Pmns matrix pdf

Generically, given that neutrino running effects are small for hierarchical neutrino spectra, the running effects on the PMNS matrix appearing above are neglected. As is well known, the form of the Yukawa matrix feeds into the flavour violating LL entries of the slepton mass matrix through the well known RG effects. At the leading log level, this expression is given by :!

Expanding Eq. The important parameter here is Ue3 which could be very small at the weak scale and could attain a non-negligible value at the high scale. From them, it is possible to estimate the generated Ue3 at high energy. The RG-generated Ue3 at the high scale would now become the dominant contribution to the LFV as long as the high-scale value of Ue3 overwhelms the limit value given by Eq. This RG generated contribution is independent of low-energy value of Ue3 and would get generated at the high scale even when Ue3 is zero.

For larger values of Ue3 this contribution would add to the low-energy number. This is best illustrated in the Fig. However there are some subtleties associated with such an assumption especially in the limit Ue3 goes to zero, which we will elaborate in the text.

It is interesting to compare the contributions in Eqs. This is best demonstrated in Fig. The evaluation of the contribution related to the running of Ue3 involves a subtlety which manifests itself in the above figure. In the present work, as we scan Ue3 for very small values starting from zero, Ue3 takes values which are negative at the high scale. As a consequence cancellations occur between the two contributions at the high scale as Ue3 is varied.

Finally before we close this section, a few comments are in order. In the above analysis, we have parameterized the unknown Ue3 by considering it as a free input parameter. This has been done with a purely phenomenological perspective, without dealing with the possible flavour symmetries giving rise to the present experimentally determined form of the UPMNS matrix.

Unless this symmetry is broken, a non-zero value for Ue3 cannot be achieved. Below such breaking scale the flavour symmetry is no more effective and the RGEs are exactly as given in [11, 12]. If the flavour symmetry breaking also has a radiative origin, then effects could be similar in magnitude with RG effects.

On the other hand, Ue3 itself can also be purely of radiative origin. The origin of such double mass-insertion is best depicted in the Feynman diagram in Fig. This contribution, which is independent of Ue3 would provide a flat contribution to the branching ratio irrespective of the value of Ue3 at the weak scale. The various scales involved here can be summarised in the Fig. II , one would expect that the Ue3 proportional contribution would be the dominant force within the SUSY-GUT framework as the neutrino mass matrix running effects are larger.

However, the double flavour violating MI Eq. In these regions the running of Ue3 would have no strong impact on the total branching ratio. The competition between these two contributions is evident in Fig.

The high-energy values of fermion masses and mixings are set by evolving them from the e. For more details about the numerical routine, we refer to [5]. In Fig. Different light neutrinos spectra could consistently change the above results. Moreover in this latter case, the scales of right handed neutrinos are much closer to the GUT scale and thus even the pure SU 5 effects coming from double MI which can enhance the BR over the yc contribution are smaller compared to the normal hierarchical case.

This can be seen in Fig. In the present paper, we have stressed the importance of considering RG running effects on the neutrino mass matrices while making such a correlation between weak scale measurements and high-scale probes of Ue3 , which has been neglected in earlier works [20].

This is the main point of our present analysis where a top-down approach with an underlying SO 10 symmetry is taken. An analogous investigation [7] where a bottom-up phenomenological approach was considered also had similar conclusions. The main difference between the two approaches concerns the information about the size of the neutrino Yukawa couplings. We have not addressed the important and interesting issue of origins of neutrino mixing angles particularly Ue3 , treating it as a free parameter.

We hope to deal with this issue at a later date. We thank S. Antusch, M. Herrero and A. Teixeira for bringing to our notice their work which is related to the topic discussed here.

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