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

I (J P ) = 0( 21 + )cCharge = 32 e

Charm = +1

c-QUARK MASS
The c-quark mass corresponds to the “running” mass m c (µ = m c ) in
the MS scheme. We have converted masses in other schemes to the
MS scheme using two-loop QCD perturbation theory with αs (µ=m c ) =0.38 ± 0.03. The value 1.2730 ± 0.0046 GeV for the MS mass corresponds
to 1.67 ± 0.07 GeV for the pole mass (see the “Note on Quark Masses”).
MS MASS (GeV)CL%

DOCUMENT ID

TECN

1.2730± 0.0046 (CL = 90%) OUR EVALUATION See the ideogram below.
+ 0.019
1 ALEXANDROU21 LATT
1.316 ± 0.022 −0.010
2 HEITGER
1.296 ± 0.019
21 LATT3
1.2723± 0.0078
HATTON
20 LATT
4 NARISON
1.266 ± 0.006
20 THEO+ 0.077
5 ABRAMOWICZ18 HERA
1.290 −
0.053
6 BAZAVOV
1.273 ± 0.010
18 LATT7
1.2737± 0.0077
LYTLE
18 LATT
8 PESET
1.223 ± 0.033
18 THEO
9 CHETYRKIN 17 THEO
1.279 ± 0.008
10
1.272 ± 0.008
ERLER
17 THEO
11 KIYO1.246 ± 0.023
16 THEO
12 DEHNADI
1.288 ± 0.020
15 THEO
13 CARRASCO
1.348 ± 0.046
14 LATT+0.03
141.24 ± 0.03 − 0.07
ALEKHIN
13 THEO
15
1.159 ± 0.075
SAMOYLOV 13 NOMD
16 BODENSTEIN 11 THEO
1.278 ± 0.009+ 0.0717 LASCHKA
1.28 −
11 THEO
0.06
18 AUBERT
1.196 ± 0.059 ± 0.050
10A BABR
19 SIGNER
1.25 ± 0.04
09 THEO• • • We do not use the following data for averages, fits, limits, etc. • • •20 NARISON
1.263 ± 0.014
18A THEO
21
1.264 ± 0.006
NARISON
18B THEO+ 0.040
1.335 ± 0.043 −0.011
1.2715± 0.0095
1.26 ± 0.05 ± 0.04
1.282 ± 0.011 ± 0.022
1.286 ± 0.066
1.36 ± 0.04 ± 0.10
1.261 ± 0.016
1.01 ± 0.09 ± 0.03
1.28 ± 0.04
1.299 ± 0.026
1.273 ± 0.006

https://pdg.lbl.gov

22 BERTONE

16

THEO

23 CHAKRABOR...15
24 ABRAMOWICZ13C
25 DEHNADI
13
26 NARISON
13
27 ALEKHIN
1228 NARISON
12A
29 ALEKHIN
1130 BLOSSIER
10
31 BODENSTEIN 10
32 MCNEILE
10

LATT
COMB
THEO
THEO
THEO
THEO
THEO
LATT
THEO
LATT

Page 1Created: 5/31/2024 10:15

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

33 NARISON
1034 CHETYRKIN 09
35 ALLISON
08
36 KUHN
07
37 BOUGHEZAL 06
38 BUCHMUEL... 06
39 HOANG
06
40 AUBERT
04X
41 HOANG
04
42 DEDIVITIIS
03
43 EIDEMULLER 03
44 ERLER
03
45 ZYABLYUK
03

1.261 ± 0.018
1.279 ± 0.013
1.268 ± 0.009
1.286 ± 0.013
1.295 ± 0.015
1.24 ± 0.09
1.224 ± 0.017 ± 0.054
1.33 ± 0.10
1.29 ± 0.07
1.319 ± 0.028
1.19 ± 0.11
1.289 ± 0.043
1.26 ± 0.02

THEO
THEO
LATT
THEO
THEO
THEO
THEO
THEO
THEO
LATT
THEO
THEO
THEO

WEIGHTED AVERAGE
1.2730±0.0028 (Error scaled by 1.0)

χ
ALEXANDROU 21
HEITGER
21
HATTON
20
NARISON
20
ABRAMOWICZ 18
BAZAVOV
18
LYTLE
18
PESET
18
CHETYRKIN 17
ERLER
17
KIYO
16
DEHNADI
15
CARRASCO
14
ALEKHIN
13
SAMOYLOV
13
BODENSTEIN 11
LASCHKA11
AUBERT
10A
SIGNER
09

LATT
LATT
LATT
THEO
HERA
LATT
LATT
THEO
THEO
THEO
THEO
THEO
LATT
THEO
NOMD
THEO
THEO
BABR
THEO

2

3.2
1.5
0.0
1.4
0.0
0.0
2.3
0.6
0.0
1.4
0.6

0.3

11.1
(Confidence Level = 0.432)
1.15

1.2

1.25

1.3

1.35

1.4

1.45

c-QUARK MASS (GeV)
1 ALEXANDROU 21 determines the quark mass using a lattice calculation of the mesonand baryon masses with a twisted mass fermion action. We have converted mc (3 GeV)
+ 0.015 to m (m ). The simulations are carried out using 2+1+1= 1.036 ± 0.017 −
c c
0.008
dynamical quarks with m u = m d 6= m s 6= m c , including gauge ensembles close to thephysical pion point.
2 HEITGER 21 determines the charm quark mass using a n = 2+1 flavor lattice QCD
fsimulation with non-perturbatively O(a) improved Wilson fermions. They also determine
mc (3 GeV) = 1.007 ± 0.016 GeV.

https://pdg.lbl.gov

Page 2Created: 5/31/2024 10:15

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

3 HATTON 20 determines the charm quark mass with a lattice QCD + quenched QED
simulation using the HISQ action and including nf = 2+1+1 flavors of sea quarks. m c
is tuned from the J/ψ meson mass giving mc (3 GeV) = 0.9841 ± 0.0051 GeV.
4 NARISON 20 determines the quark mass using QCD Laplace sum rules from the B mass,c
combined with previous determinations of the QCD condensates and c and b masses.
5 ABRAMOWICZ 18 determine m (m ) = 1.290 + 0.046 + 0.062 + 0.003 from the proc c− 0.041 − 0.014 − 0.031
duction of c quarks in e p collisions at HERA using combined H1 and ZEUS data. The
experimental/fitting errors, and those from modeling and parameterization have beencombined in quadrature.
6 BAZAVOV 18 determine the quark masses using a lattice computation with staggered
fermions and four active quark flavors.
7 LYTLE 18 combined with CHAKRABORTY 15 determine m (3 GeV) = 0.9874(48) GeVcfrom a lattice simulation with nf = 2+1+1 flavors. They also determine the quoted
value mc (mc ) for nf = 4 dynamical flavors.
8 PESET 18 determine m (m ) and m (m ) using an N3LO calculation of the η , η
c c
b b
c b
and Bc masses.
9 CHETYRKIN 17 determine m (µ = 3 GeV) = 0.993 ± 0.008 GeV and m (m ) from acc cfour-loop sum-rule computation of the cross-section for e + e − → hadrons in the charm
threshold region.
10 ERLER 17 determine m (m ) = 1.272 ± 0.008 GeV from a three-loop QCD sum-rulec ccomputation of the vector current correlator. This result is for fixed αs (MZ ) = 0.1182.
Including an αs uncertainty of ± 0.0016, the charm mass error increases from 8 to 9
MeV.
11 KIYO 16 determine m (m ) from the J/ψ(1S) mass at order α3 (N3LO).
c cs
12 DEHNADI 15 determine m (m ) using sum rules for e + e − → hadrons at order α3c cs(N3LO), and fitting to both experimental data and lattice results.
13 CARRASCO 14 is a lattice QCD computation of light quark masses using 2 + 1 + 1
dynamical quarks, with mu = md 6= ms 6= mc . The u and d quark masses are
obtained separately by using the K meson mass splittings and lattice results for theelectromagnetic contributions.
14 ALEKHIN 13 determines m from charm production in deep inelastic scattering at HERAcusing approximate NNLO QCD.
15 SAMOYLOV 13 determines m from a study of charm dimuon production in neutrinoc
iron scattering using the NLO QCD result for the charm quark production cross section.
16 BODENSTEIN 11 determine m (3 GeV) = 0.987 ± 0.009 GeV and m (m ) = 1.278 ±cc c
0.009 GeV using QCD sum rules for the charm quark vector current correlator.
17 LASCHKA 11 determine the c mass from the charmonium spectrum. The theoreticalcomputation uses the heavy QQ potential to order 1/m Q obtained by matching theshort-distance perturbative result onto lattice QCD result at larger scales.
18 AUBERT 10A determine the b- and c-quark masses from a fit to the inclusive

decay spectra in semileptonic B decays in the kinetic scheme (and convert it to
the MS scheme).
19 SIGNER 09 determines the c-quark mass using non-relativistic sum rules to analyze the e + e − → c c cross-section near threshold. Also determine the PS mass
m P S (µF = 0.7 GeV) = 1.50 ± 0.04 GeV.
20 NARISON 18A determines simultaneously m (m ) and the 4-dimension gluoncccondensate using QCD exponential sum rules and their ratios evaluated at thehttps://pdg.lbl.gov

Page 3Created: 5/31/2024 10:15

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

optimal scale µ = 2.85 GeV at N2LO-N3LO of perturbative QCD and including condensates up to dimension 6–8 in the (axial-)vector and (pseudo-)scalar
charmonium channels.
21 NARISON 18B determines m (m ) using QCD vector moment sum rules andcctheir ratios at N2LO-N3LO of perturbative QCD and including condensates up
to dimension 8.
22 BERTONE 16 determine m (m ) from HERA deep inelastic scattering data usingcc+ 0.490 using thethe FONLL scheme. Also determine mc (mc )=1.318 ± 0.054 −
0.022
fixed flavor number scheme.
23 CHAKRABORTY 15 is a lattice QCD computation using 2+1+1 dynamical flavors. Moments of pseudoscalar current-current correlators are matched to α3s accurate QCD perturbation theory with the ηc meson mass tuned to experiment.
24 ABRAMOWICZ 13C determines m from charm production in deep inelastic e p
cscattering, using the QCD prediction at NLO order. The uncertainties from modeland parameterization assumptions, and the value of αs , of ± 0.03, ± 0.02, and± 0.02 respectively, have been combined in quadrature.
25 DEHNADI 13 determines m using QCD sum rules for the charmonium specc
trum and charm continuum to order α3s (N3LO). The statistical and systematic
experimental errors of ± 0.006 and ± 0.009 have been combined in quadrature.
The theoretical uncertainties ± 0.019 from truncation of the perturbation series,± 0.010 from αs , and ± 0.002 from the gluon condensate have been combined inquadrature.
26 NARISON 13 determines m using QCD spectral sum rules to order α2 (NNLO)
csand including condensates up to dimension 6.
27 ALEKHIN 12 determines m from heavy quark production in deep inelastic scatc
tering at HERA using approximate NNLO QCD.
28 NARISON 12A determines m using sum rules for the vector current correlatorcto order α3s , including the effect of gluon condensates up to dimension eight.
29 ALEKHIN 11 determines m from heavy quark production in deep inelastic scatc
tering using fixed target and HERA data, and approximate NNLO QCD.
30 BLOSSIER 10 determines quark masses from a computation of the hadron spectrum using nf =2 dynamical twisted-mass Wilson fermions.
31 BODENSTEIN 10 determines m (3 GeV) = 1.008 ± 0.026 GeV using finitecenergy sum rules for the vector current correlator. The authors have converted
this to mc (mc ) using αs (MZ ) = 0.1189 ± 0.0020.
32 MCNEILE 10 determines m by comparing the order α3 perturbative results forcs
the pseudo-scalar current to lattice simulations with nf = 2+1 sea-quarks by the
HPQCD collaboration.
33 NARISON 10 determines m from ratios of moments of vector current correlatorsccomputed to order α3s and including the dimension-six gluon condensate.
34 CHETYRKIN 09 determine m and m from the e + e − → Q Q cross-section andcbsum rules, using an order α3s computation of the heavy quark vacuum polarization.
They also determine m c (3 GeV) = 0.986 ± 0.013GeV.
35 ALLISON 08 determine m by comparing four-loop perturbative results for thecpseudo-scalar current correlator to lattice simulations by the HPQCD collaboration. The result has been updated in MCNEILE 10.

https://pdg.lbl.gov

Page 4Created: 5/31/2024 10:15

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

36 KUHN 07 determine m (µ = 3 GeV) = 0.986 ± 0.013 GeV and m (m ) fromccca four-loop sum-rule computation of the cross-section for e + e − → hadrons in

the charm threshold region.

37 BOUGHEZAL 06 result comes from the first moment of the hadronic production

cross-section to order α3s .
38 BUCHMUELLER 06 determine m and m by a global fit to inclusive B decaybcspectra.
39 HOANG 06 determines m (m ) from a global fit to inclusive B decay data. Thecc
B decay distributions were computed to order α2s β0 , and the conversion between
different mc mass schemes to order α3s .
40 AUBERT 04X obtain m from a fit to the hadron mass and lepton energy districbutions in semileptonic B decay. The paper quotes values in the kinetic scheme.
The MS value has been provided by the BABAR collaboration.
41 HOANG 04 determines m (m ) from moments at order α2 of the charm producc
cstion cross-section in e + e − annihilation.
42 DEDIVITIIS 03 use a quenched lattice computation of heavy-heavy and heavylight meson masses.
43 EIDEMULLER 03 determines m and m using QCD sum rules.
bc
44 ERLER 03 determines m and m using QCD sum rules. Includes recent BES
b
c
data.
45 ZYABLYUK 03 determines m by using QCD sum rules in the pseudoscalar chancnel and comparing with the ηc mass.

m c m s MASS RATIOThe ratio is that of the MS masses at a common scale, for four dynamical quark
flavors.

VALUE

CL%

DOCUMENT ID

TECN

11.761± 0.047 (CL = 90%) OUR EVALUATION See the ideogram below.
+ 0.25
1 ALEXANDROU21 LATT
11.48 ± 0.12 −0.19
2 BAZAVOV
11.783± 0.025
18 LATT
3 CHAKRABOR...15 LATT
11.652± 0.065
4 CARRASCO
11.62 ± 0.16
14 LATT
5 DURR
11.27 ± 0.30 ± 0.26
12 LATT
6 DAVIES
11.85 ± 0.16
10 LATT• • • We do not use the following data for averages, fits, limits, etc. • • •+ 0.059
11.747± 0.019 −0.043

7 BAZAVOV

14A LATT

8 BLOSSIER

12.0 ± 0.3
10 LATT
1 ALEXANDROU 21 determines the quark mass using a lattice calculation of the mesonand baryon masses with a twisted mass fermion action. The simulations are carried out
using 2+1+1 dynamical quarks with m u = m d 6= m s 6= m c , including gauge ensembles
close to the physical pion point.
2 BAZAVOV 18 determine the quark masses using a lattice computation with staggered
fermions and four active quark flavors.
3 CHAKRABORTY 15 is a lattice QCD computation on gluon field configurations with
2+1+1 dynamical flavors of HISQ quarks with u/d masses down to the physical value.
m c and m s are tuned from pseudoscalar meson masses.
4 CARRASCO 14 is a lattice QCD computation of light quark masses using 2 + 1 + 1
dynamical quarks, with mu = md 6= ms 6= mc . The u and d quark masses arehttps://pdg.lbl.gov

Page 5Created: 5/31/2024 10:15

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

obtained separately by using the K meson mass splittings and lattice results for theelectromagnetic contributions.
5 DURR 12 determine m /m using a lattice computation with n = 2 dynamical fermions.
csf
The result is combined with other determinations of m c to obtain m s (2 GeV) = 97.0 ±2.6 ± 2.5 MeV.
6 DAVIES 10 determine m /m from meson masses calculated on gluon fields includingcsu, d, and s sea quarks with lattice spacing down to 0.045 fm. The Highly Improved
Staggered quark formalism is used for the valence quarks.
7 BAZAVOV 14A is a lattice computation using 4 dynamical flavors of HISQ fermions.
8 BLOSSIER 10 determine m /m from a computation of the hadron spectrum using ncsf= 2 dynamical twisted-mass Wilson fermions.
WEIGHTED AVERAGE
11.761±0.028 (Error scaled by 1.2)

χ
ALEXANDROU 21
BAZAVOV18
CHAKRABOR...15
CARRASCO
14DURR
12DAVIES
10

LATT
LATT
LATT
LATT
LATT
LATT

2

0.8
2.8
0.8

0.3
4.7
(Confidence Level = 0.198)

11.2

11.4

11.6

11.8

12

12.2

12.4

.

m c m s MASS RATIOm b m c MASS RATIOThe ratio is that of the MS masses at a common scale, for four dynamical quark
flavors.

VALUE

DOCUMENT ID

TECN

4.58 ± 0.01 OUR EVALUATION
4.580± 0.007 OUR AVERAGE
1 HATTON
4.586± 0.012
21 LATT
2 BAZAVOV
4.578± 0.008
18 LATT
3 CHAKRABOR...15 LATT
4.528± 0.054
1 HATTON 21 determine m (µ)/m (µ) = 4.586 ± 0.012 at µ = 3 GeV with a latticebc
QCD + quenched QED simulation using the HISQ action and including nf =2+1+1
flavors of sea quarks. The ratio depends weakly on µ because of QED effects.
2 BAZAVOV 18 determine the quark masses using a lattice computation with staggered
fermions and four active quark flavors for the u, d, s, c quarks and five active flavors forthe b quark.
3 CHAKRABORTY 15 is a lattice computation using 4 dynamical quark flavors.

https://pdg.lbl.gov

Page 6Created: 5/31/2024 10:15

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

m b −m c QUARK MASS DIFFERENCEVALUE (GeV)

DOCUMENT ID

TECN

3.45 ± 0.05 OUR EVALUATION• • • We do not use the following data for averages, fits, limits, etc. • • •1 AUBERT
3.472± 0.032
10A BABR
2 ABDALLAH
3.42 ± 0.06
06B DLPH
3 AUBERT
3.44 ± 0.03
04X BABR
3 BAUER
3.41 ± 0.01
04 THEO
1 AUBERT 10A determine the b- and c-quark masses from a fit to the inclusive decay
spectra in semileptonic B decays in the kinetic scheme.
2 ABDALLAH 06B determine m −m from moments of the hadron invariant mass andbclepton energy spectra in semileptonic inclusive B decays.
3 Determine m −m from a global fit to inclusive B decay spectra.
bcc-QUARK REFERENCESALEXANDROU 21
HATTON21
HEITGER
21
HATTON
20
NARISON
20
ABRAMOWICZ 18
BAZAVOV18LYTLE
18NARISON
18A
NARISON
18B
PESET
18
CHETYRKIN 17
ERLER
17
BERTONE
16KIYO
16CHAKRABOR... 15
DEHNADI15
BAZAVOV14A
CARRASCO
14
ABRAMOWICZ 13C
ALEKHIN
13
DEHNADI
13
NARISON
13
SAMOYLOV13
ALEKHIN
12DURR
12NARISON
12A
ALEKHIN
11
BODENSTEIN 11
LASCHKA11
AUBERT
10A
BLOSSIER
10BODENSTEIN 10
DAVIES
10MCNEILE
10
NARISON
10
Also
CHETYRKIN 09
SIGNER
09
ALLISON
08
KUHN
07
ABDALLAH
06B
BOUGHEZAL 06
BUCHMUEL... 06
HOANG
06
AUBERT
04X
BAUER
04

PR D104 074515
PR D103 114508
JHEP 2105 288
PR D102 054511
PL B802 135221
EPJ C78 473
PR D98 054517
PR D98 014513
IJMP A33 1850045
PL B784 261
JHEP 1809 167
PR D96 116007
EPJ C77 99
JHEP 1608 050
PL B752 122
PR D91 054508
JHEP 1508 155
PR D90 074509
NP B887 19
EPJ C73 2311
PL B720 172
JHEP 1309 103
PL B718 1321
NP B876 339
PL B718 550
PRL 108 122003
PL B706 412
PL B699 345
PR D83 074014
PR D83 094002
PR D81 032003
PR D82 114513
PR D82 114013
PRL 104 132003
PR D82 034512
PL B693 559
PL B705 544 (errat.)
PR D80 074010
PL B672 333
PR D78 054513
NP B778 192
EPJ C45 35
PR D74 074006
PR D73 073008
PL B633 526
PRL 93 011803
PR D70 094017

https://pdg.lbl.gov

C. Alexandrou et al.
(ETM Collab.)
D. Hatton et al.
(HPQCD Collab.)
J. Heitger, F. Joswig, S. Kuberski(ALPHA Collab.)
D. Hatton et al.
(HPQCD Collab.)
S. Narison(MONP)
H. Abramowicz et al.
(H1 and ZEUS Collabs.)
A. Bazavov et al. (Fermilab Lattice, MILC, TUMQCD)
A.T. Lytle et al.
(HPQCD Collab.)
S. Narison(MONP)S. Narison(MONP)
C. Peset, A. Pineda, J. Segovia(BARC, TUM)
K.G. Chetyrkin et al.
J. Erler, P. Masjuan, H. Spiesberger
V. Bertone et al.
(xFitter Developers)
Y. Kiyo, G. Mishima, Y. Sumino
B. Chakraborty et al.
(HPQCD Collab.)
B. Dehnadi, A.H. Hoang, V. Mateu
A. Bazavov et al.
(Fermi-LAT and MILC Collabs.)
N. Carrasco et al.
(European Twisted Mass Collab.)
H. Abramovicz et al.
(H1 and Zeus Collabs.)
S. Alekhin et al.
(SERP, DESYZ, WUPP+)
B. Dehnadi et al.
(SHRZ, VIEN, MPIM+)
S. Narison(MONP)
O. Samoylov et al.
(NOMAD Collab.)
S. Alekhin et al.
(SERP, WUPP, DESY+)
S. Durr, G. Koutsou(WUPP, JULI, CYPR)
S. Narison(MONP)
S. Alekhin, S. Moch
(DESY, SERP)
S. Bodenstein et al.
A. Laschka, N. Kaiser, W. Weise
B. Aubert et al.
(BABAR Collab.)
B. Blossier et al.
(ETM Collab.)
S. Bodenstein et al.
C.T.H. Davies et al.
(HPQCD Collab.)
C. McNeile et al.
(HPQCD Collab.)
S. Narison(MONP)S. Narison(MONP)
K.G. Chetyrkin et al.
(KARL, BNL)
A. Signer(DURH)
I. Allison et al.
(HPQCD Collab.)
J.H. Kuhn, M. Steinhauser, C. Sturm
J. Abdallah et al.
(DELPHI Collab.)
R. Boughezal, M. Czakon, T. Schutzmeier
O.L. Buchmueller, H.U. Flacher(RHBL)
A.H. Hoang, A.V. Manohar
B. Aubert et al.
(BABAR Collab.)
C. Bauer et al.

Page 7Created: 5/31/2024 10:15

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

HOANG
DEDIVITIISEIDEMULLERERLERZYABLYUK

04
03
03
03
03

PL B594 127
NP B675 309
PR D67 113002
PL B558 125
JHEP 0301 081

https://pdg.lbl.gov

A.H. Hoang, M. Jamin
G.M. de Divitiis et al.
M. Eidemuller
J. Erler, M. Luo
K.N. Zyablyuk

Page 8(ITEP)Created: 5/31/2024 10:15