THEORY OF ABSOLUTE

1

THEORY OF ABSOLUTE NEUTRINO MASSES
Ferruccio Feruglio
NOW 2004 Conca Specchiulla September
11-18 2004

• How many light neutrinos ?
• Why ?
• Which spectrum is favoured by theory ?
• Which is the most probable range of ?
• Is maximal?

charged fermion
2
PREMISE
it does not exist! Neither for neutrinos nor for
charged fermions. We lack a unifying principle.
theory of neutrino masses
like weak interactions before the electroweak
theory
all fermion-gauge boson interactions in terms of
2 parameters g and g
gauge invariance
Yukawa interactions between fermions and spin 0
particles many free parameters (up to 22 in the
SM!)
?
neutrino masses a survey of present
theoretical
ideas and prejudices
Warning several prejudices might turn out to be
wrong!
3
HOW MANY LIGHT ? ?
4

• 3 active neutrinos

(invisible Z width)

• all experiments but LSND explained by 3
• LSND 3 at least 1

• inclusion of worsens the fits

• solar
• atm favoured over
• - zenith angle dependence of
  high-energy SK,MACRO 3?
• (no matter effects for )
• - no NC interactions for
  SK
• - ?-like CC events SK 2?
• 22 and 31 fits have a poor quality

BahcallPena-Garay 2003
Cirelli,Marandella,Strumia,Vissani 2004

• WMAP LSS

HannestadRaffelt 2004 Crotty, Lesgourgues,
Pastor 2004

• from now on 3 light assumed

• LSND soon checked by MiniBooNE (1st event
  September 2002)
• no room for LSND with 3 (CPT
  violation disfavoured by now)

PakvasaValle 0301061
5
WHY m? ltlt mf ?
charged fermions
6
L is exactly conserved

• requires

smallest ratio is 1/100 for charged fermions in
same gen.

• theoretical prejudices
• - global symmetries are broken by quantum
  gravity
• - B/L violated in all attempts to unify
  fundamental interactions
• - B/L broken by anomalies already in the SM

Dienes, Dudas, Gherghetta, Arkani-Hamed,Dimopoulo
s, Dvali, March-Russell, Barbieri, Creminelli,
Strumia

• Interesting attempts in models with extra
  dimensions

large ED standard Yukawa couplings to a singlet
fermion who lives in the bulk
no experimental hints from oscillations
effects subdominant, if present dimension 5,
L-violating operators not sufficiently suppressed
by
alternative models warped compactifications, L
gauged in the bulk, not fully realistic in their
minimal realization
GrossmanNeubert99 Gherghetta 0312392
7
L is not conserved
leading L-violating operator
smallness of due to
GUT scale, see-saw, leptogenesis
Buchmuller, Di Bari, Plumacher 0406014 Akhmedov,
Frigerio, Smirnov 0305322

• experimental constraints

• oscillations are insensitive to L violation
• L violation can be tested in 0??? decay

90CL
uncertainty from nuclear matrix elements
future foreseen sensitivity on 10
meV

• expected range of can be predicted from

8
Normal Hierarchy
Inverted Hierarchy
F., Strumia, Vissani
PetcovPascoli 0310003 Bilenky 0403245 Bahcall,
Murayama, Pena-Garay 0403167 Joaquim
0304267 Abada, Bhattacharyya 0304159
90 CL
0.9
4.1
meV
meV
14
53
Degenerate spectrum
h0.6-2.8 uncertainty in nuclear matrix el.
mee (eV)
90 CL
0.9 h eV
m?
Lightest neutrino mass (eV)
9
ABSOLUTE SPECTRUM
10
Degenerate spectrum

• Converging evidence that this is only possible
  below the eV scale

tritium ?-decay
0??? decay
WMAP LSS depending on priors
leptogenesis from out-of-equilibrium
CP-violating decay of heavy prefers
not an absolute bound 1eV is still possible
if ? are degenerate
Buchmuller, Di Bari, Plumacher 0401240 Giudice,
Notari, Raidal, Riotto, Strumia 2003
Hambye, Lin, Notari, Papucci, Strumia 0312203

• Hints for ?

0??? of 76Ge
HM by Klapdor-K. et al. 2004

• Problems with models of degenerate neutrinos

• see-saw relation untenable
• fine-tuning between M and D sectors

connection with charged fermion masses (e.g. from
GUTs) is lost
11

• can be understood in some
  symmetry limit (e.g. )
• where angles and (mass)2 differences are
  completely undetermined

arise from symmetry breaking terms that require a
special misalignment between charged leptons and
neutrinos
specific realizations already ruled out or
strongly disfavoured, e.g. Flavour
Democracy Fritzsch, Xing
no general consensus on how to realize this

• to avoid a full-fledged theory of breaking
  terms, we can assume
• anarchy in the neutrino sector

Hall, Murayama, Weiner 2000 De Gouvea, Murayama
0301050
can be produced in part by the see-saw
accidental
fortuitous
12
Inverse Hierarchy

• the best we have, at present

corrections ltlt a, b
- leading order determined by either with or
without see-saw
- compatible with GUT

• leading order

its out by 6?
adjustable to maximal for ba
good!

• turning SB terms on

• difficulty common to many models
• Flavour Democracy (deg. spectrum)
• pseudoDirac structure in 12 sector

exception normal hierarchy
off by a factor gt 10
13

• substantial contribution to from
  charged leptons needed

standard parametrization
can be absorbed in to give
by expanding to 1st order in
Frampton, Petcov, Rodejohann 0401206 Altarelli,
F, Masina 0402155 Romanino 0402508
if, by analogy with the quark sector
1.4
0.25
0.1

excluded by tan2?12lt0.3
excluded by tan2?12gt0.64
Raidal 0404046 Minakata, Smirnov 0405088
right amount

0.05
0
0
1
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Normal Hierarchy

• Several viable mechanisms for large

GUT quark mixing

• and small
• but

O.K.
O.K.

• see-saw dominance of light
• equally coupled to and

O.K.
O.K.
King
large RH quark mixing in SU(5)

• lopsided structure of
• or/and

O.K.
Albright, Barr Altarelli, F
entries up to O(1) coefficients

• typical texture as e.g. from U(1) flavour
  symmetry

vanishes in the symmetry limit

• accidentally (semi-anarchySA)
• by a see-saw suppression as in

15
Ue3
16

• No reason why Ue3 should be tiny in realistic
  models

tiny below
double CHOOZ
JPARK-SK NuMI
?-factory
MINOS OPERA ICARUS
Present bound
NOW 04
10 yr
gtgt 10 yr
17

• inverse hierarchy from
• barring cancellations

• normal hierarchy 1st order in
  

?-dominated
if we make a similar estimate in the quark
sector
e-dominated
De Gouvea 041220
estimates by allowing 3? exp. and ( factors ½
and 2) th. uncertainties

• degenerate spectrum (examples)

- and determined by RGE
- Flavour Democracy
- Anarchy
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Ue3 in models with U(1) flavour symmetry
SS
SS
SS
NoSS
? optimised case by case to fit
Isabella Masina
inverse hierarchyIH
anarchyA
semianarchySA
normal hierarchyH
matrix elements up to unknown O(1) coeff.
19
Outcome of the optimisation procedure
by generating random, O(1), complex coefficients
and by counting the success rate in reproducing
NoSS
See-Saw
120
H
80
SA
SA
40
IH
IH
A
IH
IH
H
A
? 1 0.2 0.25 0.25
1 0.25 0.12 0.2 0.45 0.25
Altarelli,F,Masina 2003

• some amount of order is clearly preferred over
  structure-less mass matrices

• an expansion parameter close to
  is needed to account for
• the smallness of and .

20
Special models with Ue3ltlt ?2
to 1st order in
both and
required
example Z2 symmetry
however

• in realistic models the symmetry
• is broken by O(1) effects to account for
• not easy to accommodate
• at the same time

back to previous estimates Grimus,Joshipura,Kanek
o,Lavoura, Sawanaka,Tanimoto 0408123 Mohapatra
0408187
Alternatively Ue3ltlt ?2 due to compensation
between O(1) terms
example ad hoc model where all mixing from
charged lepton sector Altarelli, F, Masina
0402155
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• Most of plausible range for Ue3 explored in 10
  yr from now

double CHOOZ
JPARK-SK NuMI
?-factory
MINOS OPERA ICARUS
Present bound
NOW 04
10 yr
gtgt 10 yr
Ue3 in the range 0.05-0.23 would not favour a
particular model and/or a type of spectrum
Ue3lt0.05 would select a very narrow (not
empty) subset of existing models
similar conclusion by Barbieri, Hambye, Romanino
0302118 Ibarra, Ross 0307051 Chen, Mahanthappa
0305088 Lebed, Martin 0312219 Joshipura _at_ NOON
2004
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Lepton Flavour Violation
Lavignac, Masina, Savoy
in most of the plane up to at
mSUGRA, universal b.c. at ?
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?23 ?/4 ?
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reduction by a factor of 2 probably only by
superbeams
present 3? range
in 10 yr from now
in some symmetry limit?
of great help in our search for a unifying
principle
If breaking effects are small,
can never arise in a symmetry limit
charged lepton mass matrix
symmetry breaking effects vanishing when flavour
symmetry F is exact
symmetric limit
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ml0 has rank 1
undetermined
true for most of realistic flavour symmetries
me , m? from small symmetry breaking terms
both ml and m? modified by breaking terms
arise from a conspiracy
vacuum alignment problem
example SO(3)
several models exist based on non-abelian flavour
symmetries like SU(3) SO(3) or discrete subgroups
possible, but large O(1) symmetry breaking
effects are needed to explain why
ml0 has rank 2
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CONCLUSION

• small ? masses L at a scale ?
• absolute spectrum
• though an open experimental question,
  theoretically welcome
• (but not experimentally unavoidable) properties
  like GUTs, see-saw and
• relationship with other fermion masses favour a
  hierarchical spectrum,
• with normal hierarchy less constrained than the
  inverse one
• by current knowledge of and
• Ue3 not un-measurably small in most of models.
• - Even though the hierarchies among observable
  quantities
• are less pronounced than in the quark sector,
• an expansion parameter close to
  largely
• helps in reproducing the relative smallness of
  and
• ?23?/4 if confirmed by NOW 2014, is an
  interesting theoretical
• challenge, which would strongly constrain the
  theoretical framework.