<table>
  <tbody>
    <tr>
      <td>S<sub>f</sub>(1300) K<sub>S</sub><sup>0</sup> (B<sup>0</sup> → f<sub>f</sub>(1300) K<sub>S</sub><sup>0</sup>)</td>
      <td>-0.2 ± 0.5</td>
    </tr>
    <tr>
      <td>C<sub>f</sub>(1300) K<sub>S</sub><sup>0</sup> (B<sup>0</sup> → f<sub>f</sub>(1300) K<sub>S</sub><sup>0</sup>)</td>
      <td>0.13 ± 0.35</td>
    </tr>
    <tr>
      <td>S<sub>K</sub><sup>0</sup>π<sup>+</sup>π<sup>-</sup> (B<sup>0</sup> → K<sup>0</sup>π<sup>+</sup>π<sup>-</sup> nonresonant)</td>
      <td>-0.01 ± 0.33</td>
    </tr>
    <tr>
      <td>C<sub>K</sub><sup>0</sup>π<sup>+</sup>π<sup>-</sup> (B<sup>0</sup> → K<sup>0</sup>π<sup>+</sup>π<sup>-</sup> nonresonant)</td>
      <td>0.01 ± 0.26</td>
    </tr>
    <tr>
      <td>C<sub>K</sub><sup>0</sup><sub>S</sub> K<sub>S</sub><sup>0</sup> (B<sup>0</sup> → K<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup>)</td>
      <td>0.0 ± 0.4 (S = 1.4)</td>
    </tr>
    <tr>
      <td>S<sub>K</sub><sup>0</sup><sub>S</sub> K<sub>S</sub><sup>0</sup> (B<sup>0</sup> → K<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup>)</td>
      <td>-0.8 ± 0.5</td>
    </tr>
    <tr>
      <td>C<sub>K</sub><sup>+</sup> K<sub>S</sub><sup>-</sup> K<sub>S</sub><sup>0</sup> (B<sup>0</sup> → K<sub>S</sub><sup>+</sup> K<sub>S</sub><sup>-</sup> K<sub>S</sub><sup>0</sup> nonresonant)</td>
      <td>0.06 ± 0.08</td>
    </tr>
    <tr>
      <td>C<sub>K</sub><sup>+</sup> K<sub>S</sub><sup>-</sup> K<sub>S</sub><sup>0</sup> (B<sup>0</sup> → K<sub>S</sub><sup>+</sup> K<sub>S</sub><sup>-</sup> K<sub>S</sub><sup>0</sup> inclusive)</td>
      <td>0.01 ± 0.09</td>
    </tr>
    <tr>
      <td>C<sub>φ</sub>K<sub>S</sub><sup>0</sup> (B<sup>0</sup> → φK<sub>S</sub><sup>0</sup>)</td>
      <td>-0.09 ± 0.12</td>
    </tr>
    <tr>
      <td>S<sub>φ</sub>K<sub>S</sub><sup>0</sup> (B<sup>0</sup> → φK<sub>S</sub><sup>0</sup>)</td>
      <td>0.58 ± 0.12</td>
    </tr>
    <tr>
      <td>C<sub>K</sub><sub>S</sub> K<sub>S</sub> K<sub>S</sub> (B<sup>0</sup> → K<sub>S</sub> K<sub>S</sub> K<sub>S</sub>)</td>
      <td>-0.14 ± 0.12</td>
    </tr>
    <tr>
      <td>S<sub>K</sub><sub>S</sub> K<sub>S</sub> K<sub>S</sub> (B<sup>0</sup> → K<sub>S</sub> K<sub>S</sub> K<sub>S</sub>)</td>
      <td>-0.82 ± 0.17</td>
    </tr>
    <tr>
      <td>C<sub>K</sub><sup>0</sup><sub>S</sub> π<sup>0</sup>γ (B<sup>0</sup> → K<sub>S</sub><sup>0</sup> π<sup>0</sup>γ)</td>
      <td>0.36 ± 0.33</td>
    </tr>
    <tr>
      <td>S<sub>K</sub><sup>0</sup><sub>S</sub> π<sup>0</sup>γ (B<sup>0</sup> → K<sub>S</sub><sup>0</sup> π<sup>0</sup>γ)</td>
      <td>-0.8 ± 0.6</td>
    </tr>
    <tr>
      <td>C<sub>K</sub><sup>*</sup>(892)<sup>0</sup>γ (B<sup>0</sup> → K<sub>S</sub><sup>*</sup>(892)<sup>0</sup>γ)</td>
      <td>-0.04 ± 0.16 (S = 1.2)</td>
    </tr>
    <tr>
      <td>S<sub>K</sub><sup>*</sup>(892)<sup>0</sup>γ (B<sup>0</sup> → K<sub>S</sub><sup>*</sup>(892)<sup>0</sup>γ)</td>
      <td>-0.15 ± 0.22</td>
    </tr>
    <tr>
      <td>C<sub>η</sub>K<sub>S</sub><sup>0</sup> (B<sup>0</sup> → ηK<sub>S</sub><sup>0</sup>γ)</td>
      <td>0.1 ± 0.4 (S = 1.4)</td>
    </tr>
    <tr>
      <td>S<sub>η</sub>K<sub>S</sub><sup>0</sup> (B<sup>0</sup> → ηK<sub>S</sub><sup>0</sup>γ)</td>
      <td>-0.5 ± 0.5 (S = 1.2)</td>
    </tr>
    <tr>
      <td>C<sub>K</sub><sup>0</sup>φγ (B<sup>0</sup> → K<sup>0</sup>φγ)</td>
      <td>-0.3 ± 0.6</td>
    </tr>
    <tr>
      <td>S<sub>K</sub><sup>0</sup>φγ (B<sup>0</sup> → K<sup>0</sup>φγ)</td>
      <td>0.7<sup>+0.7</sup><sub>-1.1</sub></td>
    </tr>
    <tr>
      <td>C(B<sup>0</sup> → K<sub>S</sub><sup>0</sup>ρ<sup>0</sup>γ)</td>
      <td>-0.05 ± 0.19</td>
    </tr>
    <tr>
      <td>S(B<sup>0</sup> → K<sub>S</sub><sup>0</sup>ρ<sup>0</sup>γ)</td>
      <td>-0.04 ± 0.23</td>
    </tr>
    <tr>
      <td>C(B<sup>0</sup> → ρ<sup>0</sup>γ)</td>
      <td>0.4 ± 0.5</td>
    </tr>
    <tr>
      <td>S(B<sup>0</sup> → ρ<sup>0</sup>γ)</td>
      <td>-0.8 ± 0.7</td>
    </tr>
    <tr>
      <td>C<sub>π</sub><sup>0</sup>π<sup>0</sup> (B<sup>0</sup> → π<sup>0</sup>π<sup>0</sup>)</td>
      <td>-0.30 ± 0.20</td>
    </tr>
    <tr>
      <td>C<sub>ρ</sub>π (B<sup>0</sup> → ρ<sup>+</sup>π<sup>-</sup>)</td>
      <td>-0.03 ± 0.07 (S = 1.2)</td>
    </tr>
    <tr>
      <td>S<sub>ρ</sub>π (B<sup>0</sup> → ρ<sup>+</sup>π<sup>-</sup>)</td>
      <td>0.05 ± 0.07</td>
    </tr>
    <tr>
      <td>ΔS<sub>ρ</sub>π (B<sup>0</sup> → ρ<sup>+</sup>π<sup>-</sup>)</td>
      <td>0.01 ± 0.08</td>
    </tr>
    <tr>
      <td>C<sub>ρ</sub>π<sup>0</sup> (B<sup>0</sup> → ρ<sup>0</sup>π<sup>0</sup>)</td>
      <td>0.27 ± 0.24</td>
    </tr>
    <tr>
      <td>S<sub>ρ</sub><sup>0</sup>π<sup>0</sup> (B<sup>0</sup> → ρ<sup>0</sup>π<sup>0</sup>)</td>
      <td>-0.23 ± 0.34</td>
    </tr>
    <tr>
      <td>C<sub>a</sub><sub>1</sub>π (B<sup>0</sup> → a<sub>1</sub>(1260)<sup>+</sup>π<sup>-</sup>)</td>
      <td>-0.05 ± 0.11</td>
    </tr>
    <tr>
      <td>S<sub>a</sub><sub>1</sub>π (B<sup>0</sup> → a<sub>1</sub>(1260)<sup>+</sup>π<sup>-</sup>)</td>
      <td>-0.2 ± 0.4 (S = 3.2)</td>
    </tr>
    <tr>
      <td>ΔC<sub>a</sub><sub>1</sub>π (B<sup>0</sup> → a<sub>1</sub>(1260)<sup>+</sup>π<sup>-</sup>)</td>
      <td>0.43 ± 0.14 (S = 1.3)</td>
    </tr>
    <tr>
      <td>ΔS<sub>a</sub><sub>1</sub>π (B<sup>0</sup> → a<sub>1</sub>(1260)<sup>+</sup>π<sup>-</sup>)</td>
      <td>-0.11 ± 0.12</td>
    </tr>
    <tr>
      <td>C(B<sup>0</sup> → b<sub>1</sub><sup>-</sup> K<sup>+</sup>)</td>
      <td>-0.22 ± 0.24</td>
    </tr>
    <tr>
      <td>ΔC(B<sup>0</sup> → b<sub>1</sub><sup>-</sup> π<sup>+</sup>)</td>
      <td>-1.04 ± 0.24</td>
    </tr>
    <tr>
      <td>C<sub>ρ</sub><sup>0</sup>ρ<sup>0</sup> (B<sup>0</sup> → ρ<sup>0</sup>ρ<sup>0</sup>)</td>
      <td>0.2 ± 0.9</td>
    </tr>
    <tr>
      <td>S<sub>ρ</sub><sup>0</sup>ρ<sup>0</sup> (B<sup>0</sup> → ρ<sup>0</sup>ρ<sup>0</sup>)</td>
      <td>0.3 ± 0.7</td>
    </tr>
    <tr>
      <td>C<sub>ρ</sub>ρ (B<sup>0</sup> → ρ<sup>+</sup>ρ<sup>-</sup>)</td>
      <td>0.00 ± 0.09</td>
    </tr>
    <tr>
      <td>S<sub>ρ</sub>ρ (B<sup>0</sup> → ρ<sup>+</sup>ρ<sup>-</sup>)</td>
      <td>-0.14 ± 0.13</td>
    </tr>
    <tr>
      <td>|λ| (B<sup>0</sup> → J/ψK<sup>*</sup>(892)<sup>0</sup>)</td>
      <td>&lt;0.25, CL = 95%</td>
    </tr>
    <tr>
      <td>cos 2β (B<sup>0</sup> → J/ψK<sup>*</sup>(892)<sup>0</sup>)</td>
      <td>1.7<sup>+0.7</sup><sub>-0.9</sub> (S = 1.6)</td>
    </tr>
    <tr>
      <td>cos 2β (B<sup>0</sup> → [K<sub>S</sub><sup>0</sup>π<sup>+</sup>π<sup>-</sup>]<sub>D<sup>(s)</sup></sub> h<sup>0</sup>)</td>
      <td>0.91 ± 0.25</td>
    </tr>
    <tr>
      <td>(S<sub>+</sub> + S<sub>-</sub>)/2 (B<sup>0</sup> → D<sup>+</sup>π<sup>+</sup>)</td>
      <td>-0.039 ± 0.011</td>
    </tr>
    <tr>
      <td>(S<sub>-</sub> - S<sub>+</sub>)/2 (B<sup>0</sup> → D<sup>-</sup>π<sup>+</sup>)</td>
      <td>-0.009 ± 0.015</td>
    </tr>
    <tr>
      <td>(S<sub>+</sub> + S<sub>-</sub>)/2 (B<sup>0</sup> → D<sup>-</sup>π<sup>+</sup>)</td>
      <td>-0.046 ± 0.023</td>
    </tr>
    <tr>
      <td>(S<sub>-</sub> - S<sub>+</sub>)/2 (B<sup>0</sup> → D<sup>-</sup>π<sup>+</sup>)</td>
      <td>-0.022 ± 0.021</td>
    </tr>
    <tr>
      <td>S<sub>+</sub> (B<sup>0</sup> → D<sup>-</sup>π<sup>+</sup>)</td>
      <td>0.058 ± 0.023</td>
    </tr>
    <tr>
      <td>S<sub>-</sub> (B<sup>0</sup> → D<sup>+</sup>π<sup>-</sup>)</td>
      <td>0.038 ± 0.021</td>
    </tr>
    <tr>
      <td>(S<sub>+</sub> + S<sub>-</sub>)/2 (B<sup>0</sup> → D<sup>-</sup>ρ<sup>+</sup>)</td>
      <td>-0.024 ± 0.032</td>
    </tr>
    <tr>
      <td>(S<sub>-</sub> - S<sub>+</sub>)/2 (B<sup>0</sup> → D<sup>-</sup>ρ<sup>+</sup>)</td>
      <td>-0.10 ± 0.06</td>
    </tr>
    <tr>
      <td>C<sub>η</sub><sub>c</sub> K<sub>S</sub><sup>0</sup> (B<sup>0</sup> → η<sub>c</sub> K<sub>S</sub><sup>0</sup>)</td>
      <td>0.08 ± 0.13</td>
    </tr>
    <tr>
      <td>C<sub>c</sub>τK<sup>(s)</sup> (B<sup>0</sup> → cτK<sup>(s)</sup>γ)</td>
      <td>(-0.5 ± 1.5) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>C<sub>J/ψ</sub>(nS) K<sub>S</sub><sup>0</sup> (B<sup>0</sup> → J/ψ(nS) K<sub>S</sub><sup>0</sup>)</td>
      <td>(-0.8 ± 1.7) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>C<sub>J</sub>/ψK<sup>+</sup> (B<sup>0</sup> → J/ψK<sup>+</sup>γ)</td>
      <td>0.03 ± 0.10</td>
    </tr>
    <tr>
      <td>S<sub>J</sub>/ψK<sup>+</sup> (B<sup>0</sup> → J/ψK<sup>+</sup>γ)</td>
      <td>0.60 ± 0.25</td>
    </tr>
    <tr>
      <td>C<sub>χ<sub>c</sub>0</sub> K<sub>S</sub><sup>0</sup> (B<sup>0</sup> → χ<sub>c</sub>0 K<sub>S</sub><sup>0</sup>)</td>
      <td>-0.3<sup>+0.5</sup><sub>-0.4</sub></td>
    </tr>
    <tr>
      <td>S<sub>χ<sub>c</sub>0</sub> K<sub>S</sub><sup>0</sup> (B<sup>0</sup> → χ<sub>c</sub>0 K<sub>S</sub><sup>0</sup>)</td>
      <td>-0.7 ± 0.5</td>
    </tr>
  </tbody>
</table>

<table>
  <tbody>
    <tr>
      <td>C<sub>χ<sub>c</sub>1</sub> K<sub>S</sub><sup>0</sup> (B<sup>0</sup> → χ<sub>c1</sub> K<sub>S</sub><sup>0</sup>)</td>
      <td>0.06 ± 0.07</td>
    </tr>
    <tr>
      <td>sin(2β<sup>eff</sup>)(B<sup>0</sup> → φK<sup>0</sup>)</td>
      <td>0.22 ± 0.30</td>
    </tr>
    <tr>
      <td>sin(2β<sup>eff</sup>)(B<sup>0</sup> → φK<sub>S</sub><sup>*</sup>(1430)<sup>0</sup>)</td>
      <td>0.97<sup>+0.03</sup><sub>-0.52</sub></td>
    </tr>
    <tr>
      <td>sin(2β<sup>eff</sup>) (B<sup>0</sup> → [K<sub>S</sub><sup>0</sup>π<sup>+</sup>π<sup>-</sup>]<sub>D<sup>(s)</sup></sub> h<sup>0</sup>)</td>
      <td>0.80 ± 0.16</td>
    </tr>
    <tr>
      <td>|λ| (B<sup>0</sup> → [K<sub>S</sub><sup>0</sup>π<sup>+</sup>π<sup>-</sup>]<sub>D<sup>(s)</sup></sub> h<sup>0</sup>)</td>
      <td>1.01 ± 0.08</td>
    </tr>
    <tr>
      <td>sin(2β + γ)</td>
      <td>&gt;0.40, CL = 90%</td>
    </tr>
    <tr>
      <td>2β + γ</td>
      <td>(80 ± 60)<sup>0</sup></td>
    </tr>
    <tr>
      <td>x<sub>+</sub>(B<sup>0</sup> → DK<sup>*</sup>γ)</td>
      <td>0.04 ± 0.17</td>
    </tr>
    <tr>
      <td>x<sub>-</sub>(B<sup>0</sup> → DK<sup>*</sup>γ)</td>
      <td>-0.16 ± 0.14</td>
    </tr>
    <tr>
      <td>y<sub>+</sub>(B<sup>0</sup> → DK<sup>*</sup>γ)</td>
      <td>-0.68 ± 0.22</td>
    </tr>
    <tr>
      <td>y<sub>-</sub>(B<sup>0</sup> → DK<sup>*</sup>γ)</td>
      <td>0.20 ± 0.25 (S = 1.2)</td>
    </tr>
    <tr>
      <td>a<sub>CP</sub>(B<sup>0</sup> → pπK<sup>+</sup>π<sup>-</sup>)</td>
      <td>(0.5 ± 0.9)%</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(B → K<sup>*</sup>(892)<sup>γ</sup>)</td>
      <td>-0.003 ± 0.011</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(B → sγ)</td>
      <td>0.015 ± 0.011</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(B → (s + d)γ)</td>
      <td>0.010 ± 0.031</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(B → X<sub>S</sub>ℓ<sup>+</sup>ℓ<sup>-</sup>)</td>
      <td>0.04 ± 0.11</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(B → K<sup>*</sup>e<sup>+</sup>e<sup>-</sup>)</td>
      <td>-0.18 ± 0.15</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(B → K<sup>*</sup>μ<sup>+</sup>μ<sup>-</sup>)</td>
      <td>-0.03 ± 0.13</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(B → K<sup>*</sup>ℓ<sup>+</sup>ℓ<sup>-</sup>)</td>
      <td>-0.04 ± 0.07</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(B → ηanything)</td>
      <td>-0.13<sup>+0.04</sup><sub>-0.05</sub></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(X<sub>S</sub>γ) = A<sub>CP</sub>(B<sup>±</sup> → X<sub>S</sub>γ) - A<sub>CP</sub>(B<sup>0</sup> → X<sub>S</sub>γ)</td>
      <td>0.041 ± 0.023</td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(B → X<sub>S</sub>γ) = (A<sub>CP</sub>(B<sup>+</sup> → X<sub>S</sub>γ) + A<sub>CP</sub>(B<sup>0</sup> → X<sub>S</sub>γ))/2</td>
      <td>0.009 ± 0.012</td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(B → K<sup>*</sup>γ) = (A<sub>CP</sub>(B<sup>+</sup> → K<sup>*</sup>γ) + A<sub>CP</sub>(B<sup>0</sup> → K<sup>*</sup>γ))/2</td>
      <td>-0.001 ± 0.014</td>
    </tr>
    <tr>
      <td>Re(ε<sub>B<sup>0</sup></sub>) / (1 + |ε<sub>B<sup>0</sup></sub>|<sup>2</sup>)</td>
      <td>(-0.15 ± 0.70) × 10<sup>-3</sup></td>
    </tr>
    <tr>
      <td>S<sub>K</sub> K<sub>S</sub>(B<sup>0</sup> → K<sup>+</sup> K<sup>-</sup>)</td>
      <td>0.14 ± 0.05 (S = 1.3)</td>
    </tr>
    <tr>
      <td>δ<sub>B</sub>(B<sup>0</sup> → D<sub>S</sub><sup>+</sup>K<sup>π</sup>±π<sup>+</sup>)</td>
      <td>(-6<sup>+10</sup><sub>-13</sub>)°</td>
    </tr>
    <tr>
      <td>CP Violation phase β<sub>s</sub> (b → cτs)</td>
      <td>(2.0 ± 0.8) × 10<sup>-2</sup> rad</td>
    </tr>
    <tr>
      <td>A<sup>L</sup><sub>CP</sub>(B<sub>S</sub> → J/ψK<sup>*</sup>(892)<sup>0</sup>)</td>
      <td>-0.05 ± 0.06</td>
    </tr>
    <tr>
      <td>A<sup>L</sup><sub>CP</sub>(B<sub>S</sub> → J/ψK<sup>*</sup>(892)<sup>0</sup>)</td>
      <td>0.17 ± 0.15</td>
    </tr>
    <tr>
      <td>A<sup>L</sup><sub>CP</sub>(B<sub>S</sub> → J/ψK<sup>*</sup>(892)<sup>0</sup>)</td>
      <td>-0.05 ± 0.10</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(B<sub>S</sub><sup>0</sup> → [K<sup>+</sup> K<sup>-</sup>]<sub>D</sub> K<sup>*</sup>(892)<sup>0</sup>)</td>
      <td>-0.04 ± 0.07</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(B<sub>S</sub><sup>0</sup> → [π<sup>+</sup> K<sup>-</sup>]<sub>D</sub> K<sup>*</sup>(892)<sup>0</sup>)</td>
      <td>-0.01 ± 0.04</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(B<sub>S</sub><sup>0</sup> → [π<sup>+</sup> π<sup>-</sup>]<sub>D</sub> K<sup>*</sup>(892)<sup>0</sup>)</td>
      <td>0.06 ± 0.13</td>
    </tr>
    <tr>
      <td>S(B<sub>S</sub><sup>0</sup> → φγ)</td>
      <td>0.43 ± 0.32</td>
    </tr>
    <tr>
      <td>C(B<sub>S</sub><sup>0</sup> → φγ)</td>
      <td>0.11 ± 0.31</td>
    </tr>
    <tr>
      <td>Γ(η<sub>c</sub>(1S) → π<sup>+</sup>π<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.3 × 10<sup>-4</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(η<sub>c</sub>(1S) → π<sup>0</sup>π<sup>0</sup>)/Γ<sub>total</sub></td>
      <td>&lt;4 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(η<sub>c</sub>(1S) → K<sup>+</sup> K<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;7 × 10<sup>-4</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(η<sub>c</sub>(1S) → K<sub>S</sub><sup>0</sup> K<sub>S</sub><sup>0</sup>)/Γ<sub>total</sub></td>
      <td>&lt;4 × 10<sup>-4</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>n electric dipole moment<br>(α<sub>+</sub> + α<sub>-</sub>)/(α<sub>-</sub> + α<sub>+</sub>) in Λ → ρπ<sup>-</sup>, Λ → <span style="text-decoration: overline">π</span><sup>+</sup></td>
      <td>&lt;0.18 × 10<sup>-25</sup> ecm, CL = 90%<br>(-0.1 ± 0.4) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>[α(Ξ<sup>-</sup>)<sub>-</sub>(Λ)-α(Ξ<sup>+</sup>)<sub>+</sub>(Λ)] / [α(Ξ<sup>-</sup>)<sub>-</sub>(Λ)+α(Ξ<sup>+</sup>)<sub>+</sub>(Λ)]</td>
      <td>(0 ± 7) × 10<sup>-4</sup></td>
    </tr>
    <tr>
      <td>(α + <span style="text-decoration: overline">α</span>)/(α - <span style="text-decoration: overline">α</span>) in Ω<sup>-</sup> → ΛK<sup>-</sup>, Λ<sup>+</sup> → <span style="text-decoration: overline">Λ</span>K<sup>+</sup></td>
      <td>-0.02 ± 0.13</td>
    </tr>
    <tr>
      <td>(α + <span style="text-decoration: overline">α</span>)/(α - <span style="text-decoration: overline">α</span>) in Λ<sup>+</sup> → Λπ<sup>+</sup>, Λ<sup>-</sup> → <span style="text-decoration: overline">Λ</span>π<sup>-</sup></td>
      <td>0.020 ± 0.016</td>
    </tr>
    <tr>
      <td>(α + <span style="text-decoration: overline">α</span>)/(α - <span style="text-decoration: overline">α</span>) in Λ<sup>+</sup> → Λe<sup>+</sup>ν<sub>e</sub>, Λ<sup>-</sup> → <span style="text-decoration: overline">Λ</span>e<sup>-</sup>ν<sub>e</sub></td>
      <td>0.00 ± 0.04</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(Λ<sub>b</sub> → pπ<sup>-</sup>)</td>
      <td>-0.025 ± 0.029 (S = 1.2)</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(Λ<sub>b</sub> → pK<sup>-</sup>)</td>
      <td>-0.025 ± 0.022</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(Λ<sub>b</sub> → DpK<sup>-</sup>)</td>
      <td>0.12 ± 0.09</td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(ρK<sup>-</sup>/π<sup>-</sup>)</td>
      <td>0.014 ± 0.024</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(Λ<sub>b</sub> → p<span style="text-decoration: overline">K</span><sup>0</sup>π<sup>-</sup>)</td>
      <td>0.22 ± 0.13</td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(J/ψρπ<sup>-</sup>/K<sup>-</sup>)</td>
      <td>(5.7 ± 2.7) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(Λ<sub>b</sub> → ΛK<sup>+</sup>π<sup>-</sup>)</td>
      <td>-0.53 ± 0.25</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(Λ<sub>b</sub> → ΛK<sup>+</sup>K<sup>-</sup>)</td>
      <td>-0.28 ± 0.12</td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>b</sub><sup>0</sup> → pK<sup>-</sup>μ<sup>+</sup>μ<sup>-</sup>)</td>
      <td>(-4 ± 5) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>b</sub><sup>0</sup> → pπ<sup>-</sup>π<sup>+</sup>π<sup>-</sup>)</td>
      <td>(1.1 ± 2.6) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>b</sub><sup>0</sup> → (ρπ<sup>-</sup>π<sup>+</sup>π<sup>-</sup>))<sub>LBM</sub></td>
      <td>(4 ± 4) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>b</sub><sup>0</sup> → p<i>a</i><sub>1</sub>(1260)<sup>-</sup>)</td>
      <td>(-1 ± 4) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>b</sub><sup>0</sup> → N(1520)<sup>0</sup>ρ(770)<sup>0</sup>)</td>
      <td>(2 ± 5) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>b</sub><sup>0</sup> → Δ(1232)<sup>+</sup>π<sup>-</sup>π<sup>-</sup>)</td>
      <td>(0.1 ± 3.3) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>b</sub><sup>0</sup> → pK<sup>-</sup>π<sup>+</sup>π<sup>-</sup>)</td>
      <td>(3.2 ± 1.3) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>b</sub><sup>0</sup> → (ρK<sup>-</sup>π<sup>+</sup>π<sup>-</sup>))<sub>LBM</sub></td>
      <td>(3.5 ± 1.6) × 10<sup>-2</sup></td>
    </tr>
  </tbody>
</table>

Unless otherwise stated, limits are given at the 90% confidence level, while errors are given as ±1 standard deviation.
<table>
  <tbody>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>D</sub><sup>0</sup> → N(1520)<sup>0</sup> K*<sup>(892)</sup><sup>0</sup>)</td>
      <td>(5.5 ± 2.5) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>D</sub><sup>0</sup> → Λ(1520) ρ(770)<sup>0</sup>)</td>
      <td>(1 ± 6) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>D</sub><sup>0</sup> → Δ(1232)<sup>++</sup> K<sup>-</sup>π<sup>-</sup>)</td>
      <td>(4.4 ± 2.7) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>D</sub><sup>0</sup> → pK<sub>1</sub>(1410)<sup>-</sup>)</td>
      <td>(5 ± 4) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>D</sub><sup>0</sup> → pK<sup>-</sup> K<sup>+</sup> π<sup>-</sup>)</td>
      <td>(-7 ± 5) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>D</sub><sup>0</sup> → pK<sup>-</sup> K<sup>+</sup> K<sup>-</sup>)</td>
      <td>(0.2 ± 1.9) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>D</sub><sup>0</sup> → Λ(1520) φ(1020))</td>
      <td>(4 ± 6) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>D</sub><sup>0</sup> → (pK<sup>-</sup>)<sub>highmass</sub> φ(1020))</td>
      <td>(-0.7 ± 3.4) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>D</sub><sup>0</sup> → (pK<sup>-</sup> K<sup>+</sup> K<sup>-</sup>)<sub>LBM</sub>)</td>
      <td>(2.7 ± 2.4) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>A<sub>c</sub>(Λ)</td>
      <td>-0.22 ± 0.13</td>
    </tr>
    <tr>
      <td>A<sub>s</sub>(Λ)</td>
      <td>0.13 ± 0.13</td>
    </tr>
    <tr>
      <td>A<sub>c</sub>(φ)</td>
      <td>-0.01 ± 0.12</td>
    </tr>
    <tr>
      <td>A<sub>s</sub>(φ)</td>
      <td>-0.07 ± 0.12</td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>D</sub><sup>0</sup> → pπ<sup>-</sup>π<sup>+</sup>π<sup>-</sup>)</td>
      <td>(-0.7 ± 0.7)%</td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>D</sub><sup>0</sup> → pK<sup>-</sup>π<sup>+</sup>π<sup>-</sup>)</td>
      <td>(-0.8 ± 0.9)%</td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>D</sub><sup>0</sup> → pK<sup>-</sup> K<sup>+</sup> π<sup>-</sup>)</td>
      <td>(-1 ± 5)%</td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>D</sub><sup>0</sup> → pK<sup>-</sup> K<sup>+</sup> K<sup>-</sup>)</td>
      <td>(1.1 ± 1.5)%</td>
    </tr>
    <tr>
      <td>ΔA<sub>CP</sub>(Λ<sub>D</sub><sup>0</sup> → pK<sup>-</sup> μ<sup>+</sup> μ<sup>-</sup>)</td>
      <td>(1 ± 5)%</td>
    </tr>
  </tbody>
</table>

CP VIOLATION OBSERVED

$$
\text{Re}(\epsilon) \qquad (1.596 \pm 0.013) \times 10^{-3}
$$

charge asymmetry in K⁰₃ decays

$$
\begin{align*}
A_L &= \text{weighted average of } A_L(\mu) \text{ and } A_L(e) \\
    &\quad (0.332 \pm 0.006)\%
\end{align*}
$$

$$
\begin{align*}
A_L(\mu) &= [\Gamma(\pi^+ \mu^+ \nu_\mu) \\
&\quad - \Gamma(\pi^+ \mu^- \bar{\nu}_\mu)] / \text{sum} \\
(0.304 \pm 0.025)\%
\end{align*}
$$

$$
\begin{align*}
A_L(e) &= [\Gamma(\pi^+ e^- \nu_e) \\
&\quad - \Gamma(\pi^+ e^- \bar{\nu}_e)] / \text{sum} \\
(0.334 \pm 0.007)\%
\end{align*}
$$

parameters for K<sup>0</sup><sub>L</sub> → 2π decay

$$
\begin{align*}
|\eta_{00}| &= |A(K_L^0 \to 2\pi^0) / \\
            &\qquad A(K_S^0 \to 2\pi^0)| \qquad (2.220 \pm 0.011) \times 10^{-3} \quad (S=1.8)
\end{align*}
$$

$$
\begin{align*}
|\eta_{+-}| &= |A(K_L^0 \to \pi^+\pi^-) / \\
            &\qquad A(K_S^0 \to \pi^+\pi^-)| \qquad (2.232 \pm 0.011) \times 10^{-3} \quad (S=1.8)
\end{align*}
$$

$$
|\epsilon| = (2|\eta_{+-}| + |\eta_{00}|)/3 \qquad (2.228 \pm 0.011) \times 10^{-3} \quad (S=1.8)
$$

$$
|\eta_00/\eta_{+-}| \qquad [1] \quad 0.9950 \pm 0.0007 \quad (S=1.6)
$$

$$
\text{Re}(\epsilon'/\epsilon) = (1 - |\eta_00/\eta_{+-}|)/3 \qquad [1] \quad (1.66 \pm 0.23) \times 10^{-3} \quad (S=1.6)
$$

Assuming CPT

$$
\phi_{+-}, \text{ phase of } \eta_{+-} \qquad (43.51 \pm 0.05)^{\circ} \quad (S=1.2)
$$

$$
\phi_{00}, \text{ phase of } \eta_{00} \qquad (43.52 \pm 0.05)^{\circ} \quad (S=1.2)
$$

$$
\phi_{\epsilon} = (2\phi_{+-} + \phi_{00})/3 \qquad (43.52 \pm 0.04)^{\circ} \quad (S=1.2)
$$

Not assuming CPT

$$
\phi_{+-}, \text{ phase of } \eta_{+-} \qquad (43.4 \pm 0.5)^{\circ} \quad (S=1.2)
$$

$$
\phi_{00}, \text{ phase of } \eta_{00} \qquad (43.7 \pm 0.6)^{\circ} \quad (S=1.2)
$$

$$
\phi_{\epsilon} = (2\phi_{+-} + \phi_{00})/3 \qquad (43.5 \pm 0.5)^{\circ} \quad (S=1.3)
$$

$$
\begin{align*}
\text{CP asymmetry A in } K_L^0 &\to \pi^+\pi^- e^+e^- \\
\beta_{CP} \text{ from } K_L^0 &\to e^+e^- e^+e^- \\
\gamma_{CP} \text{ from } K_L^0 &\to e^+e^- e^+e^-
\end{align*}
\begin{align*}
(13.7 \pm 1.5)\% \\
-0.19 \pm 0.07 \\
0.01 \pm 0.11 \quad (S=1.6)
\end{align*}
$$

parameters for K<sup>0</sup><sub>L</sub> → π<sup>+</sup>π<sup>-</sup>γ decay

$$
|\eta_{+-\gamma}| = |A(K_L^0 \to \pi^+\pi^-\gamma, CP \text{ violating})/A(K_S^0 \to \pi^+\pi^-\gamma)| \qquad (2.35 \pm 0.07) \times 10^{-3}
$$

$$
\phi_{+-\gamma} = \text{phase of } \eta_{+-\gamma} \qquad (44 \pm 4)^{\circ}
$$

$$
\Gamma(K_L^0 \to \pi^+\pi^-)/\Gamma_{\text{total}} \qquad [1] \quad (1.967 \pm 0.010) \times 10^{-3} \quad (S=1.5)
$$

$$
\Gamma(K_L^0 \to \pi^0 \pi^0)/\Gamma_{\text{total}} \qquad (8.64 \pm 0.06) \times 10^{-4} \quad (S=1.8)
$$

$$
\Delta A_{CP}^{D_0} = A_{CP}(K^{+} K^{-}) - A_{CP}(\pi^{+} \pi^{-}) \qquad (-0.154 \pm 0.029)\%
$$

$$
A_{CP}(B^{+} \to [K^{-} \pi^{+} \bar{D} K^{*}(892)_{S}]) \qquad -0.75 \pm 0.16
$$

$$
A_{CP}(B^{+} \to D_{CP}(+1) K^{+}) \qquad 0.132 \pm 0.015 \quad (S=1.8)
$$

$$
A_{ADS}(B^{+} \to D K^{+}) \qquad -0.451 \pm 0.026
$$

$$
A_{CP}(B^{+} \to \eta K^{+}) \qquad -0.37 \pm 0.08
$$

$$
A_{CP}(B^{+} \to K^{+} \pi^{-} \pi^{+}) \qquad 0.015 \pm 0.006 \quad (S=1.4)
$$

$$
A_{CP}(B^{+} \to f_{2}(1270) K^{+}) \qquad -0.68 \pm 0.19
$$

$$
A_{CP}(B^{+} \to \rho^{0} K^{+}) \qquad 0.160 \pm 0.021
$$

$$
A_{CP}(B^{+} \to K^{+} K^{-} \pi^{+}) \qquad -0.115 \pm 0.008
$$

$$
A_{CP}(B^{+} \to \pi^{+} (K^{+} K^{-})_{S-wave}) \qquad -0.66 \pm 0.04
$$

$$
A_{CP}(B^{+} \to K^{+} K^{-} K^{+}) \qquad -0.036 \pm 0.004
$$

$$
A_{CP}(B^{+} \to \pi^{+} \pi^{-} \pi^{+}) \qquad 0.076 \pm 0.008 \quad (S=1.5)
$$

$$
A_{CP}(B^{+} \to f_{2}(1270) \pi^{+}) \qquad 0.40 \pm 0.06
$$

<table>
  <tbody>
    <tr>
      <td>γ</td>
      <td>(65.9+2.9)<sup>o</sup><br>(65.9+2.9)<sup>-3.1</sup></td>
    </tr>
    <tr>
      <td>τ<sub>B</sub>(B<sup>+</sup> → D<sup>0</sup>K<sup>+</sup>)</td>
      <td>(9.94 ± 0.26) × 10<sup>-2</sup></td>
    </tr>
    <tr>
      <td>δ<sub>B</sub>(B<sup>+</sup> → D<sup>0</sup>K<sup>+</sup>)</td>
      <td>(127.7+3.6)<sup>o</sup><br>(127.7+3.9)<sup>-</sup></td>
    </tr>
    <tr>
      <td>τ<sub>B</sub>(B<sup>+</sup> → D<sup>0</sup>K<sup>+</sup>*)</td>
      <td>0.016 ± 0.016<br>0.034</td>
    </tr>
    <tr>
      <td>δ<sub>B</sub>(B<sup>+</sup> → D<sup>0</sup>K<sup>+</sup>*)</td>
      <td>(48+59)<sup>o</sup><br>(48+59)<sup>-16</sup></td>
    </tr>
    <tr>
      <td>τ<sub>B</sub>(B<sup>+</sup> → D<sup>+</sup>0 K<sup>+</sup>)</td>
      <td>0.104+0.013<br>-0.014</td>
    </tr>
    <tr>
      <td>δ<sub>B</sub>(B<sup>+</sup> → D<sup>+</sup>0 K<sup>+</sup>)</td>
      <td>(314.8+7.9)<sup>o</sup><br>(314.8+7.9)<sup>-9.9</sup></td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(B<sup>0</sup> → K<sup>+</sup>π<sup>-</sup>)</td>
      <td>-0.0831 ± 0.0031</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(B<sup>0</sup> → ηK<sup>*</sup>(892)<sup>0</sup>)</td>
      <td>0.19 ± 0.05</td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(B<sup>0</sup> → K<sup>*</sup>(892)<sup>+</sup>π<sup>-</sup>)</td>
      <td>-0.27 ± 0.04</td>
    </tr>
    <tr>
      <td>S<sub>D<sup>+</sup>(2010)</sub> - D<sup>+</sup> (B<sup>0</sup> → D<sup>*</sup>(2010)<sup>-</sup> D<sup>+</sup>)</td>
      <td>-0.83 ± 0.09</td>
    </tr>
    <tr>
      <td>S<sub>D<sup>+</sup>(2010)</sub> + D<sup>-</sup> (B<sup>0</sup> → D<sup>*</sup>(2010)<sup>+</sup> D<sup>-</sup>)</td>
      <td>-0.80 ± 0.09</td>
    </tr>
    <tr>
      <td>S<sub>D<sup>+</sup> + D<sup>-</sup></sub> (B<sup>0</sup> → D<sup>+</sup> + D<sup>-</sup>)</td>
      <td>-0.59 ± 0.14 (S = 1.8)</td>
    </tr>
    <tr>
      <td>S<sub>+</sub> (B<sup>0</sup> → D<sup>+</sup> + D<sup>-</sup>)</td>
      <td>-0.73 ± 0.09</td>
    </tr>
    <tr>
      <td>S<sub>D<sup>+</sup> + D<sup>-</sup></sub> (B<sup>0</sup> → D<sup>+</sup> + D<sup>-</sup>)</td>
      <td>-0.76+0.15<br>-0.13 (S = 1.2)</td>
    </tr>
    <tr>
      <td>S<sub>J/ψ(1S)</sub>π<sup>0</sup> (B<sup>0</sup> → J/ψ(1S)π<sup>0</sup>)</td>
      <td>-0.88 ± 0.32 (S = 2.2)</td>
    </tr>
    <tr>
      <td>S<sub>B<sup>0</sup></sub> → J/ψ(1S)ρ<sup>0</sup></td>
      <td>-0.66+0.16<br>-0.12</td>
    </tr>
    <tr>
      <td>S<sub>K<sup>0</sup>π<sup>0</sup></sub> (B<sup>0</sup> → K<sup>+</sup>π<sup>-</sup>π<sup>+</sup>π<sup>-</sup>)</td>
      <td>0.64 ± 0.13</td>
    </tr>
    <tr>
      <td>S<sub>η'K<sup>0</sup></sub> (B<sup>0</sup> → η'<sub>0</sub>K<sup>0</sup>)</td>
      <td>0.63 ± 0.06</td>
    </tr>
    <tr>
      <td>S<sub>K<sup>+</sup> - K<sup>0</sup>S</sub> (B<sup>0</sup> → K<sup>+</sup> K<sup>-</sup> - K<sup>0</sup>S<sup>0</sup><br>nonresonant)</td>
      <td>-0.66 ± 0.11</td>
    </tr>
    <tr>
      <td>S<sub>K<sup>+</sup> - K<sup>0</sup>S</sub> (B<sup>0</sup> → K<sup>+</sup> K<sup>-</sup> - K<sup>0</sup>S<sup>0</sup><br>inclusive)</td>
      <td>-0.65 ± 0.12</td>
    </tr>
    <tr>
      <td>C<sub>ππ</sub> (B<sup>0</sup> → π<sup>+</sup>π<sup>-</sup>)</td>
      <td>-0.314 ± 0.030</td>
    </tr>
    <tr>
      <td>S<sub>ππ</sub> (B<sup>0</sup> → π<sup>+</sup>π<sup>-</sup>)</td>
      <td>-0.670 ± 0.030</td>
    </tr>
    <tr>
      <td>ΔC<sub>ρπ</sub> (B<sup>0</sup> → ρ<sup>+</sup>π<sup>-</sup>)</td>
      <td>0.27 ± 0.06</td>
    </tr>
    <tr>
      <td>S<sub>η<sub>c</sub>K<sub>S</sub><sup>0</sup></sub> (B<sup>0</sup> → η<sub>c</sub>K<sub>S</sub><sup>0</sup>)</td>
      <td>0.93 ± 0.17</td>
    </tr>
    <tr>
      <td>sin(2β<sub>c</sub>) (B<sup>0</sup> → J/ψK<sub>S</sub><sup>0</sup>)</td>
      <td>0.709 ± 0.011</td>
    </tr>
    <tr>
      <td>S<sub>J/ψ(nS)</sub> K<sup>0</sup> (B<sup>0</sup> → J/ψ(nS)K<sup>0</sup>)</td>
      <td>0.701 ± 0.017</td>
    </tr>
    <tr>
      <td>S<sub>χ<sub>c1</sub>K<sub>S</sub><sup>0</sup></sub> (B<sup>0</sup> → χ<sub>c1</sub>K<sub>S</sub><sup>0</sup>)</td>
      <td>0.63 ± 0.10</td>
    </tr>
    <tr>
      <td>sin(2β<sub>eff</sub>) (B<sup>0</sup> → K<sup>+</sup> K<sup>-</sup> - K<sup>0</sup>S<sup>0</sup>)</td>
      <td>0.77+0.13<br>-0.12</td>
    </tr>
    <tr>
      <td>α</td>
      <td>(84.1+3.5)<sup>o</sup><br>(84.1+3.5)<sup>-3.8</sup></td>
    </tr>
    <tr>
      <td>τ<sub>B</sub>(B<sup>0</sup> → D K<sup>+</sup>*)</td>
      <td>0.257+0.021<br>-0.023</td>
    </tr>
    <tr>
      <td>δ<sub>B</sub>(B<sup>0</sup> → D K<sup>+</sup>*)</td>
      <td>(194.1+9.6)<sup>o</sup><br>(194.1+9.6)<sup>-8.8</sup></td>
    </tr>
    <tr>
      <td>C<sub>K</sub>K (B<sup>0</sup> → K<sup>+</sup> K<sup>-</sup>)</td>
      <td>0.162 ± 0.035</td>
    </tr>
    <tr>
      <td>τ<sub>B</sub>(B<sup>0</sup><sub>S</sub> → D<sub>S</sub><sup>±</sup> K<sup>±</sup>)</td>
      <td>0.37+0.10<br>-0.09</td>
    </tr>
    <tr>
      <td>τ<sub>B</sub>(B<sup>0</sup><sub>S</sub> → D<sub>S</sub><sup>±</sup> K<sup>±</sup>π<sup>±</sup>π<sup>±</sup>)</td>
      <td>0.47 ± 0.08</td>
    </tr>
    <tr>
      <td>δ<sub>B</sub>(B<sup>0</sup><sub>S</sub> → D<sub>S</sub><sup>±</sup> K<sup>±</sup>)</td>
      <td>(358+14)<sup>o</sup></td>
    </tr>
    <tr>
      <td>A<sub>CP</sub>(B<sub>S</sub> → π<sup>+</sup> K<sup>-</sup>)</td>
      <td>0.224 ± 0.012</td>
    </tr>
  </tbody>
</table>

CPT INVARIENCE

<table>
  <tbody>
    <tr>
      <td>(m<sub>W</sub> + m<sub>W</sub>) / m<sub>average</sub></td>
      <td>(-3.7 ± 3.5) × 10<sup>-4</sup></td>
    </tr>
    <tr>
      <td>(m<sub>e</sub> + m<sub>e</sub>) / m<sub>average</sub></td>
      <td>&lt;8 × 10<sup>-9</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>|q<sub>e</sub><sup>+</sup> + q<sub>e</sub><sup>-</sup>|/e</td>
      <td>&lt;4 × 10<sup>-8</sup></td>
    </tr>
    <tr>
      <td>(g<sub>e</sub><sup>+</sup> - g<sub>e</sub><sup>-</sup>) / g<sub>average</sub></td>
      <td>(-0.5 ± 2.1) × 10<sup>-12</sup></td>
    </tr>
    <tr>
      <td>(τ<sub>μ</sub><sup>+</sup> - τ<sub>μ</sub><sup>-</sup>) / τ<sub>average</sub></td>
      <td>(2 ± 8) × 10<sup>-5</sup></td>
    </tr>
    <tr>
      <td>(g<sub>μ</sub><sup>+</sup> - g<sub>μ</sub><sup>-</sup>) / g<sub>average</sub></td>
      <td>(-0.11 ± 0.12) × 10<sup>-8</sup></td>
    </tr>
    <tr>
      <td>(m<sub>τ</sub><sup>+</sup> - m<sub>τ</sub><sup>-</sup>) / m<sub>average</sub></td>
      <td>&lt;2.8 × 10<sup>-4</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>⟨Δm<sup>2</sup><sub>21</sub> - Δm<sup>2</sup><sub>21</sub>⟩ in neutrino mixing</td>
      <td>&lt;1.1 × 10<sup>-4</sup> eV<sup>2</sup>, CL = 99.7%</td>
    </tr>
    <tr>
      <td>⟨Δm<sup>2</sup><sub>32</sub> - Δm<sup>2</sup><sub>32</sub>⟩ in neutrino mixing</td>
      <td>(-0.12 ± 0.25) × 10<sup>-3</sup> eV<sup>2</sup></td>
    </tr>
    <tr>
      <td>m<sub>t</sub> - m<sub>t̄</sub></td>
      <td>-0.15 ± 0.20 GeV (S = 1.1)</td>
    </tr>
    <tr>
      <td>(m<sub>π</sub><sup>+</sup> - m<sub>π</sub><sup>-</sup>) / m<sub>average</sub></td>
      <td>(2 ± 5) × 10<sup>-4</sup></td>
    </tr>
    <tr>
      <td>(τ<sub>π</sub><sup>+</sup> - τ<sub>π</sub><sup>-</sup>) / τ<sub>average</sub></td>
      <td>(6 ± 7) × 10<sup>-4</sup></td>
    </tr>
    <tr>
      <td>(m<sub>K</sub><sup>+</sup> - m<sub>K</sub><sup>-</sup>) / m<sub>average</sub></td>
      <td>(-0.6 ± 1.8) × 10<sup>-4</sup></td>
    </tr>
    <tr>
      <td>(τ<sub>K</sub><sup>+</sup> - τ<sub>K</sub><sup>-</sup>) / τ<sub>average</sub></td>
      <td>(0.10 ± 0.09)% (S = 1.2)</td>
    </tr>
    <tr>
      <td>K<sup>±</sup> → μ<sup>±</sup>ν<sub>μ</sub> rate difference/sum</td>
      <td>(-0.27 ± 0.21)%</td>
    </tr>
    <tr>
      <td>K<sup>±</sup> → π<sup>±</sup>π<sup>0</sup> rate difference/sum</td>
      <td>[k] (0.4 ± 0.6)%</td>
    </tr>
    <tr>
      <td>δ in K<sup>±</sup> → K<sup>0</sup> mixing</td>
      <td></td>
    </tr>
    <tr>
      <td>real part of δ</td>
      <td>(2.5 ± 2.3) × 10<sup>-4</sup></td>
    </tr>
    <tr>
      <td>imaginary part of δ</td>
      <td>(-1.5 ± 1.6) × 10<sup>-5</sup></td>
    </tr>
    <tr>
      <td>Re(y), K<sub>e3</sub> parameter</td>
      <td>(0.4 ± 2.5) × 10<sup>-3</sup></td>
    </tr>
    <tr>
      <td>Re(x<sub>-</sub>), K<sub>e3</sub> parameter</td>
      <td>(-2.9 ± 2.0) × 10<sup>-3</sup></td>
    </tr>
    <tr>
      <td>|m<sub>K<sup>0</sup></sub> - m<sub>K<sup>0</sup></sub>| / m<sub>average</sub></td>
      <td>[j] &lt;6 × 10<sup>-19</sup>, CL = 90%</td>
    </tr>
  </tbody>
</table>

Unless otherwise stated, limits are given at the 90% confidence level, while errors are given as ±1 standard deviation.
$$ (\Gamma_{K^0} - \Gamma_{K^0})/m_{\text{average}} $$

$$ (8 \pm 8) \times 10^{-18} $$

$$ \text{phase difference } \phi_{00} - \phi_{+} - $$

$$ (0.34 \pm 0.32)^{\circ} $$

$$ \text{Re}(\frac{2}{2}\eta_{+} + + \frac{1}{2}\eta_{00}) - \frac{A}{2} $$

$$ (-3 \pm 35) \times 10^{-6} $$

$$ A_{CPT}(D^0 \rightarrow \kappa^- \pi^+) $$

$$ 0.008 \pm 0.008 $$

$$ \Delta\Sigma_{CPT}^{+} (S_{\ell^{+}, K_S^0}^{-} - S_{\ell^{+}, K_S^0}^{+}) $$

$$ 0.16 \pm 0.23 $$

$$ \Delta\Sigma_{CPT}^{-} (S_{\ell^{+}, K_S^0}^{+} - S_{\ell^{+}, K_S^0}^{-}) $$

$$ -0.03 \pm 0.14 $$

$$ \Delta C_{CPT}^{+} (C_{\ell^{+}, K_S^0}^{-} - C_{\ell^{+}, K_S^0}^{+}) $$

$$ 0.14 \pm 0.17 $$

$$ \Delta C_{CPT}^{-} (C_{\ell^{+}, K_S^0}^{+} - C_{\ell^{+}, K_S^0}^{-}) $$

$$ 0.03 \pm 0.14 $$

$$ |m_p - m_{\bar{p}}|/m_p \left( \frac{q_p}{|m_p| - m_p} \right) / m_p $$

$$ [\eta] < 7 \times 10^{-10}, \text{ CL} = 90\% \quad (0.3 \pm 1.6) \times 10^{-11} $$

$$ |q_p + \phi_p|/e $$

$$ [\eta] < 7 \times 10^{-10}, \text{ CL} = 90\% $$

$$ (\mu_p + \mu_{\bar{p}})/\mu_p $$

$$ (0.002 \pm 0.004) \times 10^{-6} $$

$$ (m_n - m_{\bar{n}})/m_n $$

$$ (9 \pm 5) \times 10^{-5} $$

$$ (m_{\Lambda} - m_{\bar{\Lambda}})/m_{\Lambda} $$

$$ (-0.1 \pm 1.1) \times 10^{-5} \quad (S = 1.6) $$

$$ (\tau_{\Lambda} - \tau_{\bar{\Lambda}})/\tau_{\Lambda} $$

$$ (0.9 \pm 3.2) \times 10^{-3} $$

$$ (\tau_{\Sigma^{+}} - \tau_{\bar{\Sigma}^{-}})/\tau_{\Sigma^{+}} $$

$$ -0.0006 \pm 0.0012 $$

$$ (\mu_{\Sigma^{+}} + \mu_{\bar{\Sigma}^{-}})/\mu_{\Sigma^{+}} $$

$$ 0.014 \pm 0.015 $$

$$ (m_{\Xi^{-}} - m_{\bar{\Xi}^{+}})/m_{\Xi^{-}} $$

$$ (-3 \pm 9) \times 10^{-5} $$

$$ (\tau_{\Xi^{-}} - \tau_{\bar{\Xi}^{+}})/\tau_{\Xi^{-}} $$

$$ -0.01 \pm 0.07 $$

$$ (\mu_{\Xi^{-}} + \mu_{\bar{\Xi}^{+}})/|\mu_{\Xi^{-}}| $$

$$ +0.01 \pm 0.05 $$

$$ (m_{\Omega^{-}} - m_{\bar{\Omega}^{+}})/m_{\Omega^{-}} $$

$$ (-1 \pm 8) \times 10^{-5} $$

$$ (\tau_{\Omega^{-}} - \tau_{\bar{\Omega}^{+}})/\tau_{\Omega^{-}} $$

$$ 0.00 \pm 0.05 $$

## TESTS OF NUMBER CONSERVATION LAWS

### LEPTON FAMILY NUMBER

Lepton family number conservation means separate conservation of each of $L_e, L_\mu, L_\tau$.

$$ \Gamma(Z \rightarrow e^{\pm} \mu^{\mp})/\Gamma_{\text{total}} $$

$$ [\eta] < 2.62 \times 10^{-7}, \text{ CL} = 95\% $$

$$ \Gamma(Z \rightarrow e^{\pm} \tau^{\mp})/\Gamma_{\text{total}} $$

$$ [\eta] < 5.0 \times 10^{-6}, \text{ CL} = 95\% $$

$$ \Gamma(Z \rightarrow \mu^{\pm} \tau^{\mp})/\Gamma_{\text{total}} $$

$$ [\eta] < 6.5 \times 10^{-6}, \text{ CL} = 95\% $$

$$ \Gamma(H \rightarrow e\mu)/\Gamma_{\text{total}} $$

$$ < 4.4 \times 10^{-5}, \text{ CL} = 95\% $$

$$ \Gamma(H \rightarrow e\tau)/\Gamma_{\text{total}} $$

$$ < 2.0 \times 10^{-3}, \text{ CL} = 95\% $$

$$ \Gamma(H \rightarrow \mu\tau)/\Gamma_{\text{total}} $$

$$ < 1.5 \times 10^{-3}, \text{ CL} = 95\% $$

$$ \sigma(e^{+} e^{-} \rightarrow e^{\pm} \tau^{\mp}) / \sigma(e^{+} e^{-} \rightarrow \mu^{+} \mu^{-}) $$

$$ < 8.9 \times 10^{-6}, \text{ CL} = 95\% $$

$$ \sigma(e^{+} e^{-} \rightarrow \mu^{\pm} \tau^{\mp}) / \sigma(e^{+} e^{-} \rightarrow \mu^{+} \mu^{-}) $$

$$ < 4.0 \times 10^{-6}, \text{ CL} = 95\% $$

$$ \text{limit on } \mu^{-} \rightarrow e^{-} \text{ conversion} \\ \sigma(\mu^{-} 32S \rightarrow e^{-} 32S) / \sigma(\mu^{-} 32S \rightarrow \nu_{\mu} 32P^{*}) $$

$$ < 7 \times 10^{-11}, \text{ CL} = 90\% $$

$$ \sigma(\mu^{-} \text{Ti} \rightarrow e^{-} \text{Ti}) / \sigma(\mu^{-} \text{Ti} \rightarrow \text{capture}) $$

$$ < 4.3 \times 10^{-12}, \text{ CL} = 90\% $$

$$ \sigma(\mu^{-} \text{Pb} \rightarrow e^{-} \text{Pb}) / \sigma(\mu^{-} \text{Pb} \rightarrow \text{capture}) $$

$$ < 4.6 \times 10^{-11}, \text{ CL} = 90\% $$

$$ \sigma(\mu^{-} \text{Au} \rightarrow e^{-} \text{Au}) / \sigma(\mu^{-} \text{Au} \rightarrow \text{capture}) $$

$$ < 7 \times 10^{-13}, \text{ CL} = 90\% $$

$$ \text{limit on muonium } \rightarrow \text{antimuonium} \text{ conversion} \quad R_g = G_C / G_F $$

$$ < 0.0030, \text{ CL} = 90\% $$

$$ \Gamma(\mu^{-} \rightarrow e^{-} \nu_{e} \sigma_{\mu})/\Gamma_{\text{total}} $$

$$ [\eta] < 1.2 \times 10^{-2}, \text{ CL} = 90\% $$

$$ \Gamma(\mu^{-} \rightarrow e^{-} \gamma)/\Gamma_{\text{total}} $$

$$ < 4.2 \times 10^{-13}, \text{ CL} = 90\% $$

$$ \Gamma(\mu^{-} \rightarrow e^{-} e^{+})/\Gamma_{\text{total}} $$

$$ < 1.0 \times 10^{-12}, \text{ CL} = 90\% $$

$$ \Gamma(\mu^{-} \rightarrow e^{-} 2\gamma)/\Gamma_{\text{total}} $$

$$ < 7.2 \times 10^{-11}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} \gamma)/\Gamma_{\text{total}} $$

$$ < 3.3 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} \gamma \gamma)/\Gamma_{\text{total}} $$

$$ < 2.5 \times 10^{-4}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \gamma)/\Gamma_{\text{total}} $$

$$ < 4.2 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \gamma \gamma)/\Gamma_{\text{total}} $$

$$ < 5.8 \times 10^{-4}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} \pi^{0})/\Gamma_{\text{total}} $$

$$ < 8.0 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \pi^{0})/\Gamma_{\text{total}} $$

$$ < 1.1 \times 10^{-7}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} K_{S}^{0})/\Gamma_{\text{total}} $$

$$ < 2.6 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} K_{S}^{0})/\Gamma_{\text{total}} $$

$$ < 2.3 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} \eta)/\Gamma_{\text{total}} $$

$$ < 9.2 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \eta)/\Gamma_{\text{total}} $$

$$ < 6.5 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} \rho^{0})/\Gamma_{\text{total}} $$

$$ < 2.2 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \rho^{0})/\Gamma_{\text{total}} $$

$$ < 1.7 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} \omega)/\Gamma_{\text{total}} $$

$$ < 2.4 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \omega)/\Gamma_{\text{total}} $$

$$ < 3.9 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} K^{*}(892)^{0})/\Gamma_{\text{total}} $$

$$ < 1.9 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} K^{*}(892)^{0})/\Gamma_{\text{total}} $$

$$ < 2.9 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} K^{*}(892)^{0})/\Gamma_{\text{total}} $$

$$ < 1.7 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} K^{*}(892)^{0})/\Gamma_{\text{total}} $$

$$ < 4.3 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} \eta^{(958)})/\Gamma_{\text{total}} $$

$$ < 1.6 \times 10^{-7}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \eta^{(958)})/\Gamma_{\text{total}} $$

$$ < 1.3 \times 10^{-7}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} f_{0}(980) \rightarrow e^{-} \pi^{+} \pi^{-})/\Gamma_{\text{total}} $$

$$ < 3.2 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} \phi)/\Gamma_{\text{total}} $$

$$ < 3.4 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \phi)/\Gamma_{\text{total}} $$

$$ < 2.3 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} e^{+} e^{-})/\Gamma_{\text{total}} $$

$$ < 2.7 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} \mu^{+} \mu^{-})/\Gamma_{\text{total}} $$

$$ < 2.7 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{+} \mu^{+} \mu^{-})/\Gamma_{\text{total}} $$

$$ < 1.7 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} e^{-} e^{+})/\Gamma_{\text{total}} $$

$$ < 1.8 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{+} e^{-} e^{+})/\Gamma_{\text{total}} $$

$$ < 1.5 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \mu^{+} \mu^{-})/\Gamma_{\text{total}} $$

$$ < 2.1 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} \pi^{+} \pi^{-})/\Gamma_{\text{total}} $$

$$ < 2.3 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \pi^{-} \pi^{+})/\Gamma_{\text{total}} $$

$$ < 2.1 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \pi^{+} \pi^{-})/\Gamma_{\text{total}} $$

$$ < 3.7 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} \pi^{+} K^{+})/\Gamma_{\text{total}} $$

$$ < 3.1 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} K_{S}^{0} K_{S}^{0})/\Gamma_{\text{total}} $$

$$ < 7.1 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} K^{+} K^{-})/\Gamma_{\text{total}} $$

$$ < 3.4 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \pi^{-} K^{+})/\Gamma_{\text{total}} $$

$$ < 8.6 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \pi^{-} K^{-})/\Gamma_{\text{total}} $$

$$ < 4.5 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} K_{S}^{0} K_{S}^{0})/\Gamma_{\text{total}} $$

$$ < 8.0 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} K^{+} K^{-})/\Gamma_{\text{total}} $$

$$ < 4.4 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} \pi^{0} \pi^{0})/\Gamma_{\text{total}} $$

$$ < 6.5 \times 10^{-6}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} \eta^{(958)})/\Gamma_{\text{total}} $$

$$ < 1.4 \times 10^{-5}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \eta^{(958)})/\Gamma_{\text{total}} $$

$$ < 3.5 \times 10^{-5}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} \pi^{0} \eta)/\Gamma_{\text{total}} $$

$$ < 6.0 \times 10^{-5}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \pi^{0} \eta)/\Gamma_{\text{total}} $$

$$ < 2.4 \times 10^{-5}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow \mu^{-} \pi^{0} \eta^{(958)})/\Gamma_{\text{total}} $$

$$ < 2.2 \times 10^{-5}, \text{ CL} = 90\% $$

$$ \Gamma(\tau^{-} \rightarrow e^{-} \text{light boson})/\Gamma_{\text{total}} $$

$$ < 9 \times 10^{-4}, \text{ CL} = 95\% $$

### LEPTON FAMILY NUMBER VIOLATION IN NEUTRINOS

$$ \sin^2(\theta_{12}) $$

$$ 0.307 \pm 0.013 $$

$$ \Delta m^2_{21} $$

$$ (7.53 \pm 0.18) \times 10^{-5} \text{ eV}^2 $$

$$ \sin^2(\theta_{23}) \text{ (Inverted order)} $$

$$ 0.553 \pm 0.016 \quad (S = 1.1) $$

$$ \sin^2(\theta_{23}) \text{ (Normal order)} $$

$$ 0.558 \pm 0.015 $$

$$ \Delta m^2_{32} $$

$$ (-2.529 \pm 0.029) \times 10^{-3} \text{ eV}^2 $$

$$ \Delta m^2_{32} \text{ (Inverted order)} $$

$$ (2.455 \pm 0.028) \times 10^{-3} \text{ eV}^2 $$

$$ \Delta m^2_{32} \text{ (Normal order)} $$

$$ (2.19 \pm 0.07) \times 10^{-2} \quad (S = 1.2) $$

$$ \Gamma(t \rightarrow e^{\pm} \mu^{\mp})/\Gamma_{\text{total}} $$

$$ < 8.9 \times 10^{-7} $$

$$ \Gamma(t \rightarrow e^{\pm} \mu^{\mp} u)/\Gamma_{\text{total}} $$

$$ < 7 \times 10^{-8} $$

$$ \Gamma(\pi^{+} \rightarrow \mu^{+} \nu_{e})/\Gamma_{\text{total}} $$

$$ [\eta] < 8.0 \times 10^{-3}, \text{ CL} = 90\% $$

$$ \Gamma(\pi^{+} \rightarrow \mu^{-} e^{+} e^{+})/\Gamma_{\text{total}} $$

$$ < 1.6 \times 10^{-6}, \text{ CL} = 90\% $$

$$ \Gamma(\pi^{0} \rightarrow \mu^{+} e^{+})/\Gamma_{\text{total}} $$

$$ < 3.8 \times 10^{-10}, \text{ CL} = 90\% $$

$$ \Gamma(\pi^{0} \rightarrow \mu^{+} e^{+})/\Gamma_{\text{total}} $$

$$ < 3.2 \times 10^{-10}, \text{ CL} = 90\% $$

$$ \Gamma(\pi^{0} \rightarrow \mu^{+} e^{+} + \mu^{-} e^{+})/\Gamma_{\text{total}} $$

$$ < 3.6 \times 10^{-10}, \text{ CL} = 90\% $$

$$ \Gamma(\eta \rightarrow \mu^{+} e^{-} + \mu^{-} e^{+})/\Gamma_{\text{total}} $$

$$ < 6 \times 10^{-6}, \text{ CL} = 90\% $$

$$ \Gamma(\eta^{(958)} \rightarrow e_{\mu})/\Gamma_{\text{total}} $$

$$ < 4.7 \times 10^{-4}, \text{ CL} = 90\% $$

$$ \Gamma(\phi(1020) \rightarrow e^{\pm} \mu^{\mp})/\Gamma_{\text{total}} $$

$$ < 2 \times 10^{-6}, \text{ CL} = 90\% $$

$$ \Gamma(K^{+} \rightarrow \mu^{-} \nu_{e} e^{+} e^{+})/\Gamma_{\text{total}} $$

$$ < 8.1 \times 10^{-11}, \text{ CL} = 90\% $$

$$ \Gamma(K^{+} \rightarrow \mu^{+} \nu_{e})/\Gamma_{\text{total}} $$

$$ < 4 \times 10^{-3}, \text{ CL} = 90\% $$

$$ \Gamma(K^{+} \rightarrow \pi^{+} \mu^{+} e^{-})/\Gamma_{\text{total}} $$

$$ < 1.3 \times 10^{-11}, \text{ CL} = 90\% $$

$$ \Gamma(K^{0}_{L} \rightarrow e^{\pm} \mu^{\mp})/\Gamma_{\text{total}} $$

$$ < 6.6 \times 10^{-11}, \text{ CL} = 90\% $$

$$ \Gamma(K^{0}_{L} \rightarrow \pi^{0} \mu^{+} e^{+})/\Gamma_{\text{total}} $$

$$ [\eta] < 4.12 \times 10^{-11}, \text{ CL} = 90\% $$

$$ \Gamma(K^{0}_{L} \rightarrow \pi^{0} \mu^{0} \mu^{\mp})/\Gamma_{\text{total}} $$

$$ [\eta] < 7.6 \times 10^{-11}, \text{ CL} = 90\% $$

$$ \Gamma(K^{0}_{L} \rightarrow \pi^{0} \pi^{0} \mu^{\mp} e^{+})/\Gamma_{\text{total}} $$

$$ < 1.7 \times 10^{-10}, \text{ CL} = 90\% $$

$$ \Gamma(D^{+} \rightarrow \pi^{+} e^{+} \mu^{-})/\Gamma_{\text{total}} $$

$$ < 2.1 \times 10^{-7}, \text{ CL} = 90\% $$

$$ \Gamma(D^{+} \rightarrow \pi^{+} e^{+} \mu^{-})/\Gamma_{\text{total}} $$

$$ < 2.2 \times 10^{-7}, \text{ CL} = 90\% $$

$$ \Gamma(D^{+} \rightarrow K^{+} e^{+} \mu^{-})/\Gamma_{\text{total}} $$

$$ < 7.5 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(D^{+} \rightarrow K^{+} e^{-} \mu^{+})/\Gamma_{\text{total}} $$

$$ < 1.0 \times 10^{-7}, \text{ CL} = 90\% $$

$$ \Gamma(D^{0} \rightarrow \mu^{\pm} e^{+})/\Gamma_{\text{total}} $$

$$ [\eta] < 1.3 \times 10^{-8}, \text{ CL} = 90\% $$

$$ \Gamma(D^{0} \rightarrow \pi^{0} e^{\mp \mp})/\Gamma_{\text{total}} $$

$$ < 8.0 \times 10^{-7}, \text{ CL} = 90\% $$

Unless otherwise stated, limits are given at the 90% confidence level, while errors are given as ±1 standard deviation.
TOTAL LEPTON NUMBER

Violation of total lepton number conservation also implies violation of lepton family number conservation.

<table>
  <tbody>
    <tr>
      <td>Γ(Z → p e)/Γ<sub>total</sub></td>
      <td>&lt;1.8 × 10<sup>-6</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(Z → p μ)/Γ<sub>total</sub></td>
      <td>&lt;1.8 × 10<sup>-6</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>limit on μ<sup>-</sup> → e<sup>+</sup> conversion</td>
      <td></td>
    </tr>
    <tr>
      <td>σ(μ<sup>-</sup> 32S → e<sup>+</sup> 32Si<sup>*</sup>) / σ(μ<sup>-</sup> 32S → ν<sub>μ</sub> 32P<sup>*</sup>)</td>
      <td>&lt;9 × 10<sup>-10</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>σ(μ<sup>-</sup> 127I → e<sup>+</sup> 127Sb<sup>*</sup>) / σ(μ<sup>-</sup> 127I → anything)</td>
      <td>&lt;3 × 10<sup>-10</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>σ(μ<sup>-</sup> Ti → e<sup>+</sup> Ca) / σ(μ<sup>-</sup> Ti → capture)</td>
      <td>&lt;3.6 × 10<sup>-11</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → e<sup>+</sup> π<sup>-</sup> π<sup>-</sup>) / Γ<sub>total</sub></td>
      <td>&lt;2.0 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → μ<sup>+</sup> π<sup>-</sup> π<sup>-</sup>) / Γ<sub>total</sub></td>
      <td>&lt;3.9 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → e<sup>+</sup> π<sup>-</sup> K<sup>-</sup>) / Γ<sub>total</sub></td>
      <td>&lt;3.2 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → e<sup>+</sup> K<sup>-</sup> K<sup>-</sup>) / Γ<sub>total</sub></td>
      <td>&lt;3.3 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → μ<sup>+</sup> π<sup>-</sup> K<sup>-</sup>) / Γ<sub>total</sub></td>
      <td>&lt;4.8 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → μ<sup>+</sup> K<sup>-</sup> K<sup>-</sup>) / Γ<sub>total</sub></td>
      <td>&lt;4.7 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p e<sup>-</sup> e<sup>-</sup>) / Γ<sub>total</sub></td>
      <td>&lt;3.0 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p e<sup>+</sup> e<sup>-</sup>) / Γ<sub>total</sub></td>
      <td>&lt;3.0 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p e<sup>+</sup> μ<sup>-</sup>) / Γ<sub>total</sub></td>
      <td>&lt;2.0 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p e<sup>-</sup> μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;1.8 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p μ<sup>-</sup> μ<sup>-</sup>) / Γ<sub>total</sub></td>
      <td>&lt;4.0 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p μ<sup>+</sup> μ<sup>-</sup>) / Γ<sub>total</sub></td>
      <td>&lt;1.8 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p γ) / Γ<sub>total</sub></td>
      <td>&lt;3.5 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p π<sup>0</sup>) / Γ<sub>total</sub></td>
      <td>&lt;1.5 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p 2π<sup>0</sup>) / Γ<sub>total</sub></td>
      <td>&lt;3.3 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p η) / Γ<sub>total</sub></td>
      <td>&lt;8.9 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p π<sup>0</sup>η) / Γ<sub>total</sub></td>
      <td>&lt;2.7 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → Λ π<sup>-</sup>) / Γ<sub>total</sub></td>
      <td>&lt;7.2 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → Λ π<sup>-</sup>) / Γ<sub>total</sub></td>
      <td>&lt;1.4 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>t<sub>1/2</sub> (76Ge → 76Se + 2 e<sup>-</sup>)</td>
      <td>&gt;9.0 × 10<sup>25</sup> yr, CL = 90%</td>
    </tr>
    <tr>
      <td>t<sub>1/2</sub> (136Xe → 136Ba + 2 e<sup>-</sup>)</td>
      <td>&gt;10.7 × 10<sup>25</sup> yr, CL = 90%</td>
    </tr>
    <tr>
      <td>t<sub>1/2</sub> (130Te → 130Xe + 2 e<sup>-</sup>)</td>
      <td>&gt;1.5 × 10<sup>25</sup> yr, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(π<sup>+</sup> → μ<sup>+</sup> ν<sub>e</sub>) / Γ<sub>total</sub></td>
      <td>[q] &lt;1.5 × 10<sup>-3</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(K<sup>+</sup> → π<sup>-</sup> μ<sup>+</sup> e<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;4.2 × 10<sup>-11</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(K<sup>+</sup> → π<sup>-</sup> e<sup>+</sup> e<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;5.3 × 10<sup>-11</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(K<sup>+</sup> → π<sup>-</sup> μ<sup>+</sup> μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;4.2 × 10<sup>-11</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(K<sup>+</sup> → π<sup>-</sup> π<sub>0</sub> e<sup>+</sup> e<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;8.5 × 10<sup>-10</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(K<sup>+</sup> → μ<sup>+</sup> ν<sub>e</sub>) / Γ<sub>total</sub></td>
      <td>[q] &lt;3.3 × 10<sup>-3</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(K<sup>+</sup> → π<sub>0</sub> e<sup>+</sup> ν<sub>e</sub>) / Γ<sub>total</sub></td>
      <td>&lt;3 × 10<sup>-3</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → π<sup>-</sup> 2e<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;5.3 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → π<sup>-</sup> 2μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;1.4 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → π<sup>-</sup> e<sup>+</sup> μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;1.3 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → ρ<sup>-</sup> 2μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;5.6 × 10<sup>-4</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → K<sup>-</sup> 2e<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;9 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → K<sup>-</sup> 2μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;1.0 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → K<sup>-</sup> e<sup>+</sup> μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;1.9 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → K<sup>*</sup> (892<sup>+</sup> 2μ<sup>+</sup>)) / Γ<sub>total</sub></td>
      <td>&lt;8.5 × 10<sup>-4</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → Λ e<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;1.1 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → Λ e<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;6.5 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → Σ<sup>0</sup> e<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;1.7 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → Σ<sup>0</sup> e<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;1.3 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → 2π<sup>-</sup> 2e<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;9.1 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → 2π<sup>-</sup> 2μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;1.52 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → K<sup>-</sup> π<sup>-</sup> 2e<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;5.0 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → K<sup>-</sup> π<sup>-</sup> 2μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;5.3 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → 2K<sup>-</sup> 2e<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;3.4 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → 2K<sup>-</sup> 2μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;1.0 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → π<sup>-</sup> π<sup>-</sup> e<sup>+</sup> μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;3.06 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → K<sup>-</sup> π<sup>-</sup> e<sup>+</sup> μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;2.10 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → 2K<sup>-</sup> e<sup>+</sup> μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;5.8 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → p e<sup>-</sup>) / Γ<sub>total</sub></td>
      <td>&lt;2.2 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → p e<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;1.2 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup><sub>S</sub> → π<sup>-</sup> 2e<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;1.4 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup><sub>S</sub> → π<sup>-</sup> 2μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;8.6 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup><sub>S</sub> → π<sup>-</sup> e<sup>+</sup> μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;6.3 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup><sub>S</sub> → K<sup>-</sup> 2e<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;7.7 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup><sub>S</sub> → K<sup>-</sup> 2μ<sup>+</sup>) / Γ<sub>total</sub></td>
      <td>&lt;2.6 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
  </tbody>
</table>

<table>
  <tbody>
    <tr>
      <td>Γ(D<sup>0</sup> → ηe<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;2.25 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → π<sup>+</sup> π<sup>-</sup> e<sup>±</sup> μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.71 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → ρ<sup>0</sup> e<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;5.0 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → ωe<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.71 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → K<sup>-</sup> K<sup>+</sup> e<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.00 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → φe<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;5.1 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → R<sup>0</sup> e<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.74 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → K<sup>-</sup> π<sup>+</sup> e<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.90 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → R<sup>*</sup>(892<sup>0</sup> e<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.25 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup><sub>S</sub> → π<sup>+</sup> e<sup>+</sup> μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.1 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup><sub>S</sub> → π<sup>+</sup> e<sup>-</sup> μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;9.4 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup><sub>S</sub> → K<sup>+</sup> e<sup>+</sup> μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;7.9 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup><sub>S</sub> → K<sup>+</sup> e<sup>-</sup> μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;5.6 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → π<sup>+</sup> e<sup>+</sup> μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;6.4 × 10<sup>-3</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → π<sup>+</sup> e<sup>-</sup> μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;6.4 × 10<sup>-3</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → π<sup>+</sup> e<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.7 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → π<sup>+</sup> e<sup>+</sup> τ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;7.4 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → π<sup>+</sup> e<sup>-</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;2.0 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → π<sup>+</sup> e<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;7.5 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → π<sup>+</sup> μ<sup>+</sup> τ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;6.2 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → π<sup>+</sup> μ<sup>-</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;4.5 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → π<sup>+</sup> μ<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;7.2 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K<sup>+</sup> e<sup>+</sup> μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;7.0 × 10<sup>-9</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K<sup>+</sup> e<sup>-</sup> μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;6.4 × 10<sup>-9</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K<sup>+</sup> e<sup>±</sup> μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;9.1 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K<sup>+</sup> e<sup>+</sup> τ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.53 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K<sup>+</sup> e<sup>-</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.5 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K<sup>+</sup> e<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;3.0 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K<sup>+</sup> μ<sup>+</sup> τ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;2.45 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K<sup>+</sup> μ<sup>-</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;5.9 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K<sup>+</sup> μ<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;4.8 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K<sup>*</sup>(892<sup>+</sup> e<sup>±</sup> μ<sup>+</sup>))/Γ<sub>total</sub></td>
      <td>[0] &lt;1.3 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K<sup>*</sup>(892<sup>+</sup> e<sup>-</sup> μ<sup>+</sup>))/Γ<sub>total</sub></td>
      <td>[0] &lt;9.9 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K<sup>*</sup>(892<sup>+</sup> e<sup>±</sup> μ<sup>+</sup>))/Γ<sub>total</sub></td>
      <td>[0] &lt;1.4 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → e<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.0 × 10<sup>-9</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → π<sup>0</sup> e<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.4 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → K<sup>0</sup> e<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;3.8 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → K<sup>*</sup>(892<sup>0</sup> e<sup>±</sup> μ<sup>+</sup>))/Γ<sub>total</sub></td>
      <td>[0] &lt;6.8 × 10<sup>-9</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → K<sup>*</sup>(892<sup>0</sup> e<sup>-</sup> μ<sup>+</sup>))/Γ<sub>total</sub></td>
      <td>[0] &lt;5.7 × 10<sup>-9</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → K<sup>*</sup>(892<sup>0</sup> e<sup>±</sup> μ<sup>+</sup>))/Γ<sub>total</sub></td>
      <td>[0] &lt;1.01 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → K<sup>*</sup>(892<sup>0</sup> τ<sup>+</sup> μ<sup>-</sup>))/Γ<sub>total</sub></td>
      <td>[0] &lt;1.0 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → K<sup>*</sup>(892<sup>0</sup> τ<sup>-</sup> μ<sup>+</sup>))/Γ<sub>total</sub></td>
      <td>[0] &lt;8.2 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → e<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.6 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → μ<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.4 × 10<sup>-5</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → μ<sup>±</sup> τ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;2.2 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B → πe<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;9.2 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B → ρe<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;3.2 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B → K e<sup>±</sup> μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;3.8 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B → K<sup>*</sup>(892<sup>±</sup> e<sup>±</sup> μ<sup>+</sup>))/Γ<sub>total</sub></td>
      <td>[0] &lt;5.1 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → e<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;5.4 × 10<sup>-9</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → e<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.4 × 10<sup>-3</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → μ<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;4.2 × 10<sup>-5</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → φμ<sup>±</sup> e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.6 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(J/ψ(1S) → e<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.6 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(J/ψ(1S) → e<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;7.5 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(J/ψ(1S) → μ<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;2.0 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Γ(1S) → e<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;3.9 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Γ(1S) → μ<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;2.7 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Γ(1S) → e<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;2.7 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Γ(1S) → γe<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;4.2 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Γ(1S) → γμ<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;6.1 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Γ(1S) → γe<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;6.5 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Γ(2S) → e<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;3.2 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Γ(2S) → μ<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;3.3 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Γ(3S) → e<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;4.2 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Γ(3S) → e<sup>±</sup> μ<sup>∓</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;3.6 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Γ(3S) → μ<sup>±</sup> τ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;3.1 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sup>+</sup><sub>C</sub> → p e<sup>+</sup> μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;9.9 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sup>+</sup><sub>C</sub> → p e<sup>-</sup> μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>[0] &lt;1.9 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
  </tbody>
</table>

Unless otherwise stated, limits are given at the 90% confidence level, while errors are given as ±1 standard deviation.
<table>
  <tbody>
    <tr>
      <td>Γ(D<sub>S</sub><sup>+</sup> → K<sup>-</sup>e<sup>+</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;2.6 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sub>S</sub><sup>+</sup> → K*(892<sup>-</sup>2μ<sup>+</sup>))/Γ<sub>total</sub></td>
      <td>&lt;1.4 × 10<sup>-3</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → π<sup>-</sup>e<sup>+</sup>e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;2.3 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → π<sup>-</sup>μ<sup>+</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;4.0 × 10<sup>-9</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → π<sup>-</sup>e<sup>+</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.5 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → p<sup>-</sup>e<sup>+</sup>e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.7 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → ρ<sup>-</sup>μ<sup>+</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;4.2 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → ρ<sup>-</sup>e<sup>+</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;4.7 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K<sup>-</sup>e<sup>+</sup>e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;3.0 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K<sup>-</sup>μ<sup>+</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;4.1 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K<sup>-</sup>e<sup>+</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.6 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K*(892<sup>-</sup>e<sup>+</sup>e<sup>+</sup>))/Γ<sub>total</sub></td>
      <td>&lt;4.0 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K*(892<sup>-</sup>μ<sup>+</sup>μ<sup>+</sup>))/Γ<sub>total</sub></td>
      <td>&lt;5.9 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → K*(892<sup>-</sup>e<sup>+</sup>μ<sup>+</sup>))/Γ<sub>total</sub></td>
      <td>&lt;3.0 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → D<sup>-</sup>e<sup>+</sup>e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;2.6 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → D<sup>-</sup>e<sup>+</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.8 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → D<sup>-</sup>μ<sup>+</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;6.9 × 10<sup>-7</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → D<sup>-</sup>μ<sup>+</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;2.4 × 10<sup>-6</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → D<sub>S</sub><sup>-</sup>μ<sup>+</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;5.8 × 10<sup>-7</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → D<sup>0</sup>π<sup>-</sup>μ<sup>+</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.5 × 10<sup>-6</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → Λ<sup>0</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;6 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → Λ<sup>0</sup>e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;3.2 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → Λ<sup>0</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;6 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → Λ<sup>0</sup>e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;8 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → pμ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;2.6 × 10<sup>-9</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → Λ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.4 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → Λ<sup>+</sup>e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;4 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → Λ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.21 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sub>S</sub><sup>+</sup> → π<sup>+</sup>e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;6 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sub>S</sub><sup>+</sup> → π<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;6 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sub>S</sub><sup>+</sup> → π<sup>-</sup>e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;4 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sub>S</sub><sup>+</sup> → π<sup>-</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;6 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sub>S</sub><sup>+</sup> → K<sup>+</sup>e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;2 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sub>S</sub><sup>+</sup> → K<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;3 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sub>S</sub><sup>+</sup> → K<sup>+</sup>e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;2 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Σ<sup>-</sup> → pe<sup>-</sup>e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;6.7 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Ξ<sup>-</sup> → pμ<sup>-</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;4 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sub>C</sub><sup>+</sup> → p2e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;2.7 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sub>C</sub><sup>+</sup> → p2μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;9.4 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sub>C</sub><sup>+</sup> → pe<sup>+</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.6 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sub>C</sub><sup>+</sup> → Σ<sup>-</sup>μ<sup>+</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;7.0 × 10<sup>-4</sup>, CL = 90%</td>
    </tr>
  </tbody>
</table>

BARYON NUMBER

<table>
  <tbody>
    <tr>
      <td>Γ(Z → p e)/Γ<sub>total</sub></td>
      <td>&lt;1.8 × 10<sup>-6</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(Z → p μ)/Γ<sub>total</sub></td>
      <td>&lt;1.8 × 10<sup>-6</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p e<sup>-</sup> e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;3.0 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p e<sup>+</sup> e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;3.0 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p e<sup>+</sup> e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;2.0 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p e<sup>-</sup> e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.8 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p μ<sup>-</sup> μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;4.0 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p μ<sup>+</sup> μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.8 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p γ)/Γ<sub>total</sub></td>
      <td>&lt;3.5 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p π<sup>0</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.5 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p 2π<sup>0</sup>)/Γ<sub>total</sub></td>
      <td>&lt;3.3 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p η)/Γ<sub>total</sub></td>
      <td>&lt;8.9 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → p π<sup>0</sup> η)/Γ<sub>total</sub></td>
      <td>&lt;2.7 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → Λ π<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;7.2 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(τ<sup>-</sup> → Λ π<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.4 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → Λ e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.1 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → Λ e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;6.5 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → Σ<sup>0</sup> e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.7 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>+</sup> → Σ<sup>0</sup> e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.3 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → p e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;2.2 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(D<sup>0</sup> → p e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.2 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → Λ<sup>0</sup> μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;6 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → Λ<sup>0</sup> e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;3.2 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>+</sup> → Λ<sup>0</sup> μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;6 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
  </tbody>
</table>

<table>
  <tbody>
    <tr>
      <td>Γ(B<sup>+</sup> → Λ<sup>0</sup>e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;8 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → pμ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;2.6 × 10<sup>-9</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → Λ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.4 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → Λ<sup>+</sup>e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;4 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → pμ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.21 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>τ(N → e<sup>+</sup>π)</td>
      <td>&gt; 5300 (n), &gt; 24000 (p) × 10<sup>30</sup><br>years, CL = 90%</td>
    </tr>
    <tr>
      <td>τ(N → μ<sup>+</sup>π)</td>
      <td>&gt; 3500 (n), &gt; 16000 (p) × 10<sup>30</sup><br>years, CL = 90%</td>
    </tr>
    <tr>
      <td>τ(N → e<sup>+</sup>K)</td>
      <td>&gt; 17 (n), &gt; 1000 (p) × 10<sup>30</sup> years,<br>CL = 90%</td>
    </tr>
    <tr>
      <td>τ(N → μ<sup>+</sup>K)</td>
      <td>&gt; 26 (n), &gt; 4500 (p) × 10<sup>30</sup> years,<br>CL = 90%</td>
    </tr>
    <tr>
      <td>Mean nπ̄-oscillation time (free n)</td>
      <td>&gt;8.6 × 10<sup>7</sup> s, CL = 90%</td>
    </tr>
    <tr>
      <td>Mean nπ̄-oscillation time (bound n)</td>
      <td>[r] &gt;4.7 × 10<sup>8</sup> s, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ → π<sup>+</sup>e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;6 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ → π<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;6 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ → π<sup>-</sup>e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;4 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ → π<sup>-</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;6 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ → K<sup>+</sup>e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;2 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ → K<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;3 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ → K<sup>-</sup>e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;2 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ → K<sup>-</sup>μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;3 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ → K<sup>0</sup>ν)/Γ<sub>total</sub></td>
      <td>&lt;2 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ → pπ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;9 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sub>C</sub><sup>+</sup> → p2e<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;2.7 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sub>C</sub><sup>+</sup> → p2μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;9.4 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Λ<sub>C</sub><sup>+</sup> → p e<sup>+</sup> μ<sup>+</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.6 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
  </tbody>
</table>

ELECTRIC CHARGE (Q)

<table>
  <tbody>
    <tr>
      <td>γ charge (mixed)</td>
      <td>&lt;1 × 10<sup>-46</sup> e</td>
    </tr>
    <tr>
      <td>γ charge (single)</td>
      <td>&lt;1 × 10<sup>-35</sup> e</td>
    </tr>
    <tr>
      <td>e → ν<sub>e</sub>γ and astrophysical limits</td>
      <td>[s] &gt;6.6 × 10<sup>28</sup> yr, CL = 90%</td>
    </tr>
    <tr>
      <td>ν charge</td>
      <td>&lt;4 × 10<sup>-35</sup> e, CL = 95%</td>
    </tr>
    <tr>
      <td>|q<sub>p</sub> + q<sub>e</sub>|/e</td>
      <td>[t] &lt;1 × 10<sup>-21</sup></td>
    </tr>
    <tr>
      <td>n charge</td>
      <td>(-0.2 ± 0.8) × 10<sup>-21</sup> e</td>
    </tr>
    <tr>
      <td>Γ(n → pν<sub>e</sub>ν<sub>e</sub>)/Γ<sub>total</sub></td>
      <td>&lt;8 × 10<sup>-27</sup>, CL = 68%</td>
    </tr>
  </tbody>
</table>

ΔS = ΔQ RULE

Violations allowed in second-order weak interactions.

<table>
  <tbody>
    <tr>
      <td>Γ(K<sup>+</sup> → π<sup>+</sup>π<sup>+</sup>e<sup>-</sup>ν<sup>-</sup>e)/Γ<sub>total</sub></td>
      <td>&lt;1.3 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(K<sup>+</sup> → π<sup>+</sup>π<sup>+</sup>μ<sup>-</sup>ν<sup>-</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;3.0 × 10<sup>-6</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Re(x<sub>+</sub>), K<sub>e3</sub> parameter</td>
      <td>(-0.9 ± 3.0) × 10<sup>-3</sup></td>
    </tr>
    <tr>
      <td>x = A(√K<sup>0</sup> → π<sup>-</sup>ℓ<sup>+</sup>ν<sup>-</sup>)/A(K<sup>0</sup> → π<sup>-</sup>ℓ<sup>+</sup>ν<sup>-</sup>) = A(ΔS<sup>-</sup>ΔQ)/A(ΔS<sup>=</sup>ΔQ)</td>
      <td></td>
    </tr>
    <tr>
      <td>real part of x</td>
      <td>-0.002 ± 0.006</td>
    </tr>
    <tr>
      <td>imaginary part of x</td>
      <td>0.0012 ± 0.0021</td>
    </tr>
    <tr>
      <td>Γ(Σ<sup>+</sup> → nℓ<sup>+</sup>ν<sup>-</sup>)/Γ(Σ<sup>-</sup> → nℓ<sup>-</sup>ν<sup>-</sup>)</td>
      <td>&lt;0.043</td>
    </tr>
    <tr>
      <td>Γ(Σ<sup>+</sup> → ne<sup>+</sup>ν<sub>e</sub>)/Γ<sub>total</sub></td>
      <td>&lt;5 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Σ<sup>+</sup> → nμ<sup>+</sup>ν<sub>μ</sub>)/Γ<sub>total</sub></td>
      <td>&lt;3.0 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Ξ<sup>0</sup> → Σ<sup>-</sup> e<sup>-</sup>ν<sub>e</sub>)/Γ<sub>total</sub></td>
      <td>&lt;1.6 × 10<sup>-4</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Ξ<sup>0</sup> → Σ<sup>-</sup> μ<sup>+</sup>ν<sub>μ</sub>)/Γ<sub>total</sub></td>
      <td>&lt;9 × 10<sup>-4</sup>, CL = 90%</td>
    </tr>
  </tbody>
</table>

ΔS = 2 FORBIDDEN

Allowed in second-order weak interactions.

<table>
  <tbody>
    <tr>
      <td>Γ(Ξ<sup>0</sup> → pπ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;8 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Ξ<sup>0</sup> → p e<sup>-</sup> ν<sub>e</sub>)/Γ<sub>total</sub></td>
      <td>&lt;1.3 × 10<sup>-3</sup></td>
    </tr>
    <tr>
      <td>Γ(Ξ<sup>0</sup> → p μ<sup>-</sup> ν<sub>μ</sub>)/Γ<sub>total</sub></td>
      <td>&lt;1.3 × 10<sup>-3</sup></td>
    </tr>
    <tr>
      <td>Γ(Ξ<sup>-</sup> → nπ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.9 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Ξ<sup>-</sup> → n e<sup>-</sup> ν<sub>e</sub>)/Γ<sub>total</sub></td>
      <td>&lt;3.2 × 10<sup>-3</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Ξ<sup>-</sup> → n μ<sup>-</sup> ν<sub>μ</sub>)/Γ<sub>total</sub></td>
      <td>&lt;1.5 × 10<sup>-2</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Ξ<sup>-</sup> → p π<sup>-</sup> π<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;4 × 10<sup>-4</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Ξ<sup>-</sup> → p π<sup>-</sup> e<sup>-</sup> ν<sub>e</sub>)/Γ<sub>total</sub></td>
      <td>&lt;4 × 10<sup>-4</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(Ξ<sup>-</sup> → p π<sup>-</sup> μ<sup>-</sup> ν<sub>μ</sub>)/Γ<sub>total</sub></td>
      <td>&lt;4 × 10<sup>-4</sup>, CL = 90%</td>
    </tr>
  </tbody>
</table>

Unless otherwise stated, limits are given at the 90% confidence level, while errors are given as ±1 standard deviation.
$$ \Gamma(\Omega^- \to \Lambda\pi^-)/\Gamma_{\text{total}} < 2.9 \times 10^{-6}, \text{ CL} = 90\% $$

## ΔS = 2 VIA MIXING

Allowed in second-order weak interactions, e.g. mixing.

$$ m_{K_L^0} - m_{K_S^0} = (0.5293 \pm 0.0009) \times 10^{10} \, \hbar \, s^{-1} \quad (S = 1.3) $$

$$ m_{K_L^0} - m_{K_S^0} = (3.484 \pm 0.006) \times 10^{-12} \, \text{MeV} $$

## ΔC = 2 VIA MIXING

Allowed in second-order weak interactions, e.g. mixing.

$$ |m_{D_1^0} - m_{D_2^0}| = x\Gamma \qquad (0.997 \pm 0.116) \times 10^{10} \, \hbar \, s^{-1} $$

$$ (\Gamma_{D_1^0} - \Gamma_{D_2^0})/\Gamma = 2y \qquad (1.394 \pm 0.056) \times 10^{-2} $$

## ΔB = 2 VIA MIXING

Allowed in second-order weak interactions, e.g. mixing.

$$ \chi_d (B^0, \bar{B}^0 \text{ mixing probability}) = 0.1860 \pm 0.0011 \qquad (0.5069 \pm 0.0019) \times 10^{12} \, \hbar \, s^{-1} $$

$$ \chi_d = \Delta m_{B^0}/\Gamma_{B^0} = 0.7697 \pm 0.0035 \qquad (17.765 \pm 0.006) \times 10^{12} \, \hbar \, s^{-1} $$

$$ \chi_s = \Delta m_{B_s^0}/\Gamma_{B_s^0} = 26.99 \pm 0.09 \qquad 0.499318 \pm 0.000005 $$

## ΔS = 1 WEAK NEUTRAL CURRENT FORBIDDEN

Allowed by higher-order electroweak interactions.

$$ \begin{align*} \Gamma(K^+ \to \pi^+ e^+ e^-)/\Gamma_{\text{total}} &= (3.00 \pm 0.09) \times 10^{-7} \\ \Gamma(K^+ \to \pi^+ \mu^+ \mu^-)/\Gamma_{\text{total}} &= (9.17 \pm 0.14) \times 10^{-8} \quad (S = 1.8) \\ \Gamma(K^+ \to \pi^+ \nu\bar{\nu})/\Gamma_{\text{total}} &= (1.14 \pm 0.40) \times 10^{-10} \\ \Gamma(K^+ \to \pi^+ \pi^0 \nu\bar{\nu})/\Gamma_{\text{total}} &= <4.3 \times 10^{-5}, \text{ CL} = 90\% \\ \Gamma(K_S^0 \to \mu^+ \mu^-)/\Gamma_{\text{total}} &= <2.1 \times 10^{-10}, \text{ CL} = 90\% \\ \Gamma(K_S^0 \to e^+ e^-)/\Gamma_{\text{total}} &= <9 \times 10^{-9}, \text{ CL} = 90\% \\ \Gamma(K_S^0 \to \pi^0 e^+ e^-)/\Gamma_{\text{total}} &= [u] (3.0^{+1.5}_{-1.2}) \times 10^{-9} \\ \Gamma(K_S^0 \to \pi^0 \mu^+ \mu^-)/\Gamma_{\text{total}} &= (2.9^{+1.5}_{-1.2}) \times 10^{-9} \\ \Gamma(K_L^0 \to \mu^+ \mu^-)/\Gamma_{\text{total}} &= (6.84 \pm 0.11) \times 10^{-9} \\ \Gamma(K_L^0 \to e^+ e^-)/\Gamma_{\text{total}} &= (9^{+6}_{-4}) \times 10^{-12} \end{align*} $$

$$ \begin{align*} \Gamma(K_L^0 \to \pi^+ \pi^- e^+ e^-)/\Gamma_{\text{total}} &= [v] (3.11 \pm 0.19) \times 10^{-7} \\ \Gamma(K_0^0 \to \pi^0 \pi^+ e^- e^-)/\Gamma_{\text{total}} &= <6.6 \times 10^{-9}, \text{ CL} = 90\% \\ \Gamma(K_0^0 \to \pi^0 \pi^0 \mu^+ \mu^-)/\Gamma_{\text{total}} &= <9.2 \times 10^{-11}, \text{ CL} = 90\% \\ \Gamma(K_L^0 \to \mu^+ \mu^- e^+ e^-)/\Gamma_{\text{total}} &= (2.69 \pm 0.27) \times 10^{-9} \\ \Gamma(K_L^0 \to e^+ e^- e^+ e^-)/\Gamma_{\text{total}} &= (3.56 \pm 0.21) \times 10^{-8} \\ \Gamma(K_0^0 \to \pi^0 \mu^+ \mu^-)/\Gamma_{\text{total}} &= <3.8 \times 10^{-10}, \text{ CL} = 90\% \\ \Gamma(K_L^0 \to \pi^0 e^+ e^-)/\Gamma_{\text{total}} &= <2.8 \times 10^{-10}, \text{ CL} = 90\% \\ \Gamma(K_0^0 \to \pi^0 \nu\bar{\nu})/\Gamma_{\text{total}} &= <3.0 \times 10^{-9}, \text{ CL} = 90\% \\ \Gamma(K_0^0 \to \pi^0 \pi^0 \nu\bar{\nu})/\Gamma_{\text{total}} &= <8.1 \times 10^{-7}, \text{ CL} = 90\% \\ \Gamma(\Sigma^+ \to p e^+ e^-)/\Gamma_{\text{total}} &= <7 \times 10^{-6} \\ \Gamma(\Sigma^+ \to p \mu^+ \mu^-)/\Gamma_{\text{total}} &= (2.4^{+1.7}_{-1.3}) \times 10^{-8} \end{align*} $$

## ΔC = 1 WEAK NEUTRAL CURRENT FORBIDDEN

Allowed by higher-order electroweak interactions.

$$ \begin{align*} \Gamma(D^+ \to \pi^+ e^+ e^-)/\Gamma_{\text{total}} &< 1.1 \times 10^{-6}, \text{ CL} = 90\% \\ \Gamma(D^+ \to \pi^+ \mu^+ \mu^-)/\Gamma_{\text{total}} &< 6.7 \times 10^{-8}, \text{ CL} = 90\% \\ \Gamma(D^+ \to \rho^+ \mu^+ \mu^-)/\Gamma_{\text{total}} &< 5.6 \times 10^{-4}, \text{ CL} = 90\% \\ \Gamma(D^0 \to \gamma\gamma)/\Gamma_{\text{total}} &< 8.5 \times 10^{-7}, \text{ CL} = 90\% \\ \Gamma(D^0 \to e^+ e^-)/\Gamma_{\text{total}} &< 7.9 \times 10^{-8}, \text{ CL} = 90\% \\ \Gamma(D^0 \to \mu^+ \mu^-)/\Gamma_{\text{total}} &< 3.1 \times 10^{-9}, \text{ CL} = 90\% \\ \Gamma(D^0 \to \pi^0 e^+ e^-)/\Gamma_{\text{total}} &< 4 \times 10^{-6}, \text{ CL} = 90\% \end{align*} $$

$$ \begin{align*} \Gamma(D^0 \to \pi^0 \mu^+ \mu^-)/\Gamma_{\text{total}} &< 1.8 \times 10^{-4}, \text{ CL} = 90\% \\ \Gamma(D^0 \to \eta e^+ e^-)/\Gamma_{\text{total}} &< 3 \times 10^{-6}, \text{ CL} = 90\% \\ \Gamma(D^0 \to \eta \mu^+ \mu^-)/\Gamma_{\text{total}} &< 5.3 \times 10^{-4}, \text{ CL} = 90\% \\ \Gamma(D^0 \to \pi^+ \pi^- e^+ e^-)/\Gamma_{\text{total}} &< 7 \times 10^{-6}, \text{ CL} = 90\% \\ \Gamma(D^0 \to \rho^0 e^+ e^-)/\Gamma_{\text{total}} &< 1.0 \times 10^{-4}, \text{ CL} = 90\% \\ \Gamma(D^0 \to \pi^+ \pi^- \mu^+ \mu^-)/\Gamma_{\text{total}} &< (9.6 \pm 1.2) \times 10^{-7} \\ \Gamma(D^0 \to \rho^0 \mu^+ \mu^-)/\Gamma_{\text{total}} &< 2.2 \times 10^{-5}, \text{ CL} = 90\% \\ \Gamma(D^0 \to \omega e^+ e^-)/\Gamma_{\text{total}} &< 6 \times 10^{-6}, \text{ CL} = 90\% \\ \Gamma(D^0 \to \omega \mu^+ \mu^-)/\Gamma_{\text{total}} &< 8.3 \times 10^{-4}, \text{ CL} = 90\% \\ \Gamma(D^0 \to K^- K^+ e^+ e^-)/\Gamma_{\text{total}} &< 1.1 \times 10^{-5}, \text{ CL} = 90\% \\ \Gamma(D^0 \to \phi e^+ e^-)/\Gamma_{\text{total}} &< 5.2 \times 10^{-5}, \text{ CL} = 90\% \\ \Gamma(D^0 \to K^- K^+ \mu^+ \mu^-)/\Gamma_{\text{total}} &< (1.54 \pm 0.32) \times 10^{-7} \\ \Gamma(D^0 \to \phi \mu^+ \mu^-)/\Gamma_{\text{total}} &< 3.1 \times 10^{-5}, \text{ CL} = 90\% \\ \Gamma(D^0 \to K^- \pi^+ \mu^+ \mu^-)/\Gamma_{\text{total}} &< 3.59 \times 10^{-4}, \text{ CL} = 90\% \\ \Gamma(D^0 \to \pi^+ \pi^- \pi^0 \mu^+ \mu^-)/\Gamma_{\text{total}} &< 8.1 \times 10^{-4}, \text{ CL} = 90\% \\ \Gamma(D_S^+ \to K^+ e^+ e^-)/\Gamma_{\text{total}} &< 3.7 \times 10^{-6}, \text{ CL} = 90\% \\ \Gamma(D_S^+ \to K^+ \mu^+ \mu^-)/\Gamma_{\text{total}} &< 1.4 \times 10^{-7}, \text{ CL} = 90\% \\ \Gamma(D_S^+ \to K^*(892) \mu^+ \mu^-)/\Gamma_{\text{total}} &< 1.4 \times 10^{-3}, \text{ CL} = 90\% \\ \Gamma(\Lambda_c^+ \to p e^+ e^-)/\Gamma_{\text{total}} &< 5.5 \times 10^{-6}, \text{ CL} = 90\% \\ \Gamma(\Lambda_c^+ \to p \mu^+ \mu^- \text{ non-resonant})/\Gamma_{\text{total}} &< 7.7 \times 10^{-8}, \text{ CL} = 90\% \end{align*} $$

## ΔB = 1 WEAK NEUTRAL CURRENT FORBIDDEN

Allowed by higher-order electroweak interactions.

$$ \begin{align*} \Gamma(B^+ \to \pi^+ \ell^+ \ell^-)/\Gamma_{\text{total}} & [x] < 4.9 \times 10^{-8}, \text{ CL} = 90\% \\ \Gamma(B^+ \to \pi^+ e^+ e^-)/\Gamma_{\text{total}} & < 8.0 \times 10^{-8}, \text{ CL} = 90\% \\ \Gamma(B^+ \to \pi^+ \mu^+ \mu^-)/\Gamma_{\text{total}} & (1.78 \pm 0.23) \times 10^{-8} \\ \Gamma(B^+ \to \pi^+ \nu\bar{\nu})/\Gamma_{\text{total}} & < 1.4 \times 10^{-5}, \text{ CL} = 90\% \\ \Gamma(B^+ \to K^+ \ell^+ \ell^-)/\Gamma_{\text{total}} & [x] (4.7 \pm 0.5) \times 10^{-7} \quad (S = 2.3) \\ \Gamma(B^+ \to K^+ e^+ e^-)/\Gamma_{\text{total}} & (5.6 \pm 0.6) \times 10^{-7} \\ \Gamma(B^+ \to K^+ \mu^+ \mu^-)/\Gamma_{\text{total}} & (4.53 \pm 0.35) \times 10^{-7} \quad (S = 1.8) \\ \Gamma(B^+ \to K^+ \mu^+ \mu^- \text{ nonresonant})/\Gamma_{\text{total}} & (4.37 \pm 0.27) \times 10^{-7} \\ \Gamma(B^+ \to K^+ \tau^+ \tau^-)/\Gamma_{\text{total}} & < 2.25 \times 10^{-3}, \text{ CL} = 90\% \\ \Gamma(B^+ \to K^+ \bar{\nu}\bar{\nu})/\Gamma_{\text{total}} & < 1.6 \times 10^{-5}, \text{ CL} = 90\% \\ \Gamma(B^+ \to \rho^+ \nu\bar{\nu})/\Gamma_{\text{total}} & < 3.0 \times 10^{-5}, \text{ CL} = 90\% \\ \Gamma(B^+ \to K^*(892) \ell^+ \ell^-)/\Gamma_{\text{total}} & [x] (1.01 \pm 0.11) \times 10^{-6} \quad (S = 1.1) \\ \Gamma(B^+ \to K^*(892) e^+ e^-)/\Gamma_{\text{total}} & (1.55^{+0.40}_{-0.31}) \times 10^{-6} \\ \Gamma(B^+ \to K^*(892) \mu^+ \mu^-)/\Gamma_{\text{total}} & (9.6 \pm 1.0) \times 10^{-7} \\ \Gamma(B^+ \to K^*(892) \nu\bar{\nu})/\Gamma_{\text{total}} & < 4.0 \times 10^{-5}, \text{ CL} = 90\% \\ \Gamma(B^+ \to K^+ \pi^+ \pi^- \mu^+ \mu^-)/\Gamma_{\text{total}} & (4.3 \pm 0.4) \times 10^{-7} \\ \Gamma(B^+ \to \phi K^+ \mu^+ \mu^-)/\Gamma_{\text{total}} & (7.9^{+2.1}_{-1.7}) \times 10^{-8} \\ \Gamma(B^+ \to \lambda p \nu\bar{\nu})/\Gamma_{\text{total}} & < 3.0 \times 10^{-5}, \text{ CL} = 90\% \\ \Gamma(B^0 \to \gamma\gamma)/\Gamma_{\text{total}} & < 3.2 \times 10^{-7}, \text{ CL} = 90\% \\ \Gamma(B^0 \to e^+ e^-)/\Gamma_{\text{total}} & < 2.5 \times 10^{-9}, \text{ CL} = 90\% \\ \Gamma(B^0 \to e^+ e^- \gamma)/\Gamma_{\text{total}} & < 1.2 \times 10^{-7}, \text{ CL} = 90\% \\ \Gamma(B^0 \to \mu^+ \mu^-)/\Gamma_{\text{total}} & < 1.5 \times 10^{-10}, \text{ CL} = 90\% \\ \Gamma(B^0 \to \mu^+ \mu^- \gamma)/\Gamma_{\text{total}} & < 1.8 \times 10^{-10}, \text{ CL} = 95\% \\ \Gamma(B^0 \to S P, S \to \mu^+ \mu^-, P \to \mu^+ \mu^-)/\Gamma_{\text{total}} & [y] < 6.0 \times 10^{-10}, \text{ CL} = 95\% \\ \Gamma(B^0 \to a a, a \to \mu^+ \mu^-)/\Gamma_{\text{total}} & < 2.3 \times 10^{-10}, \text{ CL} = 95\% \\ \Gamma(B^0 \to \tau^+ \tau^-)/\Gamma_{\text{total}} & < 2.1 \times 10^{-3}, \text{ CL} = 95\% \\ \Gamma(B^0 \to \pi^0 \ell^+ \ell^-)/\Gamma_{\text{total}} & [x] < 5.3 \times 10^{-8}, \text{ CL} = 90\% \\ \Gamma(B^0 \to \pi^0 e^+ e^-)/\Gamma_{\text{total}} & < 8.4 \times 10^{-8}, \text{ CL} = 90\% \\ \Gamma(B^0 \to \pi^0 \mu^+ \mu^-)/\Gamma_{\text{total}} & < 6.9 \times 10^{-8}, \text{ CL} = 90\% \\ \Gamma(B^0 \to \eta \ell^+ \ell^-)/\Gamma_{\text{total}} & [x] < 6.4 \times 10^{-8}, \text{ CL} = 90\% \\ \Gamma(B^0 \to \eta e^+ e^-)/\Gamma_{\text{total}} & < 1.08 \times 10^{-7}, \text{ CL} = 90\% \\ \Gamma(B^0 \to \eta \mu^+ \mu^-)/\Gamma_{\text{total}} & < 1.12 \times 10^{-7}, \text{ CL} = 90\% \\ \Gamma(B^0 \to \pi^0 \nu\bar{\nu})/\Gamma_{\text{total}} & < 9 \times 10^{-6}, \text{ CL} = 90\% \\ \Gamma(B^0 \to K^0 \ell^+ \ell^-)/\Gamma_{\text{total}} & [x] (3.3 \pm 0.6) \times 10^{-7} \\ \Gamma(B^0 \to K^0 e^+ e^-)/\Gamma_{\text{total}} & (2.5^{+1.1}_{-0.9}) \times 10^{-7} \quad (S = 1.3) \\ \Gamma(B^0 \to K^0 \mu^+ \mu^-)/\Gamma_{\text{total}} & (3.39 \pm 0.35) \times 10^{-7} \quad (S = 1.1) \\ \Gamma(B^0 \to K^0 \nu\bar{\nu})/\Gamma_{\text{total}} & < 2.6 \times 10^{-5}, \text{ CL} = 90\% \\ \Gamma(B^0 \to \rho^0 \nu\bar{\nu})/\Gamma_{\text{total}} & < 4.0 \times 10^{-5}, \text{ CL} = 90\% \\ \Gamma(B^0 \to K^*(892) \ell^+ \ell^-)/\Gamma_{\text{total}} & [x] (9.9^{+1.2}_{-1.1}) \times 10^{-7} \\ \Gamma(B^0 \to K^*(892) e^+ e^-)/\Gamma_{\text{total}} & (1.03^{+0.19}_{-0.17}) \times 10^{-6} \\ \Gamma(B^0 \to K^*(892) \mu^+ \mu^-)/\Gamma_{\text{total}} & (9.4 \pm 0.5) \times 10^{-7} \\ \Gamma(B^0 \to K^*(892) \chi, \chi \to \mu^+ \mu^-)/\Gamma_{\text{total}} & — \end{align*} $$

Unless otherwise stated, limits are given at the 90% confidence level, while errors are given as ±1 standard deviation.
<table>
  <tbody>
    <tr>
      <td>Γ(B<sup>0</sup> → K<sup>*</sup>(892)<sup>0</sup>τ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;3.1 × 10<sup>-3</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → π<sup>+</sup>π<sup>-</sup>μ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>(2.1 ± 0.5) × 10<sup>-8</sup></td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → K<sup>*</sup>(892)<sup>0</sup>νν)/Γ<sub>total</sub></td>
      <td>&lt;1.8 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → invisible)/Γ<sub>total</sub></td>
      <td>&lt;2.4 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → ννγ)/Γ<sub>total</sub></td>
      <td>&lt;1.6 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → φμ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;3.2 × 10<sup>-9</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup> → φνν)/Γ<sub>total</sub></td>
      <td>&lt;1.27 × 10<sup>-4</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B → se<sup>+</sup>e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>(6.7 ± 1.7) × 10<sup>-6</sup> (S = 2.0)</td>
    </tr>
    <tr>
      <td>Γ(B → sμ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>(4.3 ± 1.0) × 10<sup>-6</sup></td>
    </tr>
    <tr>
      <td>Γ(B → sℓ<sup>+</sup>ℓ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>[x] (5.8 ± 1.3) × 10<sup>-6</sup> (S = 1.8)</td>
    </tr>
    <tr>
      <td>Γ(B → πℓ<sup>+</sup>ℓ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;5.9 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B → πe<sup>+</sup>e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;1.10 × 10<sup>-7</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B → πμ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;5.0 × 10<sup>-8</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B → Ke<sup>+</sup>e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>(4.4 ± 0.6) × 10<sup>-7</sup></td>
    </tr>
    <tr>
      <td>Γ(B → K<sup>*</sup>(892) e<sup>+</sup> e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>(1.19 ± 0.20) × 10<sup>-6</sup> (S = 1.2)</td>
    </tr>
    <tr>
      <td>Γ(B → Kμ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>(4.4 ± 0.4) × 10<sup>-7</sup></td>
    </tr>
    <tr>
      <td>Γ(B → K<sup>*</sup>(892) μ<sup>+</sup> μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>(1.06 ± 0.09) × 10<sup>-6</sup></td>
    </tr>
    <tr>
      <td>Γ(B → Kℓ<sup>+</sup>ℓ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>(4.8 ± 0.4) × 10<sup>-7</sup></td>
    </tr>
    <tr>
      <td>Γ(B → K<sup>*</sup>(892)ℓ<sup>+</sup>ℓ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>(1.05 ± 0.10) × 10<sup>-6</sup></td>
    </tr>
    <tr>
      <td>Γ(B → Kνν)/Γ<sub>total</sub></td>
      <td>&lt;1.6 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B → K*νν)/Γ<sub>total</sub></td>
      <td>&lt;2.7 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B → πνν)/Γ<sub>total</sub></td>
      <td>&lt;8 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B → ρνν)/Γ<sub>total</sub></td>
      <td>&lt;2.8 × 10<sup>-5</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B → Sνν)/Γ<sub>total</sub></td>
      <td>&lt;6.4 × 10<sup>-4</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B → μ<sup>+</sup>μ<sup>-</sup> anything)/Γ<sub>total</sub></td>
      <td>&lt;3.2 × 10<sup>-4</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → γγ)/Γ<sub>total</sub></td>
      <td>&lt;3.1 × 10<sup>-6</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → φγ)/Γ<sub>total</sub></td>
      <td>(3.4 ± 0.4) × 10<sup>-5</sup></td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → μ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>(3.34 ± 0.27) × 10<sup>-9</sup></td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → e<sup>+</sup>e<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;9.4 × 10<sup>-9</sup>, CL = 90%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → τ<sup>+</sup>τ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;6.8 × 10<sup>-3</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → μ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;2.0 × 10<sup>-9</sup></td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → μ<sup>+</sup>μ<sup>-</sup> μ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;8.6 × 10<sup>-10</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → SP, S → μ<sup>+</sup>μ<sup>-</sup>, P → μ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>[y] &lt;2.2 × 10<sup>-9</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → aa, a → μ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>&lt;5.8 × 10<sup>-10</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → φ(1020)μ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>(8.4 ± 0.4) × 10<sup>-7</sup></td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → τ<sub>2</sub>'(1525)μ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>(1.62 ± 0.22) × 10<sup>-7</sup></td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → K<sup>*</sup>(892)<sup>0</sup>μ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>(2.9 ± 1.1) × 10<sup>-8</sup></td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → π<sup>+</sup>π<sup>-</sup>μ<sup>+</sup>μ<sup>-</sup>)/Γ<sub>total</sub></td>
      <td>(8.4 ± 1.7) × 10<sup>-8</sup></td>
    </tr>
    <tr>
      <td>Γ(B<sup>0</sup><sub>S</sub> → φνν)/Γ<sub>total</sub></td>
      <td>&lt;5.4 × 10<sup>-3</sup>, CL = 90%</td>
    </tr>
  </tbody>
</table>

ΔT = 1 WEAK NEUTRAL CURRENT FORBIDDEN

Allowed by higher-order electroweak interactions.

<table>
  <tbody>
    <tr>
      <td>Γ(t → Zq(q=u,c))/Γ<sub>total</sub></td>
      <td>[z] &lt;1.2 × 10<sup>-4</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(t → H u)/Γ<sub>total</sub></td>
      <td>&lt;1.9 × 10<sup>-4</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(t → H c)/Γ<sub>total</sub></td>
      <td>&lt;4.3 × 10<sup>-4</sup>, CL = 95%</td>
    </tr>
    <tr>
      <td>Γ(t → ℓ<sup>+</sup> q̄q̄ (q=d,s,b; q'=u,c))/Γ<sub>total</sub></td>
      <td>&lt;1.6 × 10<sup>-3</sup>, CL = 95%</td>
    </tr>
  </tbody>
</table>

NOTES

In this Summary Table:

When a quantity has “(S = …)” to its right, the error on the quantity has been enlarged by the “scale factor” S, defined as S = √(χ²/(N − 1)), where N is the number of measurements used in calculating the quantity. We do this when S > 1, which often indicates that the measurements are inconsistent. When S > 1.25, we also show in the Particle Listings an ideogram of the measurements. For more about S, see the Introduction.

[a] Forbidden by angular momentum conservation.

[b] C parity forbids this to occur as a single-photon process.

[c] See the Particle Listings for the (complicated) definition of this quantity.

[d] Time-reversal invariance requires this to be 0° or 180°.

[e] This coefficient is zero if time invariance is not violated.

[f] Allowed by higher-order electroweak interactions.

[g] Violates CP in leading order. Test of direct CP violation since the in-
direct CP-violating and CP-conserving contributions are expected to be
suppressed.

[h] In the 2010 Review, the values for these quantities were given using a
measure of the asymmetry that was inconsistent with the usual definition.

[i] Re(ε'/ε) = ε'/ε to a very good approximation provided the phases satisfy CPT invariance.

[j] This mode includes gammas from inner bremsstrahlung but not the direct emission mode K<sup>0</sup><sub>L</sub> → π<sup>+</sup>π<sup>-</sup>γ(DE).

[k] Neglecting photon channels. See, e.g., A. Pais and S.B. Treiman, Phys. Rev. D12, 2744 (1975).

[l] Derived from measured values of φ<sub>+</sub>, φ<sub>00</sub>, |η|, |m<sub>K<sub>L</sub>°</sub> - m<sub>K<sub>S</sub>°</sub>|, and τ<sub>K<sub>S</sub>°</sub>, as described in the introduction to “Tests of Conservation Laws.”

[n] The |m<sub>p</sub> - m<sub>p̄</sub>|/m<sub>p</sub> and |q<sub>p</sub> + q<sub>p̄</sub>|/e are not independent, and both use the more precise measurement of |q<sub>p̄</sub>/m<sub>p̄</sub>|/(q<sub>p</sub>/m<sub>p</sub>).

[o] The value is for the sum of the charge states or particle/antiparticle states indicated.

[p] A test of additive vs. multiplicative lepton family number conservation.

[q] Derived from an analysis of neutrino-oscillation experiments.

[r] There is some controversy about whether nuclear physics and model dependence complicate the analysis for bound neutrons (from which the best limit comes). The first limit here is from reactor experiments with free neutrons.

[s] This is the best limit for the mode e⁻ → νγ.

[t] The limit is from neutrality-of-matter experiments; it assumes q<sub>n</sub> = q<sub>p</sub> + q<sub>e</sub>. See also the charge of the neutron.

[u] See the K<sup>0</sup><sub>S</sub> Particle Listings for the energy limits used in this measure-
ment.

[v] See the K<sup>0</sup><sub>L</sub> Particle Listings for the energy limits used in this measure-
ment.

[x] An ℓ indicates an e or a μ mode, not a sum over these modes.

[y] Here S and P are the hypothetical scalar and pseudoscalar particles with masses of 2.5 GeV/c² and 214.3 MeV/c², respectively.

[z] This limit is for Γ(t → Zq)/Γ(t → Wb).
REVIEWS, TABLES, AND PLOTS

Constants, Units, Atomic and Nuclear Properties

<table><tr><td>1. Physical constants (rev.)</td><td>137</td></tr><tr><td>2. Astrophysical constants and parameters (rev.)</td><td>138</td></tr><tr><td>3. International system of units (SI)</td><td>140</td></tr><tr><td>4. Periodic table of the elements (rev.)</td><td>141</td></tr><tr><td>5. Electronic structure of the elements (rev.)</td><td>142</td></tr><tr><td>6. Atomic and nuclear properties of materials (rev.)</td><td>144</td></tr><tr><td>7. Electromagnetic relations</td><td>146</td></tr><tr><td>8. Naming scheme for hadrons (rev.)</td><td>148</td></tr></table>
<figure><img src="image_13.png" /></figure>
# 1. Physical Constants

<table><caption>**Table 1.1:** Revised 2024 by D. Robinson (LBNL) and P.A. Zyla (LBNL). Mainly from “CODATA Recommended Values of the Fundamental Physical Constants: 2018,” E. Tiesinga, D.B. Newell, P.J. Mohr, and B.N. Taylor, NIST SP961 (May 2019) [1].<sup>a</sup> The electron charge magnitude *e*, and the Planck, Boltzmann, and Avogadro constants *h*, *k*, and *N*<sub>A</sub>, now join *c* as having defined values; the free-space permittivity and permeability constants *ϵ*<sub>0</sub> and *μ*<sub>0</sub> are no longer exact. These changes affect practically everything else in the Table. Figures in parentheses after the values are the 1-standard-deviation uncertainties in the last digits; the fractional uncertainties in parts per 10<sup>9</sup> (ppb) are in the last column. The full 2018 CODATA Committee on Data for Science and Technology set of constants are found at https://physics.nist.gov/cuu/Constants/archive2018.html. The last set of constants (beginning with the Fermi coupling constant) comes from the Particle Data Group. See also “The International System of Units (SI),” 9th ed. (2019) of the International Bureau of Weights and Measures (BIPM), https://www.bipm.org/utilis/common/pdf/si-brochure/SI-Brochure-9-EN.pdf.</caption><thead><tr><th>Quantity</th><th>Symbol, equation</th><th>Value</th><th>Uncertainty (ppb)</th></tr></thead><tbody><tr><td>speed of light in vacuum</td><td>c</td><td>299 792 458 m s<sup>-1</sup></td><td>exact</td></tr><tr><td>Planck constant</td><td>h</td><td>6.626 070 15×10<sup>-34</sup> J s (or J/Hz) §</td><td>exact</td></tr><tr><td>Planck constant, reduced</td><td>ħ ≡ h/2π</td><td>1.054 571 817... × 10<sup>-34</sup> J s<br>= 6.582 119 569... × 10<sup>-22</sup> MeV s</td><td>exact*<br>exact*</td></tr><tr><td>electron charge magnitude</td><td>e</td><td>1.602 176 634×10<sup>-19</sup> C</td><td>exact</td></tr><tr><td>conversion constant</td><td>ħc</td><td>197.326 980 4... MeV fm</td><td>exact*</td></tr><tr><td>conversion constant</td><td>(ħc)<sup>2</sup></td><td>0.389 379 372 1... GeV<sup>2</sup> mbarn</td><td>exact*</td></tr><tr><td>electron mass</td><td>m<sub>e</sub></td><td>0.510 998 950 00(15) MeV/c<sup>2</sup> = 9.109 383 7015(28)×10<sup>-31</sup> kg</td><td>0.30</td></tr><tr><td>proton mass</td><td>m<sub>p</sub></td><td>938.272 088 16(29) MeV/c<sup>2</sup> = 1.672 621 923 69(51)×10<sup>-27</sup> kg<br>= 1.007 276 466 621(53) u = 1836.152 673 43(11) m<sub>e</sub></td><td>0.31<br>0.053, 0.060</td></tr><tr><td>neutron mass</td><td>m<sub>n</sub></td><td>939.565 420 52(54) MeV/c<sup>2</sup> = 1.008 664 915 95(49) u</td><td>0.57, 0.48</td></tr><tr><td>deuteron mass</td><td>m<sub>d</sub></td><td>1875.612 942 57(57) MeV/c<sup>2</sup></td><td>0.30</td></tr><tr><td>unified atomic mass unit**</td><td>u = (mass <sup>12</sup>C atom)/12</td><td>931.494 102 42(28) MeV/c<sup>2</sup> = 1.660 539 066 60(50)×10<sup>-27</sup> kg</td><td>0.30</td></tr><tr><td>permittivity of free space</td><td>ε<sub>0</sub> = 1/μ<sub>0</sub>c<sup>2</sup></td><td>8.854 187 8128(13) ×10<sup>-12</sup> F m<sup>-1</sup></td><td>0.15</td></tr><tr><td>permeability of free space</td><td>μ<sub>0</sub>(4π × 10<sup>-7</sup>)</td><td>1.000 000 000 55(15) N A<sup>-2</sup></td><td>0.15</td></tr><tr><td>fine-structure constant</td><td>α = e<sup>2</sup>/4πε<sub>0</sub>ħc</td><td>7.297 352 5693(11)×10<sup>-3</sup> = 1/137.035 999 084(21) †</td><td>0.15</td></tr><tr><td>classical electron radius</td><td>r<sub>e</sub> = e<sup>2</sup>/4πε<sub>0</sub>m<sub>e</sub>c<sup>2</sup></td><td>2.817 940 3262(13)×10<sup>-15</sup> m</td><td>0.45</td></tr><tr><td>(e<sup>-</sup> Compton wavelength)/2π</td><td>λ<sub>e</sub> = h/m<sub>e</sub>c = r<sub>e</sub>α<sup>-1</sup></td><td>3.861 592 6796(12)×10<sup>-13</sup> m</td><td>0.30</td></tr><tr><td>Bohr radius (m<sub>nucleus</sub> = ∞)</td><td>a<sub>∞</sub> = 4πε<sub>0</sub>ħ<sup>2</sup>/m<sub>e</sub>c<sup>2</sup> = r<sub>e</sub>α<sup>-2</sup></td><td>0.529 177 210 903(80)×10<sup>-10</sup> m</td><td>0.15</td></tr><tr><td>wavelength of 1 eV/c particle</td><td>ħc/(1 eV)</td><td>1.239 841 984... × 10<sup>-6</sup> m</td><td>exact*</td></tr><tr><td>Rydberg energy</td><td>ħcR<sub>∞</sub> = m<sub>e</sub>e<sup>4</sup>/2(4πε<sub>0</sub>)<sup>2</sup>ħ<sup>2</sup> = m<sub>e</sub>c<sup>2</sup>α<sup>2</sup>/2</td><td>13.605 693 122 994(26) eV</td><td>1.9×10<sup>-3</sup></td></tr><tr><td>Thomson cross section</td><td>σ<sub>T</sub> = 8πr<sub>2</sub><sup>2</sup>/3</td><td>0.665 245 873 21(60) barn</td><td>0.91</td></tr><tr><td>Bohr magneton</td><td>μ<sub>B</sub> = eħ/2m<sub>e</sub></td><td>5.788 381 8060(17)×10<sup>-11</sup> MeV T<sup>-1</sup></td><td>0.30</td></tr><tr><td>nuclear magneton</td><td>μ<sub>N</sub> = eħ/2m<sub>p</sub></td><td>3.152 451 258 44(96)×10<sup>-14</sup> MeV T<sup>-1</sup></td><td>0.31</td></tr><tr><td>electron cyclotron freq./field</td><td>ω<sub>cycl</sub><sup>e</sup>/B = e/m<sub>e</sub></td><td>1.758 820 010 76(53)×10<sup>11</sup> rad s<sup>-1</sup> T<sup>-1</sup></td><td>0.30</td></tr><tr><td>proton cyclotron freq./field</td><td>ω<sub>cycl</sub><sup>p</sup>/B = e/m<sub>p</sub></td><td>9.578 833 1560(29)×10<sup>7</sup> rad s<sup>-1</sup> T<sup>-1</sup></td><td>0.31</td></tr><tr><td>gravitational constant‡</td><td>G<sub>N</sub></td><td>6.674 30(15)×10<sup>-11</sup> m<sup>3</sup> kg<sup>-1</sup> s<sup>-2</sup><br>= 6.708 83(15)×10<sup>-39</sup> ħc (GeV/c<sup>2</sup>)<sup>-2</sup></td><td>2.2 × 10<sup>4</sup><br>2.2 × 10<sup>4</sup></td></tr><tr><td>standard gravitational accel.</td><td>g<sub>N</sub></td><td>9.806 65 m s<sup>-2</sup></td><td>exact</td></tr><tr><td>Avogadro constant</td><td>N<sub>A</sub></td><td>6.022 140 76×10<sup>23</sup> mol<sup>-1</sup></td><td>exact</td></tr><tr><td>Boltzmann constant</td><td>k</td><td>1.380 649×10<sup>-23</sup> J K<sup>-1</sup><br>= 8.617 333 262... × 10<sup>-5</sup> eV K<sup>-1</sup></td><td>exact<br>exact*</td></tr><tr><td>molar volume, ideal gas at STP</td><td>N<sub>A</sub>k (273.15 K)/(101 325 Pa)</td><td>22.413 969 54... × 10<sup>-3</sup> m<sup>3</sup> mol<sup>-1</sup></td><td>exact*</td></tr><tr><td>Wien displacement law constant</td><td>b = λ<sub>max</sub>T</td><td>2.897 771 955... × 10<sup>-3</sup> m K</td><td>exact*</td></tr><tr><td>Stefan-Boltzmann constant</td><td>σ = π<sup>2</sup>k<sup>4</sup>/60ħ<sup>3</sup>c<sup>2</sup></td><td>5.670 374 419... × 10<sup>-8</sup> W m<sup>-2</sup> K<sup>-4</sup></td><td>exact*</td></tr><tr><td>Fermi coupling constant‡‡</td><td>G<sub>F</sub>/(ħc)<sup>3</sup></td><td>1.166 378 8(6)×10<sup>-5</sup> GeV<sup>-2</sup></td><td>510</td></tr><tr><td>weak-mixing angle‡‡</td><td>sin<sup>2</sup> θ(M<sub>Z</sub>) (MS)</td><td>0.231 29(4)<sup>††</sup></td><td>1.7 × 10<sup>5</sup></td></tr><tr><td>W<sup>±</sup> boson mass</td><td>m<sub>W</sub></td><td>80.3692(133) GeV/c<sup>2</sup>¶</td><td>1.7 × 10<sup>5</sup></td></tr><tr><td>Z<sup>0</sup> boson mass</td><td>m<sub>Z</sub></td><td>91.1880(20) GeV/c<sup>2</sup>||</td><td>2.2 × 10<sup>4</sup></td></tr><tr><td>strong coupling constant</td><td>α<sub>s</sub>(m<sub>Z</sub>)</td><td>0.1180(9)</td><td>7.6 × 10<sup>6</sup></td></tr><tr><td colspan="4">π = 3.141 592 653 589 793 238 ... e = 2.718 281 828 459 045 235... γ = 0.577 215 664 901 532 860...</td></tr><tr><td>1 in ≡ 0.0254 m</td><td>1 G ≡ 10<sup>-4</sup> T</td><td>1 eV = 1.602 176 634 × 10<sup>-19</sup> J (exact)</td><td>kT at 300 K = [38.681 727 0718...]<sup>-1</sup>eV (exact*)</td></tr><tr><td>1 Å ≡ 0.1 nm</td><td>1 dyne ≡ 10<sup>-5</sup> N</td><td>(1 kg)c<sup>2</sup> = 5.609 588 603... × 10<sup>35</sup> eV(exact*)</td><td>0 °C ≡ 273.15K</td></tr><tr><td>1 barn ≡ 10<sup>-28</sup> m<sup>2</sup></td><td>1 erg ≡ 10<sup>-7</sup> J</td><td>1 C = 2.997 924 58 × 10<sup>9</sup> esu</td><td>1 atmosphere ≡ 760 Torr ≡ 101 325Pa</td></tr></tbody></table>

References

[1] E. Tiesinga et al., Rev. Mod. Phys. 93, 025010 (2021).

<footnote><sup>a</sup>Updated values reflecting the “2022 CODATA recommended values”, released online in May 2024, will be incorporated in future editions of the Review.</footnote>

<footnote><sup>b</sup>CODATA recommends that the unit be J/Hz to stress that in $h = E/ν$ the frequency $ν$ is in cycles/sec (Hz), not radians/sec.</footnote>

<footnote><sup>c</sup>These are calculated from exact values and are exact to the number of places given (i.e. no rounding).</footnote>

<footnote><sup>d</sup>The molar mass of <sup>12</sup>C is 11.999 999 9958(36) g.</footnote>

<footnote><sup>e</sup>CODATA recommended value at $Q^2 = 0$. At $Q^2 \approx m_W^2$ the value is $\sim 1/128$. A world average of the latest data yields $\alpha^{-1} = 137.035999178(8)$. ‡‡</footnote>

<footnote><sup>f</sup>Absolute laboratory measurements of $G_N$ have been made only on scales of about 1 cm to 1 m.</footnote>

<footnote><sup>g</sup>See the discussion in “Electroweak model and constraints on new physics” review.</footnote>

<footnote><sup>h</sup>The corresponding $\sin^2 \theta$ for the effective angle is $\bar{s}_\ell^2 = 0.23161(4)$. The value for the collider average is $\bar{s}_\ell^2 = 0.23149(13)$.</footnote>

<footnote><sup>i</sup>See the “Mass and width of the W boson” and “Electroweak model and constraints on new physics” reviews.</footnote>

<footnote><sup>j</sup>See the “Z boson” and “Electroweak model and constraints on new physics” reviews.</footnote>
## 2. Astrophysical Constants and Parameters

<table><caption>**Table 2.1:** Revised August 2023 by D.E. Groom (LBNL) and D. Scott (U. of British Columbia). The figures in parentheses after some values give the 1-σ uncertainties in the last digit(s). Physical constants are from Ref. [1]. While every effort has been made to obtain the most accurate current values of the listed quantities, this table does not represent a critical review or adjustment of the constants, and is not intended as a primary reference. The values and uncertainties for the cosmological parameters depend on the exact data sets, priors, and basis parameters used in the fit. Many of the derived parameters reported in this table have non-Gaussian likelihoods and parameters may be highly correlated, so care must be taken in propagating errors. Unless otherwise specified, cosmological parameters are derived from a 6-parameter ΛCDM cosmology fit to Planck cosmic microwave background 2018 temperature (TT) + polarization (TE,EE+lowE) + lensing data [2]. For more information see [3] and the original papers.</caption><thead><tr><th>Quantity</th><th>Symbol, equation</th><th>Value</th><th>Reference, footnote</th></tr></thead><tbody><tr><td>Newtonian constant of gravitation</td><td>G<sub>N</sub></td><td>6.674 30(15) × 10<sup>-11</sup> m<sup>3</sup> kg<sup>-1</sup> s<sup>-2</sup></td><td>[1]</td></tr><tr><td>Planck mass</td><td>M<sub>P</sub> = &radic;(hc/G<sub>N</sub>)</td><td>1.220 890(14) × 10<sup>19</sup> GeV/c<sup>2</sup> = 2.176 434(24) × 10<sup>-8</sup> kg</td><td>[1]</td></tr><tr><td>Planck length</td><td>l<sub>P</sub> = &radic;(hG<sub>N</sub>/c<sup>3</sup>)</td><td>1.616 255(18) × 10<sup>-35</sup> m</td><td>[1]</td></tr><tr><td>tropical year (equinox to equinox, 2020)</td><td>yr</td><td>31 556 925.1 s = 365.242 189 days</td><td>[4]</td></tr><tr><td>sidereal year (period of Earth around Sun relative to stars)</td><td></td><td>31 558 149.8 s ≈ π × 10<sup>7</sup> s</td><td>[4]</td></tr><tr><td>mean sidereal day (Earth rotation period relative to stars)</td><td></td><td>23<sup>h</sup> 56<sup>m</sup> 04<sup>s</sup>090 53</td><td>[4]</td></tr><tr><td>astronomical unit</td><td>au</td><td>149 597 870 700 m</td><td>exact [5]</td></tr><tr><td>parsec (1 au/1 arcsec)</td><td>pc</td><td>3.085 677 581 49... × 10<sup>16</sup> m = 3.261 56... ly</td><td>exact [6]</td></tr><tr><td>light year (deprecated unit)</td><td>ly</td><td>0.306 601... pc = 0.946 073... × 10<sup>16</sup> m</td><td>[7]</td></tr><tr><td>solid angle</td><td>deg<sup>2</sup></td><td>(π/180)<sup>2</sup> sr = 3.046 17... × 10<sup>-4</sup> sr</td><td>[8]</td></tr><tr><td>Schwarzschild radius of the Sun</td><td>2G<sub>N</sub> M<sub>☉</sub>/c<sup>2</sup></td><td>2.953 250 1 km</td><td>[9]</td></tr><tr><td>Solar mass</td><td>M<sub>☉</sub></td><td>1.988 41(4) × 10<sup>30</sup> kg</td><td>[10]</td></tr><tr><td>nominal Solar equatorial radius</td><td>R<sub>☉</sub></td><td>6.957 × 10<sup>8</sup> m</td><td>exact [11]</td></tr><tr><td>nominal Solar constant</td><td>S<sub>☉</sub></td><td>1361 W m<sup>-2</sup></td><td>exact [11, 12]</td></tr><tr><td>nominal Solar photosphere temperature</td><td>T<sub>☉</sub></td><td>5772 K</td><td>exact [11]</td></tr><tr><td>nominal Solar luminosity</td><td>L<sub>☉</sub></td><td>3.828 × 10<sup>26</sup> W</td><td>exact [11, 13]</td></tr><tr><td>Schwarzschild radius of the Earth</td><td>2G<sub>N</sub> M<sub>⊕</sub>/c<sup>2</sup></td><td>8.870 056 mm</td><td>[9]</td></tr><tr><td>Earth mass</td><td>M<sub>⊕</sub></td><td>5.972 17(13) × 10<sup>24</sup> kg</td><td>[10]</td></tr><tr><td>nominal Earth equatorial radius</td><td>R<sub>⊕</sub></td><td>6.3781 × 10<sup>6</sup> m</td><td>exact [11]</td></tr><tr><td>Chandrasekhar mass</td><td>M<sub>Ch</sub></td><td>3.097 972 µ<sup>-2</sup> M<sub>P</sub><sup>3</sup>/m<sub>H</sub><sup>2</sup> = 1.433 77(6) (µ/2)<sup>-2</sup> M<sub>☉</sub></td><td>[14, 15]</td></tr><tr><td>Eddington luminosity</td><td>L<sub>Ed</sub></td><td>1.257 065 179 8(12) × 10<sup>31</sup> (M/M<sub>☉</sub>) W = 3.283 869 330 8(31) × 10<sup>4</sup> (M/M<sub>☉</sub>) L<sub>☉</sub></td><td>[16, 17]</td></tr><tr><td>jansky (flux density)</td><td>Jy</td><td>10<sup>-26</sup> W m<sup>-2</sup> Hz<sup>-1</sup></td><td>definition</td></tr><tr><td>luminosity conversion</td><td>f<sub>0</sub></td><td>3.0128 × 10<sup>28</sup> × 10<sup>-0.4</sup> M<sub>Bol</sub> W</td><td>exact [18]</td></tr><tr><td>flux conversion</td><td>F</td><td>(M<sub>Bol</sub> = absolute bolometric magnitude = bolometric magnitude at 10 pc) 2.518 021 002 × 10<sup>-8</sup> × 10<sup>-0.4</sup> m<sub>Bol</sub> W m<sup>-2</sup></td><td>exact [18]</td></tr><tr><td>ABolute monochromatic magnitude</td><td>AB</td><td>(m<sub>Bol</sub> = apparent bolometric magnitude) -2.5 log<sub>10</sub> f<sub>ν</sub> - 56.10 (for f<sub>ν</sub> in W m<sup>-2</sup> Hz<sup>-1</sup>) = -2.5 log<sub>10</sub> f<sub>ν</sub> + 8.90 (for f<sub>ν</sub> in Jy)</td><td>[19]</td></tr><tr><td>Solar distance from Galactic center</td><td>R<sub>0</sub></td><td>8.275 ± 0.009(stat.) ± 0.033(sys.) kpc</td><td>[20]</td></tr><tr><td>local circular angular velocity</td><td>Θ<sub>0</sub>/R<sub>0</sub></td><td>28.2(10) km s<sup>-1</sup> kpc<sup>-1</sup></td><td>[21]</td></tr><tr><td>circular velocity at R<sub>0</sub></td><td>v<sub>0</sub> or Θ<sub>0</sub></td><td>233.4 ± 0.3(stat.) ± 8.0(sys.) km s<sup>-1</sup></td><td>[22]</td></tr><tr><td>local escape velocity from the Galaxy</td><td>v<sub>esc</sub></td><td>477 km s<sup>-1</sup> &lt; v<sub>esc</sub> &lt; 502 km s<sup>-1</sup> (68%)</td><td>[23]</td></tr><tr><td>local disk density</td><td>ρ<sub>disk</sub></td><td>6.6(9) × 10<sup>-24</sup> g cm<sup>-3</sup> = 3.7(5) GeV/c<sup>2</sup> cm<sup>-3</sup></td><td>[24]</td></tr><tr><td>local dark matter density</td><td>ρ<sub>χ</sub></td><td>canonical value 0.3 GeV/c<sup>2</sup> cm<sup>-3</sup> within factor 2-3</td><td>[25]</td></tr><tr><td>present-day CMB temperature</td><td>T<sub>0</sub></td><td>2.7255(6) K</td><td>[26, 27]</td></tr><tr><td>present-day CMB dipole amplitude</td><td>d</td><td>3.3621(10) mK</td><td>[26, 28]</td></tr><tr><td>Solar velocity with respect to CMB</td><td>v<sub>☉</sub></td><td>369.82(11) km s<sup>-1</sup> towards (l, b) = (264.021(11)<sup>°</sup>, 48.253(5)<sup>°</sup>)</td><td>[28]</td></tr><tr><td>Local Group velocity with respect to CMB</td><td>v<sub>LG</sub></td><td>620(15) km s<sup>-1</sup> towards (l, b) = (271.9(20)<sup>°</sup>, 29.6(14)<sup>°</sup>)</td><td>[28]</td></tr><tr><td>number density of CMB photons</td><td>n<sub>γ</sub></td><td>410.73(27) (T/2.7255 K)<sup>3</sup> cm<sup>-3</sup></td><td>[29]</td></tr><tr><td>density of CMB photons</td><td>ρ<sub>γ</sub></td><td>4.645(4) (T/2.7255 K)<sup>4</sup> × 10<sup>-34</sup> g cm<sup>-3</sup> ≈ 0.260 eV cm<sup>-3</sup></td><td>[29]</td></tr><tr><td>entropy density/Boltzmann constant</td><td>s/k</td><td>2 891.2 (T/2.7255 K)<sup>3</sup> cm<sup>-3</sup></td><td>[29]</td></tr><tr><td>present-day Hubble expansion rate</td><td>H<sub>0</sub></td><td>100 h km s<sup>-1</sup> Mpc<sup>-1</sup> = h × (9.777 752 Gyr)<sup>-1</sup></td><td>[30]</td></tr><tr><td>scaling factor for Hubble expansion rate</td><td>h</td><td>0.674(5) from CMB anisotropies (Planck) or 0.730(10) from the distance ladder (SH0ES)</td><td>[31, 32]</td></tr><tr><td>Hubble length</td><td>c/H<sub>0</sub></td><td>0.925 0629 × 10<sup>26</sup> h<sup>-1</sup> m = 1.372(11) or 1.267(18) × 10<sup>26</sup> m</td><td>[2, 31]</td></tr><tr><td>scaling for cosmological constant</td><td>c<sup>2</sup>/3H<sub>0</sub><sup>2</sup></td><td>2.85247 × 10<sup>51</sup> h<sup>-2</sup> m<sup>2</sup> = 6.29(10) or 5.35(15) × 10<sup>51</sup> m<sup>2</sup></td><td>[2, 31]</td></tr><tr><td>critical density of the Universe</td><td>ρ<sub>crit</sub> = 3H<sub>0</sub><sup>2</sup>/8πG<sub>N</sub></td><td>1.878 34(4) × 10<sup>-29</sup> h<sup>2</sup> g cm<sup>-3</sup> = 1.053 672(24) × 10<sup>-5</sup> h<sup>2</sup> (GeV/c<sup>2</sup>) cm<sup>-3</sup> = 2.775 36627 × 10<sup>11</sup> h<sup>2</sup> M<sub>☉</sub> Mpc<sup>-3</sup></td><td></td></tr><tr><td>baryon-to-photon ratio (from BBN)</td><td>η = n<sub>b</sub>/n<sub>γ</sub></td><td>6.04(12) × 10<sup>-10</sup></td><td>[33, 34]</td></tr><tr><td>number density of baryons</td><td>n<sub>b</sub></td><td>2.515(17) × 10<sup>-7</sup> cm<sup>-3</sup> (from CMB) 2.48(5) × 10<sup>-7</sup> cm<sup>-3</sup> (from BBN, η × n<sub>γ</sub>)</td><td>[2, 35]</td></tr><tr><td>CMB radiation density of the Universe</td><td>Ω<sub>γ</sub> = ρ<sub>γ</sub>/ρ<sub>crit</sub></td><td>2.473 × 10<sup>-5</sup> (T/2.7255 K)<sup>4</sup> h<sup>-2</sup> = 5.38(15) × 10<sup>-5</sup></td><td>[29]</td></tr><tr><td>primordial helium fraction</td><td>Y<sub>p</sub></td><td>0.2448(33)</td><td>[36]</td></tr><tr><td colspan="4">--- Planck 2018 6-parameter fit to flat ΛCDM cosmology</td></tr><tr><td>baryon density of the Universe</td><td>Ω<sub>b</sub> = ρ<sub>b</sub>/ρ<sub>crit</sub></td><td>‡ 0.02237(15) h<sup>-2</sup> = † 0.0493(6)</td><td>[2, 3, 26]</td></tr><tr><td>cold dark matter density of the Universe</td><td>Ω<sub>c</sub> = ρ<sub>c</sub>/ρ<sub>crit</sub></td><td>‡ 0.1200(12) h<sup>-2</sup> = † 0.265(7)</td><td>[2, 3, 26]</td></tr><tr><td>100 × approximation to r<sub>*</sub>/D<sub>A</sub></td><td>100 × θ<sub>MC</sub></td><td>‡ 1.04092(31)</td><td>[2, 3, 26]</td></tr><tr><td>reionization optical depth</td><td>τ</td><td>‡ 0.054(7)</td><td>[2, 3, 26]</td></tr><tr><td>ln(power prim. curv. pert.) (k<sub>0</sub> = 0.05 Mpc<sup>-1</sup>)</td><td>ln(10<sup>10</sup>Δ<sub>R</sub><sup>2</sup>)</td><td>‡ 3.044(14)</td><td>[2, 3, 26]</td></tr><tr><td>scalar spectral index</td><td>n<sub>s</sub></td><td>‡ 0.965(4)</td><td>[2, 3, 26]</td></tr><tr><td>pressureless matter density parameter</td><td>Ω<sub>m</sub> = Ω<sub>c</sub> + Ω<sub>b</sub></td><td>† 0.315(7)</td><td>[2, 3]</td></tr><tr><td>dark energy density parameter</td><td>Ω<sub>Λ</sub></td><td>† 0.685(7)</td><td>[2, 3]</td></tr><tr><td>energy density of dark energy</td><td>ρ<sub>Λ</sub></td><td>† 5.83(16) × 10<sup>-30</sup> g cm<sup>-3</sup></td><td>[2]</td></tr><tr><td>cosmological constant</td><td>Λ</td><td>† 1.088(30) × 10<sup>-56</sup> cm<sup>-2</sup></td><td>[2]</td></tr><tr><td>fluctuation amplitude at 8 h<sup>-1</sup> Mpc scale</td><td>σ<sub>s</sub></td><td>† 0.811(6)</td><td>[2, 3]</td></tr></tbody></table>
<table><thead><tr><th>Quantity</th><th>Symbol, equation.</th><th>Value</th><th>Reference, footnote</th></tr></thead><tbody><tr><td>amplitude of matter fluctuations</td><td>σ<sub>S</sub> (Ω<sub>m</sub>/0.3)<sup>0.5</sup></td><td>† 0.832(13)</td><td>[2,3]</td></tr><tr><td>redshift of matter-radiation equality</td><td>z<sub>eq</sub></td><td>† 3402(26)</td><td>[2,37]</td></tr><tr><td>age at matter-radiation equality</td><td>t<sub>eq</sub></td><td>† 51.0(8) kyr</td><td>[2,38]</td></tr><tr><td>redshift at which optical depth equals unity</td><td>z<sub>*</sub></td><td>† 1089.92(25)</td><td>[2]</td></tr><tr><td>comoving size of sound horizon at z<sub>*</sub></td><td>r<sub>*</sub></td><td>† 144.43(26) Mpc</td><td>[2,39]</td></tr><tr><td>age when optical depth equals unity</td><td>t<sub>*</sub></td><td>† 371.8(10) kyr</td><td>[2,38]</td></tr><tr><td>redshift at half reionization</td><td>z<sub>i</sub></td><td>† 7.7(7)</td><td>[2,40]</td></tr><tr><td>age at half reionization</td><td>t<sub>i</sub></td><td>† 690(90) Myr</td><td>[2]</td></tr><tr><td>redshift when acceleration was zero</td><td>z<sub>q</sub></td><td>† 0.656(18)</td><td>[2,38]</td></tr><tr><td>age when acceleration was zero</td><td>t<sub>q</sub></td><td>† 7.70(10) Gyr</td><td>[2]</td></tr><tr><td>age of the Universe today</td><td>t<sub>0</sub></td><td>† 13.797(23) Gyr</td><td>[2]</td></tr><tr><td>effective number of neutrinos</td><td>N<sub>eff</sub></td><td>‡ 2.99(17) (CMB + BAO)</td><td>[2,41,42]</td></tr><tr><td>sum of neutrino masses</td><td>Σm<sub>ν</sub></td><td>‡ &lt; 0.12 eV (95%, CMB + BAO); ≥ 0.06 eV (mixing)</td><td>[2,42-44]</td></tr><tr><td>neutrino density of the Universe</td><td>Ω<sub>ν</sub> = h<sup>-2</sup>Σm<sub>ν</sub>/93.14 eV</td><td>‡ &lt; 0.003 (95%, CMB + BAO); ≥ 0.0012 (mixing)</td><td>[2,43,44]</td></tr><tr><td>curvature</td><td>Ω<sub>K</sub></td><td>‡ 0.0007(19) (CMB + BAO)</td><td>[2]</td></tr><tr><td>running spectral index, k<sub>0</sub> = 0.05 Mpc<sup>-1</sup></td><td>dn<sub>s</sub>/d ln k</td><td>‡ -0.004(7)</td><td>[2]</td></tr><tr><td>tensor-to-scalar perturbation ratio</td><td>r<sub>0.05</sub> = T/S</td><td>‡ &lt; 0.036 (95%, k<sub>0</sub> = 0.05 Mpc<sup>-1</sup>)</td><td>[2,45-48]</td></tr><tr><td>dark energy equation of state parameter</td><td>w</td><td>‡ -1.028(31) (CMB + BAO +SNe)</td><td>[2,49]</td></tr></tbody></table>

‡ Parameter in 6-parameter ΛCDM fit; † derived parameter in 6-parameter ΛCDM fit; ‡ extended model parameter, Planck + BAO data [2].

References

[1] CODATA recommended 2018 values of the fundamental physical constants: physics.nist.gov/cuu/Constants/index.html.

[2] Planck Collab. 2018 Results VI, Astron. Astrophys. 641, A6 (2020), [arXiv:1807.06209].

[3] O. Lahav and A. R. Liddle, “The Cosmological Parameters,” Sec. 25 in this Review.

[4] The Astronomical Almanac for the year 2020.

[5] The astronomical unit of length (au) in meters is re-defined (IAU XXVIII General Assembly 2012, Resolution B2) to be a conventional unit of length in agreement with the value adopted in IAU XXVII GA 2009, Resolution B2. It is to be used with all time scales.

[6] The distance at which 1 au subtends 1 arc sec: 1 au divided by π/648 000.

[7] From c × (tropical year)/pc, c × (tropical year), see IAU XVI GA 1976, Recommendations; T. Lederle, Astron. Gesellschaft 48, 59 (1980).

[8] The number of square degrees on a sphere is 360²/π = 41 259.9...

[9] Observationally determined mass parameter G<sub>N</sub> M × 2/c² [1] for either the Sun or the Earth, using the nominal values G<sub>M</sub> ⊙ = 1.327 124 4 × 10²⁰ m³ s⁻² and G<sub>M</sub> ⊙ = 3.986 004 × 10¹⁴ m³ s⁻² [11]; the calligraphic symbol indicates the recommended nominal value. The combination G<sub>N</sub> M is known much more precisely than either G<sub>N</sub> or M individually. The digits are truncated here at the point where one would need to distinguish between Barycentric Coordinate Time (TCB) and Barycentric Dynamical Time (TDB).

[10] G<sub>N</sub> M ÷ G<sub>N</sub> [1].

[11] IAU XXIX GA 2015 Resolution B3; A. Prša et al., Astron. J. 152, 2, 41 (2016), [arXiv:1605.09788].

[12] See also G. Kopp and J. L. Lean, Geophys. Res. Lett. 38, L01706 (2011), who give (1360.8 ± 0.6) W m⁻²; see paper for caveats and other measurements.

[13] 4π (1 au)² × S<sub>☉</sub>, assuming isotropic irradiance.

[14] S. Chandrasekhar, Astrophys. J. 74, 81 (1931).

[15] This value assumes an ideal Fermi gas, using a numerical constant from the Lane-Emden equation [50], and with μ the average molecular weight per electron, defined relative to the mass of the single-proton hydrogen atom.

[16] A. S. Eddington, Mon. Not. Roy. Astron. Soc. 77, 16 (1916).

[17] The maximum luminosity assuming pure electron scattering for the outward force arising from radiation pressure: 4πG<sub>N</sub> Mm<sub>p</sub>c/σ<sub>T</sub>.

[18] IAU XXIX GA 2015, Resolution B2; E. E. Mamajek et al. arXiv:1510.06262 (2015).

[19] J. B. Oke and J. E. Gunn, Astrophys. J. 266, 713 (1983).

[20] GRAVITY Collaboration, Astron. Astrophys. 647, A59 (2021), [arXiv:2101.12098].

[21] A.-C. Eilers et al., Astrophys. J. 871, 1, 120 (2019), [arXiv:1810.09466]; this is representative of other published values and the systematic uncertainty here is an estimate.

[22] Product of angular velocity and R<sub>0</sub>, derived from Ref. [21] with an estimate of the systematic uncertainty.

[23] L. Necib and T. Lin, Astrophys. J. 926, 2, 189 (2022), [arXiv:2102.02211].

[24] C. F. McKee, A. Parravano and D. J. Hollenbach, Astrophys. J. 814, 1, 13 (2015), [arXiv:1509.05334]; this is representative of other published estimates.

[25] J. I. Read, J. Phys. G41, 063101 (2014), [arXiv:1404.1938]; A. M. Green, J. Phys. G44, 8, 084001 (2017), [arXiv:1703.10102]; the conclusion is ρ<sub>local</sub> = 0.39 ± 0.03 GeV cm⁻³.

[26] D. Scott and G. F. Smoot, “Cosmic Microwave Background,” Sec. 29 in this Review.

[27] D. J. Fixsen, Astrophys. J. 707, 916 (2009), [arXiv:0911.1955].

[28] Planck Collab. 2018 Results I, Astron. Astrophys. 641, A1 (2020), [arXiv:1807.06205].

[29] n<sub>γ</sub> = (2c(3) / π²) (kT / h<sub>c</sub>)³; ρ<sub>γ</sub> = π²kT / (15c²) (kT / h<sub>c</sub>)³; s/k = (2.43·π² / (11·45)) (kT / h<sub>c</sub>)³; kT/h<sub>c</sub> = 11.90 235(T/2.7255)/cm.

[30] Conversion using length of sidereal year.

[31] A. G. Riess et al., Astrophys. J. Lett. 934, 1, L7 (2022), [arXiv:2112.04510].

[32] Distance-ladder estimates of H<sub>0</sub> tend to give higher values than derived from the CMB; Lahav and A. R. Liddle, “The Cosmological Parameters,” Sec. 25 in this Review.

[33] T.-H. Yeh et al., J. Cosmol. Astropart. Phys. 2022, 10, 046 (2022), [arXiv:2207.13133].

[34] B. D. Fields, P. Molaro and S. Sarkar, “Big-Bang Nucleosynthesis,” Sec. 24 in this Review.

[35] n<sub>b</sub> depends only upon the measured Ω<sub>b</sub>h², the average baryon mass at the present epoch (G. Steigman, J. Cosmol. Astropart. Phys., 0610, 016 (2006), [astro-ph/0606206]), and G<sub>N</sub>: n<sub>b</sub> = (Ω<sub>b</sub>h²)(h⁻²ρ<sub>crit</sub>)/(0.93711 GeV/c² per baryon).

[36] E. Aver et al., Mon. Not. Roy. Astron. Soc. 510, 1, 373 (2022), [arXiv:2109.00178].

[37] Here “radiation” includes three species of light neutrinos as well as photons.

[38] D. Scott, A. Narimani and D. N. Page, Phys. Canada 70, 258 (2014), [arXiv:1309.2381].

[39] D. H. Weinberg and M. White, “Dark Energy,” Sec. 28 in this Review.

[40] Planck Collab. Interm. Results XLVI, Astron. Astrophys. 596, A107 (2016), [arXiv:1605.02985]; the range can be extended by Δz ≈ 1, depending on the reionization model.

[41] Summary Tables in this Review list N<sub>ν</sub> = 2.984(8) (Standard Model fits to LEP-SLC data). Because neutrinos are not completely decoupled at e± annihilation, the effective number of massless neutrino species is 3.044, rather than 3.

[42] J. Lesgourgues and L. Verde, “Neutrinos in Cosmology,” Sec. 26 in this Review.

[43] The sum is over all neutrino mass eigenstates, the lower limit following from neutrino mixing results reported in this Review combined with the assumptions that there are three light neutrinos and that the lightest neutrino is substantially less massive than the others.

[44] Astrophysical determinations of Σm<sub>ν</sub>, reported in the Full Listings of this Review under “Sum of the neutrino masses,” range from < 0.17 eV to < 2.3 eV in papers published since 2003.

[45] P. A. R. Ade et al. (BICEP2, Keck Array), Phys. Rev. Lett. 121, 221301 (2018), [arXiv:1810.05216].

[46] M. Tristram et al., Astron. Astrophys. 647, A128 (2021), [arXiv:2010.01139].

[47] BICEP/Keck Collaboration, Phys. Rev. Lett. 127, 151301 (2021), [arXiv:2110.00483].

[48] Planck data alone give r < 0.056, using all power spectra; the currently tightest constraint comes from BICEP/Keck data, using WMAP and Planck to remove foregrounds.

[49] This constraint uses BAO and SNe data, as described in Ref. [2]; see discussion in D. H. Weinberg and M. White, “Dark Energy,” Sec. 28 in this Review.

[50] G. P. Horedt, Astrophys. Space Sci. 126, 2, 357 (1986).
3. International System of Units (SI)

See D.B. Newell and E. Tiesinga, ed. (2019), “The International System of Units (SI)” (National Institute of Standards and Technology, Gaithersburg, MD), NIST Special Publication 330, 2019 edition, https://doi.org/10.6028/NIST.SP.330-2019; and A. Thompson and B.N. Taylor (2008), “Guide for the Use of the International System of Units (SI)” (National Institute of Standards and Technology, Gaithersburg, MD), NIST Special Publication 811, 2008 edition, https://doi.org/10.6028/NIST.SP.811e2008.

<table><thead><tr><th colspan="3">SI prefixes</th></tr></thead><tbody><tr><td>10<sup>24</sup></td><td>yotta</td><td>(Y)</td></tr><tr><td>10<sup>21</sup></td><td>zetta</td><td>(Z)</td></tr><tr><td>10<sup>18</sup></td><td>exa</td><td>(E)</td></tr><tr><td>10<sup>15</sup></td><td>peta</td><td>(P)</td></tr><tr><td>10<sup>12</sup></td><td>tera</td><td>(T)</td></tr><tr><td>10<sup>9</sup></td><td>giga</td><td>(G)</td></tr><tr><td>10<sup>6</sup></td><td>mega</td><td>(M)</td></tr><tr><td>10<sup>3</sup></td><td>kilo</td><td>(k)</td></tr><tr><td>10<sup>2</sup></td><td>hecto</td><td>(h)</td></tr><tr><td>10</td><td>deca</td><td>(da)</td></tr><tr><td>10<sup>-1</sup></td><td>deci</td><td>(d)</td></tr><tr><td>10<sup>-2</sup></td><td>centi</td><td>(c)</td></tr><tr><td>10<sup>-3</sup></td><td>milli</td><td>(m)</td></tr><tr><td>10<sup>-6</sup></td><td>micro</td><td>(&mu;)</td></tr><tr><td>10<sup>-9</sup></td><td>nano</td><td>(n)</td></tr><tr><td>10<sup>-12</sup></td><td>pico</td><td>(p)</td></tr><tr><td>10<sup>-15</sup></td><td>femto</td><td>(f)</td></tr><tr><td>10<sup>-18</sup></td><td>atto</td><td>(a)</td></tr><tr><td>10<sup>-21</sup></td><td>zepto</td><td>(z)</td></tr><tr><td>10<sup>-24</sup></td><td>yocto</td><td>(y)</td></tr></tbody></table>

<table><thead><tr><th>Physical<br>quantity</th><th>Name<br>of unit</th><th>Symbol</th></tr></thead><tbody><tr><td colspan="3"><em>Base units</em></td></tr><tr><td>length</td><td>meter</td><td>m</td></tr><tr><td>mass</td><td>kilogram</td><td>kg</td></tr><tr><td>time</td><td>second</td><td>s</td></tr><tr><td>electric current</td><td>ampere</td><td>A</td></tr><tr><td>thermodynamic<br>temperature</td><td>kelvin</td><td>K</td></tr><tr><td>amount of substance</td><td>mole</td><td>mol</td></tr><tr><td>luminous intensity</td><td>candela</td><td>cd</td></tr><tr><td colspan="3"><em>Derived units with special names</em></td></tr><tr><td>plane angle</td><td>radian</td><td>rad</td></tr><tr><td>solid angle</td><td>steradian</td><td>sr</td></tr><tr><td>frequency</td><td>hertz</td><td>Hz</td></tr><tr><td>energy</td><td>joule</td><td>J</td></tr><tr><td>force</td><td>newton</td><td>N</td></tr><tr><td>pressure</td><td>pascal</td><td>Pa</td></tr><tr><td>power</td><td>watt</td><td>W</td></tr><tr><td>electric charge</td><td>coulomb</td><td>C</td></tr><tr><td>electric potential</td><td>volt</td><td>V</td></tr><tr><td>electric resistance</td><td>ohm</td><td>&Omega;</td></tr><tr><td>electric conductance</td><td>siemens</td><td>S</td></tr><tr><td>electric capacitance</td><td>farad</td><td>F</td></tr><tr><td>magnetic flux</td><td>weber</td><td>Wb</td></tr><tr><td>inductance</td><td>henry</td><td>H</td></tr><tr><td>magnetic flux density</td><td>tesla</td><td>T</td></tr><tr><td>luminous flux</td><td>lumen</td><td>lm</td></tr><tr><td>illuminance</td><td>lux</td><td>lx</td></tr><tr><td>celsius temperature</td><td>degree celsius</td><td>&deg;C</td></tr><tr><td>activity (of a<br>radioactive source)*</td><td>becquerel</td><td>Bq</td></tr><tr><td>absorbed dose (of<br>ionizing radiation)*</td><td>gray</td><td>Gy</td></tr><tr><td>dose equivalent*</td><td>sievert</td><td>Sv</td></tr></tbody></table>

<footnote>*See our section 37, on “Radioactivity and radiation protection.”</footnote>
5. Electronic Structure of the Elements

<table><caption>**Table 5.1:** Reviewed 2022 by A. Kramida (NIST). The electronic configurations, ground state levels, and ionization energies are from A. Kramida, Yu. Ralchenko, J. Reader, and NIST ASD Team (2022), "NIST Atomic Spectra Database" (ver. 5.10), [Online], Available: https://physics.nist.gov/asd [2023, Sept 5]. National Institute of Standards and Technology, Gaithersburg, MD. DOI: https://doi.org/10.18434/T4W30F. The electron configuration for, say, iron indicates an argon electronic core (see argon) plus six 3d electrons and two 4s electrons.</caption><thead><tr><th colspan="3">Element</th><th>Electron configuration<br>(3d<sup>5</sup> = five 3d electrons, etc.)</th><th>Ground<br>state<br>2S+1L<sub>J</sub></th><th>Ionization<br>energy<br>(eV)</th></tr></thead><tbody><tr><td>1</td><td>H</td><td>Hydrogen</td><td>1s</td><td><sup>2</sup>S<sub>1/2</sub></td><td>13.5984</td></tr><tr><td>2</td><td>He</td><td>Helium</td><td>1s<sup>2</sup></td><td><sup>1</sup>S<sub>0</sub></td><td>24.5874</td></tr><tr><td>3</td><td>Li</td><td>Lithium</td><td>(He) 2s</td><td><sup>2</sup>S<sub>1/2</sub></td><td>5.3917</td></tr><tr><td>4</td><td>Be</td><td>Beryllium</td><td>(He) 2s<sup>2</sup></td><td><sup>1</sup>S<sub>0</sub></td><td>9.3227</td></tr><tr><td>5</td><td>B</td><td>Boron</td><td>(He) 2s<sup>2</sup> 2p</td><td><sup>2</sup>P<sup>o</sup><sub>1/2</sub></td><td>8.2980</td></tr><tr><td>6</td><td>C</td><td>Carbon</td><td>(He) 2s<sup>2</sup> 2p<sup>2</sup></td><td><sup>3</sup>P<sub>0</sub></td><td>11.2603</td></tr><tr><td>7</td><td>N</td><td>Nitrogen</td><td>(He) 2s<sup>2</sup> 2p<sup>3</sup></td><td><sup>4</sup>S<sup>o</sup><sub>3/2</sub></td><td>14.5341</td></tr><tr><td>8</td><td>O</td><td>Oxygen</td><td>(He) 2s<sup>2</sup> 2p<sup>4</sup></td><td><sup>3</sup>P<sub>2</sub></td><td>13.6181</td></tr><tr><td>9</td><td>F</td><td>Fluorine</td><td>(He) 2s<sup>2</sup> 2p<sup>5</sup></td><td><sup>2</sup>P<sup>o</sup><sub>3/2</sub></td><td>17.4228</td></tr><tr><td>10</td><td>Ne</td><td>Neon</td><td>(He) 2s<sup>2</sup> 2p<sup>6</sup></td><td><sup>1</sup>S<sub>0</sub></td><td>21.5645</td></tr><tr><td>11</td><td>Na</td><td>Sodium</td><td>(Ne) 3s</td><td><sup>2</sup>S<sub>1/2</sub></td><td>5.1391</td></tr><tr><td>12</td><td>Mg</td><td>Magnesium</td><td>(Ne) 3s<sup>2</sup></td><td><sup>1</sup>S<sub>0</sub></td><td>7.6462</td></tr><tr><td>13</td><td>Al</td><td>Aluminum</td><td>(Ne) 3s<sup>2</sup> 3p</td><td><sup>2</sup>P<sup>o</sup><sub>1/2</sub></td><td>5.9858</td></tr><tr><td>14</td><td>Si</td><td>Silicon</td><td>(Ne) 3s<sup>2</sup> 3p<sup>2</sup></td><td><sup>3</sup>P<sub>0</sub></td><td>8.1517</td></tr><tr><td>15</td><td>P</td><td>Phosphorus</td><td>(Ne) 3s<sup>2</sup> 3p<sup>3</sup></td><td><sup>4</sup>S<sup>o</sup><sub>3/2</sub></td><td>10.4867</td></tr><tr><td>16</td><td>S</td><td>Sulfur</td><td>(Ne) 3s<sup>2</sup> 3p<sup>4</sup></td><td><sup>3</sup>P<sub>2</sub></td><td>10.3600</td></tr><tr><td>17</td><td>Cl</td><td>Chlorine</td><td>(Ne) 3s<sup>2</sup> 3p<sup>5</sup></td><td><sup>2</sup>P<sup>o</sup><sub>3/2</sub></td><td>12.9676</td></tr><tr><td>18</td><td>Ar</td><td>Argon</td><td>(Ne) 3s<sup>2</sup> 3p<sup>6</sup></td><td><sup>1</sup>S<sub>0</sub></td><td>15.7596</td></tr><tr><td>19</td><td>K</td><td>Potassium</td><td>(Ar) 4s</td><td><sup>2</sup>S<sub>1/2</sub></td><td>4.3407</td></tr><tr><td>20</td><td>Ca</td><td>Calcium</td><td>4s<sup>2</sup></td><td><sup>1</sup>S<sub>0</sub></td><td>6.1132</td></tr><tr><td>21</td><td>Sc</td><td>Scandium</td><td>(Ar) 3d 4s<sup>2</sup></td><td>T</td><td><sup>2</sup>D<sub>3/2</sub></td></tr><tr><td>22</td><td>Ti</td><td>Titanium</td><td>(Ar) 3d<sup>2</sup> 4s<sup>2</sup></td><td>r e</td><td><sup>3</sup>F<sub>2</sub></td></tr><tr><td>23</td><td>V</td><td>Vanadium</td><td>(Ar) 3d<sup>3</sup> 4s<sup>2</sup></td><td>a l</td><td><sup>4</sup>F<sub>3/2</sub></td></tr><tr><td>24</td><td>Cr</td><td>Chromium</td><td>(Ar) 3d<sup>5</sup> 4s</td><td>n e</td><td><sup>7</sup>S<sub>3</sub></td></tr><tr><td>25</td><td>Mn</td><td>Manganese</td><td>(Ar) 3d<sup>5</sup> 4s<sup>2</sup></td><td>s m</td><td><sup>6</sup>S<sub>5/2</sub></td></tr><tr><td>26</td><td>Fe</td><td>Iron</td><td>(Ar) 3d<sup>6</sup> 4s<sup>2</sup></td><td>i e</td><td><sup>5</sup>D<sub>4</sub></td></tr><tr><td>27</td><td>Co</td><td>Cobalt</td><td>(Ar) 3d<sup>7</sup> 4s<sup>2</sup></td><td>t n</td><td><sup>4</sup>F<sub>9/2</sub></td></tr><tr><td>28</td><td>Ni</td><td>Nickel</td><td>(Ar) 3d<sup>8</sup> 4s<sup>2</sup></td><td>i t</td><td><sup>3</sup>F<sub>4</sub></td></tr><tr><td>29</td><td>Cu</td><td>Copper</td><td>(Ar) 3d<sup>10</sup> 4s</td><td>o s</td><td><sup>2</sup>S<sub>1/2</sub></td></tr><tr><td>30</td><td>Zn</td><td>Zinc</td><td>(Ar) 3d<sup>10</sup> 4s<sup>2</sup></td><td>n</td><td><sup>1</sup>S<sub>0</sub></td></tr><tr><td>31</td><td>Ga</td><td>Gallium</td><td>(Ar) 3d<sup>10</sup> 4s<sup>2</sup> 4p</td><td></td><td><sup>2</sup>P<sup>o</sup><sub>1/2</sub></td></tr><tr><td>32</td><td>Ge</td><td>Germanium</td><td>(Ar) 3d<sup>10</sup> 4s<sup>2</sup> 4p<sup>2</sup></td><td></td><td><sup>3</sup>P<sub>0</sub></td></tr><tr><td>33</td><td>As</td><td>Arsenic</td><td>(Ar) 3d<sup>10</sup> 4s<sup>2</sup> 4p<sup>3</sup></td><td></td><td><sup>4</sup>S<sup>o</sup><sub>3/2</sub></td></tr><tr><td>34</td><td>Se</td><td>Selenium</td><td>(Ar) 3d<sup>10</sup> 4s<sup>2</sup> 4p<sup>4</sup></td><td></td><td><sup>3</sup>P<sub>2</sub></td></tr><tr><td>35</td><td>Br</td><td>Bromine</td><td>(Ar) 3d<sup>10</sup> 4s<sup>2</sup> 4p<sup>5</sup></td><td></td><td><sup>2</sup>P<sup>o</sup><sub>3/2</sub></td></tr><tr><td>36</td><td>Kr</td><td>Krypton</td><td>(Ar) 3d<sup>10</sup> 4s<sup>2</sup> 4p<sup>6</sup></td><td></td><td><sup>1</sup>S<sub>0</sub></td></tr><tr><td>37</td><td>Rb</td><td>Rubidium</td><td>(Kr) 5s</td><td></td><td><sup>2</sup>S<sub>1/2</sub></td></tr><tr><td>38</td><td>Sr</td><td>Strontium</td><td>5s<sup>2</sup></td><td></td><td><sup>1</sup>S<sub>0</sub></td></tr><tr><td>39</td><td>Y</td><td>Yttrium</td><td>(Kr) 4d 5s<sup>2</sup></td><td>T</td><td><sup>2</sup>D<sub>3/2</sub></td></tr><tr><td>40</td><td>Zr</td><td>Zirconium</td><td>(Kr) 4d<sup>2</sup> 5s<sup>2</sup></td><td>r e</td><td><sup>3</sup>F<sub>2</sub></td></tr><tr><td>41</td><td>Nb</td><td>Niobium</td><td>(Kr) 4d<sup>4</sup> 5s</td><td>a l</td><td><sup>6</sup>D<sub>1/2</sub></td></tr><tr><td>42</td><td>Mo</td><td>Molybdenum</td><td>(Kr) 4d<sup>5</sup> 5s</td><td>n e</td><td><sup>7</sup>S<sub>3</sub></td></tr><tr><td>43</td><td>Tc</td><td>Technetium</td><td>(Kr) 4d<sup>5</sup> 5s<sup>2</sup></td><td>s m</td><td><sup>6</sup>S<sub>5/2</sub></td></tr><tr><td>44</td><td>Ru</td><td>Ruthenium</td><td>(Kr) 4d<sup>7</sup> 5s</td><td>i e</td><td><sup>5</sup>F<sub>5</sub></td></tr><tr><td>45</td><td>Rh</td><td>Rhodium</td><td>(Kr) 4d<sup>8</sup> 5s</td><td>t n</td><td><sup>4</sup>F<sub>9/2</sub></td></tr><tr><td>46</td><td>Pd</td><td>Palladium</td><td>(Kr) 4d<sup>10</sup></td><td>i t</td><td><sup>1</sup>S<sub>0</sub></td></tr><tr><td>47</td><td>Ag</td><td>Silver</td><td>(Kr) 4d<sup>10</sup> 5s</td><td>o s</td><td><sup>2</sup>S<sub>1/2</sub></td></tr><tr><td>48</td><td>Cd</td><td>Cadmium</td><td>(Kr) 4d<sup>10</sup> 5s<sup>2</sup></td><td>n</td><td><sup>1</sup>S<sub>0</sub></td></tr></tbody></table>
<table><thead><tr><th></th><th>Element</th><th>Electron configuration<br>(3d<sup>5</sup> = five 3d electrons, etc.)</th><th>Ground<br>state<br>2S+1L<sub>J</sub></th><th>Ionization<br>energy<br>(eV)</th></tr></thead><tbody><tr><td>49</td><td>In Indium</td><td>(Kr) 4d<sup>10</sup> 5s<sup>2</sup> 5p</td><td><sup>2</sup>P<sub>1/2</sub></td><td>5.7864</td></tr><tr><td>50</td><td>Sn Tin</td><td>(Kr) 4d<sup>10</sup> 5s<sup>2</sup> 5p<sup>2</sup></td><td><sup>3</sup>P<sub>0</sub></td><td>7.3439</td></tr><tr><td>51</td><td>Sb Antimony</td><td>(Kr) 4d<sup>10</sup> 5s<sup>2</sup> 5p<sup>3</sup></td><td><sup>4</sup>S<sub>3/2</sub></td><td>8.6084</td></tr><tr><td>52</td><td>Te Tellurium</td><td>(Kr) 4d<sup>10</sup> 5s<sup>2</sup> 5p<sup>4</sup></td><td><sup>3</sup>P<sub>2</sub></td><td>9.0098</td></tr><tr><td>53</td><td>I Iodine</td><td>(Kr) 4d<sup>10</sup> 5s<sup>2</sup> 5p<sup>5</sup></td><td><sup>2</sup>P<sub>3/2</sub></td><td>10.4513</td></tr><tr><td>54</td><td>Xe Xenon</td><td>(Kr) 4d<sup>10</sup> 5s<sup>2</sup> 5p<sup>6</sup></td><td><sup>1</sup>S<sub>0</sub></td><td>12.1298</td></tr><tr><td>55</td><td>Cs Cesium</td><td>(Xe) 6s</td><td><sup>2</sup>S<sub>1/2</sub></td><td>3.8939</td></tr><tr><td>56</td><td>Ba Barium</td><td>(Xe) 6s<sup>2</sup></td><td><sup>1</sup>S<sub>0</sub></td><td>5.2117</td></tr><tr><td>57</td><td>La Lanthanum</td><td>(Xe) 5d 6s<sup>2</sup></td><td><sup>2</sup>D<sub>3/2</sub></td><td>5.5769</td></tr><tr><td>58</td><td>Ce Cerium</td><td>(Xe) 4f 5d 6s<sup>2</sup></td><td><sup>1</sup>G<sub>4</sub></td><td>5.5386</td></tr><tr><td>59</td><td>Pr Praseodymium</td><td>(Xe) 4f<sup>3</sup> 6s<sup>2</sup></td><td>L <sup>4</sup>I<sub>9/2</sub></td><td>5.4702</td></tr><tr><td>60</td><td>Nd Neodymium</td><td>(Xe) 4f<sup>4</sup> 6s<sup>2</sup></td><td>a <sup>5</sup>I<sub>4</sub></td><td>5.5250</td></tr><tr><td>61</td><td>Pm Promethium</td><td>(Xe) 4f<sup>5</sup> 6s<sup>2</sup></td><td>n <sup>6</sup>H<sub>5/2</sub></td><td>5.5819</td></tr><tr><td>62</td><td>Sm Samarium</td><td>(Xe) 4f<sup>6</sup> 6s<sup>2</sup></td><td>t <sup>7</sup>F<sub>0</sub></td><td>5.6437</td></tr><tr><td>63</td><td>Eu Europium</td><td>(Xe) 4f<sup>7</sup> 6s<sup>2</sup></td><td>a <sup>8</sup>S<sub>7/2</sub></td><td>5.6704</td></tr><tr><td>64</td><td>Gd Gadolinium</td><td>(Xe) 4f<sup>7</sup> 5d 6s<sup>2</sup></td><td>n <sup>9</sup>D<sub>2</sub></td><td>6.1498</td></tr><tr><td>65</td><td>Tb Terbium</td><td>(Xe) 4f<sup>9</sup> 6s<sup>2</sup></td><td>i <sup>6</sup>H<sub>15/2</sub></td><td>5.8638</td></tr><tr><td>66</td><td>Dy Dysprosium</td><td>(Xe) 4f<sup>10</sup> 6s<sup>2</sup></td><td>d <sup>5</sup>I<sub>8</sub></td><td>5.9391</td></tr><tr><td>67</td><td>Ho Holmium</td><td>(Xe) 4f<sup>11</sup> 6s<sup>2</sup></td><td>e <sup>4</sup>I<sub>15/2</sub></td><td>6.0215</td></tr><tr><td>68</td><td>Er Erbium</td><td>(Xe) 4f<sup>12</sup> 6s<sup>2</sup></td><td>s <sup>3</sup>H<sub>6</sub></td><td>6.1077</td></tr><tr><td>69</td><td>Tm Thulium</td><td>(Xe) 4f<sup>13</sup> 6s<sup>2</sup></td><td><sup>2</sup>F<sub>7/2</sub></td><td>6.1844</td></tr><tr><td>70</td><td>Yb Ytterbium</td><td>(Xe) 4f<sup>14</sup> 6s<sup>2</sup></td><td><sup>1</sup>S<sub>0</sub></td><td>6.2542</td></tr><tr><td>71</td><td>Lu Lutetium</td><td>(Xe) 4f<sup>14</sup> 5d 6s<sup>2</sup></td><td><sup>2</sup>D<sub>3/2</sub></td><td>5.4259</td></tr><tr><td>72</td><td>Hf Hafnium</td><td>(Xe) 4f<sup>14</sup> 5d<sup>2</sup> 6s<sup>2</sup></td><td><sup>3</sup>F<sub>2</sub></td><td>6.8251</td></tr><tr><td>73</td><td>Ta Tantalum</td><td>(Xe) 4f<sup>14</sup> 5d<sup>3</sup> 6s<sup>2</sup></td><td>r e <sup>4</sup>F<sub>3/2</sub></td><td>7.5496</td></tr><tr><td>74</td><td>W Tungsten</td><td>(Xe) 4f<sup>14</sup> 5d<sup>4</sup> 6s<sup>2</sup></td><td>a l <sup>5</sup>D<sub>0</sub></td><td>7.8640</td></tr><tr><td>75</td><td>Re Rhenium</td><td>(Xe) 4f<sup>14</sup> 5d<sup>5</sup> 6s<sup>2</sup></td><td>n e <sup>6</sup>S<sub>5/2</sub></td><td>7.8335</td></tr><tr><td>76</td><td>Os Osmium</td><td>(Xe) 4f<sup>14</sup> 5d<sup>6</sup> 6s<sup>2</sup></td><td>s m <sup>5</sup>D<sub>4</sub></td><td>8.4382</td></tr><tr><td>77</td><td>Ir Iridium</td><td>(Xe) 4f<sup>14</sup> 5d<sup>7</sup> 6s<sup>2</sup></td><td>i e <sup>4</sup>F<sub>9/2</sub></td><td>8.9670</td></tr><tr><td>78</td><td>Pt Platinum</td><td>(Xe) 4f<sup>14</sup> 5d<sup>9</sup> 6s</td><td>t n <sup>3</sup>D<sub>3</sub></td><td>8.9588</td></tr><tr><td>79</td><td>Au Gold</td><td>(Xe) 4f<sup>14</sup> 5d<sup>10</sup> 6s</td><td>i t <sup>2</sup>S<sub>1/2</sub></td><td>9.2256</td></tr><tr><td>80</td><td>Hg Mercury</td><td>(Xe) 4f<sup>14</sup> 5d<sup>10</sup> 6s<sup>2</sup></td><td>o s <sup>1</sup>S<sub>0</sub></td><td>10.4375</td></tr><tr><td>81</td><td>Tl Thallium</td><td>(Hg) 6p</td><td><sup>2</sup>P<sub>1/2</sub></td><td>6.1083</td></tr><tr><td>82</td><td>Pb Lead</td><td>(Hg) 6p<sup>2</sup></td><td><sup>3</sup>P<sub>0</sub></td><td>7.4167</td></tr><tr><td>83</td><td>Bi Bismuth</td><td>(Hg) 6p<sup>3</sup></td><td><sup>4</sup>S<sub>3/2</sub></td><td>7.2855</td></tr><tr><td>84</td><td>Po Polonium</td><td>(Hg) 6p<sup>4</sup></td><td><sup>3</sup>P<sub>2</sub></td><td>8.4181</td></tr><tr><td>85</td><td>At Astatine</td><td>(Hg) 6p<sup>5</sup></td><td><sup>2</sup>P<sub>3/2</sub></td><td>9.3175</td></tr><tr><td>86</td><td>Rn Radon</td><td>(Hg) 6p<sup>6</sup></td><td><sup>1</sup>S<sub>0</sub></td><td>10.7485</td></tr><tr><td>87</td><td>Fr Francium</td><td>(Rn) 7s</td><td><sup>2</sup>S<sub>1/2</sub></td><td>4.0727</td></tr><tr><td>88</td><td>Ra Radium</td><td>(Rn) 7s<sup>2</sup></td><td><sup>1</sup>S<sub>0</sub></td><td>5.2784</td></tr><tr><td>89</td><td>Ac Actinium</td><td>(Rn) 6d 7s<sup>2</sup></td><td><sup>2</sup>D<sub>3/2</sub></td><td>5.3802</td></tr><tr><td>90</td><td>Th Thorium</td><td>(Rn) 6d<sup>2</sup> 7s<sup>2</sup></td><td><sup>3</sup>F<sub>2</sub></td><td>6.3067</td></tr><tr><td>91</td><td>Pa Protactinium</td><td>(Rn) 5f<sup>2</sup> 6d 7s<sup>2</sup></td><td>A <sup>4</sup>K<sub>11/2</sub>*</td><td>5.89</td></tr><tr><td>92</td><td>U Uranium</td><td>(Rn) 5f<sup>3</sup> 6d 7s<sup>2</sup></td><td>c <sup>5</sup>L<sub>6</sub><sup>*</sup></td><td>6.1941</td></tr><tr><td>93</td><td>Np Neptunium</td><td>(Rn) 5f<sup>4</sup> 6d 7s<sup>2</sup></td><td>t <sup>6</sup>L<sub>11/2</sub>*</td><td>6.2655</td></tr><tr><td>94</td><td>Pu Plutonium</td><td>(Rn) 5f<sup>6</sup> 7s<sup>2</sup></td><td>i <sup>7</sup>F<sub>0</sub></td><td>6.0258</td></tr><tr><td>95</td><td>Am Americium</td><td>(Rn) 5f<sup>7</sup> 7s<sup>2</sup></td><td>n <sup>8</sup>S<sub>7/2</sub></td><td>5.9738</td></tr><tr><td>96</td><td>Cm Curium</td><td>(Rn) 5f<sup>7</sup> 6d 7s<sup>2</sup></td><td>i <sup>9</sup>D<sub>2</sub></td><td>5.9914</td></tr><tr><td>97</td><td>Bk Berkelium</td><td>(Rn) 5f<sup>9</sup> 7s<sup>2</sup></td><td>d <sup>6</sup>H<sub>15/2</sub></td><td>6.1979</td></tr><tr><td>98</td><td>Cf Californium</td><td>(Rn) 5f<sup>10</sup> 7s<sup>2</sup></td><td>e <sup>5</sup>I<sub>8</sub></td><td>6.2819</td></tr><tr><td>99</td><td>Es Einsteinium</td><td>(Rn) 5f<sup>11</sup> 7s<sup>2</sup></td><td>s <sup>4</sup>I<sub>15/2</sub></td><td>6.3676</td></tr><tr><td>100</td><td>Fm Fermium</td><td>(Rn) 5f<sup>12</sup> 7s<sup>2</sup></td><td><sup>3</sup>H<sub>6</sub></td><td>6.50</td></tr><tr><td>101</td><td>Md Mendelevium</td><td>(Rn) 5f<sup>13</sup> 7s<sup>2</sup></td><td><sup>2</sup>F<sub>7/2</sub></td><td>6.58</td></tr><tr><td>102</td><td>No Nobelium</td><td>(Rn) 5f<sup>14</sup> 7s<sup>2</sup></td><td><sup>1</sup>S<sub>0</sub></td><td>6.6262</td></tr><tr><td>103</td><td>Lr Lawrencium</td><td>(Rn) 5f<sup>14</sup> 7s<sup>2</sup> 7p</td><td><sup>2</sup>P<sub>1/2</sub></td><td>4.96</td></tr><tr><td>104</td><td>Rf Rutherfordium</td><td>(Rn) 5f<sup>14</sup> 6d<sup>2</sup> 7s<sup>2</sup></td><td><sup>3</sup>F<sub>2</sub></td><td>6.02</td></tr><tr><td>105</td><td>Db Dubnium</td><td>(Rn) 5f<sup>14</sup> 6d<sup>3</sup> 7s<sup>2</sup></td><td><sup>4</sup>F<sub>3/2</sub></td><td>6.8</td></tr><tr><td>106</td><td>Sg Seaborgium</td><td>(Rn) 5f<sup>14</sup> 6d<sup>4</sup> 7s<sup>2</sup></td><td>0</td><td>7.8</td></tr><tr><td>107</td><td>Bh Bohrium</td><td>(Rn) 5f<sup>14</sup> 6d<sup>5</sup> 7s<sup>2</sup></td><td>5/2</td><td>7.7</td></tr><tr><td>108</td><td>Hs Hassium</td><td>(Rn) 5f<sup>14</sup> 6d<sup>6</sup> 7s<sup>2</sup></td><td>4</td><td>7.6</td></tr></tbody></table>

<footnote>* The usual LS coupling scheme does not apply for these three elements.</footnote>

<footnote>See the introductory note to the NIST table at https://www.nist.gov/pml/data/ion_energy.cfm.</footnote>
6. Atomic and Nuclear Properties of Materials

<table><caption>**Table 6.1:** Abridged from https://pdg.lbl.gov/current/AtomicNuclearProperties by D.E. Groom (2023). See web pages for more detail about entries in this table and for several hundred others. Parentheses in the *dE/dx* and density columns indicate gases at 20° C and 1 atm. Boiling points are at 1 atm. Refractive indices *n* are evaluated at the sodium D line blend (589.2 nm); values ≫1 in brackets indicate (*n* − 1) × 10⁶ for gases at 0° C and 1 atm.</caption><thead><tr><th>Material</th><th>Z</th><th>A</th><th>⟨Z/A⟩</th><th>Nucl.coll.<br>length λ<sub>T</sub><br>{g cm<sup>-2</sup>}</th><th>Nucl.inter.<br>length λ<sub>I</sub><br>{g cm<sup>-2</sup>}</th><th>Rad.len.dE/dx|<sub>min</sub><br>X<sub>0</sub><br>{MeV<br>{g cm<sup>-2</sup>}g<sup>-1</sup>cm<sup>2</sup>} ({g l<sup>-1</sup>})</th><th>Density<br>{g cm<sup>-3</sup>} point<br>(K)</th><th>Melting<br>point<br>(K)</th><th>Boiling<br>point<br>(K)</th><th>Refract.<br>index<br>@ Na D</th></tr></thead><tbody><tr><td>H<sub>2</sub></td><td>1</td><td>1.008(7)</td><td>0.99212</td><td>42.8</td><td>52.0</td><td>63.05</td><td>(4.103)</td><td>0.071(0.084)</td><td>13.81</td><td>20.28</td><td>1.11[132.]</td></tr><tr><td>D<sub>2</sub></td><td>1</td><td>2.014101764(8)</td><td>0.49650</td><td>51.3</td><td>71.8</td><td>125.97</td><td>(2.053)</td><td>0.169(0.168)</td><td>18.7</td><td>23.65</td><td>1.11[138.]</td></tr><tr><td>He</td><td>2</td><td>4.002602(2)</td><td>0.49967</td><td>51.8</td><td>71.0</td><td>94.32</td><td>(1.937)</td><td>0.125(0.166)</td><td></td><td>4.220</td><td>1.02[35.0]</td></tr><tr><td>Li</td><td>3</td><td>6.94(2)</td><td>0.43221</td><td>52.2</td><td>71.3</td><td>82.78</td><td>1.639</td><td>0.534</td><td>453.6</td><td>1615.</td><td></td></tr><tr><td>Be</td><td>4</td><td>9.0121831(5)</td><td>0.44384</td><td>55.3</td><td>77.8</td><td>65.19</td><td>1.595</td><td>1.848</td><td>1560.</td><td>2744.</td><td></td></tr><tr><td>C diamond</td><td>6</td><td>12.0107(8)</td><td>0.49955</td><td>59.2</td><td>85.8</td><td>42.70</td><td>1.725</td><td>3.520</td><td></td><td></td><td>2.419</td></tr><tr><td>C graphite</td><td>6</td><td>12.0107(8)</td><td>0.49955</td><td>59.2</td><td>85.8</td><td>42.70</td><td>1.742</td><td>2.210</td><td>Sublimes at 4098. K</td><td></td><td></td></tr><tr><td>N<sub>2</sub></td><td>7</td><td>14.007(2)</td><td>0.49976</td><td>61.1</td><td>89.7</td><td>37.99</td><td>(1.825)</td><td>0.807(1.165)</td><td>63.15</td><td>77.29</td><td>1.20[298.]</td></tr><tr><td>O<sub>2</sub></td><td>8</td><td>15.999(3)</td><td>0.50002</td><td>61.3</td><td>90.2</td><td>34.24</td><td>(1.801)</td><td>1.141(1.332)</td><td>54.36</td><td>90.20</td><td>1.22[271.]</td></tr><tr><td>F<sub>2</sub></td><td>9</td><td>18.998403163(6)</td><td>0.47372</td><td>65.0</td><td>97.4</td><td>32.93</td><td>(1.676)</td><td>1.507(1.580)</td><td>53.53</td><td>85.03</td><td>[195.]</td></tr><tr><td>Ne</td><td>10</td><td>20.1797(6)</td><td>0.49555</td><td>65.7</td><td>99.0</td><td>28.93</td><td>(1.724)</td><td>1.204(0.839)</td><td>24.56</td><td>27.07</td><td>1.09[67.1]</td></tr><tr><td>Al</td><td>13</td><td>26.9815385(7)</td><td>0.48181</td><td>69.7</td><td>107.2</td><td>24.01</td><td>1.615</td><td>2.699</td><td>933.5</td><td>2792.</td><td></td></tr><tr><td>Si</td><td>14</td><td>28.0855(3)</td><td>0.49848</td><td>70.2</td><td>108.4</td><td>21.82</td><td>1.664</td><td>2.329</td><td>1687.</td><td>3538.</td><td>3.95</td></tr><tr><td>Cl<sub>2</sub></td><td>17</td><td>35.453(2)</td><td>0.47951</td><td>73.8</td><td>115.7</td><td>19.28</td><td>(1.630)</td><td>1.574(2.980)</td><td>171.6</td><td>239.1</td><td>[773.]</td></tr><tr><td>Ar</td><td>18</td><td>39.948(1)</td><td>0.45059</td><td>75.7</td><td>119.7</td><td>19.55</td><td>(1.519)</td><td>1.396(1.662)</td><td>83.81</td><td>87.26</td><td>1.23[281.]</td></tr><tr><td>Ti</td><td>22</td><td>47.867(1)</td><td>0.45961</td><td>78.8</td><td>126.2</td><td>16.16</td><td>1.477</td><td>4.540</td><td>1941.</td><td>3560.</td><td></td></tr><tr><td>Fe</td><td>26</td><td>55.845(2)</td><td>0.46557</td><td>81.7</td><td>132.1</td><td>13.84</td><td>1.451</td><td>7.874</td><td>1811.</td><td>3134.</td><td></td></tr><tr><td>Cu</td><td>29</td><td>63.546(3)</td><td>0.45636</td><td>84.2</td><td>137.3</td><td>12.86</td><td>1.403</td><td>8.960</td><td>1358.</td><td>2835.</td><td></td></tr><tr><td>Ge</td><td>32</td><td>72.630(1)</td><td>0.44053</td><td>86.9</td><td>143.0</td><td>12.25</td><td>1.370</td><td>5.323</td><td>1211.</td><td>3106.</td><td></td></tr><tr><td>Sn</td><td>50</td><td>118.710(7)</td><td>0.42119</td><td>98.2</td><td>166.7</td><td>8.82</td><td>1.263</td><td>7.310</td><td>505.1</td><td>2875.</td><td></td></tr><tr><td>Xe</td><td>54</td><td>131.293(6)</td><td>0.41129</td><td>100.8</td><td>172.1</td><td>8.48</td><td>(1.255)</td><td>2.953(5.483)</td><td>161.4</td><td>165.1</td><td>1.39[701.]</td></tr><tr><td>W</td><td>74</td><td>183.84(1)</td><td>0.40252</td><td>110.4</td><td>191.9</td><td>6.76</td><td>1.145</td><td>19.300</td><td>3695.</td><td>5828.</td><td></td></tr><tr><td>Pt</td><td>78</td><td>195.084(9)</td><td>0.39983</td><td>112.2</td><td>195.7</td><td>6.54</td><td>1.128</td><td>21.450</td><td>2042.</td><td>4098.</td><td></td></tr><tr><td>Au</td><td>79</td><td>196.966569(5)</td><td>0.40108</td><td>112.5</td><td>196.3</td><td>6.46</td><td>1.134</td><td>19.320</td><td>1337.</td><td>3129.</td><td></td></tr><tr><td>Pb</td><td>82</td><td>207.2(1)</td><td>0.39575</td><td>114.1</td><td>199.6</td><td>6.37</td><td>1.122</td><td>11.350</td><td>600.6</td><td>2022.</td><td></td></tr><tr><td>U</td><td>92</td><td>[238.02891(3)]</td><td>0.38651</td><td>118.6</td><td>209.0</td><td>6.00</td><td>1.081</td><td>18.950</td><td>1408.</td><td>4404.</td><td></td></tr><tr><td>Air (dry, 1 atm)</td><td></td><td></td><td>0.49919</td><td>61.3</td><td>90.1</td><td>36.62</td><td>(1.815)</td><td>(1.205)</td><td></td><td>78.80</td><td>[289]</td></tr><tr><td>Shielding concrete</td><td></td><td></td><td>0.50274</td><td>65.1</td><td>97.5</td><td>26.57</td><td>1.711</td><td>2.300</td><td></td><td></td><td></td></tr><tr><td>Borosilicate glass (Pyrex)</td><td></td><td></td><td>0.49707</td><td>64.6</td><td>96.5</td><td>28.17</td><td>1.696</td><td>2.230</td><td></td><td></td><td></td></tr><tr><td>Lead glass SF<sub>5</sub></td><td></td><td></td><td>0.44522</td><td>84.0</td><td>133.4</td><td>10.07</td><td>1.406</td><td>4.080</td><td></td><td></td><td>1.6727</td></tr><tr><td>Standard rock</td><td></td><td></td><td>0.50000</td><td>66.8</td><td>101.3</td><td>26.54</td><td>1.688</td><td>2.650</td><td></td><td></td><td></td></tr><tr><td>Methane (CH<sub>4</sub>)</td><td></td><td></td><td>0.62334</td><td>54.0</td><td>73.8</td><td>46.47</td><td>(2.417)</td><td>(0.667)</td><td>90.68</td><td>111.7</td><td>[444.]</td></tr><tr><td>Ethane (C<sub>2</sub>H<sub>6</sub>)</td><td></td><td></td><td>0.59861</td><td>55.0</td><td>75.9</td><td>45.66</td><td>(2.304)</td><td>(1.263)</td><td>90.36</td><td>184.5</td><td></td></tr><tr><td>Propane (C<sub>3</sub>H<sub>8</sub>)</td><td></td><td></td><td>0.58962</td><td>55.3</td><td>76.7</td><td>45.37</td><td>(2.262)</td><td>0.493(1.868)</td><td>85.52</td><td>231.0</td><td></td></tr><tr><td>Butane (C<sub>4</sub>H<sub>10</sub>)</td><td></td><td></td><td>0.59497</td><td>55.5</td><td>77.1</td><td>45.23</td><td>(2.278)</td><td>(2.489)</td><td>134.9</td><td>272.6</td><td></td></tr><tr><td>Octane (C<sub>8</sub>H<sub>18</sub>)</td><td></td><td></td><td>0.57778</td><td>55.8</td><td>77.8</td><td>45.00</td><td>2.123</td><td>0.703</td><td>214.4</td><td>398.8</td><td></td></tr><tr><td>Paraffin (CH<sub>3</sub>(CH<sub>2</sub>)<sub>n</sub>≈23CH<sub>3</sub>)</td><td></td><td></td><td>0.57275</td><td>56.0</td><td>78.3</td><td>44.85</td><td>2.088</td><td>0.930</td><td></td><td></td><td></td></tr><tr><td>Nylon (type 6, 6/6)</td><td></td><td></td><td>0.54790</td><td>57.5</td><td>81.6</td><td>41.92</td><td>1.973</td><td>1.18</td><td></td><td></td><td></td></tr><tr><td>Polycarbonate (Lexan)</td><td></td><td></td><td>0.52697</td><td>58.3</td><td>83.6</td><td>41.50</td><td>1.886</td><td>1.20</td><td></td><td></td><td></td></tr><tr><td>Polyethylene ([CH<sub>2</sub>CH<sub>2</sub>]<sub>n</sub>)</td><td></td><td></td><td>0.57034</td><td>56.1</td><td>78.5</td><td>44.77</td><td>2.079</td><td>0.89</td><td></td><td></td><td></td></tr><tr><td>Polyethylene terephthalate (Mylar)</td><td></td><td></td><td>0.52037</td><td>58.9</td><td>84.9</td><td>39.95</td><td>1.848</td><td>1.40</td><td></td><td></td><td></td></tr><tr><td>Polyimide film (Kapton)</td><td></td><td></td><td>0.51264</td><td>59.2</td><td>85.5</td><td>40.58</td><td>1.820</td><td>1.42</td><td></td><td></td><td></td></tr><tr><td>Polymethylmethacrylate (acrylic)</td><td></td><td></td><td>0.53937</td><td>58.1</td><td>82.8</td><td>40.55</td><td>1.929</td><td>1.19</td><td></td><td></td><td>1.49</td></tr><tr><td>Polypropylene</td><td></td><td></td><td>0.55998</td><td>56.1</td><td>78.5</td><td>44.77</td><td>2.041</td><td>0.90</td><td></td><td></td><td></td></tr><tr><td>Polystyrene ([C<sub>6</sub>H<sub>5</sub>CHCH<sub>2</sub>]<sub>n</sub>)</td><td></td><td></td><td>0.53768</td><td>57.5</td><td>81.7</td><td>43.79</td><td>1.936</td><td>1.06</td><td></td><td></td><td>1.59</td></tr><tr><td>Polytetrafluoroethylene (Teflon)</td><td></td><td></td><td>0.47992</td><td>63.5</td><td>94.4</td><td>34.84</td><td>1.671</td><td>2.20</td><td></td><td></td><td></td></tr><tr><td>Polyvinyltoluene</td><td></td><td></td><td>0.54141</td><td>57.3</td><td>81.3</td><td>43.90</td><td>1.956</td><td>1.03</td><td></td><td></td><td>1.58</td></tr><tr><td>Aluminum oxide (sapphire)</td><td></td><td></td><td>0.49038</td><td>65.5</td><td>98.4</td><td>27.94</td><td>1.647</td><td>3.970</td><td>2327.</td><td>3273.</td><td>1.77</td></tr><tr><td>Barium flouride (BaF<sub>2</sub>)</td><td></td><td></td><td>0.42207</td><td>90.8</td><td>149.0</td><td>9.91</td><td>1.303</td><td>4.893</td><td>1641.</td><td>2533.</td><td>1.47</td></tr><tr><td>Bismuth germanate (BGO)</td><td></td><td></td><td>0.42065</td><td>96.2</td><td>159.1</td><td>7.97</td><td>1.251</td><td>7.130</td><td>1317.</td><td></td><td>2.15</td></tr><tr><td>Carbon dioxide gas (CO<sub>2</sub>)</td><td></td><td></td><td>0.49989</td><td>60.7</td><td>88.9</td><td>36.20</td><td>1.819</td><td>(1.842)</td><td></td><td></td><td>[449.]</td></tr><tr><td>Solid carbon dioxide (dry ice)</td><td></td><td></td><td>0.49989</td><td>60.7</td><td>88.9</td><td>36.20</td><td>1.787</td><td>1.563</td><td>Sublimes at 194.7 K</td><td></td><td></td></tr><tr><td>Cesium iodide (CsI)</td><td></td><td></td><td>0.41569</td><td>100.6</td><td>171.5</td><td>8.39</td><td>1.243</td><td>4.510</td><td>894.2</td><td>1553.</td><td>1.79</td></tr><tr><td>Lithium fluoride (LiF)</td><td></td><td></td><td>0.46262</td><td>61.0</td><td>88.7</td><td>39.26</td><td>1.614</td><td>2.635</td><td>1121.</td><td>1946.</td><td>1.39</td></tr><tr><td>Lithium hydride (LiH)</td><td></td><td></td><td>0.50321</td><td>50.8</td><td>68.1</td><td>79.62</td><td>1.897</td><td>0.820</td><td>965.</td><td></td><td></td></tr><tr><td>Lead tungstate (PbWO<sub>4</sub>)</td><td></td><td></td><td>0.41315</td><td>100.6</td><td>168.3</td><td>7.39</td><td>1.229</td><td>8.300</td><td>1403.</td><td></td><td>2.20</td></tr><tr><td>Silicon dioxide (SiO<sub>2</sub>, fused quartz)</td><td></td><td></td><td>0.49930</td><td>65.2</td><td>97.8</td><td>27.05</td><td>1.699</td><td>2.200</td><td>1986.</td><td>3223.</td><td>1.46</td></tr><tr><td>Sodium chloride (NaCl)</td><td></td><td></td><td>0.47910</td><td>71.2</td><td>110.1</td><td>21.91</td><td>1.847</td><td>2.170</td><td>1075.</td><td>1738.</td><td>1.54</td></tr><tr><td>Sodium iodide (NaI)</td><td></td><td></td><td>0.42697</td><td>93.1</td><td>154.6</td><td>9.49</td><td>1.305</td><td>3.667</td><td>933.2</td><td>1577.</td><td>1.77</td></tr><tr><td>Water (H<sub>2</sub>O)</td><td></td><td></td><td>0.55509</td><td>58.5</td><td>83.3</td><td>36.08</td><td>1.992</td><td>1.000</td><td>273.1</td><td>373.1</td><td>1.33</td></tr><tr><td>Silica aerogel</td><td></td><td></td><td>0.50093</td><td>65.0</td><td>97.3</td><td>27.25</td><td>1.740</td><td>0.200</td><td>(0.03 H<sub>2</sub>O, 0.97 SiO<sub>2</sub>)</td><td></td><td></td></tr><tr><td>Epoxy (Epotek-301-1)</td><td></td><td></td><td>0.53409</td><td>58.1</td><td>83.0</td><td>41.22</td><td>1.925</td><td>1.190</td><td></td><td></td><td></td></tr><tr><td>G10</td><td></td><td></td><td>0.51166</td><td>56.8</td><td>78.4</td><td>32.17</td><td>1.762</td><td>1.800</td><td></td><td></td><td></td></tr></tbody></table>
<table><thead><tr><th>Material</th><th>Dielectric<br>constant (κ = ε/ε<sub>0</sub>)<br>() is (κ-1)×10<sup>6</sup><br>for gas</th><th>Young's<br>modulus<br>[10<sup>6</sup> psi]</th><th>Coeff. of<br>thermal<br>expansion<br>[10<sup>-6</sup>cm/cm<sup>-1</sup>C]</th><th>Specific<br>heat<br>[cal/g<sup>-1</sup>C]</th><th>Electrical<br>resistivity<br>[μΩcm(@°C)]</th><th>Thermal<br>conductivity<br>[cal/cm<sup>-1</sup>C<sup>-1</sup> sec]</th></tr></thead><tbody><tr><td>H<sub>2</sub></td><td>(253.9)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>He</td><td>(64)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>Li</td><td>—</td><td>—</td><td>56</td><td>0.86</td><td>8.55(0°)</td><td>0.17</td></tr><tr><td>Be</td><td>—</td><td>37</td><td>12.4</td><td>0.436</td><td>5.885(0°)</td><td>0.38</td></tr><tr><td>C</td><td>—</td><td>0.7</td><td>0.6-4.3</td><td>0.165</td><td>1375(0°)</td><td>0.057</td></tr><tr><td>N<sub>2</sub></td><td>(548.5)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>O<sub>2</sub></td><td>(495)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>Ne</td><td>(127)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>Al</td><td>—</td><td>10</td><td>23.9</td><td>0.215</td><td>2.65(20°)</td><td>0.53</td></tr><tr><td>Si</td><td>11.9</td><td>16</td><td>2.8-7.3</td><td>0.162</td><td>—</td><td>0.20</td></tr><tr><td>Ar</td><td>(517)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>Ti</td><td>—</td><td>16.8</td><td>8.5</td><td>0.126</td><td>50(0°)</td><td>—</td></tr><tr><td>Fe</td><td>—</td><td>28.5</td><td>11.7</td><td>0.11</td><td>9.71(20°)</td><td>0.18</td></tr><tr><td>Cu</td><td>—</td><td>16</td><td>16.5</td><td>0.092</td><td>1.67(20°)</td><td>0.94</td></tr><tr><td>Ge</td><td>16.0</td><td>—</td><td>5.75</td><td>0.073</td><td>—</td><td>0.14</td></tr><tr><td>Sn</td><td>—</td><td>6</td><td>20</td><td>0.052</td><td>11.5(20°)</td><td>0.16</td></tr><tr><td>Xe</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>W</td><td>—</td><td>50</td><td>4.4</td><td>0.032</td><td>5.5(20°)</td><td>0.48</td></tr><tr><td>Pt</td><td>—</td><td>21</td><td>8.9</td><td>0.032</td><td>9.83(0°)</td><td>0.17</td></tr><tr><td>Pb</td><td>—</td><td>2.6</td><td>29.3</td><td>0.038</td><td>20.65(20°)</td><td>0.083</td></tr><tr><td>U</td><td>—</td><td>—</td><td>36.1</td><td>0.028</td><td>29(20°)</td><td>0.064</td></tr></tbody></table>
# 7. Electromagnetic Relations

Revised September 2005 by H.G. Spieler (LBNL).

<table><thead><tr><th>Quantity</th><th>Gaussian CGS</th><th>SI</th></tr></thead><tbody><tr><td>Conversion factors:</td><td></td><td></td></tr><tr><td>Charge:</td><td>2.997 924 58 × 10<sup>9</sup> esu</td><td>= 1 C = 1 A s</td></tr><tr><td>Potential:</td><td>(1/299.792 458) statvolt (ergs/esu)</td><td>= 1 V = 1 J C<sup>-1</sup></td></tr><tr><td>Magnetic field:</td><td>10<sup>4</sup> gauss = 10<sup>4</sup> dyne/esu</td><td>= 1 T = 1 N A<sup>-1</sup>m<sup>-1</sup></td></tr><tr><td></td><td><b>F</b> = q(<b>E</b> + <sup><b>V</b></sup>&frasl;<sub>c</sub> × <b>B</b>)</td><td><b>F</b> = q(<b>E</b> + <b>v</b> × <b>B</b>)</td></tr><tr><td></td><td>∇·<b>D</b> = 4πρ</td><td>∇·<b>D</b> = ρ</td></tr><tr><td></td><td>∇ × <b>H</b> - <sup>1</sup>&frasl;<sub>c</sub> ∂<b>D</b> &frasl; ∂t = <sup>4π</sup>&frasl;<sub>c</sub> <b>J</b></td><td>∇ × <b>H</b> - ∂<b>D</b> &frasl; ∂t = <b>J</b></td></tr><tr><td></td><td>∇·<b>B</b> = 0</td><td>∇·<b>B</b> = 0</td></tr><tr><td></td><td>∇ × <b>E</b> + <sup>1</sup>&frasl;<sub>c</sub> ∂<b>B</b> &frasl; ∂t = 0</td><td>∇ × <b>E</b> + ∂<b>B</b> &frasl; ∂t = 0</td></tr><tr><td>Constitutive relations:</td><td><b>D</b> = <b>E</b> + 4π<b>P</b>, <b>H</b> = <b>B</b> - 4π<b>M</b></td><td><b>D</b> = ε<sub>0</sub><b>E</b> + <b>P</b>, <b>H</b> = <b>B</b>/μ<sub>0</sub> - <b>M</b></td></tr><tr><td>Linear media:</td><td><b>D</b> = ε<b>E</b>, <b>H</b> = <b>B</b>/μ<sub>0</sub><br>1<br>1</td><td><b>D</b> = ε<b>E</b>, <b>H</b> = <b>B</b>/μ<sub>0</sub><br>ε<sub>0</sub> = 8.854 187... × 10<sup>-12</sup> F m<sup>-1</sup><br>μ<sub>0</sub> = 4π × 10<sup>-7</sup> N A<sup>-2</sup></td></tr><tr><td></td><td><b>E</b> = -∇<b>V</b> - <sup>1</sup>&frasl;<sub>c</sub> ∂<b>A</b> &frasl; ∂t</td><td><b>E</b> = -∇<b>V</b> - ∂<b>A</b> &frasl; ∂t</td></tr><tr><td></td><td><b>B</b> = ∇ × <b>A</b></td><td><b>B</b> = ∇ × <b>A</b></td></tr><tr><td></td><td><b>V</b> = ∑<sub>charges</sub> <sup>q<sub>i</sub></sup>&frasl;<sub>r<sub>i</sub></sub> = ∫ <sup>ρ(r')</sup>&frasl;<sub>|r - r'|</sub> d<sup>3</sup>x'</td><td><b>V</b> = <sup>1</sup>&frasl;<sub>4πε<sub>0</sub></sub> ∑<sub>charges</sub> <sup>q<sub>i</sub></sup>&frasl;<sub>r<sub>i</sub></sub> = <sup>1</sup>&frasl;<sub>4πε<sub>0</sub></sub> ∫ <sup>ρ(r')</sup>&frasl;<sub>|r - r'|</sub> d<sup>3</sup>x'</td></tr><tr><td></td><td><b>A</b> = <sup>1</sup>&frasl;<sub>c</sub> ∮ <sup>I dℓ</sup>&frasl;<sub>|r - r'|</sub> = <sup>1</sup>&frasl;<sub>c</sub> ∫ <sup><b>J</b>(r')</sup>&frasl;<sub>|r - r'|</sub> d<sup>3</sup>x'</td><td><b>A</b> = <sup>μ<sub>0</sub></sup>&frasl;<sub>4π</sub> ∮ <sup>I dℓ</sup>&frasl;<sub>|r - r'|</sub> = <sup>μ<sub>0</sub></sup>&frasl;<sub>4π</sub> ∫ <sup><b>J</b>(r')</sup>&frasl;<sub>|r - r'|</sub> d<sup>3</sup>x'</td></tr><tr><td></td><td><b>E</b>'<sub>∥</sub> = <b>E</b>'<sub>∥</sub></td><td><b>E</b>'<sub>∥</sub> = <b>E</b>'<sub>∥</sub></td></tr><tr><td></td><td><b>E</b>'<sub>⊥</sub> = γ(<b>E</b>'<sub>⊥</sub> + <sup>1</sup>&frasl;<sub>c</sub> <b>v</b> × <b>B</b>)</td><td><b>E</b>'<sub>⊥</sub> = γ(<b>E</b>'<sub>⊥</sub> + <b>v</b> × <b>B</b>)</td></tr><tr><td></td><td><b>B</b>'<sub>∥</sub> = <b>B</b>'<sub>∥</sub></td><td><b>B</b>'<sub>∥</sub> = <b>B</b>'<sub>∥</sub></td></tr><tr><td></td><td><b>B</b>'<sub>⊥</sub> = γ(<b>B</b>'<sub>⊥</sub> - <sup>1</sup>&frasl;<sub>c</sub> <b>v</b> × <b>E</b>)</td><td><b>B</b>'<sub>⊥</sub> = γ(<b>B</b>'<sub>⊥</sub> - <sup>1</sup>&frasl;<sub>c<sup>2</sup></sub> <b>v</b> × <b>E</b>)</td></tr><tr><td colspan="3"><hr></td></tr><tr><td colspan="3">1/4πε<sub>0</sub> = c<sup>2</sup> × 10<sup>-7</sup> N A<sup>-2</sup> = 8.987 55... × 10<sup>9</sup> m F<sup>-1</sup>; ε<sub>0</sub> = 10<sup>-7</sup> N A<sup>-2</sup>; c = <sup>1</sup>&frasl;<sub>√μ<sub>0</sub>ε<sub>0</sub></sub> = 2.997 924 58 × 10<sup>8</sup> m s<sup>-1</sup></td></tr></tbody></table>

## 7.1 Impedances (SI units)

$\rho$ = resistivity at room temperature in $10^{-8}$ Ω m:

~ 1.7 for Cu ~ 5.5 for W

~ 2.4 for Au ~ 73 for SS 304

~ 2.8 for Al ~ 100 for Nichrome

(Al alloys may have double the Al value.)

For alternating currents, instantaneous current $I$, voltage $V$, angular frequency $\omega$:

$$V = V_0 e^{j\omega t} = ZI. \qquad (7.1)$$

Impedance of self-inductance $L$: $Z = j\omega L$.

Impedance of capacitance $C$: $Z = 1/j\omega C$.

Impedance of free space: $Z = \sqrt{\mu_0/\epsilon_0} = 376.7$ Ω.

High-frequency surface impedance of a good conductor:

$$Z = \frac{(1 + j) \rho}{\delta}, \quad \text{where } \delta = \text{skin depth}; \qquad (7.2)$$

$$\delta = \sqrt{\frac{\rho}{\pi \nu \mu}} \approx \frac{6.6 \text{ cm}}{\sqrt{\nu (\text{Hz})}} \quad \text{for Cu.} \qquad (7.3)$$

## 7.2 Capacitors, inductors, and transmission Lines

The capacitance between two parallel plates of area $A$ spaced by the distance $d$ and enclosing a medium with the dielectric constant $\epsilon$ is

$$C = K\epsilon A/d, \qquad (7.4)$$

where the correction factor $K$ depends on the extent of the fringing field. If the dielectric fills the capacitor volume without extending beyond the electrodes. The correction factor $K \approx 0.8$ for capacitors of typical geometry.

The inductance at high frequencies of a straight wire whose length $\ell$ is much greater than the wire diameter $d$ is

$$L \approx 2.0 \left[ \frac{nH}{cm} \right] \cdot \ell \left( \ln \left( \frac{4\ell}{d} \right) - 1 \right). \qquad (7.5)$$

For very short wires, representative of vias in a printed circuit board, the inductance is

$$L(\text{in nH}) \approx \ell/d. \qquad (7.6)$$

A transmission line is a pair of conductors with inductance $L$ and capacitance $C$. The characteristic impedance $Z = \sqrt{L/C}$ and the phase velocity $v_p = 1/\sqrt{LC} = 1/\sqrt{\mu\epsilon}$, which decreases with the inverse square root of the dielectric constant of the medium. Typical coaxial and ribbon cables have a propagation delay of about 5 ns/cm.
The impedance of a coaxial cable with outer diameter D and inner diameter d is

$$Z = 60 \Omega \cdot \frac{1}{\sqrt{\epsilon_r}} \ln \frac{D}{d}, \qquad (7.7)$$

where the relative dielectric constant $\epsilon_r = \epsilon/\epsilon_0$. A pair of parallel wires of diameter d and spacing a > 2.5 d has the impedance

$$Z = 120 \Omega \cdot \frac{1}{\sqrt{\epsilon_r}} \ln \frac{2a}{d}. \qquad (7.8)$$

This yields the impedance of a wire at a spacing h above a ground plane,

$$Z = 60 \Omega \cdot \frac{1}{\sqrt{\epsilon_r}} \ln \frac{4h}{d}. \qquad (7.9)$$

A common configuration utilizes a thin rectangular conductor above a ground plane with an intermediate dielectric (microstrip). Detailed calculations for this and other transmission line configurations are given by Gunston [1].

## 7.3 Synchrotron radiation (CGS units)

For a particle of charge e, velocity v = βc, and energy E = γmc², traveling in a circular orbit of radius R, the classical energy loss per revolution δE is

$$\delta E = \frac{4\pi}{3} \frac{e^2}{R} \beta^3 \gamma^4 . \qquad (7.10)$$

<figure><img src="image_14.png" /><figcaption>Figure 7.1: The normalized synchrotron radiation spectrum F(y).</figcaption></figure>

For high-energy electrons or positrons ($\beta \approx 1$), this becomes

$$\delta E \text{ (in MeV)} \approx 0.0885 [E(\text{in GeV})]^4/R(\text{in m}). \qquad (7.11)$$

For $\gamma \gg 1$, the energy radiated per revolution into the photon energy interval $d(\hbar\omega)$ is

$$dI = \frac{8\pi}{9} \alpha \gamma F(\omega/\omega_c) d(\hbar\omega), \qquad (7.12)$$

where $\alpha = e^2/\hbar c$ is the fine-structure constant and

$$\omega_c = \frac{3\gamma^3 c}{2R} \qquad (7.13)$$

is the critical frequency. The normalized function F(y) is

$$F(y) = \frac{9}{8\pi} \sqrt{3} y \int_{y}^{\infty} K_{5/3}(x) dx, \qquad (7.14)$$

where $K_{5/3}(x)$ is a modified Bessel function of the third kind. For electrons or positrons,

$$\hbar\omega_c \text{ (in keV)} \approx 2.22 [E(\text{in GeV})]^3/R(\text{in m}). \qquad (7.15)$$

For $\gamma \gg 1$ and $\omega \ll \omega_c$,

$$\frac{dI}{d(\hbar\omega)} \approx 3.3\alpha (\omega R/c)^{1/3}, \qquad (7.16)$$

whereas for

$\gamma \gg 1 \text{ and } \omega \gtrsim 3\omega_c,$

$$\frac{dI}{d(\hbar\omega)} \approx \sqrt{\frac{3\pi}{2}} \alpha \gamma \left(\frac{\omega}{\omega_c}\right)^{1/2} e^{-\omega/\omega_c} \left[1 + \frac{55}{72} \frac{\omega_c}{\omega} + \dots \right]. \qquad (7.17)$$

The radiation is confined to angles $\lesssim 1/\gamma$ relative to the instantaneous direction of motion. For $\gamma \gg 1$, where Eq. (7.12) applies, the mean number of photons emitted per revolution is

$$N_{\gamma} = \frac{5\pi}{\sqrt{3}} \alpha \gamma, \qquad (7.18)$$

and the mean energy per photon is

$$\langle \hbar\omega \rangle = \frac{8}{15\sqrt{3}} \hbar\omega_c . \qquad (7.19)$$

When $\langle \hbar\omega \rangle \gtrsim O(E)$, quantum corrections are important [2].<fnref n="1" />

## References

[1] M.A.R. Gunston. Microwave Transmission Line Data, No-ble Publishing Corp., Atlanta (1997) ISBN 1-884932-57-6, TK6565.T73G85.

[2] J.D. Jackson, *Classical Electrodynamics*, 3rd edition (John Wiley & Sons, New York, 1998) for more formulae and details.

<footnote n="1">¹Note that earlier editions of Ref. [2] had $\omega_c$ twice as large as Eq. (7.13).</footnote>
be $q\bar{q}$ bound states, but might be glueballs or $q\bar{q}g$ etc. (This is distinct from light unflavored mesons with $I \ge 2$ or hidden-heavy flavor mesons with $I \ge 1$, which could be interpreted as tetraquarks). For such a “manifestly exotic” unflavored meson, the naming scheme nonetheless assigns the same base symbol as solely determined by the isospin/hidden-heavy flavor and PC in Tab. 8.1. For example, an isospin-0 light unflavored $1^{-+}$ meson would be denoted $\eta_1$ while an isospin-1 $0^{--}$ light unflavored meson would be denoted $\rho_0$. The exotic nature of the meson can be inferred from its PC quantum numbers—given by the symbol— and the spin J—given by the subscript.

## 8.2 Remarks on “neutral-flavor” mesons with hidden charm or bottom not classified as $q\bar{q}$

In the heavy-quark sector, there are several states with properties – such as masses, decay patterns, and widths – that are in disagreement with predictions from the naive quark model. For example, the vector state at 4230 MeV (the $\psi(4230)$) apparently does not decay into $D\bar{D}$, although within the naive quark model its quantum numbers would call for this decay channel to be dominant. These states were originally named X, Y, or Z, with their masses added in parentheses. This nomenclature differs from the conventions outlined in the previous section, since the meson names are not related to their quantum numbers. However, these states have properties in conflict with the naive quark model and therefore deserve some special labeling.

Since their original discovery, the properties of some of these states have become better understood and it has become possible to include them in the Listings as well as Summary Tables using the name assigned according to this review. The X-, Y-, or Z-based names used at the time of the discovery are also reported in the Listings and Summary Tables from the 2018 edition onwards as a sub-header (listed are only some examples of the particles that appear in the Summary Tables),

* the state originally named X(3872) appears as '$\chi_{c1}(3872)$' also known as X(3872)';

* the state originally named $Z_c(3900)$ appears<fnref n="1" /> as '$T_{c\bar{c}1}(3900)$' also known as $Z_c(3900)$';

* the state originally named Y(4260) appears<fnref n="2" /> as '$\psi(4230)$' also known as Y(4230)';

In addition, states with quantum numbers allowed by the naive quark model but showing some peculiarities, such as an unusual decay pattern, will have the following information in the header:

This state shows properties different from a conventional $q\bar{q}$ state. A candidate for an exotic structure. See the review on <name of the proper review>.

## 8.3 Mesons with nonzero S, C and/or B

Mesons with nonzero strangeness S or heavy flavor C and/or B are not eigenstates of charge conjugation, and in each of them one of the quarks is heavier than the other (as above, states containing top quarks are not considered). The rules have been and remain:

1. The main symbol is an upper-case italic letter indicating the heavier quark as follows:

$$s \rightarrow \bar{K} \quad c \rightarrow D \quad b \rightarrow \bar{B},$$

We use the convention that the flavor quantum number and the charge of a quark have the same sign. Thus the strangeness of the s quark is negative, the charm of the c quark is positive, and the bottomness of the b quark is negative. The effect of this convention is as follows: any flavor carried by a charged meson has the same sign as its charge. Thus the $K^+$, $D^+$, and $B^+$ have positive strangeness, charm, and bottomness, respectively, and all have positive $I_3$. The $D_s^+$ has positive charm and strangeness. Furthermore, the

$\Delta(\text{flavor}) = \Delta Q$ rule, best known for the strange kaons, applies to every flavor.

2. If the lighter quark is not a u or a d quark, its identity is given by a subscript. The $D_s^+$ is an example.

3. When the spin-parity is in the natural series, $J^P = 0^+, 1^-, 2^+, \dots$, a superscript “*” is added.

4. The spin is added as a subscript except for pseudoscalar or vector mesons.

## 8.4 Baryons with ordinary quantum numbers

All baryons having quantum numbers consistent with a minimal quark content of three quarks are denoted by the symbols N, $\Delta$, $\Lambda$, $\Sigma$, $\Xi$, and $\Omega$ introduced more than 50 years ago. These symbols are followed by $J^P$ signifying their spin J and parity P. For those where the minimal content involves one or more heavier quarks than the light (u, d, and s) quarks, subscripts are added to their symbols, (c and b) as appropriate. The rules are:

1. Baryons with minimal content of three u and/or d quarks are N's (isospin 1/2) or $\Delta$'s (isospin 3/2).

2. Baryons with two u and/or d quarks are $\Lambda$'s (isospin 0) or $\Sigma$'s (isospin 1). If the third quark is a c or b quark, its identity is given by a subscript.

3. Baryons with one u or d quark are $\Xi$'s (isospin 1/2). One or two subscripts are used if one or both of the remaining quarks are heavy: thus $\Xi_c$, $\Xi_{cc}$, $\Xi_b$, etc.<fnref n="3" />

4. Baryons with no u or d quarks are $\Omega$'s (isospin 0), and subscripts indicate any heavy-quark content.

5. A baryon that decays strongly has its mass in parentheses. Examples are the $\Delta(1232)$ $3/2^+$, $\Sigma(1385)$ $3/2^+$, $N(1440)$ $1/2^+$, $\Xi_c(2645)$ $3/2^+$.

6. If individual states of isospin multiplets are addressed, the electric charge is specified as a superscript. The electric charge is not necessary for isospin-0 states ($\Lambda$ and $\Omega$), as there is no ambiguity, but may still be included.

7. Antibaryons are labeled by an overline (bar) on the base symbol. For example, $\bar{p}$ for the antiproton, or $\bar{\Lambda}_c$ for the antiparticle of $\Lambda_c^+$. Alternatively, particle and antiparticle can be distinguished by including only a charge-label superscript, so long as the flavor structure of the baryon is defined solely by the base symbol (and subscripts). Thus one may also write $\bar{\Lambda}_c$ or $p^-$ for the antiparticles of the $\Lambda_c^+$ and $p^+$, but the $\Sigma^-$ is not the antiparticle of $\Sigma^+$, which is called $\bar{\Sigma}^-$.

In short, the minimal number of u plus d quarks together with the isospin determine the main symbol, and subscripts indicate any content of heavy quarks. A $\Sigma$ always has isospin 1, an $\Omega$ always has isospin 0, etc.

## 8.5 Hadrons with a minimal quark content of $qq\bar{q}q$ or $q\bar{q}qq$

The naming scheme described above does not accommodate various $qq\bar{q}q$ mesons and $q\bar{q}qqq$ baryons. In such cases, the 1986 naming scheme must be extended. Following discussion initiated by the proposal made by the LHCb collaboration [7], we adopt the notation

$$T_{\text{quarks},J}(\text{mass})^q \quad \text{for tetraquarks}, \qquad (8.3\text{a})$$

$$P_{\text{quarks}}(\text{mass})^q J^P \quad \text{for pentaquarks}, \qquad (8.3\text{b})$$

according to the following rules:

1. The basename T or P is chosen in cases where the minimal quark content of a state is $qq\bar{q}\bar{q}$ (tetraquark) or $q\bar{q}qqq$ (pentaquark), respectively.

2. The bottom, charm, and strange quark content ($b, \bar{b}, c, \bar{c}, s, \bar{s}$) is explicitly listed as a subscript, in order from the heaviest quarks and antiquarks to the lightest and listing quarks before antiquarks. The hidden-flavor $c\bar{c}$ and $b\bar{b}$ combinations

<footnote n="1">¹The name $T_{c\bar{c}1}(3900)$ derives from the scheme outlined in a later section.</footnote>

<footnote n="2">²This is one example where the mass label needed to be shifted given improved experimental information.</footnote>

<footnote n="3">³See the "Charmed and Bottom Baryons" section of the "Quark Model" review.</footnote>
<table><caption>**Table 8.2:** Names used from the 2024 edition onward compared to those in the 2022 edition. Whenever the C-parity of a charged tetraquark is specified in the Particle Listings, it refers to the C-parity of the prospective/observed neutral isospin partner. Only one member per isospin multiplet is shown (see the Listings for more information).</caption><thead><tr><th>2024 Name</th><th>minimal quark<br>content</th><th><i>I</i><sup>(G)</sup>(<i>J</i><sup>P</sup>(<i>C</i>))</th><th>2022 Name</th><th>2024 Name</th><th>minimal quark<br>content</th><th><i>I</i><sup>(G)</sup>(<i>J</i><sup>P</sup>(<i>C</i>))</th><th>2022 Name</th></tr></thead><tbody><tr><td><i>T</i><sup>*</sup><sub>cs0</sub>(2870)<sup>0</sup></td><td><i>csūd</i></td><td>?(0<sup>+</sup>)</td><td><i>X</i><sub>0</sub>(2900)</td><td><i>T</i><sub>ce1</sub>(4430)<sup>+</sup></td><td><i>cēud</i></td><td>1<sup>+</sup>(1<sup>+-</sup>)</td><td><i>Z</i><sub>c</sub>(4430)<sup>+</sup></td></tr><tr><td><i>T</i><sup>*</sup><sub>cs1</sub>(2900)<sup>0</sup></td><td><i>csūd̄</i></td><td>?(1<sup>-</sup>)</td><td><i>X</i><sub>1</sub>(2900)</td><td><i>T</i><sub>ceš1</sub>(4000)<sup>+</sup></td><td><i>cčuš</i></td><td>1/2(1<sup>+</sup>)</td><td><i>Z</i><sub>cš</sub>(4000)<sup>+</sup></td></tr><tr><td><i>T</i><sup>*</sup><sub>cs0</sub>(2900)<sup>++</sup></td><td><i>cšuūd</i></td><td>1(0<sup>+</sup>)</td><td></td><td><i>T</i><sub>cešš1</sub>(4220)<sup>+</sup></td><td><i>cčuš</i></td><td>1/2(1<sup>+</sup>)</td><td><i>Z</i><sub>cš</sub>(4220)<sup>+</sup></td></tr><tr><td><i>T</i><sub>cc</sub>(3875)<sup>+</sup></td><td><i>ccūd̄</i></td><td>?(?<sup>?</sup>)</td><td></td><td><i>T</i><sub>bš</sub>(5568)<sup>+</sup></td><td><i>bšūd</i></td><td>1(?<sup>?</sup>)</td><td><i>X</i>(5568)<sup>+</sup></td></tr><tr><td><i>T</i><sub>ce1</sub>(3900)<sup>+</sup></td><td><i>cčuūd</i></td><td>1<sup>+</sup>(1<sup>+-</sup>)</td><td><i>Z</i><sub>c</sub>(3900)<sup>+</sup></td><td><i>T</i><sub>bš1</sub>(10610)<sup>+</sup></td><td><i>bbuūd</i></td><td>1<sup>+</sup>(1<sup>+-</sup>)</td><td><i>Z</i><sub>b</sub>(10610)<sup>+</sup></td></tr><tr><td><i>T</i><sub>cc</sub>(4020)<sup>+</sup></td><td><i>cčuūd</i></td><td>1<sup>+</sup>(?<sup>?</sup>)</td><td><i>X</i>(4020)<sup>+</sup></td><td><i>T</i><sub>bš1</sub>(10650)<sup>+</sup></td><td><i>bbuūd</i></td><td>1<sup>+</sup>(1<sup>+-</sup>)</td><td><i>Z</i><sub>b</sub>(10650)<sup>+</sup></td></tr><tr><td><i>T</i><sub>cc</sub>(4050)<sup>+</sup></td><td><i>cčuūd</i></td><td>1<sup>-</sup>(?<sup>+</sup>)</td><td><i>X</i>(4050)<sup>+</sup></td><td><i>T</i><sub>ccčč</sub>(6900)<sup>0</sup></td><td><i>ccčč</i></td><td>0<sup>+</sup>(?<sup>+</sup>)</td><td><i>X</i>(6900)</td></tr><tr><td><i>T</i><sub>cc</sub>(4055)<sup>+</sup></td><td><i>cčuūd</i></td><td>1<sup>+</sup>(?<sup>?</sup>)</td><td><i>X</i>(4055)<sup>+</sup></td><td><i>P</i><sub>cc</sub>(4312)<sup>+</sup></td><td><i>cčuud</i></td><td>1/2(?<sup>?</sup>)</td><td><i>P</i><sub>c</sub>(4312)<sup>+</sup></td></tr><tr><td><i>T</i><sub>cc</sub>(4100)<sup>+</sup></td><td><i>cčuūd</i></td><td>1<sup>-</sup>(?<sup>+</sup>)</td><td><i>X</i>(4100)<sup>+</sup></td><td><i>P</i><sub>cc</sub>(4380)<sup>+</sup></td><td><i>cčuud</i></td><td>1/2(?<sup>?</sup>)</td><td><i>P</i><sub>c</sub>(4380)<sup>+</sup></td></tr><tr><td><i>T</i><sub>ce1</sub>(4200)<sup>+</sup></td><td><i>cčuūd</i></td><td>1<sup>+</sup>(1<sup>+-</sup>)</td><td><i>Z</i><sub>c</sub>(4200)<sup>+</sup></td><td><i>P</i><sub>cc</sub>(4440)<sup>+</sup></td><td><i>cčuud</i></td><td>1/2(?<sup>?</sup>)</td><td><i>P</i><sub>c</sub>(4440)<sup>+</sup></td></tr><tr><td><i>T</i><sub>cc0</sub>(4240)<sup>+</sup></td><td><i>cčuūd</i></td><td>1<sup>+</sup>(0<sup>-</sup>)</td><td><i>R</i><sub>c0</sub>(4240)<sup>+</sup></td><td><i>P</i><sub>cc</sub>(4457)<sup>+</sup></td><td><i>cčuud</i></td><td>1/2(?<sup>?</sup>)</td><td><i>P</i><sub>c</sub>(4457)<sup>+</sup></td></tr><tr><td><i>T</i><sub>cc</sub>(4250)<sup>+</sup></td><td><i>cčuūd</i></td><td>1<sup>-</sup>(?<sup>+</sup>)</td><td><i>X</i>(4250)<sup>+</sup></td><td><i>P</i><sub>cccš</sub>(4459)<sup>0</sup></td><td><i>cčuds</i></td><td>0(?<sup>?</sup>)</td><td></td></tr></tbody></table>

are listed explicitly when their presence can be inferred from production or decay patterns.

3. The approximate mass of a state, in MeV/c², is given in parentheses.

4. The electric charge (q) can be specified as a superscript after the mass, for example when referring to a specific member of an isospin multiplet.

5. Antibaryons are marked with an overline (P). The an-tiparticle of a meson can be specified either with an over-line or by the quark content label (e.g. the charge conjugate of $T_{cc}(3875)^+$ is $\bar{T}_{cc}(3875)^-$, which is equivalent to $\bar{T}_{cc}(3875)^-$).

6. For pentaquarks, as in the case of ordinary baryons, when known the spin-parity, $J^P$, of the state is included as a suffix.

7. For tetraquarks, similarly to the naming scheme for mesons, the spin $J$ is appended as a subscript after the quark content. When the spin-parity is in the natural series, $J^P = 0^+, 1^-, 2^+, \dots$, a superscript “*” is added.

Table 8.2 summarizes PDG name changes with respect to the 2022 edition [8]. We acknowledge that experiments might choose to add $I^{(G)}J^P(C)$ information to hadron names using experiment-

specific conventions that differ from the one utilized by the PDG.

### References

[1] M. Aguilar-Benitez et al. (Particle Data Group), Phys. Lett. **170B**, 1 (1986).

[2] M. Ablikim et al. (BESIII), Phys. Rev. Lett. **110**, 252001 (2013), [arXiv:1303.5949].

[3] Z. Q. Liu et al. (Belle), Phys. Rev. Lett. **110**, 252002 (2013), [Erratum: Phys.Rev.Lett. 111, 019901 (2013)], [arXiv:1304.0121].

[4] M. Tanabashi et al. (Particle Data Group), Phys. Rev. D **98**, 3, 030001 (2018).

[5] R. Aaij et al. (LHCb), Nature Phys. **18**, 7, 751 (2022), [arXiv:2109.01038].

[6] R. Aaij et al. (LHCb), Phys. Rev. Lett. **122**, 22, 222001 (2019), [arXiv:1904.03947].

[7] LHCb (2022), [arXiv:2206.15233].

[8] R. L. Workman and Others (Particle Data Group), PTEP **2022**, 083C01 (2022).
Standard Model and Related Topics

<table><tr><td>9. Quantum chromodynamics (rev.)</td><td>153</td></tr><tr><td>10. Electroweak model and constraints on new physics (rev.)</td><td>185</td></tr><tr><td>11. Higgs boson physics, status of (rev.)</td><td>211</td></tr><tr><td>12. CKM quark-mixing matrix (rev.)</td><td>270</td></tr><tr><td>13. CP violation in the quark sector (rev.)</td><td>280</td></tr><tr><td>14. Neutrino masses, mixing, and oscillations (rev.)</td><td>295</td></tr><tr><td>15. Quark model (rev.)</td><td>322</td></tr><tr><td>16. Heavy-quark &amp; soft-collinear effective theory (rev.)</td><td>341</td></tr><tr><td>17. Lattice quantum chromodynamics (rev.)</td><td>350</td></tr><tr><td>18. Structure functions (rev.)</td><td>367</td></tr><tr><td>19. Fragmentation functions in e<sup>+</sup>e<sup>-</sup>, ep and pp collisions (rev.)</td><td>389</td></tr><tr><td>20. High Energy Soft QCD and Diffraction (rev.)</td><td>406</td></tr></table>
<figure><img src="image_15.png" /></figure>