⁸ ATHANASSOPOULOS 96 reports (0.31 ± 0.12 ± 0.05)% for the oscillation probability; the value of sin²2θ for large Δ(m²) should be twice this probability. See footnote in preceding table for further details, and see the paper for a plot showing allowed regions.

⁹ ATHANASSOPOULOS 95 error corresponds to the 1.6σ band in the plot. The expected background is 2.7 ± 0.4 events. Corresponds to an oscillation probability of (0.34±0.20) ± 0.07)%. For a different interpretation, see HILL 95. Replaced by ATHANASSOPOULOS 96.

¹⁰ HILL 95 is a report by one member of the LSND Collaboration, reporting a different conclusion from the analysis of the data of this experiment (see ATHANASSOPOULOS 95). Contrary to the rest of the LSND Collaboration, Hill finds no evidence for the neutrino oscillation $\bar{\nu}_{\mu} \to \bar{\nu}_e$ and obtains only upper limits.

### Sterile neutrino limits

$$ \Delta(m^2) \text{ for } \sin^2(2\theta) = 1 \ (\nu_\mu \to \nu_s) $$

$\nu_s$ means $\nu_T$ or any sterile (noninteracting) $\nu$.

<table><thead><tr><th>VALUE (10<sup>-5</sup> eV<sup>2</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>&lt;3000 (or &lt;550)</td><td>90</td><td>1 OYAMA</td><td>89</td><td>KAMI Water Cherenkov</td></tr><tr><td>&lt;4.2 or &gt; 54.</td><td>90</td><td>BIONTA</td><td>88</td><td>IMB Flux has $\nu_{\mu}, \bar{\nu}_{\mu}, \nu_e$, and $\bar{\nu}_e$</td></tr></table>

¹ OYAMA 89 gives a range of limits, depending on assumptions in their analysis. They argue that the region $\Delta(m^2) = (100-1000) \times 10^{-5} eV^2$ is not ruled out by any data for large mixing.

$$ \text{Search for } \nu_{\mu} \text{ or } \nu_{e} \to \nu_{s} $$

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>&lt;5</td><td>× 10<sup>-4</sup></td><td>95</td><td>1 AKER</td><td>23</td><td>T β decay</td></tr><tr><td>&lt;0.05</td><td>95</td><td>2 ALMAZAN</td><td>23</td><td>STEREO</td></tr><tr><td>&lt;0.02</td><td>95</td><td>3 AKER</td><td>22A</td><td>SPEC T β decay</td></tr><tr><td>&lt;0.0035</td><td>95</td><td>4 ATIF</td><td>22</td><td>RENO, NEOS</td></tr><tr><td>0.42</td><td>+0.15<br/>-0.17</td><td>68</td><td>5 BARINOV</td><td>22A</td><td>BEST</td></tr><tr><td>&lt;0.05</td><td>95</td><td>6 ANDRIAMIR...</td><td>21</td><td>PROSPECT</td></tr><tr><td>&lt;0.005</td><td>95</td><td>7 SEREBROV</td><td>21</td><td>Neutrino-4</td></tr><tr><td>&lt;0.008</td><td>95</td><td>8 SKROBOVA</td><td>20</td><td>DANSS</td></tr><tr><td>&lt;0.01</td><td>90</td><td>9 ALEKSEEV</td><td>18</td><td>DANSS</td></tr><tr><td>&lt;0.06</td><td>90</td><td>10 ALMAZAN</td><td>18</td><td>STEREO</td></tr><tr><td>&lt;0.1</td><td>95</td><td>11 ASHENFELT...</td><td>18</td><td>PROSPECT</td></tr><tr><td>&lt;0.4</td><td>90</td><td>12 AARTSEN</td><td>17B</td><td>ICCB IceCube-DeepCore</td></tr><tr><td>&lt;8</td><td>× 10<sup>-3</sup></td><td>95</td><td>13 ABDURASHI...</td><td>17</td><td>T β decay</td></tr><tr><td>&lt;1</td><td>× 10<sup>-2</sup></td><td>90</td><td>14 KO</td><td>17</td><td>NEOS</td></tr><tr><td>&lt;2</td><td>× 10<sup>-2</sup></td><td>90</td><td>15 AARTSEN</td><td>16</td><td>ICCB IceCube</td></tr><tr><td>&lt;4.5</td><td>× 10<sup>-4</sup></td><td>95</td><td>16 ADAMSON</td><td>16B</td><td>MINOS, DayaBay</td></tr><tr><td>&lt;8.6</td><td>× 10<sup>-2</sup></td><td>95</td><td>17 ADAMSON</td><td>16C</td><td>MINS</td></tr><tr><td>&lt;1.1</td><td>× 10<sup>-2</sup></td><td>95</td><td>18 AN</td><td>16B</td><td>DAYA</td></tr><tr><td></td><td></td><td></td><td>19 AMBROSIO</td><td>01</td><td>MCRO matter effects</td></tr><tr><td></td><td></td><td></td><td>20 FUKUDA</td><td>00</td><td>SKAM neutral currents + matter effects</td></tr></table>

¹ AKER 23 assume a 3+1 neutrino mixing model, use low-rate commissioning data of the KATRIN tritium β decay experiment to place a limit on sin²(θ₁₄) for a admixture sterile neutrino mass $m₄$ of ~ 300 eV.

² ALMAZAN 23 use inverse beta decay data collected by the STEREO experiment, placed 9 to 11 m from the ILL research reactor, to search for $\bar{\nu}_e \to \bar{\nu}_s$ oscillations. The ILL research reactor uses highly enriched ²³⁵U fuel. No indication of the oscillation to sterile neutrinos is found, the stated limit on sin²(θ₁₄) correspond to $\Delta m_{41}^2 \sim 1 eV^2$ where the exclusion is maximal. Supersedes ALMAZAN 18.

³ AKER 22A uses the first two science runs of the KATRIN tritium β decay neutrino mass experiment to search for an admixture of sterile neutrinos. No evidence is found for a spectral anomaly, indicating such admixture. The resulting limit is on sin²(2θ₁₄) for sterile neutrino masses $m₄$ < 40 eV. It is most restrictive at $\Delta m_{41}^2 \sim 400 eV^2$. A 3+1 model is assumed.

⁴ ATIF 22 report results from the combined analysis of the RENO (419 m) and NEOS (24 m) experiments data, collected at the Hanbit Nuclear Power Plant. Results, in terms of sin²(2θ₁₄), constrain for $\bar{\nu}_e \to \bar{\nu}_s$ oscillations. The authors report both excluded and allowed parameter combinations. The exclusion result reported here is based on the Feldman-Cousins method and for $\Delta m_{41}^2 \simeq 0.55 eV^2$. Part of the allowed area is excluded by the STEREO and PROSPECT experiments.

⁵ BARINOV 22A report an event deficit observed using the segmented Baksan Ga neutrino detector, exposed to a 3.4 MCl ⁵¹Cr source. Equal suppression factors are observed for the inner and outer segments. The deficit is interpreted as evidence for oscillations to sterile neutrinos. The result is in terms of sin²(2θ₁₄), for a best fit of $\Delta m_{41}^2 = 3.3^{+\infty}_{-2.3} eV^2$. Some, but not all, of the allowed neutrino parameter space conflicts with other experiments.

⁶ ANDRIAMIRADO 21 reports a search for $\bar{\nu}_e \to \bar{\nu}_s$ oscillations at the HIFR research reactor, at baselines from 6.7 to 9.2 m. The reactor has a ²³⁵U core. 4 tons of ⁶Li-doped liquid scintillator are used in a segmented detector. Oscillations into sterile neutrinos are disfavored. The stated limit for sin²(2θ₁₄) is for $\Delta m_{41}^2 \sim 2 eV^2$ where the sensitivity is maximal.

⁷ SEREBROV 21 searches for $\bar{\nu}_e \to \bar{\nu}_s$ oscillations with a moveable detector with baseline 6–12 m from the SM-3 research reactor with highly enriched ²³⁵U fuel. Analyzing the L/E dependence a $\chi^2$ minimum is found at $\Delta m_{41}^2 = 7.3 \pm 0.13 \pm 1.16 eV^2$ and $\sin^2(2\theta_{14}) = 0.36 \pm 0.12$. The quoted limit of 0.005 for $\sin^2(2\theta_{14})$ corresponds to $\Delta m_{41}^2 \sim 2 eV^2$. This is the result from 720 days of reactor ON and 860 days of reactor OFF measurements. The significance of the $\chi^2$ minimum is 2.9 σ. Supersedes SEREBROV 20, SEREBROV 19 and SEREBROV 18A.

⁸ SKROBOVA 20 searches for $\bar{\nu}_e \to \bar{\nu}_s$ oscillations using the DANSS detector at 10.7, 11.2, and 12.7 m from the 3.1 GW$_{th}$ power reactor. The DANSS detector is highly segmented and moveable; the positions are changed usually 3 times a week. The analysis is based on the ratio of the events at top and bottom position; the middle position is used for checks of consistency. No evidence for sterile neutrinos is found. The quoted limit 0.008, the smallest excluded $\sin^2(2\theta_{14})$, corresponds to $\Delta m_{41}^2 \sim 1.0 eV^2$. Supersedes ALEKSEEV 18.

⁹ ALEKSEEV 18 searches for $\bar{\nu}_e \to \bar{\nu}_s$ oscillations using the DANSS detector at 10.7, 11.2, and 12.7 m from the 3.1 GW$_{th}$ power reactor. The DANSS detector is highly segmented and moveable; the positions are changed usually 3 times a week. The analysis is based on the ratio of the events at top and bottom position; the middle position is used for checks of consistency. The best fit point is at $\Delta m_{41}^2 = 1.4 eV^2$ and $\sin^2(2\theta_{14}) = 0.05$ with $\Delta \chi^2 = 13.1$ (statistical errors only) compared to the fit with 3 active neutrinos only. The quoted limit of 0.01 for $\sin^2(2\theta_{14})$ corresponds to $\Delta m_{41}^2 \sim 1.0 eV^2$. Superseded by SKROBOVA 20.

¹⁰ ALMAZAN 18 searches for the $\bar{\nu}_e \to \bar{\nu}_s$ oscillations with baseline from 9.4 to 11.1 m from the ILL research reactor with highly enriched ²³⁵U fuel. The STEREO detector consists of six separated cells with Gd loaded scintillator, with 15 m water equivalent overburden. The detected rate is 396.3 ± 4.7 $\bar{\nu}_e$/day with signal to background ratio of about 0.9. The reported results corresponds to 66 days of reactor-on. The analysis uses the relative rates normalized to the cell number 1. No indication of the oscillation to the sterile neutrinos is found, the stated limit on $\sin^2(2\theta_{14})$ correspond to $\Delta m_{41}^2 \sim 3.5 eV^2$ where the exclusion is maximal. Supersedes ALMAZAN 23.

¹¹ ASHENFELTER 18 searches for the $\bar{\nu}_e \to \bar{\nu}_s$ oscillations at baseline from 6.7 to 9.2 m from the 85 MW research reactor with pure ²³⁵U core. The segmented 4 ton ⁶Li-doped liquid scintillator is operated with about 1 m water equivalent overburden and recorded 25461 ± 283 IBD events. No indication of oscillations into sterile neutrinos was observed. The stated limit for $\sin^2(2\theta_{14})$ is for $\Delta m_{41}^2 \sim 2 eV^2$ where the sensitivity is maximal.

¹² AARTSEN 17B uses three years of upward-going atmospheric neutrino data in the energy range of 10-60 GeV to constrain their disappearance into light sterile neutrinos. The reported limit $\sin^2\theta_{24} < 0.11$ at 90% C.L. is for $\Delta m_{41}^2 = 1.0 eV^2$. We convert the result to $\sin^2\theta_{24}$ for the listing. AARTSEN 17B also reports $\cos^2\theta_{24} \sin^2\theta_{34} < 0.15$ at 90% C.L. for $\Delta m_{41}^2 = 1.0 eV^2$.

¹³ ABDURASHITOV 17 use the Troitsk nu-nu experiment to search for sterile neutrinos with mass 0.1 - 2 keV. We convert the reported limit from $U_{34}^2 < 0.002$ to $\sin^2\theta_{14} < 0.008$ assume $U_{34} \sim \sin\theta_{14}$. The stated limit corresponds to the smallest $U_{34}^2$. The exclusion curve begins at $U_{34}^2$ of 0.02 for $m₄ = 0.1$ keV.

¹⁴ KO 17 reports on short baseline reactor oscillation search ($\bar{\nu}_e \to \bar{\nu}_s$), motivated be the so-called "reactor antineutrino anomaly". The experiment is conducted at 23.7 m from the core of unit 5 of the Hanbit Nuclear Power Complex in Korea. The reported limited on $\sin^2(2\theta_{41})$ for sterile neutrinos was determined using the reactor antineutrino spectrum determined by the Daya Bay experiment for $\Delta m_{41}^2$ around 0.55 eV² where the sensitivity is maximal. A fraction of the parameter space derived from the "reactor antineutrino anomaly" is excluded by this work. Compared to reactor models an event excess is observed at about 5 MeV, in agreement with other experiments.

¹⁵ AARTSEN 16 use one year of upward-going atmospheric muon neutrino data in the energy range of 320 GeV to 20 TeV to constrain their disappearance into light sterile neutrinos. Sterile neutrinos are expected to produce distinctive zenith distribution for these energies for 0.01 $\le \Delta m^2 \le 10 eV^2$. The stated limit is for $\sin^2\theta_{24}$ at $\Delta m^2$ around 0.3 eV².

¹⁶ ADAMSON 16B combine the results of AN 16B, ADAMSON 16C, and Bugey-3 reactor experiments to constrain $\nu_\mu$ to $\nu_e$ mixing through oscillations into light sterile neutrinos.

The stated limit for $\sin^2\theta_{\mu e}$ is at $|\Delta m_{41}^2| = 1.2 eV^2$.

¹⁷ ADAMSON 16C use the NuMI beam and exposure of 10.56 × 10²⁰ protons on target to search for the oscillation of $\nu_\mu$ dominated beam into light sterile neutrinos with detectors at 1.04 and 735 km. The reported limit $\sin^2(\theta_{24}) < 0.022$ at 95% C.L. is for $|\Delta m_{41}^2| = 0.5 eV^2$. We convert the result to $\sin^2(\theta_{24})$ for the listing.

¹⁸ AN 16B utilize 621 days of data to place limits on the $\bar{\nu}_e$ disappearance into a light sterile neutrino. The stated limit corresponds to the smallest $\sin^2(\theta_{14})$ at $|\Delta m_{41}^2| \sim 3 \times 10^{-2} eV^2$ (obtained from Figure 3 in AN 16B). The exclusion curve begins at $|\Delta m_{41}^2| \sim 1.5 \times 10^{-4} eV^2$ and extends to $\sim 0.25 eV^2$. The analysis assumes $\sin^2(2\theta_{12}) = 0.846 \pm 0.021$, $\Delta m_{21}^2 = (7.53 \pm 0.18) \times 10^{-5} eV^2$, and $|\Delta m_{32}^2| = (2.44 \pm 0.06) \times 10^{-3} eV^2$.

¹⁹ AMBROSIO 01 tested the pure 2-flavor $\nu_\mu \to \nu_s$ hypothesis using matter effects which change the shape of the zenith-angle distribution of upward through-going muons. With maximum mixing and $\Delta m^2$ around 0.0024 eV², the $\nu_\mu \to \nu_s$ oscillation is disfavored with 99% confidence level with respect to the $\nu_\mu \to \nu_\tau$ hypothesis.

²⁰ FUKUDA 00 tested the pure 2-flavor $\nu_\mu \to \nu_s$ hypothesis using three complementary atmospheric-neutrino data samples. With this hypothesis, zenith-angle distributions are expected to show characteristic behavior due to neutral currents and matter effects. In the $\Delta m^2$ and $\sin^2\theta_{24}$ region preferred by the Super-Kamiokande data, the $\nu_\mu \to \nu_s$ hypothesis isrejected at the 99% confidence level, while the $\nu_\mu \to \nu_\tau$ hypothesis consistently fits all of the data sample.
$$ \langle \Delta m^2_{21} - \Delta m^2_{32} \rangle $$

<table><thead><tr><th>VALUE (10<sup>-4</sup> eV<sup>2</sup>)</th><th>CL%</th></tr></thead><tbody><tr><td>&lt;1.1</td><td>99.7</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1 DEGOUVEA</td><td>05</td><td>solar vs. reactor</td></tr></tbody></table>

¹ DEGOUVEA 05 obtained this bound at the $3\sigma$ CL from the KamLAND (ARAKI 05) and solar neutrino data.

$$ \langle \Delta m^2_{32} - \Delta m^2_{31} \rangle $$

<table><thead><tr><th>VALUE (10<sup>-3</sup> eV<sup>2</sup>)</th><th>CL%</th></tr></thead><tbody><tr><td>-0.12<sup>+1</sup><sub>-0.24</sub></td><td>99.7</td></tr></tbody></table>

<table><thead><tr><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>1 ADAMSON</td><td>13B</td><td>beam and atmospheric</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><thead><tr><th>0.6<sup>+2</sup><sub>-0.8</sub></th><th>90</th></tr></thead><tbody><tr><td>2 ADAMSON</td><td>12B</td><td>MINOS atmospheric</td></tr></tbody></table>



¹ ADAMSON 13B quotes this difference as a negative of our convention.

² The quoted result is the single-parameter 90% C.L. interval determined from the 90% C.L. contour in the $(\Delta m^2, \Delta \bar{m}^2)$ plane, which is obtained by minimizing the four parameter log-likelihood function with respect to the other oscillation parameters.

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Samoilov</td><td>(PNPI Collab.)</td></tr><tr><td>SHIN</td><td>20</td><td>Translated from ZETFPR 112 211.</td><td></td><td></td></tr><tr><td>SKROBOVA</td><td>20</td><td>JHEP 2004 029</td><td>C.D. Shin et al.</td><td>(RENO Collab.)</td></tr><tr><td>AARTSEN</td><td>19C</td><td>PR D99 030007</td><td>N. Skrobova et al.</td><td>(DANSS Collab.)</td></tr><tr><td>ACERO</td><td>19</td><td>PR 123 151803</td><td>M.G. Aartsen et al.</td><td>(IceCube Collab.)</td></tr><tr><td>ADEY</td><td>19</td><td>PR D100 052004</td><td>M.A. Acker et al.</td><td>(NoVa Collab.)</td></tr><tr><td>AGAFONOVA</td><td>19</td><td>PR D100 051301</td><td>N. Agafonova et al.</td><td>(Opera Collab.)</td></tr><tr><td>ANDRIS</td><td>19</td><td>PR D103 096 113</td><td>A. Albert et al.</td><td>(ANTARES Collab.)</td></tr><tr><td>ANDERSON</td><td>19</td><td>PRL 099 12012</td><td>M. Anderson et al.</td><td>(SNO+ Collab.)</td></tr><tr><td>SEREBROV</td><td>19</td><td>JHEP 099 101 23</td><td>A.P. Serebrov et al.</td><td>(Neutrino-4 Collab.)</td></tr><tr><td>AARTSEN</td><td>18A</td><td>PRL 120 071801</td><td>M.G. Aartsen et al.</td><td>(IceCube Collab.)</td></tr><tr><td>ABE</td><td>18B</td><td>PR D97 072001</td><td>K. Abe et al.</td><td>(Super-Kamiokande Collab.)</td></tr><tr><td>ABE</td><td>18G</td><td>PRL 121 171802</td><td>K. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>ACERO</td><td>18</td><td>PR D99 032012</td><td>M.A. Acker et al.</td><td>(NoVa Collab.)</td></tr><tr><td>ADEY</td><td>18</td><td>PR 121 241805</td><td>D. Adey et al.</td><td>(Daya Bay Collab.)</td></tr><tr><td>AGAFONOVA</td><td>18</td><td>PRL 120 211801</td><td>N. Agafonova et al.</td><td>( Opera Collab.)</td></tr><tr><td>AGAFONOVA</td><td>18A</td><td>PRL 178 106 151</td><td>N. Agafonova et al.</td><td>( Opera Collab.)</td></tr><tr><td>AGOSTINI</td><td>18B</td><td>NAT 562 505</td><td>M. Agostini et al.</td><td>(Borexino Collab.)</td></tr><tr><td>AGUILAR-AR...</td><td>18C</td><td>PR L117 221801</td><td>A.A. Aguilar-Arevalo et al.</td><td>(MiniBooNE Collab.)</td></tr><tr><td>ALEKSEEV</td><td>18</td><td>PR B787 56</td><td>I. Akeevsev et al.</td><td>(DANSS Collab.)</td></tr><tr><td>ALMAZAN</td><td>18</td><td>PRL 121 168102</td><td>H. Almazan et al.</td><td>(STEREO Collab.)</td></tr><tr><td>ASHENFELT...</td><td>18</td><td>PRL 121 215001</td><td>J. Ashenfelter et al.</td><td>(PROSPECT Collab.)</td></tr><tr><td>BAK</td><td>18</td><td>PPL 121 201801</td><td>G. Bak et al.</td><td>(RENO Collab.)</td></tr><tr><td>CAPACZZI</td><td>18</td><td>PPNP 102 48</td><td>F. Capozzi et al.</td><td></td></tr><tr><td>PL</td><td>18</td><td>PL B782 633</td><td>P.F. de Salas et al.</td><td>(PDG Collab.)</td></tr><tr><td>PDG</td><td>18</td><td>PR D98 030001</td><td>M. Tanabashi et al.</td><td>(PDG Collab.)</td></tr><tr><td>SEO</td><td>18</td><td>PR D98 012002</td><td>S.H. Seo et al.</td><td>(RENO Collab.)</td></tr><tr><td>SEREBROV</td><td>18A</td><td>PPN 49 701</td><td>A.P. Serebrov et al.</td><td>(Neutrino-4 Collab.)</td></tr><tr><td>AARTSEN</td><td>17B</td><td>PR D95 112002</td><td>M.G. Aartsen et al.</td><td>(IceCube Collab.)</td></tr><tr><td>ABE</td><td>16</td><td>PR D93 105 753</td><td>ABDURASHI...</td><td>(Troitsk nu-mass Collab.)</td></tr><tr><td>ABE</td><td>17A</td><td>PRL 118 151801</td><td>K. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>ABE</td><td>17C</td><td>PR D96 011102</td><td>K. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>ABE</td><td>17F</td><td>PR D96 092006</td><td>K. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>Also</td><td>17</td><td>PR D96 0919902 (erat.)</td><td>K. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>ADAMSON</td><td>17A</td><td>PR D97 151 1802</td><td>P. Adamson et al.</td><td>(NoVa Collab.)</td></tr><tr><td>ADAMSON</td><td>17B</td><td>PRL 118 231801</td><td>P. Adamson et al.</td><td>(NoVa Collab.)</td></tr><tr><td>AN</td><td>17A</td><td>PR D95 072006</td><td>F.P. An et al.</td><td>(Daya Bay Collab.)</td></tr><tr><td>ESTEBAN</td><td>17</td><td>JHEP 1701 087</td><td>I. Esteban et al.</td><td></td></tr><tr><td>KO</td><td>17</td><td>PRL 118 121802</td><td>Y.J. Ko et al.</td><td>(NEOS Collab.)</td></tr><tr><td>ANYOLES</td><td>17</td><td>APJ 835 202</td><td>N. Vinyoles et al.</td><td>(IceCube Collab.)</td></tr><tr><td>AARTSEN</td><td>16</td><td>PR D97 071801</td><td>M.G. Aartsen et al.</td><td>(Daya Bay Collab.)</td></tr><tr><td>ABE</td><td>16D</td><td>JHEP 1601 163</td><td>Y. Abe et al.</td><td>(Double Chooz Collab.)</td></tr><tr><td>ABE</td><td>16C</td><td>PR D94 052010</td><td>K. Abe et al.</td><td>(Super-Kamiokande Collab.)</td></tr><tr><td>ABE</td><td>16D</td><td>PRL 116 181102</td><td>K. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>ADAMSON</td><td>16A</td><td>PRL 116 151806</td><td>P. Adamson et al.</td><td>(NoVa Collab.)</td></tr><tr><td>ADAMSON</td><td>16A</td><td>PR D93 051104</td><td>P. Adamson et al.</td><td>(NoVa Collab.)</td></tr><tr><td>ADAMSON</td><td>16B</td><td>PRL 117 151802</td><td>P. Adamson et al.</td><td>(Daya Bay and MINOS Collab.)</td></tr><tr><td>ADAMSON</td><td>16C</td><td>PRL 117 151803</td><td>P. Adamson et al.</td><td>(MINOS Collab.)</td></tr><tr><td>AN</td><td>16A</td><td>PRL 116 061801</td><td>F.P. An et al.</td><td>(Daya Bay Collab.)</td></tr><tr><td>AN</td><td>16A</td><td>PR D93 072011</td><td>F.P. An et al.</td><td>(Daya Bay Collab.)</td></tr><tr><td>AN</td><td>16B</td><td>PRL 117 151802</td><td>F.P. An et al.</td><td>(Daya Bay Collab.)</td></tr><tr><td>CHOI</td><td>16</td><td>PRL 116 211801</td><td>J.H. Choi et al.</td><td>(RENO Collab.)</td></tr></tbody></table>

<table><tbody><tr><td>PDG</td><td>16</td><td>CP C40 1610001</td><td>C. Patrignani et al.</td><td>(PDG Collab.)</td></tr><tr><td>AARTSEN</td><td>15A</td><td>PR D91 072004</td><td>M.G. Aartsen</td><td>(IceCube Collab.)</td></tr><tr><td>ABE</td><td>15B</td><td>PR D91 072010</td><td>K. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>AGAFONOVA</td><td>15A</td><td>PRL 115 121802</td><td>N. Agafonova et al.</td><td>(OPERA Collab.)</td></tr><tr><td>AN</td><td>15</td><td>PRL 115 111802</td><td>F.P. An et al.</td><td>(Daya Bay Collab.)</td></tr><tr><td>BERGSTROM</td><td>15</td><td>JHEP 1509 200</td><td>J. Bergstrom et al.</td><td>(BARC, STON, MADU+)</td></tr><tr><td>GANDO</td><td>15</td><td>PR C92 056808</td><td>A. Gando et al.</td><td>(INFELD Collab.)</td></tr><tr><td>ABE</td><td>14</td><td>PRL 112 181801</td><td>K. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>Also</td><td></td><td>PR D91 072010</td><td>K. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>ABE</td><td>14A</td><td>PL B735 51</td><td>Y. Abe et al.</td><td>(Double Chooz Collab.)</td></tr><tr><td>ABE</td><td>14B</td><td>PR D98 092003</td><td>K. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>ABE</td><td>14C</td><td>PR D12 061802</td><td>K. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>ABE</td><td>14H</td><td>JHEP 1410 086</td><td>Y. Abe et al.</td><td>(Double Chooz Collab.)</td></tr><tr><td>Also</td><td></td><td>JHEP 1502 074 (eratt.)</td><td>Y. Abe et al.</td><td>(Double Chooz Collab.)</td></tr><tr><td>ADAMSON</td><td>14</td><td>PRL 112 191801</td><td>P. Adamson et al.</td><td>(MINOS Collab.)</td></tr><tr><td>AN</td><td>14</td><td>PRL 112 061801</td><td>F.P. An et al.</td><td>(Daya Bay Collab.)</td></tr><tr><td>AN</td><td>14B</td><td>PR D90 071101</td><td>F.P. An et al.</td><td>(Daya Bay Collab.)</td></tr><tr><td>BELLINI</td><td>14A</td><td>NAT 512 383</td><td>G. Bellini et al.</td><td>(Borexino Collab.)</td></tr><tr><td>FORERO</td><td>14</td><td>PR D90 093006</td><td>D.V. Forero, M. Tortola, J.W.F. Valle</td><td></td></tr><tr><td>GONZALEZ...</td><td>14</td><td>JHEP 1411 052</td><td>M.C. Gonzalez-Garcia, M. Maltoni, T. Schwetz</td><td></td></tr><tr><td>PDG</td><td>14</td><td>CP C38 070001</td><td>K. Olive et al.</td><td>(PDG Collab.)</td></tr><tr><td>RENSHAW</td><td>14</td><td>PRL 112 091805</td><td>A. Renshaw et al.</td><td>(Super-Kamiokande Collab.)</td></tr><tr><td>AARTSEN</td><td>13B</td><td>PRL 111 081801</td><td>M.G. Aartsen et al.</td><td>(IceCube Collab.)</td></tr><tr><td>ABE</td><td>13C</td><td>PL B723 66</td><td>Y. Abe et al.</td><td>(Double Chooz Collab.)</td></tr><tr><td>ABE</td><td>13E</td><td>PR D88 032002</td><td>K. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>ABE</td><td>13G</td><td>PRL 111 218003</td><td>K. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>ADAMSON</td><td>13A</td><td>PRL 110 171801</td><td>P. Adamson et al.</td><td>(MINOS Collab.)</td></tr><tr><td>ADAMSON</td><td>13B</td><td>PRL 110 251801</td><td>P. Adamson et al.</td><td>(MINOS Collab.)</td></tr><tr><td>AGAFONOVA</td><td>13A</td><td>JHEP 1307 004</td><td>N. Agafonova et al.</td><td>(OPERA Collab.)</td></tr><tr><td>AGUILAR-AR...</td><td>13A</td><td>PR L110 161801</td><td>A.A. Aguilar-Arevalo et al.</td><td>(MiniBooNE Collab.)</td></tr><tr><td>AHARMIM</td><td>13</td><td>PR C88 025501</td><td>B. Aharmim et al.</td><td>(SNO Collab.)</td></tr><tr><td>AN</td><td>13</td><td>CP C37 011001</td><td>F.P. An et al.</td><td>(Daya Bay Collab.)</td></tr><tr><td>ANTONELLO</td><td>13A</td><td>EPJ C73 2345</td><td>M. Antonello et al.</td><td>(ICARUS Collab.)</td></tr><tr><td>ANTONELLO</td><td>13B</td><td>EPJ C73 2599</td><td>M. Antonello et al.</td><td>(ICARUS Collab.)</td></tr><tr><td>GANDO</td><td>13</td><td>PR D88 033001</td><td>A. Gando et al.</td><td>(KamLAND Collab.)</td></tr><tr><td>ABE</td><td>12</td><td>PRL 108 131801</td><td>Y. Abe et al.</td><td>(Double Chooz Collab.)</td></tr><tr><td>ABE</td><td>12A</td><td>PR D85 031103</td><td>K. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>ABE</td><td>12B</td><td>PR D86 052008</td><td>Y. Abe et al.</td><td>(Double Chooz Collab.)</td></tr><tr><td>ADAMSON</td><td>12A</td><td>PR L108 191801</td><td>A. A. Aguilar-Arevalo et al.</td><td>(MINS Collab.)</td></tr><tr><td>ADAMSON</td><td>12B</td><td>PR D86 052007</td><td>P. Adamson et al.</td><td>(MINOS Collab.)</td></tr><tr><td>ADRIAN-MAR...</td><td>12</td><td>PL B714 224</td><td>S. Adrian-Martinez et al.</td><td>(ANTARES Collab.)</td></tr><tr><td>AHN</td><td>12</td><td>PRL 108 191802</td><td>J.K. Ahn et al.</td><td>(RENO Collab.)</td></tr><tr><td>AN</td><td>12</td><td>PRL 108 171803</td><td>F.P. An et al.</td><td>(Daya Bay Collab.)</td></tr><tr><td>BELLINI</td><td>12A</td><td>PL D102 051302</td><td>G. Bellini et al.</td><td>(Borexino Collab.)</td></tr><tr><td>CHENG</td><td>12</td><td>PR D86 052009</td><td>G. Cheng et al.</td><td>(MiniBooNE/SciBooNE Collab.)</td></tr><tr><td>MAHN</td><td>12</td><td>PR D85 032007</td><td>K.B.M. Mahn et al.</td><td>(MiniBooNE/SciBooNE Collab.)</td></tr><tr><td>ABE</td><td>11</td><td>PR D83 052010</td><td>K. Abe et al.</td><td>(Super-Kamiokande Collab.)</td></tr><tr><td>ABE</td><td>11A</td><td>PR C84 035804</td><td>S. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>ABE</td><td>11B</td><td>PR L107 241801</td><td>K. Abe et al.</td><td>(Super-Kamiokande Collab.)</td></tr><tr><td>ADAMSON</td><td>11</td><td>PR 106 181801</td><td>P. Adamson et al.</td><td>(MINOS Collab.)</td></tr><tr><td>ADAMSON</td><td>11B</td><td>PR L107 021801</td><td>P. Adamson et al.</td><td>(MINOS Collab.)</td></tr><tr><td>ADAMSON</td><td>11C</td><td>PR D84 071103</td><td>P. Adamson et al.</td><td>(MINOS Collab.)</td></tr><tr><td>ADAMSON</td><td>11D</td><td>PR L107 181802</td><td>P. Adamson et al.</td><td>(MINOS Collab.)</td></tr><tr><td>BELLINI</td><td>11</td><td>PR B966 191</td><td>G. Bellini et al.</td><td>(Borexino Collab.)</td></tr><tr><td>BELLINI</td><td>11A</td><td>PR L107 141302</td><td>G. Bellini et al.</td><td>(Borexino Collab.)</td></tr><tr><td>FOGLI</td><td>11</td><td>PR D84 053007</td><td>G.L. Fogli et al.</td><td>(VPI Collab.)</td></tr><tr><td>GANDO</td><td>11</td><td>PR D83 052002</td><td>A. Gando et al.</td><td>(KamLAND Collab.)</td></tr><tr><td>HUBER</td><td>11</td><td>PR C84 024617</td><td>P. Huber</td><td>(VPI Collab.)</td></tr><tr><td>Also</td><td>11</td><td>PR C83 054615</td><td>Th. M. Mueller et al.</td><td></td></tr><tr><td>MUELLER</td><td>11</td><td>APJ 743 24</td><td>A.M. Serenelli, W.C. Haxton, C. Pena-Garay</td><td></td></tr><tr><td>ADAMSON</td><td>10A</td><td>PR D82 051102</td><td>P. Adamson et al.</td><td>(MINOS Collab.)</td></tr><tr><td>AGUILAR-AR...</td><td>10</td><td>PR L105 181801</td><td>A.A. Aguilar-Arevalo et al.</td><td>(MiniBooNE Collab.)</td></tr><tr><td>AHARMIM</td><td>10</td><td>PR C81 055504</td><td>B. Aharmim et al.</td><td>(SNO Collab.)</td></tr><tr><td>BELLINI</td><td>10</td><td>PR D81 033006</td><td>G. Bellini et al.</td><td>(Borexino Collab.)</td></tr><tr><td>DENIZ</td><td>10</td><td>PR L10 072001</td><td>M. Deniz et al.</td><td>(TEXONO Collab.)</td></tr><tr><td>KAETHER</td><td>10</td><td>PL B685 47</td><td>F. Kaether et al.</td><td></td></tr><tr><td>WENDELL</td><td>10</td><td>PR D81 092004</td><td>R. Wendell et al.</td><td>(Super-Kamiokande Collab.)</td></tr><tr><td>ABDURASHI...</td><td>09</td><td>PR C90 015807</td><td>J.N. Abdurashitov et al.</td><td>(SAGE Collab.)</td></tr><tr><td>ABE</td><td>09</td><td>PR L03 261802</td><td>P. Adamson et al.</td><td>(MINOS Collab.)</td></tr><tr><td>ABE</td><td>09B</td><td>PR L103 111801</td><td>A.A. Aguilar-Arevalo et al.</td><td>(MiniBooNE Collab.)</td></tr><tr><td>ABE</td><td>08A</td><td>PR L100 221803</td><td>S. Abe et al.</td><td>(KamLAND Collab.)</td></tr><tr><td>Also</td><td></td><td>PR L101 119904E</td><td>S. Abe et al.</td><td>(KamLAND Collab.)</td></tr><tr><td>ADAMSON</td><td>08A</td><td>PR D77 072002</td><td>P. Adamson et al.</td><td>(MINOS Collab.)</td></tr><tr><td>ADAMSON</td><td>08</td><td>PR L101 131802</td><td>P. Adamson et al.</td><td>(MINOS Collab.)</td></tr><tr><td>AHARMIM</td><td>08</td><td>PR L101 111301</td><td>B. Aharmim et al.</td><td>(SNO Collab.)</td></tr><tr><td>Also</td><td></td><td>PR C87 015502</td><td>B. Aharmim et al.</td><td>(SNO Collab.)</td></tr><tr><td>ARPESELLA</td><td>08</td><td>PR L01 091302</td><td>C. Arpesella et al.</td><td>(Borexino Collab.)</td></tr><tr><td>CRAVES</td><td>08</td><td>PR D78 032002</td><td>J.P. Cravens et al.</td><td>(Super-Kamiokande Collab.)</td></tr><tr><td>FOGLI</td><td>08</td><td>PR D75 092003</td><td>G.L. Fogli</td><td></td></tr><tr><td>ADAMSON</td><td>07</td><td>PR 98 231801</td><td>P. Adamson et al.</td><td>(MINOS Collab.)</td></tr><tr><td>AGUILAR-AR...</td><td>07</td><td>PR C75 045502</td><td>A.A. Aguilar-Arevalo et al.</td><td>(MiniBooNE Collab.)</td></tr><tr><td>ADAMSON</td><td>06</td><td>PR D73 072002</td><td>P. Adamson et al.</td><td>(MINOS Collab.)</td></tr><tr><td>AHN</td><td>06</td><td>PR D74 072003</td><td>M.H. Ahn et al.</td><td>(K2K Collab.)</td></tr><tr><td>BALATA</td><td>06</td><td>PR C47 21</td><td>M. Balata et al.</td><td>(Borexino Collab.)</td></tr><tr><td>HOSAKA</td><td>06</td><td>PR D73 112001</td><td>J. Hosaka et al.</td><td>(Super-Kamiokande Collab.)</td></tr><tr><td>HOSAKA</td><td>06</td><td>PR D74 032002</td><td>J. Hosaka et al.</td><td>(Super-Kamiokande Collab.)</td></tr><tr><td>MICHAEL</td><td>06</td><td>PR 97 191801</td><td>D. Michael et al.</td><td>(MINOS Collab.)</td></tr><tr><td>WINTER</td><td>06</td><td>PR C73 255053</td><td>W.T. Winter et al.</td><td>(K2K Collab.)</td></tr><tr><td>YAMAMOTO</td><td>06</td><td>PR C70 181801</td><td>S. Yamamoto et al.</td><td>(SNO Collab.)</td></tr><tr><td>ALIU</td><td>06</td><td>PR D96 055502</td><td>E. Aliu et al.</td><td>(K2K Collab.)</td></tr><tr><td>ALLISON</td><td>05</td><td>PR D72 052005</td><td>W.W.M. Allison et al.</td><td>(SOUAND-2 Collab.)</td></tr><tr><td>ALTMANN</td><td>05</td><td>PL B616 174</td><td>M. Altmann et al.</td><td>(GN0 Collab.)</td></tr><tr><td>ARAKI</td><td>05</td><td>PR D94 081801</td><td>T. Araki et al.</td><td>(KamLAND Collab.)</td></tr><tr><td>DE 2005</td><td>05</td><td>PR D94 081801</td><td>Y. Ashie et al.</td><td>(Super-Kamiokande Collab.)</td></tr><tr><td>BAHCALL</td><td>05</td><td>APJ 621 185</td><td>J.N. Bahcal, A.M. Serenelli, S. Basu</td><td>(IAS+)</td></tr><tr><td>DEGOUEVA</td><td>05</td><td>PR D71 093002</td><td>A. de Gouvea, C. Pena-Garay</td><td></td></tr><tr><td>AHARMIM</td><td>04</td><td>PR D70 093014</td><td>B. Aharmim et al.</td><td>(SNO Collab.)</td></tr><tr><td>AHMED</td><td>04A</td><td>PR L92 181301</td><td>S.N. Ahmed et al.</td><td>(SNO Collab.)</td></tr><tr><td>AHN</td><td>04</td><td>PR L93 051801</td><td>M.H. Ahn et al.</td><td>(K2K Collab.)</td></tr><tr><td>AMBROSIO</td><td>04</td><td>EPJ C36 323</td><td>M. Ambrosio et al.</td><td>(MACRO Collab.)</td></tr><tr><td>ASHIE</td><td>04</td><td>PR 93 101801</td><td>Y. Ashie et al.</td><td>(Super-Kamiokande Collab.)</td></tr><tr><td>EGUCHI</td><td>04</td><td>PR 92 071301</td><td>K. Eguchi et al.</td><td>(Super-Kamiokande Collab.)</td></tr><tr><td>SMY</td><td>04</td><td>PR D69 011104</td><td>M.B. Smy et al.</td><td>(K2K Collab.)</td></tr><tr><td>AHN</td><td>03</td><td>PR 90 041801</td><td>M.H. Ahn et al.</td><td>(KAMLAND Collab.)</td></tr><tr><td>AMBROSIO</td><td>03</td><td>PL B596 35</td><td>M. Ambrosio et al.</td><td>(KAMRO Collab.)</td></tr><tr><td>APOLLIONO</td><td>03</td><td>EPJ C27 331</td><td>M. Apollonio et al.</td><td>(CHOOZ Collab.)</td></tr><tr><td>ASTIER</td><td>03</td><td>PL ASTIER 19</td><td>P. Astier et al.</td><td>(NOMAD Collab.)</td></tr><tr><td>EGUCHI</td><td>03</td><td>PR 90 021802</td><td>K. Eguchi et al.</td><td>(KamLAND Collab.)</td></tr><tr><td>GANDO</td><td>03</td><td>PR L90 171302</td><td>Y. Gando et al.</td><td>(Super-Kamiokande Collab.)</td></tr><tr><td>IANNO</td><td>03</td><td>JP G2 2107</td><td>A. Ianni</td><td>(INFELD Gran Sasso)</td></tr><tr><td>SANCHEZ</td><td>03</td><td>PR D68 113004</td><td>M. Sanchez et al.</td><td>(Soudan 2 Collab.)</td></tr><tr><td>ABDURASHI...</td><td>02</td><td>JETP 95 181</td><td>J.N. Abdurashitov et al.</td><td>(SAGE Collab.)</td></tr><tr><td> Ahmad</td><td>02</td><td>PRL 89 011301</td><td>Q.R. Ahmad et al.</td><td>(SNO Collab.)</td></tr><tr><td>AHMAD</td><td>02B</td><td>PRL 89 011302</td><td>Q.R. Ahmad et al.</td><td>(SNO Collab.)</td></tr><tr><td>BRUSTER</td><td>02B</td><td>PRL D6 121001</td><td>B. Armbruster et al.</td><td>(KARMEN, 2 Collab.)</td></tr><tr><td>AVVAKUMOV</td><td>02</td><td>PRL 89 011804</td><td>S. Avvakumov et al.</td><td>(NuTEV Collab.)</td></tr></tbody></table>

Translated from ZETF 122 211.

<table><tbody><tr><td> Ahmad</td><td>02</td><td>PRL 89 011301</td><td>Q.R. Ahmad et al.</td><td>(SNO Collab.)</td></tr><tr><td>AHMAD</td><td>02B</td><td>PRL 89 011302</td><td>Q.R. Ahmad et al.</td><td>(SNO Collab.)</td></tr><tr><td>BRUSTER</td><td>02B</td><td>PRL D6 121001</td><td>B. Armbruster et al.</td><td>(KARMEN, 2 Collab.)</td></tr><tr><td>AVVAKUMOV</td><td>02</td><td>PRL 89 011804</td><td>S. Avvakumov et al.</td><td>(NuTEV Collab.)</td></tr></tbody></table>
<table><thead><tr><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>FUKUDA</td><td>02</td><td>PL B539 179</td><td>S. Fukuda et al. (Super-Kamiokande Collab.)</td></tr><tr><td>AGUILAR</td><td>01</td><td>PR D64 112007</td><td>A. Aguilar et al. (LSND Collab.)</td></tr><tr><td>AHMAD</td><td>01</td><td>PRL 87 071301</td><td>Q.R. Ahmad et al. (SNO Collab.)</td></tr><tr><td>AMBROSIO</td><td>01</td><td>PL B517 59</td><td>M. Ambrosio et al. (MACRO Collab.)</td></tr><tr><td>BOEHM</td><td>01</td><td>PR D64 112001</td><td>F. Boehm et al. (Super-Kamiokande Collab.)</td></tr><tr><td>FUKUDA</td><td>00</td><td>PRL 86 5651</td><td>S. Fukuda et al. (MACRO Collab.)</td></tr><tr><td>AMBROSIO</td><td>00</td><td>PL B478 5</td><td>M. Ambrosio et al. (Super-Kamiokande Collab.)</td></tr><tr><td>BOEHM</td><td>00</td><td>PRL 84 3764</td><td>F. Boehm et al. (Super-Kamiokande Collab.)</td></tr><tr><td>FUKUDA</td><td>00</td><td>PRL 85 3999</td><td>S. Fukuda et al. (Super-Kamiokande Collab.)</td></tr><tr><td>ALLISON</td><td>99</td><td>PL B449 137</td><td>W.W.M. Allison et al. (Soudan 2 Collab.)</td></tr><tr><td>APOLLONIO</td><td>99</td><td>PL B466 415</td><td>M. Apollonio et al. (CHOOZ Collab.)</td></tr><tr><td>Also</td><td></td><td>PL B472 434 (errat.)</td><td>(CHOOZ Collab.)</td></tr><tr><td>FUKUDA</td><td>99C</td><td>PRL 82 2644</td><td>Y. Fukuda et al. (Super-Kamiokande Collab.)</td></tr><tr><td>FUKUDA</td><td>99D</td><td>PL B467 185</td><td>Y. Fukuda et al. (Super-Kamiokande Collab.)</td></tr><tr><td>HAMPEL</td><td>99</td><td>PL B447 127</td><td>W. Hampel et al. (GALLEX Collab.)</td></tr><tr><td>AMBROSIO</td><td>98</td><td>PL B434 451</td><td>M. Ambrosio et al. (MACRO Collab.)</td></tr><tr><td>APOLLONIO</td><td>98</td><td>PL B420 397</td><td>M. Apollonio et al. (CHOOZ Collab.)</td></tr><tr><td>ATHANASSO...</td><td>98</td><td>PL B81 1774</td><td>C. Athanassopoulos et al. (LSND Collab.)</td></tr><tr><td>ATHANASSO...</td><td>98B</td><td>PR C58 2489</td><td>C. Athanassopoulos et al. (LSND Collab.)</td></tr><tr><td>CLEVELAND</td><td>98</td><td>APJ 496 505</td><td>B.T. Cleveland et al. (Homestake Collab.)</td></tr><tr><td>FELDMAN</td><td>98</td><td>PR D57 3873</td><td>G.J. Feldman, R.D. Cousins</td></tr><tr><td>FUKUDA</td><td>98C</td><td>PR 81 1562</td><td>Y. Fukuda et al. (Super-Kamiokande Collab.)</td></tr><tr><td>HATAKEYAMA</td><td>98</td><td>PR 81 2016</td><td>S. Hatakeyama et al. (Kamiokande Collab.)</td></tr><tr><td>CLARK</td><td>97</td><td>PRL 79 345</td><td>R. Clark et al. (IMB Collab.)</td></tr><tr><td>AGLIETTA</td><td>96</td><td>JETP 63 791</td><td>M. Aglietta et al. (LSD Collab.)</td></tr><tr><td colspan="4">Translated from ZETFP 63 753.</td></tr><tr><td>ATHANASSO...</td><td>96</td><td>PR C54 2685</td><td>C. Athanassopoulos et al. (LSND Collab.)</td></tr><tr><td>ATHANASSO...</td><td>96B</td><td>PRL 77 3082</td><td>C. Athanassopoulos et al. (LSND Collab.)</td></tr><tr><td>FUKUDA</td><td>96</td><td>PL B77 1683</td><td>Y. Fukuda et al. (Kamiokande Collab.)</td></tr><tr><td>FUKUDA</td><td>96B</td><td>PL B388 397</td><td>Y. Fukuda et al. (Kamiokande Collab.)</td></tr><tr><td>GREENWOOD</td><td>96</td><td>PR D53 6054</td><td>Z.D. Greenwood et al. (UCI, SVR, SCUC)</td></tr><tr><td>HAMPEL</td><td>96</td><td>PL B388 384</td><td>W. Hampel et al. (GALLEX Collab.)</td></tr><tr><td>LOVERRE</td><td>96</td><td>PL B370 156</td><td>P.F. Lovere</td></tr><tr><td>ACHKAR</td><td>95</td><td>NP B434 503</td><td>A. Achkar et al. (SING, SACLD, CPPM, CDEF+)</td></tr><tr><td>AHLEN</td><td>95</td><td>PL B357 481</td><td>S. Allen et al. (MACRO Collab.)</td></tr><tr><td>ATHANASSO...</td><td>95</td><td>PRL 75 2650</td><td>C. Athanassopoulos et al. (LSND Collab.)</td></tr><tr><td>DAUM</td><td>95</td><td>ZPHY C66 417</td><td>K. Baum et al. (FREJUS Collab.)</td></tr><tr><td>HILL</td><td>95</td><td>PRL 75 2654</td><td>J.E. Hill (PENN)</td></tr><tr><td>DECLAIS</td><td>94</td><td>Y. Declais et al.</td><td>Y. Declais et al. (Kamiokande Collab.)</td></tr><tr><td>FUKUDA</td><td>94</td><td>PL B335 237</td><td>Y. Fukuda et al. (LCHAR II Collab.)</td></tr><tr><td>VILAIN</td><td>94C</td><td>ZPHY C64 539</td><td>P. Vilain et al. (LCHAR II Collab.)</td></tr><tr><td>FREEDEMAN</td><td>93</td><td>PR D47 811</td><td>S.J. Freedman et al. (LAMPF E645 Collab.)</td></tr><tr><td>BECKER-SZ...</td><td>92B</td><td>PR D46 3720</td><td>R.A. Becker-Szendy et al. (IMB Collab.)</td></tr><tr><td>BEIER</td><td>92</td><td>PL B283 446</td><td>E.W. Beier et al. (KAM2 Collab.)</td></tr><tr><td>Also</td><td></td><td>P.TBSNL A346 63</td><td>(PENN)</td></tr><tr><td>HIRATA</td><td>92</td><td>PL B280 146</td><td>E.S. Hirata et al. (Kamiokande II Collab.)</td></tr><tr><td>CASPER</td><td>91</td><td>PRL 66 2561</td><td>D. Casper et al. (IMB Collab.)</td></tr><tr><td>HIRATA</td><td>91</td><td>PRL 66 9</td><td>K.S. Hirata et al. (Kamiokande II Collab.)</td></tr><tr><td>KUVSHINN...</td><td>91</td><td>JETP 54 253</td><td>A.A. Kuvshinnikov et al. (KIAE)</td></tr><tr><td>BERGER</td><td>90B</td><td>PL B245 305</td><td>C. Berger et al. (FREJUS Collab.)</td></tr><tr><td>HIRATA</td><td>90</td><td>PRL 65 1297</td><td>K.S. Hirata et al. (Kamiokande II Collab.)</td></tr><tr><td>AGLIETTA</td><td>89</td><td>EPL 8 611</td><td>M. Aglietta et al. (FREJUS Collab.)</td></tr><tr><td>DAVIS</td><td>89</td><td>ARNPS 39 467</td><td>R. Davis, A.K. Mann, L. Wolfenstein (BNL, PENN+)</td></tr><tr><td>OYAMA</td><td>89</td><td>PR D39 1481</td><td>Y. Oyama et al. (Kamiokande II Collab.)</td></tr><tr><td>BIONTA</td><td>88</td><td>PR D38 768</td><td>R.M. Bionta et al. (IMB Collab.)</td></tr><tr><td>DURKIN</td><td>88</td><td>PRL 61 1811</td><td>L.S. Durkin et al. (OSU, ANL, CIT+)</td></tr><tr><td>ABRAMOWICZ</td><td>86</td><td>PL 57 298</td><td>H. Abramowicz et al. (CDHS Collab.)</td></tr><tr><td>ALLABY</td><td>86</td><td>PL B177 446</td><td>J.V. Allaby et al. (CHARM Collab.)</td></tr><tr><td>ANGELINI</td><td>86</td><td>PL B179 307</td><td>C. Angelini et al. (PISA, ATHU, PADO+)</td></tr><tr><td>VULLEUMIER</td><td>82</td><td>PL 114B 298</td><td>J.L. Vuilleumier et al. (CIT, SIN, MUNI)</td></tr><tr><td>BOLIEV</td><td>81</td><td>SJNP 34 767</td><td>M.M. Boliev (INRM)</td></tr><tr><td colspan="4">Translated from YAF 34 1418.</td></tr><tr><td>KWON</td><td>81</td><td>PR D24 1997</td><td>H. Kwon et al. (CIT, ISNG, MUNI)</td></tr><tr><td>BOEHM</td><td>80</td><td>PL 97B 310</td><td>F. Boehm et al. (ILLG, CIT, ISNG, MUNI)</td></tr><tr><td>CROUCH</td><td>78</td><td>PR D18 2239</td><td>M.F. Crouch et al. (CASE, UCI, WITW)</td></tr></tbody></table>

<table><tbody><tr><td>&lt;3 × 10<sup>-4</sup></td><td>90</td><td>2 AGNES</td><td>23A</td><td>DS50</td><td>m<sub>V<sub>X</sub></sub> ~ 7-35 keV</td></tr><tr><td>&lt;3 × 10<sup>-8</sup></td><td>90</td><td>3 BAROUKI</td><td>22</td><td>RVUE</td><td>Near m<sub>D<sub>S</sub></sub> ~ m<sub>e</sub> kin. thres.</td></tr><tr><td>&lt;1 × 10<sup>-6</sup></td><td>95</td><td>4 TUMASYAN</td><td>22AD</td><td>CMS</td><td>m<sub>V<sub>X</sub></sub> ~ 8-14 GeV, pp at 13 TeV</td></tr><tr><td>&lt;2 × 10<sup>-4</sup></td><td>95</td><td>5 FRIEDRICH</td><td>21</td><td></td><td>Near m<sub>T</sub>Be ~ m<sub>T</sub>Li kin. thres.</td></tr><tr><td>&lt;1 × 10<sup>-9</sup></td><td>95</td><td>6 CORTINA-GIL</td><td>20</td><td>NA62</td><td>m<sub>V<sub>X</sub></sub> ~ 150-400 MeV</td></tr><tr><td>&lt;1 × 10<sup>-9</sup></td><td>95</td><td>7 AAD</td><td>19F</td><td>ATLS</td><td>m<sub>V<sub>X</sub></sub> ~ 15-40 GeV</td></tr><tr><td>&lt;1 × 10<sup>-4</sup></td><td>90</td><td>8 ABE</td><td>19B</td><td>T2K</td><td>Near m<sub>K</sub> ~ m<sub>e</sub> kin. thres.</td></tr><tr><td>&lt;1 × 10<sup>-4</sup></td><td>90</td><td>9 ABLIKIM</td><td>19AL</td><td>BES3</td><td>m<sub>V<sub>X</sub></sub> ~ 0.3-0.7 GeV</td></tr><tr><td>&lt;2 × 10<sup>-7</sup></td><td>90</td><td>10 BRYMAN</td><td>19</td><td>RVUE</td><td>m<sub>V<sub>X</sub></sub> ~ 55 MeV</td></tr><tr><td>&lt;1 × 10<sup>-8</sup></td><td>90</td><td>11 AGUILAR-AR...</td><td>18A</td><td>PIEN</td><td>m<sub>V<sub>X</sub></sub> ~ 60-120 MeV</td></tr><tr><td>&lt;3 × 10<sup>-7</sup></td><td>90</td><td>12 CORTINA-GIL</td><td>18</td><td>NA62</td><td>m<sub>V<sub>X</sub></sub> ~ 200-400 MeV</td></tr><tr><td>&lt;1 × 10<sup>-6</sup></td><td>90</td><td>13 PARK</td><td>16</td><td>BELL</td><td>m<sub>V<sub>X</sub></sub> ~ 1.4 GeV</td></tr><tr><td>&lt;3 × 10<sup>-5</sup></td><td>90</td><td>14 LIVENTSEV</td><td>13</td><td>BELL</td><td>Near m<sub>V<sub>X</sub></sub> ~ 2-2.5 GeV</td></tr><tr><td>&lt;3 × 10<sup>-5</sup></td><td>95</td><td>15 ABREU</td><td>97I</td><td>DLPH</td><td>m<sub>V<sub>X</sub></sub> ~ 6-50 GeV</td></tr><tr><td>&lt;2 × 10<sup>-5</sup></td><td>95</td><td>16 ABREU</td><td>97I</td><td>DLPH</td><td>Near m<sub>V<sub>X</sub></sub> ~ 3.5 GeV</td></tr><tr><td>&lt;1 × 10<sup>-5</sup></td><td>90</td><td>17 BARANOV</td><td>93</td><td></td><td>Near m<sub>π</sub> ~ m<sub>e</sub> kin. thres.</td></tr><tr><td>&lt;2 × 10<sup>-7</sup></td><td>90</td><td>17 BARANOV</td><td>93</td><td></td><td>Near m<sub>K</sub> ~ m<sub>e</sub> kin. thres.</td></tr><tr><td>&lt;1 × 10<sup>-7</sup></td><td>18,19</td><td>BERNARDI</td><td>88</td><td>CNTR</td><td>Near m<sub>π</sub> ~ m<sub>e</sub> kin. thres.</td></tr><tr><td>&lt;2 × 10<sup>-9</sup></td><td>19,20</td><td>BERNARDI</td><td>88</td><td>CNTR</td><td>Near m<sub>K</sub> ~ m<sub>e</sub> kin. thres.</td></tr><tr><td>&lt;1 × 10<sup>-7</sup></td><td>90</td><td>21 DORENBOS...</td><td>86</td><td>CHRM</td><td>Near m<sub>D</sub> ~ m<sub>e</sub> kin. thres.</td></tr><tr><td>&lt;1 × 10<sup>-7</sup></td><td>90</td><td>22 COOPER...</td><td>85</td><td>BECB</td><td>Near m<sub>D</sub> ~ m<sub>e</sub> kin. thres.</td></tr></tbody></table>

¹AAD 23AO search for $W \to \nu_X e$, for both Majorana and Dirac HNL scenarios. Also consider scenarios involving multiflavor mixing, with correspondingly weaker limits.

²Search for ionization signals in an LArTPC. Assumes the candidate particle is 100% of dark matter.

³Reanalysis of BEBC results (cf. COOPER-SARKAR 85) to update searches for $D_{S}^{\pm} \to \nu_{X} e^{\pm}$ using a corrected formula for the HNL decay probabilities, additional production channels, and an improved fit for the charm meson distributions. Assumes a Majorana HNL.

⁴TUMASYAN 22AD search for $W \to e\nu_X, \nu_X \to e\mu\nu_\mu$ and set limits for Dirac and Majorana Heavy Neutral Leptons. The data correspond to an integrated luminosity of 138 fb$^{-1}$.

⁵Search in electron capture decay $^7$Be → $^7$Li$\nu_X$. Kinematic threshold is ~ 850 keV.

⁶Search for $K^+ \to e^+ \nu_X$. Assumes lifetime of $\nu_X$ > 50 ns.

⁷Limit from prompt lepton number violating trilepton search.

⁸$K^+ \to e^+ \nu_X$, with $\nu_X$ decay through $U_{eX}$. ABE 19B also considers bounds on $|U_{eX} U'_{\nu_X}|$ for combinations of lepton flavors in the $\nu_X$ decay final state.

⁹Searches for a Majorana Heavy Neutral Lepton producing a $\pi^- e^+$ resonance in the same sign dilepton decay $D \to K\pi^- e^+ e^+$. Near $D$-neutrino mass.

¹⁰BRYMAN 19 sets best limits $|U_{eX}|^2 < 1 \times 10^{-4} - 2 \times 10^{-7}$ in the mass range $m_{\nu_X} \sim 2-55$ MeV, respectively, using the precision branching ratio measurement in AGUILAR-AREVALO 15. See also BRYMAN 19A.

¹¹Search for $\pi^+ \to e^+ \nu_X$.

¹²Search for $K^+ \to e^+ \nu_X$.

¹³PARK 16 quotes an approximate limit $B(B^+ \to e^+ \nu_X) < 3 \times 10^{-6}$ in the mass range $m_{\nu_X} \sim 0.2-1.4$ GeV.

¹⁴Search for $B^+ \to e^+ \nu_X$.

¹⁵Search for prompt $\nu_X$ decay signatures.

¹⁶Search for displaced $\nu_X$ decay signatures.

¹⁷Searches for $K$ or $\pi \to e^+ \nu_X, \nu_X \to e^+ e^- \nu_e$ using a beam dump experiment at the 70 GeV Serpukhov proton synchrotron. BARANOV 93 also considers limits for $|U_{eX} U_{\mu X}|$ from $K$ or $\pi \to \mu^+ \nu_X, \nu_X \to e^+ e^- \nu_e$.

¹⁸$\pi^+ \to e^+ \nu_X$, with $\nu_X$ decay through $U_{eX}$.

¹⁹BERNARDI 88 also considers bounds on $|U_{eX} U_{\mu X}|$.

²⁰$K^+ \to e^+ \nu_X$, with $\nu_X$ decay through $U_{eX}$.

²¹$D^+ \to e^+ \nu_X$, with $\nu_X \to e^- \ell^+ \nu_e$.

²²$D^+ \to e^+ \nu_X$, with $\nu_X \to e^- \ell^+ \nu_\ell$ or $\nu_X \to e^- \pi^+$.

### Limits on $|U_{\mu X}|^2$

Quoted limits are either the best limit near the kinematic threshold of the experiment, or a characteristic value in the mass range of the experimental sensitivity

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;5 × 10<sup>-7</sup></td><td>95</td><td>1 AAD</td><td>23AO ATLS</td><td>m<sub>V<sub>X</sub></sub> ~ 3-15 GeV, pp at 13 TeV</td></tr><tr><td>&lt;0.1</td><td>95</td><td>2 AAD</td><td>23CE ATLS</td><td>Near m<sub>V<sub>X</sub></sub> ~ 0.1-2 TeV</td></tr><tr><td>&lt;0.1</td><td>95</td><td>3 TUMASYAN</td><td>23AC CMS</td><td>Near m<sub>V<sub>X</sub></sub> ~ 0.1-3 TeV</td></tr><tr><td>&lt;5 × 10<sup>-9</sup></td><td>90</td><td>4 ABRATENKO</td><td>22A</td><td>MBNE Near m<sub>K</sub> ~ m<sub>μ</sub> kin. thres.</td></tr><tr><td>&lt;3 × 10<sup>-7</sup></td><td>95</td><td>5 TUMASYAN</td><td>22AD CMS</td><td>m<sub>V<sub>X</sub></sub> ~ 8-14 GeV, pp at 13 TeV</td></tr><tr><td>&lt;1 × 10<sup>-3</sup></td><td>95</td><td>6 AAIJ</td><td>21AA LHCB</td><td>m<sub>V<sub>X</sub></sub> ~ 5-50 GeV, pp at 7, 8</td></tr><tr><td>&lt;2 × 10<sup>-4</sup></td><td>95</td><td>7 AAIJ</td><td>21AA LHCB</td><td>m<sub>V<sub>X</sub></sub> ~ 5-50 GeV, pp at 7, 8</td></tr><tr><td>&lt;5 × 10<sup>-9</sup></td><td>90</td><td>8,9 CORTINA-GIL</td><td>21</td><td>NA62 Near m<sub>K</sub> ~ m<sub>μ</sub> kin. thres.</td></tr></tbody></table>

## Heavy Neutral Leptons, Searches for

### OMITTED FROM SUMMARY TABLE

We define searches for Heavy Neutral Leptons (HNLs) as searches for Dirac or Majorana fermions with sterile neutrino quantum numbers, that are heavy enough to not disrupt the simplest Big Bang Nucleosynthesis bounds and/or unstable on cosmological timescales: Typically HNLs have mass ~ MeV or higher.

Searches for these particles generically set bounds on the mixing between the HNL and the active neutrinos, as parametrized by the extended 3×4 PMNS matrix elements $U_{\ell X}$ (see the "Neutrino mass, mixing and oscillations" review) where $\ell = e, \mu$ or $\tau$, and we denote the HNL as $\nu_X$. While many measurements may be interpreted to place bounds on various combinations of these matrix elements, we quote below limits only for those cases in which one matrix element is assumed to be much larger than the other two, i.e. $|U_{\ell X}| \gg |U'_{\ell X}|$ for $\ell' \neq \ell$.

Experimental searches make use of various different strategies, including e.g. resonance searches in missing mass decay distributions or specific final states, searches for lepton number violating decays, and trilepton signatures. The resulting bounds on $U_{eX}$ are typically dependent on the HNL mass. The quoted limits below are either the best limit near an experimental kinematic threshold, or a characteristic value in the mass range of the experimental sensitivity.

### Limits on heavy neutral lepton mixing parameters

#### Limits on $|U_{eX}|^2$

Quoted limits are either the best limit near the kinematic threshold of the experiment, or a characteristic value in the mass range of the experimental sensitivity

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;5 × 10<sup>-7</sup></td><td>95</td><td>1 AAD</td><td>23AO ATLS</td><td>m<sub>V<sub>X</sub></sub> ~ 3-15 GeV, pp at 13 TeV</td></tr></tbody></table>
<table><tbody><tr><td>&lt;2 &times; 10<sup>-9</sup></td><td>90</td><td>10 PRIM</td><td>20 BELL</td><td>m<sub>v&chi;</sub> ~ 1 GeV</td></tr><tr><td>&lt;2 &times; 10<sup>-5</sup></td><td>95</td><td>11 AAD</td><td>19F ATLS</td><td>m<sub>v&chi;</sub> ~ 10-50 GeV</td></tr><tr><td>&lt;2 &times; 10<sup>-6</sup></td><td>95</td><td>12 AAD</td><td>19F ATLS</td><td>m<sub>v&chi;</sub> ~ 10 GeV</td></tr><tr><td>&lt;1 &times; 10<sup>-9</sup></td><td>90</td><td>13 ABE</td><td>19B T2K</td><td>Near m<sub>K</sub> &minus; m<sub>&mu;</sub> kin. thresh.</td></tr><tr><td>&lt;5 &times; 10<sup>-6</sup></td><td>90</td><td>14,15 AGUILAR-AR...19b</td><td>PIEN</td><td>m<sub>v&chi;</sub> ~ 16&ndash;30 MeV</td></tr><tr><td>&lt;1 &times; 10<sup>-5</sup></td><td>90</td><td>15 AGUILAR-AR...19b</td><td>PIEN</td><td>Near m<sub>&pi;</sub> &minus; m<sub>&mu;</sub> kin. thresh.</td></tr><tr><td>&lt;3 &times; 10<sup>-7</sup></td><td>90</td><td>8 CORTINA-GIL</td><td>18 NA62</td><td>m<sub>v&chi;</sub> ~ 250&ndash;350 MeV</td></tr><tr><td>&lt;3 &times; 10<sup>-6</sup></td><td>90</td><td>8 LAZZERONI</td><td>17A NA62</td><td>Near m<sub>K</sub> &minus; m<sub>&mu;</sub> kin. thresh.</td></tr><tr><td>&lt;5 &times; 10<sup>-2</sup></td><td>90</td><td>16 PARK</td><td>16 BELL</td><td>m<sub>v&chi;</sub> ~ 1.4 GeV</td></tr><tr><td>&lt;1 &times; 10<sup>-8</sup></td><td>90</td><td>8 ARTAMONOV</td><td>15A B949</td><td>m<sub>v&chi;</sub> ~ 200&ndash;300 MeV</td></tr><tr><td>&lt;3 &times; 10<sup>-5</sup></td><td>90</td><td>17 LIVENTSEV</td><td>13 BELL</td><td>Near m<sub>v&chi;</sub> ~ 2&ndash;2.5 GeV</td></tr><tr><td>&lt;2.0 &times; 10<sup>-8</sup></td><td>95</td><td>18 DAUM</td><td>00 KARM</td><td>m<sub>v&chi;</sub> = 33.905 MeV</td></tr><tr><td>&lt;8 &times; 10<sup>-8</sup></td><td>90</td><td>19 VAITAITIS</td><td>99 CCFR</td><td>Near m<sub>K</sub> &minus; m<sub>&mu;</sub> kin. thresh.</td></tr><tr><td>&lt;6 &times; 10<sup>-8</sup></td><td>90</td><td>20 VAITAITIS</td><td>99 CCFR</td><td>Near m<sub>D<sub>S</sub></sub> &minus; m<sub>&mu;</sub> kin. thresh.</td></tr><tr><td>&lt;3 &times; 10<sup>-5</sup></td><td>95</td><td>21 ABREU</td><td>97I DLPH</td><td>m<sub>v&chi;</sub> ~ 6&ndash;50 GeV</td></tr><tr><td>&lt;2 &times; 10<sup>-5</sup></td><td>95</td><td>22 ABREU</td><td>97I DLPH</td><td>Near m<sub>v&chi;</sub> ~ 3.5 GeV</td></tr><tr><td>&lt;3 &times; 10<sup>-5</sup></td><td>90</td><td>23 VILAIN</td><td>95C CHM2</td><td>Near m<sub>K</sub> &minus; m<sub>&mu;</sub> kin. thresh.</td></tr><tr><td>&lt;3 &times; 10<sup>-8</sup></td><td>24,25 BERNARDI</td><td>88 CNTR</td><td>Near m<sub>&mu;</sub> + m<sub>&pi;</sub> kin. thresh.</td></tr><tr><td>&lt;2 &times; 10<sup>-9</sup></td><td>25,26 BERNARDI</td><td>88 CNTR</td><td>Near m<sub>K</sub> &minus; m<sub>&mu;</sub> kin. thresh.</td></tr><tr><td>&lt;1 &times; 10<sup>-7</sup></td><td>90</td><td>27 DORENBOS...</td><td>86 CHRM</td><td>Near m<sub>D</sub> &minus; m<sub>&mu;</sub> kin. thresh.</td></tr><tr><td>&lt;1 &times; 10<sup>-7</sup></td><td>90</td><td>28 COOPER...</td><td>85 BEBC</td><td>Near m<sub>D</sub> &minus; m<sub>&mu;</sub> kin. thresh.</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>&lt;1 &times; 10<sup>-7</sup></td><td>90</td><td>29 ABRATENKO</td><td>20 MBNE</td><td>Superseded by ABRATENKO 22A</td></tr></tbody></table>

1. AAD 23A0 search for $W \to \nu_X \mu$, for both Majorana and Dirac HNL scenarios. Also consider scenarios involving multiflavor mixing, with correspondingly weaker limits.

2. AAD 23CE search for Majorana HNLs via vector boson fusion $W^\pm W^\pm \to \mu^\pm \mu^\pm$. Limits set in a $m_{\nu_X}$ mass range from 50 GeV up to 20 TeV, using the Phenomenological Type-I Seesaw model as a benchmark scenario.

3. TUMASYAN 23AC search for Majorana HNLs via vector boson fusion $W^\pm W^\pm \to \mu^\pm \mu^\pm$. Limits set in a $m_{\nu_X}$ mass range from 50 GeV up to 25 TeV.

4. ABRATENKO 22A search for $K^+ \to \mu^+ \nu_X$, with $\nu_X \to \mu^\mp \nu^\pm$, in the mass range $m_{\nu_X} \sim 246-385$ MeV. Also considers limits from $\nu_X \to \mu^- \pi^+$ only, for the case of a Dirac HNL.

5. TUMASYAN 22AD search for $W \to \mu^+ \nu_X$, $\nu_X \to \mu^- \nu_X$ and set limits for Dirac and Majorana Heavy Neutral Leptons. The data correspond to an integrated luminosity of 138 fb$^{-1}$.

6. Limit from prompt lepton number conserving $W \to \mu\mu j$ search.

7. Limit from prompt lepton number violating $W \to \mu\mu j$ search.

8. Search for $K^+ \to \mu^+ \nu_X$.

9. Assumes a lifetime exceeding 50 ns, and searches over $m_{\nu_X}$ range 200-384 MeV.

10. Search for $B^+ \to \mu^+ \nu_X$ in the mass range $m_{\nu_X} \sim 0-1.5$ GeV.

11. Limit from prompt lepton number violating trilepton search.

12. Limit from displaced lepton violating or conserving trilepton searches.

13. $K^+ \to \mu^+ \nu_X$, with $\nu_X$ decay through $U_{\mu X}$. ABE 19b also considers bounds on $|U_{\ell X} U_{\ell' X}|$ for combinations of lepton flavors in the $\nu_X$ decay final state.

14. Limit requires muon kinetic energy $> 1.2$ MeV.

15. Search for $\pi^+ \to \mu^+ \nu_X$.

16. PARK 16 quotes an approximate limit $B(B^+ \to \mu^+ \nu_X) < 3 \times 10^{-6}$ in the mass range $m_{\nu_X} \sim 0.2-1.4$ GeV.

17. Search for $B^+ \to \mu^+ \nu_X$.

18. DAUM 00 quotes a branching ratio bound $B(\pi^+ \to \mu^+ \nu_X) < 6.0 \times 10^{-10}$ at 95% CL.

19. $K^+ \to \mu^+ \nu_X$, with $\nu_X \to \mu \pi^-$.

20. $D_S \to \mu^+ \nu_X$, with $\nu_X \to \mu X$.

21. Search for prompt $\nu_X$ decay signatures.

22. Search for displaced $\nu_X$ decay signatures.

23. Search for Heavy Neutral Leptons produced by neutral current muon neutrino interactions, with $\nu_X \to \mu^+ \mu^- \nu_X$.

24. $K^+ \to \mu^+ \nu_X$, with $\nu_X$ decay through $U_{\mu X}$ and $m_{\nu_X} < m_\mu + m_\pi$.

25. BERNARDI 88 also considers bounds on $|U_{\ell X} U_{\mu X}|$.

26. $K^+ \to \mu^+ \nu_X$, with $\nu_X \to \mu^- \pi^+$.

27. $D^+ \to \mu^+ \nu_X$, with $\nu_X \to \mu^- \ell^+ \nu_\ell$.

28. $D^+ \to \mu^+ \nu_X$, with $\nu_X \to \mu^- \ell^+ \nu_\ell$ or $\nu_X \to \mu^- \pi^+$.

29. $K^+ \to \mu^+ \nu_X$, with $\nu_X \to \mu^- \pi^+$, in the mass range $m_{\nu_X} \sim 260-385$ MeV.

ABRATENKO 20 also considers $\nu_X \to \mu^+ \pi^-$ for the case of a Majorana HNL.

## Limits on $|U_{\tau X}|^2$

Quoted limits are either the best limit near the kinematic threshold of the experiment, or a characteristic value in the mass range of the experimental sensitivity

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>&lt;1 &times; 10<sup>-5</sup></td><td>95</td><td>1 LEES</td><td>23A BABR</td><td>Near m<sub>&tau;</sub> &minus; 3m<sub>&pi;</sub> kin. thresh.</td></tr><tr><td>&lt;2 &times; 10<sup>-6</sup></td><td>90</td><td>2 BAROUKI</td><td>22 RVUE</td><td>Near m<sub>&tau;</sub> &minus; m<sub>&nu;</sub> kin. thresh.</td></tr><tr><td>&lt;3 &times; 10<sup>-4</sup></td><td>90</td><td>3 ACCIARRI</td><td>21 ARNT</td><td>Near m<sub>&nu;</sub> &sim; 970 MeV</td></tr><tr><td>&lt;3 &times; 10<sup>-6</sup></td><td>90</td><td>4 BOIARSKA</td><td>21 RVUE</td><td>Near m<sub>&nu;</sub> &sim; 0.8-1.6 GeV</td></tr><tr><td>&lt;2 &times; 10<sup>-4</sup></td><td>90</td><td>5 ORLOFF</td><td>02 CHRM</td><td>Near m<sub>D</sub> &minus; m<sub>&tau;</sub> kin. thresh.</td></tr><tr><td>&lt;1 &times; 10<sup>-4</sup></td><td>90</td><td>6 ORLOFF</td><td>02 CHRM</td><td>Near m<sub>&nu;</sub> &sim; 200-250 MeV</td></tr><tr><td>&lt;3 &times; 10<sup>-5</sup></td><td>95</td><td>7 ABREU</td><td>97I DLPH</td><td>Near m<sub>&nu;</sub> &sim; 6-50 GeV</td></tr><tr><td>&lt;2 &times; 10<sup>-5</sup></td><td>95</td><td>8 ABREU</td><td>97I DLPH</td><td>Near m<sub>&nu;</sub> &sim; 3.5 GeV</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

9 LIVENTSEV 23 BELL Near $m_{\nu_X} \sim 0.8-1.2$ GeV

10 TUMASYAN 22H CMS pp at 13 TeV

1. Search for $\tau^+ \to \pi^+ \pi^+ \nu^- \nu_X$.

2. Reanalysis of BEBC results (cf. COOPER-SARKAR 85) to include searches for $D_S^+ \to \nu_\tau \tau^+$, $\tau^+ \to \nu_X \pi^+$, $\nu_X \rho^+$, or $\nu_X \nu_\tau \ell^+$ via $U_{\tau X}$. Assumes a Majorana HNL.

3. Search for $\nu_X \to \mu^+ \mu^- \nu_\tau$.

4. Reanalysis of CHARM results (cf. ORLOFF 02) to include searches for $\nu_X \to \nu \ell^+ \ell^-$ decays, and including the production of HNLs from $\tau$ decays.

5. $D_S \to \tau^+ \nu_X$, with $\nu_X$ decay via $U_{\tau X}$.

6. $D_S \to \nu_\tau \tau^+$, $\tau^+ \to \nu_X X$, with $\nu_X$ decay via $U_{\tau X}$.

7. Search for prompt $\nu_X$ decay signatures.

8. Search for displaced $\nu_X$ decay signatures. Kinematical suppression of $\nu_X \to \tau X$ at lower masses leads to rapid loosening of the $|U_{\tau X}|$ bound compared to that for $|U_{\ell X}|$ and $|U_{\mu X}|$.

9. Search for $\tau \to \pi \nu_X$, $\nu_X \to \pi e$ or $\pi \mu$ in the range 0.2-1.6 GeV. LIVENTSEV 23 reports results for the sum $\Sigma_{\ell=e, \mu, \tau} |U_{\ell X}|^2$ in a model-dependent context, but which may be roughly reinterpreted as a limit $|U_{\ell X} U_{\tau X}|^2 + |U_{\mu X} U_{\tau X}|^2 \lesssim 5 \times 10^{-9}$ in either Majorana or Dirac HNL scenarios.

10. TUMASYAN 22h sets limits on an approximately mass-degenerate vector-like lepton SU(2) doublet coupling to the $\tau$. Some of the reported signal region distributions might be used to set limits for heavy neutral leptons coupled to the $\tau$. The data correspond to an integrated luminosity of 138 fb$^{-1}$.

## REFERENCES FOR Heavy Neutral Leptons, Searches for

<table><tbody><tr><td>AAD</td><td>23A0 PRL 131 061803</td><td>G. Aad et al.</td><td>(ATLAS Collab.)</td></tr><tr><td>AAD</td><td>23CE PRL 83 824</td><td>G. Aad et al.</td><td>(ATLAS Collab.)</td></tr><tr><td>AGNES</td><td>23A PRL 101002</td><td>P. Agnes et al.</td><td>(DarkSide-50 Collab.)</td></tr><tr><td>LEES</td><td>23A PR D107 052009</td><td>J.P. Lees et al.</td><td>(BABAR Collab.)</td></tr><tr><td>LIVENTSEV</td><td>23 PRL 131 211802</td><td>D. Liventsev et al.</td><td>(BELLE Collab.)</td></tr><tr><td>TUMASYAN</td><td>23AC PRL 131 011803</td><td>A. Tumasyan et al.</td><td>(CMS Collab.)</td></tr><tr><td>ABRATENKO</td><td>22A PR D106 092006</td><td>P. Abratenko et al.</td><td>(MicroBooNE Collab.)</td></tr><tr><td>BAROUKI</td><td>22 SCP 13 118</td><td>R. Barouki, G. Marocco, S. Sarkar</td><td>(OXF)</td></tr><tr><td>TUMASYAN</td><td>22AD JHEP 2207 081</td><td>A. Tumasyan et al.</td><td>(CMS Collab.)</td></tr><tr><td>TUMASYAN</td><td>22H PR D105 112007</td><td>A. Tumasyan et al.</td><td>(CMS Collab.)</td></tr><tr><td>AAIJ</td><td>21AA EPJ C81 248</td><td>R. Aaij et al.</td><td>(LHCb Collab.)</td></tr><tr><td>ACCIARRI</td><td>21 PRL 127 121801</td><td>R. Acciarroni et al.</td><td>(ArgoNeuT Collab.)</td></tr><tr><td>BOIARSKA</td><td>21 PR D104 095019</td><td>I. Bojarska et al.</td><td>(BOHR, LEID)</td></tr><tr><td>CORTINA-GIL</td><td>21 PL B816 136259</td><td>E. Cortina Gil et al.</td><td>(NA62 Collab.)</td></tr><tr><td>FRIEDRICH</td><td>21 PR 126 021803</td><td>S. Friedrich et al.</td><td>(BeEST Collab.)</td></tr><tr><td>ABRATENKO</td><td>20 PR D101 052001</td><td>P. Abratenko et al.</td><td>(MiniBooNE Collab.)</td></tr><tr><td>CORTINA-GIL</td><td>20 PL B807 135599</td><td>E. Cortina Gil et al.</td><td>(NA62 Collab.)</td></tr><tr><td>PRIM</td><td>20 PL D101 032007</td><td>M.T. Prim et al.</td><td>(BELLE Collab.)</td></tr><tr><td>AAD</td><td>19F JHEP 1910 265</td><td>G. Aad et al.</td><td>(ATLAS Collab.)</td></tr><tr><td>ABE</td><td>19B PR D100 052006</td><td>K. Abe et al.</td><td>(T2K Collab.)</td></tr><tr><td>ADLIKIM</td><td>19AL PR D99 112002</td><td>M. Ablikim et al.</td><td>(BESIII Collab.)</td></tr><tr><td>AGUILAR-AR...</td><td>19B PL B798 134980</td><td>A. Aguilar-Arevalo et al.</td><td>(PIENU Collab.)</td></tr><tr><td>BRYMAN</td><td>19 PR D100 053006</td><td>D.A. Bryman, R. Shrock</td><td>(BRCO, TRIU, STON)</td></tr><tr><td>BRYMAN</td><td>19A PR D100 073011</td><td>D.A. Bryman, R. Shrock</td><td>(BRCO, TRIU, STON)</td></tr><tr><td>AGUILAR-AR...</td><td>18A PR D97 072012</td><td>A. Aguilar-Arevalo et al.</td><td>(PIENU Collab.)</td></tr><tr><td>CORTINA-GIL</td><td>18 PL B778 137</td><td>E. Cortina Gil et al.</td><td>(NA62 Collab.)</td></tr><tr><td>LAZZERONI</td><td>17A PL B772 712</td><td>C. Lazzeroni et al.</td><td>(NA62 Collab.)</td></tr><tr><td>PARK</td><td>16 PR D94 012003</td><td>C.-S. Park et al.</td><td>(BELLE Collab.)</td></tr><tr><td>AGUILAR-AR...</td><td>15 PR 115 071801</td><td>A. Aguilar-Arevalo et al.</td><td>(PIENU Collab.)</td></tr><tr><td>ARTAMONOV</td><td>15A PR D91 052001</td><td>A.V. Artamanov et al.</td><td>(E949 Collab.)</td></tr><tr><td>LIVENTSEV</td><td>13 PR D87 071102</td><td>D. Liventsev et al.</td><td>(BELLE Collab.)</td></tr><tr><td>Also</td><td>13 PR D95 099903 (errat.)</td><td>D. Liventsev et al.</td><td>(BELLE Collab.)</td></tr><tr><td>ORLOFF</td><td>02 PL B550 8</td><td>J. Orloff et al.</td><td>(CHARM Collab.)</td></tr><tr><td>DAUM</td><td>00 PRL 85 1815</td><td>M. Daum et al.</td><td>(KARMEN Collab.)</td></tr><tr><td>VAITAITIS</td><td>99 PRL 83 943</td><td>A. Vaitaitis et al.</td><td>(CCFR Collab.)</td></tr><tr><td>ABREU</td><td>97I ZPHY C74 57</td><td>P. Abreu et al.</td><td>(DELPHI Collab.)</td></tr><tr><td>Also</td><td>97I ZPHY C75 580 (errat.)</td><td>P. Abreu et al.</td><td>(DELPHI Collab.)</td></tr><tr><td>VILAIN</td><td>95C PL B351 387</td><td>P. Villain et al.</td><td>(CHARM II Collab.)</td></tr><tr><td>Also</td><td>PL B343 453</td><td>P. Villain et al.</td><td>(CHARM II Collab.)</td></tr><tr><td>BARANDOV</td><td>93 PL B302 336</td><td>S.A. Baranov et al.</td><td>(JINR, SERP, BUDA)</td></tr><tr><td>BERNARDI</td><td>88 PL B203 332</td><td>G. Bernardi et al.</td><td>(PARIN, CERN, INFN+)</td></tr><tr><td>DORENBOS...</td><td>86 PL 166B 473</td><td>J. Dorenbosch et al.</td><td>(CHARM Collab.)</td></tr><tr><td>COOPER...</td><td>85 PL 160B 207</td><td>A.M. Cooper-Sarkar et al.</td><td>(CERN, LOIC+)</td></tr></tbody></table>
QUARKS

<table><tr><td>u</td><td>1371</td></tr><tr><td>d</td><td>1371</td></tr><tr><td>s</td><td>1371</td></tr><tr><td>c</td><td>1375</td></tr><tr><td>b</td><td>1377</td></tr><tr><td>t</td><td>1379</td></tr><tr><td>b' (Fourth Generation) Quark</td><td>1398</td></tr><tr><td>t' (Fourth Generation) Quark</td><td>1401</td></tr><tr><td>Free Quark Searches</td><td>1403</td></tr></table>

Related Reviews in Volume 1

<table><tr><td>60. Quark masses (rev.)</td><td>834</td></tr><tr><td>61. Top quark (rev.)</td><td>844</td></tr></table>
<figure><img src="image_417.png" /></figure>
# QUARKS

See the related review(s):

Quark Masses

u

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

$$\text{Mass } m = 2.16 \pm 0.07 \text{ MeV}$$

$$\text{Charge} = \frac{2}{3} e$$

$$I_z = +\frac{1}{2}$$

$$m_u/m_d = 0.462 \pm 0.020$$

d

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

$$\text{Mass } m = 4.70 \pm 0.07 \text{ MeV}$$

$$\text{Charge} = -\frac{1}{3} e$$

$$I_z = -\frac{1}{2}$$

$$m_s/m_d = 17-22$$

$$\bar{m} = (m_u + m_d)/2 = 3.49 \pm 0.07 \text{ MeV}$$

s

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

$$\text{Mass } m = 93.5 \pm 0.8 \text{ MeV}$$

$$\text{Charge} = -\frac{1}{3} e$$

$$\text{Strangeness} = -1$$

$$(m_s - (m_u + m_d)/2)/(m_d - m_u) = 27.33^{+0.18}_{-0.14}$$

## 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 $\mu = 2$ GeV. Results quoted in the literature at $\mu = 1$ 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.

<table><thead><tr><th>MS MASS (MeV)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>2.16 ±0.07 (CL = 90%)</td><td></td><td>OUR EVALUATION</td><td>See the ideogram below.</td></tr><tr><td>2.6 ±0.4</td><td></td><td>1 DOMINGUEZ</td><td>19 THEO</td></tr><tr><td>2.130±0.041</td><td></td><td>2 BAZAVOV</td><td>18 LATT</td></tr><tr><td>2.27 ±0.06 ±0.06</td><td></td><td>3 FODOR</td><td>16 LATT</td></tr><tr><td>2.36 ±0.24</td><td></td><td>4 CARRASCO</td><td>14 LATT</td></tr><tr><td>2.24 ±0.10 ±0.34</td><td></td><td>5 BLUM</td><td>10 LATT</td></tr><tr><td>2.01 ±0.14</td><td></td><td>6 MCNEILE</td><td>10 LATT</td></tr></tbody></table>

<table><tbody><tr><td>2.57 ±0.26 ±0.07</td><td>7 AOKI</td><td>12 LATT</td></tr><tr><td>2.15 ±0.03 ±0.10</td><td>8 DURR</td><td>11 LATT</td></tr><tr><td>1.9 ±0.2</td><td>9 BAZAVOV</td><td>10 LATT</td></tr><tr><td>2.01 ±0.14</td><td>6 DAVIES</td><td>10 LATT</td></tr><tr><td>2.9 ±0.2</td><td>10 DOMINGUEZ</td><td>09 THEO</td></tr><tr><td>2.9 ±0.8</td><td>11 DEANDREA</td><td>08 THEO</td></tr><tr><td>3.02 ±0.33</td><td>12 BLUM</td><td>07 LATT</td></tr><tr><td>2.7 ±0.4</td><td>13 JAMIN</td><td>06 THEO</td></tr><tr><td>1.9 ±0.2</td><td>14 MASON</td><td>06 LATT</td></tr><tr><td>2.8 ±0.2</td><td>15 NARISON</td><td>06 THEO</td></tr><tr><td>1.7 ±0.3</td><td>16 AUBIN</td><td>04A LATT</td></tr></tbody></table>

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, $m_s/\bar{m}$ and $m_u/m_d$.

WEIGHTED AVERAGE
2.16±0.04 (Error scaled by 1.2)

<figure><img src="image_418.png" /></figure>

Values above of weighted average, error, and scale factor are based upon the data in this 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.

u-QUARK MASS (MeV)

### d-QUARK MASS

See the comment for the u quark above.

We have normalized the MS masses at a renormalization scale of $\mu = 2$ GeV. Results quoted in the literature at $\mu = 1$ 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.

<table><thead><tr><th>MS MASS (MeV)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>4.70 ±0.07 (CL = 90%)</td><td></td><td>OUR EVALUATION</td><td>See the ideogram below.</td></tr></tbody></table>

<table><tbody><tr><td>5.3 ±0.4</td><td>1 DOMINGUEZ</td><td>19 THEO</td></tr><tr><td>4.675±0.056</td><td>2 BAZAVOV</td><td>18 LATT</td></tr><tr><td>4.67 ±0.06 ±0.06</td><td>3 FODOR</td><td>16 LATT</td></tr><tr><td>5.03 ±0.26</td><td>4 CARRASCO</td><td>14 LATT</td></tr><tr><td>4.65 ±0.15 ±0.32</td><td>5 BLUM</td><td>10 LATT</td></tr><tr><td>4.77 ±0.15</td><td>6 MCNEILE</td><td>10 LATT</td></tr></tbody></table><table><tbody><tr><td>3.68 ±0.29 ±0.10</td><td>7 AOKI</td><td>12 LATT</td></tr><tr><td>4.79 ±0.07 ±0.12</td><td>8 DURR</td><td>11 LATT</td></tr><tr><td>4.6 ±0.3</td><td>9 BAZAVOV</td><td>10 LATT</td></tr><tr><td>4.79 ±0.16</td><td>6 DAVIES</td><td>10 LATT</td></tr><tr><td>5.3 ±0.4</td><td>10 DOMINGUEZ</td><td>09 THEO</td></tr><tr><td>4.7 ±0.8</td><td>11 DEANDREA</td><td>08 THEO</td></tr><tr><td>5.49 ±0.39</td><td>12 BLUM</td><td>07 LATT</td></tr><tr><td>4.8 ±0.5</td><td>13 JAMIN</td><td>06 THEO</td></tr><tr><td>4.4 ±0.3</td><td>14 MASON</td><td>06 LATT</td></tr><tr><td>5.1 ±0.4</td><td>15 NARISON</td><td>06 THEO</td></tr><tr><td>3.9 ±0.5</td><td>16 AUBIN</td><td>04A LATT</td></tr></tbody></table>

<footnote n="1">¹ DOMINGUEZ 19 determine the quark mass from a QCD finite energy sum rule for the divergence of the axial current.</footnote>

<footnote n="2">² BAZAVOV 18 determine the quark masses using a lattice computation with staggered fermions and four active quark flavors.</footnote>

<footnote n="3">³ FODOR 16 is a lattice simulation with $n_f = 2 + 1$ dynamical flavors and includes partially quenched QED effects.</footnote>

<footnote n="4">⁴ CARRASCO 14 is a lattice QCD computation of light quark masses using $2+1+1$ dynamical quarks, with $m_u = m_d \neq m_s \neq m_c$. The u and d quark masses are obtained separately by using the K meson mass splittings and lattice results for the electromagnetic contributions.</footnote>

<footnote n="5">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.</footnote>

<footnote n="6">⁶ DAVIES 10 and MCNEILE 10 determine $\bar{m}_c(\mu)/\bar{m}_s(\mu) = 11.85 \pm 0.16$ using a lattice computation with $n_f = 2 + 1$ dynamical fermions of the pseudoscalar meson masses.</footnote>

<footnote n="7">⁷ AOKI 12 is a lattice computation using $1+1+1$ dynamical quark flavors.</footnote>

<footnote n="8">⁸ DURR 11 determine quark mass from a lattice computation of the meson spectrum using $n_f = 2+1$ dynamical flavors. The lattice simulations were done at the physical quark mass, so that extrapolation in the quark mass was not needed. The individual $m_u, m_d$ values are obtained using the lattice determination of the average mass $m_{ud}$ and of the ratio $m_s/m_{ud}$ and the value of $Q = (m_s^2 - m_{ud}^2)/(m_d^2 - m_u^2)$ as determined from $\eta \to 3\pi$ decays.</footnote>

<footnote n="9">⁹ BAZAVOV 10 is a lattice computation using $2+1$ dynamical quark flavors.</footnote>

<footnote n="10">¹⁰ DOMINGUEZ 09 use QCD finite energy sum rules for the two-point function of the divergence of the axial vector current computed to order $\alpha_s^3$.</footnote>

<footnote n="11">¹¹ DEANDREA 08 determine $m_u-m_d$ from $\eta \to 3\pi 0$, and combine with the PDG 06 lattice average value of $m_u+m_d = 7.6 \pm 1.6$ to determine $m_u$ and $m_d$.</footnote>

<footnote n="12">¹² BLUM 07 determine quark masses from the pseudoscalar meson masses using a QED plus QCD lattice computation with two dynamical quark flavors.</footnote>

<footnote n="13">¹³ JAMIN 06 determine $m_u(2$ GeV) by combining the value of $m_s$ obtained from the spectral function for the scalar $K\pi$ form factor with other determinations of the quark mass ratios.</footnote>

<footnote n="14">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 and d 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.</footnote>

<footnote n="15">¹⁵ NARISON 06 uses sum rules for $e^+e^- \to$ hadrons to order $\alpha_s^3$ to determine $m_s$ combined with other determinations of the quark mass ratios.</footnote>

<footnote n="16">¹⁶ AUBIN 04A employ a partially quenched lattice calculation of the pseudoscalar meson masses.</footnote>

<footnote n="1">¹ DOMINGUEZ 19 determine the quark mass from a QCD finite energy sum rule for the divergence of the axial current.</footnote>

<footnote n="2">² BAZAVOV 18 determine the quark masses using a lattice computation with staggered fermions and four active quark flavors.</footnote>

<footnote n="3">³ FODOR 16 is a lattice simulation with $n_f = 2+1$ dynamical flavors and includes partially quenched QED effects.</footnote>
# Quark Particle Listings

## Light Quarks (u, d, s)

⁴ CARRASCO 14 is a lattice QCD computation of light quark masses using 2 + 1 + 1 dynamical quarks, with $m_u = m_d \neq m_s \neq m_c$. The u and d quark masses are obtained separately by using the K meson mass splittings and lattice results for the electromagnetic 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 $\bar{m}_c(\mu)/\bar{m}_s(\mu) = 11.85 \pm 0.16$ using a lattice computation with $n_f = 2 + 1$ 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, $m_s/\bar{m}$ 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 $n_f = 2 + 1$ dynamical flavors. The lattice simulations were done at the physical quark mass, so that extrapolation in the quark mass was not needed. The individual $m_u, m_d$ values are obtained using the lattice determination of the average mass $m_{ud}$ and of the ratio $m_s/m_{ud}$ and the value of $Q = (m_s^2 - m_{ud}^2)/(m_d^2 - m_u^2)$ as determined from $\eta \to 3\pi$ 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 the divergence of the axial vector current computed to order $\alpha_s^4$.

¹¹ DEANDREA 08 determine $m_u - m_d$ from $\eta \to 3\pi^0$, and combine with the PDG 06 lattice average value of $m_u + m_d = 7.6 \pm 1.6$ to determine $m_u$ and $m_d$.

¹² BLUM 07 determine quark masses from the pseudoscalar meson masses using a QED plus QCD lattice computation with two dynamical quark flavors.

¹³ JAMIN 06 determine $m_d(2 \text{ GeV})$ by combining the value of $m_s$ obtained from the spectral function for the scalar $K\pi$ 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 and d 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 $e^+e^- \to$ hadrons to order $\alpha_s^3$ to determine $m_s$ combined with other determinations of the quark mass ratios.

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

<figure><img src="image_419.png" /><figcaption>WEIGHTED AVERAGE
4.70±0.04 (Error scaled by 1.0)</figcaption></figure>

Values above of weighted average, error, and scale factor are based upon the data in this 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.

$$ \bar{m} = (m_u + m_d)/2 $$

See the comments for the u quark above.

We have normalized the $\overline{MS}$ masses at a renormalization scale of $\mu = 2$ GeV. Results quoted in the literature at $\mu = 1$ 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.

<table><thead><tr><th>MS</th><th>MASS (MeV)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>3.49</td><td>±0.07 (CL = 90%)</td><td>OUR</td><td>EVALUATION</td><td>See the ideogram below.</td></tr></tbody></table>

$$ 3.636 \pm 0.066 \begin{array}{c} +0.060 \\ -0.057 \end{array} $$

$$ 3.54 \pm 0.12 \pm 0.09 $$

$$ 3.9 \pm 0.3 $$

$$ 4.7 \pm 0.8 \begin{array}{c} +0.8 \\ -0.7 \end{array} $$

$$ 3.70 \pm 0.17 $$

$$ 3.45 \pm 0.12 $$

$$ 3.469 \pm 0.047 \pm 0.048 $$

$$ 3.6 \pm 0.2 $$

$$ 3.39 \pm 0.06 $$

1 ALEXANDROU 21 LATT

2 BRUNO 20 LATT

3 DOMINGUEZ 19 THEO

4 YUAN 17 THEO

5 CARRASCO 14 LATT

6 ARTHUR 13 LATT

7 DURR 11 LATT

8 BLOSSIER 10 LATT

9 MCNEILE 10 LATT

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>3.59</td><td>±0.21</td><td>10 AOKI</td><td>11A LATT</td></tr><tr><td>3.40</td><td>±0.07</td><td>9 DAVIES</td><td>10 LATT</td></tr><tr><td>4.1</td><td>±0.2</td><td>11 DOMINGUEZ</td><td>09 THEO</td></tr><tr><td>3.72</td><td>±0.41</td><td>12 ALLTON</td><td>08 LATT</td></tr><tr><td>3.85</td><td>±0.12</td><td>13 BLOSSIER</td><td>08 LATT</td></tr><tr><td>≥ 4.85</td><td>±0.20</td><td>14 DOMINGUEZ</td><td>08B THEO</td></tr><tr><td>3.55</td><td>±0.65</td><td>15 ISHIKAWA</td><td>08 LATT</td></tr><tr><td>-0.28</td><td></td><td>16 NAKAMURA</td><td>08 LATT</td></tr><tr><td>4.026</td><td>±0.048</td><td>17 BLUM</td><td>07 LATT</td></tr><tr><td>4.25</td><td>±0.35</td><td>18 GOCKELER</td><td>06 LATT</td></tr><tr><td>4.08</td><td>±0.25</td><td>19 GOCKELER</td><td>06A LATT</td></tr><tr><td>4.7</td><td>±0.2</td><td>20 MASON</td><td>06 LATT</td></tr><tr><td>3.2</td><td>±0.3</td><td>21 NARISON</td><td>06 THEO</td></tr><tr><td>3.95</td><td>±0.3</td><td>22 AUBIN</td><td>04 LATT</td></tr><tr><td>2.8</td><td>±0.3</td><td>23 AOKI</td><td>03 LATT</td></tr><tr><td>4.29</td><td>±0.14</td><td>24 AOKI</td><td>03B LATT</td></tr><tr><td>3.223</td><td>±0.3</td><td>25 BECIREVIC</td><td>03 LATT</td></tr><tr><td>4.4</td><td>±0.1</td><td>26 CHIU</td><td>03 LATT</td></tr><tr><td>4.1</td><td>±0.3</td><td></td><td></td></tr></tbody></table>

¹ ALEXANDROU 21 determines the quark mass using a lattice calculation of the meson and baryon masses with a twisted mass fermion action. The simulations are carried out using 2+1+1 dynamical quarks with $m_u = m_d \neq m_s \neq m_c$, including gauge ensembles close to the physical pion point.

² BRUNO 20 determines the light quark mass using a lattice calculation with $n_f = 2+1$ flavors of Wilson fermions. The scale has been set from $\bar{\pi}$ and $f_K$. The tuning was done using the masses of the lightest ($\pi$) and strange ($K$) pseudoscalar mesons.

³ DOMINGUEZ 19 determines the quark mass from a QCD finite energy sum rule for the divergence of the axial current.

⁴ YUAN 17 determines $\bar{m}$ using QCD sum rules in the isospin $I=0$ scalar channel. At the end of the "Numerical Results" section of YUAN 17 the authors discuss the significance of 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 $m_u = m_d \neq m_s \neq m_c$. The u and d quark masses are obtained separately by using the K meson mass splittings and lattice results for the electromagnetic contributions.

⁶ ARTHUR 13 is a lattice computation using 2+1 dynamical domain wall fermions. Masses at $\mu = 3$ GeV have been converted to $\mu = 2$ GeV using conversion factors given in their paper.

⁷ DURR 11 determine quark mass from a lattice computation of the meson spectrum using $n_f = 2 + 1$ 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 $n_f = 2$ dynamical twisted-mass Wilson fermions.

⁹ DAVIES 10 and MCNEILE 10 determine $\bar{m}_-(\mu)/\bar{m}_s(\mu) = 11.85 \pm 0.16$ using a lattice computation with $n_f = 2 + 1$ dynamical fermions of the pseudoscalar meson masses. Mass $\bar{m}$ is obtained from this using the value of $m_s$ from ALLISON 08 or MCNEILE 10 and the BAZAVOV 10 values for the light quark mass ratio, $m_s/\bar{m}$.

¹⁰ AOKI 11A determine quark masses from a lattice computation of the hadron spectrum using $n_f = 2 + 1$ dynamical flavors of domain wall fermions.

¹¹ DOMINGUEZ 09 use QCD finite energy sum rules for the two-point function of the divergence of the axial vector current computed to order $\alpha_s^4$.

¹² ALLTON 08 use a lattice computation of the $\pi, K$, and $\Omega$ masses with 2+1 dynamical flavors of domain wall quarks, and non-perturbative renormalization.

¹³ BLOSSIER 10 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 two-point correlator.

¹⁵ ISHIKAWA 08 use a lattice computation of the light meson spectrum with 2+1 dynamical flavors of $\mathcal{O}(a)$ improved Wilson quarks, and one-loop perturbative renormalization.

¹⁶ NAKAMURA 08 do a lattice computation using quenched domain wall fermions and non-perturbative renormalization.

¹⁷ BLUM 07 determine quark masses from the pseudoscalar meson masses using a QED plus QCD lattice computation with two dynamical quark flavors.

¹⁸ GOCKELER 06 use an unquenched lattice computation of the axial Ward Identity with $n_f = 2$ dynamical light quark flavors, and non-perturbative renormalization, to obtain $\bar{m}(2 \text{ GeV}) = 4.08 \pm 0.25 \pm 0.19 \pm 0.23 \text{ MeV}$, 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 $n_f = 2$ 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 and d quarks. Perturbative corrections were included at NNLO order.

²¹ NARISON 06 uses sum rules for $e^+e^- \to$ hadrons to order $\alpha_s^3$ to determine $m_s$ combined 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 $^{+0.046}_{-0.069}$. We changed them to $\pm 0.3$ for calculating 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 $\mathcal{O}(a)$ improved Wilson action.

²⁵ BECIREVIC 03 perform quenched lattice computation using the vector and axial Ward identities. Uses $\mathcal{O}(a)$ 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)

<figure><img src="image_420.png" /></figure>

$$ \bar{m} = (m_u + m_d)/2 \text{ (MeV)} $$

Values above of weighted average, error, and scale factor are based upon the data in this 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.

## $m_u/m_d$ MASS RATIO

<table><thead><tr><th>VALUE</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.462 ±0.020 (CL = 90%)</strong></td><td><strong>OUR EVALUATION</strong></td><td></td><td></td><td>See the ideogram below.</td></tr><tr><td>0.485 ±0.011 ±0.016</td><td>1 FODOR</td><td>16</td><td>LATT</td><td></td></tr><tr><td>0.4482 ±0.0173 ±0.0206</td><td>2 BASAK</td><td>15</td><td>LATT</td><td></td></tr><tr><td>0.470 ±0.056</td><td>3 CARRASCO</td><td>14</td><td>LATT</td><td></td></tr><tr><td>0.42 ±0.01 ±0.04</td><td>4 BAZAVOV</td><td>10</td><td>LATT</td><td></td></tr><tr><td>0.4818 ±0.0096 ±0.0860</td><td>5 BLUM</td><td>10</td><td>LATT</td><td></td></tr><tr><td colspan="5"><strong>• • • We do not use the following data for averages, fits, limits, etc. • • •</strong></td></tr><tr><td>0.698 ±0.051</td><td>6 AOKI</td><td>12</td><td>LATT</td><td></td></tr><tr><td>0.550 ±0.031</td><td>7 BLUM</td><td>07</td><td>LATT</td><td></td></tr><tr><td>0.43 ±0.08</td><td>8 AUBIN</td><td>04A</td><td>LATT</td><td></td></tr><tr><td>0.410 ±0.036</td><td>9 NELSON</td><td>03</td><td>LATT</td><td></td></tr><tr><td>0.553 ±0.043</td><td>10 LEUTWYLER</td><td>96</td><td>THEO</td><td>Compilation</td></tr></tbody></table>

¹ FODOR 16 is a lattice simulation with $n_f = 2 + 1$ dynamical flavors and includes partially quenched 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 $m_u = m_d \neq m_s \neq m_c$. The u and d quark masses are obtained separately by using the K meson mass splittings and lattice results for the electromagnetic 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.

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 QED plus QCD lattice computation with two dynamical quark flavors.

⁸ AUBIN 04A perform three flavor dynamical lattice calculation of pseudoscalar meson masses, with continuum estimate of electromagnetic effects in the kaon masses.

⁹ NELSON 03 computes coefficients in the order $p^4$ chiral Lagrangian using a lattice calculation with three dynamical flavors. The ratio $m_u/m_d$ is obtained by combining this with the chiral perturbation theory computation of the meson masses to order $p^4$.

¹⁰ LEUTWYLER 96 uses a combined fit to $\eta \to 3\pi$ and $\psi' \to J/\psi(\pi,\eta)$ decay rates, and the electromagnetic mass differences of the $\pi$ and $K$.

WEIGHTED AVERAGE
0.462±0.013 (Error scaled by 1.0)

<figure><img src="image_421.png" /></figure>

$$ m_u/m_d \text{ MASS RATIO} $$

Values above of weighted average, error, and scale factor are based upon the data in this 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.

## s-QUARK MASS

See the comment for the u quark above.

We have normalized the MS masses at a renormalization scale of $\mu = 2$ GeV. Results quoted in the literature at $\mu = 1$ GeV have been rescaled by dividing by 1.35.

<table><thead><tr><th>MS MASS (MeV)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>93.5 ± 0.8 (CL = 90%)</strong></td><td><strong>OUR EVALUATION</strong></td><td></td><td>See the ideogram below.</td></tr><tr><td>98.7 ± 2.4 ± 4.0</td><td>1</td><td>ALEXANDROU21</td><td>LATT</td></tr><tr><td>95.7 ± 2.5 ± 2.4</td><td>2</td><td>BRUNO</td><td>LATT</td></tr><tr><td>92.47 ± 0.69</td><td>3</td><td>BAZAVOV</td><td>18 LATT</td></tr><tr><td>93.85 ± 0.75</td><td>4</td><td>LYTLE</td><td>18 LATT</td></tr><tr><td>87.6 ± 6.0</td><td>5</td><td>ANANTHANA.16</td><td>THEO</td></tr><tr><td>99.6 ± 4.3</td><td>6</td><td>CARRASCO</td><td>14 LATT</td></tr><tr><td>94.4 ± 2.3</td><td>7</td><td>ARTHUR</td><td>13 LATT</td></tr><tr><td>94 ± 9</td><td>8</td><td>BODENSTEIN</td><td>13 THEO</td></tr><tr><td>95.5 ± 1.1 ± 1.5</td><td>9</td><td>DURR</td><td>11 LATT</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>93.6 ± 0.8</td><td>10 CHAKRABORTY.15</td><td>LATT</td></tr><tr><td>102 ± 3 ± 1</td><td>11 FRITZSCH</td><td>12 LATT</td></tr><tr><td>96.2 ± 2.7</td><td>12 AOKI</td><td>11A LATT</td></tr><tr><td>95 ± 6</td><td>13 BLOSSIER</td><td>10 LATT</td></tr><tr><td>97.6 ± 2.9 ± 5.5</td><td>14 BLUM</td><td>10 LATT</td></tr><tr><td>92.4 ± 1.5</td><td>15 DAVIES</td><td>10 LATT</td></tr><tr><td>92.2 ± 1.3</td><td>15 MCNEILE</td><td>10 LATT</td></tr><tr><td>107.3 ± 11.7</td><td>16 ALLTON</td><td>08 LATT</td></tr><tr><td>105 ± 3 ± 9</td><td>17 BLOSSIER</td><td>08 LATT</td></tr><tr><td>102 ± 8</td><td>18 DOMINGUEZ</td><td>08A THEO</td></tr><tr><td>90.1 ± 17.2</td><td>19 ISHIKAWA</td><td>08 LATT</td></tr><tr><td>-6.1</td><td>20 NAKAMURA</td><td>08 LATT</td></tr><tr><td>105.6 ± 1.2</td><td>21 BLUM</td><td>07 LATT</td></tr><tr><td>119.5 ± 9.3</td><td>22 CHETYRKIN</td><td>06 THEO</td></tr><tr><td>105 ± 6 ± 7</td><td>23 GOCKELER</td><td>06 LATT</td></tr><tr><td>111 ± 6 ± 10</td><td>24 GOCKELER</td><td>06A LATT</td></tr><tr><td>119 ± 5 ± 8</td><td>25 JAMIN</td><td>06 THEO</td></tr><tr><td>92 ± 9</td><td>26 MASON</td><td>06 LATT</td></tr><tr><td>87 ± 6</td><td>27 NARISON</td><td>06 THEO</td></tr><tr><td>104 ± 15</td><td>28 NARISON</td><td>06 THEO</td></tr><tr><td>≥71 ± 4, ≤151 ± 14</td><td>29 BAIKOV</td><td>05 THEO</td></tr><tr><td>96 ± 5 ± 16</td><td>30 GAMIZ</td><td>05 THEO</td></tr><tr><td>-18</td><td>31 GORBUNOV</td><td>05 THEO</td></tr><tr><td>81 ± 22</td><td>32 NARISON</td><td>05 THEO</td></tr><tr><td>125 ± 28</td><td>33 AUBIN</td><td>04 LATT</td></tr><tr><td>93 ± 32</td><td>34 AOKI</td><td>03 LATT</td></tr><tr><td>76 ± 8</td><td>35 AOKI</td><td>03B LATT</td></tr><tr><td>116 ± 6 ± 0.65</td><td>36 BECIREVIC</td><td>03 LATT</td></tr><tr><td>84.5 ± 12</td><td>37 CHIU</td><td>03 LATT</td></tr><tr><td>-1.7</td><td>38 GAMIZ</td><td>03 THEO</td></tr><tr><td>106 ± 2 ± 8</td><td>39 GAMIZ</td><td>03 THEO</td></tr><tr><td>92 ± 9 ± 16</td><td></td><td></td></tr><tr><td>117 ± 17</td><td></td><td></td></tr><tr><td>103 ± 17</td><td></td><td></td></tr></tbody></table>

¹ ALEXANDROU 21 determines the quark mass using a lattice calculation of the meson and baryon masses with a twisted mass fermion action. The simulations are carried out using 2+1+1 dynamical quarks with $m_u = m_d \neq m_s \neq m_c$, including gauge ensembles close to the physical pion point.

² BRUNO 20 determines the light quark mass using a lattice calculation with $n_f = 2+1$ flavors of Wilson fermions. The scale has been set from $\bar{\eta}_\pi$ and $\bar{\eta}_K$. The tuning was done using the masses of the lightest ($\pi$) and strange ($K$) pseudoscalar mesons.

³ BAZAVOV 18 determines the quark masses using a lattice computation with staggered fermions and four active quark flavors.

⁴ LYTLE 18 combined with CHAKRABORTY 2015 determine $\bar{m}_s$ (3 GeV) = 84.78 ± 0.65 MeV from a lattice simulation with $n_f = 2+1+1$ flavors. They also determine the quoted value $\bar{m}_s$ (2 GeV) for $n_f = 4$ dynamical flavors.

⁵ ANANTHANARAYAN 16 determine $\bar{m}_s$ (2 GeV) = 106.70 ± 9.36 MeV and 74.47 ± 7.77 MeV from fits to ALEPH and OPAL $\tau$ decay data, respectively. We have used the weighted average of the two.

⁶ CARRASCO 14 is a lattice QCD computation of light quark masses using 2 + 1 + 1 dynamical quarks, with $m_u = m_d \neq m_s \neq m_c$. The u and d quark masses are obtained separately by using the K meson mass splittings and lattice results for the electromagnetic contributions.

⁷ ARTHUR 13 is a lattice computation using 2+1 dynamical domain wall fermions. Masses at $\mu = 3$ GeV have been converted to $\mu = 2$ GeV using conversion factors given in their paper.

⁸ BODENSTEIN 13 determines $m_c$ from QCD finite energy sum rules, and the perturbative computation of the pseudoscalar correlator to five-loop order.

⁹ DURR 11 determine quark mass from a lattice computation of the meson spectrum using $n_f = 2 + 1$ 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 $m_c$ and $m_c/m_s$ using 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 determines $m_s$ using a lattice computation with $n_f = 2$ dynamical flavors.

¹² AOKI 11A determine quark masses from a lattice computation of the hadron spectrum using $n_f = 2 + 1$ dynamical flavors of domain wall fermions.

¹³ BLOSSIER 10 determines quark masses from a computation of the hadron spectrum using $n_f = 2$ 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.

15. DAVIES 10 and MCNEILE 10 determine $\bar{m}_c(\mu)/\bar{m}_s(\mu) = 11.85 \pm 0.16$ using a lattice computation with $n_f = 2 + 1$ 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 $\pi$, $K$, and $\Omega$ masses with 2+1 dynamical flavors 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 $\alpha_s^4$.

19. ISHIKAWA 08 use a lattice computation of the light meson spectrum with 2+1 dynamical flavors of $O(a)$ improved Wilson quarks, and one-loop perturbative renormalization.

20. NAKAMURA 08 do a lattice computation using quenched domain wall fermions and non-perturbative renormalization.

21. BLUM 07 determine quark masses from the pseudoscalar meson masses using a QED plus QCD lattice computation with two dynamical quark flavors.

22. CHETYRKIN 06 use QCD sum rules in the pseudoscalar channel to order $\alpha_s^4$.

23. GOCKELER 06 use an unquenched lattice computation of the axial Ward Identity with $n_f = 2$ dynamical light quark flavors, and non-perturbative renormalization, to obtain $\bar{m}_s(2 \text{ GeV}) = 111 \pm 6 \pm 4 \pm 6 \text{ MeV}$, 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.

24. GOCKELER 06A use an unquenched lattice computation of the pseudoscalar meson masses with $n_f = 2$ dynamical light quark flavors, and non-perturbative renormalization.

25. JAMIN 06 determine $\bar{m}_s(2 \text{ GeV})$ from the spectral function for the scalar $K\pi$ form factor.

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 $u$ and $d$ quarks. Perturbative corrections were included at NNLO order.

27. NARISON 06 uses sum rules for $e^+e^- \to$ hadrons to order $\alpha_s^3$.

28. NARISON 06 obtains the quoted range from positivity of the spectral functions.

29. BAIKOV 05 determines $\bar{m}_s(M_\tau) = 100 \pm 5 \pm 17$ from sum rules using the strange spectral function in $\tau$ decay. The computations were done to order $\alpha_s^3$, with an estimate of the $\alpha_s^4$ terms. We have converted the result to $\mu = 2 \text{ GeV}$.

30. GAMIZ 05 determines $\bar{m}_s(2 \text{ GeV})$ from sum rules using the strange spectral function in $\tau$ decay. The computations were done to order $\alpha_s^2$, with an estimate of the $\alpha_s^3$ terms.

31. GORBUNOV 05 use hadronic tau decays to N3LO, including power corrections.

32. NARISON 05 determines $\bar{m}_s(2 \text{ GeV})$ from sum rules using the strange spectral function in $\tau$ decay. The computations were done to order $\alpha_s^2$.

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. Determines $m_s = 113.8 \pm 2.3 \pm 5.8 \pm 0$ using $K$ mass as input and $m_s = 142.3 \pm 5.8 \pm 22 \pm 0$ using $\phi$ 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 Ward identities. Uses $O(a)$ improved Wilson action and nonperturbative renormalization. They also quote $\bar{m}/m_s = 24.3 \pm 0.2 \pm 0.6$.

37. CHIU 03 determines quark masses from the pion and kaon masses using a lattice simulation with a chiral fermion action in quenched approximation.

38. GAMIZ 03 determines $m_s$ from SU(3) breaking in the $\tau$ hadronic width. The value of $V_{US}$ is chosen to satisfy CKM unitarity.

39. GAMIZ 03 determines $m_s$ from SU(3) breaking in the $\tau$ hadronic width. The value of $V_{US}$ is taken from the PDG.

WEIGHTED AVERAGE
93.5±0.5 (Error scaled by 1.1)

<figure><img src="image_422.png" /></figure>

## OTHER LIGHT QUARK MASS RATIOS

### $m_s/m_d$ MASS RATIO

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="4"><strong>17-22 OUR EVALUATION</strong></td></tr><tr><td>20.0</td><td>1 GAO</td><td>97</td><td>THEO</td></tr><tr><td>18.9±0.8</td><td>2 LEUTWYLER</td><td>96</td><td>THEO</td></tr><tr><td>21</td><td>3 DONOGHUE</td><td>92</td><td>THEO</td></tr><tr><td>18</td><td>4 GERARD</td><td>90</td><td>THEO</td></tr><tr><td>18 to 23</td><td>5 LEUTWYLER</td><td>90B</td><td>THEO</td></tr></tbody></table>

1. GAO 97 uses electromagnetic mass splittings of light mesons.

2. LEUTWYLER 96 uses a combined fit to $\eta \to 3\pi$ and $\psi' \to J/\psi(\pi,\eta)$ decay rates, and the electromagnetic mass differences of the $\pi$ and $K$.

3. DONOGHUE 92 result is from a combined analysis of meson masses, $\eta \to 3\pi$ using second-order chiral perturbation theory including nonanalytic terms, and $(\psi(25) \to J/\psi(15)\pi)/(\psi(25) \to J/\psi(15)\eta)$.

4. GERARD 90 uses large $N$ and $\eta-\eta'$ 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 $L_7$.

### $m_s/\bar{m}$ MASS RATIO

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td colspan="3"><strong>27.33<sup>+0.18</sup><sub>-0.14</sub> (CL = 90%) OUR EVALUATION</strong> See the ideogram below.</td></tr></tbody></table>

<table><tbody><tr><td>27.17±0.32<sup>+0.56</sup><sub>-0.38</sub></td><td>1 ALEXANDROU21</td><td>LATT</td></tr><tr><td>27.0±1.0 ±0.4</td><td>2 BRUNO</td><td>20 LATT</td></tr><tr><td>27.35±0.05<sup>+0.10</sup><sub>-0.07</sub></td><td>3 BAZAVOV</td><td>14A LATT</td></tr><tr><td>26.66±0.32</td><td>4 CARRASCO</td><td>14 LATT</td></tr><tr><td>27.36±0.54</td><td>5 ARTHUR</td><td>13 LATT</td></tr><tr><td>27.53±0.20±0.08</td><td>6 DURR</td><td>11 LATT</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>26.8 ±1.4</td><td>7 AOKI</td><td>11A LATT</td></tr><tr><td>27.3 ±0.9</td><td>8 BLOSSIER</td><td>10 LATT</td></tr><tr><td>28.8 ±1.65</td><td>9 ALLTON</td><td>08 LATT</td></tr><tr><td>27.3 ±0.3 ±1.2</td><td>10 BLOSSIER</td><td>08 LATT</td></tr><tr><td>23.5 ±1.5</td><td>11 OLLER</td><td>07A THEO</td></tr><tr><td>27.4 ±0.4</td><td>12 AUBIN</td><td>04 LATT</td></tr></tbody></table>

1. ALEXANDROU 21 determines the quark mass using a lattice calculation of the meson and baryon masses with a twisted mass fermion action. The simulations are carried out using $2+1$ dynamical quarks with $m_u = m_d \neq m_s \neq m_c$, including gauge ensembles close to the physical pion point.

2. BRUNO 20 determines the light quark mass using a lattice calculation with $n_f = 2+1$ flavors of Wilson fermions. The scale has been set from $\bar{\pi}$ and $\bar{f}_c$. The tuning was done using the masses of the lightest $(\pi)$ 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 $2+1$ dynamical quarks, with $m_u = m_d \neq m_s \neq m_c$. 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 determines quark mass from a lattice computation of the meson spectrum using $n_f = 2+1$ 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 determines quark masses from a lattice computation of the hadron spectrum using $n_f = 2+1$ dynamical flavors of domain wall fermions.

8. BLOSSIER 10 determines quark masses from a computation of the hadron spectrum using $n_f=2$ dynamical twisted-mass Wilson fermions.

9. ALLTON 08 use a lattice computation of the $\pi$, $K$, and $\Omega$ 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 $p^4$.

12. Three flavor dynamical lattice calculation of pseudoscalar meson masses.

WEIGHTED AVERAGE
27.33+0.11-0.09 (Error scaled by 1.2)

<figure><img src="image_423.png" /></figure>

(Confidence Level = 0.251)

$m_s/\bar{m}$ MASS RATIO
Q MASS RATIO

$$Q \equiv \sqrt{(m^2_s - m^2)/((m^2_d - m^2_u))}; \quad \bar{m} \equiv (m_u + m_d)/2$$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>22.1 ± 0.7</td><td>1 COLANGELO 18</td><td>THEO</td></tr><tr><td>22.0 ± 0.7</td><td>2 COLANGELO 17</td><td>THEO</td></tr><tr><td>21.6 ± 1.1</td><td>3 GUO</td><td>THEO</td></tr><tr><td>23.4 ± 0.4 ± 0.5</td><td>4 FODOR 16</td><td>LATT</td></tr><tr><td>21.4 ± 0.4</td><td>5 GUO</td><td>15F THEO</td></tr><tr><td>22.8 ± 0.4</td><td>6 MARTEMYA... 05</td><td>THEO</td></tr><tr><td>22.7 ± 0.8</td><td>7 ANISOVICH 96</td><td>THEO</td></tr></tbody></table>

1. COLANGELO 18 obtain Q from a dispersive analysis of $\eta \to 3\pi$ decay.

2. COLANGELO 17 obtain Q from a dispersive analysis of KLOE collaboration data on $\eta \to \pi^+\pi^-\pi^0$ decays and chiral perturbation theory input.

3. GUO 17 determine Q from a dispersive model fit to KLOE and WASA-at-COSY data on $\eta \to \pi^+\pi^-\pi^0$ decay and matching to chiral perturbation theory.

4. FODOR 16 is a lattice simulation with $n_f = 2 + 1$ dynamical flavors and includes partially quenched QED effects.

5. GUO 15r determine Q from a Khuri-Treiman analysis of $\eta \to 3\pi$ decays.

6. MARTEMYANOV 05 determine Q from $\eta \to 3\pi$ decay.

7. ANISOVICH 96 find Q from $\eta \to \pi^+\pi^-\pi^0$ decay using dispersion relations and chiral perturbation theory.

LIGHT QUARKS (u, d, s) REFERENCES

<table><tr><td>BAZANDROU 21</td><td>PR D104 074515</td><td>C. Alexandrou et al. (ETM Collab.)</td></tr><tr><td>BRUNO 20</td><td>EPJ C80 169</td><td>M. Bruno et al. (ALPHA Collab.)</td></tr><tr><td>DOMINGUEZ 19</td><td>JHEP 1902 057</td><td>C.A. Dominguez, A. Mes, K. Schilcher (CAPE, MAINZ)</td></tr><tr><td>BAZAVOV 18</td><td>PR D98 054517</td><td>A. Bazavov et al. (Fermilab Lattice, MILC, TUMQCD)</td></tr><tr><td>COLANGELO 18</td><td>EPJ C78 947</td><td>G. Colangelo et al. (HPQCD Collab.)</td></tr><tr><td>LYTLE 18</td><td>PR D98 014513</td><td>A.T. Lytle et al. (HPQCD Collab.)</td></tr><tr><td>COLANGELO 17</td><td>PRL 118 022001</td><td>G. Colangelo et al. (BERN, IND, JLAB)</td></tr><tr><td>GUO 17</td><td>PL B771 497</td><td>P. Guo et al.</td></tr><tr><td>YUAN 17</td><td>PR D96 014034</td><td>J-M. Yuan et al.</td></tr><tr><td>ANANTHANA... 16</td><td>PR D94 116014</td><td>A. Ananthanarayan, D. Das (BANG, AHMED)</td></tr><tr><td>FODOR 16</td><td>PRL 101 082001</td><td>Z. Fodor et al. (BMW Collab.)</td></tr><tr><td>BASAK 15</td><td>JPCS 640 012052</td><td>S. Basak et al. (MILC Collab.)</td></tr><tr><td>CHAKRABORT... 15</td><td>PR D91 054508</td><td>B. Chakraborty et al. (HPQCD Collab.)</td></tr><tr><td>GUO 15F</td><td>PR D92 054016</td><td>P. Guo et al. (Fermi-LAT and MILC Collabs.)</td></tr><tr><td>BAZAVOV 14A</td><td>PR D90 074509</td><td>N. Carrasco et al. (European Twisted Mass Collab.)</td></tr><tr><td>CARRASCO 14</td><td>NP B887 19</td><td>R. Arthur et al. (RBC and UKQCD Collabs.)</td></tr><tr><td>ARTHUR 13</td><td>PR D87 094514</td><td>S. Bodensteini, C.A. Dominguez, K. Schilcher</td></tr><tr><td>BODENSTEIN 13</td><td>JHEP 1307 138</td><td>S. Aoki et al. (PACS-CS Collab.)</td></tr><tr><td>AOKI 12</td><td>PR D86 034507</td><td>P. Fritzsch et al. (ALPHA Collab.)</td></tr><tr><td>FRITZSCH 12</td><td>NP B865 397</td><td>Y. Aoki et al. (RBC-UKQCD Collab.)</td></tr><tr><td>AOKI 11A</td><td>PR D83 074508</td><td>S. Durr et al. (BMW Collab.)</td></tr><tr><td>DURR 11</td><td>PL B701 265</td><td>A. Bazavov et al. (MILC Collab.)</td></tr><tr><td>BAZAVOV 10</td><td>RMP 82 1349</td><td>B. Blossier et al. (ETM Collab.)</td></tr><tr><td>BLOSSIER 10</td><td>PR D82 114513</td><td>T. Blum et al.</td></tr><tr><td>BLUM 10</td><td>PR D82 094508</td><td>C.T.H. Davies et al. (HPQCD Collab.)</td></tr><tr><td>DAVIES 10</td><td>PR D104 132003</td><td>C. McNeile et al. (HPQCD Collab.)</td></tr><tr><td>MCNEILE 10</td><td>PR D82 034512</td><td>C.A. Dominguez et al. (HPQCD Collab.)</td></tr><tr><td>DOMINGUEZ 09</td><td>PR D79 014009</td><td>I. Allison et al. (HPQCD Collab.)</td></tr><tr><td>ALLISON 08</td><td>PR D78 054513</td><td>C. Allton et al. (RBC and UKQCD Collabs.)</td></tr><tr><td>ALLTON 08</td><td>PR D78 114509</td><td>A. Aoki et al. (ETM Collab.)</td></tr><tr><td>BLOSSIER 08</td><td>JHEP 0804 020</td><td>B. Blossier et al. (HPQCD Collab.)</td></tr><tr><td>DEANDREA 08</td><td>PR D78 034032</td><td>A. Deandrea, A. Nehme, P. Talavara</td></tr><tr><td>DOMINGUEZ 08A</td><td>JHEP 0805 020</td><td>C.A. Dominguez et al. (HPQCD Collab.)</td></tr><tr><td>DOMINGUEZ... 08B</td><td>PL B660 49</td><td>A. Dominguez-Clarimon, E. de Rafael, J. Taron</td></tr><tr><td>ISHIKAWA 08</td><td>PR D78 011502</td><td>T. Ishikawa et al. (CP-PACS and JLQCD Collabs.)</td></tr><tr><td>NAKAMURA 08</td><td>PR D78 034502</td><td>Y. Nakamura et al. (CP-PACS Collab.)</td></tr><tr><td>URUM 07</td><td>PR D76 114508</td><td>T. Blum et al. (RBC Collab.)</td></tr><tr><td>OLLER 07A</td><td>EPJ A34 371</td><td>J.A. Oller, L. Roca</td></tr><tr><td>CHETYRKIN 06</td><td>EPJ C46 721</td><td>K.G. Chetyrkin, A. Khodjamirian</td></tr><tr><td>GOCKELER 06</td><td>PR D73 054508</td><td>M. Gockeler et al. (QCDSF and UKQCD Collabs)</td></tr><tr><td>GOCKELER 06A</td><td>PL B639 307</td><td>M. Gockeler et al. (QCDSF and UKQCD Collabs)</td></tr><tr><td>JAMIN 06</td><td>PR D74 074009</td><td>M. Jamin, J.A. Oller, A. Pich</td></tr><tr><td>MASON 06</td><td>PR D73 114501</td><td>Q. Mason et al. (HPQCD Collab.)</td></tr><tr><td>NARISON 06</td><td>PR D74 034013</td><td>S. Narison</td></tr><tr><td>PDG 06</td><td>JP G33 1</td><td>W.-M. Yao et al. (PDG Collab.)</td></tr><tr><td>BAIKOV 05</td><td>PRL 95 012003</td><td>P.A. Balkov, K.G. Chetyrkin, J.H. Kuhn</td></tr><tr><td>GAMIZ 05</td><td>PRL 94 011803</td><td>E. Gamiz et al. (HPQCD Collab.)</td></tr><tr><td>GORBUNOV 05</td><td>PR D71 013002</td><td>D.S. Gorbunov, A.A. Pivovarov</td></tr><tr><td>MARTEMYA... 05</td><td>PR D71 017501</td><td>B.V. Martemyanov, V.S. Sopov</td></tr><tr><td>NARISON 05</td><td>PL B626 101</td><td>S. Narison</td></tr><tr><td>AUBIN 04</td><td>PR D70 031504</td><td>C. Aubin et al. (HPQCD, MILC, UKQCD Collabs.)</td></tr><tr><td>AUBIN 04A</td><td>PR D70 114501</td><td>C. Aubin et al. (MILC Collab.)</td></tr><tr><td>AOKI 03</td><td>PR D67 034503</td><td>S. Aoki et al. (CP-PACS Collab.)</td></tr><tr><td>AOKI 03B</td><td>PR D68 054502</td><td>S. Aoki et al. (CP-PACS Collab.)</td></tr><tr><td>BECIREVIC 03</td><td>PL B558 69</td><td>D. Becirevic, V. Lubic, C. Tarantino</td></tr><tr><td>CHIU 03</td><td>NP B673 217</td><td>T.-W. Chiu, T.-H. Hsieh</td></tr><tr><td>GAMIZ 03</td><td>JHEP 0301 060</td><td>E. Gamiz et al. (HPQCD Collab.)</td></tr><tr><td>NEISON 03</td><td>PRL 90 021601</td><td>D. Nelson, G.T. Fleming, G.W. Kilkup</td></tr><tr><td>GAON 97</td><td>PR D56 4115</td><td>D.-N. Gao, B.A. Li, M.-L. Yan</td></tr><tr><td>ANISOVICH 96</td><td>PL B375 335</td><td>A.V. Anisovich, H. Leutwyler</td></tr><tr><td>LEUTWYLER 96</td><td>PL B378 313</td><td>H. Leutwyler</td></tr><tr><td>DONOGHUE 92</td><td>PRL 69 3444</td><td>J.F. Donoghue, B.R. Holstein, D. Wyler (MASA+)</td></tr><tr><td>GERARD 90</td><td>MPL A5 391</td><td>J.M. Gerard (MPIM)</td></tr><tr><td>LEUTWYLER 90B</td><td>NP B337 108</td><td>H. Leutwyler (BERN)</td></tr></table>

0.38 ± 0.03. The value 1.2730 ± 0.0046 GeV for the $\overline{\text{MS}}$ 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.

<table><tr><td>1.316 ± 0.022</td><td>+0.019</td><td>1 ALEXANDROU21</td><td>LATT</td></tr><tr><td>1.296 ± 0.019</td><td>-0.010</td><td>2 HEITGER 21</td><td>LATT</td></tr><tr><td>1.2723 ± 0.0078</td><td></td><td>3 HATTON 20</td><td>LATT</td></tr><tr><td>1.266 ± 0.006</td><td></td><td>4 NARISON 20</td><td>THEO</td></tr><tr><td>1.290 ± 0.077</td><td>-0.053</td><td>5 ABRAMOWICZ18</td><td>HERA</td></tr><tr><td>1.273 ± 0.010</td><td></td><td>6 BAZAVOV 18</td><td>LATT</td></tr><tr><td>1.2737 ± 0.0077</td><td></td><td>7 LYTLIE 18</td><td>LATT</td></tr><tr><td>1.223 ± 0.033</td><td></td><td>8 PESET 18</td><td>THEO</td></tr><tr><td>1.279 ± 0.008</td><td></td><td>9 CHETYRKIN 17</td><td>THEO</td></tr><tr><td>1.272 ± 0.008</td><td></td><td>10 ERLER 17</td><td>THEO</td></tr><tr><td>1.246 ± 0.023</td><td></td><td>11 KIYO 16</td><td>THEO</td></tr><tr><td>1.288 ± 0.020</td><td></td><td>12 DEHNADI 15</td><td>THEO</td></tr><tr><td>1.348 ± 0.046</td><td></td><td>13 CARRASCO 14</td><td>LATT</td></tr><tr><td>1.24 ± 0.03</td><td>+0.03</td><td>14 ALEKHIN 13</td><td>THEO</td></tr><tr><td>1.159 ± 0.075</td><td>-0.07</td><td>15 SAMOYLOV 13</td><td>NOMD</td></tr><tr><td>1.278 ± 0.009</td><td></td><td>16 BODENSTEIN 11</td><td>THEO</td></tr><tr><td>1.28 ± 0.07</td><td>-0.06</td><td>17 LASCHKA 11</td><td>THEO</td></tr><tr><td>1.196 ± 0.059</td><td>± 0.050</td><td>18 AUBERT 10A</td><td>BABR</td></tr><tr><td>1.25 ± 0.04</td><td></td><td>19 SIGNER 09</td><td>THEO</td></tr></table>

0.00 We do not use the following data for averages, fits, limits, etc. 0.00

<table><tr><td>1.263 ± 0.014</td><td></td><td>20 NARISON 18A</td><td>THEO</td></tr><tr><td>1.264 ± 0.006</td><td></td><td>21 NARISON 18B</td><td>THEO</td></tr><tr><td>1.335 ± 0.043</td><td>+0.040</td><td>22 BERTONE 16</td><td>THEO</td></tr><tr><td>1.2715 ± 0.0095</td><td>-0.011</td><td>23 CHAKRABORT... 15</td><td>LATT</td></tr><tr><td>1.26 ± 0.05</td><td>± 0.04</td><td>24 ABRAMOWICZ13C</td><td>COMB</td></tr><tr><td>1.282 ± 0.011</td><td>± 0.022</td><td>25 DEHNADI 13</td><td>THEO</td></tr><tr><td>1.286 ± 0.066</td><td></td><td>26 NARISON 13</td><td>THEO</td></tr><tr><td>1.36 ± 0.04</td><td>± 0.10</td><td>27 ALEKHIN 12</td><td>THEO</td></tr><tr><td>1.261 ± 0.016</td><td></td><td>28 NARISON 12A</td><td>THEO</td></tr><tr><td>1.01 ± 0.09</td><td>± 0.03</td><td>29 ALEKHIN 11</td><td>THEO</td></tr><tr><td>1.28 ± 0.04</td><td></td><td>30 BLOSSIER 10</td><td>LATT</td></tr><tr><td>1.299 ± 0.026</td><td></td><td>31 BODENSTEIN 10</td><td>THEO</td></tr><tr><td>1.273 ± 0.006</td><td></td><td>32 MCNEILE 10</td><td>LATT</td></tr><tr><td>1.261 ± 0.018</td><td></td><td>33 NARISON 10</td><td>THEO</td></tr><tr><td>1.279 ± 0.013</td><td></td><td>34 CHETYRKIN 09</td><td>THEO</td></tr><tr><td>1.268 ± 0.009</td><td></td><td>35 ALLISON 08</td><td>LATT</td></tr><tr><td>1.286 ± 0.013</td><td></td><td>36 KUHN 07</td><td>THEO</td></tr><tr><td>1.295 ± 0.015</td><td></td><td>37 BOUGHEZAL 06</td><td>THEO</td></tr><tr><td>1.24 ± 0.09</td><td></td><td>38 BUCHMUEL... 06</td><td>THEO</td></tr><tr><td>1.224 ± 0.017</td><td>± 0.054</td><td>39 HOANG 06</td><td>THEO</td></tr><tr><td>1.33 ± 0.10</td><td></td><td>40 AUBERT 04X</td><td>THEO</td></tr><tr><td>1.29 ± 0.07</td><td></td><td>41 ONG 04</td><td>THEO</td></tr><tr><td>1.319 ± 0.028</td><td></td><td>42 DEDIVITIIS 03</td><td>LATT</td></tr><tr><td>1.19 ± 0.11</td><td></td><td>43 EIDEMULLER 03</td><td>THEO</td></tr><tr><td>1.289 ± 0.043</td><td></td><td>44 ERLER 03</td><td>THEO</td></tr><tr><td>1.26 ± 0.02</td><td></td><td>45 ZYABLYUK 03</td><td>THEO</td></tr></table>

1. ALEXANDROU 21 determines the quark mass using a lattice calculation of the meson and baryon masses with a twisted mass fermion action. We have converted $\bar{m}_c(3 \text{ GeV}) = 1.036 \pm 0.017^{+0.015}_{-0.008}$ to $\bar{m}_c(\bar{m}_c)$. The simulations are carried out using $2+1+1$ dynamical quarks with $m_u = m_d \neq m_s \neq m_c$, including gauge ensembles close to the physical pion point.

2. HEITGER 21 determines the charm quark mass using a $n_f = 2+1$ flavor lattice QCD simulation with non-perturbatively O(a) improved Wilson fermions. They also determine $\bar{m}_c(3 \text{ GeV}) = 1.007 \pm 0.016 \text{ GeV}$.

3. HATTON 20 determines the quark mass with a lattice QCD + quenched QED simulation using the HISQ action and including $n_f = 2+1+1$ flavors of sea quarks. $m_c$ is tuned from the $J/\psi$ meson mass giving $\bar{m}_c(3 \text{ GeV}) = 0.9841 \pm 0.0051 \text{ GeV}$.

4. NARISON 20 determines the quark mass using QCD Laplace sum rules from the $B_c$ mass, combined with previous determinations of the QCD condensates and c and b masses.

5. ABRAMOWICZ 18 determine $\bar{m}_c(\bar{m}_c) = 1.290^{+0.046}_{-0.041} \pm 0.062 \pm 0.003$ from the production of c quarks in $e\bar{p}$ collisions at HERA using combined H1 and ZEUS data. The experimental/fitting errors, and those from modeling and parameterization have been combined in quadrature.

6. BAZAVOV 18 determines the quark masses using a lattice computation with staggered fermions and four active quark flavors.

7. LYTLE 18 combined with CHAKRABORTY 15 determine $\bar{m}_c(3 \text{ GeV}) = 0.9874(48) \text{ GeV}$ from a lattice simulation with $n_f = 2+1+1$ flavors. They also determine the quoted value $\bar{m}_c(\bar{m}_c)$ for $n_f = 4$ dynamical flavors.

8. PESET 18 determines $\bar{m}_c(\bar{m}_c)$ and $\bar{m}_b(\bar{m}_b)$ using an N3LO calculation of the $\eta_c$, $\eta_b$ and $B_c$ masses.

9. CHETYRKIN 17 determine $\bar{m}_c(\mu = 3 \text{ GeV}) = 0.993 \pm 0.008 \text{ GeV}$ and $\bar{m}_c(\bar{m}_c)$ from a four-loop sum-rule computation of the cross-section for $e^+e^- \to$ hadrons in the charm threshold region.

10. ERLER 17 determine $\bar{m}_c(\bar{m}_c) = 1.272 \pm 0.008 \text{ GeV}$ from a three-loop QCD sum-rule computation of the vector current correlator. This result is for fixed $\alpha_s(M_Z) = 0.1182$. Including an $\alpha_s$ uncertainty of $\pm 0.0016$, the charm mass error increases from 8 to 9 MeV.

11. KIYO 16 determine $\bar{m}_c(\bar{m}_c)$ from the $J/\psi(1S)$ mass at order $\alpha_s^3$ (N3LO).

C

$$I(J^P) = 0 \quad (1^+$$

$$\text{Charge} = \frac{2}{3} e$$

$$\text{Charm} = +1$$

c-QUARK MASS

The c-quark mass corresponds to the “running” mass $m_c$ ($\mu = m_c$) in the $\overline{\text{MS}}$ scheme. We have converted masses in other schemes to the $\overline{\text{MS}}$ scheme using two-loop QCD perturbation theory with $\alpha_s(\mu = m_c) =$
¹²DEHNADI 15 determines $\overline{m}_c(\overline{m}_c)$ using sum rules for $e^+e^- \to$ hadrons at order $\alpha_s^3$ (N3LO), and fitting to both experimental data and lattice results.

¹³CARRASCO 14 is a lattice QCD computation of light quark masses using $2+1+1$ dynamical quarks, with $m_u = m_d \neq m_s \neq m_c$. The u and d quark masses are obtained separately by using the K meson mass splittings and lattice results for the electromagnetic contributions.

¹⁴ALEKHIN 13 determines $m_c$ from charm production in deep inelastic scattering at HERA using approximate NNLO QCD.

¹⁵SAMOYLOV 13 determines $m_c$ from a study of charm dimuon production in neutrino-iron scattering using the NLO QCD result for the charm quark production cross section.

¹⁶BODENSTEIN 11 determines $\overline{m}_c(3 \text{ GeV}) = 0.987 \pm 0.009 \text{ GeV}$ and $\overline{m}_c(\overline{m}_c) = 1.278 \pm 0.009 \text{ GeV}$ using QCD sum rules for the charm quark vector current correlator.

¹⁷LASCHKA 11 determines the c mass from the charmonium spectrum. The theoretical computation uses the heavy $Q\bar{Q}$ potential to order $1/m_Q$ obtained by matching the short-distance perturbative result onto lattice QCD result at larger scales.

¹⁸AUBERT 10a determines 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).

¹⁹SIGNER 09 determines the c-quark mass using non-relativistic sum rules to analyze the $e^+e^- \to c\bar{c}$ cross-section near threshold. Also determine the PS mass $m_{PS}(\mu_F = 0.7 \text{ GeV}) = 1.50 \pm 0.04 \text{ GeV}$.

²⁰NARISON 18a determines simultaneously $\overline{m}_c(\overline{m}_c)$ and the 4-dimension gluon condensate using QCD exponential sum rules and their ratios evaluated at the optimal scale $\mu = 2.85 \text{ GeV}$ at N2LO-N3LO of perturbative QCD and including condensates up to dimension 6-8 in the (axial-)vector and (pseudo-)scalar charmonium channels.

²¹NARISON 18b determines $\overline{m}_c(\overline{m}_c)$ using QCD vector moment sum rules and their ratios at N2LO-N3LO of perturbative QCD and including condensates up to dimension 8.

²²BERTERT 16 determines $\overline{m}_c(\overline{m}_c)$ from HERA deep inelastic scattering data using the FONLL scheme. Also determine $\overline{m}_c(\overline{m}_c) = 1.318 \pm 0.054^{+0.490}_{-0.022}$ using the fixed flavor number scheme.

²³CHAKRABORTY 15 is a lattice QCD computation using $2+1+1$ dynamical flavors. Moments of pseudoscalar current-current correlators are matched to $\alpha_s^3$-accurate QCD perturbation theory with the $\eta_c$ meson mass tuned to experiment.

²⁴ABRAMOWICZ 13c determines $m_c$ from charm production in deep inelastic ep scattering, using the QCD prediction at NLO order. The uncertainties from model and parametrization assumptions, and the value of $\alpha_s$, of $\pm 0.03, \pm 0.02$, and $\pm 0.02$ respectively, have been combined in quadrature.

²⁵DEHNADI 13 determines $m_c$ using QCD sum rules for the charmonium spectrum and charm continuum to order $\alpha_s^3$ (N3LO). The statistical and systematic experimental errors of $\pm 0.006$ and $\pm 0.009$ have been combined in quadrature. The theoretical uncertainties $\pm 0.019$ from truncation of the perturbation series, $\pm 0.010$ from $\alpha_s$, and $\pm 0.002$ from the gluon condensate have been combined in quadrature.

²⁶NARISON 13 determines $m_c$ using QCD spectral sum rules to order $\alpha_s^2$ (NNLO) and including condensates up to dimension 6.

²⁷ALEKHIN 12 determines $m_c$ from heavy quark production in deep inelastic scattering at HERA using approximate NNLO QCD.

²⁸NARISON 12A determines $m_c$ using sum rules for the vector current correlator to order $\alpha_s^3$, including the effect of gluon condensates up to dimension eight.

²⁹ALEKHIN 11 determines $m_c$ from heavy quark production in deep inelastic scattering using fixed target and HERA data, and approximate NNLO QCD.

³⁰BLOSSIER 10 determines quark masses from a computation of the hadron spectrum using $n_f = 2$ dynamical twisted-mass Wilson fermions.

³¹BODENSTEIN 10 determines $\overline{m}_c(3 \text{ GeV}) = 1.008 \pm 0.026 \text{ GeV}$ using finite energy sum rules for the vector current correlator. The authors have converted this to $\overline{m}_c(\overline{m}_c)$ using $\alpha_s(M_Z) = 0.1189 \pm 0.0002$.

³²MCNEILE 10 determines $m_c$ by comparing the order $\alpha_s^3$ perturbative results for the pseudo-scalar current to lattice simulations with $n_f = 2+1$ sea-quarks by the HPQCD collaboration.

³³NARISON 10 determines $m_c$ from ratios of moments of vector current correlators computed to order $\alpha_s^3$ and including the dimension-six gluon condensate.

³⁴CHETYRKIN 09 determines $m_c$ and $m_b$ from the $e^+e^- \to Q\bar{Q}$ cross-section and sum rules, using an order $\alpha_s^3$ computation of the heavy quark vacuum polarization. They also determine $m_c(3 \text{ GeV}) = 0.986 \pm 0.013 \text{ GeV}$.

³⁵ALLISON 08 determines $m_c$ by comparing four-loop perturbative results for the pseudoscalar current correlator to lattice simulations by the HPQCD collaboration. The result has been updated in MCNEILE 10.

³⁶KUHN 07 determines $\overline{m}_c(\mu = 3 \text{ GeV}) = 0.986 \pm 0.013 \text{ GeV}$ and $\overline{m}_c(\overline{m}_c)$ from a four-loop sum-rule computation of the cross-section for $e^+e^- \to$ hadrons in the charm threshold region.

³⁷BOUGHEZAL 06 result comes from the first moment of the hadronic production cross-section to order $\alpha_s^2$.

³⁸BUCHMUELLER 06 determines $m_b$ and $m_c$ by a global fit to inclusive B decay spectra.

³⁹HOANG 06 determines $\overline{m}_c(\overline{m}_c)$ from a global fit to inclusive B decay data. The B decay distributions were computed to order $\alpha_s^2\rho_0$, and the conversion between different $m_c$ mass schemes to order $\alpha_s^3$.

⁴⁰AUBERT 04x obtain $m_c$ from a fit to the hadron mass and lepton energy distributions in semileptonic B decay. The paper quotes values in the kinetic scheme. The MS value has been provided by the BABAR collaboration.

⁴¹HOANG 04 determines $\overline{m}_c(\overline{m}_c)$ from moments at order $\alpha_s^2$ of the charm production cross-section in $e^+e^- \to$ annihilation.

⁴²DEDIVITIIS 03 use a quenched lattice computation of heavy-heavy and heavy-light meson masses.

⁴³EIDEMULLER 03 determines $m_b$ and $m_c$ using QCD sum rules.

⁴⁴ERLER 03 determines $m_b$ and $m_c$ using QCD sum rules. Includes recent BES data.

⁴⁵ZYABLYUK 03 determines $m_c$ by using QCD sum rules in the pseudoscalar channel and comparing with the $\eta_c$ mass.

<figure><img src="image_424.png" /><figcaption>c-QUARK MASS (GeV)</figcaption></figure>

$m_c/m_s$ MASS RATIO

The ratio is that of the $\overline{m}_s$ 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.

<table><tr><td>11.48 ±0.12</td><td>+0.25</td><td>1</td><td>ALEXANDROU21</td><td>LATT</td></tr><tr><td>11.783±0.025</td><td>-0.19</td><td>2</td><td>BAZAVOV</td><td>18 LATT</td></tr><tr><td>11.652±0.065</td><td></td><td>3</td><td>CHAKRABOR...15</td><td>LATT</td></tr><tr><td>11.62 ±0.16</td><td></td><td>4</td><td>CARRASCO</td><td>14 LATT</td></tr><tr><td>11.27 ±0.30 ±0.26</td><td></td><td>5</td><td>DURR</td><td>12 LATT</td></tr><tr><td>11.85 ±0.16</td><td></td><td>6</td><td>DAVIES</td><td>10 LATT</td></tr></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>11.747±0.019</td><td>+0.059</td><td>7</td><td>BAZAVOV</td><td>14A LATT</td></tr><tr><td>12.0 ±0.3</td><td>-0.043</td><td>8</td><td>BLOSSIER</td><td>10 LATT</td></tr></table>

¹ALEXANDROU 21 determines the quark mass using a lattice calculation of the meson and baryon masses with a twisted mass fermion action. The simulations are carried out using $2+1+1$ dynamical quarks with $m_u = m_d \neq m_s \neq m_c$, including gauge ensembles close to the physical pion point.

²BAZAVOV 18 determines the quark masses using a lattice computation with staggered fermions and four active quark flavors.

³CHAKRABORTY 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.

⁴CARRASCO 14 is a lattice QCD computation of light quark masses using $2+1+1$ dynamical quarks, with $m_u = m_d \neq m_s \neq m_c$. The u and d quark masses are obtained separately by using the K meson mass splittings and lattice results for the electromagnetic contributions.

⁵DURR 12 determines $m_c/m_s$ using a lattice computation with $n_f = 2$ dynamical fermions. The result is combined with other determinations of $m_c$ to obtain $m_s(2 \text{ GeV}) = 97.0 \pm 2.6 \pm 2.5 \text{ MeV}$.

⁶DAVIES 10 determine $m_c/m_s$ from meson masses calculated on gluon fields including u, 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.

⁷BAZAVOV 14a is a lattice computation using 4 dynamical flavors of HISQ fermions.

⁸BLOSSIER 10 determines $m_c/m_s$ from a computation of the hadron spectrum using $n_f = 2$ dynamical twisted-mass Wilson fermions.

<figure><img src="image_425.png" /><figcaption>$m_c/m_s$ MASS RATIO</figcaption></figure>
$m_b/m_c$ MASS RATIO

The ratio is that of the $\overline{\text{MS}}$ masses at a common scale, for four dynamical quark flavors.

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>4.58 ±0.01</strong></td><td></td><td><strong>OUR EVALUATION</strong></td></tr><tr><td><strong>4.580 ±0.07</strong></td><td></td><td><strong>OUR AVERAGE</strong></td></tr><tr><td>4.586 ±0.012</td><td>1 HATTON</td><td>21 LATT</td></tr><tr><td>4.578 ±0.008</td><td>2 BAZAVOV</td><td>18 LATT</td></tr><tr><td>4.528 ±0.054</td><td>3 CHAKRABORT...</td><td>15 LATT</td></tr></tbody></table>

¹ HATTON 21 determine $\overline{m}_b(\mu)/\overline{m}_c(\mu) = 4.586 \pm 0.012$ at $\mu = 3$ GeV with a lattice QCD + quenched QED simulation using the HISQ action and including $n_f = 2+1+1$ flavors of sea quarks. The ratio depends weakly on $\mu$ 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 for the b quark.

³ CHAKRABORTY 15 is a lattice computation using 4 dynamical quark flavors.

$m_b-m_c$ QUARK MASS DIFFERENCE

<table><thead><tr><th>VALUE (GeV)</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td><strong>3.45 ±0.05</strong></td><td></td><td><strong>OUR EVALUATION</strong></td></tr><tr><td>3.472 ±0.032</td><td>1 AUBERT</td><td>10A BABR</td></tr><tr><td>3.42 ±0.06</td><td>2 ABDALLAH</td><td>06B DLPH</td></tr><tr><td>3.44 ±0.03</td><td>3 AUBERT</td><td>04X BABR</td></tr><tr><td>3.41 ±0.01</td><td>3 BAUER</td><td>04 THEO</td></tr></tbody></table>

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 $m_b-m_c$ from moments of the hadron invariant mass and lepton energy spectra in semileptonic inclusive B decays.

³ Determine $m_b-m_c$ from a global fit to inclusive B decay spectra.

c-QUARK REFERENCES

<table><tbody><tr><td>ALEXANDROU 21</td><td>PR D104 074515</td><td>C. Alexandrou et al. (ETM Collab.)</td></tr><tr><td>HATTON 21</td><td>PR D103 114508</td><td>D. Hatton et al. (HPQCD Collab.)</td></tr><tr><td>HEITGER 21</td><td>JHEP 2105 288</td><td>J. Heitger, F. Joswig, S. Kuberski (ALPHA Collab.)</td></tr><tr><td>HATTON 20</td><td>PR D102 054511</td><td>D. Hatton et al. (HPQCD Collab.)</td></tr><tr><td>NARISON 20</td><td>PL B802 135221</td><td>S. Narison (MONP)</td></tr><tr><td>ABRAMOWICZ 18</td><td>EPJ C78 473</td><td>H. Abramowicz et al. (H1 and ZEUS Collabs.)</td></tr><tr><td>BAZAVOV 18</td><td>PR D98 054517</td><td>A. Bazavov et al. (Fermilab Lattice, MILC, TUMQCD)</td></tr><tr><td>LYTLE 18</td><td>PR D98 014513</td><td>A.T. Lytse et al. (HPQCD Collab.)</td></tr><tr><td>NARISON 18A</td><td>IJMP A33 1850045</td><td>S. Narison (MONP)</td></tr><tr><td>NARISON 18B</td><td>PL B784 261</td><td>S. Narison (MONP)</td></tr><tr><td>PESET 18</td><td>JHEP 1809 167</td><td>C. Peset, A. Pineda, J. Segovia (BARC, TUM)</td></tr><tr><td>CHETYRKIN 17</td><td>PR D96 116007</td><td>K.G. Chetyrkin et al.</td></tr><tr><td>ERLER 17</td><td>EPJ C77 99</td><td>J. Erler, P. Masjuan, H. Spiesberger</td></tr><tr><td>BERTONE 16</td><td>JHEP 1608 050</td><td>V. Bertone et al. (xFitter Developers)</td></tr><tr><td>KIYO 16</td><td>PL B752 122</td><td>Y. Kiyo, G. Mishima, Y. Sumino</td></tr><tr><td>CHAKRABORT... 15</td><td>PR D91 054508</td><td>B. Chakraborty et al. (HPQCD Collab.)</td></tr><tr><td>DEHNADI 15</td><td>JHEP 1508 155</td><td>B. Dehnadi, A.H. Hoang, V. Mateu</td></tr><tr><td>BAZAVOV 14A</td><td>PR D90 074509</td><td>A. Bazavov et al. (Fermi-LAT and MILC Collabs.)</td></tr><tr><td>CARRASCO 14</td><td>NP B887 19</td><td>N. Carrasco et al. (European Twisted Mass Collab.)</td></tr><tr><td>ABRAMOWICZ 13C</td><td>EPJ C73 2311</td><td>H. Abramowicz et al. (H1 and Zeus Collabs.)</td></tr><tr><td>ALEKHIN 13</td><td>PL B720 172</td><td>S. Alekhin et al. (SERP, DESYZ, WUPP+)</td></tr><tr><td>DEHNADI 13</td><td>JHEP 1309 103</td><td>B. Dehnadi et al. (SHRZ, VIEN, MPIM+)</td></tr><tr><td>NARISON 13</td><td>PL B718 1321</td><td>S. Narison (MONP)</td></tr><tr><td>SAMOYLOV 13</td><td>NP B876 339</td><td>O. Samoylov et al. (NOMAD Collab.)</td></tr><tr><td>ALEKHIN 12</td><td>PL B718 550</td><td>S. Alekhin et al. (SERP, WUPP, DESY+)</td></tr><tr><td>DURR 12A</td><td>PRL 108 122003</td><td>S. Durr, G. Koutsou (WUPP, JULI, CYPR)</td></tr><tr><td>NARISON 12A</td><td>PL B705 412</td><td>S. Narison (MONP)</td></tr><tr><td>ALEKHIN 11</td><td>PL B699 345</td><td>S. Alekhin, S. Moch (DESY, SERP)</td></tr><tr><td>BODENSTEIN 11</td><td>PR D83 074014</td><td>S. Bodenstein et al.</td></tr><tr><td>LASCHKA 11</td><td>PR D83 094002</td><td>A. Laschka, N. Kaiser, W. Weise</td></tr><tr><td>AUBERT 10A</td><td>PR D81 0832003</td><td>B. Aubert et al. (BABAR Collab.)</td></tr><tr><td>BLOSSIER 10</td><td>PR D82 114513</td><td>B. Blossier et al. (ETM Collab.)</td></tr><tr><td>BODENSTEIN 10</td><td>PR D82 114013</td><td>S. Bodenstein et al.</td></tr><tr><td>DAVIES 10</td><td>PRL 104 132003</td><td>C.T.H. Davies et al. (HPQCD Collab.)</td></tr><tr><td>MCNEILE 10</td><td>PR D82 034512</td><td>C. McNile et al. (HPQCD Collab.)</td></tr><tr><td>NARISON 10</td><td>PL B693 559</td><td>S. Narison (MONP)</td></tr><tr><td>Also</td><td>PL B705 544 (errat.)</td><td>S. Narison (MONP)</td></tr><tr><td>CHETYRKIN 09</td><td>PR D80 074010</td><td>K.G. Chetyrkin et al. (KARL, BNL)</td></tr><tr><td>SIGNER 09</td><td>PL B672 333</td><td>A. Signer (DURH)</td></tr><tr><td>ALLISON 08</td><td>PR D78 054513</td><td>I. Allison et al. (HPQCD Collab.)</td></tr><tr><td>KUHN 07</td><td>NP B778 192</td><td>J.H. Kuhn, M. Steinhäuser, C. Sturm</td></tr><tr><td>ABDALLAH 06B</td><td>EPJ C45 35</td><td>J. Abdallah et al. (DELPHI Collab.)</td></tr><tr><td>BOUGHEZAL 06</td><td>PR D74 074006</td><td>R. Boughezal, M. Czakon, T. Schützmeyer</td></tr><tr><td>BUCHMUELL... 06</td><td>PR D73 073008</td><td>O.L. Buchmüeller, H.U. Flacher (RHBL)</td></tr><tr><td>HOANG 06</td><td>PL B633 526</td><td>A.H. Hoang, A.V. Manohar (BABAR Collab.)</td></tr><tr><td>AUBERT 04X</td><td>PRL 93 011803</td><td>B. Aubert et al.</td></tr><tr><td>BAUER 04</td><td>PR D70 094017</td><td>C. Bauer et al.</td></tr><tr><td>HOANG 04</td><td>PL B594 127</td><td>A.H. Hoang, M. Jamin</td></tr><tr><td>DEDIVITIIS 03</td><td>NP B675 309</td><td>G.M. de Divitissi et al.</td></tr><tr><td>EIDEMULLER 03</td><td>PR D67 113002</td><td>M. Eidemuller</td></tr><tr><td>ERLER 03</td><td>PL B558 125</td><td>J. Erler, M. Luo</td></tr><tr><td>ZYABLYUK 03</td><td>JHEP 0301 081</td><td>K.N. Zyablyuk (ITEP)</td></tr></tbody></table>

b

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

$$\text{Charge} = -\frac{1}{3} e \qquad \text{Bottom} = -1$$

b-QUARK MASS

b-quark mass corresponds to the "running mass" $\overline{m}_b(\mu = \overline{m}_b)$ in the $\overline{\text{MS}}$ scheme. We have converted masses in other schemes to the $\overline{\text{MS}}$ mass using two-loop QCD perturbation theory with $\alpha_s(\mu = \overline{m}_b) = 0.223 \pm 0.008$. The value $4.18^{+0.04}_{-0.03}$ GeV for the $\overline{\text{MS}}$ mass corresponds to $4.78 \pm 0.06$ GeV

for the pole mass, using the two-loop conversion formula. A discussion of masses in different schemes can be found in the "Note on Quark Masses."

<table><thead><tr><th>MS MASS (GeV)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th></tr></thead><tbody><tr><td>3.94 <sup>+0.46</sup><sub>-0.40</sub></td><td></td><td>1 APARISI</td><td>22 THEO</td></tr><tr><td>4.202 ±0.021</td><td></td><td>2 HATTON</td><td>21 LATT</td></tr><tr><td>4.197 ±0.008</td><td></td><td>3 NARISON</td><td>20 THEO</td></tr><tr><td>4.049 <sup>+0.138</sup><sub>-0.118</sub></td><td></td><td>4 ABRAMOWICZ18</td><td>HERA</td></tr><tr><td>4.195 ±0.014</td><td></td><td>5 BAZAVOV</td><td>18 LATT</td></tr><tr><td>4.186 ±0.037</td><td></td><td>6 PESET</td><td>18 THEO</td></tr><tr><td>4.197 ±0.022</td><td></td><td>7 KIYO</td><td>16 THEO</td></tr><tr><td>4.183 ±0.037</td><td></td><td>8 ALBERTI</td><td>15 THEO</td></tr><tr><td>4.203 <sup>+0.016</sup><sub>-0.034</sub></td><td></td><td>9 BENEKE</td><td>15 THEO</td></tr><tr><td>4.196 ±0.023</td><td></td><td>10 COLQUHOUN</td><td>15 LATT</td></tr><tr><td>4.176 ±0.023</td><td></td><td>11 DEHNADI</td><td>15 THEO</td></tr><tr><td>4.21 ±0.11</td><td></td><td>12 BERNARDONI</td><td>14 LATT</td></tr><tr><td>4.169 ±0.002 ±0.008</td><td></td><td>13 PENIN</td><td>14 THEO</td></tr><tr><td>4.166 ±0.043</td><td></td><td>14 LEE</td><td>130 LATT</td></tr><tr><td>4.247 ±0.034</td><td></td><td>15 LUCHA</td><td>13 THEO</td></tr><tr><td>4.171 ±0.009</td><td></td><td>16 BODENSTEIN</td><td>12 THEO</td></tr><tr><td>4.29 ±0.14</td><td></td><td>17 DIMOPOUL...</td><td>12 LATT</td></tr><tr><td>4.18 <sup>+0.05</sup><sub>-0.04</sub></td><td></td><td>18 LASCHKA</td><td>11 THEO</td></tr><tr><td>4.186 ±0.044 ±0.015</td><td></td><td>19 AUBERT</td><td>10A BABR</td></tr><tr><td>4.163 ±0.016</td><td></td><td>20 CHETYRKIN</td><td>09 THEO</td></tr><tr><td>4.243 ±0.049</td><td></td><td>21 SCHWANDA</td><td>08 BELL</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>4.184 ±0.111</td><td>22 NARISON</td><td>18A THEO</td></tr><tr><td>4.188 ±0.008</td><td>23 NARISON</td><td>18B THEO</td></tr><tr><td>4.07 ±0.17</td><td>24 ABRAMOWICZ14</td><td>ZEUS</td></tr><tr><td>4.201 ±0.043</td><td>25 AYALA</td><td>14A THEO</td></tr><tr><td>4.236 ±0.069</td><td>26 NARISON</td><td>13 THEO</td></tr><tr><td>4.213 ±0.059</td><td>27 NARISON</td><td>13A THEO</td></tr><tr><td>4.235 ±0.003 ±0.055</td><td>28 HOANG</td><td>12 THEO</td></tr><tr><td>4.212 ±0.032</td><td>29 NARISON</td><td>12 THEO</td></tr><tr><td>4.177 ±0.011</td><td>30 NARISON</td><td>12 THEO</td></tr><tr><td>4.171 ±0.014</td><td>31 NARISON</td><td>12A THEO</td></tr><tr><td>4.164 ±0.023</td><td>32 MCNEILE</td><td>10 LATT</td></tr><tr><td>4.173 ±0.010</td><td>33 NARISON</td><td>10 THEO</td></tr><tr><td>5.26 ±1.2</td><td>34 ABDALLAH</td><td>08D DLPH</td></tr><tr><td>4.42 ±0.06 ±0.08</td><td>35 GUAZZINI</td><td>08 LATT</td></tr><tr><td>4.164 ±0.048 ±0.08</td><td>36 DELLA-MOR... 07</td><td>LATT</td></tr><tr><td>4.164 ±0.025</td><td>37 KUHN</td><td>07 THEO</td></tr><tr><td>4.19 ±0.40</td><td>38 ABDALLAH</td><td>06D DLPH</td></tr><tr><td>4.205 ±0.058</td><td>39 BOUGHEZAL</td><td>06 THEO</td></tr><tr><td>4.20 ±0.04</td><td>40 BUCHMUELL...</td><td>06 THEO</td></tr><tr><td>4.19 ±0.06</td><td>41 PINEDA</td><td>06 THEO</td></tr><tr><td>4.4 ±0.3</td><td>42 GRAY</td><td>05 LATT</td></tr><tr><td>4.22 ±0.06</td><td>43 AUBERT</td><td>04X THEO</td></tr><tr><td>4.17 ±0.03</td><td>44 BAUER</td><td>04 THEO</td></tr><tr><td>4.22 ±0.11</td><td>45 HOANG</td><td>04 THEO</td></tr><tr><td>4.25 ±0.11</td><td>46 MCNEILE</td><td>04 LATT</td></tr><tr><td>4.22 ±0.09</td><td>47 BAUER</td><td>03 THEO</td></tr><tr><td>4.19 ±0.05</td><td>48 BORDES</td><td>03 THEO</td></tr><tr><td>4.20 ±0.09</td><td>49 CORCELLA</td><td>03 THEO</td></tr><tr><td>4.33 ±0.10</td><td>50 DEDIVITIIS</td><td>03 LATT</td></tr><tr><td>4.24 ±0.10</td><td>51 EIDEMULLER</td><td>03 THEO</td></tr><tr><td>4.207 ±0.03</td><td>52 ERLER</td><td>03 THEO</td></tr><tr><td>4.33 ±0.06 ±0.10</td><td>53 MAHMOOD</td><td>03 CLEO</td></tr><tr><td>4.190 ±0.032</td><td>54 BRAMBILLA</td><td>02 THEO</td></tr><tr><td>4.346 ±0.070</td><td>55 PENIN</td><td>02 THEO</td></tr></tbody></table>

¹ APARISI 22 determine $m_b$ at the Higgs mass, $\overline{m}_b(m_H) = 2.60^{+0.36}_{-0.31}$ GeV from Higgs boson decay rates at the LHC, which is used to obtain $\overline{m}_b(\overline{m}_b)$.

² HATTON 21 determine $\overline{m}_b(3$ GeV) = 4.513 ± 0.026 GeV using a lattice QCD + quenched QED simulation using the HISQ action and including $n_f = 2+1+1$ flavors of sea quarks, by combining the $\overline{m}_b/\overline{m}_c$ and $\overline{m}_c$ determinations.

³ NARISON 20 determines the quark mass using QCD Laplace sum rules from the $B_c$ mass, combined with previous determinations of the QCD condensates and $c$ and $b$ masses.

⁴ ABRAMOWICZ 18 determine $\overline{m}_b(\overline{m}_b) = 4.049^{+0.104}_{-0.109} \pm 0.090 \pm 0.001$ from the production of b quarks in ep collisions at HERA using combined H1 and ZEUS data. The experimental/fitting errors, and those from modeling and parameterization have been combined in quadrature.

⁵ BAZAVOV 18 determine the $b$ mass using a lattice computation with staggered fermions and five active quark flavors.

⁶ PESET 18 determine $\overline{m}_c(\overline{m}_c)$ and $\overline{m}_b(\overline{m}_b)$ using an N3LO calculation of the $\eta_c$, $\eta_b$ and $B_c$ masses.

⁷ KIYO 16 determine $\overline{m}_b(\overline{m}_b)$ from the $\Upsilon(1S)$ mass at order $\alpha_s^3$ (N3LO).

⁸ ALBERTI 15 determine $\overline{m}_b(\overline{m}_b)$ from fits to inclusive $B \to X_c e\bar{\nu}$ decay. They also find $m_b^{\text{kin}}(1 \text{ GeV}) = 4.553 \pm 0.020 \text{ GeV}$.

⁹ BENEKE 15 determine $\overline{m}_b(\overline{m}_b)$ using sum rules for $e^+ e^- \to \text{hadrons at N3LO}$ including finite $m_c$ effects. They find $m_b^{\text{kin}}(2 \text{ GeV}) = 4.532^{+0.013}_{-0.039}$ GeV, and $\overline{m}_b(\overline{m}_b) = 4.193^{+0.022}_{-0.035}$ GeV. The value quoted is obtained using the four-loop conversion given in BENEKE 16.
¹⁰ COLQUHOUN 15 determine $\overline{m}_b(\overline{m}_b)$ from moments of the vector current correlator computed with a lattice simulation using the NRQCD action.

¹¹ DEHNADI 15 determine $\overline{m}_b(\overline{m}_b)$ using sum rules for $e^+e^- \to$ hadrons at order $\alpha_s^3$ (N3LO), and fitting to both experimental data and lattice results.

¹² BERNARDONI 14 determine $m_b$ from $n_f = 2$ lattice calculations using heavy quark effective theory non-perturbatively renormalized and matched to QCD at $1/m$ order.

¹³ PENIN 14 determine $\overline{m}_b(\overline{m}_b) = 4.169 \pm 0.008 \pm 0.002$ using an estimate of the order $\alpha_s^3$ b-quark vacuum polarization function in the threshold region, including finite $m_c$ effects. The errors of $\pm 0.008$ from theoretical uncertainties, and $\pm 0.002$ from $\alpha_s$ have been combined in quadrature.

¹⁴ LEE 130 determines $m_b$ using lattice calculations of the $\mathcal{T}$ and $B_s$ binding energies in NRQCD, including three light dynamical quark flavors. The quark mass shift in NRQCD is determined to order $\alpha_s^2$, with partial $\alpha_s^2$ contributions.

¹⁵ LUCHA 13 determines $m_b$ from QCD sum rules for heavy-light currents using the lattice value for $f_B$ of $191.5 \pm 7.3$ GeV.

¹⁶ BODENSTEIN 12 determine $m_b$ using sum rules for the vector current correlator and the $e^+e^- \to Q\bar{Q}$ total cross-section.

¹⁷ DIMOPOULOS 12 determine quark masses from a lattice computation using $n_f = 2$ dynamical flavors of twisted mass fermions.

¹⁸ LASCHKA 11 determine the $b$ mass from the charmonium spectrum. The theoretical computation uses the heavy $Q\bar{Q}$ potential to order $1/m_Q$ obtained by matching the short-distance perturbative result onto lattice QCD result at larger scales.

¹⁹ 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 $\overline{MS}$ scheme).

²⁰ CHETYRKIN 09 determine $m_c$ and $m_b$ from the $e^+e^- \to Q\bar{Q}$ cross-section and sum rules, using an order $\alpha_s^3$ (N3LO) computation of the heavy quark vacuum polarization.

²¹ SCHWANDA 08 measure moments of the inclusive photon spectrum in $B \to X_s \gamma$ decay to determine $m_b^{1S}$. We have converted this to $\overline{MS}$ scheme.

²² NARISON 18A determines $\overline{m}_b(\overline{m}_b)$ as a function of $\alpha_s$ using QCD exponential sum rules and their ratios evaluated at the optimal scale $\mu = 9.5$ GeV at N2LO-N3LO of perturbative QCD and including condensates up to dimension 6–8 in the (axial-)vector and (pseudo-)scalar bottomonium channels.

²³ NARISON 18b determines $\overline{m}_b(\overline{m}_b)$ using QCD vector moment sum rules and their ratios at N2LO-N3LO of perturbative QCD and including condensates up to dimension 8.

²⁴ ABRAMOWICZ 14A determine $\overline{m}_b(\overline{m}_b) = 4.07 \pm 0.14^{+0.01}_{-0.05} + 0.05 \pm 0.08$ from the production of $b$ quarks in $e^+e^-$ collisions at HERA. The errors due to fitting, modeling, PDF parameterization, and theoretical QCD uncertainties due to the values of $\alpha_s$, $m_c$, and the renormalization scale $\mu$ have been combined in quadrature.

²⁵ AYALA 14A determine $\overline{m}_b(\overline{m}_b)$ from the $\mathcal{T}$ (15) mass computed to N3LO order in perturbation theory using a renormalon subtracted scheme.

²⁶ NARISON 13 determines $m_b$ using QCD spectral sum rules to order $\alpha_s^2$ (NNLO) and including condensates up to dimension 6.

²⁷ NARISON 13A determines $m_b$ using HQET sum rules to order $\alpha_s^2$ (NNLO) and the $B$ meson mass and decay constant.

²⁸ HOANG 10 determines $m_b$ using non-relativistic sum rules for the $\mathcal{T}$ system at order $\alpha_s^2$ (NNLO) with renormalization group improvement.

²⁹ NARISON 12 determines $m_b$ using exponential sum rules for the vector current correlator to order $\alpha_s^3$, including the effect of gluon condensates up to dimension eight.

³⁰ Determines $m_b$ to order $\alpha_s^3$ (N3LO), including the effect of gluon condensates up to dimension eight combining the methods of NARISON 12 and NARISON 12A.

³¹ NARISON 12A determines $m_b$ using sum rules for the vector current correlator to order $\alpha_s^3$, including the effect of gluon condensates up to dimension eight.

³² MCNEILE 10 determines $m_b$ by comparing order $\alpha_s^3$ (N3LO) perturbative results for the pseudo-scalar current to lattice simulations with $n_f = 2+1$ sea-quarks by the HPQCD collaboration.

³³ NARISON 10 determines $m_b$ from ratios of moments of vector current correlators computed to order $\alpha_s^3$ and including the dimension-six gluon condensate. These values are taken from the eratum to that reference.

³⁴ ABDALLAH 08d determine $\overline{m}_b(M_Z) = 3.76 \pm 1.0$ GeV from a leading order study of four-jet rates at LEP.

³⁵ GUAZZINI 08 determine $\overline{m}_b(\overline{m}_b)$ from a quenched lattice simulation of heavy meson masses. The $\pm 0.08$ is an estimate of the quenching error.

³⁶ DELLA-MORTE 07 determine $\overline{m}_b(\overline{m}_b)$ from a computation of the spin-averaged $B$ meson mass using quenched lattice HQET at order $1/m$. The $\pm 0.08$ is an estimate of the quenching error.

³⁷ KUHN 07 determine $\overline{m}_b(\mu = 10 \text{ GeV}) = 3.609 \pm 0.025 \text{ GeV}$ and $\overline{m}_b(\overline{m}_b)$ from a four-loop sum-rule computation of the cross-section for $e^+e^- \to$ hadrons in the bottom threshold region.

³⁸ ABDALLAH 06d determine $m_b(M_Z) = 2.85 \pm 0.32$ GeV from $Z$-decay three-jet events containing a b-quark.

³⁹ BOUGHEZAL 06 $\overline{MS}$ scheme result comes from the first moment of the hadronic production cross-section to order $\alpha_s^3$.

⁴⁰ BUCHMUELLER 06 determine $m_b$ and $m_c$ by a global fit to inclusive $B$ decay spectra.

⁴¹ PINEDA 06 $\overline{MS}$ scheme result comes from a partial NNLL evaluation (complete at order $\alpha_s^2$ (NNLO)) of sum rules of the bottom production cross-section in $e^+e^-$ annihilation.

⁴² GRAY 05 determines $\overline{m}_b(\overline{m}_b)$ from a lattice computation of the $\mathcal{T}$ spectrum. The simulations have $2+1$ dynamical light flavors. The b quark is implemented using NRQCD.

⁴³ AUBERT 04x obtain $m_b$ from a fit to the hadron mass and lepton energy distributions in semileptonic $B$ decay. The paper quotes values in the kinetic scheme. The $\overline{MS}$ value has been provided by the BABAR collaboration.

⁴⁴ BAUER 04 determine $m_b$, $m_c$ and $m_b-m_c$ by a global fit to inclusive $B$ decay spectra.

⁴⁵ HOANG 04 determines $\overline{m}_b(\overline{m}_b)$ from moments at order $\alpha_s^2$ of the bottom production cross-section in $e^+e^-$ annihilation.

⁴⁶ MCNEILE 04 use lattice QCD with dynamical light quarks and a static heavy quark to compute the masses of heavy-light mesons.

⁴⁷ BAUER 03 determine the b quark mass by a global fit to $B$ decay observables. The experimental data includes lepton energy and hadron invariant mass moments in semileptonic

$B \to X_c \ell \nu_\ell$ decay, and the inclusive photon spectrum in $B \to X_s \gamma$ decay. The theoretical expressions used are of order $1/m^3$, and $\alpha_s^2 \beta_0$.

⁴⁸ BORDES 03 determines $m_b$ using QCD finite energy sum rules to order $\alpha_s^2$.

⁴⁹ CORCELLA 03 determines $\overline{m}_b$ using sum rules computed to order $\alpha_s^2$. Includes charm quark mass effects.

⁵⁰ DEDIVITIIS 03 use a quenched lattice computation of heavy-heavy and heavy-light meson masses.

⁵¹ EIDEMULLER 03 determines $\overline{m}_b$ and $\overline{m}_c$ using QCD sum rules.

⁵² ERLER 03 determines $\overline{m}_b$ and $\overline{m}_c$ using QCD sum rules. Includes recent BES data.

⁵³ MAHMOOD 03 determines $m_b^{1S}$ by a fit to the lepton energy moments in $B \to X_c \ell \nu_\ell$ decay. The theoretical expressions used are of order $1/m^3$ and $\alpha_s^2 \beta_0$. We have converted their result to the $\overline{MS}$ scheme.

⁵⁴ BRAMBILLA 02 determines $\overline{m}_b(\overline{m}_b)$ from a computation of the $\mathcal{T}$ (15) mass to order $\alpha_s^4$, including finite $m_c$ corrections.

⁵⁵ PENIN 02 determines $\overline{m}_b$ from the spectrum of the $\mathcal{T}$ system.

<figure><img src="image_426.png" /><figcaption>b-QUARK $\overline{MS}$ MASS (GeV)</figcaption></figure>

$m_b/m_s$ MASS RATIO

VALUE

DOCUMENT ID

53.94±0.12

1 BAZAVOV 18 LATT

52.55±0.55

2 CHAKRABORTY 15 LATT

¹ 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 for the $b$ quark.

² CHAKRABORTY 15 determine $m_b/m_c$ from lattice QCD using the HISQ action and including $n_f = 2+1$ flavors of sea quarks.

b-QUARK REFERENCES

<table><tr><td>APARISI</td><td>22</td><td>PRL 128 122001</td><td>J. Aprasi et al.</td><td>(VALE, WIEN, PSI+)</td></tr><tr><td>HATTON</td><td>21</td><td>PR D103 114508</td><td>D. Hatton et al.</td><td>(HPQCD Collab.)</td></tr><tr><td>NARISON</td><td>20</td><td>PL B002 135221</td><td>S. Narison</td><td>(MONP)</td></tr><tr><td>ABRAMOWICZ</td><td>19</td><td>EJ P C78 473</td><td>H. Abramowicz et al.</td><td>(H1 and ZEUS Collabs.)</td></tr><tr><td>BAZAVOV</td><td>18</td><td>PR D98 054517</td><td>A. Bazavov et al. (Fermilab Lattice, MILC, TUMQCD)</td><td></td></tr><tr><td>NARISON</td><td>18A</td><td>JMP A33 1850045</td><td>S. Narison</td><td>(MONP)</td></tr><tr><td>NARISON</td><td>18B</td><td>PL B784 261</td><td>S. Narison</td><td>(MONP)</td></tr><tr><td>PESET</td><td>18</td><td>JHEP 1809 167</td><td>C. Peset, A. Pineda, J. Segovia</td><td>(BARC, TUM)</td></tr><tr><td>BENEKE</td><td>16</td><td>PoS RADCOR2015 035</td><td>M. Beneke et al.</td><td></td></tr><tr><td>KIYO</td><td>16</td><td>PL B752 122</td><td>Y. Kiyo, G. Mishima, Y. Sumino</td><td></td></tr><tr><td>ALBERTI</td><td>15</td><td>PN P11 061802</td><td>A. Alberti et al.</td><td></td></tr><tr><td>BENEKE</td><td>15</td><td>PR B891 42</td><td>M. Beneke et al.</td><td></td></tr><tr><td>CHAKRABORTY</td><td>15</td><td>PR D91 054508</td><td>B. Chakraborty et al.</td><td>(HPQCD Collab.)</td></tr><tr><td>COLQUHOUN</td><td>15</td><td>PR D91 074514</td><td>B. Colquhoun et al.</td><td>(HPQCD Collab.)</td></tr><tr><td>DEHNADI</td><td>15</td><td>JHEP 1508 155</td><td>B. Dehnadi, A.H. Hoang, V. Mateu</td><td></td></tr><tr><td>ABRAMOWICZ</td><td>14A</td><td>JHEP 1409 127</td><td>H. Abramowicz et al.</td><td>(ZEUS Collab.)</td></tr><tr><td>AYALA</td><td>14A</td><td>JHEP 1409 045</td><td>C. Ayala, G. Cvetic, A. Pineda</td><td></td></tr><tr><td>BERNARDONI</td><td>14</td><td>PL B730 171</td><td>F. Bernardoni et al.</td><td>(ALPHA Collab.)</td></tr><tr><td>PENIN</td><td>14</td><td>PR B740 120</td><td>A.A. Penin, N. Zerf</td><td></td></tr><tr><td>LEE</td><td>130</td><td>PR D87 074018</td><td>A.J. Lee et al.</td><td>(HPQCD Collab.)</td></tr><tr><td>LUCHA</td><td>13</td><td>PR D88 056011</td><td>W. Lucha, D. Melikhov, S. Simula</td><td>(VIEN, MOSU+)</td></tr><tr><td>NARISON</td><td>13</td><td>PL B718 1321</td><td>S. Narison</td><td>(MONP)</td></tr><tr><td>NARISON</td><td>13A</td><td>PL B721 269</td><td>S. Narison</td><td>(MONP)</td></tr><tr><td>BODENSTEIN</td><td>12</td><td>PR D85 034003</td><td>S. Bodenstein et al.</td><td>(CAPE, VALE, MAINZ+)</td></tr><tr><td>DIMOPOUL...</td><td>12</td><td>JHEP 1201 046</td><td>P. Dimopoulos et al.</td><td>(ETM Collab.)</td></tr><tr><td>HOANG</td><td>12</td><td>JHEP 1210 188</td><td>A.H. Hoang, P. Ruiz-Femenia, M. Stahlhofen</td><td>(WIEN+)</td></tr><tr><td>NARISON</td><td>12</td><td>PL B707 259</td><td>S. Narison</td><td>(MONP)</td></tr><tr><td>NARISON</td><td>12A</td><td>PL B706 412</td><td>S. Narison</td><td>(MONP)</td></tr><tr><td>LASCHKA</td><td>11</td><td>PR D83 094002</td><td>A. Laschka, N. Kaiser, W. Weise</td><td></td></tr><tr><td>AUBERT</td><td>10A</td><td>PR D81 032003</td><td>B. Aubert et al.</td><td>(BABAR Collab.)</td></tr><tr><td>MCNEILE</td><td>10</td><td>PR D82 034512</td><td>C. McNelie et al.</td><td>(HPQCD Collab.)</td></tr><tr><td>NARISON</td><td>10</td><td>PL B693 559</td><td>S. Narison</td><td>(MONP)</td></tr><tr><td>Also</td><td>10</td><td>PL B705 544 (erratum)</td><td>S. Narison</td><td>(MONP)</td></tr><tr><td>CHETYRKIN</td><td>09</td><td>PR D80 074010</td><td>K.G. Chetyrkin et al.</td><td>(KARL, BNL)</td></tr><tr><td>ABDALLAH</td><td>08D</td><td>EJ P C55 525</td><td>J. Abdallah et al.</td><td>(DELPHI Collab.)</td></tr><tr><td>GUAZZINI</td><td>08</td><td>JHEP 0801 076</td><td>D. Guazzini, R. Sommer, N. Tantalo</td><td></td></tr><tr><td>SCHWANDA</td><td>08</td><td>PR D78 032016</td><td>C. Schwanda et al.</td><td>(BELLE Collab.)</td></tr><tr><td>DELLA-MOR...</td><td>07</td><td>JHEP 0701 007</td><td>M. Della Morte et al.</td><td></td></tr><tr><td>KUHN</td><td>07</td><td>NP B778 192</td><td>J.H. Kuhn, M. Steinhauser, C. Sturm</td><td>(DELPHI Collab.)</td></tr><tr><td>ABDALLAH</td><td>06D</td><td>EJ P C46 569</td><td>J. Abdallah et al.</td><td>(DELPHI Collab.)</td></tr><tr><td>BOUGHEZAL</td><td>06</td><td>PR D74 074006</td><td>R. Boughezal, M. Czakon, T. Schutzmeier</td><td></td></tr><tr><td>BUCHMUELL...</td><td>06</td><td>PR D73 073008</td><td>O.L. Buchmueler, H.U. Flacher</td><td>(RHBL)</td></tr><tr><td>PINEDA</td><td>06</td><td>PR D73 111501</td><td>A. Pineda, A. Signer</td><td></td></tr><tr><td>GRAY</td><td>05</td><td>PR D72 04507</td><td>A. Gray et al.</td><td>(HPQCD and UKQCD Collab.)</td></tr><tr><td>AUBERT</td><td>04X</td><td>PRL 93 011803</td><td>B. Aubert et al.</td><td>(BABAR Collab.)</td></tr><tr><td>BAUER</td><td>04</td><td>PR D70 094017</td><td>C. Bauer et al.</td><td></td></tr></table>
<table><tr><td>HOANG</td><td>04</td><td>PL B594 127</td></tr><tr><td>MCNEILE</td><td>04</td><td>PL B600 77</td></tr><tr><td>BAUER</td><td>03</td><td>PR D67 054012</td></tr><tr><td>BORDES</td><td>03</td><td>PL B562 81</td></tr><tr><td>CORCELLA</td><td>03</td><td>PL B554 133</td></tr><tr><td>DEDIVITIS</td><td>03</td><td>NP B675 309</td></tr><tr><td>EIDEMULLER</td><td>03</td><td>PR D67 113002</td></tr><tr><td>ERLER</td><td>03</td><td>PL B558 125</td></tr><tr><td>MAHMOOD</td><td>03</td><td>PR D67 072001</td></tr><tr><td>BRAMBILLIA</td><td>02</td><td>PL D65 034000</td></tr><tr><td>PENIN</td><td>02</td><td>PL B538 335</td></tr></table>

<table><tr><td>A.H. Hoang, M. Jamin</td></tr><tr><td>C. McNelie, C. Michael, G. Thompson (UKQCD Collab.)</td></tr><tr><td>C.W. Bauer et al.</td></tr><tr><td>J. Bordes, J. Penarrocha, K. Schilcher</td></tr><tr><td>G. Corcella, A.H. Hoang</td></tr><tr><td>G.M. de Divitis et al.</td></tr><tr><td>M. Eidemuller</td></tr><tr><td>J. Erler, M. Luo</td></tr><tr><td>A.H. Mahmood et al.</td></tr><tr><td>N. Brambilla, Y. Sumino, A. Vairo</td></tr><tr><td>A. Penin, M. Steinhauser</td></tr></table>

<table><tr><td>(CLEO Collab.)</td></tr></table>

t

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

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

See the related review(s):
Top Quark

t-QUARK MASS

We first list the direct measurements of the top quark mass which employ the event kinematics and then list the measurements which extract a top quark mass from the measured $t\bar{t}$ cross-section using theory calculations. A discussion of the definition of the top quark mass in these measurements can be found in the review "The Top Quark."

For earlier search limits see PDG 96, Physical Review D54 1 (1996). We no longer include a compilation of indirect top mass determinations from Standard Model Electroweak fits in the Listings (our last compilation can be found in the Listings of the 2007 partial update). For a discussion of current results see the reviews "The Top Quark" and "Electroweak Model and Constraints on New Physics."

t-Quark Mass (Direct Measurements)

The following measurements extract a t-quark mass from the kinematics of $t\bar{t}$ events. They are sensitive to the top quark mass used in the MC generator that is usually interpreted as the pole mass, but the theoretical uncertainty in this interpretation is hard to quantify. See the review "The Top Quark" and references therein for more information.

OUR AVERAGE of $172.57 \pm 0.29$ GeV is an average of top mass measurements from LHC and Tevatron Runs. The latest Tevatron average, $174.30 \pm 0.35 \pm 0.54$ GeV, was provided by the Tevatron Electroweak Working Group (TEVEWWG).

<table><thead><tr><th>VALUE (GeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="4"><strong>172.57 ± 0.29 OUR AVERAGE</strong> Error includes scale factor of 1.5. See the ideogram below.</td></tr><tr><td>174.41 ± 0.39 ± 0.71</td><td>1 AAD</td><td>23N ATLS</td><td>leptonic invariant mass in $\ell^+\ell^-$ channel</td></tr><tr><td>171.77 ± 0.37</td><td>2 TUMASYAN</td><td>23BB CMS</td><td>$\ell^+ \ge 4j$ (2b)</td></tr><tr><td>173.06 ± 0.24 ± 0.80</td><td>3 TUMASYAN</td><td>23Z CMS</td><td>boosted top; $\ell^+\ell^-$ channel</td></tr><tr><td>172.13<sup>+</sup> - 0.77</td><td>4 TUMASYAN</td><td>21G CMS</td><td>t-channel single top production</td></tr><tr><td>172.6 ± 2.5</td><td>5 SIRUNYAN</td><td>20AR CMS</td><td>jet mass from boosted top</td></tr><tr><td>172.69 ± 0.25 ± 0.41</td><td>6 AABOUD</td><td>19AC ATLS</td><td>7, 8 TeV ATLAS combination</td></tr><tr><td>172.34 ± 0.20 ± 0.70</td><td>7 SIRUNYAN</td><td>19AP CMS</td><td>$\ge 6$ jets ($\ge 2b$)</td></tr><tr><td>172.33 ± 0.14<sup>+</sup> - 0.72</td><td>8 SIRUNYAN</td><td>19AR CMS</td><td>dilepton channel ($e\mu$, 2e, 2$\mu$)</td></tr><tr><td>172.44 ± 0.13 ± 0.47</td><td>9 KHACHATRY...16AK CMS</td><td></td><td>7, 8 TeV CMS combination</td></tr><tr><td>174.30 ± 0.35 ± 0.54</td><td>10 TEVEWWG</td><td>16 TEVA</td><td>Tevatron combination</td></tr><tr><td colspan="4"><strong>• • • We do not use the following data for averages, fits, limits, etc. • • •</strong></td></tr><tr><td>172.08 ± 0.39 ± 0.82</td><td>11 AABOUD</td><td>19AC ATLS</td><td>$\ell^+ \ge 4j$ (2b)</td></tr><tr><td>172.26 ± 0.07 ± 0.61</td><td>12 SIRUNYAN</td><td>19AP CMS</td><td>lepton+jets, all-jets channels</td></tr><tr><td>172.25 ± 0.08 ± 0.62</td><td>13 SIRUNYAN</td><td>18DE CMS</td><td>$\ell^+ \ge 4j$ (2b)</td></tr><tr><td>173.72 ± 0.55 ± 1.01</td><td>14 AABOUD</td><td>17AH ATLS</td><td>$\ge 5$ jets (2b)</td></tr><tr><td>174.95 ± 0.40 ± 0.64</td><td>15 ABAZOV</td><td>17B D0</td><td>$\ell^+$ jets and dilepton channels</td></tr><tr><td>172.95 ± 0.77<sup>+</sup> - 0.93</td><td>16 SIRUNYAN</td><td>17L CMS</td><td>t-channel single top production</td></tr><tr><td>170.8 ± 9.0</td><td>17 SIRUNYAN</td><td>17N CMS</td><td>jet mass in highly-boosted $t\bar{t}$ events</td></tr><tr><td>172.22 ± 0.18<sup>+</sup> - 0.93</td><td>18 SIRUNYAN</td><td>17O CMS</td><td>Dilepton channel</td></tr><tr><td>172.99 ± 0.41 ± 0.74</td><td>19 AABOUD</td><td>16T ATLS</td><td>dilepton channel</td></tr><tr><td>172.84 ± 0.34 ± 0.61</td><td>20 AABOUD</td><td>16T ATLS</td><td>combination of ATLAS</td></tr><tr><td>173.32 ± 1.36 ± 0.85</td><td>21 ABAZOV</td><td>16 D0</td><td>$\ell^+ \ell^+ E_T + \ge 2j$ ($\ge 2b$)</td></tr><tr><td>173.93 ± 1.61 ± 0.88</td><td>22 ABAZOV</td><td>16D D0</td><td>$\ell^+ \ell^+ E_T + \ge 2j$ ($\ge 2b$)</td></tr><tr><td>172.35 ± 0.16 ± 0.48</td><td>23,24 KHACHATRY...16AK CMS</td><td></td><td>$\ell^+ \ge 4j$ (2b)</td></tr><tr><td>172.32 ± 0.25 ± 0.59</td><td>23,24 KHACHATRY...16AK CMS</td><td></td><td>$\ge 6$ jets (2b)</td></tr><tr><td>172.82 ± 0.19 ± 1.22</td><td>23,25 KHACHATRY...16AK CMS</td><td>(ee/$\mu\mu$)+$E_T + \ge 2b$</td><td>$e\mu\mu + \ge 2b$</td></tr><tr><td>173.68 ± 0.20<sup>+</sup> - 0.97</td><td>26 KHACHATRY...16AL CMS</td><td></td><td>semi- + di-leptonic channels</td></tr><tr><td>173.5 ± 3.0 ± 0.9</td><td>27 KHACHATRY...16CB CMS</td><td></td><td>$t \to (W \to \ell\nu)(b \to J/\psi X \to \mu^+\mu^- X)$</td></tr><tr><td>175.1 ± 1.4 ± 1.2</td><td>28 AAD</td><td>15AW ATLS</td><td>small $E_T$, $\ge 6$ jets (2b-tag)</td></tr><tr><td>172.99 ± 0.48 ± 0.78</td><td>29 AAD</td><td>15BF ATLS</td><td>$\ell^+$ jets and dilepton</td></tr><tr><td>171.5 ± 1.9 ± 2.5</td><td>30 AALTONEN</td><td>15D CDF</td><td>$\ell^+ \ell^+ E_T + \ge 2j$</td></tr><tr><td>175.07 ± 1.19<sup>+</sup> - 1.58</td><td>31 AALTONEN</td><td>14N CDF</td><td>small $E_T$, 6-8 jets ($\ge 1b$-tag)</td></tr><tr><td>174.98 ± 0.58 ± 0.49</td><td>32 ABAZOV</td><td>14C D0</td><td>$\ell^+ \ell^+ E_T + 4$ jets ($\ge 1$ b-tag)</td></tr><tr><td>173.49 ± 0.69 ± 1.24</td><td>33 CHATRCHYAN 14C CMS</td><td></td><td>$\ge 6$ jets ($\ge 2$ b-tag)</td></tr><tr><td>173.93 ± 1.64 ± 0.87</td><td>34 AALTONEN</td><td>13H CDF</td><td>$E_T + 4$ jets ($\ge 1$ b)</td></tr><tr><td>173.9 ± 0.9 ± 1.7</td><td>35 CHATRCHYAN 13S CMS</td><td></td><td>$\ell^+ \ell^+ E_T + \ge 2b$-tag (MT2(T))</td></tr><tr><td>174.5 ± 0.6 ± 2.3</td><td>36 AAD</td><td>12I ATLS</td><td>$\ell^+ \ell^+ E_T + 4$ jets ($\ge 1$ b), MT</td></tr></tbody></table>

<table><tr><td>172.85 ± 0.71 ± 0.85</td></tr><tr><td>172.7 ± 9.3 ± 3.7</td></tr><tr><td>173.18 ± 0.56 ± 0.75</td></tr><tr><td>173.1 ± 1.4 ± 1.5</td></tr><tr><td>173.7 ± 2.8 ± 1.5</td></tr><tr><td>173.9 ± 1.9 ± 1.6</td></tr><tr><td>172.5 ± 0.4 ± 1.5</td></tr><tr><td>173.49 ± 0.43 ± 0.98</td></tr><tr><td>172.4 ± 1.4 ± 1.3</td></tr><tr><td>172.3 ± 2.4 ± 1.0</td></tr><tr><td>172.1 ± 1.1 ± 0.9</td></tr><tr><td>176.9 ± 8.0 ± 2.7</td></tr></table>

<table><tr><td>174.94 ± 0.83 ± 1.24</td></tr><tr><td>174.0 ± 1.8 ± 2.4</td></tr><tr><td>175.5 ± 4.6 ± 4.6</td></tr><tr><td>173.0 ± 0.9 ± 0.9</td></tr><tr><td>169.3 ± 2.7 ± 3.2</td></tr><tr><td>170.7 ± 6.3 ± 2.6</td></tr><tr><td>174.8 ± 2.4<sup>+</sup> - 1.0</td></tr><tr><td>180.5 ± 12.0 ± 3.6</td></tr><tr><td>172.7 ± 1.8 ± 1.2</td></tr><tr><td>171.1 ± 3.7 ± 2.1</td></tr><tr><td>171.9 ± 1.7 ± 1.1</td></tr><tr><td>171.2 ± 2.7 ± 2.9</td></tr><tr><td>165.5<sup>+</sup> - 3.3<sup>+</sup> ± 3.1</td></tr><tr><td>174.7 ± 4.4 ± 2.0</td></tr><tr><td>170.7 ± 4.2<sup>+</sup> - 3.9<sup>+</sup> ± 3.5</td></tr><tr><td>171.5 ± 1.8 ± 1.1</td></tr><tr><td>177.1 ± 4.9 ± 4.7</td></tr><tr><td>172.3<sup>+</sup> - 9.6<sup>+</sup> ± 10.8</td></tr><tr><td>174.0 ± 2.2 ± 4.8</td></tr><tr><td>170.8 ± 2.2 ± 1.4</td></tr><tr><td>173.7 ± 4.4<sup>+</sup> - 2.0<sup>+</sup> ± 2.0</td></tr><tr><td>176.2 ± 9.2 ± 3.9</td></tr><tr><td>179.5 ± 7.4 ± 5.6</td></tr><tr><td>164.5 ± 3.9 ± 3.9</td></tr><tr><td>180.7<sup>+15.5</sup> - 13.4<sup>-</sup> ± 8.6</td></tr><tr><td>170.3 ± 4.1<sup>+</sup> - 4.5<sup>-</sup> ± 1.2</td></tr><tr><td>173.2<sup>+</sup> - 2.6<sup>+</sup> - 2.4<sup>-</sup> ± 3.2</td></tr><tr><td>173.5<sup>+</sup> - 3.7<sup>+</sup> - 3.6<sup>-</sup> ± 1.3</td></tr><tr><td>165.2 ± 6.1 ± 3.4</td></tr><tr><td>170.1 ± 6.0 ± 4.1</td></tr><tr><td>178.1 ± 13.7 ± 7.7</td></tr><tr><td>180.5 ± 3.6 ± 3.9</td></tr><tr><td>176.1 ± 5.1 ± 5.3</td></tr><tr><td>176.1 ± 6.6</td></tr><tr><td>172.1 ± 5.2 ± 4.9</td></tr><tr><td>176.0 ± 6.5</td></tr><tr><td>167.4 ± 10.3 ± 4.8</td></tr><tr><td>168.4 ± 12.3 ± 3.6</td></tr><tr><td>173.3 ± 5.6 ± 5.5</td></tr><tr><td>175.9 ± 4.8 ± 5.3</td></tr><tr><td>161 ± 17 ± 10</td></tr><tr><td>172.1 ± 5.2 ± 4.9</td></tr><tr><td>173.8 ± 5.0</td></tr><tr><td>173.3 ± 5.6 ± 6.2</td></tr><tr><td>186 ± 10 ± 5.7</td></tr><tr><td>199<sup>+19</sup> - 21<sup>-</sup> ± 22</td></tr><tr><td>176 ± 8 ± 10</td></tr><tr><td>174 ± 10<sup>+13</sup> - 12<sup>-</sup></td></tr></table>

<table><tr><td>37 AALTONEN</td><td>12A1 CDF</td><td>$\ell^+ \ell^+ E_T + \ge 4j$ (0,1,2b) template</td></tr><tr><td>38 AALTONEN</td><td>12A1 CDF</td><td>$\tau_h E_T + 4j$ ($\ge 1b$)</td></tr><tr><td>39 AALTONEN</td><td>12A2 TEVA</td><td>CDF, D0 combination</td></tr><tr><td>40 AALTONEN</td><td>12G CDF</td><td>6-8 jets with $\ge 1$ b</td></tr><tr><td>41 ABAZOV</td><td>12AB D0</td><td>$\ell^+ \ell^+ E_T + \ge 2j$ ($\nu$WT)</td></tr><tr><td>42 ABAZOV</td><td>12AB D0</td><td>$\ell^+ \ell^+ E_T + \ge 2j$ ($\nu$WT+MWT)</td></tr><tr><td>43 CHATRCHYAN 12BA CMS</td><td></td><td>$\ell^+ \ell^+ E_T + \ge 2j$ ($\ge 1b$), AMWT</td></tr><tr><td>44 CHATRCHYAN 12BP CMS</td><td></td><td>$\ell^+ \ell^+ E_T + \ge 4j$ ($\ge 2b$)</td></tr><tr><td>45 AALTONEN</td><td>11AC CDF</td><td>$\ell^+ \ell^+ E_T + 4$ jets ($\ge 1$ b-tag)</td></tr><tr><td>46 AALTONEN</td><td>11AK CDF</td><td>Repl. by AALTONEN 13H</td></tr><tr><td>47 AALTONEN</td><td>11E CDF</td><td>$\ell^+$ jets and dilepton</td></tr><tr><td>48 AALTONEN</td><td>11T CDF</td><td>$\ell^+ \ell^+ E_T + 4$ jets ($\ge 1$ b-tag), $p_T(\ell)$ shape</td></tr><tr><td>49 ABAZOV</td><td>11P D0</td><td>$\ell^+ \ell^+ E_T + 4$ jets ($\ge 1$ b-tag)</td></tr><tr><td>50 ABAZOV</td><td>11R D0</td><td>dilepton + $E_T + \ge 2$ jets</td></tr><tr><td>51 CHATRCHYAN 11F CMS</td><td></td><td>dilepton + $E_T +$ jets</td></tr><tr><td>52 AALTONEN</td><td>10AE CDF</td><td>$\ell^+ \ell^+ E_T + 4$ jets ($\ge 1$ b-tag), ME method</td></tr><tr><td>53 AALTONEN</td><td>10C CDF</td><td>dilepton + $b$-tag (MT2+NWA)</td></tr><tr><td>54 AALTONEN</td><td>10D CDF</td><td>$\ell^+ \ell^+ E_T + 4$ jets (b-tag)</td></tr><tr><td>55 AALTONEN</td><td>10E CDF</td><td>$\ge 6$ jets, vtx b-tag</td></tr><tr><td>56 AALTONEN</td><td>09AK CDF</td><td>$\ell^+ \ell^+ E_T +$ jets (soft $\mu$ b-tag)</td></tr><tr><td>57 AALTONEN</td><td>09J CDF</td><td>$\ell^+ \ell^+ E_T + 4$ jets (b-tag)</td></tr><tr><td>58 AALTONEN</td><td>09K CDF</td><td>6 jets, vtx b-tag</td></tr><tr><td>59 AALTONEN</td><td>09L CDF</td><td>$\ell^+$ jets, $\ell^+ \ell^+$ jets</td></tr><tr><td>60 AALTONEN</td><td>09O CDF</td><td>dilepton</td></tr><tr><td>61 AALTONEN</td><td>09X CDF</td><td>$\ell^+ \ell^+ E_T$ ($\nu\phi$ weighting)</td></tr><tr><td>62 ABAZOV</td><td>09AH D0</td><td>dilepton + $b$-tag ($\nu$WT+MWT)</td></tr><tr><td>63,64 AALTONEN</td><td>08C CDF</td><td>dilepton, $\sigma_{t\bar{t}}$ constrained</td></tr><tr><td>65 ABAZOV</td><td>08AH D0</td><td>$\ell^+ \ell^+ E_T + 4$ jets</td></tr><tr><td>66,67 AALTONEN</td><td>07 CDF</td><td>6 jets with $\ge 1$ b vtx</td></tr><tr><td>68 AALTONEN</td><td>07B CDF</td><td>$\ge 4$ jets (b-tag)</td></tr><tr><td>69 AALTONEN</td><td>07D CDF</td><td>$\ge 6$ jets, vtx b-tag</td></tr><tr><td>70,71 AALTONEN</td><td>07I CDF</td><td>lepton + jets (b-tag)</td></tr><tr><td>67,72 ABAZOV</td><td>07F D0</td><td>lepton + jets</td></tr><tr><td>73 ABAZOV</td><td>07W D0</td><td>dilepton (MWT)</td></tr><tr><td>73 ABAZOV</td><td>07W D0</td><td>dilepton ($\nu$WT)</td></tr><tr><td>71,74 ABULENCIA</td><td>07D CDF</td><td>dilepton</td></tr><tr><td>75 ABULENCIA</td><td>07J CDF</td><td>lepton + jets</td></tr><tr><td>71,76 ABAZOV</td><td>06U D0</td><td>lepton + jets (b-tag)</td></tr><tr><td>77,78 ABULENCIA</td><td>06D CDF</td><td>lepton + jets</td></tr><tr><td>64,77 ABULENCIA</td><td>06D CDF</td><td>lepton + jets</td></tr><tr><td>71,79 ABULENCIA</td><td>06G CDF</td><td>dilepton</td></tr><tr><td>64,80 ABULENCIA</td><td>06V CDF</td><td>dilepton</td></tr><tr><td>81,82 ABAZOV</td><td>05 D0</td><td>6 or more jets</td></tr><tr><td>83,84 ABAZOV</td><td>04G D0</td><td>lepton + jets</td></tr><tr><td>85 AFFOLDER</td><td>01 CDF</td><td>lepton + jets</td></tr><tr><td>86 AFFOLDER</td><td>01 CDF</td><td>dilepton, lepton+jets, all-jets</td></tr><tr><td>87 ABBOTT</td><td>99D G0</td><td>di-lepton, lepton+jets</td></tr><tr><td>88,89 ABE</td><td>99B CDF</td><td>dilepton, lepton+jets, all-jets</td></tr><tr><td>89,90 ABE</td><td>99B CDF</td><td>dilepton, lepton+jets, all-jets</td></tr><tr><td>84 ABBOTT</td><td>98D D0</td><td>dilepton</td></tr><tr><td>84,91 ABBOTT</td><td>98F D0</td><td>dilepton</td></tr><tr><td>90,92 ABE</td><td>98E CDF</td><td>lepton + jets</td></tr><tr><td>90 ABE</td><td>98E CDF</td><td>lepton + jets</td></tr><tr><td>93 BHAT</td><td>98B RVUE</td><td>dilepton and lepton+jets</td></tr><tr><td>94 BHAT</td><td>98B RVUE</td><td>dilepton, lepton+jets, all-jets</td></tr><tr><td>84 ABACHI</td><td>97E D0</td><td>lepton + jets</td></tr><tr><td>90,95 ABE</td><td>97R CDF</td><td>6 or more jets</td></tr><tr><td>199<sup>+19</sup> - 21<sup>-</sup> ± 22</td><td>95 D0</td><td>lepton + jets</td></tr><tr><td>176 ± 8 ± 10</td><td>95F CDF</td><td>lepton + $b$-jet</td></tr><tr><td>174 ± 10<sup>+13</sup> - 12<sup>-</sup></td><td>94E CDF</td><td>lepton + $b$-jet</td></tr></table>

1 AAD 23N based on 36.1 fb$^{-1}$ of $pp$ data at $\sqrt{s} = 13$ TeV. The second error is the sum of systematic ($\pm 0.66$) and that from changing parton-shower gluon recoil scheme ($\pm 0.25$) uncertainties. The distribution of the invariant mass $m_{\ell\ell\mu}$ ($\ell$ from W and $\mu$ from $b$-hadron decay) is used, which is less sensitive to jet energy uncertainties and top production modelling.

2 TUMASYAN 23BB based on 36.3 fb$^{-1}$ of $pp$ data at $\sqrt{s} = 13$ TeV. For each event, the mass is reconstructed from a kinematic fit of the decay products to a $t\bar{t}$ hypothesis. A profile likelihood method is applied using up to four observables per event.

3 TUMASYAN 23Z based on 138 fb$^{-1}$ of $pp$ data at $\sqrt{s} = 13$ TeV. The second error is the sum of experimental ($\pm 0.61$), model ($\pm 0.47$), and theoretical ($\pm 0.23$) uncertainties. The products of the hadronic decay of a top quark with $p_T > 400$ GeV, in the $\ell^+$ jets channel of $t\bar{t}$, are reconstructed as a single jet. The top quark mass is determined from the normalized differential cross section measurement in the $m_{jet}$ distribution.

4 TUMASYAN 21G based on 35.9 fb$^{-1}$ of $pp$ data at $\sqrt{s} = 13$ TeV. Events are selected by requiring $1\ell + 2$jets(1b jet) final state.

5 SIRUNYAN 20AR based on 35.9 fb$^{-1}$ of $pp$ data at $\sqrt{s} = 13$ TeV. The products of the hadronic decay of a top quark with $p_T > 400$ GeV, in the $\ell^+$ jets channel of $t\bar{t}$ are reconstructed as a single jet. The top quark mass is determined from the normalized differential cross section measurement in the $m_{jet}$ distribution.
# Quark Particle Listings

t

⁶ AABOUD 19AC is an ATLAS combination of 7 and 8 TeV top-quark mass determination in the dilepton, lepton + jets, and all jets channels.

⁷ SIRUNYAN 19AP based on 35.9 fb⁻¹ of pp data at $\sqrt{s}$ = 13 TeV. A kinematical fit is applied to each event assuming the signal event topology. $m_t$ is determined simultaneously with a jet energy scale factor (JSF). The second error represents stat.+JSF. Modeling uncertainties are larger than in the measurements at $\sqrt{s}$ = 7 and 8 TeV because of the use of new alternative color reconnection models.

⁸ SIRUNYAN 19AR based on 35.9 fb⁻¹ of pp data at $\sqrt{s}$ = 13 TeV. Obtained from a simultaneous fit of the cross section and the top quark mass in the POWHEG simulation. The cross section is used also to extract the $\overline{\text{MS}}$ mass and the strong coupling constant for different PDF sets.

⁹ KHACHATRYAN 16AK based on 19.7 fb⁻¹ of pp data at $\sqrt{s}$ = 8 TeV. Combination of the three top mass measurements in KHACHATRYAN 16AK and with the CMS results at $\sqrt{s}$ = 7 TeV.

¹⁰ TEVEWWG 16 is the latest Tevatron average (July 2016) provided by the Tevatron Electroweak Working Group. It takes correlated uncertainties into account and has a $\chi^2$ of 10.8 for 11 degrees of freedom.

¹¹ AABOUD 19AC based on 20.2 fb⁻¹ in pp collisions at $\sqrt{s}$ = 8 TeV. Uses optimized event selection to suppress well-reconstructed events and template fits to determine $m_t$ together with a global jet energy scale factor and a relative b-to-light-jet energy scale factor.

¹² SIRUNYAN 19AP based on 35.9 fb⁻¹ of pp data at $\sqrt{s}$ = 13 TeV. A combined measurement using the lepton+jets and all-jets channels through a single likelihood function. See SIRUNYAN 18DE.

¹³ SIRUNYAN 18DE based on 35.9 fb⁻¹ of pp data at $\sqrt{s}$ = 13 TeV. $m_t$ is determined simultaneously with an overall jet energy scale factor constrained by the mass of the hadronically decayed W. Compared to the Run 1 analysis more advanced treatment of modeling uncertainties are employed, in particular concerning color-reconnection models. Superseded by TUMASYAN 23BB.

¹⁴ AABOUD 17AH based on 20.2 fb⁻¹ of pp data at $\sqrt{s}$ = 8 TeV. Uses template fits to the ratio of the masses of three-jets (from t candidate) and dijets (from W candidate), to suppress jet energy scale uncertainty. Large QCD background is modelled using a data-driven method.

¹⁵ ABAZOV 17b is a combination of measurements of the top quark mass by D0 in the lepton+jets and dilepton channels, using all data collected in Run I (1992–1996) at $\sqrt{s}$ = 1.8 TeV and Run II (2001–2011) at $\sqrt{s}$ = 1.96 TeV of the Tevatron, corresponding to integrated luminosities of 0.1 fb⁻¹ and 9.7 fb⁻¹, respectively.

¹⁶ SIRUNYAN 17L based on 19.7 fb⁻¹ of pp data at $\sqrt{s}$ = 8 TeV. $m_t$ is reconstructed from a fit to the invariant mass distribution of $\mu\nu b$, where $p_T^{\text{miss}}$ and W mass constraint are used to reconstruct $\nu$ momentum. The number of events for various contributions, except for the t-channel single top one, are fixed to the values extracted from simulation. Superseded by TUMASYAN 21G.

¹⁷ SIRUNYAN 17N based on 19.7 fb⁻¹ of pp data at $\sqrt{s}$ = 8 TeV. The fully hadronic decay of a highly-boosted $t$ is reconstructed in the $\ell^+\text{jets}$ channel and unfolded at the particle level. The sensitivity of the peak position of the $m_{\text{jet}}$ distribution is used to test quality of the modelling by the simulation.

¹⁸ SIRUNYAN 17O based on 19.7 fb⁻¹ of pp data at $\sqrt{s}$ = 8 TeV. Analysis is based on the kinematical observables $M(\ell\ell)$, $M_{T2}$ and $M(\ell\ell\ell)$. A fit is performed to determine $m_t$ and an overall jet energy scale factor simultaneously.

¹⁹ AABOUD 16T based on 20.2 fb⁻¹ of pp data at $\sqrt{s}$ = 8 TeV. The analysis is refined using the $p_T$ and invariant mass distributions of $\ell^+\text{jet}$ system. A combination with measurements from $\sqrt{s}$ = 7 TeV data in the dilepton and lepton+jets channels gives 172.84 ± 0.34 ± 0.61 GeV.

²⁰ AABOUD 16T is an ATLAS combination of 8 TeV top-quark mass in the dilepton channel with previous measurements from $\sqrt{s}$ = 7 TeV data in the dilepton and lepton + jets channels.

²¹ ABAZOV 16 based on 9.7 fb⁻¹ of data in $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. Employs improved fit to minimize statistical errors and improved jet energy calibration, using lepton + jets mode, which reduces error of jet energy scale. Based on previous determination in ABAZOV 12AB with increased integrated luminosity and improved fit and calibrations.

²² ABAZOV 16b based on 9.7 fb⁻¹ of data in $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV, using the matrix element technique. Based on previous determination in ABAZOV 11R with increased integrated luminosity. There is a strong correlation with the determination in ABAZOV 16. (See ABAZOV 17B.)

²³ KHACHATRYAN 16AK based on 19.7 fb⁻¹ of pp data at $\sqrt{s}$ = 8 TeV. Combination of the three top mass measurements in KHACHATRYAN 16AK and with the CMS results at $\sqrt{s}$ = 7 TeV gives 172.44 ± 0.13 ± 0.47 GeV.

²⁴ The top mass and jet energy scale factor are determined by a fit.

²⁵ Uses the analytical matrix weighting technique method.

²⁶ KHACHATRYAN 16AL based on 19.7 fb⁻¹ in pp collisions at $\sqrt{s}$ = 8 TeV. Determined from the invariant mass distribution of leptons and reconstructed secondary vertices from b decays using only charged particles. The uncertainty is dominated by modeling of b fragmentation and top $p_T$ distribution.

²⁷ KHACHATRYAN 16CB based on 666 candidate reconstructed events corresponding to 19.7 fb⁻¹ of pp data at $\sqrt{s}$ = 8 TeV. The measurement exploits correlation of $m_t$ with $(M/\psi\ell)$ in the same top quark decay, using a high-purity event sample. A study on modeling of b-quark fragmentation is given in Sec.3.3.

²⁸ AAD 15AW based on 4.6 fb⁻¹ of pp data at $\sqrt{s}$ = 7 TeV. Uses template fits to the ratio of the masses of three-jets (from t candidate) and dijets (from W candidate). Large background from multijet production is modeled with data-driven methods.

²⁹ AAD 15Bf based on 4.6 fb⁻¹ in pp collisions at $\sqrt{s}$ = 7 TeV. Using a three-dimensional template likelihood technique the lepton plus jets ($\ge$ 1b-tagged) channel gives 172.33 ± 0.75 ± 1.02 GeV, while exploiting a one dimensional template method using $m_{\ell b}$ the dilepton channel (1 or 2b-tags) gives 173.79 ± 0.54 ± 1.30 GeV. The results are combined.

³⁰ AALTONEN 15d based on 9.1 fb⁻¹ of $p\bar{p}$ data at $\sqrt{s}$ = 1.96 TeV. Uses a template technique to fit a distribution of a variable defined by a linear combination of variables sensitive and insensitive to jet energy scale to optimize reduction of systematic errors. b-tagged and non-b-tagged events are separately analyzed and combined.

³¹ Based on 9.3 fb⁻¹ of $p\bar{p}$ data at $\sqrt{s}$ = 1.96 TeV. Multivariate algorithm is used to discriminate signal from backgrounds, and templates are used to measure $m_t$.

³² Based on 9.7 fb⁻¹ of $p\bar{p}$ data at $\sqrt{s}$ = 1.96 TeV. A matrix element method is used to calculate the probability of an event to be signal or background, and the overall jet energy scale is constrained in situ by $m_W$. See ABAZOV 15G for further details.

³³ Based on 3.54 fb⁻¹ of pp data at $\sqrt{s}$ = 7 TeV. The mass is reconstructed for each event employing a kinematic fit of the jets to a tbar hypothesis. The combination

with the pervious CMS measurements in the dilepton and the lepton+jets channels gives 173.54 ± 0.33 ± 0.96 GeV.

³⁴ Based on 8.7 fb⁻¹ in $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. Events with an identified charged lepton or small $E_T$ are rejected from the event sample, so that the measurement is statistically independent from those in the $\ell^+$ jets and all hadronic channels while being sensitive to those events with a $\tau$ lepton in the final state.

³⁵ Based on 5.0 fb⁻¹ of pp data at $\sqrt{s}$ = 7 TeV. CHATRCHYAN 13s studied events with di-lepton + $E_T$ ≥ 2 b-jets, and looked for kinematical endpoints of MT2, MT2T, and subsubsystem variables.

³⁶ AAD 12I based on 1.04 fb⁻¹ of pp data at $\sqrt{s}$ = 7 TeV. Uses 2d-template analysis (MT) with $m_t$ and jet energy scale factor (JSF) from $m_W$ mass fit.

³⁷ Based on 8.7 fb⁻¹ of data in $p\bar{p}$ collisions at 1.96 TeV. The JES is calibrated by using the dijet mass from the W boson decay.

³⁸ Use the ME method based on 2.2 fb⁻¹ of data in $p\bar{p}$ collisions at 1.96 TeV.

³⁹ Combination based on up to 5.8 fb⁻¹ of data in $p\bar{p}$ collisions at 1.96 TeV.

⁴⁰ Based on 5.8 fb⁻¹ of data in $p\bar{p}$ collisions at 1.96 TeV the quoted value is $m_t$ = 172.5 ± 1.4(stat) ± 1.0(JES) ± 1.1(syst) GeV. The measurement is performed with a likelihood fit technique which simultaneously determines $m_t$ and JES (Jet Energy Scale).

⁴¹ Based on 4.3 fb⁻¹ of data in p-pbar collisions at 1.96 TeV. The measurement reduces the JES uncertainty by using the single lepton channel study of ABAZOV 11P.

⁴² Combination with the result in 1 fb⁻¹ of preceding data reported in ABAZOV 09AH as well as the MWT result of ABAZOV 11R with a statistical correlation of 60%.

⁴³ Based on 5.0 fb⁻¹ of pp data at $\sqrt{s}$ = 7 TeV. Uses an analytical matrix weighting technique (AMWT) and full kinematic analysis (KIN).

⁴⁴ Based on 5.0 fb⁻¹ of pp data at $\sqrt{s}$ = 7 TeV. The first error is statistical and JES combined, and the second is systematic. Ideogram method is used to obtain 2D likelihood for the kinematical fit with two parameters mtp and JES.

⁴⁵ Based on 3.2 fb⁻¹ in $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. The first error is from statistics and JES combined, and the latter is from the other systematic uncertainties. The result is obtained using an unbinned maximum likelihood method where the top quark mass and the JES are measured simultaneously, with $\Delta_{JES}$ = 0.3 ± 0.3(stat).

⁴⁶ Based on 5.7 fb⁻¹ in $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. Events with an identified charged lepton or small $E_T$ are rejected from the event sample, so that the measurement is statistically independent from those in the $\ell^+$ jets and all hadronic channels while being sensitive to those events with a $\tau$ lepton in the final state. Supersedes AALTONEN 07B.

⁴⁷ AALTONEN 11E based on 5.6 fb⁻¹ in $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. Employs a multi-dimensional template likelihood technique where the lepton plus jets (one or two b-tags) channel gives 172.2 ± 1.2 ± 0.9 GeV while the dilepton channel yields 170.3 ± 2.0 ± 3.1 GeV. The results are combined. OUR EVALUATION includes the measurement in the dilepton channel only.

⁴⁸ Uses a likelihood fit of the lepton $p_T$ distribution based on 2.7 fb⁻¹ in $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV.

⁴⁹ Based on 3.6 fb⁻¹ in $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. ABAZOV 11P reports 174.94 ± 0.83 ± 0.78 ± 0.96 GeV, where the first uncertainty is from statistics, the second from JES, and the last from other systematic uncertainties. We combine the JES and systematic uncertainties. A matrix-element method is used where the JES uncertainty is constrained by the W mass. ABAZOV 11P describes a measurement based on 2.6 fb⁻¹ that is combined with ABAZOV 08AH, which employs an independent 1 fb⁻¹ of data.

⁵⁰ Based on a matrix-element method which employs 5.4 fb⁻¹ in $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. Supersedes by ABAZOV 12AB.

⁵¹ Based on 36 fb⁻¹ of pp collisions at $\sqrt{s}$ = 7 TeV. A Kinematical Method using b-tagging and an analytical Matrix Weighting Technique give consistent results and are combined. Superseded by CHATRCHYAN 12BA.

⁵² Based on 5.6 fb⁻¹ in $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. The likelihood calculated using a matrix element method gives $m_t$ = 173.0 ± 0.7(stat) ± 0.6(JES) ± 0.9(syst) GeV, for a total uncertainty of 1.2 GeV.

⁵³ Based on 3.4 fb⁻¹ of $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. The result is obtained by combining the MT2 variable method and the NWA (Neutrino Weighting Algorithm). The MT2 method alone gives $m_t$ = 168.0 ± 4.8 (stat) ± 2.9(syst) GeV with smaller systematic error due to small JES uncertainty.

⁵⁴ Based on 1.9 fb⁻¹ of $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. The result is from the measurement using the transverse decay length of b-hadrons and that using the transverse momentum of the W decay muons, which are both insensitive to the JES (jet energy scale) uncertainty. OUR EVALUATION uses only the measurement exploiting the decay length significance which yields 166.9 ± 9.5 (stat) ± 2.9 (syst) GeV. The measurement that uses the lepton transverse momentum is excluded from the average because of a statistical correlation with other samples.

⁵⁵ Based on 2.9 fb⁻¹ of $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. The first error is from statistics and JES uncertainty, and the latter is from the other systematics. Neural-network-based kinematical selection of 6 highest $E_T$ jets with a $v\pi$ b-tag is used to distinguish signal from background. Superseded by AALTONEN 12G.

⁵⁶ Based on 2 fb⁻¹ of data at $\sqrt{s}$ = 1.96 TeV. The top mass is obtained from the measurement of the invariant mass of the lepton (e or $\mu$) from W decays and the soft $\mu$ in b-jet. The result is insensitive to jet energy scaling.

⁵⁷ Based on 1.9 fb⁻¹ of data at $\sqrt{s}$ = 1.96 TeV. The first error is from statistics and jet energy scale uncertainty, and the latter is from the other systematics. Matrix element method with effective propagators.

⁵⁸ Based on 943 pb⁻¹ of data at $\sqrt{s}$ = 1.96 TeV. The first error is from statistical and jet-energy-scale uncertainties, and the latter is from other systematics. AALTONEN 09k selected 6 jet events with one or more vertex b-tags and used the tree-level matrix element to construct template models of signal and background.

⁵⁹ Based on 1.9 fb⁻¹ of data at $\sqrt{s}$ = 1.96 TeV. The first error is from statistical and jet-energy-scale (JES) uncertainties, and the second is from other systematics. Events with lepton + jets and those with dilepton + jets were simultaneously fit to constrain $m_t$ and JES. Lepton + jets data only give $m_t$ = 171.8 ± 2.2 GeV, and dilepton data only give $m_t$ = 171.2 ± 5.3 (stat) ± 1.5 GeV.

⁶⁰ Based on 2 fb⁻¹ of data at $\sqrt{s}$ = 1.96 TeV. Matrix Element method. Optimal selection criteria for candidate events with two high $p_T$ leptons, high $E_T$, and two or more jets with and without b-tag are obtained by neural network with neuroevolution technique to minimize the statistical error of $m_t$.

⁶¹ Based on 2.9 fb⁻¹ of data at $\sqrt{s}$ = 1.96 TeV. Mass $m_t$ is estimated from the likelihood for the eight-fold kinematical solutions in the plane of the azimuthal angles of the two neutrino momenta.
62 Based on 1 fb⁻¹ of data at $\sqrt{s} = 1.96$ TeV. Events with two identified leptons, and those with one lepton plus one isolated track and a b-tag were used to constrain $m_t$. The result is a combination of the $\nu$WT (νWT Weighting Technique) result of 176.2 ± 4.8 ± 2.1 GeV and the MWT (Matrix-element Weighting Technique) result of 173.2 ± 4.9 ± 2.0 GeV.

63 Reports measurement of $170.7^{+4.2}_{-3.9} \pm 2.6 \pm 2.4$ GeV based on 1.2 fb⁻¹ of data at $\sqrt{s} = 1.96$ TeV. The last error is due to the theoretical uncertainty on $\sigma_{t\bar{t}}$. Without the cross-section constraint a top mass of $169.7^{+5.2}_{-4.9} \pm 3.1$ GeV is obtained.

64 Template method.

65 Result is based on 1 fb⁻¹ of data at $\sqrt{s} = 1.96$ TeV. The first error is from statistics and jet energy scale uncertainty, and the latter is from the other systematics.

66 Based on 310 pb⁻¹ of data at $\sqrt{s} = 1.96$ TeV.

67 Ideogram method.

68 Based on 311 pb⁻¹ of data at $\sqrt{s} = 1.96$ TeV. Events with 4 or more jets with $E_T > 15$ GeV, significant missing $E_T$, and secondary vertex b-tag are used in the fit. About 44% of the signal acceptance is from $\tau\nu + 4$ jets. Events with identified $e$ or $\mu$ are vetoed to provide a statistically independent measurement.

69 Based on 1.02 fb⁻¹ of data at $\sqrt{s} = 1.96$ TeV. Superseded by AALTONEN 126.

70 Based on 955 pb⁻¹ of data at $\sqrt{s} = 1.96$ TeV, $m_t$ and JES (Jet Energy Scale) are fitted simultaneously, and the first error contains the JES contribution of 1.5 GeV.

71 Matrix element method.

72 Based on 425 pb⁻¹ of data at $\sqrt{s} = 1.96$ TeV. The first error is a combination of statistics and JES (Jet Energy Scale) uncertainty, which has been measured simultaneously to give JES = 0.989 ± 0.029(stat).

73 Based on 370 pb⁻¹ of data at $\sqrt{s} = 1.96$ TeV. Combined result of MWT (Matrix-element Weighting Technique) and $\nu$WT (ν Weighting Technique) analyses is 178.1 ± 6.7 ± 4.8 GeV.

74 Based on 1.0 fb⁻¹ of data at $\sqrt{s} = 1.96$ TeV. ABULENCIA 07D improves the matrix element description by including the effects of initial-state radiation.

75 Based on 695 pb⁻¹ of data at $\sqrt{s} = 1.96$ TeV. The transverse decay length of the b hadron is used to determine $m_t$, and the result is free from the JES (jet energy scale) uncertainty.

76 Based on ~400 pb⁻¹ of data at $\sqrt{s} = 1.96$ TeV. The first error includes statistical and systematic jet energy scale uncertainties, the second error is from the other systematics. The result is obtained with the b-tagging information. The result without b-tagging is $169.2^{+5.0}_{-7.4} \pm 1.4$ GeV. Superseded by ABAZOV 08AH.

77 Based on 318 pb⁻¹ of data at $\sqrt{s} = 1.96$ TeV.

78 Dynamical likelihood method.

79 Based on 340 pb⁻¹ of data at $\sqrt{s} = 1.96$ TeV.

80 Based on 360 pb⁻¹ of data at $\sqrt{s} = 1.96$ TeV.

81 Based on 110.2 ± 5.8 pb⁻¹ at $\sqrt{s} = 1.8$ TeV.

82 Based on the all hadronic decays of $t\bar{t}$ pairs. Single b-quark tagging via the decay chain $b \to c \to \mu$ was used to select signal enriched multijet events. The result was obtained by the maximum likelihood method after bias correction.

83 Obtained by re-analysis of the lepton + jets candidate events that led to ABBOTT 98F. It is based upon the maximum likelihood method which makes use of the leading order matrix elements.

84 Based on 125 ± 7 pb⁻¹ of data at $\sqrt{s} = 1.8$ TeV.

85 Based on ~106 pb⁻¹ of data at $\sqrt{s} = 1.8$ TeV.

86 Obtained by combining the measurements in the lepton + jets [AFFOLDER 01], all-jets [ABE 97R, ABE 99b], and dilepton [ABE 99b] decay topologies.

87 Obtained by combining the DØ results of $m_t$ (GeV) = 168.4 ± 12.3 ± 3.6 from 6 di-lepton events (see also ABBOTT 98D) and $m_t$ (GeV) = 173.3 ± 5.6 ± 5.5 from lepton+jet events (ABBOTT 98f).

88 Obtained by combining the CDF results of $m_t$ (GeV) = 167.4 ± 10.3 ± 4.8 from 8 dilepton events, $m_t$ (GeV) = 175.9 ± 4.8 ± 5.3 from lepton+jet events (ABE 98e), and $m_t$ (GeV) = 186.0 ± 10.0 ± 5.7 from all-jet events (ABE 97R). The systematic errors in the latter two measurements are changed in this paper.

89 See AFFOLDER 01 for details of systematic error re-evaluation.

90 Based on 109 ± 7 pb⁻¹ of data at $\sqrt{s} = 1.8$ TeV.

91 See ABAZOV 04G.

92 The updated systematic error is listed. See AFFOLDER 01, appendix C.

93 Obtained by combining the DØ results of $m_t$ (GeV) = 168.4 ± 12.3 ± 3.6 from 6 dilepton events and $m_t$ (GeV) = 173.3 ± 5.6 ± 5.5 from 77 lepton+jet events.

94 Obtained by combining the DØ results from dilepton and lepton+jet events, and the CDF results (ABE 99b) from dilepton, lepton+jet events, and all-jet events.

95 Based on the first observation of all hadronic decays of $t\bar{t}$ pairs. Single b-quark tagging with jet-shape variable constraints was used to select signal enriched multi-jet events. The updated systematic error is listed. See AFFOLDER 01, appendix C.

<figure><img src="image_427.png" /><figcaption>t-Quark Mass (Direct Measurements) (GeV)</figcaption></figure>

t-Quark Mass from Cross-Section Measurements

The top quark $\overline{\text{MS}}$ or pole mass can be extracted from a measurement of $\sigma(t\bar{t})$ by using theory calculations. We quote below the $\overline{\text{MS}}$ mass. See the review “The Top Quark” and references therein for more information.

<table><thead><tr><th>VALUE (GeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>162.5<sup>+2.1</sup><sub>-1.5</sub> OUR AVERAGE</strong></td><td></td><td></td><td></td></tr></tbody></table>

$162.9 \pm 0.5 \pm 1.0 \pm 2.1 \pm 1.2$

1 AAD

19G ATLS $\ell + \ell_T^+ \ge 5$ j (2b-j)

$160.0 \pm 4.3$

2 ABAZOV

11s D0 $\sigma(t\bar{t})$ + theory

• • • We do not use the following data for averages, fits, limits, etc. • • •

3 ABAZOV

09AG D0

cross sects, theory + exp

4 ABAZOV

09R D0

cross sects, theory + exp

1 AAD 19G based on 20.2 fb⁻¹ of data in $pp$ collisions at $\sqrt{s} = 8$ TeV. Normalized $t\bar{t} + 1$-jet differential cross section as a function of $t\bar{t}^j$ invariant mass is measured in the $\ell +$ jets mode. The unfolded parton-level distribution is compared with the NLO QCD prediction. The three errors are from statistics, systematics, and theory.

2 Based on 5.3 fb⁻¹ in $p\bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV. ABAZOV 11s uses the measured $t\bar{t}$ production cross section of $8.13^{+1.02}_{-0.90}$ pb [ABAZOV 11s] in the lepton plus jets channel to obtain the top quark $\overline{\text{MS}}$ mass by using an approximate NNLO computation (MOCH 08, LANGENFELD 09). The corresponding top quark pole mass is $167.5^{+5.4}_{-4.9}$ GeV. A different theory calculation (AHRENS 10, AHRENS 10A) is also used and yields $m_t^{\overline{\text{MS}}}=154.5^{+5.0}_{-4.3}$ GeV.

3 Based on 1 fb⁻¹ of data at $\sqrt{s} = 1.96$ TeV. Uses the $\ell +$ jets, $\ell\ell$, and $\ell\tau^+$ jets channels. ABAZOV 09AG extract the pole mass of the top quark using two different calculations that yield $169.1^{+5.9}_{-5.2}$ GeV (MOCH 08, LANGENFELD 09) and $168.2^{+5.9}_{-5.4}$ GeV (KIDONAKIS 08).

4 Based on 1 fb⁻¹ of data at $\sqrt{s} = 1.96$ TeV. Uses the $\ell\ell$ and $\ell\tau^+$ jets channels. ABAZOV 09R extract the pole mass of the top quark using two different calculations that yield $173.3^{+9.8}_{-8.6}$ GeV (MOCH 08, LANGENFELD 09) and $171.5^{+9.9}_{-8.8}$ GeV (CAC-CIARI 08).

t-Quark Pole Mass from Cross-Section Measurements

<table><thead><tr><th>VALUE (GeV)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>172.4 ±0.7 OUR AVERAGE</strong></td><td></td><td></td><td></td></tr><tr><td>173.4 <sup>+1.8</sup><sub>-2.0</sub></td><td>1 AAD</td><td>23AY LHC</td><td>e<sup>+</sup>μ<sup>+</sup> pair; ATLAS+CMS combined</td></tr><tr><td>172.93 ±1.36</td><td>2 TUMASYAN</td><td>23R CMS</td><td>t<sup>+</sup>t<sup>-</sup>jet; e<sup>+</sup>ℓ<sup>+</sup> mode</td></tr><tr><td>173.1 <sup>+2.0</sup><sub>-2.1</sub></td><td>3 AAD</td><td>20Q ATLS</td><td>e + μ + 1 or 2 b-jets</td></tr><tr><td>171.1 ± 0.4 ±0.9<sup>+0.7</sup><sub>-0.3</sub></td><td>4 AAD</td><td>19G ATLS</td><td>ℓ + E<sub>T</sub> + ≥ 5 j (2b-j)</td></tr><tr><td>170.6 ±2.7</td><td>5 SIRUNYAN</td><td>17W CMS</td><td>ℓ + ≥ 1j</td></tr><tr><td>172.8 ±1.1 ±3.3<sup>+3.1</sup><sub>-3.1</sub></td><td>6 ABAZOV</td><td>16F D0</td><td>ℓℓ, ℓ+jets channels</td></tr><tr><td>173.7 <sup>+2.3</sup><sub>-2.1</sub></td><td>7 AAD</td><td>15BWATLS</td><td>ℓ + E<sub>T</sub> + ≥ 5j (2b-tag)</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

170.5 ± 0.8

8 SIRUNYAN

20BV CMS

$t\bar{t}$ normalized multi-

173.2 ± 0.9 ±0.8 ±1.2

9 AABOUD

17BC ATLS

differential cross sections

173.8 <sup>+1.7</sup><sub>-1.8</sub>

10 KHACHATRY...16AW CMS

e + μ + ≥ 1b jets

e + μ + $E_T$ + ≥ 0j

172.9 <sup>+2.5</sup><sub>-2.6</sub>

11 AAD

14AY ATLS

pp at $\sqrt{s} = 7$, 8 TeV

176.7 <sup>+3.0</sup><sub>-2.8</sub>

12 CHATRCHYAN

141 CMS

pp at $\sqrt{s} = 7$ TeV

1 AAD 23AY based on 5 fb⁻¹ and 20 fb⁻¹ of $pp$ data at $\sqrt{s} = 7$ TeV and 8 TeV, respectively. The result is combined inclusive cross section measurements and the NNLO+NNLL predictions fixing $\alpha_s(m_Z) = 0.118$.

2 TUMASYAN 23R based on 36.3 fb⁻¹ of data in $pp$ collisions at $\sqrt{s} = 13$ TeV. Normalized $t\bar{t} + 1$-jet differential cross section as a function of $t\bar{t}^j$ invariant mass is measured in the dilepton mode. The unfolded parton-level distribution is compared with the NLO QCD prediction. The result depends on the PDF and ABMP16NLO is used.

3 AAD 20Q based on 36.1 fb⁻¹ of $pp$ data at $\sqrt{s} = 13$ TeV. The result is obtained from the inclusive cross section measurement and the NNLO+NNLL prediction.

4 AAD 19G based on 20.2 fb⁻¹ of data in $pp$ collisions at $\sqrt{s} = 8$ TeV. Normalized $t\bar{t} + 1$-jet differential cross section as a function of $t\bar{t}^j$ invariant mass is measured in the $\ell +$ jets mode. The unfolded parton-level distribution is compared with the NLO QCD prediction. The three errors are from statistics, systematics, and theory.

5 SIRUNYAN 17w based on 2.2 fb⁻¹ of $pp$ data at $\sqrt{s} = 13$ TeV. Events are categorized according to the jet multiplicity and the number of b-tagged jets. The pole mass is obtained from the inclusive cross section measurement and the NNLO prediction.

6 ABAZOV 16F based on 9.7 fb⁻¹ of data in $p\bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV. The result is obtained from the inclusive cross section measurement and the NNLO+NNLL prediction.

7 AAD 15BW based on 4.6 fb⁻¹ of $pp$ data at $\sqrt{s} = 7$ TeV. Uses normalized differential cross section for $t\bar{t} + 1$ jet as a function of the inverse of the invariant mass of the $t\bar{t}$ + 1 jet system. The measured cross section is corrected to the parton level. Then a fit to the data using NLO + parton shower prediction is performed.

8 SIRUNYAN 20BV based on 35.9 fb⁻¹ of $pp$ data at $\sqrt{s} = 13$ TeV. The error accounts for both experimental and theoretical uncertainties. Events containing two oppositely charged leptons are used. The pole mass is particularly sensitive to the $t\bar{t}$ invariant mass distribution close to the threshold. However, the Coulomb and soft gluon resummation effects are not taken into account, hence, an additional theoretical uncertainty of order +1 GeV is assumed.

9 AABOUD 17BC based on 20.2 fb⁻¹ of $pp$ data at $\sqrt{s} = 8$ TeV. The pole mass is extracted from a fit of NLO predictions to eight single lepton and dilepton differential distributions, while simultaneously constraining uncertainties due to PDFs and QCD scales. The three reported uncertainties come from statistics, experimental systematics, and theoretical sources.