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Recent developments in Neutrino Physics

Davide Meloni Dipartimento di Matematica e Fisica and INFN RomaTre
QFTHEP2015 Samara


Plan



Oscillation sector


Standard 3-neutrino oscillation Anomalies in neutrino data

Flavor sector



Problem of neutrino masses and mixings: the role of family symmetries

D.Meloni


Introduction


New data from neutrino oscillation experiments have given precise results on mixing parameters Possible leptonic CP violation (<=5 y) (T2K, NoVA...)





However: not a unique extension of the Standard Model that allows to explain: - origin of masses and mixing angles - differences with respect to the quark sector
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3- state formalism
Neutrinos can be described in terms of mass or weak eigenstates



=


3 i=1

U

i



i



neutrino matrix matrix

Simple time evolutions of the vector (t)= (e(t),(t),(t)):

d i ( t ) = H ( t ) dt

1 2 2 2 2 H= U Diag [ 0, m2 -m1 , m3 - m1 ] U 2 E
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+

there exist a probability of a change of the neutrino flavour


Theory of neutrino oscillation


Flavour changing transitions

P ( ) = ( t ) = j U j e
= disappearance != appearance


2



-i m j L 2 E

2

U

j



2

In the case of two neutrinos only:

m L P ( e )= sin 2 sin 4 E
2 2

(

2

)
)

distance sourcedetector

mixing angle
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U = cos sin -sin cos

(

U = unitary matrix


Theory of neutrino oscillation


The neutrino mixing matrix depends on 4 real parameters

U

PMNS

1 0 = 0 c23 0 -s 2

(


3

c 13 0 s 23 в 0 - c 23 -s 13 e

)(


reactor mixing

i

0 1 0

s13 e 0 c 13

i

)(

c12 s 12 0 в -s 12 c 12 0 0 0 1
solar mixing

)

atmospheric mixing



A more complicated mismatch between the bases

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Experiments measure...
Mixing angles Mass differences

m3

23 13 1
2

m223 m2 m1 m2
12



unknowns: leptonic CP violationand the ordering of the mass eigenstates
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Global fit
Gonzalez-Garcia et al. JHEP1212,(2012)123

Parameter sign? octant? m
2 23 12 12 13

Result 33.36 8.66
+0.81 -0.78 -0.46 -1.5 +0.44

23

40.0 300 2.47

+2-1

(10-3 eV2) (10-5 eV2)

+66

-138 -0.07 -0.19

+0.07 +0.18

m

2

7.50



Masses @3% Angles between 5% and 10%

CP?
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Global fit
Gonzalez-Garcia et al. JHEP1212,(2012)123

Parameter sign? octant? m
2 23 12 12 13

Result 33.36 8.66
+0.81 -0.78 -0.46 -1.5 +0.44

23

40.0 300 2.47

+2-1

(10-3 eV2) (10-5 eV2)

+66

-138 -0.07 -0.19

+0.07 +0.18

m

2

7.50

CP?
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Neutrino oscillation anomalies


LSND evidence for oscillations -> e with L/E~ 1 km/GeV (e appearance)



Anomalies in Gallium experiments (SAGE & GALLEX)
they measured an electron neutrino flux from the Sun smaller than expected

(e disappearance)


Anomalies due to new computations of reactor neutrino fluxes
fluxes from reactor neutrinos are ~ 3.5% larger than in the past experiments with L<= 100 m show deficit of neutrinos (e disappearanceBugey, Rovno...

)

In addition there are null results: disappearance (CDHS,SK, MINOS) e e appearance (KARMEN, NOMAD, ICARUS, OPERA) which gave no signal
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Neutrino oscillation anomalies

Joachim Kopp August 21, Aspen



LSND evidence for oscillations e-> con L/E~ 1 km/GeV

m6 m5 m4 m3 m2 m1

m m m m

2 45 2 34 2 23 2 12



MiniBooNE no significative excess of e o e in the LSND preferred region but antinu results consistent with LSND
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explanation in terms of sterile neutrinos


3+1 scheme
m4
These states are considered as "degenearate"
m m m
2 34

m4 is at a much higher scale, around 1 eV2: effective description in terms of two-flavor

m2 m1

m3

2 23 2 12

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e appearance
Global fit of nue appearance data are consistent

Kopp, Machado, Maltoni, Schwetz2013

sin2 2e = 0.013 m
2 2

41

= 0.42 eV

2

min

/dof =87.9/66

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e disappearance
Global fit on nue disappearance data are consistent among themselves


Kopp, Machado, Maltoni, Schwetz2013

sin2 2ee = 0.09 m
2 2

41

= 1.78 eV

2

min/do

f =403/427

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disappearance


Global fit on numu disappearance data:

Kopp, Machado, Maltoni, Schwetz2013

no signal strong constraints on masses and mixing

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Global picture
Tension between appearance and disappearance Tension between exp's with and without signal

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The (hard) job of a theorist
Take hints from experiments seriously And explain: Smallnesssoofmaasses Smallne s f m sses

Valueesooftthe Valu s f he mixinngaangles mixi g ngles
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Some ideas...


On the masses

Easy part: neutrino Yukawa couplings smaller than those of the other fermions Neutrinos are Dirac fermions: we have to introduce a right-handed neutrino field neutrinos: Y L H Ї

~

R

electrons: Y e L H e Ї

c

Y -5 10 Ye
But we want to go beyond this "unnatural" scheme...
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Neutrino mass terms
we assume the existence of L and the SM singlet R


Dirac mass term

(same for quarks and leptons)

must be conserved: Weak isospin I I3 R 0 0 Lepton number 1

I =0
H = (h+,h0) 1/2 (+1/2,-1/2) -1
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lepton number L is conserved

L D = mD L H

R

L

1/2 1/2



Majorana mass term

lepton number L is not conserved

L M = mM

T R

R


The see-saw mechanism


Total lagrangian

~ T Ї L m= m D L H R + m M R
Electroweak symmetry breaking see-saw

R

H = 0 v

()



m =

(

0 m
T D

m m

D

M

)

1 m = - m m mM
T D
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D


The see-saw mechanism


An indicative numerical example

m ~ mD2/mM
for mD~100 GeV, m ~ 0.05 eV

mM ~ 1014-10

15

GeV

Probe into GUT !
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Mixing angles
Two different approaches and equally (not?) promising


Models with non-trivial dynamics: means that the structure of the mixing matrix is determined by discrete symmetries such symmetries are motivated by the fact that the data themselves suggest rotations with fixed special angles (Ѕ, 1/3...) - permutational groups like A4, S4 ...



Models where the main idea is that there is no need of introducing additional symmetries to explain the mixing angles In such models, the chance plays the fundamental role (anarchical models and variants)
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Special mixing matrices


mixing angles are obtained from the diagonalization of the mass matrix

m


Diag

=U m U
Tri-Bimaximal Mixing
2

T

Good starting point suggested by the data:

1 sin 12= 3 1 sin 23= 2
2

( TBM )
Bimaximal Mixing

sin 13= 0

2

1 sin 12= 2
2 2

( BM )
Golden Ratio

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2 sin 12= 5 + 5

( GR )


Special mixing matrices


How good are such starting points ?

sin 12

2

c = Cabibbo angle

sin

13

Corrections are needed to stay on the experimental data
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Special mixing matrices


in models with no baroque dynamics, all mixing angles receive corrections of the same order of magnitude TBM

1 1 2 2 2 sin 12= + O ( C ) sin 23 = + O ( 2 ) sin 13=O ( C ) C 3 2
2

ok

ok

not really good

BM

1 1 2 sin 12= + O ( C ) sin 23 = + O ( C ) sin 13=O ( C ) 2 2
2

ok
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ok

ok

This pattern seems to be favored


Special mixing matrices
Possible origin of corrections


UPM

NS

receives contributions from the charged lepton diagonalization

=U
diagonalizes the neutrino mass matrix

i

i

l =U l

l i i

diagonalizes the charged lepton mass matrix


lЇ W
Charged current

U i U
U
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PMNS

+l

j

Їi j W l




Additional symmetries


The previous patterns are easily obtained using flavor symmetries

- gauge symmetries act on members of particle multiplets - flavor symmetries act on different families

Vantages: strong correlation among the entries of the mass matrices, so less free parameters predictability
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Additional symmetries at work


The models work as follows:

Altarelli-Feruglio2012

Theory invariant under GF
Flavor group


Symmetry breaking of the flavor group: new scalar fields in the theory with non vanishing vevs

Residual symmetry given by a subset of the generators of GF in the neutrino sector G U
l

in the charged lepton sector Gl U

U

PMNS

= U l+ U



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A possible flavor group: A4
A4 : is the group of even permutation of 4 objects (also the symmetry of a tetrahedron) generators of the group

The 12 elements are obtained considering all possible even permutations of given a of G , { g-1 a g , g G 1234. They belong to 4 conjugacy classes... A4 has 4 irreducible representations - three singlets 1, 1' and 1'' - 1 triplet 3
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}


A possible flavor group: A4
After breaking of A


4

charged lepton mass matrix (residual symmetry generated by T)

Ul = I


neutrino mass matrix (generated by a non-diagonal generator S of A4)

U=
sin 23 =
2

1 2

sin 12 =
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2

1 3

sin 13= 0

2


A possible flavor group: A4
After breaking of T and S


Charged lepton rotation



neutrino rotation

O ( 0.1)
Altarelli, Feruglio, Merlo, Stamou `12

from charged lepton rotation

from neutrino rotation
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Typical predictions of A4 models
cij = random complex with abs. value gaussian around 1 with variance 0.5
Altarelli, Feruglio, Merlo, Stamou `12

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Models with no special dynamics


The chance is the basis of the success Only abelian U(1) to generate the hierarchies among fermions
iq



- fields tranform as: e




i (- q + q + qH )
R L

- so a mass term transforms as:

Ї y L H R e

Ї y L H

R

If (-q + q + q H )= 0 the mass term is allowed, otherwise we need R L a new scalar field with charge qand vev v:

y L H

R

(

e )

k

i (- q + q + q H + k q)
R L

y

()

v L H R
Suppression factor

k

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A GUT example


Standard Model particles in the 10 and 5 representations (3 copies)

1 = right-handed neutrino



SU(5) mass terms:

mup10в10 md =mT 10 в Ї 5 e Ї m 5в 1
D

m M 1в1
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Models with no special dynamics
Choosing appropriate U(1) charges we can get several mass matrices structures:


Anarchycal models (A)
q Ї=( 0,0,0 ) 5 q 10=( 3,2,0 ) q 1=( 0,0,0 )

m l = 2 2 2 , 111

(

3

3

3

)

111 m = 1 1 1 111

()
4 3 2



Hierachycal model (H)
q Ї=( 2,1,0 ) 5 q 10=( 5,3,0 ) q 1=( 2,1,0 )

ml =

(

7 5 2

4 3 , 1
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6

5

)

m =

(

2 1

3

2

)


Models with no special dynamics
no see-saw see-saw

= m12/m

23

= m12/m

23

message: H performs better than A
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The future (personal view)



Oscillation sector


Better determination of the oscillation parameters and the mass pattern Check for new physics effects



Flavor sector


Interplay of flavor symmetries and realistic GUT theories Differences among quarks and leptons
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backup

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Global fit

Egidio Lisi, talk a Moriond2015

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New results from Planck
For T < me , radiation content of the Univers is
Ninetta Saviano, talk a Moriond2015

non-elettromagnetic contribution is parametrized in terms of effective neutrino species Neff

3.046
(relativistic degrees of freedom)

Extra radiation, for example from sterile neutrinos

Planck 2015:

Neff = 3.15 ± 0.46
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Not a large room for sterile states!


A peculiarity of the neutrino


For electrons: 4 different helicity states and all of them are needed
spin moving faster: the boosted observer see a RH object charge is conserved spin

e-

p

e-

p

left-handed particle: eL


-

right-handed particle: eR

-

For neutrinos: from experiments we have identified nL and nR only
moving faster: we see again a RH object left-handed particle:

R R

Dirac particle

L

Majorana particle

if L ~R no additive quantum numbers are conserved
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A4
(4!/2 = 12 elements) generated by S and T

take this as an example

A4 is the discrete group of even permutations of 4 objects S2=T3=(ST)3=1

The action of the generators S and T can be assigned as follows: S: (1234) (4321) T:(1234) (2314) irreducible representations: a triplet and 3 different singlets 3, 1, 1', 1" (promising for 3 generations) invariance under S and T is automatic while A
VEV's)
23

is not contained in A

4

(2-3 symmetry happens in A4 if 1' and 1" symm. breaking flavons are absent or have equal
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A comment on the CP violating phase

Egidio Lisi, Moriond2015



Long Baseline experiments (T2K) indicates ~ 3/2



Reactor experiments model the CL form for sin213 ~ 0.02

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Appearance-disappearance tension

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