Revisiting Minimal Lepton Flavour Violation in the light of leptonic CP violation
Received: May
Minimal Lepton Flavour Violation in the light of leptonic CP violation
D.N. Dinh 0 1 2 4 5 6
L. Merlo 0 1 2 5 6
S.T. Petcov 0 1 2 3 5 6
R. Vega-Alvarez 0 1 2 5 6
Tokyo 0 1 2 5 6
Japan 0 1 2 5 6
0 Universidad Autonoma de Madrid
1 Charlottesville , VA 22904-4714 , U.S.A
2 10 Dao Tan , Ba Dinh, Hanoi , Viet Nam
3 Kavli IPMU, University of Tokyo , WPI
4 Department of Physics, University of Virginia , USA
5 Via Bonomea 265 , 34136 Trieste , Italy
6 Cantoblanco , 28049, Madrid , Spain
The Minimal Lepton Flavour Violation (MLFV) framework is discussed after the recent indication for CP violation in the leptonic sector. Among the three distinct versions of MLFV, the one with degenerate right-handed neutrinos will be disfavoured, if this indication is con rmed. The predictions for leptonic radiative rare decays and muon conversion in nuclei are analysed, identifying strategies to disentangle the di erent MLFV scenarios. The claim that the present anomalies in the semi-leptonic B-meson decays can be explained within the MLFV context is critically re-examined concluding that such an explanation is not compatible with the present bounds from purely leptonic processes.
CP violation; E ective Field Theories; Global Symmetries; Neutrino Physics
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Revisiting
1 Introduction 2
Minimal (Lepton) Flavour Violation
2.1 The lepton sector
3 Phenomenology in the lepton sector
3.1
3.2
The LFV e ective Lagrangian
Rare radiative leptonic decays and conversion in nuclei
3.2.1
3.2.2
Bounds on the LFV scale
Ratios of branching ratios
4 b ! s anomalies
4.1 B semi-leptonic decays
5 Conclusions
The discovery [1{5] of a non-vanishing reactor angle 1`3 in the lepton mixing matrix led
to a huge fervour in the avour community and to a deep catharsis in the model building
When the value of this angle was still unknown, the closeness to a maximal mixing
value of the atmospheric angle 2`3 was suggesting a maximal oscillation between
muonand tau-neutrinos: in terms of symmetries of the Lagrangian acting on the avour space, it
could be described by a discrete Abelian Z2 symmetry, which, in turn, implied a vanishing
reactor angle. The simplicity and the elegance of this pattern, i.e. one maximal angle and
one vanishing one, convinced part of the community that Nature could have made us a
favour and that neutrino physics could indeed be described, at least in the atmospheric
and reactor sectors, by this texture [6, 7].
An approach followed for such constructions was to write a Lagrangian whose leading
order terms described speci c textures for the Yukawa matrices, leading to 1`3 = 0 and
`
23 = 45 . Often, this was done such that the Yukawa matrix for the charged leptons
was diagonal while the Yukawa matrix for the light active neutrinos was diagonalised
sin2 1`2 = 1=3, in a very good agreement with the neutrino oscillation data.
by the so-called Tri-Bimaximal mixing matrix [8{10], which predicts, besides a vanishing
reactor mixing angle and a maximal atmospheric one 2`3 = 45 , a solar angle satisfying to
Pioneer models can be found in refs. [11{15], where the discrete non-Abelian group A4
was taken as a avour symmetry of the lepton sector. Several distinct proposals followed,
{ 1 {
i) attempting to achieve the Tri-Bimaximal pattern, but with other avour symmetries
(see for example refs. [16{19]); or ii) adopting other mixing patterns to describe neutrino
oscillations, such as the Bimaximal mixing1 [21, 22], the Golden Ratio mixing [23, 24] and
the Trimaximal mixing [25]; iii) analysing the possible perturbations or modi cations to
Bimaximal mixing, Tri-Bimaximal mixing etc., arising from the charged lepton sector [26{29],
vi) implementing the so-called quark-lepton complementarity [30, 31] which suggests that
the lepton and quark sectors should not be treated independently, but a common dynamics
could explain both the mixings [32{34]. Further details could be found for example in these
reviews [35{40].
After the discovery of a non-vanishing 1`3 and the improved sensitivity on the other
two mixing angles, which pointed out that 2`3 best t is not 45 (the most recent global ts
on neutrino oscillation data can be found in refs. [41{43]), models based on discrete
symmetries underwent to a deep rethinking. A few strategies have been suggested: introduction
of additional parameters in preexisting minimal models, see for example refs. [44, 45];
implementation of features that allow sub-leading corrections only in speci c directions in
the avour space [46{49]; search for alternative avour symmetries or mixing patterns that
lead already in rst approximation to 1`3 6= 0 and 2`3 6= 45 [50, 51]. One can fairly say
that the latest neutrino data can still be described in the context of discrete symmetries,
but at the prize of ne-tunings and/or less minimal mechanisms.
Alternative approaches to discrete avour model building strengthened after 2011 and,
in particular, constructions based on continuous symmetries were considered int (...truncated)