1 Journees Neutrino France – November 27, 2003 Modeles Theoriques Andrea Romanino CERN
Jan 07, 2016
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
Andrea Romanino, CERN Journees Neutrino France – November 27, 20033
(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)
Andrea Romanino, CERN Journees Neutrino France – November 27, 20034
Smallness of neutrino masses
Natural scale of fermion masses: v = 174 GeV
Why
(must have a different origin than
?10/ 12vmν
)103.0/ 5vme
Andrea Romanino, CERN Journees Neutrino France – November 27, 20035
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
Andrea Romanino, CERN Journees Neutrino France – November 27, 20036
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
Andrea Romanino, CERN Journees Neutrino France – November 27, 20037
DTDν
T
mM
mm
λM
λh
LHLHh
1
1Λ
))((Λ
X
H
L
H
Lcν cν
M
See-saw
: out Integrate cν
Andrea Romanino, CERN Journees Neutrino France – November 27, 20038
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
Andrea Romanino, CERN Journees Neutrino France – November 27, 20039
• (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
Andrea Romanino, CERN Journees Neutrino France – November 27, 200310
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
Andrea Romanino, CERN Journees Neutrino France – November 27, 200311
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
Andrea Romanino, CERN Journees Neutrino France – November 27, 200312
nscorrelatio no large 2123 mmθν
AB
θ 23tan
Hierarchy Inverse - from large A 23 νmθ
scorrection
BA
BAmν
Andrea Romanino, CERN Journees Neutrino France – November 27, 200313
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]
Andrea Romanino, CERN Journees Neutrino France – November 27, 200314
• 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
Andrea Romanino, CERN Journees Neutrino France – November 27, 200315
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
Andrea Romanino, CERN Journees Neutrino France – November 27, 200316
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
Andrea Romanino, CERN Journees Neutrino France – November 27, 200317
• 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
Andrea Romanino, CERN Journees Neutrino France – November 27, 200318
(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
Andrea Romanino, CERN Journees Neutrino France – November 27, 200319
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
Andrea Romanino, CERN Journees Neutrino France – November 27, 200320
• 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
Andrea Romanino, CERN Journees Neutrino France – November 27, 200321
Barb
ieri
, H
am
bye,
AR
eemθ , for sPrediction 13
Andrea Romanino, CERN Journees Neutrino France – November 27, 200322
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
Andrea Romanino, CERN Journees Neutrino France – November 27, 200323
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