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

Light Quarks (u, d, s)
OMITTED FROM SUMMARY TABLE

See the related review(s):Quark Masses
u-QUARK MASS
The u-, d-, and s-quark masses are estimates of so-called “current-quark
masses,” in a mass- independent subtraction scheme such as MS. The
ratios m u /m d and m s /m d are extracted from pion and kaon masses
using chiral symmetry. The estimates of d and u masses are not without
controversy and remain under active investigation. Within the literature
there are even suggestions that the u quark could be essentially massless.
The s-quark mass is estimated from SU(3) splittings in hadron masses.
We have normalized the MS masses at a renormalization scale of µ = 2
GeV. Results quoted in the literature at µ = 1 GeV have been rescaled by
dividing by 1.35. The values of “Our Evaluation” were determined in part
via Figures 2 and 3 in the “Quark masses” review.
MS MASS (MeV)

CL%

DOCUMENT ID

TECN

2.16 ± 0.07 (CL = 90%) OUR EVALUATION See the ideogram below.
1 DOMINGUEZ 19 THEO
2.6 ± 0.4
2 BAZAVOV
2.130± 0.041
18 LATT
3 FODOR
2.27 ± 0.06 ± 0.06
16 LATT
4 CARRASCO
2.36 ± 0.24
14 LATT
5 BLUM
2.24 ± 0.10 ± 0.34
10 LATT
6 MCNEILE
2.01 ± 0.14
10 LATT• • • We do not use the following data for averages, fits, limits, etc. • • •7 AOKI
2.57 ± 0.26 ± 0.07
12 LATT
8 DURR
2.15 ± 0.03 ± 0.10
11 LATT
9 BAZAVOV
1.9 ± 0.2
10 LATT
6 DAVIES
2.01 ± 0.14
10 LATT10
2.9 ± 0.2
DOMINGUEZ 09 THEO
11 DEANDREA 08 THEO
2.9 ± 0.8
12 BLUM3.02 ± 0.33
07 LATT
13 JAMIN
2.7 ± 0.4
06 THEO
14 MASON
1.9 ± 0.2
06 LATT
15 NARISON
2.8 ± 0.2
06 THEO
16 AUBIN
1.7 ± 0.3
04A LATT
1 DOMINGUEZ 19 determine the quark mass from a QCD finite energy sum rule for thedivergence of the axial current.
2 BAZAVOV 18 determine the quark masses using a lattice computation with staggered
fermions and four active quark flavors.
3 FODOR 16 is a lattice simulation with n = 2 + 1 dynamical flavors and includes partiallyfquenched QED effects.
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

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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.
WEIGHTED AVERAGE
2.16±0.04 (Error scaled by 1.2)
Values above of weighted average, error,and scale factor are based upon the data inthis ideogram only. They are not necessarily the same as our ‘best’ values,
obtained from a least-squares constrained fit
utilizing measurements of other (related)
quantities as additional information.

χ
DOMINGUEZBAZAVOVFODORCARRASCOBLUM
MCNEILE

19
18
16
14
10
10

THEO
LATT
LATT
LATT
LATT
LATT

2

0.4
1.8
0.7

1.1
4.0
(Confidence Level = 0.260)

1.5

2

2.5

3

3.5

u-QUARK MASS (MeV)

5 BLUM 10 determines light quark masses using a QCD plus QED lattice computation of
the electromagnetic mass splittings of the low-lying hadrons. The lattice simulations use
2+1 dynamical quark flavors.
6 DAVIES 10 and MCNEILE 10 determine m (µ)/m (µ) = 11.85 ± 0.16 using a latticecscomputation with nf = 2 + 1 dynamical fermions of the pseudoscalar meson masses.
Mass m u is obtained from this using the value of m c from ALLISON 08 or MCNEILE 10
and the BAZAVOV 10 values for the light quark mass ratios, m s /m and m u /m d .
7 AOKI 12 is a lattice computation using 1 + 1 + 1 dynamical quark flavors.
8 DURR 11 determine quark mass from a lattice computation of the meson spectrum using
nf = 2 + 1 dynamical flavors. The lattice simulations were done at the physical quark
mass, so that extrapolation in the quark mass was not needed. The individual m u , m dvalues are obtained using the lattice determination of the average mass m ud and of theratio m s /m ud and the value of Q = (m 2 − m 2 ) / (m 2 − m 2 ) as determined fromsuddu
η → 3π decays.
9 BAZAVOV 10 is a lattice computation using 2+1 dynamical quark flavors.
10 DOMINGUEZ 09 use QCD finite energy sum rules for the two-point function of thedivergence of the axial vector current computed to order α4 .
s
11 DEANDREA 08 determine m −m from η → 3π 0 , and combine with the PDG 06
udlattice average value of m u +m d = 7.6 ± 1.6 to determine m u and m d .
12 BLUM 07 determine quark masses from the pseudoscalar meson masses using a QEDplus QCD lattice computation with two dynamical quark flavors.

https://pdg.lbl.gov

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

13 JAMIN 06 determine m (2 GeV) by combining the value of m obtained from theusspectral function for the scalar K π form factor with other determinations of the quark
mass ratios.
14 MASON 06 extract light quark masses from a lattice simulation using staggered fermions
with an improved action, and three dynamical light quark flavors with degenerate u andd quarks. Perturbative corrections were included at.NNLO order. The quark masses
m u and m d were determined from their (m u +m d ) 2 measurement and AUBIN 04A.
m u m d value.
15 NARISON 06 uses sum rules for e + e − → hadrons to order α3 to determine mss

combined with other determinations of the quark mass ratios.

16 AUBIN 04A employ a partially quenched lattice calculation of the pseudoscalarmeson masses.

d-QUARK MASS
See the comment for the u quark above.
We have normalized the MS masses at a renormalization scale of µ = 2
GeV. Results quoted in the literature at µ = 1 GeV have been rescaled by
dividing by 1.35. The values of “Our Evaluation” were determined in part
via Figures 2 and 3 in the “Quark masses” review.
MS MASS (MeV)

CL%

DOCUMENT ID

TECN

4.70 ± 0.07 (CL = 90%) OUR EVALUATION See the ideogram below.
1 DOMINGUEZ 19 THEO
5.3 ± 0.4
2 BAZAVOV
4.675± 0.056
18 LATT
3 FODOR
4.67 ± 0.06 ± 0.06
16 LATT
4 CARRASCO
5.03 ± 0.26
14 LATT
5 BLUM
4.65 ± 0.15 ± 0.32
10 LATT
6 MCNEILE
4.77 ± 0.15
10 LATT• • • We do not use the following data for averages, fits, limits, etc. • • •7 AOKI
3.68 ± 0.29 ± 0.10
12 LATT
8 DURR
4.79 ± 0.07 ± 0.12
11 LATT
9 BAZAVOV
4.6 ± 0.3
10 LATT
6 DAVIES
4.79 ± 0.16
10 LATT
10 DOMINGUEZ 09 THEO
5.3 ± 0.4
11 DEANDREA 08 THEO
4.7 ± 0.8
12 BLUM
5.49 ± 0.39
07 LATT
13 JAMIN
4.8 ± 0.5
06 THEO
14 MASON
4.4 ± 0.3
06 LATT15
5.1 ± 0.4
NARISON
06 THEO
16 AUBIN
3.9 ± 0.5
04A LATT
1 DOMINGUEZ 19 determine the quark mass from a QCD finite energy sum rule for thedivergence of the axial current.
2 BAZAVOV 18 determine the quark masses using a lattice computation with staggered
fermions and four active quark flavors.
3 FODOR 16 is a lattice simulation with n = 2 + 1 dynamical flavors and includes partiallyfquenched QED effects.

https://pdg.lbl.gov

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

WEIGHTED AVERAGE
4.70±0.04 (Error scaled by 1.0)
Values above of weighted average, error,and scale factor are based upon the data inthis ideogram only. They are not necessarily the same as our ‘best’ values,
obtained from a least-squares constrained fit
utilizing measurements of other (related)
quantities as additional information.

χ
DOMINGUEZBAZAVOVFODORCARRASCOBLUM
MCNEILE

19
18
16
14
10
10

THEO
LATT
LATT
LATT
LATT
LATT

2

0.2
0.1
1.6

0.2
2.1
(Confidence Level = 0.544)

4

4.5

5

5.5

6

6.5

d -QUARK MASS (MeV)

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 are
obtained separately by using the K meson mass splittings and lattice results for theelectromagnetic contributions.
5 BLUM 10 determines light quark masses using a QCD plus QED lattice computation of
the electromagnetic mass splittings of the low-lying hadrons. The lattice simulations use
2+1 dynamical quark flavors.
6 DAVIES 10 and MCNEILE 10 determine m (µ)/m (µ) = 11.85 ± 0.16 using a latticecscomputation with nf = 2 + 1 dynamical fermions of the pseudoscalar meson masses.
Mass m d is obtained from this using the value of m c from ALLISON 08 or MCNEILE 10
and the BAZAVOV 10 values for the light quark mass ratios, m s /m and m u /m d .
7 AOKI 12 is a lattice computation using 1 + 1 + 1 dynamical quark flavors.
8 DURR 11 determine quark mass from a lattice computation of the meson spectrum using
nf = 2 + 1 dynamical flavors. The lattice simulations were done at the physical quark
mass, so that extrapolation in the quark mass was not needed. The individual m u , m dvalues are obtained using the lattice determination of the average mass m ud and of theratio m s /m ud and the value of Q = (m 2 − m 2 ) / (m 2 − m 2 ) as determined fromsuddu
η → 3π decays.
9 BAZAVOV 10 is a lattice computation using 2+1 dynamical quark flavors.
10 DOMINGUEZ 09 use QCD finite energy sum rules for the two-point function of thedivergence of the axial vector current computed to order α4 .
s
11 DEANDREA 08 determine m −m from η → 3π 0 , and combine with the PDG 06
udlattice average value of m u +m d = 7.6 ± 1.6 to determine m u and m d .
12 BLUM 07 determine quark masses from the pseudoscalar meson masses using a QEDplus QCD lattice computation with two dynamical quark flavors.

https://pdg.lbl.gov

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

13 JAMIN 06 determine m (2 GeV) by combining the value of m obtained from thedsspectral function for the scalar K π form factor with other determinations of the quark
mass ratios.
14 MASON 06 extract light quark masses from a lattice simulation using staggered fermions
with an improved action, and three dynamical light quark flavors with degenerate u andd quarks. Perturbative corrections were included at.NNLO order. The quark masses
m u and m d were determined from their (m u +m d ) 2 measurement and AUBIN 04A.
m u m d value.
15 NARISON 06 uses sum rules for e + e − → hadrons to order α3 to determine mss

combined with other determinations of the quark mass ratios.

16 AUBIN 04A perform three flavor dynamical lattice calculation of pseudoscalarmeson masses, with continuum estimate of electromagnetic effects in the kaon
masses, and one-loop perturbative renormalization constant.

m = (m u +m d ) 2
See the comments for the u quark above.
We have normalized the MS masses at a renormalization scale of µ = 2
GeV. Results quoted in the literature at µ = 1 GeV have been rescaled by
dividing by 1.35. The values of “Our Evaluation” were determined in part
via Figures 2 and 3 in the “Quark masses” review.

MS MASS (MeV)

CL%

DOCUMENT ID

TECN

3.49 ± 0.07 (CL = 90%) OUR EVALUATION See the ideogram below.
+ 0.060
1 ALEXANDROU21 LATT
3.636± 0.066 −0.057
2 BRUNO
3.54 ± 0.12 ± 0.09
20 LATT
3 DOMINGUEZ 19 THEO
3.9 ± 0.3
+ 0.8
4 YUAN
4.7 −17 THEO
0.7
5
3.70 ± 0.17
CARRASCO
14 LATT
6 ARTHUR
3.45 ± 0.12
13 LATT
7 DURR
3.469± 0.047 ± 0.048
11 LATT
8 BLOSSIER
3.6 ± 0.2
10 LATT9
3.39 ± 0.06
MCNEILE
10 LATT• • • We do not use the following data for averages, fits, limits, etc. • • •10 AOKI
3.59 ± 0.21
11A LATT9 DAVIES
3.40 ± 0.07
10 LATT
11 DOMINGUEZ 09 THEO
4.1 ± 0.2
12 ALLTON
3.72 ± 0.41
08 LATT
13 BLOSSIER
3.85 ± 0.12 ± 0.4
08 LATT
14 DOMINGUEZ...08B THEO
≥ 4.85 ± 0.20
+ 0.65
3.55 −
0.28

15 ISHIKAWA

08

LATT

4.026± 0.048
4.25 ± 0.35
4.08 ± 0.25 ± 0.42

16 NAKAMURA
17 BLUM18 GOCKELER

08
07
06

LATT
LATT
LATT

https://pdg.lbl.gov

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

19 GOCKELER
4.7 ± 0.2 ± 0.3
06A LATT20
3.2 ± 0.3
MASON
06 LATT
21 NARISON
3.95 ± 0.3
06 THEO
22 AUBIN
2.8 ± 0.3
04 LATT
23 AOKI
4.29 ± 0.14 ± 0.65
03 LATT24
3.223± 0.3
AOKI
03B LATT
25 BECIREVIC
4.4 ± 0.1 ± 0.4
03 LATT
26 CHIU
4.1 ± 0.3 ± 1.0
03 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 BRUNO 20 determines the light quark mass using a lattice calculation with n = 2+1
fflavors of Wilson fermions. The scale has been set from fπ and fK . The tuning wasdone using the masses of the lightest (π) and strange (K ) pseudoscalar mesons.
3 DOMINGUEZ 19 determine the quark mass from a QCD finite energy sum rule for thedivergence of the axial current.
4 YUAN 17 determine m using QCD sum rules in the isospin I =0 scalar channel. At theend of the ”Numerical Results” section of YUAN 17 the authors discuss the significanceof their larger value of the light quark mass compared to previous determinations.
5 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.
6 ARTHUR 13 is a lattice computation using 2+1 dynamical domain wall fermions. Masses
at µ = 3 GeV have been converted to µ = 2 GeV using conversion factors given in theirpaper.
7 DURR 11 determine quark mass from a lattice computation of the meson spectrum using
nf = 2 + 1 dynamical flavors. The lattice simulations were done at the physical quark
mass, so that extrapolation in the quark mass was not needed.
8 BLOSSIER 10 determines quark masses from a computation of the hadron spectrum
using nf =2 dynamical twisted-mass Wilson fermions.
9 DAVIES 10 and MCNEILE 10 determine m (µ)/m (µ) = 11.85 ± 0.16 using a latticecscomputation with nf = 2 + 1 dynamical fermions of the pseudoscalar meson masses.
Mass m is obtained from this using the value of m c from ALLISON 08 or MCNEILE 10
and the BAZAVOV 10 values for the light quark mass ratio, m s /m.
10 AOKI 11A determine quark masses from a lattice computation of the hadron spectrum
using nf = 2 + 1 dynamical flavors of domain wall fermions.
11 DOMINGUEZ 09 use QCD finite energy sum rules for the two-point function of thedivergence of the axial vector current computed to order α4 .
s
12 ALLTON 08 use a lattice computation of the π, K , and Ω masses with 2+1 dynamicalflavors of domain wall quarks, and non-perturbative renormalization.
13 BLOSSIER 08 use a lattice computation of pseudoscalar meson masses and decay constants with 2 dynamical flavors and non-perturbative renormalization.
14 DOMINGUEZ-CLARIMON 08B obtain an inequality from sum rules for the scalar twopoint correlator.
15 ISHIKAWA 08 use a lattice computation of the light meson spectrum with 2+1 dynamicalflavors of O(a) improved Wilson quarks, and one-loop perturbative renormalization.
16 NAKAMURA 08 do a lattice computation using quenched domain wall fermions andnon-perturbative renormalization.
17 BLUM 07 determine quark masses from the pseudoscalar meson masses using a QEDplus QCD lattice computation with two dynamical quark flavors.
18 GOCKELER 06 use an unquenched lattice computation of the axial Ward Identity with
nf = 2 dynamical light quark flavors, and non-perturbative renormalization, to obtainhttps://pdg.lbl.gov

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Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)m(2 GeV) = 4.08 ± 0.25 ± 0.19 ± 0.23 MeV, where the first error is statistical, the second
and third are systematic due to the fit range and force scale uncertainties, respectively.
We have combined the systematic errors linearly.
19 GOCKELER 06A use an unquenched lattice computation of the pseudoscalar meson
masses with nf = 2 dynamical light quark flavors, and non-perturbative renormalization.
20 MASON 06 extract light quark masses from a lattice simulation using staggered fermions
with an improved action, and three dynamical light quark flavors with degenerate u andd quarks. Perturbative corrections were included at NNLO order.
21 NARISON 06 uses sum rules for e + e − → hadrons to order α3 to determine m comssbined with other determinations of the quark mass ratios.
22 AUBIN 04 perform three flavor dynamical lattice calculation of pseudoscalar meson
masses, with one-loop perturbative renormalization constant.
23 AOKI 03 uses quenched lattice simulation of the meson and baryon masses with degenerate light quarks. The extrapolations are done using quenched chiral perturbation
theory.
24 The errors given in AOKI 03B were + 0.046 . We changed them to ± 0.3 for calculating− 0.069
the overall best values. AOKI 03B uses lattice simulation of the meson and baryon masses
with two dynamical light quarks. Simulations are performed using the O(a) improved
Wilson action.
25 BECIREVIC 03 perform quenched lattice computation using the vector and axial Wardidentities. Uses O(a) improved Wilson action and nonperturbative renormalization.
26 CHIU 03 determines quark masses from the pion and kaon masses using a lattice simulation with a chiral fermion action in quenched approximation.
WEIGHTED AVERAGE
3.49±0.04 (Error scaled by 1.2)
Values above of weighted average, error,and scale factor are based upon the data inthis ideogram only. They are not necessarily the same as our ‘best’ values,
obtained from a least-squares constrained fit
utilizing measurements of other (related)
quantities as additional information.

χ
ALEXANDROU 21
BRUNO20
DOMINGUEZ 19
YUAN
17
CARRASCO
14ARTHUR
13
DURR
11BLOSSIER10MCNEILE
10

LATT
LATT
THEO
THEO
LATT
LATT
LATT
LATT
LATT

2

2.7
0.1
1.8

1.5
0.1
0.1
0.3
3.0
9.6
(Confidence Level = 0.212)

3

3.5

4

4.5

5

.

m = (m u +m d ) 2 (MeV)

https://pdg.lbl.gov

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Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)m u m d MASS RATIO
VALUE

CL%

DOCUMENT ID

TECNCOMMENT

0.462 ± 0.020 (CL = 90%) OUR EVALUATION See the ideogram below.
1 FODOR0.485 ± 0.011 ± 0.016
16 LATT+
0.01732
0.4482 − 0.0206
BASAK
15 LATT30.470 ± 0.056
CARRASCO
14 LATT
4 BAZAVOV
0.42 ± 0.01 ± 0.04
10 LATT
5 BLUM
0.4818± 0.0096 ± 0.0860
10 LATT• • • We do not use the following data for averages, fits, limits, etc. • • •6 AOKI
0.698 ± 0.051
12 LATT70.550 ± 0.031
BLUM
07 LATT
8 AUBIN
0.43 ± 0.08
04A LATT
9 NELSON
0.410 ± 0.036
03 LATT
10 LEUTWYLER 96 THEO Compilation
0.553 ± 0.043
WEIGHTED AVERAGE
0.462±0.013 (Error scaled by 1.0)
Values above of weighted average, error,and scale factor are based upon the data inthis ideogram only. They are not necessarily the same as our ‘best’ values,
obtained from a least-squares constrained fit
utilizing measurements of other (related)
quantities as additional information.

χ
FODOR
BASAK
CARRASCOBAZAVOV
BLUM

16
15
14
10
10

LATT
LATT
LATT
LATT
LATT

2

1.5
0.6
0.0
1.0

3.1
(Confidence Level = 0.381)
0.3

0.4

0.5

0.6

0.7

0.8

.

m u m d MASS RATIO
1 FODOR 16 is a lattice simulation with n = 2 + 1 dynamical flavors and includes partiallyfquenched QED effects.
2 BASAK 15 is a lattice computation using 2+1 dynamical quark flavors.
3 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.
4 BAZAVOV 10 is a lattice computation using 2+1 dynamical quark flavors.
5 BLUM 10 is a lattice computation using 2+1 dynamical quark flavors.

https://pdg.lbl.gov

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

6 AOKI 12 is a lattice computation using 1 + 1 + 1 dynamical quark flavors.
7 BLUM 07 determine quark masses from the pseudoscalar meson masses using a QEDplus QCD lattice computation with two dynamical quark flavors.
8 AUBIN 04A perform three flavor dynamical lattice calculation of pseudoscalarmeson masses, with continuum estimate of electromagnetic effects in the kaon
masses.
9 NELSON 03 computes coefficients in the order p4 chiral Lagrangian using alattice calculation with three dynamical flavors. The ratio m u /m d is obtainedby combining this with the chiral perturbation theory computation of the meson
masses to order p4 .
10 LEUTWYLER 96 uses a combined fit to η → 3π and ψ ′ → J/ψ (π,η) decay
rates, and the electromagnetic mass differences of the π and K .

s-QUARK MASS
See the comment for the u quark above.
We have normalized the MS masses at a renormalization scale of µ = 2
GeV. Results quoted in the literature at µ = 1 GeV have been rescaled by
dividing by 1.35.
MS MASS (MeV)

CL%

DOCUMENT ID

TECN

93.5 ± 0.8 (CL = 90%) OUR EVALUATION See the ideogram below.
4.0
1 ALEXANDROU21 LATT
98.7 ± 2.4 +− 3.2
2 BRUNO
95.7 ± 2.5 ± 2.4
20 LATT3
92.47± 0.69
BAZAVOV
18 LATT
4 LYTLE
93.85± 0.75
18 LATT
5 ANANTHANA...16 THEO
87.6 ± 6.0
6 CARRASCO
99.6 ± 4.3
14 LATT
7 ARTHUR
94.4 ± 2.3
13 LATT
8 BODENSTEIN 13 THEO
94 ± 99 DURR
95.5 ± 1.1 ± 1.5
11 LATT• • • We do not use the following data for averages, fits, limits, etc. • • •10 CHAKRABOR...15 LATT
93.6 ± 0.8
11 FRITZSCH
102 ± 3 ± 1
12 LATT
12 AOKI96.2 ± 2.7
11A LATT
13 BLOSSIER
95 ± 610 LATT
14 BLUM97.6 ± 2.9 ± 5.5
10 LATT
15 DAVIES
92.4 ± 1.5
10 LATT
15 MCNEILE
92.2 ± 1.3
10 LATT
16 ALLTON
107.3 ± 11.7
08 LATT
17 BLOSSIER
105 ± 3 ± 9
08 LATT18
102 ± 8DOMINGUEZ 08A THEO
17.2
90.1 +− 6.1
105.6 ± 1.2
119.5 ± 9.3
105 ± 6 ± 7
111 ± 6 ± 10
119 ± 5 ± 8

https://pdg.lbl.gov

19 ISHIKAWA

08

LATT

20 NAKAMURA
21 BLUM
22 CHETYRKIN
23 GOCKELER
24 GOCKELER

08
07
06
06
06A

LATT
LATT
THEO
LATT
LATT

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

25 JAMIN
92 ± 906 THEO
26 MASON
87 ± 606 LATT
27 NARISON
104 ± 15
06 THEO
28 NARISON≥ 71 ± 4, ≤ 151 ± 14
06 THEO+
5+
16
29 BAIKOV
96 − 305 THEO− 1830
81 ± 22GAMIZ
05 THEO
31 GORBUNOV 05 THEO
125 ± 28
32 NARISON
93 ± 32
05 THEO
33 AUBIN
76 ± 804 LATT
34 AOKI
116 ± 6 ± 0.65
03 LATT+1235
84.5 − 1.7
AOKI
03B LATT
36 BECIREVIC
106 ± 2 ± 8
03 LATT37
92 ± 9 ± 16
CHIU
03 LATT
38 GAMIZ
117 ± 1703 THEO
39 GAMIZ
103 ± 1703 THEO
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 BRUNO 20 determines the light quark mass using a lattice calculation with n = 2+1
fflavors of Wilson fermions. The scale has been set from fπ and fK . The tuning wasdone using the masses of the lightest (π) and strange (K ) pseudoscalar mesons.
3 BAZAVOV 18 determine the quark masses using a lattice computation with staggered
fermions and four active quark flavors.
4 LYTLE 18 combined with CHAKRABORTY 2015 determine m (3 GeV) = 84.78 ± 0.65s
MeV from a lattice simulation with nf = 2+1+1 flavors. They also determine the quoted
value ms (2 GeV) for nf = 4 dynamical flavors.
5 ANANTHANARAYAN 16 determine m (2 GeV) = 106.70 ± 9.36 MeV and 74.47 ± 7.77
s
MeV from fits to ALEPH and OPAL τ decay data, respectively. We have used theweighted average of the two.
6 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.
7 ARTHUR 13 is a lattice computation using 2+1 dynamical domain wall fermions. Masses
at µ = 3 GeV have been converted to µ = 2 GeV using conversion factors given in theirpaper.
8 BODENSTEIN 13 determines m from QCD finite energy sum rules, and the perturbativescomputation of the pseudoscalar correlator to five-loop order.
9 DURR 11 determine quark mass from a lattice computation of the meson spectrum using
nf = 2 + 1 dynamical flavors. The lattice simulations were done at the physical quark
mass, so that extrapolation in the quark mass was not needed.
10 CHAKRABORTY 15 is a lattice QCD computation that determines m and m /mccsusing pseudoscalar mesons masses tuned on gluon field configurations with 2+1+1 dynamical flavors of HISQ quarks with u/d masses down to the physical value.
11 FRITZSCH 12 determine m using a lattice computation with n = 2 dynamical flavors.
sf
12 AOKI 11A determine quark masses from a lattice computation of the hadron spectrum
using nf = 2 + 1 dynamical flavors of domain wall fermions.
13 BLOSSIER 10 determines quark masses from a computation of the hadron spectrum
using nf =2 dynamical twisted-mass Wilson fermions.
14 BLUM 10 determines light quark masses using a QCD plus QED lattice computation of
the electromagnetic mass splittings of the low-lying hadrons. The lattice simulations use
2+1 dynamical quark flavors.

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

15 DAVIES 10 and MCNEILE 10 determine m (µ)/m (µ) = 11.85 ± 0.16 using a latticecscomputation with nf = 2 + 1 dynamical fermions of the pseudoscalar meson masses.
Mass m s is obtained from this using the value of m c from ALLISON 08 or MCNEILE 10.
16 ALLTON 08 use a lattice computation of the π, K , and Ω masses with 2+1 dynamicalflavors of domain wall quarks, and non-perturbative renormalization.
17 BLOSSIER 08 use a lattice computation of pseudoscalar meson masses and decay constants with 2 dynamical flavors and non-perturbative renormalization.
18 DOMINGUEZ 08A make determination from QCD finite energy sum rules for the pseudoscalar two-point function computed to order α4 .
s
19 ISHIKAWA 08 use a lattice computation of the light meson spectrum with 2+1 dynamicalflavors of O(a) improved Wilson quarks, and one-loop perturbative renormalization.
20 NAKAMURA 08 do a lattice computation using quenched domain wall fermions andnon-perturbative renormalization.
21 BLUM 07 determine quark masses from the pseudoscalar meson masses using a QEDplus QCD lattice computation with two dynamical quark flavors.
22 CHETYRKIN 06 use QCD sum rules in the pseudoscalar channel to order α4 .
s
23 GOCKELER 06 use an unquenched lattice computation of the axial Ward Identity with
nf = 2 dynamical light quark flavors, and non-perturbative renormalization, to obtain
ms (2 GeV) = 111 ± 6 ± 4 ± 6 MeV, where the first error is statistical, the second andthird are systematic due to the fit range and force scale uncertainties, respectively. We
have combined the systematic errors linearly.
24 GOCKELER 06A use an unquenched lattice computation of the pseudoscalar meson
masses with nf = 2 dynamical light quark flavors, and non-perturbative renormalization.
25 JAMIN 06 determine m (2 GeV) from the spectral function for the scalar K π formsfactor.
26 MASON 06 extract light quark masses from a lattice simulation using staggered fermions
with an improved action, and three dynamical light quark flavors with degenerate u andd quarks. Perturbative corrections were included at NNLO order.
27 NARISON 06 uses sum rules for e + e − → hadrons to order α3 .
s28 NARISON 06 obtains the quoted range from positivity of the spectral functions.
29 BAIKOV 05 determines m (M ) = 100 + 5 + 17 from sum rules using the strange spectrals τ− 3 − 19function in τ decay. The computations were done to order α3 , with an estimate of thes
α4 terms. We have converted the result to µ = 2 GeV.
s
30 GAMIZ 05 determines m (2 GeV) from sum rules using the strange spectral function insτ decay. The computations were done to order α2 , with an estimate of the α3 terms.
ss
31 GORBUNOV 05 use hadronic tau decays to N3LO, including power corrections.
32 NARISON 05 determines m (2 GeV) from sum rules using the strange spectral functionsin τ decay. The computations were done to order α3 .
s
33 AUBIN 04 perform three flavor dynamical lattice calculation of pseudoscalar meson
masses, with one-loop perturbative renormalization constant.
34 AOKI 03 uses quenched lattice simulation of the meson and baryon masses with degenerate light quarks. The extrapolations are done using quenched chiral perturbation theory.
+ 5.8 using K mass as input and m =142.3 ± 5.8 + 22 using
Determines ms =113.8 ± 2.3 −
s
2.9
− 0
φ mass as input. We have performed a weighted average of these values.
35 AOKI 03B uses lattice simulation of the meson and baryon masses with two dynamical
light quarks. Simulations are performed using the O(a) improved Wilson action.
36 BECIREVIC 03 perform quenched lattice computation using the vector and axial Wardidentities. Uses O(a) improved Wilson action and nonperturbative renormalization. They
also quote m/ms =24.3 ± 0.2 ± 0.6.
37 CHIU 03 determines quark masses from the pion and kaon masses using a lattice simulation with a chiral fermion action in quenched approximation.

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

38 GAMIZ 03 determines m from SU(3) breaking in the τ hadronic width. The value ofs
Vu s is chosen to satisfy CKM unitarity.
39 GAMIZ 03 determines m from SU(3) breaking in the τ hadronic width. The value ofs
Vu s is taken from the PDG.
WEIGHTED AVERAGE
93.5±0.5 (Error scaled by 1.1)

χ
ALEXANDROU 21
BRUNO20
BAZAVOV
18LYTLE
18ANANTHANA... 16
CARRASCO
14ARTHUR
13
BODENSTEIN 13
DURR
11

LATT
LATT
LATT
LATT
THEO
LATT
LATT
THEO
LATT

2

1.7
0.4
2.1
0.2
0.2

1.2
5.8
(Confidence Level = 0.322)

80

85

90

95

100

105

110

115

s-QUARK MASS (MeV)OTHER LIGHT QUARK MASS RATIOSm s m d MASS RATIOVALUEDOCUMENT ID

TECNCOMMENT

17–22 OUR EVALUATION
1 GAO
20.0
97 THEO
2 LEUTWYLER 96 THEO Compilation
18.9± 0.8
3 DONOGHUE 92 THEO
21
4 GERARD
18
90 THEO
5 LEUTWYLER 90B THEO
18 to 23
1 GAO 97 uses electromagnetic mass splittings of light mesons.
2 LEUTWYLER 96 uses a combined fit to η → 3π and ψ ′ → J/ψ (π,η) decay rates,
and the electromagnetic mass differences of the π and K .
3 DONOGHUE 92 result is from a combined analysis of meson masses, η → 3π using second-order chiral perturbation theory including nonanalytic terms, and (ψ(2S) →J/ψ(1S) π)/(ψ(2S) → J/ψ(1S) η).
4 GERARD 90 uses large N and η-η ′ mixing.
5 LEUTWYLER 90B determines quark mass ratios using second-order chiral perturbation
theory for the meson and baryon masses, including nonanalytic corrections. Also uses
Weinberg sum rules to determine L7 .

https://pdg.lbl.gov

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

m s m MASS RATIO
VALUEm ≡ (m u + m d ) 2

CL%

DOCUMENT ID

TECN+ 0.18 (CL = 90%) OUR EVALUATION
27.33 −
See the ideogram below.
0.14+ 0.56
1 ALEXANDROU21 LATT
27.17± 0.32 −0.38
2 BRUNO
27.0 ± 1.0 ± 0.4
20 LATT+0.10
327.35± 0.05 − 0.07
BAZAVOV
14A LATT
4
26.66± 0.32
CARRASCO
14 LATT
5 ARTHUR
27.36± 0.54
13 LATT
6 DURR
27.53± 0.20 ± 0.08
11 LATT• • • We do not use the following data for averages, fits, limits, etc. • • •7 AOKI
26.8 ± 1.4
11A LATT
8
27.3 ± 0.9
BLOSSIER
10 LATT
9 ALLTON
28.8 ± 1.65
08 LATT
10 BLOSSIER
27.3 ± 0.3 ± 1.2
08 LATT
11 OLLER
23.5 ± 1.5
07A THEO
12 AUBIN
27.4 ± 0.4
04 LATTWEIGHTED AVERAGE
27.33+0.11-0.09 (Error scaled by 1.2)

χ
ALEXANDROU 21
BRUNO20
BAZAVOV14A
CARRASCO
14ARTHUR
13
DURR
11

LATT
LATT
LATT
LATT
LATT
LATT

2

0.1

0.1
4.3
0.0
0.9
5.4
(Confidence Level = 0.251)

25

26

27

28

29

30

.

m s m MASS RATIO
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.

https://pdg.lbl.gov

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

2 BRUNO 20 determines the light quark mass using a lattice calculation with n = 2+1
fflavors of Wilson fermions. The scale has been set from fπ and fK . The tuning wasdone using the masses of the lightest (π) and strange (K ) pseudoscalar mesons.
3 BAZAVOV 14A is a lattice computation using 4 dynamical flavors of HISQ fermions.
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 are obtained separately by using the K meson mass splittings and lattice
results for the electromagnetic contributions.
5 ARTHUR 13 is a lattice computation using 2+1 dynamical domain wall fermions.
6 DURR 11 determine quark mass from a lattice computation of the meson spectrum using nf = 2 + 1 dynamical flavors. The lattice simulations were done at
the physical quark mass, so that extrapolation in the quark mass was not needed.
7 AOKI 11A determine quark masses from a lattice computation of the hadron
spectrum using nf = 2 + 1 dynamical flavors of domain wall fermions.
8 BLOSSIER 10 determines quark masses from a computation of the hadron spectrum using nf =2 dynamical twisted-mass Wilson fermions.
9 ALLTON 08 use a lattice computation of the π, K , and Ω masses with 2+1
dynamical flavors of domain wall quarks, and non-perturbative renormalization.
10 BLOSSIER 08 use a lattice computation of pseudoscalar meson masses and decay
constants with 2 dynamical flavors and non-perturbative renormalization.
11 OLLER 07A use unitarized chiral perturbation theory to order p4 .
12 Three flavor dynamical lattice calculation of pseudoscalar meson masses.

Q MASS q
RATIO
Q≡(m 2 s −m2 )/(m 2 d −m 2 u );

VALUE


m ≡ (m u + m d ) 2

DOCUMENT ID

TECN• • • We do not use the following data for averages, fits, limits, etc. • • •1 COLANGELO 18 THEO
22.1± 0.7
2 COLANGELO 17 THEO
22.0± 0.7
3 GUO
21.6± 1.1
17 THEO
4 FODOR23.4± 0.4 ± 0.5
16 LATT
5 GUO
21.4± 0.4
15F THEO
6 MARTEMYA... 05 THEO
22.8± 0.4
7 ANISOVICH
22.7± 0.8
96 THEO
1 COLANGELO 18 obtain Q from a dispersive analysis of η → 3π decay.
2 COLANGELO 17 obtain Q from a dispersive analysis of KLOE collaboration data on
η → π + π − π 0 decays and chiral perturbation theory input.
3 GUO 17 determine Q from a dispersive model fit to KLOE and WASA-at-COSY data on
η → π + π − π 0 decay and matching to chiral perturbation theory .
4 FODOR 16 is a lattice simulation with n = 2 + 1 dynamical flavors and includes partiallyfquenched QED effects.
5 GUO 15F determine Q from a Khuri-Treiman analysis of η → 3π decays.
6 MARTEMYANOV 05 determine Q from η → 3π decay.
7 ANISOVICH 96 find Q from η → π + π − π 0 decay using dispersion relations and chiralperturbation theory.

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

LIGHT QUARKS (u, d, s) REFERENCESALEXANDROU 21
BRUNO20
DOMINGUEZ 19
BAZAVOV18
COLANGELO 18
LYTLE18
COLANGELO 17
GUO
17
YUAN
17
ANANTHANA...16
FODOR
16
BASAK
15
CHAKRABOR... 15GUO
15F
BAZAVOV14A
CARRASCO
14ARTHUR
13
BODENSTEIN 13
AOKI
12
FRITZSCH
12
AOKI
11A
DURR
11
BAZAVOV10BLOSSIER
10BLUM
10DAVIES
10MCNEILE10
DOMINGUEZ 09
ALLISON
08
ALLTON08
BLOSSIER
08
DEANDREA
08
DOMINGUEZ 08A
DOMINGUEZ... 08B
ISHIKAWA08
NAKAMURA 08
BLUM
07
OLLER
07A
CHETYRKIN 06
GOCKELER
06
GOCKELER
06A
JAMIN
06
MASON
06
NARISON
06
PDG
06
BAIKOV
05
GAMIZ
05
GORBUNOV
05
MARTEMYA... 05
NARISON
05
AUBIN
04
AUBIN
04A
AOKI
03
AOKI
03B
BECIREVIC
03
CHIU
03
GAMIZ
03
NELSON
03
GAO
97
ANISOVICH
96
LEUTWYLER 96
DONOGHUE92
GERARD90
LEUTWYLER 90B

PR D104 074515
EPJ C80 169
JHEP 1902 057
PR D98 054517
EPJ C78 947
PR D98 014513
PRL 118 022001
PL B771 497
PR D96 014034
PR D94 116014
PRL 117 082001
JPCS 640 012052
PR D91 054508
PR D92 054016
PR D90 074509
NP B887 19
PR D87 094514
JHEP 1307 138
PR D86 034507
NP B865 397
PR D83 074508
PL B701 265
RMP 82 1349
PR D82 114513
PR D82 094508
PRL 104 132003
PR D82 034512
PR D79 014009
PR D78 054513
PR D78 114509
JHEP 0804 020
PR D78 034032
JHEP 0805 020
PL B660 49
PR D78 011502
PR D78 034502
PR D76 114508
EPJ A34 371
EPJ C46 721
PR D73 054508
PL B639 307
PR D74 074009
PR D73 114501
PR D74 034013
JP G33 1
PRL 95 012003
PRL 94 011803
PR D71 013002
PR D71 017501
PL B626 101
PR D70 031504
PR D70 114501
PR D67 034503
PR D68 054502
PL B558 69
NP B673 217
JHEP 0301 060
PRL 90 021601
PR D56 4115
PL B375 335
PL B378 313
PRL 69 3444
MPL A5 391
NP B337 108

https://pdg.lbl.gov

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(ETM Collab.)
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Page 15

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