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International Meeting in Lepton Physics Colombia 07. Alberto Casas. (IFT-UAM/CSIC, Madrid). What can we learn about the See-Saw mechanism from experimental data?. Collab. with Alejandro Ibarra, Fernando Jiménez. The see-saw is a beautiful mechanism to produce (small)  -masses.

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what can we learn about the see saw mechanism from experimental data

International Meeting in Lepton Physics

Colombia 07

Alberto Casas

(IFT-UAM/CSIC, Madrid)

What can we learn about the See-Saw mechanism from experimental data?

Collab. with

Alejandro Ibarra,

Fernando Jiménez

slide2

The see-saw is a beautiful mechanism to produce (small) -masses

...but it has (too) many parameters

“Freedom is nice, but too much freedom is not so nice”

Pasquale di Bari 2007

slide3

with

Recall

slide4

Any can be accommodated

Many give the “observed”

slide5

...maybe just looking at the experimental data we can hardly say anything about the (high-energy) parameters of the see-saw

slide6

Still we can ask:

How the present data restrict the (high-energy) see-saw parameters

Which choices, among the allowed ones, produce more naturally the experimental data

slide7

Take the example of the MSSM

The theory beyond the SM has several parameters:

Many combinations of them give the right , BUT not all of them are equally natural

slide8

To obtain with no fine-tuningswe need

That’s why we expect SUSY within the LHC reach

slide9

Note:

The problem is more involved than in the MSSM

The information about is incomplete

Maybe we can use experimental datato restrict the most natural patterns of the see-saw parameters

which may be good!

slide10

suggests

unknown

Experimental information about the neutrino sector

Note: All -features are opposite to other fermions’

slide11

This is an opportunity for the see-saw mechanism:

Maybe the peculiar pattern of -masses and mixings is a consequence of the peculiar way they are generated (through the see-saw).(as it happens with the smallness of )

slide13

Consider first

This ratio contrasts with other fermions:

For neutrinos

Hierarchy in ms

Same hierarchy inys

slide14

Additional question:

Is it possible (and natural) to get starting with hierarchical similar to otherfermions?

yi

slide15

top-down & basis-independent parametrization of the see-saw

For this kind of analysis it is convenient to have a

slide16

A botton-up parametrization, like

(High-energy)R-Yukawa matrix

Low-energy-masses and mixings

(High-energy)R-masses

(Complex)orthogonal matrix

does not allow e.g.to guess easily the values of yior to play with them to see how change

slide17

So we parametrize the see-saw by the following 18 basis-independent (high-energy) parameters:

(Convention: )

slide22

VL is related to UMNS :

Defining WLas:

then

(uniquely determined)

slide24

Comment on the relation to the orthogonal (R) parametrization

The R-matrix is related to Mi, yi and the VRmatrix as:

slide25

The top-down problem for the -masses in the see-saw can be written as

3 par.

3 par.

6 par.

3 par.

VL becomes decoupled

slide26

We come back to the questions:

How the present data restrict the (high-energy) see-saw parameters

Which choices, among the allowed ones, produce more naturally the experimental data

Is it possible (and natural) to get starting with hierarchical similar to otherfermions?

yi

slide27

Example:

If VR =1

Normally (far) too large, unless

What about VR 1 ??

slide29

For random VR entries:

M1≈M2≈M3

Mi/Mj ~ yi/yj

Normally huge

huge!!

slide31

If M1≈M2≈M3

requires a delicate cancellation in the numerator

Should be « 1

≤ 1

Normally huge

unnatural

slide32

The numerator can be small with no cancellations if

In addition

sizeable

maximizes the denominator

Should be « 1

≤ 1

Normally huge

If M1«M2«M3

slide33

sizeable

If M1«M2«M3 a clear pattern emerges:

just as VCKM!

slide35

Suppose

suppr.factor

An intuitive to understand these results:

slide36

can be made soft, but only with a strong fine-tuning

In consequence:

is softened, and is typically huge

slide37

If yihierarchical

M1≈M2≈M3 disfavoured

M1<<M2<<M3 favoured, with , large

typically huge

VR~ VCKM structure,

Some conclusions

and

from

slide38

If yinon-hierarchical

More possibilities are allowed.M1<<M2<<M3 is not consistent with random VR(e.g. is still required)

slide39

A suggestive ansatz

Try VR~ VCKM

More precisely

Try also

slide40

The identification must be made at large energy (~ M). At that scale

This represents a very regular hierarchy of O(300)

In addition we have taken

slide42

Recall that

VR = 1 would produce

VR random would produce

It is highly non-trivial for VR~ VCKM to

produce the correct ratio

slide43

To see this more clearly, recall the previous plot

Only a tiny part of the plane is consistent with

slide47

Recall

with

we expect to constrain and also

Consider now

(work in progress with A. Ibarra)

slide48

How do these relations constrain ?

and

From

Consider the case

slide49

case

6 possibilities for consistent with unitarity

slide50

completely general

case

for

Note that

can we go further

Recall that

and similar expressions for

Can we go further ??
slide53

If the M-hierarchy is softer than the y2-hierarchy,

and , then all the mixing comes from

is consistent with some of

the a) - f) possibilities only when

slide54

Comment

(unfortunately)

slide55

If is not so small, say

then can be

(with very mild tuning)

and the mixing comes from both

If the M-hierarchy is softer than the y2-hierarchy,

and , then all the mixing comes from

slide56

CONCLUSIONS

We have studied how the low-energy data + naturalness constrain the see-saw.

We have used a basis-independent top-down parametrization. The -spectrum depends on the VR matrix.

For hierarchical yi and random VR we expect a hugem3/m2 hierarchy (VR cannot be random)

~ Degenerate Ms are disfavoured (they require tuning)

If the M-hierarchy is softer than the y2-hierarchy, then the m3/m2 ratio is softened when VR takes a defined structure, which remarkably is consistent with VCKM

A prediction of this scenario is an extremely tiny m1.

slide57

CONCLUSIONS (cont.)

If sin θ130 and the M-hierarchy is softer than the y2-hierarchy, UMNS comes entirely from VL

If sin θ13 is not far from its upper bound, UMNS can come from both VL and VR

& EXPLORE

Implications for Leptogenesis and LFV processes (in SUSY)

Translation of these bounds to the R-parametrization