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Master Majorana neutrino mass parametrization

Isabel Cordero-Carrión University of Valencia

The quest for new physics Valencia

In collaboration with

Martin Hirsch and Avelino Vicente

arXiv:1812.03896

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There are MANY

Majorana neutrino mass models...

Tree-level

Radiative: 1-loop, 2-loop, 3-loop, ...

High scale Low scale

Dimension-5: Weinberg operator Higher dimensions: dim-7, dim-9, ...

...but also two extraordinary

theoretical physicists.

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Outline

An illustrative example

Master formula

Master parametrization An application

The most general solution to the master formula

One formula to rule them all

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Master formula

One formula

to rule them all

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The master formula

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The master formula

: symmetric Majorana neutrino mass matrix

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: global factor [numerical factors, model parameters, mass ratios, ...]

The master formula

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: Yukawa matrix

: Yukawa matrix [ ]

The master formula

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: symmetric Majorana neutrino mass matrix

: Yukawa matrix

: matrix [dimensions of mass]

: Yukawa matrix [ ]

The master formula

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Some examples

To convince you that the master formula in indeed

valid for all Majorana neutrino mass models

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Type-I seesaw

[ Minkowski, 1977 ]

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Inverse seesaw

[ Mohapatra, Valle, 1986 ]

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Scotogenic model

[ Ma, 2006 ]

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BNT model

[ Babu, Nandi, Tavartkiladze, 2009 ]

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Towards a master parametrization

Objective:

Neutrino oscillation experiments

Model parameters

Casas-Ibarra parametrization [ Casas, Ibarra, 2001 ]

To establish a general, complete and programmable parametrization of the and Yukawa matrices

Particular case: Type-I seesaw

Master parametrization

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The master parametrization

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unitary matrix

Leptonic mixing matrix

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Singular-value decomposition

Unitary matrices

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Arbitrary matrices

[ Note: absent if ]

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unitary matrix

Absent if

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Invertible upper triangular matrix Numerical matrix whose form depends on

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antisymmetric

Matrix whose form depends on

Absent if

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Experimental input:

Model input:

Free parameters:

n-data

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Different matrix forms for other values of

Particular case:

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The Casas-Ibarra limit

Particular case: Type-I seesaw

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, and are absent

orthogonal

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Casas-Ibarra parametrization [Casas, Ibarra, 2001]

, and are absent

orthogonal

The Casas-Ibarra limit

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An application: the BNT model

An example of

Lepton number violation

Two extra

representations

beyond the SM:

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Black: Trivial scan

Purple: General scan

[ & ]

Model in SARAH and scans with SSP [Staub]

BR computed with FlavorKit [Porod, Staub, AV]

A large parameter space that can only be covered with the

master parametrization

n-data NH within 3 n-data NH BFP

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Conclusions

· The master parametrization allows one to explore the parameter space of any Majorana neutrino mass model in a complete way .

· Potential limitation (also in other parametrizations): models with Yukawas that have additional restrictions.

· Easy to program: parameter space exploration easier than ever.

· The master parametrization may also provide analytical insight on some

scenarios.

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Backup slides

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Type-II seesaw

[ Schechter, Valle, 1982 ]

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Cases (I)

1

^st

& 2

^nd

columns of ...

l.i.

l.d.

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Cases (II)

1

^st

& 2

^nd

columns of ...

l.i.

l.d.

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Parameter counting

: any extra condition on

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Absent if Absent if

Absent if

The general parameter counting can be easily adapted to any model

Parameter counting

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A philosophical moment

Occam’s razor:

Occam’s laser:

Occam’s hammer:

All credit goes to Alberto Aparici

The simplest explanation is the correct one

The most awesome explanation is the correct one

My explanation is the correct one