of neutrino mass
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A. Yu. Smirnov
Max-Planck Institute for Nuclear Physics, Heidelberg, Germany
NOW 2014 September 8– 13, 2014
strongly suppresses
There is something hidden and beyond the standards which
badly confuses and mixes violates the law
or maybe, does not violate the
law which is difficult to prove
and probably the first and the second are because of the third
1. Smallness of neutrino mass in comparison to masses of the charged leptons and quarks
what is behind of
2. “Unusual” lepton mixing pattern with two large mixing angles (one is close to maximal) and one small which differs from the quark mixing3. Weaker (or no) mass hierarchy than the hierarchy of charged leptons and quarks
In general, what is the type of mass spectrum and mass ordering?
New
physics?
are they of Dirac or Majorana type?
are they “hard” or “soft” (medium dependent)?
Does the nature of neutrino mass differ from the nature of the quarks and charged lepton masses?
Are sterile neutrinos (if exist) relevant for the solution ?
Nature of neutrino mass
Recall that in oscillation experiments we probe dispersion relations and not masses immediately Effective neutrino masses in oscillation experiments in beta decay in cosmology and bb-decay can be different
Usual neutrino masses can be strongly suppressed, e.g. by the seesaw, so that ”unusual contributions” dominate
are we asking right questions?
do we interpret the data correctly?
It is not excluded that the correct solution (or the key to the solution) already exists among hundreds of approaches, models, mechanisms, schemes, etc.
The problem is
then to identify the
correct solution
Still something fundamental can be missed
Special
m3 mt
~ 3 10-
11
Normal? Neutrinos: no clear generation structure as well as the correspondence light flavor – light mass, especially if the mass hierarchy is inverted or spectrum is quasi-degenerate
m3 me
~ 3 10-
6
me mt
~ 3 10-6
106
Similar for other generations if spectrum is hierarchical
103 101210910-3 100
mass, eV
gap
comparing within generation:
?due to neutrality of neutrinos?
The riddle is formulated as comparison with masses (and mixing) of quarksThere is no solution of the riddle of quark
masses
Yes, if
Can we solve the neutrino mass riddle?Do efforts make sense?
neutrino mass generation and generation of the charged lepton and quark masses are independent we will try to explain
the difference of masses and mixing of neutrinos and quarks, and not masses and mixing completely
we still hope (as it was before) that neutrinos will uncover something simple and insightful which will allow to solve the quark mass riddle
Higgs triplet Radiative mechanismsSeesaw type III, etc.
Should mixing be included in the riddle?
QuarksRelation between masses and mixing md
ms
sinqC ~
LeptonsMaximal mixing - quasi-
degenerate mass states ?
Tri-Bi-Maximal mixing (TBM)
no connection between masses and mixing (at least in the lowest order)
Realized in the residual symmetry approach
In 3 generations: Fritzsch ansatz
Form invariance of the mass matrices
Completelyrelated
Partiallyrelated
Largely unrelated
Higgs triplet
Radiative mechanisms
Seesaw type II and III
Seesaw type I, Quark-lepton unification
with the only difference that originates from Majorana nature of neutrinos, symmetries
GUT, seesaw type II
Dark MatterRiddle
Dark EnergyRiddle
Neutrino massriddle
Solution may come
from unexpected
side
Dark radiation
Baryon asymmetry in the UniverseInflation
The riddle of new physics
additional structures in lepton sector such as the see – saw
responsible for small quark mixing and hierarchical structure of the Dirac masses
common for quarks and leptons
responsible forsmallness of neutrino mass and large lepton mixing
These two types are different but probably should somehow “know” about each other
A guess
Counter example, seesaw with degenerate RH neutrinos does not work in this framework
High scale seesawQuark- lepton symmetry /analogyGUT
Low scale seesaw, radiative mechanisms, RPV, high dimensionaloperators
Scale of neutrino masses themselves Relation to dark energy, MAVAN?
VEW2
mn
Uni
ficat
ion
Looking under the lamp
Neutrino mass itself is the fundamental scale of new physics
28 orders of
magnitude
Spurious scale?
mn = - mDT mD 1MR
MGUT2
MPl
for the heaviest in the presence of mixingMGUT ~ 1016 GeV
Leptogenesis
N ~ 102
many heavy singlets (RH neutrinos)…string theory
q – l similarity: mD ~ mq ~ ml
MR ~ 108 - 1014 GeV
double seesaw
1016 - 1017 GeV
Gauge coupling unification
BICEP-II ?
In favor
Natural, minimalistic, in principles
Realizes relations:
Neutrality,
zero charges Majorana
Nature Smallness of
mass – high
mass scale Large mixing
Testable? - Proton decay- Majorana masses
Fine tuning
“Neutrinoful Universe” Seesaw sector is responsible for inflation (scalar which breaks B-L and gives masses of RH neutrinos), dark matter, leptogenesis
T. Higaki et al, arViv:1405.0013
Partial relation of the quark and neutrino properties
<< MPl
New physics below Planck scale
dmH2 ~ MR
2 log (q /MR)
HH
nL
nR
“Partial” SUSY?
Simplest seesaw implies new physical scale
MR ~ mD2
/mn ~ 1014 GeV
nR
F. Vissanihep-phl9709409
(Another indication: unification of gauge couplings)
y2 (2 p )2
~ log (q /MR)MR
3 mn
(2 p v)2
J Elias-Miro et al, 1112.3022 [hep-ph]
MR < 107 GeVSmall Yukawas,Leptogenesis ?
Cancellation?M. Fabbrichesi
AYS
Neutralino as RH neutrino
Rp-SUSY
L-RnMSM
- No hierarchy problem (even without SUSY) - testable at LHC, new particles at 0.1 – few TeV scale- LNV decays
Higgs Triplet
New Higgs
doublets
0ne loopTwo loops
Three loops
Low scale
Inverseseesaw Connection
to Dark Matter
High dimensional operators
L R
NormalMass hierarchy
3 - 10 kev - warm dark matter - radiative decays 3.5 kev line
Few 100 MeV – GeV
- generate light mass of neutrinos- generate via oscillations lepton asymmetry in the Universe- can be produced in B-decays (BR ~ 10-10 )
split ~ eV
M. Shaposhnikov et al
BAU
WDM
Everything below EW scale small Yukawa couplings
EW seesaw Higgs inflation
Nothing new below Planck scale
RH neutrino?
very small split
very small mixing
Maybe related to Dark energy, MAVAN
Very light sector which may include
eV scale Seesaw with RH neutrinos for sterile anomalies LSND/ MiniBooNE ....
- new scalar bosons, majorons, axions, - new fermions (sterile neutrinos, baryonic nu) , - new gauge bosons (e.g. Dark photons)
A. De Gouvea
Tests: 5th force searches experimentsModification of dynamics of neutrino oscillationsChecks of standard oscillation formulas,searches for deviations
Generate finite neutrino masses, usual Dirac masses can be suppressed by seesaw with MR = MPl or multi singlet mechanism
M. Pospelov
H. Minakata, A Y S
From charged leptons or Dirac matrices of charged leptons and neutrinos
Related to mechanism of neutrino mass generation
UPMNS = VCKM
+ UX C. Giunti, M. Tanimoto
CKM type new physics
New neutrino structure
In a spirit two types of new physics and partial relations
In general, has similar hierarchical structure determined (as in Wolfenstein parametrization) by powers of
Related to (any) mechanism that explains smallness of neutrino mass Should be fixed to reproduce correct Lepton mixing angles VCKM ~ I UX ~ UTBM
l = sin qC
H. Minakata, A Y S……………………………….
Realized in QLC (Quark-Lepton Complementarity)
U12 (qc) U23(p/2)
q13~ ½ qc
permutation - to reduce the lepton mixing matrix to the standard form leads to
UPMNS = VCKM
+ UX
e.g. UX = UBM, UTBM
C. Giunti, M. Tanimoto
Pheno. level
UX = U23(p/2) U12
sin 2q13~ ½sin2qC
can be obtained in the context of
if
TBM-Cabibbo schemeS. F. King et al
q13 ~ ½ qc
``Naturalness’’ , absence of fine tuning of mass matrix
Dm212
Dm322
O(1)
sin2q13
~ ½sin2qC
Quark-Lepton ComplementarityGUT, family symmetry, …
~ ½cos2 2q23universal nm - nt – symmetry violation
The same value with completely different implications
Mixing anarchy
> 0.025
¼ sin2q12sin2q23
Analogy with quark mixing relation
q13 = 21/2( /4p - q23)
Eby,Frampton, Matsuzaki
relation implications
?
B. Dasgupta, A.S.
UPMNS ~ VCKM
+ UX
If the only source of CP violation
No CPV
sinq13 sin dCP = (-cos q23) sinq13q
sindqsin dCP ~ l3/s13 ~ l2
~ 0.046
dq = 1.2 +/- 0.08 rad
dCP ~ - d or p + d
where d = (s13q /s13) c23
sin dq
New sources may have specific symmetries or structures which lead to particular values of dCP e.g. -p /2, and q - l unification will give just small corrections
l3l
If the phase dCP deviates substantially from 0 or p, new sources of CPV beyond CKM should exists (e.g. from the RH sector) or another framework
sin dCP = s13-1 [sin(am + dX)Vud|Xe3| – sin ae |Vcd|Xm3
]
neglecting terms of the order ~ l3
here am , dX and ae are parameters of the RH neutrinos
if Xe3 = 0 we have
sin dCP ~ – sin ae
if ae = p /2
Some special values of dCP can be obtained under certain assumptions
dCP ~ 3p/2
One can find structure of the RH sector which lead to these conditions
B Dasgupta A.S
MX = - mDdiag
UR+ (MR)-1 UR
* mDdiag
Ux is the matrix diagonalizes
mD = UL (mD
diag) UR
+
Here
Minimal extension is the L- R symmetry:
UR = UL ~ VCKM
* and no CPV in MR
Seesaw can enhance this small CPV effect so that resulting phase in PMNS is large
In contrast to quarks for Majorana neutrinos the RH rotation that diagonalizes mD becomes relevant and contributes to PMNS
mDn ~
mDq
UX = UR
US In the LR symmetric basis
From seesaw
Normal mass hierarhy, relation between masses and mixing Flavor alignment in mass matrix
Similar structure of mass matrices but with different expansion parameter
sinq13 ~ ½ sinq12
sinq23
The same relations between coupling strength between generations
Vub = ½ Vus Vcb
Fritzsch Anzatz similar to quark sector, RH neutrinos with equal masses
A guess
ll = 1 - lq
Realization:
Expectations:
(2 – 4) 10-3 eV
0.5 - 2 eV
5 - 10 keV- Warm Dark matter- Pulsar kick
- Solar neutrinos- Extra radiation in the Universe
- LSND, MB- Reactor Ga anomalies - Extra radiation
ns
1 eV
1 keV
1 MeV
10-3 eV
mixing
dm ~ qaS2
mS
(1 – 2) 10-8 eV2 10-11
10-6 eV
qaS2
0.02 0.02 eV
10-3
Compare with large elements of the mass matrix 0.02 eV
mn = ma + dm
Original active mass matrix e.g. from see-saw
dm can change structure (symmetries) of the original mass matrix completely
Induced mass matrix due to mixing with nu sterile
UPMNS
be origin of difference of VCKM
and
on the 3n structure
For keV
ma = 0.025 eV
dm << ma
Decouples from generation of the light neutrino masses argument that this is not RH neutrino but has some other origin
For eV dm ~ ma Not a small perturbation
For meV dm << ma can be be considered as very small perturbation of the 3n system
L H F
where F is the fermionic operator
nL nR
S
S
S
H
nR
is the key to the solution of the riddle?
New structure (but physics is the same) 1
Ln(F) - 3/2
Neutrino new physics
Through this portal neutrino gets mass
S
S
S
Ss
s
ss
Scalesymmetries
Two different types of new physics are involved in explanation of data: the CKM type common to quarks and leptons and physics responsible for smallness of neutrino mass and large lepton mixing. The latter may have certain symmetries
It makes sense to identify the second one which explains the difference between the quarks and leptons
Still generation of quark and neutrino masses can be essentially independent
High (GUT) scale new physics: still appealingEW scale: see LHC14 resultsSub eV –eV scale: interesting, worth to explore
New neutrino physics may have certain symmetries which leads to specific values of mixing angles and CP phase. Phase from CKM part is strongly suppressed
Sterile neutrinos may be the key to solution to a riddle
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