Modeles Theoriques

1 Journees Neutrino France – November 27, 2003

Modeles Theoriques

Andrea RomaninoCERN

Andrea Romanino, CERN Journees Neutrino France – November 27, 20032

Plan of the talk

• Interpretation of ATM and SUN data

• Expectations for and

• Precise predictions for and

13θ

eem

eem

13θ


(ATM, K2K)

(SUN, KamLAND)

(CHOOZ, Palo Verde)

(Heidelberg-Moscow)

(Mainz, Troitsk)

(Cosmology)

Guidelines for model building:

1 035.0Δ/Δ

10

)5( 453530~

?)45( 45~

GeV 174«

232

221

o13

oo12

oo23

«mm

θ

σθ

θ

mi

Experimental constraints

eV7.0

eV)2.2(||)(

eV4.0)1(||

10

3530~eV107.0~Δ

45~eV102~Δ

222

2

o13

o12

24221

o23

23232

†

i i

ieiee

ieiee

m

mUmm

OmUm

θ

θm

θm

68% C.L.90% C.L.99% C.L.

FC + PC + up-going 1489 days

(Hayato, SK, HEP 2003) (SNO, nucl-ex/0309004)


Smallness of neutrino masses

Natural scale of fermion masses: v = 174 GeV

Why

(must have a different origin than

?10/ 12vmν

)103.0/ 5vme


GeV)102(

eV05.0GeV105.0~Λ

Λ

))((Λ

16GUT

15

renSM

effSM

M

mh

vhvm

LHLHh

LL

ν

ν

Rν no :SM the in masses Neutrino


cc

cc

eedd

ννuu

Right-handed neutrinos

vλmLHvλ νc

B-LRLc xU(1)xSU(2)xSU(2)SU(3)

YLc xU(1)xSU(2)SU(3) SO(10)

heavy be therefore can and singlet SM a is cv


DTDν

T

mM

mm

λM

λh

LHLHh

1

1Λ

))((Λ

X

H

L

H

Lcν cν

M

See-saw

: out Integrate cν


Origin of large mixings

diagD

TdD

diagU

TuU

mUm

mUm

c

c

uU

dU

diagE

TeE

diagν

Tνν

mUm

mUm

c

νU

eU

†duUUV

†νeUUU

The large angles can in principle originate from either or

(the distinction is physical in terms of the physics giving rise to the masses)

νm em


• (from in the case of degenerate neutrinos)

• from in the case of normal hierarchy

• from in the case of inverse hierarchy

• from

• (anarchy)

23 of Origin θ

νm

νm

νm

Em


Large angles?

1«1«, νeq θθθ

321231

22132 1«Δ/Δ, mmmmmmm

: Dirac and Majorana mass terms trasform differently under symmetries

E.g.: . In the symmetric limit:

However, it only works with degenerate ν’s:

E.g.:

Requires a non abelian symmetry acting on the three familiesOften unstable

o0eθ o45νθ

τμ LL

0110

100 νE mam

11

1

νm


Hierarchy Normal - from large A 23 νmθ

However A, B are not fundamental parameters

see-saw:

Natural solution:

:unnatural seems « 32 mmlarge 23νθ and

1AABmν

1«2 BA :« 32 mm

1~~BA:large 23νθ

μMμm Tν

1

2

333332

3332232

22232322

2322222

223

3

223

11,

μμμ

μμμMμμμ

μμμM

mMM

M ν

232232 ~,« μμMM [King]

det ≠ 0

det = 0

det = 0


nscorrelatio no large 2123 mmθν

AB

θ 23tan

Hierarchy Inverse - from large A 23 νmθ

scorrection

BA

BAmν


04.0~ε

Emθ from large A 23

3.00.1 A

1Em 'ε

A

1Dm

ε'A

not incompatible even in SU(5), where (up to GJ factors)

TDE mm

[e.g. Altarelli Feruglio and refs]


• Inverse Hierarchy: barring tunings or cancellations, must be close to the experimental limit

In fact: – an inverse hierarchy requires, barring tunings, a

correction to from– a correction to from contributes to

13 for nsExpectatio θ

13θ

12θ

12θEm

Em 13θ


Correction from :

Correction from :2

45~ 12

o

12θ

θ e

o12

rotation 45 11

23

θm

BA

BAm ν

θν

– an inverse hierarchy requires, barring tunings, a correction to from

νm

em

oo12 35-30~νθ 1~~ if ba

21 mm baba or 1«, if

b

amν 1

1

12θ Em


limit exp ~2

45~

245

~ 12o

23121312

o

12θ

sssθ

θ ee

– a correction to from contributes to12θ Em 13θ

1

2/12/12/12/11

1 232323231212

1212

cssccs

sc

U ee

ee


• In all cases, contributes to

is also model-dependent, but involves the charged fermions

Implementing the same pattern in (e.g. SU(5))

Central value observable with suberbeams (but > O(1) uncertainty)

(precise):successful is1

''0

s

dcD m

mθεε

εm

331

12c

s

d

μ

ee θm

m

mm

θ

o2313 3~limit exp

31

~ μ

emm

sθ

eθ12

eθ12 13θ

[Gatto Sartori]

Em


(Genius)eV 01.0)1(Moscow)-g(HeidelbereV 4.0)1(||

(Katrin)eV) 3.0(Troitsk) (Mainz,eV) 2.2()( 22†

OOm

mm

ee

ee

Feruglio Strumia Vissani

||Δ 2212

212

223

αiee escmm

ee for nsExpectatio m


Minimal models

• Use the minimal number of “effective” parameters needed to account for the data: 4+1

• Produce 2 correlations among

i.e. a prediction for

eemmmδθθθ 221

232131223 ΔΔ

eemθ ,13


• Simplest possibility: assume the presence of (2) zeros in the neutrino mass matrix written in the flavor basis,

• However, the parameters in are only combinations of the parameters in the basic lagrangian

• Our approach:– assume the relative smallness (vanishing) of some

parameters in the basic lagrangian – assume there are no correlations among those

parameters (non-abelian symmetries could give rise to further possibilities)

• We find only 5 possible predictions

[Barbieri, Hambye, AR]

Reducing the number of parameters

[Frampton, Glashow, Marfatia]

[e.g. Ibarra, Ross]

jieeνm )(

jieeνm )(

),,( MμmE


Barb

ieri

, H

am

bye,

AR

eemθ , for sPrediction 13


E is the only case which corresponds to IH and in which the predictions depend on δ (hence the lower limit and the constraint cos δ > 0.8)

In case D, (hence the upper limit)

Cases A, B, E are within the sensitivity of superbeams; case C requires SB + BB; case D has chances with a nu-factory.

Cases A, B, C, D assume no “12” rotation in the charged lepton sector

There are good prospects for 0ν2β decay only in the IH case (E), but as long as δ is not known, there is no special prediction.

Case A has been first studied by Frampton, Glashow, Yanagida.

23o

13 45 θθ


Summary

• The present data can be comfortably accommodated in the standard framework for the origin of neutrino masses and provides valuable information on the structure of the basic lagrangian

• Based on the interpretation of present data, on our understanding of the charged fermion sector, and on naturalness considerations, there are good prospects of measuring with superbeams

• Despite the large number of model building possibilities, there is a relatively small number of possible predictions for compatible with not having correlations among the parameters in the basic lagrangian

13θ

13θ

Modeles Theoriques

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