NEUTRINO MASSES

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NEUTRINO MASSES AND MIXING
ANGLES an overview
Ferruccio Feruglio PADOVA
QCD Workshop , 16-20 June 2005, Conversano
2
low-energy parameters
? masses
order
3 light active ?
i.e. 1 and 2 are, by definition, the closest
levels
2
3
1
normal hierarchy
two possibilities
inverted hierarchy
2
1
3
Mixing matrix (analogous to VCKM)
- only if ? are Majorana
- drops in oscillations
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Summary
Fogli, Lisi, Marrone, Palazzo, 0506083
? are much lighter than quarks
two lepton mixing angles are large
some parameters measured already quite precisely
quark-lepton complementarity?
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How many light ??

• 3 active neutrinos

(invisible Z width)

• (almost) all experiments explained by 3

4 independent ? sources sun, cosmic rays,
reactors and accelerators
spanning more than 12 orders of
magnitudes in L/E

• hint for a 3rd independent ?m2 from an
  accelerator ? beam (LSND)

sterile
if confirmed

• inclusion of worsens the fits

HannestadRaffelt Crotty, Lesgourgues, Pastor
2004

• WMAP LSS

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

• from now on 3 light assumed

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WHY m? ltlt mf ?
charged fermions
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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
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L is not conserved
SM fields only
Weinbergs list
?scale of new physics
p-decay still unobserved!
1st effects of new physics expected from
leading L-violating operator
smallness of due to

• experimental constraints

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

90CL
uncertainty from nuclear matrix elements
GUT scale, see-saw, leptogenesis
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• expected range of
• can be predicted from

mee (eV)
Future expected sensitivity on

CUORE 130Te (30-50) meV Majorana
76Ge (20-70) meV GERDA 76 Ge
(90-290) meV (phase II)
10 meV (phase III ?)
Lightest neutrino mass (eV)
F, Strumia, Vissani 2003 PetcovPascoli 0310003
Bilenky 0403245 Bahcall, Murayama, Pena-Garay
0403167 Joaquim 0304267
positive signal -- L violation AND degenerate
spectrum or inverted hierarchy
negative signal -- help from cosmology needed
to constrain at least the type of spectrum
next CMB satellite weak grav. lensing

improved galaxy survey
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Sources of L violation

• MSSM with R-parity violation

doesnt fit Weinberg list
not especially appealing
tree-level only 1 massive neutrino
? fine-tuned
one-loop m1,2 too small

• back to Weinberg list

not far from the GUT scale
-- ? as a window on GUT physics
-- present in many GUTs as SO(10), E6,
dim5 operator can be obtained

through the see-saw formula
-- link to baryogenesis through leptogenesis
Fukugita, Yanagida 86 CP violating,
out-of-equilibrium decay of lightest net
(converted into
by sphalerons)
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in GUTs

• gauge coupling unification

• particle classification
• electric charge quantization,
• cancellation of gauge anomalies,

common representations for quark and leptons
?
SMALL QUARK MIXING
LARGE LEPTON MIXING
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• STRETCHING

accidental constructive interference between O(?)
contributions from Ue and U?

• ANARCHY

Hall, Murayama, Weiner 2000
structureless
ordered
e.g. in SU(5)
relative suppression between Yukawas of close
generations
can be produced in part by the see-saw
accidental
fortuitous
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• LARGE MIXING BY SEE-SAW

in a basis where charged leptons are diagonal
no clear structure in the sum
separately, both II and III leads to
good starting point for
large mixing if
Examples
all mass matrices nearly diagonal! large mixing
from nothing
in SU(5) large mixing between
for instance, large ?23 mixing from large mixing
between l2 and l3
large mixing between d2c and d3c unobservable
in 1st approximation
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On a speculative ground
not a bad 1st order approximation! Harrison,
Perkins and Scott
mixing matrix
reminiscent of
in some symmetry limit?
under general conditions, they can never arise in
the limit of exact symmetry
determined entirely by breaking
effects (different, in general, for ? and e
sectors)
Altarelli, F. 0504165
vacuum alignment problem should have specific
magnitudes and relative directions in flavour
space.
if symmetry breaking is spontaneous
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example only lepton sector Altarelli, F.
0504165
controls charged lepton mass hierarchies
flavour symmetry
Ma, Rajasekaran 2001 Babu, Ma, Valle
2003 Hirsch, Romao, Skandage, Valle, Villanova
de Moral 2003 Ma 0409075
group of even permutations of four objects

3 1 1 1 3 3 1 0
higher orders in
expected
alignment is natural and it is not spoiled by
higher dim operators
prediction
? spectrum is between normal and degenerate
units
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SUMMARY

• Experimental side
  entered a precision era
• 
  reasonably well-known
• 
  still missing!

• several key points still unknown - how many
  light neutrinos?
• 
  - is L violated or not?

• theory of neutrino (and fermion) masses is still
  in its infancy

• light neutrino masses are naturally explained by
  L violation
• at a large scale, possibly close to GUT scale
• several common mechanisms that
  accommodate small quark mixing angles
• and large lepton mixing angles in GUTs are
  available

• If future date will require very small
• some special mechanism is expected both
  to enforce the 1st order
• approximation and to protect it from higher
  order corrections