Abstract
We calculate loop induced lepton flavor violating Higgs decays in the Littlest Higgs model with T-parity. We find that a finite amplitude is obtained only when all contributions from the T-odd lepton sector are included. This is in contrast to lepton flavor violating processes mediated by gauge bosons where the partners of the right-handed mirror leptons can be decoupled from the spectrum. These partners are necessary to cancel the divergence in the Higgs mass introduced by the mirror leptons but are otherwise unnecessary and assumed to be decoupled in previous phenomenological studies. Further-more, as we emphasize, including the partner leptons in the spectrum also introduces a new source of lepton flavor violation via their couplings to the physical pseudo-Goldstone electroweak triplet scalar. Although this extra source also affects lepton flavor changing gauge transitions, it decouples from these amplitudes in the limit of heavy mass for the partner leptons. We find that the corresponding Higgs branching ratio into taus and muons can be as large as ∼ 0.2 × 10−6 for T-odd masses of the order a few TeV, a demanding challenge even for the high luminosity LHC.
Highlights
SU(2)×U(1) subgroups of SU(5) are gauged with equal strength and broken spontaneously down to a diagonal subgroup which is identified with the SM gauge group, while the broken gauge symmetries lead to a set of massive vector bosons with mass ∼ f
We find that a finite amplitude is obtained only when all contributions from the T-odd lepton sector are included. This is in contrast to lepton flavor violating processes mediated by gauge bosons where the partners of the right-handed mirror leptons can be decoupled from the spectrum
These partners are necessary to cancel the divergence in the Higgs mass introduced by the mirror leptons but are otherwise unnecessary and assumed to be decoupled in previous phenomenological studies
Summary
We summarize the LHT to fix our notation and provide the new Feynman rules necessary for the one loop calculation of the h → τ μ amplitude. Where ψR = −iσ2( ̃lL)c andlL = (νLL)T (with T meaning transpose) It does not have any consequence in our calculation, we comment that the Yukawa-type Lagrangian LYH fixes the transformation properties of the heavy fermions including their gauge couplings. Dμ = ∂μ − 2ig(W1aμQa1 + W2aμQa2) + 2ig (Y1B1μ + Y2B2μ) This Lagrangian includes the proper O(v2/f 2) couplings to Goldstone fields that render the one-loop lepton flavor changing amplitudes mediated by gauge bosons ultraviolet finite [25, 26]. As discussed above, in order to assign the proper SM hypercharge Y = −1 to the charged right-handed leptons R, one can enlarge the global SU(5) with two extra U(1) groups for which we can write down the corresponding gauge and T-invariant Lagrangian. The corresponding masses and eigenfields up to O(v2/f 2) and the relevant Feynman rules are collected below and are obtained by expanding L to the required order
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