Perspectives for detecting lepton flavour violation in left-right symmetric models
Received: November
Perspectives for detecting lepton avour violation in left-right symmetric models
Cesar Bonilla 0 1 2 4
Manuel E. Krauss 0 1 2 3 4
Toby Opferkuch 0 1 2 3 4
Werner Porod 0 1 2 4
Open Access 0 1 2 4
c The Authors. 0 1 2 4
0 Am Hubland , 97074 Wurzburg , Germany
1 Nussallee 12 , 53115 Bonn , Germany
2 Edi cio de Institutos de Paterna, C/Catedratico Jose Beltran 2
3 Bethe Center for Theoretical Physics & Physikalisches Institut der Universitat Bonn
4 avour violating -decays have a
We investigate lepton avour violation in a class of minimal left-right symmetric models where the left-right symmetry is broken by triplet scalars. In this context we present a method to consistently calculate the triplet-Yukawa couplings which takes into account the experimental data while simultaneously respecting the underlying symmetries. Analysing various scenarios, we then calculate the full set of tree-level and one-loop contributions to all radiative and three-body avour-violating fully leptonic decays as well as e conversion in nuclei. Our method illustrates how these processes depend on the underlying parameters of the theory. To that end we observe that, for many choices of the model parameters, there is a strong complementarity between the di erent observables. For instance, in a large part of the parameter space, lepton large enough branching ratio to be measured in upcoming experiments. Our results further show that experiments coming online in the immediate future, like Mu3e and BELLE II, or longer-term, such as PRISM/PRIME, will probe signi cant portions of the currently allowed parameter space.
left-right; symmetric; models; cInstitut fur Theoretische Physik und Astronomie; Universitat Wurzburg
Contents
1 Introduction 2 The minimal left-right symmetric model Neutrino sector
Model de nition
Discrete symmetries
Scalar sector and gauge symmetry breaking
Neutrino masses
Parametrisation of the Yukawa matrices
Numerical set-up
Numerical results
Case I: MD / 1
Case II: MD / Mup type
Case III: MD / VCyKMMup typeVCKM
Impact of the CP phase
Measurement prospects
Conclusions and outlook
A Determination of the triplet-Yukawa couplings
Alternative neutrino parameters
C Scalar mass matrices
Doubly charged
C.2 Singly charged
C.3 Neutral CP-odd
D SARAH model le
Neutral CP-even
Introduction
Pati-Salam group [7].
A further attractive feature of LR models is parity restoration
context [8].
each sector a triplet [9]. As a consequence, lepton
avour violating (LFV) decays are
10 12 [11] which will be further constrained by upcoming experiments like
observables and their current bounds as well as expected future sensitivities.
has been developed which can have breaking scales down to O(TeV).1
considered in the past, investigating lepton
avour and lepton number violation [9, 21{
Higgs signals at the LHC [31{34] as well as lepton
avour and number violating signals
as discussed e.g. in [18]. In addition, the
parameter [43, 44], or more generally the
checking whether the other parts are consistently implemented.
considerations [18], or gauge coupling uni cation [19, 20].
LFV Process
Present Bound
Future Sensitivity
10 10 [55, 57]
10 10 [55, 57]
10 10 [55, 57]
10 10 [55, 57]
10 18 [59, 60]
10 17 [62{64]
neutrino mass hierarchy which are not covered in the main text.
Model de nition
SU(2)R
U(1)B L, are given by:
The minimal particle content and the irreducible representations under SU(3)c
QL =
LL =
2 (3; 2; 1; 1=3) ;
L = @ 02
2 (1; 2; 2; 0) ;
QR =
LR =
2 (3; 1; 2; 1=3) ;
R = @ 02
Here we use the convention that the electric charge is given by
Qem = T3L + T3R +
for the neutrinos after LR-symmetry-breaking. The respective terms are
where ~
C =
C = i 2 0 :
Discrete symmetries
LY = QL YQ1
QR + LL YL1
LR + h:c: ;
Once again invariance of the Lagrangian yields
= Q; L and i = 1; 2.
Charge conjugation symmetry C. Charge conjugation symmetry exchanges
Y i = Y yi ;
Y L = Y R
Y i = Y Ti ;
Y L = Y R
Scalar sector and gauge symmetry breaking
discrete parity and charge conjugation symmetries is given by [9]
VLR =
23 hTr( L yL) + Tr( R yR)i
hTr( ~ y)i2 + hTr( ~ y )
hTr( L yL)i2 + hTr( R yR)i2
+ 1Tr( y ) hTr( L yL) + Tr( R yR)i
and -odd components:
01 = p (v1 + 1 + i'1) ;
02 = p (v2 + 2 + i'2) ;
L0 = p (vL + L + i'L) ;
R0 = p (vR + R + i'R) ;
21 = v2
22 = v2
23 =
2 = ( 1
+ vLvR( 1
where we use the generic symbols
and ' to label the CP-even and -odd states, respectively.
parametrisation:
v1 = v cos ;
v2 = v sin ;
where vL
vR so that v can be identi ed as the SM VEV. The masses of the new
gauge bosons therefore read
Using the above expressions
, where i = 1; 2; 3, and
2 can be eliminated from the
scalar masses:
m2H ' 2(2 2 + 3)v2 +
Here, h corresponds to the SM-like Higgs boson; H; A and H
are the bidoublet-like heavier
The triplet-scalar sector masses are:
Particles with an index L(R) mostly consist of
L(R) components. The doubly-charged
Neutrino sector
mass matrix m
which we express as follows
is (...truncated)