low-energy neutrino physics belén gavela universidad autónoma de madrid and ift
Post on 20-Dec-2015
219 views
TRANSCRIPT
![Page 1: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/1.jpg)
Low-energy neutrino physics
Belén GavelaUniversidad Autónoma de Madrid and IFT
![Page 2: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/2.jpg)
Low-energy neutrino physics
Belén GavelaUniversidad Autónoma de Madrid and IFT
and leptogenesis
![Page 3: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/3.jpg)
What are the main physics goals in physics?
• To determine the absolute scale of masses
• To determine whether they are Dirac or Majorana
* To discover Leptonic CP-violation in neutrino oscillations
![Page 4: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/4.jpg)
What are the main physics goals in physics?
• To determine the absolute scale of masses
• To determine whether they are Dirac or Majorana
* To discover Leptonic CP-violation in neutrino oscillations
What is the relation of those putative discoveries to the matter-antimatter asymmetry of the universe?
Can leptogenesis be “proved”?
![Page 5: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/5.jpg)
The short, and rather accurate answer, is NO
Nevertheless, a positive discovery of both 2 last points, that is:
• To establish the Majorana character (neutrinoless decay)
• Leptonic CP-violation in neutrino oscillations
(at -e oscillations at superbeams, betabeams…. neutrino factory)
would constitute a very compelling argument in favour of leptogenesis
plus
![Page 6: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/6.jpg)
The short, and rather accurate answer, is NO
Nevertheless, a positive discovery of both 2 last points, that is:
• To establish the Majorana character (neutrinoless decay)
• Leptonic CP-violation in neutrino oscillations
(at -e oscillations at superbeams, betabeams…. neutrino factory)
would constitute a very compelling argument in favour of leptogenesis
Go for those discoveries!
plus
![Page 7: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/7.jpg)
masses ---->
Beyond SM scale
* What is the prize for TeVwithout unnatural fine-tunings?
* What observable observable effects could we then expect?
…..This talk deals much with the Majorana character
![Page 8: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/8.jpg)
No masses in the SM because the SM accidentally
preserves B-L
……only left-handed neutrinos
and
……only scalar doublets (Higgs)
![Page 9: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/9.jpg)
No masses in the SM because the SM accidentally
preserves B-L
• right-handed R →
Would require Y~10-12 !!! Why s are so light???Why R does not acquire large Majorana mass?
.. .. ~
chmchlHY RLDRL +→+
i.e. Adding singlet neutrino fields NR
L M (RROK with gauge invariance
NR+ NR+
NR
NR Y
Y
L-
![Page 10: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/10.jpg)
No masses in the SM because the SM accidentally
preserves B-L
• right-handed R →
Would require Y~10-12 !!! Why s are so light???
Why R does not acquire large Majorana mass?
.. .. ~
chmchlHY RLDRL +→+
i.e. Adding singlet neutrino fields NR
L M (RROK with gauge invariance
NR+ NR+
NR
YNR L-
![Page 11: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/11.jpg)
No masses in the SM because the SM accidentally
preserves B-L
• right-handed R →
Would require Y~10-12 !!! Why s are so light???
Why R does not acquire large Majorana mass?
.. .. ~
chmchlHY RLDRL +→+
i.e. Adding singlet neutrino fields NR
L M (RROK with gauge invariance
NR+ NR+
NR
Seesaw modelSeesaw model
YNR
Which allows YN~1 --> M~MGut
L-
![Page 12: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/12.jpg)
No masses in the SM because the SM accidentally
preserves B-L
• right-handed R →
Would require Y~10-12 !!! Why s are so light???
Why R does not acquire large Majorana mass?
.. .. ~
chmchlHY RLDRL +→+
i.e. Adding singlet neutrino fields NR
L M (RROK with gauge invariance
NR+ NR+
NR
Seesaw modelSeesaw model
YNR
Which allows YN~1 --> M~MGut
L-
YN~10-6 --> M~TeV
![Page 13: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/13.jpg)
masses beyond the SM
Favorite options: new physics at higher scale M Heavy fields manifest in the low energy effective theory (SM)via higher dimensional operators
Dimension 5 operator:
It’s unique → very special role of masses:lowest-order effect of higher energy physics
→/M (L L H H)v/M (2
O d=5
L=ciO i
![Page 14: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/14.jpg)
masses beyond the SM
Favorite options: new physics at higher scale M Heavy fields manifest in the low energy effective theory (SM)via higher dimensional operators
Dimension 5 operator:
This mass term violates lepton number (B-L) → Majorana neutrinos
It’s unique → very special role of masses:lowest-order effect of higher energy physics
→/M (L L H H)v/M (2
O d=5
L=ciO i
![Page 15: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/15.jpg)
masses beyond the SM
Favorite options: new physics at higher scale M Heavy fields manifest in the low energy effective theory (SM)via higher dimensional operators
Dimension 5 operator:
This mass term violates lepton number (B-L) → Majorana neutrinos
It’s unique → very special role of masses:lowest-order effect of higher energy physics
→/M (L L H H)v/M (2
is common to all models of Majorana s
O d=5
L=ciO i
O d=5
![Page 16: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/16.jpg)
Dimension 6 operators,
O
discriminate among models.
d=6
Which are the d=6 operators characteristic of Seesaw models?
(A. Abada, C. Biggio, F.Bonnet, T. Hambye +MBG )
![Page 17: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/17.jpg)
masses beyond the SM : tree level
m ~ v2 cd=5 = v2 YN YN /MN
T
Fermionic Singlet Seesaw ( or type I)
2 x 2 = 1 + 3
![Page 18: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/18.jpg)
masses beyond the SM : tree level
Fermionic Singlet Seesaw ( or type I)
2 x 2 = 1 + 3
L
H
++
LEPTOGENESIS:
NR’NR’
NR
(Fukugita, Yanagida)
(Flanz, Paschos, Sarkar,Covi, Roulet,Vissani, Pilaftsis)
![Page 19: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/19.jpg)
masses beyond the SM : tree level
Fermionic Triplet Seesaw ( or type III)
m ~ v2 cd=5 = v2 Y Y /M
T
2 x 2 = 1 + 3
![Page 20: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/20.jpg)
masses beyond the SM : tree level
Fermionic Triplet Seesaw ( or type III)
T
L
H
++ +R R R’ R R’
LEPTOGENESIS:2 x 2 = 1 + 3
(Hambye, Li, Papucci, Notari, Strumia))
![Page 21: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/21.jpg)
masses beyond the SM : tree level
2 x 2 = 1 + 3
Scalar Triplet Seesaw ( or type II)
m ~ v2 cd=5 = v2 Y /M
2
![Page 22: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/22.jpg)
masses beyond the SM : tree level
2 x 2 = 1 + 3
Scalar Triplet Seesaw ( or type II)
T
+ + ’
LEPTOGENESIS:
LL
(Ma, Sarkar, Hambye)
![Page 23: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/23.jpg)
L
L
NR
Or hybrid models, i.e Fermionic Singlet + Scalar Triplet
H
H
( O'Donnell, Sarkar, Hambye, Senjanovic; Antusch, King )
![Page 24: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/24.jpg)
Heavy fermion singlet NR (Type I See-Saw) Minkowski, Gell-Mann, Ramond, Slansky, Yanagida, Glashow, Mohapatra, Senjanovic
masses beyond the SM : tree level
Heavyscalar triplet Magg, Wetterich, Lazarides, Shafi, Mohapatra, Senjanovic, Schecter, Valle
Heavy fermion triplet RMa, Roy, Senjanovic, Hambye et al., …
![Page 25: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/25.jpg)
Minimal see-saw (fermionic singlet)
...11 6
25 +
Λ+
Λ+= == dd
SMeff LLLLIntegrate out NR
d=5 operatorit gives mass to
d=6 operatorit renormalises kinetic energy
Broncano, Gavela, Jenkins 02
L = LSM+ i NRdNR - Y L H NR - M NR NR _ _
M M2
YN YN/M (L L H H)T YN YN/M2 (L H) (H L)
+
![Page 26: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/26.jpg)
Minimal see-saw (fermionic singlet)
...11 6
25 +
Λ+
Λ+= == dd
SMeff LLLLIntegrate out NR
d=5 operatorit gives mass to
d=6 operatorit renormalises kinetic energy
Kaluza-Klein model: De Gouvea, Giudice, Strumia, Tobe
L = LSM+ i NRdNR - Y L H NR - M NR NR _ _
M M2
YN YN/M (L L H H)T YN YN/M2 (L H) (H L)
+
![Page 27: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/27.jpg)
cd=6 ~ (cd=5)2
For Y´s ~ O(1),
and the smallness of neutrino masses would preclude in
practice observable effects from cd=6
with
m ~ v2 cd=5 = v2 YN YN /MN
T
while cd=6 = Y Y/M2
+
How to evade this without ad-hoc cancelations of Yukawas?
![Page 28: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/28.jpg)
Fermionic triplet seesaw
...11 6
25 +
Λ+
Λ+= == dd
SMeff LLLLIntegrate out NR
d=5 operatorit gives mass to
d=6 operatorit renormalises kinetic energy+…
L = LSM+ i RDR - Y L .H R - M R R _ _
M M2
YY/M (L L H H)T
Y Y/M2 (L H) D (H L) +
![Page 29: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/29.jpg)
Scalar triplet see-saw
L = LSM + DD - +M2 +
Y L . L + H . H + V(H,, i)
Y /M2 (L L H H) d=5
d=6
Y Y/M2 (L L) (L L) + _ _
/M4 (H+H)3
i/M4(HH)DD(HH)
2
2
![Page 30: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/30.jpg)
![Page 31: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/31.jpg)
Y Y M
+2
![Page 32: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/32.jpg)
Y Y M
+Notice that the combination
also is crucial to the LEPTOGENESIS CP-asymmetries
i.e., in Type I:
L
H
++NR’
NR’NR+
YNT YN
in addition to the mcombination ~ YNT YN v2/M
2
![Page 33: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/33.jpg)
Indeed, in Type I (fermionic seesaw)
the individual CP asymmetries:
vanish for
degenerate cd=5 (that is, m ) eigenvalues
or
degenerate cd=6 eigenvalues (Broncano, Gavela, Jenkins)
![Page 34: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/34.jpg)
Y Y M
+2
Can M be close to EW scale, say ~ TeV?
![Page 35: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/35.jpg)
M~1 TeV is suggested by electroweak hierarchy problem
NH
H
H
L
L
(Vissani, Casas et al., Schmaltz)
![Page 36: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/36.jpg)
M~1 TeV actively searched for in colliders
-> m> 136 GeV by CDF
Atlas groups studying searches of Triplet Seesaws (scalar and fermionic)
(Ma……….Bajc, Senjanovic)
i.e. Scalar Triplet
l+
l+
Same sign dileptons….~ no SM background
![Page 37: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/37.jpg)
Is it possible to have
M ~ 1 TeV
with large Yukawas (even O(1) ) ?
It requires to decouple the coefficient cd=5 of Od=5
from cd=6 of Od=6
![Page 38: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/38.jpg)
Notice that all d=6 operators preserve B-L, in contrast to the d=5 operator.
This suggests that, from the point of view of symmetries, it may be natural to have large cd=6, while having small cd=5 .
![Page 39: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/39.jpg)
Light Majorana m should vanish:
- inversely proportional to a Majorana scale ( cd=5 ~ 1/M)
- or directly proportional to it
![Page 40: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/40.jpg)
Light Majorana m should vanish:
- inversely proportional to a Majorana scale ( cd=5 ~ 1/M)
- or directly proportional to it Ansatz:
When the breaking of L is proportional to a small scale << M, while M ~ O(TeV), c d=5 is suppressed while c d=6 is large:
cd=5 ~
cd=6 ~
1
![Page 41: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/41.jpg)
Light Majorana m should vanish:
- inversely proportional to a Majorana scale ( cd=5 ~ 1/M)
- or directly proportional to it Ansatz:
When the breaking of L is proportional to a small scale << M, while M ~ O(TeV), c d=5 is suppressed while c d=6 is large:
cd=5 ~
cd=6 ~
f(Y)
Y Y+
![Page 42: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/42.jpg)
Y Y M
+2
![Page 43: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/43.jpg)
Y Y M
+2
M2
Y
![Page 44: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/44.jpg)
* The minimal scalar triplet model obeys that ansatz:
Y
Y Y+
HH
LL
cd=6 ~
cd=5 ~
In fact, any Scalar mediated Seesaw will give 1/(D2-M2) ~ -1/M2 - D2/M4 + ……
m ~ v2 cd=5 ~1/M2
![Page 45: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/45.jpg)
* Singlet fermion seesaws with M~1 TeV also obey it !!! :
i.e. INVERSE SEESAW
What about fermionic-mediated Seesaws?
![Page 46: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/46.jpg)
INVERSE SEESAW texture
L N1 N2
L
N1
N2
* Toy: 1 light
Mohapatra, Valle, Glez- Garcia
![Page 47: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/47.jpg)
INVERSE SEESAW texture
L N1 N2
L
N1
N2
* Toy: 1 light
![Page 48: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/48.jpg)
INVERSE SEESAW texture
L N1 N2
L
N1
N2
* 3 generation Inverse Seesaw: e , , , N1, N2, N3
* Toy: 1 light
Abada et al., Kersten+Smirnov
![Page 49: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/49.jpg)
Were M ~ TeV and Y’s ~ 1, is LEPTOGENESIS possible?
It would require resonant leptogenesis
NR
with rather degenerate heavy states M-M’ <<M
Yes, but not easy
![Page 50: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/50.jpg)
Were M ~ TeV and Y’s ~ 1, is LEPTOGENESIS possible?
It would require resonant leptogenesis
NR
with rather degenerate heavy states M-M’ <<M
•Very interesting for FERMIONIC inverse seesaws, as they are naturally resonant ( have 2 NR or 2 SR degenerate)
Yes, but not easy
![Page 51: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/51.jpg)
Were M ~ TeV and Y’s ~ 1, is LEPTOGENESIS possible?
It would require resonant leptogenesis
NR
with rather degenerate heavy states M-M’ <<M
* Difficult in Triplet Seesaws (fermionic or scalar) because the extra gauge scattering processes push towards thermal equilibrium. Needs M-M’ ~
•Very interesting for FERMIONIC inverse seesaws, as they are naturally resonant ( have 2 NR or 2 SR degenerate)
Yes, but not easy
![Page 52: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/52.jpg)
d=6 operator is crucial for leptog.:
if observed at E~TeV ---> at least one N (or or ) at low scale
--------> only resonant leptogenesis is possible
![Page 53: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/53.jpg)
cd=6 ~
Y Y+
Experimental information on
from:
--- 4 fermion operators (Scalar triplet seesaw) MW, W decays…
--- Unitarity corrections (Fermionic seesaws)
![Page 54: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/54.jpg)
Scalar triplet seesaw Bounds on cd=6
![Page 55: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/55.jpg)
Scalar triplet seesaw
Combined bounds on cd=6
![Page 56: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/56.jpg)
Fermionic seesaws ---> Non unitarity
![Page 57: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/57.jpg)
i.e, a neutrino mass matrix larger than 3x3
3 x 3
The complete theory ofmasses is unitary.
• Unitarity violations arise in models for masses with heavy fermions
![Page 58: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/58.jpg)
→ YES deviations from unitarity
Fermion singlet NR (Type I See-Saw)
Scalar triplet
Fermion triplet R
→ NO deviations from unitarity
→ YES deviations from unitarity
Broncano, Gavela, Jenkins 02
![Page 59: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/59.jpg)
A general statement…
We have unitarity violation whenever we integrate out heavy fermions:
...11
2+
/−−=
−/ MDi
MMDi
vv
There’s a : it connects fermionswith the same chirality → correction to the kinetic terms
It connects fermions withopposite chirality → mass term
Y Y/M2 (L H) D (H L)
YN YN/M2 (L H) (H L)
Fermionic seesaws:
I
II
A flavour dependent rescaling is needed, which is NOT a unitary transformation
![Page 60: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/60.jpg)
In all fermionic Seesaws, the departures from unitarity give directly |cd=6|
i.e. Fermion singlet Seesaws
N
UPMNS --------> N (non-unitary)
![Page 61: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/61.jpg)
Antusch, Biggio, Fernández-Martínez, López-Pavón, M.B.G. 06
→ Worthwhile to analyze neutrino data relaxing the hypothesis of unitarity of the mixing matrix
![Page 62: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/62.jpg)
The general idea…
13 12 12 13 13
12 23 23 13 12 12 23 23 13 12 23 13
23 12 23 13 12 23 12 23 13 12 23 13
i
i i
i i
c c s c s e
U s c s s c e c c s s s e s c
s s c s c e s c c s s e c c
− −
− −
⎛ ⎞⎜ ⎟= − − −⎜ ⎟⎜ ⎟− − −⎝ ⎠
1 2 3
1 2 3
1 2 3
e e eN N N
N N N N
N N N
⎛ ⎞⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠
The general idea………
U=
W -i
iNα≈
lα
e
iα
i
e
1
![Page 63: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/63.jpg)
KamLAND+CHOOZ+K2K
SNO
UNITARITY
Atmospheric + K2K
This affects oscillation probabilities …
![Page 64: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/64.jpg)
KamLAND+CHOOZ+K2K
SNO
UNITARITY
Atmospheric + K2K
This affects oscillation probabilities …
.... raw of N remains unconstrained
![Page 65: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/65.jpg)
Unitarity constraints on (NN ) from:+
* Near detectors…• MINOS, NOMAD, BUGEY, KARMEN
* Weak decays…
* W decays * Invisible Z width * Universality tests * Rare lepton decays
![Page 66: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/66.jpg)
Unitarity constraints on (NN ) from:+
* Near detectors…• MINOS, NOMAD, BUGEY, KARMEN
* Weak decays…
* W decays * Invisible Z width * Universality tests * Rare lepton decays
|N| is unitary at the % level
![Page 67: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/67.jpg)
All in all, as of today, for the Singlet-fermion Seesaws:
(NN+-1)α
![Page 68: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/68.jpg)
New CP-violation signals even in the two-family approximation
i.e. P ( ---> ) = P ( ---> ) _ _
Increased sensitivity to the moduli |N| in future Neutrino Factories
E. Fdez-Martinez, J.Lopez, O. Yasuda, M.B.G.
![Page 69: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/69.jpg)
Fermion-triplet seesaws:
similar - although richer! - analysis
![Page 70: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/70.jpg)
Singlet and triplet Seesaws differ in the the pattern of the Z couplings
![Page 71: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/71.jpg)
@ tree level in Type III
(not in Type I)
Bounds on Yukawas type III
→eee→eee→ee→e→
Z→eZ→eZ→
→e→e→
Ma, Roy 02Bajc, Nemevsek, Senjanovic 07
Production @ colliders
For M ≈ TeV → |Y| < 10-2
+W decaysInvisible Z widthUniversality tests
![Page 72: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/72.jpg)
For the Triplet-fermion Seesaws (type III):
(NN+-1)α
![Page 73: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/73.jpg)
In summary, for all scalar and fermionic Seesaw models, present bounds:
or stronger
![Page 74: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/74.jpg)
Conclusions* d= 6 operators discriminate among models of Majorana s. - we have determined them for the 3 families of Seesaw models.
![Page 75: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/75.jpg)
Conclusions* d= 6 operators discriminate among models of Majorana s. - we have determined them for the 3 families of Seesaw models. * While the d=5 operator violates B-L, all d=6 ops. conserve it
--> natural ansatz: cd=5 ~/M2,
allowing M~TeV and large Yukawa couplings (even O(1)).
![Page 76: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/76.jpg)
Conclusions* d= 6 operators discriminate among models of Majorana s. - we have determined them for the 3 families of Seesaw models. * While the d=5 operator violates B-L, all d=6 ops. conserve it
--> natural ansatz: cd=5 ~/M2,
allowing M~TeV and large Yukawa couplings (even O(1)). •d=6 operator crucial: if observed at low energies, only resonant leptogenesis is possible
![Page 77: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/77.jpg)
Conclusions* d= 6 operators discriminate among models of Majorana s. - we have determined them for the 3 families of Seesaw models. * While the d=5 operator violates B-L, all d=6 ops. conserve it
--> natural ansatz: cd=5 ~/M2,
allowing M~TeV and large Yukawa couplings (even O(1)). •d=6 operator crucial: if observed at low energies, only resonant leptogenesis is possible
* cd=6 ~Y+Y/M2 bounded from 4-interactions + unitarity deviations
CP-asymmetry may be a clean probe of the new phases of
seesaw scenarios.
-> Keep tracking these deviations in the future. They are excellent signals of new physics.
![Page 78: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/78.jpg)
Back-up slides
![Page 79: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/79.jpg)
Low-energy effective theoryAfter EWSB, in the flavour basis:
( ) ( ) ( ) .....)(cos22
1 † ++−−−∂/= + chNNPZg
NPlWg
miL jijLiW
iiLiiiic
ii νγνθ
νγνννν μμα
μαμ
Mα → diagonalized → unitary transformation
Kα → diagonalized and normalized → unitary transf. + rescaling
N non-unitary
In the mass basis:
![Page 80: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/80.jpg)
A general statement…
We have unitarity violation whenever we integrate out heavy fermions:
The propagator of a scalar fieldscalar field does not contain → if it generates neutrino mass, it cannot correct the kinetic term
1/(D2-M2) ~ -1/M2 - D2/M4 + …….
...11
2+
/−−=
−/ MDi
MMDi
vv
There’s a : it connects fermionswith the same chirality → correction to the kinetic terms
It connects fermions withopposite chirality → mass term
![Page 81: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/81.jpg)
Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions.
Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...)
They add 4-fermion exotic operators to production or detection or propagation in matter
_ _
![Page 82: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/82.jpg)
3 generation Inverse Seesaw
and also similar extensions of the fermionic triplet Seesaw
e , , , N1, N2, N3
Abada et al.Kersten+Smirnov
![Page 83: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/83.jpg)
M(inimal) U(nitarity) V(iolation) :
( ) ( ) .....)(cos
..2
++−+−+∂/= ++ chNNPZg
chNPlWg
miL jijLiW
iiLiiiiii νγνθ
νγνννν μμα
μαμ
with only 3 light
W -i
Z
i
j
iNα≈ ( )ijNN +≈
![Page 84: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/84.jpg)
N elements from oscillations & decays
with unitarityOSCILLATIONS
without unitarityOSCILLATIONS
+DECAYS
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−−−−−−
<−−=
66.031.055.019.028.004.0
67.034.053.018.027.004.0
04.037.022.077.062.02
U
3
.79 - .88 .47 -
.61 < .20 |U| = .19 - .52 .42 - .73 .58 - .82
.20 - .53 .44 - .74 .56 - .81
M. C. Gonzalez Garcia hep-ph/0410030
.75 - .89 .45 - .65 <.20 |N| = .19 - .55 .42 - .74 .57 - .82
.13 - .56 .36 - .75 .54 - .82
MUV
Antusch, Biggio, Fernández-Martínez, López-Pavón, M.B.G. 06
![Page 85: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/85.jpg)
If we parametrize
with
22
4sin)2sin(2 ⎟⎟
⎠
⎞⎜⎜⎝
⎛−≈
ELm
iP θεαα
If L/E small
Can we measure the phases of N ? E. Fdez-Martinez, J.Lopez, O. Yasuda, M.B.G.
PMNSUN ⋅+≈ )1( ε+ε)
(1 + ε) εv2cd=6
εα
4
![Page 86: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/86.jpg)
If we parametrize
with
22
4sin)2sin(2 ⎟⎟
⎠
⎞⎜⎜⎝
⎛−≈
ELm
iP θεαα
If L/E small
Can we measure the phases of N ? E. Fdez-Martinez, J.Lopez, O. Yasuda, M.B.G.
PMNSUN ⋅+≈ )1( ε+ε)
(1 + ε) εv2cd=6
εα
222
22 42
sin)2sin()Im(24
sin)2(sin ααα εθεθ +⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟⎠
⎞⎜⎜⎝
⎛=
ELm
ELm
P Im(εα- εα
4
![Page 87: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/87.jpg)
If we parametrize
with
22
4sin)2sin(2 ⎟⎟
⎠
⎞⎜⎜⎝
⎛−≈
ELm
iP θεαα
If L/E small
Can we measure the phases of N ? E. Fdez-Martinez, J.Lopez, O. Yasuda, M.B.G.
PMNSUN ⋅+≈ )1( ε+ε)
(1 + ε) εv2cd=6
εα
222
22 42
sin)2sin()Im(24
sin)2(sin ααα εθεθ +⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟⎠
⎞⎜⎜⎝
⎛=
ELm
ELm
P
SM
Im(εα-
4
εα
![Page 88: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/88.jpg)
If we parametrize
with
22
4sin)2sin(2 ⎟⎟
⎠
⎞⎜⎜⎝
⎛−≈
ELm
iP θεαα
If L/E small
Can we measure the phases of N ? E. Fdez-Martinez, J.Lopez, O. Yasuda, M.B.G.
PMNSUN ⋅+≈ )1( ε+ε)
(1 + ε) εv2cd=6
εα
222
22 42
sin)2sin()Im(24
sin)2(sin ααα εθεθ +⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟⎠
⎞⎜⎜⎝
⎛=
ELm
ELm
P
SM Zero dist. effect
Im(εα- εα
4
![Page 89: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/89.jpg)
If we parametrize
with
22
4sin)2sin(2 ⎟⎟
⎠
⎞⎜⎜⎝
⎛−≈
ELm
iP θεαα
If L/E small
Can we measure the phases of N ? E. Fdez-Martinez, J.Lopez, O. Yasuda, M.B.G.
PMNSUN ⋅+≈ )1( ε+ε)
(1 + ε) εv2cd=6
εα
222
22 42
sin)2sin()Im(24
sin)2(sin ααα εθεθ +⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟⎠
⎞⎜⎜⎝
⎛=
ELm
ELm
P
SM CP violating interference
Zero dist. effect
Im(εα- εα
4
![Page 90: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/90.jpg)
Measuring non-unitary phases
Present bound from →
Sensitivity to
|ε|
Sensitivity to
εFor non-trivial , one order of magnitude
improvement for |N|
![Page 91: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/91.jpg)
⎟⎟⎠
⎞⎜⎜⎝
⎛−=−
E
LmPP
2sin)2sin()Im(4
223
23θε μττμμτ
The CP phase can be measured
At a Neutrino Factory of 50 GeV with L = 130 Km
In P there is
no13sinθ 12or suppression:
ε
![Page 92: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/92.jpg)
New CP-violation signals even in the two-family approximation
i.e. P ( ---> ) = P ( ---> ) _ _
![Page 93: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/93.jpg)
New CP-violation signals even in the two-family approximation
i.e. P ( ---> ) = P ( ---> ) _ _
![Page 94: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/94.jpg)
The effects of non-unitarity…
… appear in the interactions
( )ααα+== ∑ NNN SM
iiSM
2 ( )∑ +=ij
ijSM NN2
This affects weak decays…
W -i
Z
i
j
iNα≈ ( )ijNN +≈
ααα
… and oscillation probabilities…
NN+ =
![Page 95: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/95.jpg)
( )ααα+== ∑ NNN SM
iiSM
2 ( )∑ +=ij
ijSM NN2
This affects weak decays…
![Page 96: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/96.jpg)
( )ααα+== ∑ NNN SM
iiSM
2 ( )∑ +=ij
ijSM NN2
This affects weak decays…
… and oscillation probabilities…
( ) ( ) ( )αα
α
α ††
2
*
,NNNN
NeN
LEP ii
LiPi
i∑=
Zero-distance effect at near detectors:
( ) ααα ≠∝→ ∑2
*0;i
ii NNP
![Page 97: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/97.jpg)
( )ααα+== ∑ NNN SM
iiSM
2 ( )∑ +=ij
ijSM NN2
This affects weak decays…
… and oscillation probabilities…
( ) ( ) ( )αα
α
α ††
2
*
,NNNN
NeN
LEP ii
LiPi
i∑=
Zero-distance effect at near detectors:
( ) ααα ≠∝→ ∑2
*0;i
ii NNP
W -
Matter
ee
e
u
d
NNNN
NNNN
NN
+
++
Non-Unitary Mixing Matrix
![Page 98: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/98.jpg)
W -
Matter
ee
e
u
d
NNNN
NNNN
NN
+
++
( ) ( ) ( )αα
α
α ††
2
*
,NNNN
NeN
LEP ii
LiPi
i∑=
Zero-distance effect at near detectors:
( ) ααα ≠∝→ ∑2
*0;i
ii NNP
( )( )
( )
⎟⎠
⎞⎜⎝
⎛
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
⎟⎟⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜⎜⎜
⎝
⎛
−−
−−
+⎟⎠⎞
⎜⎝⎛=⎟
⎠
⎞⎜⎝
⎛
∑∑∑
∑
∑∑
∑∑
−
e
iiNC
iiei
ii
iei
NCCC
iiei
iei
ii
NCi
eiNCCC
e
NVNNN
NVV
NNN
NVNVV
NE
EN
dtdi
2*
2
2
*2
2
2
1*
2
1*
00
In matter
![Page 99: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/99.jpg)
Number of events
( ) ( ) )()(),()(
~ EENNLEPNNdE
EddEn SM
SM
ev εσ βββαβααα ++Φ
∫
)()(),()(
~ EELEPdE
EddEnev ε α
αΦ∫
( )2
*,ˆ ∑=i
iLiP
i NeNLEP iβααβ
Exceptions:• measured flux• leptonic production mechanism• detection via NC
( )αααα +ΦΦ
NNdE
d
dE
d SM
~
( ) +NNSM~ produced and detected in CC
![Page 100: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/100.jpg)
N elements from oscillations: -row
( ) ( ) ( ) ( )23
2
3
2
2
2
1
4
3
22
2
2
1 cos2ˆ Δ++++≅→ μμμμμμμμ νν NNNNNNP
1. Degeneracy
2. cannot be disentangled
2
3
2
2
2
1 NNN ↔+
2
2
2
1 , NN
Atmospheric + K2K: Δ12≈0
UNITARITY
![Page 101: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/101.jpg)
N elements from oscillations: e-row
( ) ( )12
2
2
2
1
4
3
4
2
4
1 cos2ˆ Δ+++≅→ eeeeeee NNNNNP ννKamLAND:
SNO:
( ) 2
2
2
1 9.01.0ˆeeee NNP +≅→νν
→ all |Nei|2 determined
KamLAND+CHOOZ+K2K
SNO
( ) ( ) ( ) ( )23
2
3
2
2
2
1
4
3
22
2
2
1 cos2 Δ++++≅→ eeeeeeee NNNNNNP ννCHOOZ
ELmijij 22=
![Page 102: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/102.jpg)
N elements from oscillations only
with unitarityOSCILLATIONS
without unitarityOSCILLATIONS
3 .79 - .89 .47
- .61 < .20 |U| = .19 - .52 .42 - .73 .58 - .82
.20 - .53 .44 - .74 .56 - .81
M. C. Gonzalez Garcia hep-ph/0410030
.75 - .89 .45
- .66 < .34 |N| = [(|N | +|N | )1/2= 0.57-0.86] .57- .86
? ? ?
1 22 2
MUV
![Page 103: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/103.jpg)
Unitarity constraints on (NN ) from:+
* Near detectors…
• KARMEN: (NN†)e 0.05
• NOMAD: (NN†)0.09 (NN†)e0.013• MINOS: (NN†)1±0.05
• BUGEY: (NN†)ee 1±0.04
* Weak decays…
![Page 104: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/104.jpg)
|N| is unitary at the % level
At 90% CL
![Page 105: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/105.jpg)
In the future…
TESTS OF UNITARITY (90%CL)
OOP P EERRAAlikelike
![Page 106: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/106.jpg)
![Page 107: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/107.jpg)
Measuring unitarity deviations
The bounds on
εε 21)1( 2† +≈+=NNAlso apply
toε
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
⋅<⋅<⋅<⋅<⋅<⋅<⋅<⋅<⋅<
≈−−−
−−−
−−−
333
335
353
105.2100.5100.8
100.5105.2106.3
100.8106.3105.2
ε
The constraints on εefrom → e are very strong
We will study the sensitivity to the CP violating terms
εe and ε in Pe and P
![Page 108: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/108.jpg)
Measuring unitarity deviations
In Pe the CP violating term is supressed by
13sinθ 12or appart from⎟⎟⎠
⎞⎜⎜⎝
⎛E
Lme 2
sin223
τε
The zero distance term
in |εe|2 dominates
No sensitivity to the
CP phase e
![Page 109: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/109.jpg)
W -
Matter
Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions.
ee
e
u
d
Standard
Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...)
![Page 110: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/110.jpg)
Matter
ee
e
u
d
Exotic production
Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions.
Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...)
![Page 111: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/111.jpg)
W -
Matter
e e
u
d
e
Exotic propagation
Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions.
Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...)
![Page 112: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/112.jpg)
W -
Matter
ee
e
u
d
Exotic detection
Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions.
Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...)
![Page 113: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/113.jpg)
W -
Matter
ee
e
u
d
Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions.
Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...)
W -
Matter
ee
e
u
d
![Page 114: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/114.jpg)
W -
Matter
ee
e
u
d
NNNN
NNNN
NN
+
++
Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions.
Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...)
W -
Matter
ee
e
u
d
Non-Unitary Mixing Matrix
![Page 115: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/115.jpg)
Matter
e ee
u
d
Non-Unitary Mixing Matrix
Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions.
Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...)
W -
Matter
ee
e
u
d
![Page 116: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/116.jpg)
masses beyond the SM
• radiative mechanisms: ex.) 1 loop:
Other realizations
• SUSY models with R-parity violation
• Models with large extra dimensions: i.e., R are Kaluza-Klein replicas
• …
SMRψ ⊃Dirac mass suppressed by (2R)d/2
Frigerio
![Page 117: Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT](https://reader033.vdocuments.mx/reader033/viewer/2022050714/56649d485503460f94a239d6/html5/thumbnails/117.jpg)
Quarks are detected in the final state → we can directly measure |Vab|
ex: |Vus| from K0 →- e+ e
→ Measurements of VCKM elements relies on UPMNS unitarity
Unitarity in the quark sector
With Vab we check unitarity conditions: ex: |Vud|2+|Vus|2+|Vub|2 -1 = -0.0008±0.0011
• decays → only (NN†) and (N†N)• N elements → we need oscillations• to study the unitarity of N: no assumptions on VCKM
With leptons:
uK0 -
d d
sW+
Vus*
ee+ Uei
→ ∑i|Uei|2 =1 if U unitary