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Putting m$_{2}$ ∼ m$_{Z}$ and examining Table I, we obtain 

Since m$_{2}$/M$_{2}$ ∼ 10 − 6 (10 − $^{1}$) for model LE (LL,EE), we have 

$^{10}$$^{−}$$^{12}$$^{y}$$^{2}$ 10 − 2 EE Exact calculations confirm these rough estimates. We made similar calculations for Δ S ( χ ) and Δ U ( χ ). We find that for m$_{2}$/m (lightest χ ) ∼ < 0 . 1, our models satisfy the constraints from electroweak precision measurements. 

## III. LHC PHENOMENOLOGY 

## A. Production 

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Since the heavy leptons are SU (2)-doublets, the main production mechanism at the LHC will be qq ′ → χχ via electroweak interactions. The production rate is model independent. It is suppressed by the electroweak gauge couplings, but not by any flavor factors. The most significant process involves an intermediate W $^{+}$-boson, producing a heavy charged lepton along with a heavy neutral lepton, u ¯ d → χ $^{+}$χ$^{0}$. The second most important process is Drell- Yan production involving an intermediate photon or Z $^{0}$-boson, q ¯ q → χ $^{+}$χ $^{−}$. The production cross sections for a single generation of vector-like heavy leptons are shown in Fig. 1. The simulation was done using MadGraph v4 [24] with default cut values at E$_{cm}$ = 14 TeV and using CTEQ6L1 parton distribution functions [25]. 

There are two points that we need to emphasize: 

1. Within the MLFV framework, the production is always of a same flavor pair, i.e. χ$_{i}$χ$_{i}$ (and not χ$_{i}$ ¯ χ$_{j}$ with i ̸ = j ). 

2. Since the coupling of heavy and light leptons is suppressed by O ( v/M$_{2}$ ), single heavy lepton production is negligible. 

