Tau Lepton g-2 And Electric Dipole Moment (EDM)

The substance of a new paper considering new physics that could arise in the tau lepton anomalous magnetic moment (g-2) and electric dipole moment (EDM) is purely ill-motivated speculation and doesn't deserve any discussion here. 

But the introduction to the paper (PDF) conveniently recaps the current state of experimental measurements of these properties (that are established to high precision in electrons and muons), and the Standard Model predictions for these quantities (which have been confirmed for electrons and muons):

The SM contributions to the electron and muon g−2 are precisely calculated and compared with experiments. On the other hand, a nonzero EDM requires CP violation which arises predominantly from the phase in the Cabibbo-Kobayashi-Maskawa (CKM) matrix within the SM, resulting in extremely suppressed predictions for charged lepton EDMs. Therefore, the discovery of a nonzero EDM indicates the existence of physics beyond the SM. 

In fact, precise measurements of the electron EDM [ed. the absolute value of which is currently experimentally limited to not more than 4.1 * 10^-30 ecm] already put stringent constraints on a wide range of new physics models [ed. especially supersymmetry]. While the current upper limit on the muon EDM [ed. the absolute value of which is currently experimentally limited to not more than 1 * 10^-19 ecm] hardly gives a constraint by itself, the projected experiments will reach the sensitivity to explore new physics at the electroweak scale. 

The dipole moments of the tau lepton are currently much less constrained than those of the electron and muon due to the tau’s short lifetime, but they will provide a valuable window into new physics effects that scale with lepton mass. 

The SM contribution to the tau g −2 is precisely calculated and found as a(SM)(τ) = (117717.1 ± 3.9) × 10^−8 [ed. i.e. 0.001177171(39)], including updates of the hadronic vacuum polarization contributions. On the other hand, its measurements at the Large Hadron Collider (LHC) are still not as precise: 

ATLAS: −0.057 < a(τ) < 0.024 (95% C.L.), (1.4) 

CMS: −0.0042 < a(τ) < 0.0062 (95% C.L.). (1.5) 

The SM contribution to the tau EDM is tiny. At the quark level, the leading contribution is given at the four-loop level, dSM τ = O(10^−47) ecm, while the hadron level long distance effect enhances the contribution to dSM τ ≃ −7.32 × 10^−38 ecm. 

The current experimental upper limits are:

−1.85 × 10^−17 ecm < Re(dτ) < 0.61 × 10^−17 ecm (95% C.L.), (1.6)

−1.03 ×10^−17 ecm < Im(dτ) < 0.23 × 10^−17 ecm (95% C.L.), (1.7) 

|dτ| < 2.9 × 10^−17 ecm (95% C.L.).  (1.8) 

Note that the complex form of the limits is due to the off-shell photon in the e+e− → τ+τ− process. 

There is also an indirect limit on |dτ| from the electron EDM constraint via the three-loop light-by-light mechanism, which is

 |dτ| < 1.1 ×10^−18 ecm for |de| < 1.1 × 10^−29 ecm, 

 |dτ| < 4.1 ×10^−19 ecm for |de| < 4.1 × 10^−30 ecm (1.9) 

providing a stronger constraint compared with the direct bounds. 

Although measurements of the tau g − 2 and EDM remain experimentally challenging, we can expect improved sensitivities for these observables by ongoing and projected experiments such as the Belle II experiment, Beijing Electron-Positron Collider (BEPCII) and Circular Electron-Positron Collider (CEPC). They will reach the sensitivities of |aτ| ∼ 10^−5 and |dτ| ∼ 10^−19 ecm.

Thus, the ongoing and projected experiments, which improve upon the status quo by about two orders of magnitude each, should show a tau g-2 consistent with 0.00118(1) and a tau EDM that is experimentally indistinguishable from zero. 

A different result would suggest new physics, which there is no good reason to suspect, or serious systemic errors in the experiments.

Previous discussion of the tau lepton's properties can be found in posts at this blog on May 28, 2024 and May 23, 2023. 

The Koide's rule predicted value for the tau lepton mass is 1776.96894(7) MeV.

The Particle Data Group's world average of the tau lepton mass is 1776.93 ± 0.09 MeV which is a precision of slightly under one part per 20,000. 

The experimentally measured mass of the tau lepton is consistent with the Koide's rule prediction made in 1981 at the 0.4 sigma level, even though the relevant masses were known much less precisely in 1981, and the experimental value has grown closer to the predicted value over time. 

There are dozens of lepton decay modes with a branching fraction of more than 1% in addition to many more less common decay modes. About 85% of those decay modes involve a decay to an electron or muon, plus one or more neutral particles (such as neutrinos, neutral pions, and/or neutral kaons).