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تسجيل مستخدم جديدTenth-Order QED Contribution to the Lepton Anomalous Magnetic Moment -- Sixth-Order Vertices Containing an Internal Light-by-Light-Scattering Subdiagram
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This paper reports the tenth-order QED contribution to the lepton g-2 from the gauge-invariant set, called Set III(c), which consists of 390 Feynman vertex diagrams containing an internal fourth-order light-by-light-scattering subdiagram. The mass-independent contribution of Set III(c) to the electron g-2 (a_e) is 4.9210(103) in units of (alpha/pi)^5. The mass-dependent contributions to a_e from diagrams containing a muon loop is 0.00370(37) (alpha/pi)^5. The tau-lepton loop contribution is negligible at present. Altogether the contribution of Set III(c) to a_e is 4.9247 (104) (alpha/pi)^5. We have also evaluated the contribution of the closed electron loop to the muon g-2 (a_mu). The result is 7.435(134) (alpha/pi)^5. The contribution of the tau-lepton loop to a_mu is 0.1999(28)(alpha/pi)^5. The total contribution of variousleptonic loops (electron, muon, and tau-lepton) of Set III(c) to a_mu is 12.556 (135) (alpha/pi)^5.
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This paper reports the tenth-order contributions to the g-2 of the electron a_e and those of the muon a_mu from the gauge-invariant Set II(c), which consists of 36 Feynman diagrams, and Set II(d), which consists of 180 Feynman diagrams. Both sets are
obtained by insertion of sixth-order vacuum-polarization diagrams in the fourth-order anomalous magnetic moment. The mass-independent contributions from Set II(c) and Set II(d) are -0.116 489 (32)(alpha/pi)^5 and -0.243 00 (29)(alpha/pi)^5, respectively. The leading contributions to a_mu, which involve electron loops only, are -3.888 27 (90)(alpha/pi)^5 and 0.4972 (65)(alpha/pi)^5 for Set II(c) and Set II(d), respectively. The total contributions of the electron, muon, and tau-lepton loops to a_e are -0.116 874 (32) (alpha/pi)^5 for Set II(c) and -0.243 10 (29) (alpha/pi)^5 for Set II(d). The contributions of electron, muon, and tau-lepton loops to a_mu are -5.5594 (11) (alpha/pi)^5 for Set II(c) and 0.2465 (65) (alpha/pi)^5 for Set II(d).
This paper reports the result of our evaluation of the tenth-order QED correction to the lepton g-2 from Feynman diagrams which have sixth-order light-by-light-scattering subdiagrams, none of whose vertices couple to the external magnetic field. The
gauge-invariant set of these diagrams, called Set II(e), consists of 180 vertex diagrams. In the case of the electron g-2 (a_e), where the light-by-light subdiagram consists of the electron loop, the contribution to a_e is found to be - 1.344 9 (10) (alpha /pi)^5. The contribution of the muon loop to a_e is - 0.000 465 (4) (alpha /pi)^5. The contribution of the tau-lepton loop is about two orders of magnitudes smaller than that of the muon loop and hence negligible. The sum of all of these contributions to a_e is - 1.345 (1) (alpha /pi)^5. We have also evaluated the contribution of Set II(e) to the muon g-2 (a_mu). The contribution to a_mu from the electron loop is 3.265 (12) (alpha /pi)^5, while the contribution of the tau-lepton loop is -0.038 06 (13) (alpha /pi)^5. The total contribution to a_mu, which is the sum of these two contributions and the mass-independent part of a_e, is 1.882 (13) (alpha /pi)^5.
This paper reports the tenth-order QED contribution to lepton g-2 from diagrams of three gauge-invariant sets VI(d), VI(g), and VI(h), which are obtained by including various fourth-order radiative corrections to the sixth-order g-2 containing light-
by-light-scattering subdiagrams. In the case of electron g-2, they consist of 492, 480, and 630 vertex Feynman diagrams, respectively. The results of numerical integration, including mass-dependent terms containing muon loops, are 1.8418(95) (alpha/pi)^5 for the Set VI(d), -1.5918(65) (alpha/pi)^5 for the Set VI(g), and 0.1797(40) (alpha/pi)^5 for the Set VI(h), respectively. We also report the contributions to the muon g-2, which derive from diagrams containing an electron, muon or tau lepton loop: Their sums are -5.876(802) (alpha/pi)^5 for the Set VI(d), 5.710(490) (alpha/pi)^5 for the Set VI(g), and -8.361(232) (alpha/pi)^5 for the Set VI(h), respectively.
This paper presents a detailed account of evaluation of the electron anomalous magnetic moment a_e which arises from the gauge-invariant set, called Set V, consisting of 6354 tenth-order Feynman diagrams without closed lepton loops. The latest value
of the sum of Set V diagrams evaluated by the Monte-Carlo integration routine VEGAS is 8.726(336)(alpha/pi)^5, which replaces the very preliminary value reported in 2012. Combining it with other 6318 tenth-order diagrams published previously we obtain 7.795(336)(alpha/pi)^5 as the complete mass-independent tenth-order term. Together with the improved value of the eighth-order term this leads to a_e(theory)=1 159 652 181.643(25)(23)(16)(763) times 10^{-12}, where first three uncertainties are from the eighth-order term, tenth-order term, and hadronic and elecroweak terms. The fourth and largest uncertainty is from alpha^{-1}=137.035 999 049(90), the fine-structure constant derived from the rubidium recoil measurement. Thus, a_e(experiment) - a_e(theory)= -0.91(0.82) times 10^{-12}. Assuming the validity of the standard model, we obtain the fine-structure constant alpha^{-1}(a_e)=137.035 999 1570(29)(27)(18)(331), where uncertainties are from the eighth-order term, tenth-order term, hadronic and electroweak terms, and the measurement of a_e. This is the most precise value of alpha available at present and provides a stringent constraint on possible theories beyond the standard model.
In order to improve the theoretical prediction of the electron anomalous magnetic moment $a_e$ we have carried out a new numerical evaluation of the 389 integrals of Set V, which represent 6,354 Feynman vertex diagrams without lepton loops. During th
is work, we found that one of the integrals, called $X024$, was given a wrong value in the previous calculation due to an incorrect assignment of integration variables. The correction of this error causes a shift of $-1.25$ to the Set~V contribution, and hence to the tenth-order universal (i.e., mass-independent) term $ A_1^{(10)}$. The previous evaluation of all other 388 integrals is free from errors and consistent with the new evaluation. Combining the new and the old (excluding $X024$) calculations statistically, we obtain $7.606~(192) (alpha/pi)^5$ as the best estimate of the Set V contribution. Including the contribution of the diagrams with fermion loops, the improved tenth-order universal term becomes $A_1^{(10)}=6.678~(192)$. Adding hadronic and electroweak contributions leads to the theoretical prediction $a_e (text{theory}) =1~159~652~182.032~(720)times 10^{-12}$. From this and the best measurement of $a_e$, we obtain the inverse fine-structure constant $alpha^{-1}(a_e) = 137.035~999~1491~(331)$. The theoretical prediction of the muon anomalous magnetic moment is also affected by the update of QED contribution and the new value of $alpha$, but the shift is much smaller than the theoretical uncertainty.
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