neutrino masses from a minimum principle fileneutrino masses from a minimum principle rodrigo alonso...
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![Page 1: Neutrino masses from a minimum principle fileNeutrino masses from a minimum principle Rodrigo Alonso Nu@Fermilab, 07/23, 2015 in collaboration with B. Gavela, L. Merlo, L. Maiani,](https://reader033.vdocuments.us/reader033/viewer/2022041421/5e1f517d8fc81a17d1105bd5/html5/thumbnails/1.jpg)
Neutrino masses from a minimum principle
Rodrigo Alonso
Nu@Fermilab, 07/23, 2015in collaboration with B. Gavela, L. Merlo, L. Maiani,
D. Hernandez, G. Isidori and S. Rigolin
arXiv:1103.2915, arXiv:1306.5927 & arXiv:1306.5922
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Flavour Puzzle
why are masses so separated from one another?
eV
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Flavour Puzzle
why are masses so separated from one another?
lightness of neutrinos due to a Majorana character?
eV
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Flavour Puzzle
why is the mixing pattern so different?
![Page 5: Neutrino masses from a minimum principle fileNeutrino masses from a minimum principle Rodrigo Alonso Nu@Fermilab, 07/23, 2015 in collaboration with B. Gavela, L. Merlo, L. Maiani,](https://reader033.vdocuments.us/reader033/viewer/2022041421/5e1f517d8fc81a17d1105bd5/html5/thumbnails/5.jpg)
Flavour Puzzle
why is the mixing pattern so different?
Maybe because of the Majorana Character?
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Gauge GroupFe
rmio
ns
The Standard Theory
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Gauge GroupFe
rmio
ns
The Standard Theory
![Page 8: Neutrino masses from a minimum principle fileNeutrino masses from a minimum principle Rodrigo Alonso Nu@Fermilab, 07/23, 2015 in collaboration with B. Gavela, L. Merlo, L. Maiani,](https://reader033.vdocuments.us/reader033/viewer/2022041421/5e1f517d8fc81a17d1105bd5/html5/thumbnails/8.jpg)
Neutrino Masses: type I seesaw
Addition of a gauge singlet
with the only “bare” and Majorana mass allowed
after EWSB andfor vY<<M
R
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Leptons
Flavour Symmetry
The largest global symmetry that thefree Lagrangian can display:
that is:
[Georgi, Chivukula, 1987
D’Ambrosio, Giudice, Isidori, Strumia, 2002]
Quarks
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Leptons
Flavour Symmetry
The largest global symmetry that thefree Lagrangian can display:
that is:
Quarks
![Page 11: Neutrino masses from a minimum principle fileNeutrino masses from a minimum principle Rodrigo Alonso Nu@Fermilab, 07/23, 2015 in collaboration with B. Gavela, L. Merlo, L. Maiani,](https://reader033.vdocuments.us/reader033/viewer/2022041421/5e1f517d8fc81a17d1105bd5/html5/thumbnails/11.jpg)
Leptons
Flavour Symmetry
The largest global symmetry that thefree Lagrangian can display:
that is:
Quarks
![Page 12: Neutrino masses from a minimum principle fileNeutrino masses from a minimum principle Rodrigo Alonso Nu@Fermilab, 07/23, 2015 in collaboration with B. Gavela, L. Merlo, L. Maiani,](https://reader033.vdocuments.us/reader033/viewer/2022041421/5e1f517d8fc81a17d1105bd5/html5/thumbnails/12.jpg)
Leptons
Flavour Symmetry
The largest global symmetry that thefree Lagrangian can display:
that is:
Quarks
![Page 13: Neutrino masses from a minimum principle fileNeutrino masses from a minimum principle Rodrigo Alonso Nu@Fermilab, 07/23, 2015 in collaboration with B. Gavela, L. Merlo, L. Maiani,](https://reader033.vdocuments.us/reader033/viewer/2022041421/5e1f517d8fc81a17d1105bd5/html5/thumbnails/13.jpg)
Leptons
Flavour Symmetry
The largest global symmetry that thefree Lagrangian can display:
that is:
Quarks
![Page 14: Neutrino masses from a minimum principle fileNeutrino masses from a minimum principle Rodrigo Alonso Nu@Fermilab, 07/23, 2015 in collaboration with B. Gavela, L. Merlo, L. Maiani,](https://reader033.vdocuments.us/reader033/viewer/2022041421/5e1f517d8fc81a17d1105bd5/html5/thumbnails/14.jpg)
Flavour Symmetry Breaking
(QL)α(DR)β
H(YD)αβ
...which we assume spontaneously broken to generate the Yukawa couplings
[C. D. Froggat, H. B. NielsenBerezhiani, Rosi,Cabibbo, Maiani
Michel, Radicati ...]
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Flavour Fields
A single and therefore “bi-fundamental” field
(d=5)
(QL)α(DR)β
H(YD)αβ
...which we assume spontaneously broken to generate the Yukawa couplings
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Flavour Symmetry Breaking
To prevent Goldstone Bosons the symmetry can beGauged
[Grinstein, Redi, VilladoroGuadagnoli, Mohapatra
Feldman]
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Flavour Field’s Scalar Potential
The potential shall respect
• Gauge invariance
• Flavour invariance
This means that the potential depends oninvariant combinations of the fields: “I”
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Minimization
a variational principle fixes the vevs of the Fields
This is an homogenous linear equation;
study rank of the Jacobian ,
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Natural Breaking Patterns
[Cabibbo, Maiani,1969]
[Michel, Radicati, 1969]
The “most” natural ones are the maximal subgroups
identifies especial solutionswith unbroken symmetry
e.g. [Glashow, Georgi, 1974]
guaranteed a extremum point in any function
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Quarks
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Bi-fundamental Flavour Fieldsei
genv
alues
only
eigenvalues and mixing [Feldmann, Jung, Mannel;Jenkins, Manohar]
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Jacobian Analysis: [40 yearsago...] [Cabibbo, Maiani]Breaking of
-
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Jacobian Analysis: Mixing
the rank is reduced the most for:
VCKM= PERMUTATION
no mixing: reordering of states
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Quark Natural Flavour Pattern
a hierarchical mass spectrum without mixing
a good approximation to the observed Yukawas to order (λC)2
Summarizing, a possible and natural breaking pattern arises:
[RA, Gavela, Merlo, Rigolin]
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Leptons
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Bi-fundamental Flavour Fields
The better suited parametrization is the bi-unitary
the connection with neutrino masses being
Physical parameters=Independent Invariants
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LeptonsEig
enva
lues
only
UL and eigenvalues
UR and eigenvalues
New
Inv
aria
nts
w.r.t. Q
uar
ks
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Jacobian Analysis: Mixing
same as for VCKM
O(3) vs U(3)
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...which is now not trivial mixing...
...but maximal mixing
Jacobian Analysis: Mixing
+degeneracy and maximal Majorana phase[RA, Gavela, Hernandez, Merlo, Rigolin
RA, Gavela Isidori, Maiani]
![Page 30: Neutrino masses from a minimum principle fileNeutrino masses from a minimum principle Rodrigo Alonso Nu@Fermilab, 07/23, 2015 in collaboration with B. Gavela, L. Merlo, L. Maiani,](https://reader033.vdocuments.us/reader033/viewer/2022041421/5e1f517d8fc81a17d1105bd5/html5/thumbnails/30.jpg)
Lepton Natural Flavour Pattern
Summarizing, a possible and natural breaking pattern:
brings along hierarchical charged leptons
and (at least) two degenerate neutrinosand maximal angle and Majorana phase
θ23 =45o; Majorana Phase Pattern (1,1,i)& Mass degeneracy: mν2 = mν3
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Perturbations can produce a second large angle
if the three neutrinos are quasidegenerate, perturbations:
produce a second large angle and a perturbative one together with mass splittings
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accommodation of angles requires degenerate spectrum at reach in future neutrinoless double β exps.!
rough estimate ~0.1eV
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accommodation of angles requires degenerate spectrum at reach in future neutrinoless double β exps.!
rough estimate ~0.1eV
![Page 34: Neutrino masses from a minimum principle fileNeutrino masses from a minimum principle Rodrigo Alonso Nu@Fermilab, 07/23, 2015 in collaboration with B. Gavela, L. Merlo, L. Maiani,](https://reader033.vdocuments.us/reader033/viewer/2022041421/5e1f517d8fc81a17d1105bd5/html5/thumbnails/34.jpg)
Where do the differences in Mixing originate?
From theMAJORANA vs DIRAC nature of fermions
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Where do the differences in Mixing originate?
From theMAJORANA vs DIRAC nature of fermions
THANK YOU
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Backup
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Boundaries Exhibit Unbroken Symmetry
Extra-Dimensions Example
The smallest boundaries are extremal points of any function
[Michel, Radicati, 1969]
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Boundaries
for a reduced rank of the Jacobian,
there exists (at least) a direction in whicha variation of the field variables does
not vary the invariants
that is a Boundary of the I-manifold
[Cabibbo, Maiani,1969]