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

Number of Neutrino Types
The neutrinos referred to in this section are those of the Standard
SU(2)×U(1) Electroweak Model possibly extended to allow nonzero
neutrino masses. Light neutrinos are those with m < m Z /2. The
limits are on the number of neutrino mass eigenstates, including ν1 ,
ν2 , and ν3 .

THE NUMBER OF LIGHT NEUTRINO TYPESFROM COLLIDER EXPERIMENTS
Revised June 2020 by C.-J. Lin (LBNL). Written by D. Karlen(University of Victoria and TRIUMF).
The most precise measurements of the number of lightneutrino types, Nν , come from studies of Z production in e+ e−collisions. The invisible partial width, Γinv , is determined bysubtracting the measured visible partial widths, corresponding
to Z decays into quarks and charged leptons, from the total Zwidth. The invisible width is assumed to be due to Nν lightneutrino species each contributing the neutrino partial widthΓν as given by the Standard Model. In order to reduce themodel dependence, the Standard Model value for the ratio ofthe neutrino to charged leptonic partial widths, (Γν /Γℓ )SM =1.991±0.001, is used instead of (Γν )SM to determine the numberof light neutrino types:
 Γinv Γℓ.
(1)Nν =ΓℓΓν SM
The combined result from the four LEP experiments is Nν =2.984 ± 0.008 [1]. Recent analyses applied corrections to theLEP result [1] by including the effect of correlated luminosity
systematics and also using an improved Bhabha cross section
calculation [2,3] to obtain Nν = 2.9963 ± 0.0074.
In the past, when only small samples of Z decays had beenrecorded by the LEP experiments and by the Mark II at SLC,
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Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

the uncertainty in Nν was reduced by using Standard Modelfits to the measured hadronic cross sections at several centerof-mass energies near the Z resonance. Since this method ismuch more dependent on the Standard Model, the approachdescribed above is favored.
Before SLC and LEP, limits on the number of neutrino generations were placed by experiments at lower-energy e+ e− colliders by measuring the cross section of the process e+ e− → ννγ.
The ASP, CELLO, MAC, MARK J, and VENUS experiments
observed a total of 3.9 events above background [4], leading toa 95% CL limit of Nν < 4.8. This process has a much larger
cross section at center-of-mass energies near the Z mass and has
been measured at LEP by the ALEPH, DELPHI, L3, and OPAL
experiments [5]. These experiments have observed several thousand such events, and the combined result is Nν = 3.00 ± 0.08.
The same process has also been measured by the LEP experiments at much higher center-of-mass energies, between 130 and208 GeV, in searches for new physics [6]. Combined with thelower energy data, the result is Nν = 2.92 ± 0.05.
Experiments at pp colliders also placed limits on Nν bydetermining the total Z width from the observed ratio ofW ± → ℓ± ν to Z → ℓ+ ℓ− events [7]. This involved a calculationthat assumed Standard Model values for the total W width andthe ratio of W and Z leptonic partial widths, and used an
estimate of the ratio of Z to W production cross sections.
Now that the Z width is very precisely known from the LEP
experiments, the approach is now one of those used to determine
the W width.
References
1. ALEPH, DELPHI, L3, OPAL, and SLD Collaborations, andLEP Electroweak Working Group, and SLD Electroweak
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Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

2.
3.
4.

5.

6.

7.

Group, and SLD Heavy Flavour Group, Phys. Reports 427,257 (2006).
P. Janot and S. Jadach, Phys. Lett. B803, 135319 (2020).
G. Voutsinas et al., Phys. Lett. B800, 135068 (2020).
VENUS: K. Abe et al., Phys. Lett. B232, 431 (1989);
ASP: C. Hearty et al., Phys. Rev. D39, 3207 (1989);
CELLO: H.J. Behrend et al., Phys. Lett. B215, 186 (1988);
MAC: W.T. Ford et al., Phys. Rev. D33, 3472 (1986);
MARK J: H. Wu, Ph.D. Thesis, Univ. Hamburg (1986).
L3: M. Acciarri et al., Phys. Lett. B431, 199 (1998);
DELPHI: P. Abreu et al., Z. Phys. C74, 577 (1997);
OPAL: R. Akers et al., Z. Phys. C65, 47 (1995);
ALEPH: D. Buskulic et al., Phys. Lett. B313, 520 (1993).
DELPHI: J. Abdallah et al., Eur. Phys. J. C38, 395 (2005);
L3: P. Achard et al., Phys. Lett. B587, 16 (2004);
ALEPH: A. Heister et al., Eur. Phys. J. C28, 1 (2003);
OPAL: G. Abbiendi et al., Eur. Phys. J. C18, 253 (2000).
UA1: C. Albajar et al., Phys. Lett. B198, 271 (1987);
UA2: R. Ansari et al., Phys. Lett. B186, 440 (1987).
Number from e + e − Colliders

Number of Light ν Types
VALUE

DOCUMENT ID

TECN

1 JANOT
2.9963± 0.0074
20• • • We do not use the following data for averages, fits, limits, etc. • • •2 VOUTSINAS 20
2.9918± 0.0081
3
2.9840± 0.0082
LEP-SLC
06 RVUE
4 LEP
3.00 ± 0.05
92 RVUE1 JANOT 20 applies a correction to LEP-SLC 06 using an updated Bhabha cross section
calculation. This result also includes a correction to account for correlated luminosity
bias as presented in VOUTSINAS 20.
2 VOUTSINAS 20 applies a correction to LEP-SLC 06 to account for correlated luminosity
bias.
3 Combined fit from ALEPH, DELPHI, L3 and OPAL Experiments.
4 Simultaneous fits to all measured cross section data from all four LEP experiments.

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

Number of Light ν Types from Direct Measurement of Invisible Z Width
In the following, the invisible Z width is obtained from studies of single-photon eventsfrom the reaction e + e − → ν ν γ. All are obtained from LEP runs in the E ee
cm range
88–209 GeV.
VALUE

DOCUMENT ID

TECNCOMMENT

2.92± 0.05 OUR AVERAGE Error includes scale factor of 1.2.
√
2.84± 0.10 ± 0.14
ABDALLAH
05B DLPH
s = 180–209 GeV
2.98± 0.05 ± 0.04
ACHARD
04E L3
1990-2000 LEP runs√s = 189–209 GeV
2.86± 0.09
HEISTER
03C ALEP
2.69± 0.13 ± 0.11
ABBIENDI,G 00D OPAL 1998 LEP run
2.89± 0.32 ± 0.19
ABREU
97J DLPH 1993–1994 LEP runs
3.23± 0.16 ± 0.10
AKERS
95C OPAL 1990–1992 LEP runs
2.68± 0.20 ± 0.20
BUSKULIC
93L ALEP 1990–1991 LEP runs
• • • We do not use the following data for averages, fits, limits, etc. • • •2.84± 0.15 ± 0.14
3.01± 0.08
3.1 ± 0.6 ± 0.1

ABREU
ACCIARRI
ADAM00Z DLPH 1997–1998 LEP runs
99R L31991–1998 LEP runs√s = 130, 136 GeV
96C DLPH

Limits from Astrophysics and Cosmology
Effective Number of Light ν Types“Light” means here with a mass < about 1 MeV. The quoted values correspond toNeff , where Neff = 3.045 in the Standard Model with Nν = 3. See also reviews on”Big-Bang Nucleosynthesis” and ”Neutrinos in Cosmology.”
VALUE

CL%

DOCUMENT ID

TECNCOMMENT• • • We do not use the following data for averages, fits, limits, etc. • • •1 BRIEDEN
3.12± 0.38
95
22 COSM BOSS, eBOSS, CMB
2 KUMAR2.90± 0.15
68
22 COSM BOSS + CMB
3 YEH
2.89± 0.14
68
22 COSM BBN + CMB
4 AGHANIM
2.99± 0.1768
20 COSM
5 FIELDS
2.84± 0.15
68
20 COSM BBN
6 IVANOV
2.88± 0.176820 COSM Planck and BOSS
7 VERDE
2.3–3.295
17 COSM
8 CYBURT
2.88± 0.1668
16 COSM BBN
92.88± 0.20
95
ROSSI
15 COSM
10 ADE
3.3 ± 0.595
14 COSM Planck+ 0.31
3.78 −0.30

3.29± 0.31
< 3.80< 4.10< 5.79< 4.08
0.9–8.2
3–7
2.7–4.6
3.6–7.4< 4.4< 3.3
1.4–6.8

https://pdg.lbl.gov

11 COSTANZI

95
95
95
95
95
95
95

12 HOU
13 LEISTEDT
14 MORESCO
15 XIA

1414141212MANGANO
1116 ICHIKAWA
07
17 CIRELLI
06
18 HANNESTAD 06
17 SELJAK
06
19 CYBURT
05
20 BARGER
03C
21 CROTTY
03Page 4

COSM
COSM
COSM
COSM
COSM
COSM BBN
COSM
COSM
COSM
COSM
COSM
COSM
COSM

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

1.9–6.6
2–4
< 4.3
< 4.9
< 3.6
< 4.0
< 4.7
< 3.9
< 4.5
< 3.6
< 3.3
< 3.4
< 4< 4< 7<1621 PIERPAOLI

03
LISI
99
OLIVE
99
COPI
97
HATA
97B
OLIVE
97
CARDALL
96B
FIELDS96
KERNAN96
OLIVE
95
WALKER
91OLIVE90
YANG
84
YANG
79
STEIGMAN77
PEEBLES71
22 SHVARTSMAN69
HOYLE
64

COSM
COSM BBNCOSM BBN
Cosmology
High D/H quasar abs.
BBN; high 4 He and 7 Li
COSM High D/H quasar abs.
COSM BBN; high 4 He and 7 Li
COSM High D/H quasar abs.
BBN; ≥ 3 massless ν
Cosmology
Cosmology
Cosmology
Cosmology
Cosmology
Cosmology
Cosmology
Cosmology

1 BRIEDEN 22 combines large scale structure data from BOSS and eBOSS including theshape of the matter power spectrum with Planck CMB data.
2 KUMAR 22 combine the reconstructed galaxy power spectrum from BOSS data withPlanck CMB data.
3 YEH 22 combines Planck 2018 CMB data with BBN and observations of deuterium andHelium-4. Supersedes FIELDS 20.
4 AGHANIM 20 best fit on number of neutrino types is based on Planck data combined+ 0.18 .
with lensing and baryon acoustic oscillations (BAO). Without BAO, they find 2.89 −0.19
Several other values are quoted using different combinations of data.
5 FIELDS 20 combines Planck 2018 CMB data with BBN and observations of deuteriumand Helium-4.
6 IVANOV 20 combines 2018 Planck CMB data with baryon acoustic oscillation data fromBOSS. This study is based on a full-shape likelhood for the redshift-space galaxy power
spectrum of the BOSS data.
7 Uses Planck Data combined with an independent standard measure of distance to thesound horizon to set a limit on the total number of neutrinos. Only CMB and early-time
information are used.
8 CYBURT 16 combines Planck 2015 CMB data with BBN and observations of deuteriumand Helium-4.
9 ROSSI 15 sets limits on the number of neutrino types using BOSS Lyman alpha forest
data combined with Planck CMB data and baryon acoustic oscillations.
10 Fit to the number of neutrino degrees of freedom from Planck CMB data along with
WMAP polarization, high L, and BAO data.
11 Fit to the number of neutrinos degrees of freedom from Planck CMB data along with
BAO, shear and cluster data.
12 Fit based on the SPT-SZ survey combined with CMB, BAO, and H data.
013 Constrains the number of neutrino degrees of freedom (marginalizing over the total mass)from CMB, CMB lensing, BAO, and galaxy clustering data.
14 Limit on the number of light neutrino types from observational Hubble parameter datawith seven-year WMAP data, SPT, and the most recent estimate of H0 . Best fit is3.45 ± 0.65.
15 Limit on the number of light neutrino types from the CFHTLS combined with seven-year+ 1.62 . Limit is
WMAP data and a prior on the Hubble parameter. Best fit is 4.17 −1.26+ 2.02 when small scales affected by non-linearities are removed.
relaxed to 3.98 −1.20

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16 Constrains the number of neutrino types from recent CMB and large scale structure data.
No priors on other cosmological parameters are used.
17 Constrains the number of neutrino types from recent CMB, large scale structure, Lymanalpha forest, and SN1a data. The slight preference for Nν > 3 comes mostly from theLyman-alpha forest data.
18 Constrains the number of neutrino types from recent CMB and large scale structure data.
See also HAMANN 07.
19 Limit on the number of neutrino types based on 4 He and D/H abundance assuming abaryon density fixed to the WMAP data. Limit relaxes to 4.6 if D/H is not used or to5.8 if only D/H and the CMB are used. See also CYBURT 01 and CYBURT 03.
20 Limit on the number of neutrino types based on combination of WMAP data and bigbang nucleosynthesis. The limit from WMAP data alone is 8.3. See also KNELLER 01.
Nν ≥ 3 is assumed to compute the limit.
21 95% confidence level range on the number of neutrino flavors from WMAP data combinedwith other CMB measurements, the 2dfGRS data, and HST data.
22 SHVARTSMAN 69 limit inferred from his equations.

Number Coupling with Less Than Full Weak Strength
VALUE

DOCUMENT ID

TECN• • • We do not use the following data for averages, fits, limits, etc. • • •1 OLIVE<2081C COSM
1<20STEIGMAN
79 COSM
1 Limit varies with strength of coupling. See also WALKER 91.

REFERENCES FOR Limits on Number of Neutrino Types
BRIEDENKUMAR
YEH
AGHANIMFIELDSAlso
IVANOVJANOTVOUTSINASVERDECYBURTROSSIADECOSTANZIHOU
LEISTEDTMORESCOXIAMANGANOHAMANNICHIKAWA
CIRELLIHANNESTAD
LEP-SLCSELJAKABDALLAHCYBURT
ACHARDBARGER
CROTTYCYBURTHEISTERPIERPAOLICYBURT
KNELLER

22222220202020201716151414141412121107070606060605B
05
04E
03C
03
0303C030101

JCAP 2208 024
JCAP 2209 060
JCAP 2210 046
AA 641 A6
JCAP 2003 010
JCAP 2011 E02 (errat.)
PR D101 083504
PL B803 135319
PL B800 135068
JCAP 1704 023
RMP 88 015004
PR D92 063505
AA 571 A16
JCAP 1410 081
APJ 782 74
PRL 113 041301
JCAP 1207 053
JCAP 1206 010
PL B701 296
JCAP 0708 021
JCAP 0705 007
JCAP 0612 013
JCAP 0611 016
PRPL 427 257
JCAP 0610 014
EPJ C38 395
ASP 23 313
PL B587 16
PL B566 8
PR D67 123005
PL B567 227
EPJ C28 1
MNRAS 342 L63
ASP 17 87
PR D64 123506

https://pdg.lbl.gov

S. Brieden, Hector Gil-Marin, Licia Verde
S. Kumar, R. Nunes, P.Yadav
T.-H. Yeh et al.
(ILL, MINN)
N. Aghanim et al.
(Planck Collab.)
B. Fields et al.
(ILL, MINN)
B. Fields et al.
(ILL, MINN)
M.M. Ivanov, M. SImonovic, M. Zaldarriaga(NYU,+)
P. Janot, S. Jadach(CERN, CRAC)
G. Voutsinas et al.
(CERN, BOHR)
L. Verde et al.
R.H. Cyburt et al.
(MSU, ILL, MINN)
G. Rossi et al.
P.A.R. Ade et al.
(Planck Collab.)
M. Costanzi et al.
(TRST, TRSTI)
Z. Hou et al.
B. Leistedt, H.V. Peiris, L. Verde
M. Moresco et al.
J.-Q. Xia et al.
G. Mangano, P. Serpico
J. Hamann et al.
K. Ichikawa, M. Kawasaki, F. Takahashi
M. Cirelli et al.
S. Hannestad, G. RaffeltALEPH, DELPHI, L3, OPAL, SLD and working groups
U. Seljak, A. Slosar, P. McDonald
J. Abdallah et al.
(DELPHI Collab.)
R.H. Cyburt et al.
P. Achard et al.
(L3 Collab.)
V. Barger et al.
P. Crotty, J. Lesgourgues, S. Pastor
R.H. Cyburt, B.D. Fields, K.A. Olive
A. Heister et al.
(ALEPH Collab.)
E. Pierpaoli
R.H. Cyburt, B.D. Fields, K.A. Olive
J.P. Kneller et al.

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

ABBIENDI,G
00D EPJ C18 253
G. Abbiendi et al.
(OPAL Collab.)
ABREU
00Z EPJ C17 53
P. Abreu et al.
(DELPHI Collab.)
ACCIARRI
99R PL B470 268
M. Acciarri et al.
(L3 Collab.)
LISI
99
PR D59 123520
E. Lisi, S. Sarkar, F.L. Villante
OLIVE
99
ASP 11 403
K.A. Olive, D. Thomas
ABREU
97J ZPHY C74 577
P. Abreu et al.
(DELPHI Collab.)
COPI
97
PR D55 3389
C.J. Copi, D.N. Schramm, M.S. Turner(CHIC)HATA
97B PR D55 540
N. Hata et al.
(OSU, PENN)OLIVE97
ASP 7 27
K.A. Olive, D. Thomas(MINN, FLOR)ADAM
96C PL B380 471
W. Adam et al.
(DELPHI Collab.)
CARDALL
96B APJ 472 435
C.Y. Cardall, G.M. Fuller(UCSD)FIELDS96
New Ast 1 77
B.D. Fields et al.
(NDAM, CERN, MINN+)
KERNAN96
PR D54 3681
P.S. Kernan, S. Sarkar(CASE, OXFTP)AKERS
95C ZPHY C65 47
R. Akers et al.
(OPAL Collab.)
OLIVE
95
PL B354 357
K.A. Olive, G. Steigman(MINN, OSU)BUSKULIC
93L PL B313 520
D. Buskulic et al.
(ALEPH Collab.)LEP92
PL B276 247
LEP Collabs.
(LEP, ALEPH, DELPHI, L3, OPAL)
WALKER91
APJ 376 51
T.P. Walker et al.
(HSCA, OSU, CHIC+)
OLIVE
90
PL B236 454
K.A. Olive et al.
(MINN, CHIC, OSU+)
YANG
84
APJ 281 493
J. Yang et al.
(CHIC, BART)OLIVE
81C NP B180 497
K.A. Olive, D.N. Schramm, G. Steigman(CHIC+)STEIGMAN79
PRL 43 239
G. Steigman, K.A. Olive, D.N. Schramm(BART+)YANG79
APJ 227 697
J. Yang et al.
(CHIC, YALE, UVA)STEIGMAN77
PL 66B 202
G. Steigman, D.N. Schramm, J.E. Gunn (YALE, CHIC+)PEEBLES
71
Physical Cosmology
P.Z. Peebles(PRIN)
Princeton Univ. Press (1971)
SHVARTSMAN 69
JETPL 9 184
V.F. Shvartsman(MOSU)
Translated from ZETFP 9 315.
HOYLE64
NAT 203 1108
F. Hoyle, R.J. Tayler(CAMB)

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