Abstract
In this work we assess the potential of discovering new physics by searching for lepton-flavour-violating (LFV) decays of the Z boson, Zrightarrow ell _i ell _j, at the proposed circular e^+e^- colliders CEPC and FCC-ee. Both projects plan to run at the Z-pole as a “Tera Z factory”, i.e., collecting {mathcal {O}}left( 10^{12} right) Z decays. In order to discuss the discovery potential in a model-independent way, we revisit the LFV Z decays in the context of the Standard Model effective field theory and study the indirect constraints from LFV mu and tau decays on the operators that can induce Zrightarrow ell _i ell _j. We find that, while the Zrightarrow mu e rates are beyond the expected sensitivities, a Tera Z factory is promising for Zrightarrow tau ell decays, probing New Physics at the same level of future low-energy LFV observables.
Highlights
10−8–10−10 10−9 10−9 run of the LHC (HL-LHC)
It is interesting to analyse their effect when only one of these operators is present, assuming other operators are absent at that time, and to compare the potential of the LFVZD to that of other low-energy LFV observables in the search for new physics
We will see how other operators beyond those in Eq (7) could play an important role in this case, Page 7 of 18 1054 and we will assess whether they could suppress some of the low-energy LFV decays, allowing larger LFV Z decay rates
Summary
Throughout this work, we will assume that the new particles related to the NP scale responsible for LFV effects are quite heavy ( mW ) and that there are no other particles in between these scales. Out of the 59 (without counting the combinations of flavour indices) dimension-6 operators [17,18] that can be constructed from SM fields and respect SU (3)C × SU (2)L ×U (1)Y invariance (and baryon-number conservation), only a subset is relevant to us, namely the operators which contribute to LFV processes at tree-level or at 1-loop level. Such an operator can be generated by the RG running if at least one of the five operators mentioned above is induced by the UV theory This effect is proportional to at least one power of a small lepton Yukawa coupling (due to the necessary flip of the chirality of the leptons) and their contributions are substantially suppressed [54,55].5. In the context of the SMEFT, Z and Higgs LFV effects are practically decoupled and we are not going to discuss the latter in this work
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