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Junpei Fujimoto | KEK | Japan

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Size of electron

This is continuation of the previous blog. Electron has various nature. PDG is reporting the following values;
1) Electron mass:0.510998910 +/- 0.000000013 MeV/C2.
2) Mass difference between electron(e) and positro(e+) : (Me+–Me)/(Me++Me) < 8×10–9.
3) Charge difference between e+ and e : (qe+–qe)/e < 4×10–8.
4) Electron magnetic moment(g) anomaly: (g-2)/2=(1159.65218111 +/- 0.00000074)x10–6.
5) g anomaly difference between e+ and e: (g_e+-g_e/g(average) = (-0.5 +/- 2.1)x10–12.
6) Electron dipole moment(d): d = (0.069 +/- 0.074)x 10–26 ecm
7) Electron mean life from e to electron neutrino and photon : > 4.6×1026 yr .

You see electron is so stable more than 1024 years from 7) .

How about the size of electron? As a matter of fact, there is no direct report on it. Alternatively, there is a measurement on the compositeness of electron. In the framework of the standard theory, electron and positron are assumed as point-like particle, which means they have no spread and no structure in space, and they can be scattered just via photon.

But one can consider that we just can’t see the size of electron because we have poor accelerators. If electron has a structure, we must observe the reaction of direct scattering of electron and positron using enough magnification by the more powerful accelerator.

This effect can be introduced to put assumed compositeness scale into the equation of electron of which dimension should be the energy. Experiments have measured the angular distribution of electron or positron through the reaction: e+ e going to e+ e, so called Bhabha scattering, and have seen the difference from the distribution predicted by the standard theory. Up to now, the distribution is consistent well with the theory, then the statistical treatment tells us the lower limit of the compositeness.

In PDG, it is reported in “Other searches (SUSY, Compositeness, …)” after “Particle Listing”, the scale of contact interactions should be more than 8 TeV. Because the corresponding length is inverse of energy scale, it means that electron has no structure more than in 1/1018 m.


1) 電子の質量:0.510998910 +/- 0.000000013 MeV/C2.
2) 電子と陽電子の質量の差
:(Me+–Me)/(Me++Me) < 8×10–9.(つまり差は観測されていなし)
3) 電子と陽電子の電荷の差:(qe+–qe)/e < 4×10–8(やはり差は観測されていない)
4) 電子の異常磁気モーメント(2からのずれ): (g-2)/2=(1159.65218111 +/- 0.00000074)x10–6. (非常に精度よく測定されています。)
5) 電子と陽電子の異常磁気モーメントの差: (g_e+-g_e/g(average) = (-0.5 +/- 2.1)x10–12.(これも差はないということ)
6) 電子の2重極モーメント(d):d = (0.069 +/- 0.074)x 10–26 ecm
7) 電子がニュートリノと光子に崩壊する平均寿命: 4.6×1026 年以上(つまり崩壊は観測されていない)





PDGでは、”Particle Listing”で、”Other searches (SUSY, Compositeness, …)”をクリックすると実験結果が報告されており、それによると、そのエネルギースケールの下限値は8000GeVであることがわかります。このエネルギースケールの逆数が”長さ”に対応するので、結局電子の大きさは1/1018 m以下であると測定されていると言えるのです。