. The choice of $1/\delta x_i$ for the area is somewhat arbitrary. With this choice, the center of gravity of the ideogram corresponds to an average that uses weights $1/\delta x_i$ rather than the $(1/\delta x_i)^2$ actually used in the averages. This may be appropriate when some of the experiments have seriously underestimated systematic errors. However, since for this choice of area the height of the Gaussian for each measurement is proportional to $(1/\delta x_i)^2$, the peak position of the ideogram will often favor the high-precision measurements at least as much as does the least-squares average. See our 1986 edition [3] for a detailed discussion of the use of ideograms.

### 5.2.3 Constrained fits

In some cases, such as branching ratios or masses and mass differences, a constrained fit may be needed to obtain the best values of a set of parameters. For example, most branching ratios and rate measurements are analyzed by making a simultaneous least-squares fit to all the data and extracting the partial decay fractions $P_i$, the partial widths $\Gamma_i$, the full width $\Gamma$ (or mean life), and the associated error matrix.

Assume, for example, that a state has $m$ partial decay fractions $P_i$, where $\sum P_i = 1$. These have been measured in $N_r$ different ratios $R_r$, where, e.g., $R_1 = P_1/P_2$, $R_2 = P_1/P_3$, etc. [We can handle any ratio $R$ of the form $\sum \alpha_i P_i / \sum \beta_i P_i$, where $\alpha_i$ and $\beta_i$ are constants, usually 1 or 0. The forms $R = P_i P_j$ and $R = (P_i P_j)^{1/2}$ are also allowed.] Further, assume that each ratio $R$ has been measured by $N_k$ experiments (we designate each experiment with a subscript $k$, e.g., $R_{1k}$). We then find the best values of the fractions $P_i$ by minimizing the $\chi^2$ as a function of the $m-1$ independent parameters:

$$ \chi^2 = \sum_{r=1}^{N_r} \sum_{k=1}^{N_k} \left( \frac{R_{rk} - R_r}{\delta R_{rk}} \right)^2, \quad (3) $$

where the $R_{rk}$ are the measured values and $R_r$ are the fitted values of the branching ratios.

In addition to the fitted values $\bar{P}_i$, we calculate an error matrix $\langle\delta\bar{P}_i, \delta\bar{P}_j\rangle$. We tabulate the diagonal elements of $\delta\bar{P}_i = \langle\delta\bar{P}_i, \delta\bar{P}_j\rangle^{1/2}$ (except that some errors are scaled as discussed below). In the Particle Listings, we give the complete correlation matrix; we also calculate the fitted value of each ratio, for comparison with the input data, and list it above the relevant input, along with a simple unconstrained average of the same input.

Three comments on the example above:

(1) There was no connection assumed between measurements of the full width and the branching ratios. But often we also have information on partial widths $\Gamma_i$ as well as the total width $\Gamma$. In this case we must introduce $\Gamma$ as a parameter in the fit, along with the $P_i$, and we give correlation matrices for the widths in the Particle Listings.

(2) We try to pick those ratios and widths that are as independent and as close to the original data as possible. When one experiment measures all the branching fractions and constrains their sum to be one, we leave one of them (usually the least well-determined one) out of the fit to make the set of input data more nearly independent. We now do allow for correlations between input data.

(3) We calculate scale factors for both the $R_r$ and $P_i$ when the measurements for any $R$ give a larger-than-expected contribution to the $\chi^2$. According to Eq. (3), the double sum for $\chi^2$ is first summed over experiments $k=1$ to $N_k$, leaving a single sum over ratios $\chi^2 = \sum \chi_r^2$. One is tempted to define a scale factor for the ratio $r$ as $S_r^2 = \chi_r^2/\langle\chi_r^2\rangle$. However, since $\langle\chi_r^2\rangle$ is not a fixed quantity (it is somewhere between $N_k$ and $N_{k-1}$), we do not know
<figure><img src="image_5.png" /><figcaption>**Figure 1:** A typical ideogram. The arrow at the top shows the position of the weighted average, while the width of the shaded pattern shows the error in the average after scaling by the factor $S$. The column on the right gives the $\chi^2$ contribution of each of the experiments. Note that the next-to-last experiment, denoted by the incomplete error flag ($\perp$), is not used in the calculation of $S$ (see the text).</figcaption></figure>

how to evaluate this expression. Instead, we define

$$S_r^2 = \frac{1}{N_k} \sum_{k=1}^{N_k} \frac{(R_{rk} - \bar{R}_r)^2}{\langle (R_{rk} - \bar{R}_r)^2 \rangle}. \quad (4)$$

With this definition the expected value of $S_r^2$ is one. We can show that

$$\langle (R_{rk} - \bar{R}_r)^2 \rangle = \langle (\delta R_{rk})^2 \rangle - (\delta \bar{R}_r)^2, \quad (5)$$

where $\delta \bar{R}_r$ is the fitted error for ratio $r$.

The fit is redone using errors for the branching ratios that are scaled by the larger of $S_r$ and unity, from which new and often larger errors $\delta \bar{P}'_i$ are obtained. The scale factors we finally list in such cases are defined by $S_i = \delta \bar{P}'_i / \delta \bar{P}_i$. However, in line with our policy of not letting $S$ affect the central values, we give the values of $\bar{P}_i$ obtained from the original (unscaled) fit.

There is one special case in which the errors that are obtained by the preceding procedure may be changed. When a fitted branching ratio (or rate) $\bar{P}_i$ turns out to be less than three standard deviations $(\delta \bar{P}'_i)$ from zero, a new smaller error $(\delta \bar{P}''_i)^-$ is calculated on the low side by requiring the area under the Gaussian between $\bar{P}_i - (\delta \bar{P}''_i)^-$ and $\bar{P}_i$ to be 68.3% of the area between zero and $\bar{P}_i$. A similar correction is made for branching fractions that are within three standard deviations of one. This keeps the quoted errors from overlapping the boundary of the physical region.

## 5.3 Rounding

While the results shown in the Particle Listings are usually exactly those published by the experiments, the numbers that appear in the Summary Tables (means, averages and limits) are subject to a set of rounding rules.

The basic rule states that if the three highest order digits of the error lie between 100 and 354, we round to two significant digits. If they lie between 355 and 949, we round to one significant digit. Finally, if they lie between 950 and 999, we round up to 1000 and keep two significant digits. In all cases, the central value is given with a precision that matches that of the error. So, for example, the result (coming from an average) 0.827 ± 0.119 would appear as 0.83 ± 0.12, while 0.827 ± 0.367 would turn into 0.8 ± 0.4.

In cases where there are asymmetric errors, if these errors differ by less than 10 percent of the average of the two errors, the average is instead used as a symmetric error in the displayed result and the rounding is determined by this average. Otherwise, the narrower of the two asymmetric errors is used to determine the rounding on both.

Rounding of this form is also performed on the value of limits that come from calculations (but not on limits that are directly taken from a single source).

Finally, we should point out that in several instances, when a group of results come from a single fit to a set of data, we have chosen to keep two significant digits for all the results. This happens, for instance, for several properties of the $W$ and $Z$ bosons and the $\tau$ lepton.

## 5.4 Discussion

The problem of averaging data containing discrepant values is nicely discussed by Taylor in Ref. [6]. He considers a number of algorithms that attempt to incorporate inconsistent data into a meaningful average. However, it is difficult to develop a procedure that handles simultaneously in a reasonable way two basic types of situations: (a) data that lie apart from the main body of the data are incorrect (contain unreported errors); and (b) the opposite— it is the main body of data that is incorrect. Unfortunately, as Taylor shows, case (b) is not infrequent. He concludes that the choice of procedure is less significant than the initial choice of data to include or exclude.

We place much emphasis on this choice of data. Often we solicit the help of outside experts (consultants). Sometimes, however, it is simply impossible to determine which of a set of discrepant measurements are correct. Our scale-factor technique is an attempt to address this ignorance by increasing the error. In effect, we are saying that present experiments do not allow a precise determination of this quantity because of unresolvable discrepancies, and one must await further measurements. The reader is warned of this situation by the size of the scale factor, and if he or she desires can go back to the literature (via the Particle Listings) and redo the average with a different choice of data.

Our situation is less severe than most of the cases Taylor considers, such as estimates of the fundamental constants like $\hbar$, etc. Most of the errors in his case are dominated by systematic effects. For our data, statistical errors are often at least as large as systematic errors, and statistical errors are usually easier to estimate. A notable exception occurs in partial-wave analyses, where different techniques applied to the same data yield different results. In this case, as stated earlier, we often do not make an average but just quote a range of values.

A brief history of early Particle Data Group averages is given in Ref. [5]. Our History Plots show the time evolution of some of our values of a few particle properties. Sometimes large changes occur. These usually reflect the introduction of significant new data or the discarding of older data. Older data are discarded in favor of newer data when it is felt that the newer data have smaller systematic errors, or have more checks on systematic errors, or have made corrections unknown at the time of the older experiments, or simply have much smaller errors. Sometimes, the scale factor becomes large near the time at which a large jump takes place, reflecting the uncertainty introduced by the new and inconsistent data. By and large, however, a full scan of our history plots shows a dull progression toward greater precision at central values quite consistent with the first data points shown.

We conclude that the reliability of the combination of experimental data and our averaging procedures is usually good, but it is important to be aware that fluctuations outside of the quoted errors can and do occur.

## ACKNOWLEDGMENTS

The publication of the Review of Particle Physics is supported by the Director, Office of Science, Office of High Energy Physics of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231; by an implementing arrangement between the governments of Japan (MEXT: Ministry of Education, Culture, Sports, Science and Technology) and the United States (DOE) on cooperative research and development; by the Italian National Institute of Nuclear Physics (INFN); and by the European Laboratory for Particle Physics (CERN). Individual collaborators receive support for their PDG activities from their respective institutes or funding agencies.

We thank all those who have assisted in the many phases of preparing this Review. We particularly thank the many who have
responded to our requests for verification of data entered in the
Listings, and those who have made suggestions or pointed out
errors.

We are grateful to the staff at CERN, DESY, IHEP Beijing,
KEK, LBNL, and NISER who take care of the mailing and dis-
tribution of our products.

This work used resources of the National Energy Research Sci-
entific Computing Center, a DOE Office of Science User Facility
supported by the Office of Science of the U.S. Department of En-
ergy under Contract No. DE-AC02-05CH11231.

References

[1] The previous edition was: R.L. Workman *et al*. (Particle Data Group), Prog. Theor. Exp. Phys. **2022**, 083C01 (2022).

[2] C. Patrignani et al. (Particle Data Group), Chin. Phys. C40, 10, 100001 (2016).

[3] M. Aguilar-Benitez et al. (Particle Data Group), Phys. Lett. **170B**, 1 (1986).

[4] M. Tanabashi et al. (Particle Data Group), Phys. Rev. D **98**, 3, 030001 (2018).

[5] A. H. Rosenfeld, Ann. Rev. Nucl. Part. Sci. **25**, 555 (1975).

[6] B.N. Taylor, “Numerical Comparisons of Several Algorithms for Treating Inconsistent Data in a Least-Squares Adjustment of the Fundamental Constants,” U.S. National Bureau of Standards NBSIR 81-2426 (1982).
<figure><img src="image_6.png" /><figcaption>**Figure 1:** A historical perspective of values of a few particle properties tabulated in this *Review* as a function of date of publication of the *Review*. A full error bar indicates the quoted error; a thick-lined portion indicates the same but without the "scale factor."</figcaption></figure>
# Online Particle Physics Information

Revised August 2023 by K. Assamagan (BNL) and H.B. O'Connell (FNAL).

<table><tr><td>1</td><td>Introduction</td><td>20</td></tr><tr><td>2</td><td>Particle Data Group (PDG) resources</td><td>20</td></tr><tr><td>3</td><td>Particle physics information platform</td><td>20</td></tr><tr><td>4</td><td>Literature databases</td><td>20</td></tr><tr><td>5</td><td>Journals</td><td>21</td></tr><tr><td>6</td><td>Conference and seminars databases</td><td>21</td></tr><tr><td>7</td><td>Research institutions</td><td>21</td></tr><tr><td>8</td><td>People</td><td>21</td></tr><tr><td>9</td><td>Experiments</td><td>21</td></tr><tr><td>10</td><td>Jobs</td><td>21</td></tr><tr><td>11</td><td>Software packages and repositories</td><td>22</td></tr><tr><td>12</td><td>Data repositories and preservation</td><td>22</td></tr><tr><td>13</td><td>Particle physics education and outreach</td><td>22</td></tr><tr><td>14</td><td>Regional HEP efforts</td><td>22</td></tr></table>

## 1 Introduction

Online resources are used in a diverse and expanding set of ways in particle physics. Many of these resources have become central to our collective work. We provide a brief curated selection of the major resources here. An expanded and regularly updated online repository is referred to below and can be found at

https://github.com/particledatagroup/hep-resources

By contrast, it is meant to be inclusive and catalog all useful resources related to particle physics. The community is warmly invited to contribute in order to ensure a broad and up to date coverage of relevant resources. Practical details are available online.

## 2 Particle Data Group (PDG) resources

* **Review of Particle Physics (RPP):** A comprehensive report on the fields of particle physics and related areas of cosmology and astrophysics, including both review articles and a compilation/evaluation of data on particle properties. The review section includes articles, tables and plots on a wide variety of theoretical and experimental topics of interest to particle physicists and astrophysicists. The particle properties section provides tables of published measurements as well as the Particle Data Group's best values and limits for particle properties such as masses, widths, lifetimes, and branching fractions, as well as an extensive summary of searches for hypothetical particles. RPP is published as a large book every two years, with partial updates made available once each year on the web.

All the contents of the book version of RPP are available online:

https://pdg.lbl.gov

The printed book can be ordered:

https://pdg.lbl.gov/order

Of historical interest is the complete RPP collection which can be found online:

https://pdg.lbl.gov/publications

* **Particle Physics booklet:** An abridged version of the Review of Particle Physics, available as a pocket-sized 250-page booklet. It is one of the most useful summaries of physics data. The booklet contains an abbreviated set of reviews and the summary tables from the most recent edition of the Review of Particle Physics.

The PDF file of the booklet can be downloaded:

https://pdg.lbl.gov/current/booklet.pdf

The printed booklet can be ordered:

https://pdg.lbl.gov/order

A mobile version of the booklet is also available:

https://pdg.lbl.gov/booklet

* **PDGLive:** A web application for browsing the contents of the PDG database that contains the information published in the Review of Particle Physics. It allows one to navigate to a particle of interest, see a summary of the information available, and then proceed to the detailed information published

in the Review of Particle Physics. Data entries are directly linked to the corresponding bibliographic information in INSPIRE.

https://pdglive.lbl.gov

* **Computer-readable files:** Data files that can be downloaded from the PDG include tables of particle masses and widths, PDG Monte Carlo particle numbers, and cross-section data. The files are updated with each new edition of the Review of Particle Physics.

https://pdg.lbl.gov/files

* **PDG API:** In addition to the fixed-format data files that have been available for many years, PDG is developing new tools to access PDG data in machine-readable format (currently available as beta versions).

https://pdg.lbl.gov/api

## 3 Particle physics information platform

**INSPIRE:** INSPIRE serves as a one-stop information platform for the particle physics community, comprising interlinked databases on literature, authors, jobs, seminars, conferences, institutions and experiments (each described in more detail below). Run in collaboration by CERN (which hosts INSPIRE), DESY, Fermilab, IHEP, IN2P3 and SLAC, it has been serving the scientific community for almost 50 years. Previously hosted at SLAC and known as SPIRES, it was the first website outside Europe and the first database on the web. Close interaction with the user community and with arXiv, ADS, HEPData, ORCID, PDG and publishers is the backbone of INSPIRE's evolution. Since 2020, it is running on a modernized platform that is continuously being improved.

https://inspirehep.net/

## 4 Literature databases

Most research articles in the field of high-energy physics are first made available on the arXiv eprint server, where researchers can learn about the latest developments by browsing through the new announcements five days a week. They are indexed, together with all other publications in high-energy physics and related fields, in the INSPIRE literature collection. For neighboring fields such as astrophysics or mathematics, other databases are more exhaustive.

* **ADS:** The SAO/NASA Astrophysics Data System is a Digital Library portal offering access to 15 million bibliographic records in Astronomy and Physics. The ADS search engine also indexes the full-text for many publications in this collection and tracks citations. The system also provides access and links to a wealth of external resources, including electronic articles hosted by publishers and arXiv, data catalogs and a variety of data products hosted by the astronomy archives worldwide. The ADS can be accessed at:

http://ads.harvard.edu/

* **arXiv.org:** A repository of full-text articles in physics, astronomy, mathematics, computer science, statistics, nonlinear sciences, quantitative finance, quantitative biology, electrical engineering and systems science, and economics. Papers are submitted by registered authors to arXiv, often as preprints in advance of submission to a journal for publication; includes postprints, working papers, and other relevant material. Established in 1991, the repository is interlinked with ADS and INSPIRE, among others. Readers can browse subject categories or search by author, title, abstract, date, and other fields. Receive daily update alerts for subfields by email or RSS.

https://arxiv.org

* **INSPIRE Literature:** The literature collection, the flagship of the INSPIRE suite, serves more than 1.5 million bibliographic records with a growing number of full-text articles attached and metadata including author affiliations, abstracts, references, experiments, keywords as well as links to arXiv, ADS, PDG, HEPData, publisher platforms and other servers. It provides fast metadata searches that can be eas-
ily refined using facets, plots extracted from full text, author disambiguation, author profile pages and citation analysis.

https://inspirehep.net/literature

* **MathSciNet:** This database of almost 4 million items provides reviews, abstracts and bibliographic information for much of the mathematical sciences literature. Over 125,000 new items, most of them classified according to the Mathematics Subject Classification, and more than 90,000 reviews of the current published literature are added each year. Author identification allows users to search for publications by author and citation data allows users to track the history and influence of research publications.

https://www.ams.org/mathscinet

**OSTI.GOV:** A portal to free, publicly available DOE-sponsored R&D results including technical reports, bibliographic citations, journal articles, conference papers, books, multimedia and data information. It consolidates OSTI's home page and the now-retired primary search tool SciTech Connect. It contains over 3 million records, including citations to 1.5 million journal articles, 1 million of which have digital object identifiers (DOIs) linking to full-text articles on publishers' websites.

https://www.osti.gov/

## 5 Journals

* **CERN Journal List:** This list of journals and conference series publishing particle physics content provides information on Open Access, copyright policies and terms of use for CERN authors.

https://scientific-info.cern/submit-and-publish/
publish-open-access

* **INSPIRE Journals:** A database of almost 4,000 journals relevant to HEP and related fields. Each entry displays the papers published in the journal that are included in the INSPIRE Literature database.

https://inspirehep.net/journals

* **SCOAP³ Journals:** A list of journals currently financed by the SCOAP³ consortium. All HEP publications in those journals are made freely available under Open Access conditions at no cost for the authors.

https://www.scoap3.org/phase3-journals/

## 6 Conference and seminars databases

* **INSPIRE Conferences:** The database of more than 26,000 past, present, and future conferences, schools, and meetings relevant to high-energy physics and related fields is searchable by title, acronym, series, date and location. Included are information about published proceedings, links to conference contributions in the INSPIRE HEP database, and links to the conference website when available. New conferences can be submitted from the entry page.

https://inspirehep.net/conferences

* **INSPIRE Seminars:** Created to support the surge of online seminars during the COVID-19 pandemic, this database already contains more than 2,700 seminars in high-energy physics and related fields. Seminars can be filtered by date, series and subject and exported to a calendar. Direct links to join the online seminar and external resources are included. All seminars are community-maintained and can be submitted from the entry page.

https://inspirehep.net/seminars

* **researchseminars.org:** A list of research seminars and conferences, organized by topic and seminars series or conference.

https://researchseminars.org/

## 7 Research institutions

* **INSPIRE Institutions:** INSPIRE Institutions contains over 11,500 institutes, laboratories, and universities, where research on particle physics and astrophysics is led. Every record includes, whenever possible, as detailed information, such as address, web links, experiments, and links to INSPIRE papers authored by people affiliated to that institution.

One can search for a particular institution by name, acronym, and location.

https://inspirehep.net/institutions

* **Research Organization Registry (ROR):** The Research Organization Registry (ROR) is a global, community-led registry of open persistent identifiers for research organizations. It includes IDs and metadata for more than 100,000 organizations and counting. Registry updates are curated through a community process and released on a rolling basis.

https://ror.org/

## 8 People

* **INSPIRE Authors:** Searchable worldwide database of more than a hundred thousand active, departed, retired, and deceased people associated with particle physics and related fields. The affiliation history of these researchers, their e-mail addresses, ORCIDs, web pages, experiments they participated in, PhD advisor, information on their graduate students and links to their papers and seminars are provided, as well as a user interface to update this information.

https://inspirehep.net/authors

* **ORCID:** Registry providing persistent digital identifiers allowing to unambiguously identify researchers. Through integration in key research workflows such as manuscript and grant submission, it supports automated linkages between scientists and their professional activities ensuring that their work is recognized.

https://orcid.org

## 9 Experiments

* **INSPIRE Experiments:** Contains more than 3,700 past, present, and future experiments in particle physics. It lists and classifies both accelerator and non-accelerator experiments as well as theory collaborations. Includes official experiment name and number, location, and collaboration lists. Simple searches by participant, title, experiment number, institution, date approved, accelerator, or detector, return a description of the experiment, including a complete list of authors, title, overview of the experiment's goals and methods, and a link to the experiment's web page if available. Recently, it has expanded its scope to include particle accelerators besides experiments and to link them together.

https://inspirehep.net/experiments

* **Cosmic ray/Gamma ray/Neutrino and similar experiments:** This extensive collection of experiment websites is organized by focus of study and by location. Additional sections link to educational materials, organizations, and other useful resources. The site is maintained at the Max Planck Institute for Nuclear Physics, Heidelberg.

https://www.mpi-hd.mpg.de/hfm/CosmicRay/CosmicRaySites.html

* **Wikipedia particle experiments:** A list of particle experiments with Wikipedia pages.

https://en.wikipedia.org/wiki/Category:Particle_experiments

## 10 Jobs

* **AAS Job Register:** The American Astronomical Society publishes once a month graduate, postgraduate, faculty and other positions mainly in astronomy and astrophysics.

https://jobregister.aas.org/

* **Academic Jobs Online:** A full-service online recruiting site for academic institutions worldwide in all disciplines and areas.

https://academicjobsonline.org/

* **APS Careers:** A gateway for physicists, students, and physics enthusiasts to information about physics jobs and careers. It contains Physics job listings, career advice, upcoming workshops and meetings, and career and job-related resources provided by the American Physical Society.

https://www.aps.org/careers/employment/
* **INSPIRE Jobs:** Lists academic and research jobs in high energy physics, nuclear physics, accelerator physics and astrophysics with the option to post a job or to receive email notices of new job listings. Several hundreds of jobs are listed all year round, with more activity during the application season.

https://inspirehep.net/jobs

* **IOP Careers:** Career information and resources primarily aimed at university students are provided by the UK Institute of Physics.

https://www.iop.org/careers-physics/
your-future-with-physics

* **Physics Today Jobs:** Online recruitment advertising website for Physics Today magazine, published by the American Institute of Physics. Physics Today Jobs is the managing partner of the AIP Career Network, an online job board network for the physical science, engineering, and computing disciplines. Over 6,000 resumes are currently available, and nearly 5,000 jobs were posted in 2018.

https://jobs.physicstoday.org/

* **Physicsworld Jobs:** A recruitment service run by IOP Publishing that connects employers from different industry sectors with jobseekers who have a background in physics and engineering.

https://www.physicsworldjobs.com/

## 11 Software packages and repositories

A vast number of software tools are used for various aspects of high-energy physics research. Due to their number, their often specialized purpose and the quickly-changing nature of software, no attempt has been made to present them in this chapter. The accompanying online version contains an extensive categorized list of software.

## 12 Data repositories and preservation

Initiatives to preserve and disseminate data produced during different stages of research, from Monte Carlo events to machine-readable versions of tables in papers, have grown in recent years. Unfortunately, there currently exists no central resource aggregating all these data as is the case for the more established means of scholarly communication. Instead, there are a number of repositories targeting different types of data and research subjects. They are listed in the online version.

## 13 Particle physics education and outreach

Particle physics public engagement efforts are widespread, with laboratories, experiments, universities and individual researchers engaged in a range of efforts. The online version of this chapter provides links to resources for particle physicists wanting to become engaged in public education as well as resources that physicists can provide directly to students, teachers or lay people. There are classroom activities, interactive websites, films, and direct links to education offices at institutions and experiments. Many researchers also engage the public via a variety of social media platforms. Additionally, a selection of news sites relevant for experts and for the general public are provided.

## 14 Regional HEP efforts

The online version of this chapter provides links to summaries of regional HEP activities across Europe, Japan, the US, Africa, Latin America, and other regions that may be classified as developing or emerging. This list of summaries is not exhaustive and is based on the expert knowledge of the authors at the time of information gathering; the narrative was developed in July 2023 and will require periodic updates as the HEP landscape changes.
SUMMARY TABLES OF PARTICLE PHYSICS

<table><tr><td>Gauge and Higgs bosons</td><td>25</td></tr><tr><td>Leptons</td><td>28</td></tr><tr><td>Quarks</td><td>32</td></tr><tr><td>Mesons</td><td>33</td></tr><tr><td>Baryons</td><td>93</td></tr><tr><td>Searches not in Other Sections*</td><td>112</td></tr><tr><td>Tests of conservation laws</td><td>114</td></tr></table>

<table><tr><td>Meson Quick Reference Table</td><td>91</td></tr><tr><td>Baryon Quick Reference Table</td><td>92</td></tr></table>

<footnote>* There are also search limits in the Summary Tables for the Gauge and Higgs Bosons, the Leptons, the Quarks, and the Mesons.</footnote>
<figure><img src="image_7.png" /></figure>
# SUMMARY TABLES OF PARTICLE PROPERTIES

Extracted from the Particle Listings of the
*Review of Particle Physics*

S. Navas et al. (Particle Data Group),
Phys. Rev. D. **110**, 030001 (2024)

Available at https://pdg.lbl.gov

## Particle Data Group

S. Navas, C. Amsler, T. Gutsche, C. Hanhart, J.J. Hernández-Rey, C. Lourenço, A. Masoni, M. Mikhasenko, R.E. Mitchell, C. Patrignani, C. Schwanda, S. Spanier, G. Venanzoni, C.Z. Yuan, K. Agashe, G. Aielli, B.C. Allanach, J. Alvarez-Muñiz, M. Antonelli, E.C. Aschenauer, D.M. Asner, K. Assamagan, H. Baer, Sw. Banerjee, R.M. Barnett, L. Baudis, C.W. Bauer, J.J. Beatty, J. Beringer, A. Bettini, O. Biebel, K.M. Black, E. Blucher, R. Bonventre, R.A. Briere, A. Buckley, V.D. Burkert, M.A. Bychkov, R.N. Cahn, Z. Cao, M. Carena, G. Casarosa, A. Ceccucci, A. Cerri, R.S. Chivukula, G. Cowan, K. Cranmer, V. Crede, O. Cremonesi, G. D'Ambrosio, T. Damour, D. de Florian, A. de Gouvêa, T. DeGrand, S. Demers, Z. Demiragli, B.A. Dobrescu, M. D'Onofrio, M. Doser, H.K. Dreiner, P. Eerola, U. Egede, S. Eidelman, A.X. El-Khadra, J. Ellis, S. C. Eno, J. Erler, V.V. Ezhela, A. Fava, W. Fetscher, B.D. Fields, A. Freitas, H. Gallagher, T. Gershon, Y. Gershstein, T. Gherghetta, M.C. Gonzalez-Garcia, M. Goodman, C. Grab, A.V. Gritsan, C. Grojean, D.E. Groom, M. Grünewald, A. Gurtu, H.E. Haber, M. Hamel, S. Hashimoto, Y. Hayato, A. Hebecker, S. Heinemeyer, K. Hikasa, J. Hisano, A. Höcker, J. Holder, L. Hsu, J. Huston, T. Hyodo, Al. Ianni, M. Kado, M. Karliner, U.F. Katz, M. Kenzie, V.A. Khoze, S.R. Klein, F. Krauss, M. Kreps, P. Križan, B. Krusche, Y. Kwon, O. Lahav, L.P. Lellouch, J. Lesgourgues, A.R. Liddle, Z. Ligeti, C.-J. Lin, C. Lippmann, T.M. Liss, A. Lister, L. Littenberg, K.S. Lugovsky, S.B. Lugovsky, A. Lusiani, Y. Makida, F. Maltoni, A.V. Manohar, W.J. Marciano, J. Matthews, U.-G. Meißner, I.-A. Melzer-Pellmann, P. Mertsch, D.J. Miller, D. Milstead, K. Mönig, P. Molaro, F. Moortgat, M. Moskovic, N. Nagata, K. Nakamura, M. Narain, P. Nason, A. Nelles, M. Neubert, Y. Nir, H.B. O'Connell, C.A.J. O'Hare, K.A. Olive, J.A. Peacock, E. Pianori, A. Pich, A. Piepke, F. Pietropaolo, A. Pomarol, S. Pordes, S. Profumo, A. Quadt, K. Rabbertz, J. Rademacker, G. Raffelt, M. Ramsey-Musolf, P. Richardson, A. Ringwald, D.J. Robinson, S. Roesler, S. Rolli, A. Romaniouk, L.J. Rosenberg, J.L. Rosner, G. Rybka, M.G. Ryskin, R.A. Ryutin, B. Safdi, Y. Sakai, S. Sarkar, F. Sauli, O. Schneider, S. Schönert, K. Scholberg, A.J. Schwartz, J. Schwiening, D. Scott, F. Sefkow, U. Seljak, V. Sharma, S.R. Sharpe, V. Shiltsev, G. Signorelli, M. Silari, F. Simon, T. Sjöstrand, P. Skands, T. Skwarnicki, G.F. Smoot, A. Soffer, M.S. Sozzi, C. Spiering, A. Stahl, Y. Sumino, F. Takahashi, M. Tanabashi, J. Tanaka, M. Taševský, K. Terao, K. Terashi, J. Terning, U. Thoma, R.S. Thorne, L. Tiator, M. Titov, D.R. Tovey, K. Trabelsi, P. Urquijo, G. Valencia, R. Van de Water, N. Varelas, L. Verde, I. Vivarelli, P. Vogel, W. Vogelsang, V. Vorobyev, S.P. Wakely, W. Walkowiak, C.W. Walter, D. Wands, D.H. Weinberg, E.J. Weinberg, N. Wermes, M. White, L.R. Wiencke, S. Willocq, C.L. Woody, R.L. Workman, W.-M. Yao, M. Yokoyama, R. Yoshida, G. Zanderighi, G.P. Zeller, R.-Y. Zhu, S.-L. Zhu, F. Zimmermann, P.A. Zyla

## Technical Associates:

J. Anderson, M. Kramer, P. Schaffner, W. Zheng

©2024

(Approximate closing date for data: January 15, 2024)

# GAUGE AND HIGGS BOSONS

## γ (photon)

$$I(J^{PC}) = 0,1(1^{--})$$

Mass $m < 1 \times 10^{-18}$ eV

Charge $q < 1 \times 10^{-46}$ e (mixed charge)

Charge $q < 1 \times 10^{-35}$ e (single charge)

Mean life $\tau = \text{Stable}$

## g (gluon)

$$I(J^P) = 0(1^{-})$$

Mass $m = 0$ [a]

SU(3) color octet

## graviton

$$J = 2$$

Mass $m < 1.76 \times 10^{-23}$ eV

## W

$$J = 1$$

Charge = $\pm 1$ e

Mass $m = 80.3692 \pm 0.0133$ GeV [b]

$W/Z$ mass ratio = $0.88136 \pm 0.00015$

$m_Z - m_W = 10.818 \pm 0.013$ GeV

$m_{W^+} - m_{W^-} = -0.029 \pm 0.028$ GeV

Full width $\Gamma = 2.085 \pm 0.042$ GeV

$\langle N_{\pi^{\pm}} \rangle = 15.70 \pm 0.35$

$\langle N_{K^{\pm}} \rangle = 2.20 \pm 0.19$

$\langle N_p \rangle = 0.92 \pm 0.14$

$\langle N_{\text{charged}} \rangle = 19.39 \pm 0.08$

$W^-$ modes are charge conjugates of the modes below.

<table><thead><tr><th colspan="2">W<sup>+</sup> DECAY MODES</th><th>Fraction (Γ<sub>i</sub>/Γ)</th><th>Confidence level</th><th>p<br>(MeV/c)</th></tr></thead><tbody><tr><td>ℓ<sup>+</sup>ν</td><td>[c]</td><td>(10.86 ± 0.09) %</td><td></td><td>—</td></tr><tr><td>e<sup>+</sup>ν</td><td></td><td>(10.71 ± 0.16) %</td><td></td><td>40185</td></tr><tr><td>μ<sup>+</sup>ν</td><td></td><td>(10.63 ± 0.15) %</td><td></td><td>40185</td></tr><tr><td>τ<sup>+</sup>ν</td><td></td><td>(11.38 ± 0.21) %</td><td></td><td>40165</td></tr><tr><td>hadrons</td><td></td><td>(67.41 ± 0.27) %</td><td></td><td>—</td></tr><tr><td>π<sup>+</sup>γ</td><td></td><td>&lt; 7</td><td>× 10<sup>-6</sup></td><td>95%</td></tr><tr><td>D<sub>s</sub><sup>+</sup>γ</td><td></td><td>&lt; 6</td><td>× 10<sup>-4</sup></td><td>95%</td></tr><tr><td>cX</td><td></td><td>(33.3 ± 2.6) %</td><td></td><td>—</td></tr><tr><td>c<span style="text-decoration: overline;">3</span></td><td></td><td>(31 <sup>+13</sup><sub>-11</sub>) %</td><td></td><td>—</td></tr><tr><td>invisible</td><td>[d]</td><td>(1.4 ± 2.9) %</td><td></td><td>—</td></tr><tr><td>π<sup>+</sup> π<sup>+</sup> π<sup>-</sup></td><td></td><td>&lt; 1.01</td><td>× 10<sup>-6</sup></td><td>95%</td></tr></tbody></table>

## Z

$$J = 1$$

Charge = 0

Mass $m = 91.1880 \pm 0.0020$ GeV [e]

Full width $\Gamma = 2.4955 \pm 0.0023$ GeV

$\Gamma(\ell^+\ell^-) = 83.984 \pm 0.086$ MeV [c]

$\Gamma(\text{invisible}) = 499.2 \pm 1.5$ MeV [f]

$\Gamma(\text{hadrons}) = 1744.4 \pm 2.0$ MeV

$\Gamma(\mu^+\mu^-)/\Gamma(e^+e^-) = 1.0001 \pm 0.0024$

$\Gamma(\tau^+\tau^-)/\Gamma(e^+e^-) = 1.0020 \pm 0.0032$ [g]

## Average charged multiplicity

$$\langle N_{\text{charged}} \rangle = 20.76 \pm 0.16 \quad (S = 2.1)$$

## Couplings to quarks and leptons

$g_V^\ell = -0.03783 \pm 0.00041$

$g_V^u = 0.266 \pm 0.034$

$g_V^d = -0.38^{+0.04}_{-0.05}$

$g_A^\ell = -0.50123 \pm 0.00026$

$g_A^u = 0.519^{+0.028}_{-0.033}$

$g_A^d = -0.527^{+0.040}_{-0.028}$

$g_{\nu\ell} = 0.5008 \pm 0.0008$

$g_{\nu_e} = 0.53 \pm 0.09$

$g_{\nu_\mu} = 0.502 \pm 0.017$
Asymmetry parameters [n]

<table><tr><td>A<sub>e</sub></td><td>= 0.1515 ± 0.0019</td></tr><tr><td>A<sub>μ</sub></td><td>= 0.142 ± 0.015</td></tr><tr><td>A<sub>τ</sub></td><td>= 0.143 ± 0.004</td></tr><tr><td>A<sub>s</sub></td><td>= 0.90 ± 0.09</td></tr><tr><td>A<sub>c</sub></td><td>= 0.670 ± 0.027</td></tr><tr><td>A<sub>b</sub></td><td>= 0.923 ± 0.020</td></tr></table>

Charge asymmetry (%) at Z pole

<table><tr><td>A<sup>(0)</sup><sub>FB</sub></td><td>= 1.71 ± 0.10</td></tr><tr><td>A<sup>(0u)</sup><sub>FB</sub></td><td>= 4 ± 7</td></tr><tr><td>A<sup>(0s)</sup><sub>FB</sub></td><td>= 9.8 ± 1.1</td></tr><tr><td>A<sup>(0c)</sup><sub>FB</sub></td><td>= 7.07 ± 0.35</td></tr><tr><td>A<sup>(0b)</sup><sub>FB</sub></td><td>= 9.92 ± 0.16</td></tr></table>

<table><thead><tr><th>Z DECAY MODES</th><th>Fraction (Γ<sub>f</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th><th>ρ<br>(MeV/c)</th></tr></thead><tbody><tr><td>e<sup>+</sup> e<sup>-</sup></td><td>( 3.3632±0.0042 ) %</td><td></td><td>45594</td></tr><tr><td>μ<sup>+</sup> μ<sup>-</sup></td><td>( 3.3662±0.0066 ) %</td><td></td><td>45594</td></tr><tr><td>τ<sup>+</sup> τ<sup>-</sup></td><td>( 3.3696±0.0083 ) %</td><td></td><td>45559</td></tr><tr><td>ℓ<sup>+</sup> ℓ<sup>-</sup></td><td>[c] ( 3.3658±0.0023 ) %</td><td></td><td>-</td></tr><tr><td>ℓ<sup>+</sup> ℓ<sup>-</sup> ℓ<sup>+</sup> ℓ<sup>-</sup></td><td>[l] ( 4.55 ± 0.17 ) × 10<sup>-6</sup></td><td></td><td>45594</td></tr><tr><td>invisible</td><td>(20.000 ± 0.055 ) %</td><td></td><td>-</td></tr><tr><td>hadrons</td><td>(69.911 ± 0.056 ) %</td><td></td><td>-</td></tr><tr><td>(uū+cū)/2</td><td>(11.6 ± 0.6 ) %</td><td></td><td>-</td></tr><tr><td>(dū+dū+bū)/3</td><td>(15.6 ± 0.4 ) %</td><td></td><td>-</td></tr><tr><td>cū</td><td>(12.03 ± 0.21 ) %</td><td></td><td>-</td></tr><tr><td>bū</td><td>(15.12 ± 0.05 ) %</td><td></td><td>-</td></tr><tr><td>būbū</td><td>( 3.6 ± 1.3 ) × 10<sup>-4</sup></td><td></td><td>-</td></tr><tr><td>ggg</td><td>&lt; 1.1</td><td>%</td><td>CL=95%</td></tr><tr><td>π<sup>0</sup>γ</td><td>&lt; 2.01</td><td>× 10<sup>-5</sup></td><td>CL=95%</td></tr><tr><td>ηγ</td><td>&lt; 5.1</td><td>× 10<sup>-5</sup></td><td>CL=95%</td></tr><tr><td>ρ<sup>0</sup>γ</td><td>&lt; 4.0</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>ωγ</td><td>&lt; 3.9</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>η'(958)γ</td><td>&lt; 4.2</td><td>× 10<sup>-5</sup></td><td>CL=95%</td></tr><tr><td>φγ</td><td>&lt; 7</td><td>× 10<sup>-7</sup></td><td>CL=95%</td></tr><tr><td>γγ</td><td>&lt; 1.46</td><td>× 10<sup>-5</sup></td><td>CL=95%</td></tr><tr><td>π<sup>0</sup>π<sup>0</sup></td><td>&lt; 1.52</td><td>× 10<sup>-5</sup></td><td>CL=95%</td></tr><tr><td>γγγ</td><td>&lt; 2.2</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>π<sup>±</sup> W<sup>∓</sup></td><td>[J] &lt; 7</td><td>× 10<sup>-5</sup></td><td>CL=95%</td></tr><tr><td>ρ<sup>±</sup> W<sup>∓</sup></td><td>[J] &lt; 8.3</td><td>× 10<sup>-5</sup></td><td>CL=95%</td></tr><tr><td>J/ψ(1S)X</td><td>( 3.51 <sup>+0.23</sup><sub>-0.25</sub> ) × 10<sup>-3</sup></td><td>S=1.1</td><td>-</td></tr><tr><td>J/ψ(1S)γ</td><td>&lt; 1.2</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>ψ(2S)X</td><td>( 1.60 ± 0.29 ) × 10<sup>-3</sup></td><td></td><td>-</td></tr><tr><td>ψ(2S)γ</td><td>&lt; 2.4</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>J/ψ(1S)J/ψ(1S)</td><td>&lt; 2.2</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>χc1(1P)X</td><td>( 2.9 ± 0.7 ) × 10<sup>-3</sup></td><td></td><td>-</td></tr><tr><td>χc2(1P)X</td><td>&lt; 3.2</td><td>× 10<sup>-3</sup></td><td>CL=90%</td></tr><tr><td>Υ(1S) X + Υ(2S) X + Υ(3S) X</td><td>( 1.0 ± 0.5 ) × 10<sup>-4</sup></td><td></td><td>-</td></tr><tr><td>Υ(1S)X</td><td>&lt; 4.4</td><td>× 10<sup>-5</sup></td><td>CL=95%</td></tr><tr><td>Υ(1S)γ</td><td>&lt; 1.1</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>Υ(2S)X</td><td>&lt; 1.39</td><td>× 10<sup>-4</sup></td><td>CL=95%</td></tr><tr><td>Υ(2S)γ</td><td>&lt; 1.3</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>Υ(3S)X</td><td>&lt; 9.4</td><td>× 10<sup>-5</sup></td><td>CL=95%</td></tr><tr><td>Υ(3S)γ</td><td>&lt; 2.4</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>Υ(1,2,3S) Υ(1,2,3S)</td><td>&lt; 1.5</td><td>× 10<sup>-6</sup></td><td>CL=95%</td></tr><tr><td>D<sup>0</sup>γ</td><td>&lt; 2.2</td><td>× 10<sup>-3</sup></td><td>CL=95%</td></tr><tr><td>(D<sup>0</sup>/D<sup>0</sup>) X</td><td>( 20.7 ± 2.0 ) %</td><td></td><td>-</td></tr><tr><td>D<sup>±</sup>X</td><td>( 12.2 ± 1.7 ) %</td><td></td><td>-</td></tr><tr><td>D<sup>*</sup>(2010)±X</td><td>[J] ( 11.4 ± 1.3 ) %</td><td></td><td>-</td></tr><tr><td>D<sub>s</sub>(2536)±X</td><td>( 3.6 ± 0.8 ) × 10<sup>-3</sup></td><td></td><td>-</td></tr><tr><td>D<sub>s</sub>,J(2573)±X</td><td>( 5.8 ± 2.2 ) × 10<sup>-3</sup></td><td></td><td>-</td></tr><tr><td>D<sup>*</sup>'(2629)±X</td><td>searched for</td><td></td><td>-</td></tr><tr><td>B<sup>+</sup>X</td><td>[k] ( 6.08 ± 0.13 ) %</td><td></td><td>-</td></tr><tr><td>B<sup>0</sup>X</td><td>[k] ( 1.59 ± 0.13 ) %</td><td></td><td>-</td></tr><tr><td>B<sup>+</sup>X</td><td>searched for</td><td></td><td>-</td></tr><tr><td>Λ<sup>+</sup>X</td><td>( 1.54 ± 0.33 ) %</td><td></td><td>-</td></tr><tr><td>Ξ<sup>+</sup>X</td><td>seen</td><td></td><td>-</td></tr><tr><td>Ξ<sup>-</sup>X</td><td>seen</td><td></td><td>-</td></tr><tr><td>Ξ<sup>-</sup>X</td><td>seen</td><td></td><td>-</td></tr><tr><td>b-baryon X</td><td>[k] ( 1.38 ± 0.22 ) %</td><td></td><td>-</td></tr><tr><td>anomalous γ + hadrons</td><td>[J] &lt; 3.2</td><td>× 10<sup>-3</sup></td><td>CL=95%</td></tr><tr><td>e<sup>+</sup> e<sup>-</sup>γ</td><td>[J] &lt; 5.2</td><td>× 10<sup>-4</sup></td><td>CL=95%</td></tr></tbody></table>

<table><tr><td>μ<sup>+</sup> μ<sup>-</sup> γ</td><td>[l] &lt; 5.6</td><td>× 10<sup>-4</sup></td><td>CL=95%</td><td>45594</td></tr><tr><td>τ<sup>+</sup> τ<sup>-</sup> γ</td><td>[l] &lt; 7.3</td><td>× 10<sup>-4</sup></td><td>CL=95%</td><td>45559</td></tr><tr><td>ℓ<sup>+</sup> ℓ<sup>-</sup> γγ</td><td>[n] &lt; 6.8</td><td>× 10<sup>-6</sup></td><td>CL=95%</td><td>-</td></tr><tr><td>qūūγγ</td><td>[n] &lt; 5.5</td><td>× 10<sup>-6</sup></td><td>CL=95%</td><td>-</td></tr><tr><td>νūνγγ</td><td>[n] &lt; 3.1</td><td>× 10<sup>-6</sup></td><td>CL=95%</td><td>45594</td></tr><tr><td>e<sup>±</sup> μ<sup>∓</sup></td><td>LF [J] &lt; 2.62</td><td>× 10<sup>-7</sup></td><td>CL=95%</td><td>45594</td></tr><tr><td>e<sup>±</sup> τ<sup>∓</sup></td><td>LF [J] &lt; 5.0</td><td>× 10<sup>-6</sup></td><td>CL=95%</td><td>45577</td></tr><tr><td>μ<sup>±</sup> τ<sup>∓</sup></td><td>LF [J] &lt; 6.5</td><td>× 10<sup>-6</sup></td><td>CL=95%</td><td>45577</td></tr><tr><td>pe</td><td>L,B &lt; 1.8</td><td>× 10<sup>-6</sup></td><td>CL=95%</td><td>45589</td></tr><tr><td>ρμ</td><td>L,B &lt; 1.8</td><td>× 10<sup>-6</sup></td><td>CL=95%</td><td>45589</td></tr></table>

H

was H⁰

J = 0

Mass m = 125.20 ± 0.11 GeV (S = 1.4)

Full width Γ = 3.7<sup>+1.9</sup><sub>-1.4</sub> MeV (assumes equal on-shell and off-shell effective couplings)

H Signal Strengths in Different Channels

Combined Final States = 1.03 ± 0.04

WW* = 1.00 ± 0.08

ZZ* = 1.02 ± 0.08

γγ = 1.10 ± 0.06

cū Final State < 14, CL = 95%

bū = 0.99 ± 0.12

μ<sup>+</sup> μ<sup>-</sup> = 1.21 ± 0.35

τ<sup>+</sup> τ<sup>-</sup> = 0.91 ± 0.09

Zγ = 2.2 ± 0.7

γ*γ Final State = 1.5 ± 0.5

Fermion coupling (κ<sub>F</sub>) = 0.94 ± 0.05

Gauge boson coupling (κ<sub>V</sub>) = 1.023 ± 0.026

t<span style="text-decoration: overline;">t</span>H Production = 1.10 ± 0.18

HH Production Cross Section in pp Collisions < 2.4, CL = 95%

tH production = 6 ± 4

H Production Cross Section in pp Collisions at √s = 13 TeV = 56.8 ± 3.4 pb

<table><thead><tr><th>H DECAY MODES</th><th>Fraction (Γ<sub>f</sub>/Γ)</th><th>Confidence level</th><th>ρ<br>(MeV/c)</th></tr></thead><tbody><tr><td>WW*</td><td>(25.7 ± 2.5 ) %</td><td></td><td>-</td></tr><tr><td>ZZ*</td><td>( 2.80 ± 0.30 ) %</td><td></td><td>-</td></tr><tr><td>γγ</td><td>( 2.50 ± 0.20 ) × 10<sup>-3</sup></td><td></td><td>62600</td></tr><tr><td>būū</td><td>( 53 ± 8 ) %</td><td></td><td>-</td></tr><tr><td>e<sup>+</sup> e<sup>-</sup></td><td>&lt; 3.0</td><td>× 10<sup>-4</sup></td><td>95%</td></tr><tr><td>μ<sup>+</sup> μ<sup>-</sup></td><td>( 2.6 ± 1.3 ) × 10<sup>-4</sup></td><td></td><td>62600</td></tr><tr><td>τ<sup>+</sup> τ<sup>-</sup></td><td>( 6.0 <sup>+0.8</sup><sub>-0.7</sub> ) %</td><td></td><td>62575</td></tr><tr><td>Zγ</td><td>( 3.4 ± 1.1 ) × 10<sup>-3</sup></td><td></td><td>29392</td></tr><tr><td>Zρ(770)</td><td>&lt; 1.21</td><td>%</td><td>95%</td></tr><tr><td>Zφ(1020)</td><td>&lt; 3.6</td><td>× 10<sup>-3</sup></td><td>95%</td></tr><tr><td>ZJ/ψ</td><td>&lt; 1.9</td><td>× 10<sup>-3</sup></td><td>95%</td></tr><tr><td>Zψ(2S)</td><td>&lt; 6.6</td><td>× 10<sup>-3</sup></td><td>95%</td></tr><tr><td>J/ψγ</td><td>&lt; 2.0</td><td>× 10<sup>-4</sup></td><td>95%</td></tr><tr><td>J/ψJ/ψ</td><td>&lt; 3.8</td><td>× 10<sup>-4</sup></td><td>95%</td></tr><tr><td>ψ(2S)γ</td><td>&lt; 1.05</td><td>× 10<sup>-3</sup></td><td>95%</td></tr><tr><td>ψ(2S)J/ψ</td><td>&lt; 2.1</td><td>× 10<sup>-3</sup></td><td>95%</td></tr><tr><td>ψ(2S)ψ(2S)</td><td>&lt; 3.0</td><td>× 10<sup>-3</sup></td><td>95%</td></tr><tr><td>Υ(1S)γ</td><td>&lt; 2.5</td><td>× 10<sup>-4</sup></td><td>95%</td></tr><tr><td>Υ(1S)Υ(1S)</td><td>&lt; 1.7</td><td>× 10<sup>-3</sup></td><td>95%</td></tr><tr><td>Υ(2S)γ</td><td>&lt; 4.2</td><td>× 10<sup>-4</sup></td><td>95%</td></tr><tr><td>Υ(3S)γ</td><td>&lt; 3.4</td><td>× 10<sup>-4</sup></td><td>95%</td></tr><tr><td>Υ(nS)Υ(mS)</td><td>&lt; 3.5</td><td>× 10<sup>-4</sup></td><td>95%</td></tr><tr><td>ρ(770)γ</td><td>&lt; 1.04</td><td>× 10<sup>-3</sup></td><td>95%</td></tr><tr><td>ω(782)γ</td><td>&lt; 5.5</td><td>× 10<sup>-4</sup></td><td>95%</td></tr><tr><td>K*(892)γ</td><td>&lt; 2.2</td><td>× 10<sup>-4</sup></td><td>95%</td></tr><tr><td>φ(1020)γ</td><td>&lt; 5</td><td>× 10<sup>-4</sup></td><td>95%</td></tr><tr><td>eμ</td><td>LF &lt; 4.4</td><td>× 10<sup>-5</sup></td><td>95%</td></tr><tr><td>eτ</td><td>LF &lt; 2.0</td><td>× 10<sup>-3</sup></td><td>95%</td></tr><tr><td>μτ</td><td>LF &lt; 1.5</td><td>× 10<sup>-3</sup></td><td>95%</td></tr><tr><td>invisible</td><td>&lt; 10.7</td><td>%</td><td>95%</td></tr><tr><td>γ invisible</td><td>&lt; 2.9</td><td>%</td><td>95%</td></tr></tbody></table>
Neutral Higgs Bosons, Searches for

Mass limits for heavy neutral Higgs bosons ($H_0^0, A^0$) in the MSSM

m > 1121 GeV, CL = 95% (tanβ = 10)

m > 1475 GeV, CL = 95% (tanβ = 20)

m > 1677 GeV, CL = 95% (tanβ = 30)

m > 1826 GeV, CL = 95% (tanβ = 40)

m > 1950 GeV, CL = 95% (tanβ = 50)

m > 2062 GeV, CL = 95% (tanβ = 60)

Charged Higgs Bosons ($H^±$ and $H^{±±}$), Searches for

Mass limits for $m_{H^+} < m(\text{top})$ in the MSSM

m > 155 GeV, CL = 95%

Mass limits for $m_{H^+} > m(\text{top})$ in the MSSM

m > 181 GeV, CL = 95% (tanβ = 10)

m > 249 GeV, CL = 95% (tanβ = 20)

m > 390 GeV, CL = 95% (tanβ = 30)

m > 894 GeV, CL = 95% (tanβ = 40)

m > 1017 GeV, CL = 95% (tanβ = 50)

m > 1103 GeV, CL = 95% (tanβ = 60)

New Heavy Bosons ($W'$, $Z'$, leptoquarks, etc.), Searches for

Additional W Bosons

W' with standard couplings

Mass m > 6000 GeV, CL = 95% (pp direct search)

$W_R$ (Right-handed W Boson)

Mass m > 715 GeV, CL = 90% (electroweak fit)

Additional Z Bosons

$Z'_{SM}$ with standard couplings

Mass m > 5150 GeV, CL = 95% (pp direct search)

$Z_{LR}$ of $SU(2)_L \times SU(2)_R \times U(1)$ (with $g_L = g_R$)

Mass m > 630 GeV, CL = 95% (p$\bar{p}$ direct search)

Mass m > 1162 GeV, CL = 95% (electroweak fit)

$Z_\chi$ of $SO(10) \to SU(5) \times U(1)_\chi$ (with $g_\chi=e/\cos\theta_W$)

Mass m > 4800 GeV, CL = 95% (pp direct search)

$Z_\psi$ of $E_6 \to SO(10) \times U(1)_\psi$ (with $g_\psi=e/\cos\theta_W$)

Mass m > 4560 GeV, CL = 95% (pp direct search)

$Z_\eta$ of $E_6 \to SU(3) \times SU(2) \times U(1) \times U(1)_\eta$ (with $g_\eta=e/\cos\theta_W$)

Mass m > 3.900 × 10³ GeV, CL = 95% (pp direct search)

Scalar Leptoquarks

m > 1800 GeV, CL = 95% (1st gen., pair prod., B(eq)=1)

m > 1755 GeV, CL = 95% (1st gen., single prod., B(eq)=1)

m > 1700 GeV, CL = 95% (2nd gen., pair prod., B(μq)=1)

m > 660 GeV, CL = 95% (2nd gen., single prod., B(μq)=1)

m > 1460 GeV, CL = 95% (3rd gen., pair prod., B(τb)=1)

m > 1280 GeV, CL = 95% (3rd gen., single prod., B(τb)=1)

(See the Particle Listings for assumptions on leptoquark quantum numbers and branching fractions.)

Diquarks

Mass m > 7200 GeV, CL = 95% ($E_6$ diquark)

Axigluon

Mass m > 6600 GeV, CL = 95%

Axions ($A^0$) and Other Very Light Bosons, Searches for

See the review on "Axions and other similar particles."

The best limit for the half-life of neutrinoless double beta decay with Majoron emission is > 7.2 × 10²⁴ years (CL = 90%).

NOTES

In this Summary Table:

When a quantity has "($S = ...$)" to its right, the error on the quantity has been enlarged by the "scale factor" S, defined as $S = \sqrt{\chi^2/(N-1)}$, where N is the number of measurements used in calculating the quantity. We do this when $S > 1$, which often indicates that the measurements are inconsistent. When $S > 1.25$, we also show in the Particle Listings an ideogram of the measurements. For more about S, see the Introduction.

A decay momentum p is given for each decay mode. For a 2-body decay, p is the momentum of each decay product in the rest frame of the decaying particle. For a 3-or-more-body decay, p is the largest momentum any of the products can have in this frame.

[a] Theoretical value. A mass as large as a few MeV may not be precluded.

[b] This value does not include the AALTONEN 22 measurement by CDF. See the W mass section in the listings for details.

[c] $\ell$ indicates each type of lepton (e, μ, and τ), not sum over them.

[d] This represents the width for the decay of the W boson into a charged particle with momentum below detectability, $p<200$ MeV.

[e] The Z-boson mass listed here corresponds to a Breit-Wigner resonance parameter. It lies approximately 34 MeV above the real part of the position of the pole (in the energy-squared plane) in the Z-boson propagator.

[f] This partial width takes into account Z decays into $\nu\bar{\nu}$ and any other possible undetected modes.

[g] This ratio has not been corrected for the $\tau$ mass.

[h] Here $A \equiv 2g_Vg_A/(g_V^2+g_A^2)$.

[i] Here $\ell$ indicates e or μ.

[j] The value is for the sum of the charge states or particle/antiparticle states indicated.

[k] This value is updated using the product of (i) the $Z \to b\bar{b}$ fraction from this listing and (ii) the b-hadron fraction in an unbiased sample of weakly decaying b-hadrons produced in Z-decays provided by the Heavy Flavor Averaging Group (HFLAV, http://www.slac.stanford.edu/xorg/hflav/osc/PDG2009/#FRACZ).

[l] See the Z Particle Listings for the $\gamma$ energy range used in this measurement.

[n] For $m_{\gamma\gamma} = (60 \pm 5)$ GeV.
LEPTONS

e

$J = \frac{1}{2}$

$$ \text{Mass } m = (548.579909065 \pm 0.000000016) \times 10^{-6} \text{ u} $$

$$ \text{Mass } m = 0.51099895000 \pm 0.00000000015 \text{ MeV} $$

$$ \begin{aligned} |m_{e^+} - m_{e^-}|/m &< 8 \times 10^{-9}, \text{ CL} = 90\% \\ |q_{e^+} + q_{e^-}|/e &< 4 \times 10^{-8} \end{aligned} $$

Magnetic moment anomaly

$$ (g-2)/2 = (1159.65218062 \pm 0.00000012) \times 10^{-6} $$

$$ (g_{e^+} - g_{e^-}) / g_{\text{average}} = (-0.5 \pm 2.1) \times 10^{-12} $$

$$ \text{Electric dipole moment } d < 0.041 \times 10^{-28} \text{ e cm, CL} = 90\% $$

$$ \text{Mean life } \tau > 6.6 \times 10^{28} \text{ yr, CL} = 90\% \text{ [a]} $$

μ

$J = \frac{1}{2}$

$$ \text{Mass } m = 0.1134289259 \pm 0.0000000025 \text{ u} $$

$$ \text{Mass } m = 105.6583755 \pm 0.00000023 \text{ MeV} $$

$$ \text{Mean life } \tau = (2.1969811 \pm 0.00000022) \times 10^{-6} \text{ s} $$

$$ \begin{aligned} \tau_{\mu^+}/\tau_{\mu^-} &= 1.00002 \pm 0.00008 \\ c\tau &= 658.6384 \text{ m} \end{aligned} $$

$$ \text{Magnetic moment anomaly } (g-2)/2 = (11659205.9 \pm 2.2) \times 10^{-10} $$

$$ (g_{\mu^+} - g_{\mu^-}) / g_{\text{average}} = (-0.11 \pm 0.12) \times 10^{-8} $$

$$ \text{Electric dipole moment } |d| < 1.8 \times 10^{-19} \text{ e cm, CL} = 95\% $$

Decay parameters [b]

$$ \rho = 0.74979 \pm 0.00026 $$

$$ \eta = 0.057 \pm 0.034 $$

$$ \delta = 0.75047 \pm 0.00034 $$

$$ \xi P_{\mu} = 1.0009^{+0.0016}_{-0.0007} \text{ [c]} $$

$$ \xi P_{\mu} \delta / \rho = 1.0018^{+0.0016}_{-0.0007} \text{ [c]} $$

$$ \xi' = 1.00 \pm 0.04 $$

$$ \xi'' = 0.98 \pm 0.04 $$

$$ \alpha/A = (0 \pm 4) \times 10^{-3} $$

$$ \alpha'/A = (-10 \pm 20) \times 10^{-3} $$

$$ \beta/A = (4 \pm 6) \times 10^{-3} $$

$$ \beta'/A = (2 \pm 7) \times 10^{-3} $$

$$ \bar{\eta} = 0.02 \pm 0.08 $$

$\mu^+$ modes are charge conjugates of the modes below.

<table><thead><tr><th>μ<sup>-</sup> DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>Confidence level</th><th>ρ<br>(MeV/c)</th></tr></thead><tbody><tr><td>e<sup>-</sup>ν<sub>e</sub>ν<sub>μ</sub></td><td colspan="3">≈ 100%</td></tr><tr><td>e<sup>-</sup>ν<sub>e</sub>ν<sub>μ</sub>γ</td><td colspan="3">[d] (6.0±0.5) × 10<sup>-8</sup></td></tr><tr><td>e<sup>-</sup>ν<sub>e</sub>ν<sub>μ</sub> e<sup>+</sup> e<sup>-</sup></td><td colspan="3">[e] (3.4±0.4) × 10<sup>-5</sup></td></tr><tr><td colspan="4"><strong>Lepton Family number (LF) violating modes</strong></td></tr><tr><td>e<sup>-</sup>ν<sub>e</sub>ν<sub>μ</sub></td><td>LF</td><td>[f] &lt; 1.2</td><td>% 90%</td></tr><tr><td>e<sup>-</sup>γ</td><td>LF</td><td>&lt; 4.2</td><td>× 10<sup>-13</sup></td></tr><tr><td>e<sup>-</sup> e<sup>+</sup> e<sup>-</sup></td><td>LF</td><td>&lt; 1.0</td><td>× 10<sup>-12</sup></td></tr><tr><td>e<sup>-</sup> 2γ</td><td>LF</td><td>&lt; 7.2</td><td>× 10<sup>-11</sup></td></tr></tbody></table>

τ

$J = \frac{1}{2}$

$$ \text{Mass } m = 1776.93 \pm 0.09 \text{ MeV} $$

$$ (m_{\tau^+} - m_{\tau^-})/m_{\text{average}} < 2.8 \times 10^{-4}, \text{ CL} = 90\% $$

$$ \text{Mean life } \tau = (290.3 \pm 0.5) \times 10^{-15} \text{ s} $$

$$ c\tau = 87.03 \text{ μm} $$

$$ \text{Magnetic moment anomaly} = -0.057 \text{ to } 0.024, \text{ CL} = 95\% $$

$$ \text{Re}(d_{\tau}) = -0.185 \text{ to } 0.061 \times 10^{-16} \text{ e cm, CL} = 95\% $$

$$ \text{Im}(d_{\tau}) = -0.103 \text{ to } 0.0230 \times 10^{-16} \text{ e cm, CL} = 95\% $$

Weak dipole moment

$$ \text{Re}(d_{\tau}^{W}) < 0.50 \times 10^{-17} \text{ e cm, CL} = 95\% $$

$$ \text{Im}(d_{\tau}^{W}) < 1.1 \times 10^{-17} \text{ e cm, CL} = 95\% $$

Weak anomalous magnetic dipole moment

$$ \text{Re}(\alpha_{\tau}^{W}) < 1.1 \times 10^{-3}, \text{ CL} = 95\% $$

$$ \text{Im}(\alpha_{\tau}^{W}) < 2.7 \times 10^{-3}, \text{ CL} = 95\% $$

$$ \tau^{\pm} \rightarrow \pi^{\pm} K_{S}^{0} \nu_{\tau} \text{ (RATE DIFFERENCE) / (RATE SUM)} = (-0.36 \pm 0.25)\% $$

Decay parameters

See the τ Particle Listings for a note concerning τ-decay parameters.

$$ \rho(e \text{ or } \mu) = 0.745 \pm 0.008 $$

$$ \rho(e) = 0.747 \pm 0.010 $$

$$ \rho(\mu) = 0.763 \pm 0.020 $$

$$ \xi(e \text{ or } \mu) = 0.985 \pm 0.030 $$

$$ \xi(e) = 0.994 \pm 0.040 $$

$$ \xi(\mu) = 1.030 \pm 0.059 $$

$$ \eta(e \text{ or } \mu) = 0.013 \pm 0.020 $$

$$ \eta(\mu) = 0.094 \pm 0.073 $$

$$ (\delta\xi)(e \text{ or } \mu) = 0.746 \pm 0.021 $$

$$ (\delta\xi)(e) = 0.734 \pm 0.028 $$

$$ (\delta\xi)(\mu) = 0.778 \pm 0.037 $$

$$ \xi(\pi) = 0.993 \pm 0.022 $$

$$ \xi(\rho) = 0.994 \pm 0.008 $$

$$ \xi(a_1) = 1.001 \pm 0.027 $$

$$ \xi(\text{all hadronic modes}) = 0.995 \pm 0.007 $$

$$ \xi'(\mu) = 0.2 \pm 1.0 $$

$$ \bar{\eta}(\mu) = -1.3 \pm 1.7 $$

$$ (\xi\kappa)(e \text{ or } \mu) = 0.5 \pm 0.4 $$

$$ (\xi\kappa)(e) = -0.4 \pm 1.2 $$

$$ (\xi\kappa)(\mu) = 0.8 \pm 0.6 $$

$\tau^+$ modes are charge conjugates of the modes below. “$h^{\pm}$” stands for $\pi^{\pm}$ or $K^{\pm}$. “$e^+$” stands for $e$ or $\mu$. “Neutrals” stands for $\gamma$'s and/or $\pi^0$'s.

<table><thead><tr><th>τ<sup>-</sup> DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th><th>ρ<br>(MeV/c)</th></tr></thead><tbody><tr><td colspan="4"><strong>Modes with one charged particle</strong></td></tr><tr><td>particle<sup>-</sup> ≥ 0 neutrals<br>("1-prong")</td><td colspan="3">≥ 0 K<sup>0</sup>ν<sub>τ</sub> (85.24 ± 0.06) %</td></tr><tr><td>particle<sup>-</sup> ≥ 0 neutrals ≥ 0 K<sup>0</sup><sub>L</sub>ν<sub>τ</sub></td><td colspan="3">(84.58 ± 0.06) %</td></tr><tr><td>μ<sup>-</sup>ν<sub>μ</sub>ν<sub>τ</sub></td><td colspan="3">[g] (17.39 ± 0.04) %</td></tr><tr><td>μ<sup>-</sup>ν<sub>μ</sub>ν<sub>τ</sub>γ</td><td colspan="3">[e] (3.67 ± 0.08) × 10<sup>-3</sup></td></tr><tr><td>e<sup>-</sup>ν<sub>e</sub>ν<sub>τ</sub></td><td colspan="3">[g] (17.82 ± 0.04) %</td></tr><tr><td>e<sup>-</sup>ν<sub>e</sub>ν<sub>τ</sub>γ</td><td colspan="3">[e] (1.83 ± 0.05) %</td></tr><tr><td>h<sup>-</sup> ≥ 0 K<sup>0</sup><sub>L</sub>ν<sub>τ</sub></td><td colspan="3">(12.03 ± 0.05) %</td></tr><tr><td>h<sup>-</sup>ν<sub>τ</sub></td><td colspan="3">(11.51 ± 0.05) %</td></tr><tr><td>π<sup>-</sup>ν<sub>τ</sub></td><td colspan="3">[g] (10.82 ± 0.05) %</td></tr><tr><td>K<sup>-</sup>ν<sub>τ</sub></td><td colspan="3">[g] (6.96 ± 0.10) × 10<sup>-3</sup></td></tr><tr><td>h<sup>-</sup> ≥ 1 neutralsν<sub>τ</sub></td><td colspan="3">(37.00 ± 0.09) %</td></tr><tr><td>h<sup>-</sup> ≥ 1 π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td colspan="3">(36.50 ± 0.09) %</td></tr><tr><td>h<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td><td colspan="3">(25.93 ± 0.09) %</td></tr><tr><td>π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td><td colspan="3">[g] (25.49 ± 0.09) %</td></tr><tr><td>π<sup>-</sup>π<sup>0</sup> non-ρ(770)ν<sub>τ</sub></td><td colspan="3">(3.0 ± 3.2) × 10<sup>-3</sup></td></tr><tr><td>K<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td><td colspan="3">[g] (4.33 ± 0.15) × 10<sup>-3</sup></td></tr><tr><td>h<sup>-</sup> ≥ 2π<sup>0</sup>ν<sub>τ</sub></td><td colspan="3">(10.81 ± 0.09) %</td></tr><tr><td>h<sup>-</sup>2π<sup>0</sup>ν<sub>τ</sub></td><td colspan="3">(9.48 ± 0.10) %</td></tr><tr><td>h<sup>-</sup>2π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td colspan="3">(9.32 ± 0.10) %</td></tr><tr><td>π<sup>-</sup>2π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td colspan="3">[g] (9.26 ± 0.10) %</td></tr><tr><td>π<sup>-</sup>2π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>),<br>scajar</td><td colspan="3">&lt; 9 × 10<sup>-3</sup>CL=95%</td></tr><tr><td>π<sup>-</sup>2π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>),<br>vector</td><td colspan="3">&lt; 7 × 10<sup>-3</sup>CL=95%</td></tr><tr><td>K<sup>-</sup>2π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td colspan="3">[g] (6.5 ± 2.2) × 10<sup>-4</sup></td></tr><tr><td>h<sup>-</sup> ≥ 3π<sup>0</sup>ν<sub>τ</sub></td><td colspan="3">(1.34 ± 0.07) %</td></tr><tr><td>h<sup>-</sup> ≥ 3π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td colspan="3">(1.25 ± 0.07) %</td></tr><tr><td>h<sup>-</sup>3π<sup>0</sup>ν<sub>τ</sub></td><td colspan="3">(1.18 ± 0.07) %</td></tr><tr><td>π<sup>-</sup>3π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td colspan="3">[g] (1.04 ± 0.07) %</td></tr><tr><td>K<sup>-</sup>3π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>,<br>η)</td><td colspan="3">[g] (4.8 ± 2.1) × 10<sup>-4</sup></td></tr><tr><td>h<sup>-</sup>4π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td colspan="3">(1.6 ± 0.4) × 10<sup>-3</sup></td></tr><tr><td>h<sup>-</sup>4π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>,η)</td><td colspan="3">[g] (1.1 ± 0.4) × 10<sup>-3</sup></td></tr><tr><td>a<sub>1</sub>(1260)ν<sub>τ</sub> → π<sup>-</sup>γν<sub>τ</sub></td><td colspan="3">(4.0 ± 1.5) × 10<sup>-4</sup></td></tr><tr><td>K<sup>-</sup> ≥ 0π<sup>0</sup> ≥ 0K<sup>0</sup> ≥ 0γν<sub>τ</sub></td><td colspan="3">(1.552 ± 0.029) %</td></tr><tr><td>K<sup>-</sup> ≥ 1 (π<sup>0</sup> or K<sup>0</sup> or γ)ν<sub>τ</sub></td><td colspan="3">(8.59 ± 0.28) × 10<sup>-3</sup></td></tr><tr><td colspan="4"><strong>Modes with K<sup>0</sup>'s</strong></td></tr><tr><td>K<sup>0</sup> (particles)<sup>-</sup>ν<sub>τ</sub></td><td colspan="3">(9.43 ± 0.28) × 10<sup>-3</sup></td></tr><tr><td>h<sup>-</sup>K<sup>0</sup>ν<sub>τ</sub></td><td colspan="3">(9.87 ± 0.14) × 10<sup>-3</sup></td></tr><tr><td>π<sup>-</sup>K<sup>0</sup>ν<sub>τ</sub></td><td colspan="3">[g] (8.38 ± 0.14) × 10<sup>-3</sup></td></tr><tr><td>π<sup>-</sup>K<sup>0</sup></td><td colspan="3">(5.4 ± 2.1) × 10<sup>-4</sup></td></tr><tr><td>(non-K<sup>0</sup>*(892)<sup>-</sup>)ν<sub>τ</sub></td><td colspan="3">[g] (1.486 ± 0.034) × 10<sup>-3</sup></td></tr><tr><td>K<sup>-</sup>K<sup>0</sup>ν<sub>τ</sub></td><td colspan="3">(2.99 ± 0.07) × 10<sup>-3</sup></td></tr><tr><td>h<sup>-</sup>K<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub></td><td colspan="3">(5.32 ± 0.13) × 10<sup>-3</sup></td></tr></tbody></table>
<table><tbody><tr><td>π<sup>-</sup>K<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>[g] (3.82 ± 0.13) × 10<sup>-3</sup></td><td>794</td></tr><tr><td>K<sup>0</sup>ρ<sup>-</sup>ν<sub>τ</sub></td><td>(2.2 ± 0.5) × 10<sup>-3</sup></td><td>612</td></tr><tr><td>K<sup>-</sup>K<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>[g] (1.50 ± 0.07) × 10<sup>-3</sup></td><td>685</td></tr><tr><td>π<sup>-</sup>K<sup>0</sup> ≥ 1π<sup>0</sup>ν<sub>τ</sub></td><td>(4.08 ± 0.25) × 10<sup>-3</sup></td><td>-</td></tr><tr><td>π<sup>-</sup>K<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>[g] (2.6 ± 2.3) × 10<sup>-4</sup></td><td>763</td></tr><tr><td>K<sup>-</sup>K<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>&lt; 1.6 × 10<sup>-4</sup>CL=95%</td><td>619</td></tr><tr><td>π<sup>-</sup>K<sup>0</sup>K<sup>0</sup>ν<sub>τ</sub></td><td>(1.55 ± 0.24) × 10<sup>-3</sup></td><td>682</td></tr><tr><td>π<sup>-</sup>K<sup>0</sup>K<sup>0</sup>S<sup>0</sup>ν<sub>τ</sub></td><td>[g] (2.35 ± 0.06) × 10<sup>-4</sup></td><td>682</td></tr><tr><td>π<sup>-</sup>K<sup>0</sup>K<sup>0</sup>L<sup>0</sup>ν<sub>τ</sub></td><td>[g] (1.08 ± 0.24) × 10<sup>-3</sup></td><td>682</td></tr><tr><td>π<sup>-</sup>K<sup>0</sup>K<sup>0</sup>L<sup>0</sup>ν<sub>τ</sub></td><td>(2.35 ± 0.06) × 10<sup>-4</sup></td><td>682</td></tr><tr><td>π<sup>-</sup>K<sup>0</sup>K<sup>0</sup>R<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>(3.6 ± 1.2) × 10<sup>-4</sup></td><td>614</td></tr><tr><td>π<sup>-</sup>K<sup>0</sup>S<sup>0</sup>K<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>[g] (1.82 ± 0.21) × 10<sup>-5</sup></td><td>614</td></tr><tr><td>K<sup>*-</sup>K<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub> →</td><td>(1.08 ± 0.21) × 10<sup>-5</sup></td><td>-</td></tr><tr><td>π<sup>-</sup>K<sup>0</sup>S<sup>0</sup>K<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>f<sub>1</sub>(1285)π<sup>-</sup>ν<sub>τ</sub> →</td><td>(6.8 ± 1.5) × 10<sup>-6</sup></td><td>-</td></tr><tr><td>π<sup>-</sup>K<sup>0</sup>S<sup>0</sup>K<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>f<sub>1</sub>(1285)π<sup>-</sup>ν<sub>τ</sub> →</td><td>(2.4 ± 0.8) × 10<sup>-6</sup></td><td>-</td></tr><tr><td>π<sup>-</sup>K<sup>0</sup>K<sup>0</sup>L<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>[g] (3.2 ± 1.2) × 10<sup>-4</sup></td><td>614</td></tr><tr><td>π<sup>-</sup>K<sup>0</sup>L<sup>0</sup>K<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>(1.82 ± 0.21) × 10<sup>-5</sup></td><td>614</td></tr><tr><td>K<sup>-</sup>K<sup>0</sup>K<sup>0</sup>ν<sub>τ</sub></td><td>&lt; 6.3 × 10<sup>-7</sup>CL=90%</td><td>466</td></tr><tr><td>K<sup>-</sup>K<sup>0</sup>S<sup>0</sup>K<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>&lt; 4.0 × 10<sup>-7</sup>CL=90%</td><td>337</td></tr><tr><td>K<sup>0</sup>h<sup>+</sup>h<sup>-</sup> ≥ 0 neutrals ν<sub>τ</sub></td><td>&lt; 1.7 × 10<sup>-3</sup>CL=95%</td><td>760</td></tr><tr><td>K<sup>0</sup>h<sup>+</sup>h<sup>-</sup>ν<sub>τ</sub></td><td>[g] (2.5 ± 2.0) × 10<sup>-4</sup></td><td>760</td></tr></tbody></table>

### Modes with three charged particles

<table><tbody><tr><td>h<sup>-</sup>h<sup>-</sup>h<sup>+</sup> ≥ 0 neutrals ≥ 0K<sup>0</sup>ν<sub>τ</sub></td><td>(15.20 ± 0.06) %</td><td>861</td></tr><tr><td>h<sup>-</sup>h<sup>-</sup>h<sup>+</sup> ≥ 0 neutrals ν<sub>τ</sub> (ex. K<sup>0</sup><sub>S</sub> → π<sup>+</sup>π<sup>-</sup>)<br/>("3-prong")</td><td>(14.55 ± 0.06) %</td><td>861</td></tr><tr><td>h<sup>-</sup>h<sup>-</sup>h<sup>+</sup>ν<sub>τ</sub></td><td>(9.80 ± 0.05) %</td><td>861</td></tr><tr><td>h<sup>-</sup>h<sup>-</sup>h<sup>+</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>(9.46 ± 0.05) %</td><td>861</td></tr><tr><td>h<sup>-</sup>h<sup>-</sup>h<sup>+</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>,ω)</td><td>(9.43 ± 0.05) %</td><td>861</td></tr><tr><td>π<sup>-</sup>π<sup>+</sup>π<sup>-</sup>ν<sub>τ</sub></td><td>(9.31 ± 0.05) %</td><td>861</td></tr><tr><td>π<sup>-</sup>π<sup>+</sup>π<sup>-</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>(9.02 ± 0.05) %</td><td>861</td></tr><tr><td>π<sup>-</sup>π<sup>+</sup>π<sup>-</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>),<br/>non-axial vector</td><td>&lt; 2.4 % CL=95%</td><td>861</td></tr><tr><td>π<sup>-</sup>π<sup>+</sup>π<sup>-</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>,ω)</td><td>[g] (8.99 ± 0.05) %</td><td>861</td></tr><tr><td>h<sup>-</sup>h<sup>-</sup>h<sup>+</sup> ≥ 1 neutrals ν<sub>τ</sub></td><td>(5.29 ± 0.05) %</td><td>-</td></tr><tr><td>h<sup>-</sup>h<sup>-</sup>h<sup>+</sup> ≥ 1π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>(5.09 ± 0.05) %</td><td>-</td></tr><tr><td>h<sup>-</sup>h<sup>-</sup>h<sup>+</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>(4.76 ± 0.05) %</td><td>834</td></tr><tr><td>h<sup>-</sup>h<sup>-</sup>h<sup>+</sup>π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>(4.57 ± 0.05) %</td><td>834</td></tr><tr><td>h<sup>-</sup>h<sup>-</sup>h<sup>+</sup>π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>, ω)</td><td>(2.79 ± 0.07) %</td><td>834</td></tr><tr><td>π<sup>-</sup>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>(4.62 ± 0.05) %</td><td>834</td></tr><tr><td>π<sup>-</sup>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>(4.49 ± 0.05) %</td><td>834</td></tr><tr><td>π<sup>-</sup>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>,ω)</td><td>[g] (2.74 ± 0.07) %</td><td>834</td></tr><tr><td>h<sup>-</sup>h<sup>-</sup>h<sup>+</sup> ≥ 2π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>(5.17 ± 0.31) × 10<sup>-3</sup></td><td>-</td></tr><tr><td>h<sup>-</sup>h<sup>-</sup>h<sup>+</sup>2π<sup>0</sup>ν<sub>τ</sub></td><td>(5.05 ± 0.31) × 10<sup>-3</sup></td><td>797</td></tr><tr><td>h<sup>-</sup>h<sup>-</sup>h<sup>+</sup>2π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>(4.95 ± 0.31) × 10<sup>-3</sup></td><td>797</td></tr><tr><td>h<sup>-</sup>h<sup>-</sup>h<sup>+</sup>2π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>,ω,η)</td><td>(10 ± 4) × 10<sup>-4</sup></td><td>797</td></tr><tr><td>h<sup>-</sup>h<sup>-</sup>h<sup>+</sup>3π<sup>0</sup>ν<sub>τ</sub></td><td>(2.13 ± 0.30) × 10<sup>-4</sup></td><td>749</td></tr><tr><td>2π<sup>-</sup>π<sup>+</sup>3π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>(1.94 ± 0.30) × 10<sup>-4</sup></td><td>749</td></tr><tr><td>2π<sup>-</sup>π<sup>+</sup>3π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>, η, f<sub>1</sub>(1285))</td><td>(1.7 ± 0.4) × 10<sup>-4</sup></td><td>-</td></tr><tr><td>2π<sup>-</sup>π<sup>+</sup>3π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>, η, ω, f<sub>1</sub>(1285))</td><td>(1.4 ± 2.7) × 10<sup>-5</sup></td><td>-</td></tr><tr><td>K<sup>-</sup>h<sup>+</sup>h<sup>-</sup> ≥ 0 neutrals ν<sub>τ</sub></td><td>(6.29 ± 0.14) × 10<sup>-3</sup></td><td>794</td></tr><tr><td>K<sup>-</sup>h<sup>+</sup>π<sup>-</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>(4.37 ± 0.07) × 10<sup>-3</sup></td><td>794</td></tr><tr><td>K<sup>-</sup>h<sup>+</sup>π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>(8.6 ± 1.2) × 10<sup>-4</sup></td><td>763</td></tr><tr><td>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup> ≥ 0 neutrals ν<sub>τ</sub></td><td>(4.77 ± 0.14) × 10<sup>-3</sup></td><td>794</td></tr><tr><td>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup> ≥ 0π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>(3.73 ± 0.13) × 10<sup>-3</sup></td><td>794</td></tr><tr><td>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>,ω)</td><td>(3.45 ± 0.07) × 10<sup>-3</sup></td><td>794</td></tr><tr><td>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>,ω)</td><td>(2.93 ± 0.07) × 10<sup>-3</sup></td><td>794</td></tr><tr><td>K<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub> →</td><td>(1.4 ± 0.5) × 10<sup>-3</sup></td><td>-</td></tr><tr><td>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup>ν<sub>τ</sub></td><td>(1.31 ± 0.12) × 10<sup>-3</sup></td><td>763</td></tr><tr><td>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>(7.9 ± 1.2) × 10<sup>-4</sup></td><td>763</td></tr><tr><td>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>,η)</td><td>(7.6 ± 1.2) × 10<sup>-4</sup></td><td>763</td></tr><tr><td>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>,ω)</td><td>(3.7 ± 0.9) × 10<sup>-4</sup></td><td>763</td></tr><tr><td>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>,ω,η)[g]</td><td>(3.9 ± 1.4) × 10<sup>-4</sup></td><td>763</td></tr><tr><td>K<sup>-</sup>π<sup>+</sup>K<sup>0</sup> ≥ 0 neut. ν<sub>τ</sub></td><td>&lt; 9 × 10<sup>-4</sup>CL=95%</td><td>685</td></tr><tr><td>K<sup>-</sup>π<sup>+</sup>π<sup>-</sup> ≥ 0 neut. ν<sub>τ</sub></td><td>(1.496 ± 0.033) × 10<sup>-3</sup></td><td>685</td></tr><tr><td>K<sup>-</sup>K<sup>0</sup>π<sup>+</sup>ν<sub>τ</sub></td><td>[g] (1.435 ± 0.027) × 10<sup>-3</sup></td><td>685</td></tr><tr><td>K<sup>-</sup>K<sup>0</sup>π<sup>+</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>[g] (6.1 ± 1.8) × 10<sup>-5</sup></td><td>618</td></tr></tbody></table>

<table><tbody><tr><td>K<sup>-</sup>K<sup>+</sup>K<sup>-</sup>ν<sub>τ</sub></td><td>(2.2 ± 0.8) × 10<sup>-5</sup> S=5.4</td><td>472</td></tr><tr><td>K<sup>-</sup>K<sup>+</sup>K<sup>-</sup>ν<sub>τ</sub> (ex. φ)</td><td>&lt; 2.5 × 10<sup>-6</sup>CL=90%</td><td>-</td></tr><tr><td>K<sup>-</sup>K<sup>+</sup>K<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>&lt; 4.8 × 10<sup>-6</sup>CL=90%</td><td>346</td></tr><tr><td>π<sup>-</sup>K<sup>+</sup>π<sup>-</sup> ≥ 0 neut. ν<sub>τ</sub></td><td>&lt; 2.5 × 10<sup>-3</sup>CL=95%</td><td>794</td></tr><tr><td>e<sup>-</sup>e<sup>+</sup>e<sup>-</sup>ν<sub>e</sub>ν<sub>τ</sub></td><td>(2.8 ± 1.5) × 10<sup>-5</sup></td><td>888</td></tr><tr><td>μ<sup>-</sup>e<sup>-</sup>e<sup>+</sup>ν<sub>μ</sub>ν<sub>τ</sub></td><td>&lt; 3.2 × 10<sup>-5</sup>CL=90%</td><td>885</td></tr><tr><td>π<sup>-</sup>e<sup>-</sup>e<sup>+</sup>ν<sub>τ</sub></td><td>seen</td><td>883</td></tr><tr><td>π<sup>-</sup>μ<sup>-</sup>μ<sup>+</sup>ν<sub>τ</sub></td><td>&lt; 1.14 × 10<sup>-5</sup>CL=90%</td><td>870</td></tr></tbody></table>

### Modes with five charged particles

<table><tbody><tr><td>3h<sup>-</sup>2h<sup>+</sup> ≥ 0 neutrals ν<sub>τ</sub> (ex. K<sup>0</sup><sub>S</sub> → π<sup>-</sup>π<sup>+</sup>)<br/>("5-prong")</td><td>(9.9 ± 0.4) × 10<sup>-4</sup></td><td>794</td></tr><tr><td>3h<sup>-</sup>2h<sup>+</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>(8.29 ± 0.31) × 10<sup>-4</sup></td><td>794</td></tr><tr><td>3π<sup>-</sup>2π<sup>+</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>, ω)</td><td>(8.27 ± 0.31) × 10<sup>-4</sup></td><td>794</td></tr><tr><td>3π<sup>-</sup>2π<sup>+</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>, ω, f<sub>1</sub>(1285))</td><td>[g] (7.75 ± 0.30) × 10<sup>-4</sup></td><td>-</td></tr><tr><td>K<sup>-</sup>2π<sup>-</sup>2π<sup>+</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>[g] (6 ± 12) × 10<sup>-7</sup></td><td>716</td></tr><tr><td>K<sup>+</sup>3π<sup>-</sup>π<sup>+</sup>ν<sub>τ</sub></td><td>&lt; 5.0 × 10<sup>-6</sup>CL=90%</td><td>716</td></tr><tr><td>K<sup>+</sup>K<sup>-</sup>2π<sup>-</sup>π<sup>+</sup>ν<sub>τ</sub></td><td>&lt; 4.5 × 10<sup>-7</sup>CL=90%</td><td>528</td></tr><tr><td>3h<sup>-</sup>2h<sup>+</sup>π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>(1.65 ± 0.11) × 10<sup>-4</sup></td><td>746</td></tr><tr><td>3π<sup>-</sup>2π<sup>+</sup>π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>(1.64 ± 0.11) × 10<sup>-4</sup></td><td>746</td></tr><tr><td>3π<sup>-</sup>2π<sup>+</sup>π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>, η, f<sub>1</sub>(1285))</td><td>(1.11 ± 0.10) × 10<sup>-4</sup></td><td>-</td></tr><tr><td>3π<sup>-</sup>2π<sup>+</sup>π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>, η, ω, f<sub>1</sub>(1285))</td><td>[g] (3.8 ± 0.9) × 10<sup>-5</sup></td><td>-</td></tr><tr><td>K<sup>-</sup>2π<sup>-</sup>2π<sup>+</sup>π<sup>0</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>[g] (1.1 ± 0.6) × 10<sup>-6</sup></td><td>657</td></tr><tr><td>K<sup>+</sup>3π<sup>-</sup>π<sup>+</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>&lt; 8 × 10<sup>-7</sup>CL=90%</td><td>657</td></tr><tr><td>3h<sup>-</sup>2h<sup>+</sup>2π<sup>0</sup>ν<sub>τ</sub></td><td>&lt; 3.4 × 10<sup>-6</sup>CL=90%</td><td>687</td></tr></tbody></table>

### Miscellaneous other allowed modes

<table><tbody><tr><td>(5π)<sup>-</sup>ν<sub>τ</sub></td><td>(7.8 ± 0.5) × 10<sup>-3</sup></td><td>800</td></tr><tr><td>4h<sup>-</sup>3h<sup>+</sup> ≥ 0 neutrals ν<sub>τ</sub> ("7-prong")</td><td>&lt; 3.0 × 10<sup>-7</sup>CL=90%</td><td>682</td></tr><tr><td>4h<sup>-</sup>3h<sup>+</sup>ν<sub>τ</sub></td><td>&lt; 4.3 × 10<sup>-7</sup>CL=90%</td><td>682</td></tr><tr><td>4h<sup>-</sup>3h<sup>+</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>&lt; 2.5 × 10<sup>-7</sup>CL=90%</td><td>612</td></tr><tr><td>X<sup>-</sup> (S=-1)ν<sub>τ</sub></td><td>(2.92 ± 0.04) %</td><td>-</td></tr><tr><td>K<sup>*</sup>(892)<sup>-</sup> ≥ 0 neutrals ≥ 0K<sup>0</sup>L<sup>0</sup>ν<sub>τ</sub></td><td>(1.42 ± 0.18) % S=1.4</td><td>665</td></tr><tr><td>K<sup>*</sup>(892)<sup>-</sup>ν<sub>τ</sub></td><td>(1.20 ± 0.07) %</td><td>S=1.8</td></tr><tr><td>K<sup>*</sup>(892)<sup>-</sup>ν<sub>τ</sub> → π<sup>-</sup>K<sup>0</sup>ν<sub>τ</sub></td><td>(7.82 ± 0.26) × 10<sup>-3</sup></td><td>-</td></tr><tr><td>K<sup>*</sup>(892)<sup>0</sup>K<sup>-</sup> ≥ 0 neutrals ν<sub>τ</sub></td><td>(3.2 ± 1.4) × 10<sup>-3</sup></td><td>542</td></tr><tr><td>K<sup>*</sup>(892)<sup>0</sup>K<sup>-</sup>ν<sub>τ</sub></td><td>(2.1 ± 0.4) × 10<sup>-3</sup></td><td>542</td></tr><tr><td>K<sup>*</sup>(892)<sup>0</sup>π<sup>-</sup> ≥ 0 neutrals ν<sub>τ</sub></td><td>(3.8 ± 1.7) × 10<sup>-3</sup></td><td>656</td></tr><tr><td>K<sup>*</sup>(892)<sup>0</sup>π<sup>-</sup>ν<sub>τ</sub></td><td>(2.2 ± 0.5) × 10<sup>-3</sup></td><td>656</td></tr><tr><td>(K<sup>*</sup>(892)π)<sup>-</sup>ν<sub>τ</sub> → π<sup>-</sup>K<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>(1.0 ± 0.4) × 10<sup>-3</sup></td><td>-</td></tr><tr><td>K<sub>1</sub>(1270)<sup>-</sup>ν<sub>τ</sub></td><td>(4.7 ± 1.1) × 10<sup>-3</sup></td><td>447</td></tr><tr><td>K<sub>1</sub>(1400)<sup>-</sup>ν<sub>τ</sub></td><td>(1.7 ± 2.6) × 10<sup>-3</sup> S=1.7</td><td>335</td></tr><tr><td>K<sup>*</sup>(1410)<sup>-</sup>ν<sub>τ</sub></td><td>(1.5 ± 1.4) × 10<sup>-3</sup></td><td>326</td></tr><tr><td>K<sup>*</sup><sub>0</sub>(1430)<sup>-</sup>ν<sub>τ</sub></td><td>&lt; 5 × 10<sup>-4</sup>CL=95%</td><td>317</td></tr><tr><td>K<sup>*</sup><sub>2</sub>(1430)<sup>-</sup>ν<sub>τ</sub></td><td>&lt; 3 × 10<sup>-3</sup>CL=95%</td><td>315</td></tr><tr><td>ηπ<sup>-</sup>ν<sub>τ</sub></td><td>&lt; 9.9 × 10<sup>-5</sup>CL=95%</td><td>797</td></tr><tr><td>ηπ<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>[g] (1.39 ± 0.07) × 10<sup>-3</sup></td><td>778</td></tr><tr><td>ηπ<sup>-</sup>π<sup>0</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>[g] (1.9 ± 0.4) × 10<sup>-4</sup></td><td>746</td></tr><tr><td>ηK<sup>-</sup>ν<sub>τ</sub></td><td>[g] (1.55 ± 0.08) × 10<sup>-4</sup></td><td>720</td></tr><tr><td>ηK<sup>*</sup>(892)<sup>-</sup>ν<sub>τ</sub></td><td>(1.38 ± 0.15) × 10<sup>-4</sup></td><td>511</td></tr><tr><td>ηK<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>[g] (4.8 ± 1.2) × 10<sup>-5</sup></td><td>665</td></tr><tr><td>ηK<sup>-</sup>π<sup>0</sup>(non-K<sup>*</sup>(892))ν<sub>τ</sub></td><td>&lt; 3.5 × 10<sup>-5</sup>CL=90%</td><td>-</td></tr><tr><td>ηK<sup>0</sup>π<sup>-</sup>ν<sub>τ</sub></td><td>[g] (9.4 ± 1.5) × 10<sup>-5</sup></td><td>661</td></tr><tr><td>ηK<sup>0</sup>π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>&lt; 5.0 × 10<sup>-5</sup>CL=90%</td><td>590</td></tr><tr><td>ηK<sup>-</sup>K<sup>0</sup>ν<sub>τ</sub></td><td>&lt; 9.0 × 10<sup>-6</sup>CL=90%</td><td>430</td></tr><tr><td>ηπ<sup>+</sup>π<sup>-</sup>π<sup>-</sup> ≥ 0 neutrals ν<sub>τ</sub></td><td>&lt; 3 × 10<sup>-3</sup>CL=90%</td><td>744</td></tr><tr><td>ηπ<sup>-</sup>π<sup>+</sup>π<sup>-</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>[g] (2.20 ± 0.13) × 10<sup>-4</sup></td><td>744</td></tr><tr><td>ηπ<sup>-</sup>π<sup>+</sup>π<sup>-</sup>ν<sub>τ</sub> (ex. K<sup>0</sup>,f<sub>1</sub>(1285))</td><td>(9.9 ± 1.6) × 10<sup>-5</sup></td><td>-</td></tr><tr><td>ηa<sub>1</sub>(1260)<sup>-</sup>ν<sub>τ</sub> → ηπ<sup>-</sup>ρ<sup>0</sup>ν<sub>τ</sub></td><td>&lt; 3.9 × 10<sup>-4</sup>CL=90%</td><td>-</td></tr><tr><td>ηηπ<sup>-</sup>ν<sub>τ</sub></td><td>&lt; 7.4 × 10<sup>-6</sup>CL=90%</td><td>637</td></tr><tr><td>ηηπ<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>&lt; 2.0 × 10<sup>-4</sup>CL=95%</td><td>559</td></tr><tr><td>ηηK<sup>-</sup>ν<sub>τ</sub></td><td>&lt; 3.0 × 10<sup>-6</sup>CL=90%</td><td>382</td></tr><tr><td>η<sup>-</sup>(958)π<sup>-</sup>ν<sub>τ</sub></td><td>&lt; 4.0 × 10<sup>-6</sup>CL=90%</td><td>620</td></tr><tr><td>η<sup>-</sup>(958)π<sup>-</sup>π<sup>0</sup>ν<sub>τ</sub></td><td>&lt; 1.2 × 10<sup>-5</sup>CL=90%</td><td>591</td></tr><tr><td>η<sup>-</sup>(958)K<sup>-</sup>ν<sub>τ</sub></td><td>&lt; 2.4 × 10<sup>-6</sup>CL=90%</td><td>495</td></tr><tr><td>φπ<sup>-</sup>ν<sub>τ</sub></td><td>(3.4 ± 0.6) × 10<sup>-5</sup></td><td>585</td></tr><tr><td>φK<sup>-</sup>ν<sub>τ</sub></td><td>(4.4 ± 1.6) × 10<sup>-5</sup></td><td>445</td></tr><tr><td>f<sub>1</sub>(1285)π<sup>-</sup>ν<sub>τ</sub></td><td>(3.9 ± 0.5) × 10<sup>-4</sup> S=1.9</td><td>408</td></tr><tr><td>f<sub>1</sub>(1285)π<sup>-</sup>ν<sub>τ</sub> → ηπ<sup>-</sup>π<sup>+</sup>π<sup>-</sup>ν<sub>τ</sub></td><td>(1.18 ± 0.07) × 10<sup>-4</sup> S=1.3</td><td>-</td></tr></tbody></table>
# Lepton Summary Table

<table><tr><td>f<sub>1</sub>(1285) π<sup>-</sup> ν<sub>τ</sub> →<br>3π<sup>-</sup> 2π<sup>+</sup> ν<sub>τ</sub></td><td>[g] ( 5.2 ± 0.4 ) × 10<sup>-5</sup></td><td>-</td></tr><tr><td>π(1300)<sup>-</sup> ν<sub>τ</sub> → (ρπ)<sup>-</sup> ν<sub>τ</sub> →<br>(3π)<sup>-</sup> ν<sub>τ</sub></td><td>&lt; 1.0</td><td>× 10<sup>-4</sup> CL=90%</td><td>-</td></tr><tr><td>π(1300)<sup>-</sup> ν<sub>τ</sub> →<br>((ππ)<sub>S-wave</sub> π)<sup>-</sup> ν<sub>τ</sub> →<br>(3π)<sup>-</sup> ν<sub>τ</sub></td><td>&lt; 1.9</td><td>× 10<sup>-4</sup> CL=90%</td><td>-</td></tr><tr><td>h<sup>-</sup> ω ≥ 0 neutrals ν<sub>τ</sub></td><td>( 2.40 ± 0.08 ) %</td><td>708</td></tr><tr><td>h<sup>-</sup> ων<sub>τ</sub></td><td>( 1.99 ± 0.06 ) %</td><td>708</td></tr><tr><td>π<sup>-</sup> ων<sub>τ</sub></td><td>[g] ( 1.95 ± 0.06 ) %</td><td>708</td></tr><tr><td>K<sup>-</sup> ων<sub>τ</sub></td><td>[g] ( 4.1 ± 0.9 ) × 10<sup>-4</sup></td><td>610</td></tr><tr><td>h<sup>-</sup> ωπ<sup>0</sup> ν<sub>τ</sub></td><td>[g] ( 4.1 ± 0.4 ) × 10<sup>-3</sup></td><td>684</td></tr><tr><td>h<sup>-</sup> ω2π<sup>0</sup> ν<sub>τ</sub></td><td>( 1.4 ± 0.5 ) × 10<sup>-4</sup></td><td>644</td></tr><tr><td>π<sup>-</sup> ω2π<sup>0</sup> ν<sub>τ</sub></td><td>[g] ( 7.2 ± 1.6 ) × 10<sup>-5</sup></td><td>644</td></tr><tr><td>h<sup>-</sup> 2ων<sub>τ</sub></td><td>&lt; 5.4</td><td>× 10<sup>-7</sup> CL=90%</td><td>250</td></tr><tr><td>2h<sup>-</sup> h<sup>+</sup> ων<sub>τ</sub></td><td>( 1.20 ± 0.22 ) × 10<sup>-4</sup></td><td>641</td></tr><tr><td>2π<sup>-</sup> π<sup>+</sup> ων<sub>τ</sub> (ex. K<sup>0</sup>)</td><td>[g] ( 8.4 ± 0.6 ) × 10<sup>-5</sup></td><td>641</td></tr></table>

## Lepton Family number (LF), Lepton number (L), or Baryon number (B) violating modes

L means lepton number violation (e.g. $\tau^- \to e^+\pi^-\pi^-$). Following common usage, LF means lepton family violation and not lepton number violation (e.g. $\tau^- \to e^+\pi^+\pi^-$). B means baryon number violation.

<table><tr><td>e<sup>-</sup>γ</td><td>LF</td><td>&lt; 3.3</td><td>× 10<sup>-8</sup> CL=90%</td><td>888</td></tr><tr><td>e<sup>-</sup>γγ</td><td>LF</td><td>&lt; 2.5</td><td>× 10<sup>-4</sup> CL=90%</td><td>888</td></tr><tr><td>μ<sup>-</sup>γ</td><td>LF</td><td>&lt; 4.2</td><td>× 10<sup>-8</sup> CL=90%</td><td>885</td></tr><tr><td>μ<sup>-</sup>γγ</td><td>LF</td><td>&lt; 5.8</td><td>× 10<sup>-4</sup> CL=90%</td><td>885</td></tr><tr><td>μ<sup>-</sup>π<sup>0</sup></td><td>LF</td><td>&lt; 8.0</td><td>× 10<sup>-8</sup> CL=90%</td><td>883</td></tr><tr><td>μ<sup>-</sup>π<sup>0</sup></td><td>LF</td><td>&lt; 1.1</td><td>× 10<sup>-7</sup> CL=90%</td><td>880</td></tr><tr><td>e<sup>-</sup> K<sup>0</sup><sub>S</sub></td><td>LF</td><td>&lt; 2.6</td><td>× 10<sup>-8</sup> CL=90%</td><td>819</td></tr><tr><td>μ<sup>-</sup> K<sup>0</sup><sub>S</sub></td><td>LF</td><td>&lt; 2.3</td><td>× 10<sup>-8</sup> CL=90%</td><td>815</td></tr><tr><td>e<sup>-</sup>η</td><td>LF</td><td>&lt; 9.2</td><td>× 10<sup>-8</sup> CL=90%</td><td>804</td></tr><tr><td>μ<sup>-</sup>η</td><td>LF</td><td>&lt; 6.5</td><td>× 10<sup>-8</sup> CL=90%</td><td>800</td></tr><tr><td>e<sup>-</sup>ρ<sup>0</sup></td><td>LF</td><td>&lt; 2.2</td><td>× 10<sup>-8</sup> CL=90%</td><td>719</td></tr><tr><td>μ<sup>-</sup>ρ<sup>0</sup></td><td>LF</td><td>&lt; 1.7</td><td>× 10<sup>-8</sup> CL=90%</td><td>715</td></tr><tr><td>e<sup>-</sup>ω</td><td>LF</td><td>&lt; 2.4</td><td>× 10<sup>-8</sup> CL=90%</td><td>716</td></tr><tr><td>μ<sup>-</sup>ω</td><td>LF</td><td>&lt; 3.9</td><td>× 10<sup>-8</sup> CL=90%</td><td>711</td></tr><tr><td>e<sup>-</sup> K<sup>*</sup>(892)<sup>0</sup></td><td>LF</td><td>&lt; 1.9</td><td>× 10<sup>-8</sup> CL=90%</td><td>665</td></tr><tr><td>μ<sup>-</sup> K<sup>*</sup>(892)<sup>0</sup></td><td>LF</td><td>&lt; 2.9</td><td>× 10<sup>-8</sup> CL=90%</td><td>659</td></tr><tr><td>e<sup>-</sup> K<sup>*</sup>(892)<sup>0</sup></td><td>LF</td><td>&lt; 1.7</td><td>× 10<sup>-8</sup> CL=90%</td><td>665</td></tr><tr><td>μ<sup>-</sup> K<sup>*</sup>(892)<sup>0</sup></td><td>LF</td><td>&lt; 4.3</td><td>× 10<sup>-8</sup> CL=90%</td><td>659</td></tr><tr><td>e<sup>-</sup>η'(958)</td><td>LF</td><td>&lt; 1.6</td><td>× 10<sup>-7</sup> CL=90%</td><td>630</td></tr><tr><td>μ<sup>-</sup>η'(958)</td><td>LF</td><td>&lt; 1.3</td><td>× 10<sup>-7</sup> CL=90%</td><td>625</td></tr><tr><td>e<sup>-</sup> f<sub>0</sub>(980) → e<sup>-</sup>π<sup>+</sup>π<sup>-</sup></td><td>LF</td><td>&lt; 3.2</td><td>× 10<sup>-8</sup> CL=90%</td><td>-</td></tr><tr><td>μ<sup>-</sup> f<sub>0</sub>(980) → μ<sup>-</sup>π<sup>+</sup>π<sup>-</sup></td><td>LF</td><td>&lt; 3.4</td><td>× 10<sup>-8</sup> CL=90%</td><td>-</td></tr><tr><td>e<sup>-</sup>φ</td><td>LF</td><td>&lt; 2.0</td><td>× 10<sup>-8</sup> CL=90%</td><td>596</td></tr><tr><td>μ<sup>-</sup>φ</td><td>LF</td><td>&lt; 2.3</td><td>× 10<sup>-8</sup> CL=90%</td><td>590</td></tr><tr><td>e<sup>-</sup> e<sup>+</sup> e<sup>-</sup></td><td>LF</td><td>&lt; 2.7</td><td>× 10<sup>-8</sup> CL=90%</td><td>888</td></tr><tr><td>e<sup>-</sup> μ<sup>+</sup> μ<sup>-</sup></td><td>LF</td><td>&lt; 2.7</td><td>× 10<sup>-8</sup> CL=90%</td><td>882</td></tr><tr><td>e<sup>+</sup> μ<sup>-</sup> μ<sup>-</sup></td><td>LF</td><td>&lt; 1.7</td><td>× 10<sup>-8</sup> CL=90%</td><td>882</td></tr><tr><td>μ<sup>-</sup> e<sup>+</sup> e<sup>-</sup></td><td>LF</td><td>&lt; 1.8</td><td>× 10<sup>-8</sup> CL=90%</td><td>885</td></tr><tr><td>μ<sup>+</sup> e<sup>-</sup> e<sup>-</sup></td><td>LF</td><td>&lt; 1.5</td><td>× 10<sup>-8</sup> CL=90%</td><td>885</td></tr><tr><td>μ<sup>-</sup> μ<sup>+</sup> μ<sup>-</sup></td><td>LF</td><td>&lt; 2.1</td><td>× 10<sup>-8</sup> CL=90%</td><td>873</td></tr><tr><td>e<sup>-</sup> π<sup>+</sup> π<sup>-</sup></td><td>LF</td><td>&lt; 2.3</td><td>× 10<sup>-8</sup> CL=90%</td><td>877</td></tr><tr><td>e<sup>+</sup> π<sup>-</sup> π<sup>-</sup></td><td>L</td><td>&lt; 2.0</td><td>× 10<sup>-8</sup> CL=90%</td><td>877</td></tr><tr><td>μ<sup>-</sup> π<sup>+</sup> π<sup>-</sup></td><td>LF</td><td>&lt; 2.1</td><td>× 10<sup>-8</sup> CL=90%</td><td>866</td></tr><tr><td>μ<sup>+</sup> π<sup>+</sup> π<sup>-</sup></td><td>L</td><td>&lt; 3.9</td><td>× 10<sup>-8</sup> CL=90%</td><td>866</td></tr><tr><td>e<sup>-</sup> π<sup>+</sup> K<sup>-</sup></td><td>LF</td><td>&lt; 3.7</td><td>× 10<sup>-8</sup> CL=90%</td><td>813</td></tr><tr><td>e<sup>-</sup> π<sup>-</sup> K<sup>+</sup></td><td>LF</td><td>&lt; 3.1</td><td>× 10<sup>-8</sup> CL=90%</td><td>813</td></tr><tr><td>e<sup>+</sup> π<sup>-</sup> K<sup>-</sup></td><td>L</td><td>&lt; 3.2</td><td>× 10<sup>-8</sup> CL=90%</td><td>813</td></tr><tr><td>e<sup>-</sup> K<sup>0</sup><sub>S</sub> K<sup>0</sup><sub>S</sub></td><td>LF</td><td>&lt; 7.1</td><td>× 10<sup>-8</sup> CL=90%</td><td>736</td></tr><tr><td>e<sup>-</sup> K<sup>+</sup> K<sup>-</sup></td><td>LF</td><td>&lt; 3.4</td><td>× 10<sup>-8</sup> CL=90%</td><td>739</td></tr><tr><td>e<sup>+</sup> K<sup>-</sup> K<sup>-</sup></td><td>L</td><td>&lt; 3.3</td><td>× 10<sup>-8</sup> CL=90%</td><td>739</td></tr><tr><td>μ<sup>-</sup> π<sup>+</sup> K<sup>-</sup></td><td>LF</td><td>&lt; 8.6</td><td>× 10<sup>-8</sup> CL=90%</td><td>800</td></tr><tr><td>μ<sup>-</sup> π<sup>-</sup> K<sup>+</sup></td><td>LF</td><td>&lt; 4.5</td><td>× 10<sup>-8</sup> CL=90%</td><td>800</td></tr><tr><td>μ<sup>+</sup> π<sup>-</sup> K<sup>-</sup></td><td>L</td><td>&lt; 4.8</td><td>× 10<sup>-8</sup> CL=90%</td><td>800</td></tr><tr><td>μ<sup>-</sup> K<sup>0</sup><sub>S</sub> K<sup>0</sup><sub>S</sub></td><td>LF</td><td>&lt; 8.0</td><td>× 10<sup>-8</sup> CL=90%</td><td>696</td></tr><tr><td>μ<sup>+</sup> K<sup>+</sup> K<sup>-</sup></td><td>LF</td><td>&lt; 4.4</td><td>× 10<sup>-8</sup> CL=90%</td><td>699</td></tr><tr><td>μ<sup>+</sup> K<sup>-</sup> K<sup>-</sup></td><td>L</td><td>&lt; 4.7</td><td>× 10<sup>-8</sup> CL=90%</td><td>699</td></tr><tr><td>e<sup>-</sup> π<sup>0</sup> π<sup>0</sup></td><td>LF</td><td>&lt; 6.5</td><td>× 10<sup>-6</sup> CL=90%</td><td>878</td></tr><tr><td>μ<sup>-</sup> π<sup>0</sup> π<sup>0</sup></td><td>LF</td><td>&lt; 1.4</td><td>× 10<sup>-5</sup> CL=90%</td><td>867</td></tr><tr><td>e<sup>-</sup>ηη</td><td>LF</td><td>&lt; 3.5</td><td>× 10<sup>-5</sup> CL=90%</td><td>699</td></tr><tr><td>μ<sup>-</sup>ηη</td><td>LF</td><td>&lt; 6.0</td><td>× 10<sup>-5</sup> CL=90%</td><td>653</td></tr><tr><td>e<sup>-</sup>π<sup>0</sup>η</td><td>LF</td><td>&lt; 2.4</td><td>× 10<sup>-5</sup> CL=90%</td><td>798</td></tr><tr><td>μ<sup>+</sup>π<sup>0</sup>η</td><td>LF</td><td>&lt; 2.2</td><td>× 10<sup>-5</sup> CL=90%</td><td>784</td></tr><tr><td>p e<sup>-</sup> e<sup>-</sup></td><td>L,B</td><td>&lt; 3.0</td><td>× 10<sup>-8</sup> CL=90%</td><td>641</td></tr><tr><td>p e<sup>+</sup> e<sup>-</sup></td><td>L,B</td><td>&lt; 3.0</td><td>× 10<sup>-8</sup> CL=90%</td><td>641</td></tr></table>

<table><tr><td>p e<sup>+</sup> μ<sup>-</sup></td><td>L,B</td><td>&lt; 2.0</td><td>× 10<sup>-8</sup> CL=90%</td><td>635</td></tr><tr><td>p e<sup>-</sup> μ<sup>+</sup></td><td>L,B</td><td>&lt; 1.8</td><td>× 10<sup>-8</sup> CL=90%</td><td>635</td></tr><tr><td>p μ<sup>-</sup> μ<sup>-</sup></td><td>L,B</td><td>&lt; 4.0</td><td>× 10<sup>-8</sup> CL=90%</td><td>618</td></tr><tr><td>p μ<sup>+</sup> μ<sup>-</sup></td><td>L,B</td><td>&lt; 1.8</td><td>× 10<sup>-8</sup> CL=90%</td><td>618</td></tr><tr><td>p γ</td><td>L,B</td><td>&lt; 3.5</td><td>× 10<sup>-6</sup> CL=90%</td><td>641</td></tr><tr><td>p π<sup>0</sup></td><td>L,B</td><td>&lt; 1.5</td><td>× 10<sup>-5</sup> CL=90%</td><td>632</td></tr><tr><td>p 2π<sup>0</sup></td><td>L,B</td><td>&lt; 3.3</td><td>× 10<sup>-5</sup> CL=90%</td><td>604</td></tr><tr><td>p η</td><td>L,B</td><td>&lt; 8.9</td><td>× 10<sup>-6</sup> CL=90%</td><td>475</td></tr><tr><td>p π<sup>0</sup> η</td><td>L,B</td><td>&lt; 2.7</td><td>× 10<sup>-5</sup> CL=90%</td><td>360</td></tr><tr><td>Λπ<sup>-</sup></td><td>L,B</td><td>&lt; 7.2</td><td>× 10<sup>-8</sup> CL=90%</td><td>525</td></tr><tr><td>Λπ<sup>-</sup></td><td>L,B</td><td>&lt; 1.4</td><td>× 10<sup>-7</sup> CL=90%</td><td>525</td></tr><tr><td>e<sup>-</sup> light boson</td><td>LF</td><td>&lt; 9</td><td>× 10<sup>-4</sup> CL=95%</td><td>-</td></tr><tr><td>μ<sup>-</sup> light boson</td><td>LF</td><td>&lt; 6</td><td>× 10<sup>-4</sup> CL=95%</td><td>-</td></tr></table>

## Heavy Charged Lepton Searches

### L$^{±}$ – charged lepton

Mass $m > 100.8$ GeV, CL = 95% [h] Decay to $νW$.

### L$^{±}$ – stable charged heavy lepton

Mass $m > 102.6$ GeV, CL = 95%

## Neutrino Properties

See the note on "Neutrino properties listings" in the Particle Listings.

Mass $m < 0.8$ eV, CL = 90% (tritium decay)

Mean life/mass, $τ/m > 300$ s/eV, CL = 90% (reactor)

Mean life/mass, $τ/m > 7 \times 10^9$ s/eV (solar)

Mean life/mass, $τ/m > 15.4$ s/eV, CL = 90% (accelerator)

Magnetic moment $μ < 0.064 \times 10^{-10}$ μ$_B$, CL = 90% (solar + radiochemical)

## Number of Neutrino Types

Number $N = 2.996 \pm 0.007$ (Standard Model fits to LEP-SLC data)

Number $N = 2.92 \pm 0.05$ ($S = 1.2$) (Direct measurement of invisible $Z$ width)

## Neutrino Mixing

The following values are obtained through data analyses based on the 3-neutrino mixing scheme described in the review "Neutrino Masses, Mixing, and Oscillations."

$$ \sin^2(\theta_{12}) = 0.307 \pm 0.013 $$

$$ \Delta m^2_{21} = (7.53 \pm 0.18) \times 10^{-5} \text{ eV}^2 $$

$$ \sin^2(\theta_{23}) = 0.553_{-0.024}^{+0.016} \quad (S = 1.1) \quad \text{(Inverted order)} $$

$$ \sin^2(\theta_{23}) = 0.558_{-0.021}^{+0.015} \quad \text{(Normal order)} $$

$$ \Delta m^2_{32} = (-2.529 \pm 0.029) \times 10^{-3} \text{ eV}^2 \quad \text{(Inverted order)} $$

$$ \Delta m^2_{32} = (2.455 \pm 0.028) \times 10^{-3} \text{ eV}^2 \quad \text{(Normal order)} $$

$$ \sin^2(\theta_{13}) = (2.19 \pm 0.07) \times 10^{-2} \quad (S = 1.2) $$

$$ \delta, CP \text{ violating phase} = 1.19 \pm 0.22 \pi \text{ rad} \quad (S = 1.2) $$

$$ \langle \Delta m^2_{21} - \Delta m^2_{32} \rangle < 1.1 \times 10^{-4} \text{ eV}^2, \text{ CL} = 99.7\% $$

$$ \langle \Delta m^2_{32} - \Delta m^2_{32} \rangle = (-0.12 \pm 0.25) \times 10^{-3} \text{ eV}^2 $$

## NOTES

In this Summary Table:

When a quantity has "$\langle S = ... \rangle$" to its right, the error on the quantity has been enlarged by the "scale factor" S, defined as $S = \sqrt{\chi^2/(N-1)}$, where N is the number of measurements used in calculating the quantity. We do this when $S > 1$, which often indicates that the measurements are inconsistent. When $S > 1.25$, we also show in the Particle Listings an ideogram of the measurements. For more about S, see the Introduction.

A decay momentum p is given for each decay mode. For a 2-body decay, p is the momentum of each decay product in the rest frame of the decaying particle. For a 3-or-more-body decay, p is the largest momentum any of the products can have in this frame.

[a] This is the best limit for the mode $e^− → νγ$.
[b] See the review on "Muon Decay Parameters" for definitions and details.

[c] $P_\mu$ is the longitudinal polarization of the muon from pion decay. For $V-A$ coupling, $P_\mu = 1$ and $\rho = \delta = 3/4$.

[d] This only includes events with energy of $e > 45$ MeV and energy of $\gamma > 40$ MeV. Since the $e^-\bar{\nu}_e\nu_\mu$ and $e^-\bar{\nu}_e\nu_\mu\gamma$ modes cannot be clearly separated, we regard the latter mode as a subset of the former.

[e] See the relevant Particle Listings for the energy limits used in this measurement.

[f] A test of additive vs. multiplicative lepton family number conservation.

[g] Basis mode for the $\tau$.

[h] $L^\pm$ mass limit depends on decay assumptions; see the Full Listings.
## QUARKS

The u-, d-, and s-quark masses are the $\overline{\text{MS}}$ masses at the scale $\mu = 2$ GeV. The c- and b-quark masses are the $\overline{\text{MS}}$ masses renormalized at the $\overline{\text{MS}}$ mass, i.e. $\overline{m} = \overline{m}(\mu = \overline{m})$. The t-quark mass is extracted from event kinematics (see the review "The Top Quark").

u

$$I(J^P) = \frac{1}{2}(\frac{1}{2}^+)$$

$$ \begin{aligned} m_u &= 2.16 \pm 0.07 \text{ MeV, CL} = 90\% & \text{Charge} &= \frac{2}{3} e & I_z &= +\frac{1}{2} \\ m_u/m_d &= 0.462 \pm 0.020, \text{ CL} = 90\% \end{aligned} $$

d

$$I(J^P) = \frac{1}{2}(\frac{1}{2}^+)$$

$$ \begin{aligned} m_d &= 4.70 \pm 0.07 \text{ MeV, CL} = 90\% & \text{Charge} &= -\frac{1}{3} e & I_z &= -\frac{1}{2} \\ m_s/m_d &= 17-22 & & & \\ \bar{m} &= (m_u+m_d)/2 = 3.49 \pm 0.07 \text{ MeV, CL} = 90\% \end{aligned} $$

s

$$I(J^P) = 0(\frac{1}{2}^+)$$

$$ \begin{aligned} m_s &= 93.5 \pm 0.8 \text{ MeV, CL} = 90\% & \text{Charge} &= -\frac{1}{3} e & \text{Strangeness} &= -1 \\ m_s / ((m_u + m_d)/2) &= 27.33^{+0.18}_{-0.14}, \text{ CL} = 90\% \end{aligned} $$

c

$$I(J^P) = 0(\frac{1}{2}^+)$$

$$ \begin{aligned} m_c &= 1.2730 \pm 0.0046 \text{ GeV, CL} = 90\% & \text{Charge} &= \frac{2}{3} e & \text{Charm} &= +1 \\ m_b - m_c &= 3.45 \pm 0.05 \text{ GeV} & & & & \end{aligned} $$

b

$$I(J^P) = 0(\frac{1}{2}^+)$$

$$m_b = 4.183 \pm 0.007 \text{ GeV, CL} = 90\% \quad \text{Charge} = -\frac{1}{3} e \quad \text{Bottom} = -1$$

t

$$I(J^P) = 0(\frac{1}{2}^+)$$

$$ \text{Charge} = \frac{2}{3} e \qquad \text{Top} = +1 $$

$$ \text{Mass (direct measurements)} m = 172.57 \pm 0.29 $$

$$ \text{GeV}^{[a,b]} \quad (S = 1.5) $$

$$ \text{Mass (from cross-section measurements)} m = 162.5^{+2.1}_{-1.5} \text{ GeV}^{[a]} $$

$$ \text{Mass (Pole from cross-section measurements)} m = 172.4 \pm 0.7 \text{ GeV} $$

$$ m_t - m_{\bar{t}} = -0.15 \pm 0.20 \text{ GeV} \quad (S = 1.1) $$

$$ \text{Full width } \Gamma = 1.42^{+0.19}_{-0.15} \text{ GeV} \quad (S = 1.4) $$

$$ \Gamma(W b)/\Gamma(W q(q=b, s, d)) = 0.957 \pm 0.034 \quad (S = 1.5) $$

### t-quark EW Couplings

$$ F_0 = 0.693 \pm 0.013 $$

$$ F_{-} = 0.315 \pm 0.010 $$

$$ F_{+} = -0.005 \pm 0.007 $$

$$ F_{V+A} < 0.29, \text{ CL} = 95\% $$

<table><thead><tr><th>t DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>Confidence level</th><th>p (MeV/c)</th></tr></thead><tbody><tr><td>W q (q = b, s, d)</td><td></td><td></td><td>—</td></tr><tr><td>W b</td><td></td><td></td><td>—</td></tr><tr><td>eν<sub>e</sub> b</td><td>(11.10±0.30) %</td><td></td><td>—</td></tr><tr><td>μν<sub>μ</sub> b</td><td>(11.40±0.20) %</td><td></td><td>—</td></tr><tr><td>τν<sub>τ</sub> b</td><td>(10.7 ±0.5) %</td><td></td><td>—</td></tr><tr><td>q<span style="text-decoration: overline;">q</span> b</td><td>(66.5 ±1.4) %</td><td></td><td>—</td></tr><tr><td>γ q (q=u,c)</td><td>[c] &lt; 4.5</td><td>× 10<sup>-5</sup></td><td>95%</td></tr></tbody></table>

### ΔT = 1 weak neutral current (T1) modes

<table><tbody><tr><td>Z q (q=u,c)</td><td>T1</td><td>[d] &lt; 1.2</td><td>× 10<sup>-4</sup></td><td>95%</td></tr><tr><td>H u</td><td>T1</td><td>&lt; 1.9</td><td>× 10<sup>-4</sup></td><td>95%</td></tr><tr><td>H c</td><td>T1</td><td>&lt; 4.3</td><td>× 10<sup>-4</sup></td><td>95%</td></tr><tr><td>ℓ<sup>+</sup> <span style="text-decoration: overline;">q</span> q' (q=d,s,b; q'=u,c)</td><td>T1</td><td>&lt; 1.6</td><td>× 10<sup>-3</sup></td><td>95%</td></tr></tbody></table>

### Lepton Family number (LF) violating modes

<table><tbody><tr><td>e<sup>±</sup> μ<sup>∓</sup> c</td><td>LF</td><td>&lt; 8.9</td><td>× 10<sup>-7</sup></td><td>—</td></tr><tr><td>e<sup>±</sup> μ<sup>∓</sup> u</td><td>LF</td><td>&lt; 7</td><td>× 10<sup>-8</sup></td><td>—</td></tr></tbody></table>

### b' (4th Generation) Quark, Searches for

$$ \text{Mass } m > 190 \text{ GeV, CL} = 95\% \quad (p\bar{p}, \text{quasi-stable } b') $$

$$ \text{Mass } m > 1390 \text{ GeV, CL} = 95\% \quad (B(b' \rightarrow Z b) = 1) $$

$$ \text{Mass } m > 1350 \text{ GeV, CL} = 95\% \quad (B(b' \rightarrow W t) = 1) $$

$$ \text{Mass } m > 1570 \text{ GeV, CL} = 95\% \quad (B(b' \rightarrow H b) = 1) $$

$$ \text{Mass } m > 46.0 \text{ GeV, CL} = 95\% \quad (e^{+} e^{-}, \text{ all decays}) $$

### t' (4th Generation) Quark, Searches for

$$ m(t'(2/3)) > 1280 \text{ GeV, CL} = 95\% \quad (B(t' \rightarrow Z t) = 1) $$

$$ m(t'(2/3)) > 1295 \text{ GeV, CL} = 95\% \quad (B(t' \rightarrow W b) = 1) $$

$$ m(t'(2/3)) > 1310 \text{ GeV, CL} = 95\% \quad (\text{singlet } t') $$

$$ m(t'(2/3)) > 1350 \text{ GeV, CL} = 95\% \quad (t' \text{ in a weak isospin doublet } (t',b')) $$

$$ m(t'(5/3)) > 1.460 \times 10^3 \text{ GeV, CL} = 95\% \quad (t'(5/3) \rightarrow t W^+) $$

### Free Quark Searches

All searches since 1977 have had negative results.

### NOTES

[a] A discussion of the definition of the top quark mass in these measurements can be found in the review "The Top Quark."

[b] Based on published top mass measurements using data from Tevatron Run-I and Run-II and LHC at $\sqrt{s} = 7$ TeV. Including the most recent unpublished results from Tevatron Run-II, the Tevatron Electroweak Working Group reports a top mass of 173.2 ± 0.9 GeV. See the note "The Top Quark" in the Quark Particle Listings of this Review.

[c] This limit is for $\Gamma(t \rightarrow \gamma q)/\Gamma(t \rightarrow W b)$.

[d] This limit is for $\Gamma(t \rightarrow Z q)/\Gamma(t \rightarrow W b)$.
LIGHT UNFLAVORED MESONS
(S = C = B = 0)

For $l = 1$ ($\pi, b, \rho, a$): $u\bar{d}, (u\bar{u}-d\bar{d})/\sqrt{2}, d\bar{u}$;
for $l = 0$ ($\eta, \eta', h, h', \omega, \phi, f, f'$): $c_1(u\bar{u} + d\bar{d}) + c_2(s\bar{s})$

$\pi^{\pm}$

$I^G(J^P) = 1^{-}(0^{-})$

$\text{Mass } m = 139.57039 \pm 0.00018 \text{ MeV} \quad (S = 1.8)$

$\text{Mean life } \tau = (2.6033 \pm 0.0005) \times 10^{-8} \text{ s} \quad (S = 1.2)$

$c\tau = 7.8045 \text{ m}$

$\pi^{\pm} \rightarrow \ell^{\pm} \nu \gamma$ form factors [a]

$F_V = 0.0254 \pm 0.0017$

$F_A = 0.0119 \pm 0.0001$

$F_V$ slope parameter $a = 0.10 \pm 0.06$

$R = 0.059^{+0.009}_{-0.008}$

$\pi^{-}$ modes are charge conjugates of the modes below.

For decay limits to particles which are not established, see the section on
Searches for Axions and Other Very Light Bosons.

<table><thead><tr><th>π<sup>+</sup> DECAY MODES</th><th>Fraction (Γ<sub>f</sub>/Γ)</th><th>Confidence level</th><th>p<br>(MeV/c)</th></tr></thead><tbody><tr><td>μ<sup>+</sup> ν<sub>μ</sub></td><td>[b] (99.98770±0.00004) %</td><td></td><td>30</td></tr><tr><td>μ<sup>+</sup> ν<sub>μ</sub> γ</td><td>[c] (2.00 ±0.25) × 10<sup>-4</sup></td><td></td><td>30</td></tr><tr><td>e<sup>+</sup> ν<sub>e</sub></td><td>[b] (1.230 ±0.004) × 10<sup>-4</sup></td><td></td><td>70</td></tr><tr><td>e<sup>+</sup> ν<sub>e</sub> γ</td><td>[c] (7.39 ±0.05) × 10<sup>-7</sup></td><td></td><td>70</td></tr><tr><td>e<sup>+</sup> ν<sub>e</sub> π<sup>0</sup></td><td>(1.036 ±0.006) × 10<sup>-8</sup></td><td></td><td>4</td></tr><tr><td>e<sup>+</sup> ν<sub>e</sub> e<sup>+</sup> e<sup>-</sup></td><td>(3.2 ±0.5) × 10<sup>-9</sup></td><td></td><td>70</td></tr><tr><td>μ<sup>+</sup> ν<sub>μ</sub> ν̄ν</td><td>&lt; 9</td><td>× 10<sup>-6</sup></td><td>90%</td></tr><tr><td>e<sup>+</sup> ν<sub>e</sub> ν̄ν</td><td>&lt; 1.6</td><td>× 10<sup>-7</sup></td><td>90%</td></tr><tr><td colspan="4">Lepton Family number (LF) or Lepton number (L) violating modes</td></tr><tr><td>μ<sup>+</sup> ν̄e</td><td>L [d] &lt; 1.5</td><td></td><td>× 10<sup>-3</sup></td><td>90%</td></tr><tr><td>μ<sup>+</sup> ν<sub>e</sub></td><td>LF [d] &lt; 8.0</td><td></td><td>× 10<sup>-3</sup></td><td>90%</td></tr><tr><td>μ<sup>+</sup> e<sup>+</sup> e<sup>+</sup> ν</td><td>LF &lt; 1.6</td><td></td><td>× 10<sup>-6</sup></td><td>90%</td></tr></tbody></table>

$\pi^0$

$I^G(J^{PC}) = 1^{-}(0^{-+})$

$\text{Mass } m = 134.9768 \pm 0.0005 \text{ MeV} \quad (S = 1.1)$

$m_{\pi^{\pm}} - m_{\pi^{0}} = 4.5936 \pm 0.0005 \text{ MeV}$

$\text{Mean life } \tau = (8.43 \pm 0.13) \times 10^{-17} \text{ s} \quad (S = 1.2)$

$c\tau = 25.3 \text{ nm}$

For decay limits to particles which are not established, see the appropriate
Search sections ($A^0$ (axion) and Other Light Boson ($\chi^0$) Searches, etc.).

<table><thead><tr><th>π<sup>0</sup> DECAY MODES</th><th>Fraction (Γ<sub>f</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th><th>p<br>(MeV/c)</th></tr></thead><tbody><tr><td>2γ</td><td>(98.823±0.034) %</td><td>S=1.5</td><td>67</td></tr><tr><td>e<sup>+</sup> e<sup>-</sup> γ</td><td>(1.174±0.035) %</td><td>S=1.5</td><td>67</td></tr><tr><td>γ positronium</td><td>(1.82 ±0.29) × 10<sup>-9</sup></td><td></td><td>67</td></tr><tr><td>e<sup>+</sup> e<sup>+</sup> e<sup>-</sup> e<sup>-</sup></td><td>(3.34 ±0.16) × 10<sup>-5</sup></td><td></td><td>67</td></tr><tr><td>e<sup>+</sup> e<sup>-</sup></td><td>(6.46 ±0.33) × 10<sup>-8</sup></td><td>CL=90%</td><td>67</td></tr><tr><td>4γ</td><td>&lt; 2</td><td>× 10<sup>-8</sup></td><td>CL=90%</td><td>67</td></tr><tr><td>invisible</td><td>&lt; 4.4</td><td>× 10<sup>-9</sup></td><td>CL=90%</td><td>—</td></tr><tr><td>ν<sub>e</sub>ν̄e</td><td>&lt; 1.7</td><td>× 10<sup>-6</sup></td><td>CL=90%</td><td>67</td></tr><tr><td>ν<sub>μ</sub>ν̄μ</td><td>&lt; 1.6</td><td>× 10<sup>-6</sup></td><td>CL=90%</td><td>67</td></tr><tr><td>ν<sub>τ</sub>ν̄τ</td><td>&lt; 2.1</td><td>× 10<sup>-6</sup></td><td>CL=90%</td><td>67</td></tr><tr><td>γν̄ν</td><td>&lt; 1.9</td><td>× 10<sup>-7</sup></td><td>CL=90%</td><td>67</td></tr></tbody></table>

Charge conjugation (C) or Lepton Family number (LF) violating modes

<table><tbody><tr><td>3γ</td><td>C</td><td>&lt; 3.1</td><td>× 10<sup>-8</sup></td><td>CL=90%</td><td>67</td></tr><tr><td>μ<sup>+</sup> e<sup>-</sup></td><td>LF</td><td>&lt; 3.8</td><td>× 10<sup>-10</sup></td><td>CL=90%</td><td>26</td></tr><tr><td>μ<sup>-</sup> e<sup>+</sup></td><td>LF</td><td>&lt; 3.2</td><td>× 10<sup>-10</sup></td><td>CL=90%</td><td>26</td></tr><tr><td>μ<sup>+</sup> e<sup>+</sup> + μ<sup>-</sup> e<sup>+</sup></td><td>LF</td><td>&lt; 3.6</td><td>× 10<sup>-10</sup></td><td>CL=90%</td><td>26</td></tr></tbody></table>

$\eta$

$I^G(J^{PC}) = 0^{+}(0^{-+})$

$\text{Mass } m = 547.862 \pm 0.017 \text{ MeV}$

$\text{Full width } \Gamma = 1.31 \pm 0.05 \text{ keV}$

C-nonconserving decay parameters

$\pi^+\pi^-\pi^0 \text{ left-right asymmetry} = (0.09^{+0.11}_{-0.12}) \times 10^{-2}$

$\pi^+\pi^-\pi^0 \text{ sextant asymmetry} = (0.12^{+0.10}_{-0.11}) \times 10^{-2}$

$\pi^+\pi^-\pi^0 \text{ quadrant asymmetry} = (-0.09 \pm 0.09) \times 10^{-2}$

$\pi^+\pi^-\pi \text{ left-right asymmetry} = (0.9 \pm 0.4) \times 10^{-2}$

$\pi^+\pi^-\pi \beta(D\text{-wave}) = -0.02 \pm 0.07 \quad (S = 1.3)$

CP-nonconserving decay parameters

$\pi^+\pi^- e^+e^- \text{ decay-plane asymmetry } A_\phi = (-0.6 \pm 3.1) \times 10^{-2}$

Other decay parameters

$\pi^0\pi^0\pi^0 \text{ Dalitz plot } \alpha = -0.0296 \pm 0.0016 \quad (S = 1.7)$

$\text{Parameter } \Lambda \text{ in } \eta \rightarrow \ell^+\ell^-\gamma \text{ decay} = 0.716 \pm 0.011 \text{ GeV/c}^2$

<table><thead><tr><th>η DECAY MODES</th><th>Fraction (Γ<sub>f</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th><th>p<br>(MeV/c)</th></tr></thead><tbody><tr><td colspan="4"><strong>Neutral modes</strong></td></tr><tr><td>neutral modes</td><td>(71.96±0.30) %</td><td>S=1.3</td><td>—</td></tr><tr><td>2γ</td><td>(39.36±0.18) %</td><td>S=1.1</td><td>274</td></tr><tr><td>3π<sup>0</sup></td><td>(32.57±0.21) %</td><td>S=1.2</td><td>179</td></tr><tr><td>π<sup>0</sup>2γ</td><td>(2.55±0.22) × 10<sup>-4</sup></td><td></td><td>257</td></tr><tr><td>2π<sup>0</sup>2γ</td><td>&lt; 1.2</td><td>× 10<sup>-3</sup></td><td>CL=90%</td><td>238</td></tr><tr><td>4γ</td><td>&lt; 2.8</td><td>× 10<sup>-4</sup></td><td>CL=90%</td><td>274</td></tr><tr><td>invisible</td><td>&lt; 1.0</td><td>× 10<sup>-4</sup></td><td>CL=90%</td><td>—</td></tr><tr><td colspan="4"><strong>Charged modes</strong></td></tr><tr><td>charged modes</td><td>(28.04±0.30) %</td><td>S=1.3</td><td>—</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td><td>(23.02±0.25) %</td><td>S=1.2</td><td>174</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>γ</td><td>(4.28±0.07) %</td><td>S=1.1</td><td>236</td></tr><tr><td>e<sup>+</sup>e<sup>-</sup>γ</td><td>(6.9 ±0.4) × 10<sup>-3</sup></td><td>S=1.2</td><td>274</td></tr><tr><td>μ<sup>+</sup>μ<sup>-</sup>γ</td><td>(3.1 ±0.4) × 10<sup>-4</sup></td><td></td><td>253</td></tr><tr><td>e<sup>+</sup>e<sup>-</sup></td><td>&lt; 7</td><td>× 10<sup>-7</sup></td><td>CL=90%</td><td>274</td></tr><tr><td>μ<sup>+</sup>μ<sup>-</sup></td><td>(5.8 ±0.8) × 10<sup>-6</sup></td><td></td><td>253</td></tr><tr><td>2e<sup>+</sup>2e<sup>-</sup></td><td>(2.40±0.22) × 10<sup>-5</sup></td><td></td><td>274</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>e<sup>+</sup>e<sup>-</sup>(γ)</td><td>(2.68±0.11) × 10<sup>-4</sup></td><td></td><td>235</td></tr><tr><td>e<sup>+</sup>e<sup>-</sup> μ<sup>+</sup>μ<sup>-</sup></td><td>&lt; 1.6</td><td>× 10<sup>-4</sup></td><td>CL=90%</td><td>253</td></tr><tr><td>2μ<sup>+</sup>2μ<sup>-</sup></td><td>(5.0 ±1.3) × 10<sup>-9</sup></td><td></td><td>161</td></tr><tr><td>μ<sup>+</sup>μ<sup>-</sup>π<sup>+</sup>π<sup>-</sup></td><td>&lt; 3.6</td><td>× 10<sup>-4</sup></td><td>CL=90%</td><td>113</td></tr><tr><td>π<sup>+</sup>e<sup>-</sup>ν̄e + c.c.</td><td>&lt; 1.7</td><td>× 10<sup>-4</sup></td><td>CL=90%</td><td>256</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>2γ</td><td>&lt; 2.1</td><td>× 10<sup>-3</sup></td><td>CL=90%</td><td>236</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>γ</td><td>&lt; 6</td><td>× 10<sup>-4</sup></td><td>CL=90%</td><td>174</td></tr><tr><td>π<sup>0</sup>μ<sup>+</sup>μ<sup>-</sup>γ</td><td>&lt; 3</td><td>× 10<sup>-6</sup></td><td>CL=90%</td><td>210</td></tr></tbody></table>

Charge conjugation (C), Parity (P), Charge conjugation × Parity (CP), or Lepton Family number (LF) violating modes

<table><tbody><tr><td>π<sup>0</sup>γ</td><td>C [e] &lt; 9</td><td>× 10<sup>-5</sup></td><td>CL=90%</td><td>257</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup></td><td>P<sub>f</sub>,CP &lt; 4.4</td><td>× 10<sup>-6</sup></td><td>CL=90%</td><td>236</td></tr><tr><td>2π<sup>0</sup></td><td>P<sub>f</sub>,CP &lt; 3.5</td><td>× 10<sup>-4</sup></td><td>CL=90%</td><td>238</td></tr><tr><td>2π<sup>0</sup>γ</td><td>C &lt; 5</td><td>× 10<sup>-4</sup></td><td>CL=90%</td><td>238</td></tr><tr><td>3π<sup>0</sup>γ</td><td>C &lt; 6</td><td>× 10<sup>-5</sup></td><td>CL=90%</td><td>179</td></tr><tr><td>3γ</td><td>C &lt; 1.6</td><td>× 10<sup>-5</sup></td><td>CL=90%</td><td>274</td></tr><tr><td>4π<sup>0</sup></td><td>P<sub>f</sub>,CP &lt; 6.9</td><td>× 10<sup>-7</sup></td><td>CL=90%</td><td>40</td></tr><tr><td>π<sup>0</sup>e<sup>+</sup>e<sup>-</sup></td><td>C [f] &lt; 8</td><td>× 10<sup>-6</sup></td><td>CL=90%</td><td>257</td></tr><tr><td>π<sup>0</sup>μ<sup>+</sup>μ<sup>-</sup></td><td>C [f] &lt; 5</td><td>× 10<sup>-6</sup></td><td>CL=90%</td><td>210</td></tr><tr><td>μ<sup>+</sup>e<sup>-</sup> + μ<sup>-</sup>e<sup>+</sup></td><td>LF &lt; 6</td><td>× 10<sup>-6</sup></td><td>CL=90%</td><td>264</td></tr></tbody></table>

$f_0(500)$

$I^G(J^{PC}) = 0^{+}(0^{++})$

also known as $\sigma_f$; was $f_0(600)$, $f_0(400-1200)$

See the review on "Scalar Mesons below 1 GeV."

$\text{Mass (T-Matrix Pole } \sqrt{s}) = (400-550) - i(200-350) \text{ MeV}$

$\text{Mass (Breit-Wigner)} = 400 \text{ to } 800 \text{ MeV}$

$\text{Full width (Breit-Wigner)} = 100 \text{ to } 800 \text{ MeV}$

<table><thead><tr><th>f<sub>0</sub>(500) DECAY MODES</th><th>Fraction (Γ<sub>f</sub>/Γ)</th><th>p<br>(MeV/c)</th></tr></thead><tbody><tr><td>ππ</td><td>seen</td><td>—</td></tr><tr><td>γγ</td><td>seen</td><td>—</td></tr></tbody></table>

$\rho(770)$

$I^G(J^{PC}) = 1^{+}(1^{--})$

See the review on "Spectroscopy of Light Meson Resonances."

$\text{T-Matrix Pole } \sqrt{s} = (761-765) - i(71-74) \text{ MeV}$

$\rho^0 \text{ mass (Breit-Wigner)} = 775.26 \pm 0.23 \text{ MeV [g]}$

$\rho^0 \text{ full width (Breit-Wigner)} = 147.4 \pm 0.8 \text{ MeV [g]} \quad (S = 2.0)$

<table><thead><tr><th>ρ(770) DECAY MODES</th><th>Fraction (Γ<sub>f</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th><th>p<br>(MeV/c)</th></tr></thead><tbody><tr><td>ππ</td><td>~ 100</td><td>%</td><td>363</td></tr><tr><td colspan="4"><strong>ρ(770)<sup>±</sup> decays</strong></td></tr><tr><td>π<sup>±</sup>γ</td><td>( 4.5 ±0.5)</td><td>× 10<sup>-4</sup></td><td>S=2.2</td><td>375</td></tr><tr><td>π<sup>±</sup>η</td><td>&lt; 6</td><td>× 10<sup>-3</sup></td><td>CL=84%</td><td>152</td></tr><tr><td>π<sup>±</sup>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td><td>&lt; 2.0</td><td>× 10<sup>-3</sup></td><td>CL=84%</td><td>254</td></tr></tbody></table>
# Meson Summary Table

<table><thead><tr><th colspan="3" style="text-align:center;">ρ(770)<sup>0</sup> decays</th></tr></thead><tbody><tr><td>π<sup>+</sup>π<sup>-</sup>γ</td><td>( 9.9 ±1.6 ) × 10<sup>-3</sup></td><td>362</td></tr><tr><td>π<sup>0</sup>γ</td><td>( 4.7 ±0.8 ) × 10<sup>-4</sup></td><td>S=1.7</td><td>376</td></tr><tr><td>ηγ</td><td>( 3.00±0.21 ) × 10<sup>-4</sup></td><td></td><td>194</td></tr><tr><td>π<sup>0</sup>π<sup>0</sup>γ</td><td>( 4.5 ±0.8 ) × 10<sup>-5</sup></td><td></td><td>363</td></tr><tr><td>μ<sup>+</sup>μ<sup>-</sup></td><td>[h] ( 4.55±0.28 ) × 10<sup>-5</sup></td><td></td><td>373</td></tr><tr><td>e<sup>+</sup>e<sup>-</sup></td><td>[h] ( 4.72±0.05 ) × 10<sup>-5</sup></td><td></td><td>388</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td><td>( 1.01<sup>+0.54</sup><sub>-0.36</sub>±0.34) × 10<sup>-4</sup></td><td></td><td>323</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>π<sup>+</sup>π<sup>-</sup></td><td>( 1.8 ±0.9 ) × 10<sup>-5</sup></td><td></td><td>251</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>π<sup>0</sup></td><td>( 1.6 ±0.8 ) × 10<sup>-5</sup></td><td></td><td>257</td></tr><tr><td>π<sup>0</sup>e<sup>+</sup>e<sup>-</sup></td><td>&lt; 1.2</td><td>× 10<sup>-5</sup></td><td>CL=90%</td><td>376</td></tr></tbody></table>

$$\omega(782)$$

$$I^G(JPC) = 0^{+}(1^{-})$$

Mass $m = 782.66 \pm 0.13$ MeV (S = 2.0)

Full width $\Gamma = 8.68 \pm 0.13$ MeV

<table><thead><tr><th>ω(782) DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th><th>ρ<br>(MeV/c)</th></tr></thead><tbody><tr><td>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td><td>(89.2 ±0.7) %</td><td></td><td>327</td></tr><tr><td>π<sup>0</sup>γ</td><td>( 8.35±0.27) %</td><td>S=2.2</td><td>380</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup></td><td>( 1.53±0.12) %</td><td>S=1.2</td><td>366</td></tr><tr><td>neutrals (excluding π<sup>0</sup>γ)</td><td>( 7 <sup>+8</sup><sub>-4</sub> ) × 10<sup>-3</sup></td><td>S=1.1</td><td>—</td></tr><tr><td>ηγ</td><td>( 4.5 ±0.4 ) × 10<sup>-4</sup></td><td>S=1.1</td><td>200</td></tr><tr><td>π<sup>0</sup>e<sup>+</sup>e<sup>-</sup></td><td>( 7.7 ±0.6 ) × 10<sup>-4</sup></td><td></td><td>380</td></tr><tr><td>π<sup>0</sup>μ<sup>+</sup>μ<sup>-</sup></td><td>( 1.34±0.18) × 10<sup>-4</sup></td><td>S=1.5</td><td>349</td></tr><tr><td>e<sup>+</sup>e<sup>-</sup></td><td>( 7.38±0.22) × 10<sup>-5</sup></td><td>S=1.9</td><td>391</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>π<sup>0</sup></td><td>&lt; 2</td><td>× 10<sup>-4</sup></td><td>CL=90%</td><td>262</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>π<sup>+</sup>γ</td><td>&lt; 3.6</td><td>× 10<sup>-3</sup></td><td>CL=95%</td><td>366</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>π<sup>+</sup>π<sup>-</sup></td><td>&lt; 1</td><td>× 10<sup>-3</sup></td><td>CL=90%</td><td>256</td></tr><tr><td>π<sup>0</sup>π<sup>0</sup>γ</td><td>( 6.7 ±1.1 ) × 10<sup>-5</sup></td><td></td><td>367</td></tr><tr><td>ηπ<sup>0</sup>γ</td><td>&lt; 3.3</td><td>× 10<sup>-5</sup></td><td>CL=90%</td><td>162</td></tr><tr><td>μ<sup>+</sup>μ<sup>-</sup></td><td>( 7.4 ±1.8 ) × 10<sup>-5</sup></td><td></td><td>377</td></tr><tr><td>3γ</td><td>&lt; 1.9</td><td>× 10<sup>-4</sup></td><td>CL=95%</td><td>391</td></tr></tbody></table>

Charge conjugation (C) violating modes

<table><tbody><tr><td>ηπ<sup>0</sup></td><td>C</td><td>&lt; 2.1</td><td>× 10<sup>-4</sup></td><td>CL=90%</td><td>162</td></tr><tr><td>2π<sup>0</sup></td><td>C</td><td>&lt; 2.2</td><td>× 10<sup>-4</sup></td><td>CL=90%</td><td>367</td></tr><tr><td>3π<sup>0</sup></td><td>C</td><td>&lt; 2.3</td><td>× 10<sup>-4</sup></td><td>CL=90%</td><td>330</td></tr><tr><td>invisible</td><td></td><td>&lt; 7</td><td>× 10<sup>-5</sup></td><td>CL=90%</td><td>—</td></tr></tbody></table>

$$\eta'(958)$$

$$I^G(JPC) = 0^{+}(0^{-})$$

Mass $m = 957.78 \pm 0.06$ MeV

Full width $\Gamma = 0.188 \pm 0.006$ MeV

<table><thead><tr><th>η'(958) DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th><th>ρ<br>(MeV/c)</th></tr></thead><tbody><tr><td>π<sup>+</sup>π<sup>-</sup>η</td><td>(42.5 ±0.5) %</td><td></td><td>232</td></tr><tr><td>ρ<sup>0</sup>γ (including non-resonant<br>π<sup>+</sup>π<sup>-</sup>γ)</td><td>(29.5 ±0.4) %</td><td></td><td>165</td></tr><tr><td>π<sup>0</sup>π<sup>0</sup>η</td><td>(22.4 ±0.5) %</td><td></td><td>239</td></tr><tr><td>ωγ</td><td>( 2.52 ±0.07 ) %</td><td></td><td>159</td></tr><tr><td>ωe<sup>+</sup>e<sup>-</sup></td><td>( 2.0 ±0.4 ) × 10<sup>-4</sup></td><td></td><td>159</td></tr><tr><td>γγ</td><td>( 2.307±0.033) %</td><td></td><td>479</td></tr><tr><td>3π<sup>0</sup></td><td>( 2.50 ±0.17 ) × 10<sup>-3</sup></td><td></td><td>430</td></tr><tr><td>μ<sup>+</sup>μ<sup>-</sup>γ</td><td>( 1.13 ±0.28 ) × 10<sup>-4</sup></td><td></td><td>467</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>μ<sup>+</sup>μ<sup>-</sup></td><td>( 1.9 ±0.4 ) × 10<sup>-5</sup></td><td></td><td>401</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td><td>( 3.61 ±0.17 ) × 10<sup>-3</sup></td><td></td><td>428</td></tr><tr><td>(π<sup>+</sup>π<sup>-</sup>π<sup>0</sup>) S-wave</td><td>( 3.8 ±0.5 ) × 10<sup>-3</sup></td><td></td><td>428</td></tr><tr><td>π<sup>+</sup>ρ<sup>±</sup></td><td>( 7.4 ±2.3 ) × 10<sup>-4</sup></td><td></td><td>106</td></tr><tr><td>2(π<sup>+</sup>π<sup>-</sup>)</td><td>( 8.3 ±0.9 ) × 10<sup>-5</sup></td><td></td><td>372</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>2π<sup>0</sup></td><td>( 1.8 ±0.4 ) × 10<sup>-4</sup></td><td></td><td>376</td></tr><tr><td>2(π<sup>+</sup>π<sup>-</sup>) neutrals</td><td>&lt; 1</td><td>%</td><td>95%</td><td>—</td></tr><tr><td>2(π<sup>+</sup>π<sup>-</sup>)π<sup>0</sup></td><td>&lt; 1.8</td><td>× 10<sup>-3</sup></td><td>90%</td><td>298</td></tr><tr><td>2(π<sup>+</sup>π<sup>-</sup>)2π<sup>0</sup></td><td>&lt; 1</td><td>%</td><td>95%</td><td>197</td></tr><tr><td>3(π<sup>+</sup>π<sup>-</sup>)</td><td>&lt; 3.1</td><td>× 10<sup>-5</sup></td><td>90%</td><td>189</td></tr><tr><td>K<sup>±</sup>π<sup>±</sup></td><td>&lt; 4</td><td>× 10<sup>-5</sup></td><td>90%</td><td>334</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>e<sup>+</sup>e<sup>-</sup></td><td>( 2.42 ±0.10 ) × 10<sup>-3</sup></td><td></td><td>458</td></tr><tr><td>π<sup>+</sup>e<sup>-</sup>ν<sub>e</sub> + c.c.</td><td>&lt; 2.1</td><td>× 10<sup>-4</sup></td><td>90%</td><td>469</td></tr><tr><td>γe<sup>+</sup>e<sup>-</sup></td><td>( 4.91 ±0.27 ) × 10<sup>-4</sup></td><td></td><td>479</td></tr><tr><td>π<sup>0</sup>γγ</td><td>( 3.20 ±0.24 ) × 10<sup>-3</sup></td><td></td><td>469</td></tr><tr><td>π<sup>0</sup>γγ(non resonant)</td><td>( 6.2 ±0.9 ) × 10<sup>-4</sup></td><td></td><td>—</td></tr><tr><td>ηγγ</td><td>&lt; 1.33</td><td>× 10<sup>-4</sup></td><td>90%</td><td>322</td></tr><tr><td>4π<sup>0</sup></td><td>&lt; 4.94</td><td>× 10<sup>-5</sup></td><td>90%</td><td>380</td></tr></tbody></table>

<table><tbody><tr><td>e<sup>+</sup>e<sup>-</sup></td><td>&lt; 5.6</td><td>× 10<sup>-9</sup></td><td>90%</td><td>479</td></tr><tr><td>e<sup>+</sup>e<sup>-</sup>e<sup>+</sup>e<sup>-</sup></td><td>( 4.5 ±1.1 )</td><td>× 10<sup>-6</sup></td><td></td><td>479</td></tr><tr><td>invisible</td><td>&lt; 6</td><td>× 10<sup>-4</sup></td><td>90%</td><td>—</td></tr></tbody></table>

Charge conjugation (C), Parity (P), Lepton family number (LF) violating modes

<table><tbody><tr><td>π<sup>+</sup>π<sup>-</sup></td><td>P<sub>j</sub>CP</td><td>&lt; 1.8</td><td>× 10<sup>-5</sup></td><td>90%</td><td>458</td></tr><tr><td>π<sup>0</sup>π<sup>0</sup></td><td>P<sub>j</sub>CP</td><td>&lt; 4</td><td>× 10<sup>-4</sup></td><td></td><td>459</td></tr><tr><td>π<sup>0</sup>e<sup>+</sup>e<sup>-</sup></td><td>C</td><td>[f] &lt; 1.4</td><td>× 10<sup>-3</sup></td><td>90%</td><td>469</td></tr><tr><td>π<sup>0</sup>ρ<sup>0</sup></td><td>C</td><td>&lt; 4</td><td>%</td><td>90%</td><td>111</td></tr><tr><td>ηe<sup>+</sup>e<sup>-</sup></td><td>C</td><td>[f] &lt; 2.4</td><td>× 10<sup>-3</sup></td><td>90%</td><td>322</td></tr><tr><td>3γ</td><td>C</td><td>&lt; 1.0</td><td>× 10<sup>-4</sup></td><td>90%</td><td>479</td></tr><tr><td>μ<sup>+</sup>μ<sup>-</sup>π<sup>0</sup></td><td>C</td><td>[f] &lt; 6.0</td><td>× 10<sup>-5</sup></td><td>90%</td><td>445</td></tr><tr><td>μ<sup>+</sup>μ<sup>-</sup>η</td><td>C</td><td>[f] &lt; 1.5</td><td>× 10<sup>-5</sup></td><td>90%</td><td>273</td></tr><tr><td>eμ</td><td>LF</td><td>&lt; 4.7</td><td>× 10<sup>-4</sup></td><td>90%</td><td>473</td></tr></tbody></table>

$$f_0(980)$$

$$I^G(JPC) = 0^{+}(0^{++})$$

See the review on "Scalar Mesons below 1 GeV."

T-matrix pole $\sqrt{s} = (980-1010) - i (20-35)$ MeV [f]

Mass (Breit-Wigner) = 990 $\pm$ 20 MeV [f]

Full width (Breit-Wigner) = 10 to 100 MeV [f]

<table><thead><tr><th>f<sub>0</sub>(980) DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>ρ (MeV/c)</th></tr></thead><tbody><tr><td>ππ</td><td>seen</td><td>476</td></tr><tr><td>K<sup>+</sup>K<sup>-</sup></td><td>seen</td><td>36</td></tr><tr><td>γγ</td><td>seen</td><td>495</td></tr></tbody></table>

$$a_0(980)$$

$$I^G(JPC) = 1^{-}(0^{++})$$

See the review on "Scalar Mesons below 1 GeV."

T-matrix pole $\sqrt{s} = (970-1020) - i (30-70)$ MeV [f]

Mass $m = 980 \pm 20$ MeV [f]

Full width $\Gamma = 50$ to 100 MeV [f]

<table><thead><tr><th>a<sub>0</sub>(980) DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>ρ (MeV/c)</th></tr></thead><tbody><tr><td>ηπ</td><td>seen</td><td>319</td></tr><tr><td>K<sup>+</sup>K<sup>-</sup></td><td>seen</td><td>†</td></tr><tr><td>η'π</td><td>seen</td><td>†</td></tr><tr><td>ρπ</td><td>not seen</td><td>137</td></tr><tr><td>γγ</td><td>seen</td><td>490</td></tr></tbody></table>

$$\phi(1020)$$

$$I^G(JPC) = 0^{-}(1^{--})$$

Mass $m = 1019.461 \pm 0.016$ MeV

Full width $\Gamma = 4.249 \pm 0.013$ MeV (S = 1.1)

<table><thead><tr><th>φ(1020) DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th><th>ρ<br>(MeV/c)</th></tr></thead><tbody><tr><td>K<sup>+</sup>K<sup>-</sup></td><td>(49.1 ±0.5) %</td><td></td><td>127</td></tr><tr><td>K<sup>0</sup><sub>L</sub>K<sup>0</sup><sub>S</sub></td><td>(33.9 ±0.4) %</td><td></td><td>127</td></tr><tr><td>ρπ + π<sup>+</sup>π<sup>-</sup>π<sup>0</sup></td><td>(15.4 ±0.4) %</td><td></td><td>127</td></tr><tr><td>ηγ</td><td>( 1.301±0.024) %</td><td></td><td>127</td></tr><tr><td>π<sup>0</sup>γ</td><td>( 1.32 ±0.05 ) × 10<sup>-3</sup></td><td></td><td>501</td></tr><tr><td>ℓ<sup>+</sup>ℓ<sup>-</sup></td><td>—</td><td></td><td>510</td></tr><tr><td>e<sup>+</sup>e<sup>-</sup></td><td>( 2.979±0.033) × 10<sup>-4</sup></td><td>S=1.2</td><td>510</td></tr><tr><td>μ<sup>+</sup>μ<sup>-</sup></td><td>( 2.85 ±0.22) × 10<sup>-4</sup></td><td>S=1.2</td><td>499</td></tr><tr><td>ηe<sup>+</sup>e<sup>-</sup></td><td>( 1.08 ±0.04 ) × 10<sup>-4</sup></td><td></td><td>363</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup></td><td>( 7.3 ±1.3 ) × 10<sup>-5</sup></td><td></td><td>490</td></tr><tr><td>ωπ<sup>0</sup></td><td>( 4.7 ±0.5 ) × 10<sup>-5</sup></td><td></td><td>171</td></tr><tr><td>ωγ</td><td>&lt; 5</td><td>%</td><td>CL=84%</td><td>209</td></tr><tr><td>ργ</td><td>&lt; 1.2</td><td>× 10<sup>-5</sup></td><td>CL=90%</td><td>215</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>γ</td><td>( 4.1 ±1.3 ) × 10<sup>-5</sup></td><td></td><td>490</td></tr><tr><td>f<sub>0</sub>(980)γ</td><td>( 3.22 ±0.19 ) × 10<sup>-4</sup></td><td>S=1.1</td><td>29</td></tr><tr><td>π<sup>0</sup>π<sup>0</sup>γ</td><td>( 1.12 ±0.06 ) × 10<sup>-4</sup></td><td></td><td>492</td></tr><tr><td>π<sup>+</sup>π<sup>-</sup>π<sup>+</sup>π<sup>-</sup></td><td>( 3.9 <sup>+2.8</sup><sub>-2.2</sub> ) × 10<sup>-6</sup></td><td></td><td>410</td></tr><tr><td>π<sup>+</sup>π<sup>+</sup>π<sup>-</sup>π<sup>-</sup>π<sup>0</sup></td><td>&lt; 4.6</td><td>× 10<sup>-6</sup></td><td>CL=90%</td><td>342</td></tr><tr><td>π<sup>0</sup>e<sup>+</sup>e<sup>-</sup></td><td>( 1.33 <sup>+0.07</sup><sub>-0.10</sub> ) × 10<sup>-5</sup></td><td></td><td>501</td></tr><tr><td>π<sup>0</sup>ηγ</td><td>( 7.27 ±0.30 ) × 10<sup>-5</sup></td><td></td><td>1.5</td><td>346</td></tr><tr><td>a<sub>0</sub>(980)γ</td><td>( 7.6 ±0.6 ) × 10<sup>-5</sup></td><td></td><td>39</td></tr><tr><td>K<sup>0</sup><sub>R</sub>K<sup>0</sup><sub>S</sub>γ</td><td>&lt; 1.9</td><td>× 10<sup>-8</sup></td><td>CL=90%</td><td>110</td></tr><tr><td>η'(958)γ</td><td>( 6.21 ±0.20 ) × 10<sup>-5</sup></td><td></td><td>60</td></tr></tbody></table>
Meson Summary Table

<table><tr><td>ηπ<sup>0</sup>π<sup>0</sup>γ</td><td>&lt; 2</td><td>× 10<sup>-5</sup></td><td>CL=90%</td><td>293</td></tr><tr><td>μ<sup>+</sup> μ<sup>-</sup> γ</td><td>( 1.4 ± 0.5 )</td><td>× 10<sup>-5</sup></td><td></td><td>499</td></tr><tr><td>ργγ</td><td>&lt; 1.2</td><td>× 10<sup>-4</sup></td><td>CL=90%</td><td>215</td></tr><tr><td>ηπ<sup>+</sup> π<sup>-</sup></td><td>&lt; 1.8</td><td>× 10<sup>-5</sup></td><td>CL=90%</td><td>288</td></tr><tr><td>ημ<sup>+</sup> μ<sup>-</sup></td><td>&lt; 9.4</td><td>× 10<sup>-6</sup></td><td>CL=90%</td><td>321</td></tr><tr><td>ηU → ηe<sup>+</sup> e<sup>-</sup></td><td>&lt; 1</td><td>× 10<sup>-6</sup></td><td>CL=90%</td><td>—</td></tr><tr><td>invisible</td><td>&lt; 1.7</td><td>× 10<sup>-4</sup></td><td>CL=90%</td><td>—</td></tr></table>

Lepton Family number (LF) violating modes

<table><tr><td>e<sup>±</sup> μ<sup>∓</sup></td><td>LF</td><td>&lt; 2</td><td>× 10<sup>-6</sup></td><td>CL=90%</td><td>504</td></tr></table>

h₁(1170)

$I^G(J^{PC}) = 0^{-(1 + -)}$

Mass $m = 1166 \pm 6$ MeV

Full width $\Gamma = 375 \pm 35$ MeV

<table><thead><tr><th>h<sub>1</sub>(1170) DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>ρ (MeV/c)</th></tr></thead><tbody><tr><td>ρπ</td><td>seen</td><td>305</td></tr></tbody></table>

b₁(1235)

$I^G(J^{PC}) = 1^{+(1 + -)}$

Mass $m = 1229.5 \pm 3.2$ MeV (S = 1.6)

Full width $\Gamma = 142 \pm 9$ MeV (S = 1.2)

<table><thead><tr><th>b<sub>1</sub>(1235) DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>Confidence level</th><th>ρ (MeV/c)</th></tr></thead><tbody><tr><td>ωπ</td><td>seen</td><td></td><td>348</td></tr><tr><td>π<sup>±</sup>γ</td><td>(1.6 ± 0.4) × 10<sup>-3</sup></td><td></td><td>607</td></tr><tr><td>ηρ</td><td>seen</td><td></td><td>†</td></tr><tr><td>π<sup>+</sup> π<sup>+</sup> π<sup>-</sup> π<sup>0</sup></td><td>&lt; 50 %</td><td>84%</td><td>535</td></tr><tr><td>K<sup>*</sup>(892)K<sup>∓</sup></td><td>seen</td><td></td><td>†</td></tr><tr><td>(K<span style="text-decoration: overline">K</span>)<sup>±</sup>π<sup>0</sup></td><td>&lt; 8 %</td><td>90%</td><td>248</td></tr><tr><td>K<sup>0</sup> K<sup>0</sup> π<sup>±</sup></td><td>&lt; 6 %</td><td>90%</td><td>235</td></tr><tr><td>K<sup>0</sup> S K<sup>0</sup> π<sup>±</sup></td><td>&lt; 2 %</td><td>90%</td><td>235</td></tr><tr><td>φπ</td><td>&lt; 1.5 %</td><td>84%</td><td>147</td></tr></tbody></table>

a₁(1260) [i]

$I^G(J^{PC}) = 1^{-(1 + +)}$

T-Matrix Pole $\sqrt{s} = (1209_{-10}^{+13}) - i(288_{-12}^{+45})$ MeV

Mass (Breit-Wigner) = 1230 ± 40 MeV [i]

Full width (Breit-Wigner) = 250 to 600 MeV [i]

<table><thead><tr><th>a<sub>1</sub>(1260) DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>ρ (MeV/c)</th></tr></thead><tbody><tr><td>3π</td><td>seen</td><td>577</td></tr><tr><td>(ρπ)<sub>S-wave</sub>, ρ → ππ</td><td>seen</td><td>353</td></tr><tr><td>(ρπ)<sub>D-wave</sub>, ρ → ππ</td><td>seen</td><td>353</td></tr><tr><td>(ρ(1450)π)<sub>S-wave</sub>, ρ → ππ</td><td>seen</td><td>†</td></tr><tr><td>(ρ(1450)π)<sub>D-wave</sub>, ρ → ππ</td><td>seen</td><td>†</td></tr><tr><td>f<sub>0</sub>(500)π, f<sub>0</sub> → ππ</td><td>seen</td><td>—</td></tr><tr><td>f<sub>0</sub>(980)π, f<sub>0</sub> → ππ</td><td>seen</td><td>179</td></tr><tr><td>f<sub>0</sub>(1370)π, f<sub>0</sub> → ππ</td><td>seen</td><td>†</td></tr><tr><td>f<sub>2</sub>(1270)π, f<sub>2</sub> → ππ</td><td>seen</td><td>†</td></tr><tr><td>π<sup>+</sup> π<sup>-</sup> π<sup>0</sup></td><td>seen</td><td>576</td></tr><tr><td>π<sup>0</sup> π<sup>0</sup> π<sup>0</sup></td><td>not seen</td><td>577</td></tr><tr><td>KKπ</td><td>seen</td><td>250</td></tr><tr><td>K<sup>*</sup>(892)K</td><td>seen</td><td>†</td></tr><tr><td>πγ</td><td>seen</td><td>608</td></tr></tbody></table>

f₂(1270)

$I^G(J^{PC}) = 0^{+(2 + +)}$

T-Matrix Pole $\sqrt{s} = (1260-1283) - i(90-110)$ MeV

Mass (Breit-Wigner) = 1275.4 ± 0.8 MeV (S = 1.1)

Full width (Breit-Wigner) = 186.6<sup>+2.8</sup><sub>-2.2</sub> MeV (S = 1.5)

<table><thead><tr><th>f<sub>2</sub>(1270) DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th><th>ρ<br>(MeV/c)</th></tr></thead><tbody><tr><td>ππ</td><td>(84.3<sup>+2.8</sup><sub>-1.0</sub> %)</td><td>S=1.2</td><td>623</td></tr><tr><td>π<sup>+</sup> π<sup>+</sup> 2π<sup>0</sup></td><td>(7.7<sup>+1.2</sup><sub>-3.1</sub> %)</td><td>S=1.2</td><td>563</td></tr><tr><td>K<span style="text-decoration: overline">K</span></td><td>(4.6 ± 0.4) %</td><td>S=2.7</td><td>404</td></tr><tr><td>2π<sup>+</sup> 2π<sup>-</sup></td><td>(2.8 ± 0.4) %</td><td>S=1.2</td><td>559</td></tr></tbody></table>

<table><tr><td>ηη</td><td>(4.0 ± 0.8) × 10<sup>-3</sup></td><td>S=2.1</td><td>326</td></tr><tr><td>4π<sup>0</sup></td><td>(3.0 ± 1.0) × 10<sup>-3</sup></td><td></td><td>565</td></tr><tr><td>γγ</td><td>(1.42 ± 0.24) × 10<sup>-5</sup></td><td>S=1.4</td><td>638</td></tr><tr><td>ηππ</td><td>&lt; 8 × 10<sup>-3</sup></td><td>CL=95%</td><td>478</td></tr><tr><td>K<sup>0</sup> K<sup>-</sup> π<sup>+</sup> + c.c.</td><td>&lt; 3.4 × 10<sup>-3</sup></td><td>CL=95%</td><td>293</td></tr><tr><td>e<sup>+</sup> e<sup>-</sup></td><td>&lt; 6 × 10<sup>-10</sup></td><td>CL=90%</td><td>638</td></tr></table>

f₁(1285)

$I^G(J^{PC}) = 0^{+(1 + +)}$

Mass $m = 1281.8 \pm 0.5$ MeV (S = 1.7)

Full width $\Gamma = 23.0 \pm 1.1$ MeV (S = 1.6)

<table><thead><tr><th>f<sub>1</sub>(1285) DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th><th>ρ<br>(MeV/c)</th></tr></thead><tbody><tr><td>4π</td><td>(32.7 ± 1.8) %</td><td>S=1.2</td><td>568</td></tr><tr><td>π<sup>0</sup> π<sup>0</sup> π<sup>+</sup> π<sup>-</sup></td><td>(21.8 ± 1.2) %</td><td>S=1.2</td><td>566</td></tr><tr><td>2π<sup>+</sup> 2π<sup>-</sup></td><td>(10.9 ± 0.6) %</td><td>S=1.2</td><td>563</td></tr><tr><td>ρ<sup>0</sup> π<sup>+</sup> π<sup>-</sup></td><td>(10.9 ± 0.6) %</td><td>S=1.2</td><td>336</td></tr><tr><td>ρ<sup>0</sup> ρ<sup>0</sup></td><td>seen</td><td></td><td>†</td></tr><tr><td>4π<sup>0</sup></td><td>&lt; 7 × 10<sup>-4</sup></td><td>CL=90%</td><td>568</td></tr><tr><td>ηπ<sup>+</sup> π<sup>-</sup></td><td>(35 ± 15) %</td><td></td><td>479</td></tr><tr><td>ηππ</td><td>(52.2 ± 1.9) %</td><td>S=1.2</td><td>482</td></tr><tr><td>a<sub>0</sub>(980)π [ignoring a<sub>0</sub>(980) → K<span style="text-decoration: overline">K</span>]</td><td>(38 ± 4) %</td><td></td><td>238</td></tr><tr><td>ηππ [excluding a<sub>0</sub>(980)π]</td><td>(14 ± 4) %</td><td></td><td>482</td></tr><tr><td>K<span style="text-decoration: overline">K</span>π<sup>+</sup></td><td>(9.0 ± 0.4) %</td><td>S=1.1</td><td>308</td></tr><tr><td>K<span style="text-decoration: overline">K</span>* (892)</td><td>not seen</td><td></td><td>†</td></tr><tr><td>π<sup>+</sup> π<sup>-</sup> π<sup>0</sup></td><td>(3.0 ± 0.9) × 10<sup>-3</sup></td><td></td><td>603</td></tr><tr><td>ρ<sup>±</sup> π<sup>∓</sup></td><td>&lt; 3.1 × 10<sup>-3</sup></td><td>CL=95%</td><td>390</td></tr><tr><td>γρ<sup>0</sup></td><td>(6.1 ± 1.0) %</td><td>S=1.7</td><td>406</td></tr><tr><td>φγ</td><td>(7.4 ± 2.6) × 10<sup>-4</sup></td><td></td><td>235</td></tr><tr><td>e<sup>+</sup> e<sup>-</sup></td><td>&lt; 9.4 × 10<sup>-9</sup></td><td>CL=90%</td><td>641</td></tr></tbody></table>

η(1295)

$I^G(J^{PC}) = 0^{+(0 - +)}$

See the review on "Spectroscopy of Light Meson Resonances."

Mass $m = 1294 \pm 4$ MeV (S = 1.6)

Full width $\Gamma = 55 \pm 5$ MeV

<table><thead><tr><th>η(1295) DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>ρ (MeV/c)</th></tr></thead><tbody><tr><td>ηπ<sup>+</sup> π<sup>-</sup></td><td>seen</td><td>487</td></tr><tr><td>a<sub>0</sub>(980)π</td><td>seen</td><td>248</td></tr><tr><td>ηπ<sup>0</sup> π<sup>0</sup></td><td>seen</td><td>490</td></tr><tr><td>η(ππ)<sub>S-wave</sub></td><td>seen</td><td>—</td></tr><tr><td>ση</td><td>seen</td><td>—</td></tr><tr><td>K<span style="text-decoration: overline">K</span>π</td><td>seen</td><td>320</td></tr></tbody></table>

π(1300)

$I^G(J^{PC}) = 1^{-(0 - +)}$

Mass $m = 1300 \pm 100$ MeV [i]

Full width $\Gamma = 200$ to 600 MeV [i]

<table><thead><tr><th>π(1300) DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>ρ (MeV/c)</th></tr></thead><tbody><tr><td>ρπ</td><td>seen</td><td>404</td></tr><tr><td>π(ππ)<sub>S-wave</sub></td><td>seen</td><td>—</td></tr></tbody></table>

a₂(1320)

$I^G(J^{PC}) = 1^{-(2 + +)}$

T-Matrix Pole $\sqrt{s} = (1305-1321) - i(52-58)$ MeV

Mass (Breit-Wigner) = 1318.2 ± 0.6 MeV (S = 1.2)

Full width $\Gamma = 107 \pm 5$ MeV

<table><thead><tr><th>a<sub>2</sub>(1320) DECAY MODES</th><th>Fraction (Γ<sub>j</sub>/Γ)</th><th>Scale factor/<br>Confidence level</th><th>ρ<br>(MeV/c)</th></tr></thead><tbody><tr><td>3π</td><td>(70.1 ± 2.7) %</td><td>S=1.2</td><td>624</td></tr><tr><td>ηπ</td><td>(14.5 ± 1.2) %</td><td></td><td>535</td></tr><tr><td>ωππ</td><td>(10.6 ± 3.2) %</td><td>S=1.3</td><td>366</td></tr><tr><td>K<span style="text-decoration: overline">K</span></td><td>(4.9 ± 0.8) %</td><td></td><td>437</td></tr><tr><td>η'(958)π</td><td>(5.5 ± 0.9) × 10<sup>-3</sup></td><td></td><td>288</td></tr><tr><td>π<sup>±</sup>γ</td><td>(2.91 ± 0.27) × 10<sup>-3</sup></td><td></td><td>652</td></tr><tr><td>γγ</td><td>(9.4 ± 0.7) × 10<sup>-6</sup></td><td></td><td>659</td></tr><tr><td>e<sup>+</sup> e<sup>-</sup></td><td>&lt; 5 × 10<sup>-9</sup></td><td>CL=90%</td><td>659</td></tr></tbody></table>