μ − e conversion in the Littlest Higgs model with T-parity

Abstract

Little Higgs models provide a natural explanation of the little hierarchy between the electroweak scale and a few TeV scale, where new physics is expected. Under the same inspiring naturalness arguments, this work completes a previous study on lepton flavor-changing processes in the Littlest Higgs model with T-parity exploring the channel that will eventually turn out to be the most sensitive, µ − e conversion in nuclei. All one-loop contributions are carefully taken into account, results for the most relevant nuclei are provided and a discussion of the influence of the quark mixing is included. The results for the Ti nucleus are in good agreement with earlier work by Blanke et al., where a degenerate mirror quark sector was assumed. The conclusion is that, although this particular model reduces the tension with electroweak precision tests, if the restrictions on the parameter space derived from lepton flavor violation are taken seriously, the degree of fine tuning necessary to meet these constraints also disfavors this model. * Note that amplitudes must be at least suppressed by one of these ratios, and then cross sections are at least quadratically suppressed.

Lepton flavor violation in the Simplest Little Higgs model

“…A similar effect can be seen in the LHT model (see figure 4 of Ref. [19]), where the γ and Z penguins can equate the box contribution in absolute value at specific points but with opposite sign. In the same figure, one can also see that the penguin contributions vanish at some points, where they flip sign.…”

“…Only normalized values below the unity are experimentally allowed. The general behavior of the SLH model is very similar to that of the LHT model studied previously in [18,19]. Tables 11 and 12 contain generic constraints on the scale f , δ and sin 2θ for standard values for the rest of the parameters in each case.…”

“…These amplitudes are ultraviolet finite, as they are in the case of the LHT model [18,19,21,22]. On the other hand, the heavy neutrino Yukawa exhibits a nondecoupling behavior (figure 5): both Z and Z ′ penguin contributions to the amplitudes grow with m 2 N /M 2 X , a result that is well known and was discussed in [18,19]. To simplify the phenomenological analysis, we have assumed, as in previous studies, that only two lepton families mix.…”

“…We follow closely the analysis in [18,19] and restrict ourselves to the case of two lepton families to illustrate the physical behavior of the amplitudes. This leaves us with four basic parameters:…”

“…Hence, the corresponding limits can be satisfied sending f to a high enough value or aligning both sectors with a high enough precision. For instance, in the Littlest Higgs model with T-parity (LHT) present bounds on lepton flavor violating (LFV) processes require f > ∼ 10 TeV or a misalignment of at most 1% between the SM and the heavy fermion mass matrices [16][17][18][19]. These limits are not stronger because T-parity forbids tree-level flavor changing Z couplings.…”