Introduction

1

Introduction
1 Overview
The Review of Particle Physics is a comprehensive review of the field of Particle Physics andof 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 evennumbered 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 andexperimental topics. Together with the Summary Tables they provide an exhaustive reference forthe practicing particle physicist. Two more review articles, Online Particle Physics Information andTests 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 containall 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 andaddress 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 referinterested 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 theParticle 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 forhadrons, 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 ofany 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:
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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2

Introduction• The printed PDG Book includes volume 1 only, i.e. it contains the Summary Tables andmost 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, andequations 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, andas 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 andSouth 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 relatedareas. 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 bosonsγ
A. Bettini, D.E. Groom*
GluonsR.M. Barnett,* A.V. Manohar
Graviton
A. Bettini,* D.E. Groom
W, Z
M. Grünewald,* A. Gurtu*
Higgs bosons S. Heinemeyer,* K. Hikasa, J. Tanaka
Heavy bosons R. Bonventre,* K.A. Olive, M. Tanabashi
AxionsC. O’Hare, K.A. Olive, G. Raffelt,*
F. Takahashi

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Introduction

3• Leptons
Neutrinos
Double-β decaye, µτ• Quarks
QuarksTop quarkb0 , t0
Free quark

M. Goodman, C.-J. Lin,* K. Nakamura,
K.A. Olive, A. Piepke
A. Bettini*, A. Piepke
A. Bettini,* C. Grab
A. Lusiani, K. Mönig*R.M. Barnett,* A.V. Manohar
Y. Sumino, W.-M. Yao*
Y. Sumino, W.-M. Yao*
A. Bettini,* C.-J. Lin• Mesonsπ, ηK (stable)
D (stable)
B (stable)
Unstable mesons• Baryons
Stable baryons
Unstable baryons
Charmed baryons
Bottom baryons

A. Bettini,* C. Grab
G. D’Ambrosio, C.-J. Lin*G. Casarosa, J. Rademacker,
D. Robinson*
A. Cerri,* P. Eerola, M. Kreps,
Y. Kwon, W.-M. Yao*
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

C. Grab, D. Robinson*
V. Burkert, V. Crede, U. Thoma,
L. Tiator, R.L. Workman*
G. Casarosa, J. Rademacker,
D. Robinson*
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
CompositenessM. Tanabashi, J. Terning*
Extra Dimensions
T. Gherghetta, K.A. Olive,
D. Robinson*
WIMP, DM, Other H. Baer, A. Bettini,* W.-M. Yao*

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Introduction

4

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)
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Introduction• 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)

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Introduction• 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.)

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Introduction• 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)

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Introduction• 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)

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Introduction• 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.)

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Introduction• 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)

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Introduction• 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)

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Introduction

12• 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 fromolder terminology affected mainly the heavier mesons made of u, d, and s quarks. Otherwise, theonly important change to known hadrons was that the F ± became the Ds± . None of the lightest
pseudoscalar or vector mesons changed names, nor did the cc or bb mesons (we do, however, now
use χc for the cc χ states), nor did any of the established baryons. The Summary Tables give boththe 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 andpentaquarks containing qq q̄ q̄ and q q̄qqq minimal quark content, respectively — has rendered the2018 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, Λ, π 0 , KL , Ds+ , b. Charge is indicated by a superscript: B − , ∆++ . Charge
is not normally indicated for p, n, or the quarks, and is optional for neutral isosinglets: η or
η 0 . Antiparticles and particles are distinguished by charge for charged leptons and mesons: τ + ,0+
K − . Otherwise, distinct antiparticles are indicated by a bar (overline): ν µ , t, p, K , and Σ (theantiparticle of the Σ − ).

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
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Introduction

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 thefollowing:• 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 thenstate the criterion, which sometimes is quite subjective, for selecting “more reliable” data foraveraging. 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, arequoted 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 notaverage or combine upper limits except in a very few cases where they may be re-expressed asmeasured 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 CP T as
well as other conservation laws.
We use the following indicators in the Particle Listings to tell how we get values from thetabulated 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 measurementsof related quantities.
• OUR ESTIMATE —Based on the observed range of the data. Not from a formal statisticalprocedure.
• OUR LIMIT —For special cases where the limit is evaluated by us from measured ratios orother 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 bymore 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 begiven. For more detailed discussions, see the reviews section on Particle Properties.
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Introduction

5.2 Averages and fits
We divide this discussion on obtaining averages and errors into three sections: (1) treatment oferrors; (2) unconstrained averaging; (3) constrained fits.
5.2.1 Treatment of errors
In what follows, the “error” δx means that the range x±δx 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, δx is the usual one standard deviation (1σ). Many experimenters now give statisticaland systematic errors separately, in which case we usually quote both errors, with the statisticalerror first. For averages and fits, we then add the two errors in quadrature and use this combined
error for δx.
When experimenters quote asymmetric errors (δx)+ and (δx)− for a measurement x, the errorthat we use for that measurement in making an average or a fit with other measurements is acontinuous function of these three quantities. When the resultant average or fit x is less thanx − (δx)− , we use (δx)− ; when it is greater than x + (δx)+ , we use (δx)+ . In between, the error weuse 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 Ai ± σi ± ∆ that have identicalsystematic errors ∆. In this case, one can first average the Ai ± σi and then combine the resulting
statistical error with ∆. One obtains, however, the same result by averaging Ai ± (σi2 + ∆2i )1/2 ,P
where ∆i = σi ∆[ (1/σj2 )]1/2 . This procedure has the advantage that, with the modified systematic
errors ∆i , each measurement may be treated as independent and averaged in the usual way withother data. Therefore, when appropriate, we adopt this procedure. We tabulate ∆ and invoke anautomated procedure that computes ∆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., m1 , m2 , and ∆ = m2 − m1 . We cannot enter allof m1 , m2 and ∆ into a constrained fit because they are not independent. In some cases, it is agood approximation to ignore the quantity with the largest error and put the other two into thefit. However, in some cases correlations are such that the errors on m1 , m2 and ∆ are comparable
and none of the three values can be ignored. In this case, we put all three values into the fit andinvoke 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 measurementsof a given quantity are uncorrelated, and calculate a weighted average and error asPP
wi x ix ± δx = Pi
± ( i wi )−1/2 ,
i wi

(1)

where
wi = 1/(δxi )2 .
Here xi and δxi are the value and error reported by the ith experiment, and the sums run over theP
N experiments. We then calculate χ2 = wi (x − xi )2 and compare it with N − 1, which is the
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15

Introduction

expectation value of χ2 if the measurements are from a Gaussian distribution.
If χ2 /(N − 1) is less than or equal to 1, and there are no known problems with the data, we
accept the results.
If χ2 /(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 χ2 /(N − 1) is greater than 1, but not greatly so, we still average the data, but thenalso do the following:(a) We increase our quoted error, δx in Eq. (1), by a scale factor S defined ashi1/2

S = χ2 /(N − 1).

(2)

Our reasoning is as follows. The large value of the χ2 is likely to be due to underestimation oferrors 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 thisfactor, the χ2 becomes N − 1, and of course the output error δx 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 δxi is arbitrarily chosen
to beδ0 = 3N 1/2 δx ,where δx 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 x and δx, they can make significant
contributions to the χ2 , and the contribution of the high-precision experiments thus tends to be
obscured. Note that if each experiment has the same error δxi , then δx is δxi /N 1/2 , so each δxi iswell 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 δ 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 δx, simply divide the quoted error by S.
(b) If the number M of experiments with an error smaller than δ0 is at least three, and if2
χ /(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 thedata 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 xi , error
δxi , and area proportional to 1/δxi . The choice of 1/δxi for the area is somewhat arbitrary. With
this choice, the center of gravity of the ideogram corresponds to an average that uses weights 1/δxi
rather than the (1/δxi )2 actually used in the averages. This may be appropriate when some ofthe experiments have seriously underestimated systematic errors. However, since for this choiceof area the height of the Gaussian for each measurement is proportional to (1/δ xi )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.
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Introduction

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 andextracting the partial decay fractions Pi , the partial widths Γi , the full width Γ (or mean life), andthe associated error matrix.
P
Assume, for example, that a state has m partial decay fractions Pi , where
Pi = 1. These
have been measured in Nr different ratios Rr , where, e.g., R1 = P1 /P2 , R2 = P1 /P3 , etc. [We canPPhandle any ratio R of the form
αi Pi / βi Pi , where αi and βi are constants, usually 1 or 0.
The forms R = Pi Pj and R = (Pi Pj )1/2 are also allowed.] Further, assume that each ratio R has
been measured by Nk experiments (we designate each experiment with a subscript k, e.g., R1k ).
We then find the best values of the fractions Pi by minimizing the χ2 as a function of the m − 1
independent parameters:

Nk 
Nr X
X
Rrk − Rr 2
χ2 =
,
(3)
δRrk
r=1 k=1
where the Rrk are the measured values and Rr are the fitted values of the branching ratios.
In addition to the fitted values P i , we calculate an error matrix hδP i δP j i. We tabulate thediagonal elements of δ P i = hδ P i δ P i i1/2 (except that some errors are scaled as discussed below).
In the Particle Listings, we give the complete correlation matrix; we also calculate the fitted valueof each ratio, for comparison with the input data, and list it above the relevant input, along witha 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 branchingratios. But often we also have information on partial widths Γi as well as the total width Γ . In
this case we must introduce Γ as a parameter in the fit, along with the Pi , 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 theirsum to be one, we leave one of them (usually the least well-determined one) out of the fit to makethe set of input data more nearly independent. We now do allow for correlations between input
data.
(3) We calculate scale factors for both the Rr and Pi when the measurements for any R give alarger-than-expected contribution to the χ2 . According to Eq. (3), the double sum for χ2 is firstPsummed over experiments k = 1 to Nk , leaving a single sum over ratios χ2 = χ2r . One is tempted
to define a scale factor for the ratio r as Sr2 = χ2r /hχ2r i. However, since hχ2r i is not a fixed quantity(it is somewhere between Nk and Nk−1 ), we do not know how to evaluate this expression. Instead,we define

2
Nk
R
−
R
X
r
rk
1
Sr2 =
.
(4)
Nk k=1 h(Rrk − Rr )2 i
With this definition the expected value of Sr2 is one. We can show thath(Rrk − Rr )2 i = h(δRrk )2 i − (δRr )2 ,(5)

where δRr is the fitted error for ratio r.
The fit is redone using errors for the branching ratios that are scaled by the larger of Sr and0
unity, from which new and often larger errors δP i are obtained. The scale factors we finally list in
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Introduction

17

WEIGHTED AVERAGE
0.006 ± 0.018 (Error scaled by 1.3)

2

χ
SMITH
NIEBERGALLFACKLERHART
MALLARYBURGUNGRAHAM
MANN
WEBBERCHO
BENNETT
LITTENBERGJAMESFELDMANAUBERTBALDO-...
FRANZINI

75B WIRE
74 ASPK
73 OSPK
73 OSPK
73 OSPK
72 HBC
72 OSPK
72 HBC
71 HBC70 DBC
69 CNTR
69 OSPK
68 HBC67B OSPK
65 HLBC
65 HLBC
65 HBC

0.3
1.3
0.1
0.3
4.4
0.2
0.4
3.3
7.4
1.6
1.1
0.3
0.9
0.3
0.1

0.2
22.0
(Confidence Level = 0.107)

− 0.4

− 0.2

0

0.2

0.4

0.6

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 χ2 contribution of each of the experiments. Note that the
next-to-last experiment, denoted by the incomplete error flag (⊥), is not used in the calculation of
S (see the text).
0such cases are defined by Si = δP i /δP i . However, in line with our policy of not letting S affectthe central values, we give the values of 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) P i turns out to be less than three standard
000
deviations (δP i ) from zero, a new smaller error (δP i )− is calculated on the low side by requiring
00
the area under the Gaussian between P i −(δ P i )− and P i to be 68.3% of the area between zero andP i . A similar correction is made for branching fractions that are within three standard deviationsof 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 theexperiments, 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 allcases, the central value is given with a precision that matches that of the error. So, for example,
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Introduction

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 theaverage 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 asymmetricerrors is used to determine the rounding on both.
Rounding of this form is also performed on the value of limits that come from calculations (butnot 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 asingle 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 τ 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 ameaningful average. However, it is difficult to develop a procedure that handles simultaneously ina reasonable way two basic types of situations: (a) data that lie apart from the main body of thedata are incorrect (contain unreported errors); and (b) the opposite—it is the main body of datathat 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 discrepantmeasurements are correct. Our scale-factor technique is an attempt to address this ignorance byincreasing 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 adifferent choice of data.
Our situation is less severe than most of the cases Taylor considers, such as estimates of thefundamental constants like ~, 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 unknownat 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 thefirst 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.
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Introduction

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: Ministryof 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); andby 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 whotake care of the mailing and distribution of our products.
This work used resources of the National Energy Research Scientific Computing Center, a DOE
Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy
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).

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