Light and Superlight Sterile Neutrinos in the Minimal Radiative Inverse Seesaw Model · 2018. 9....
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Light and Superlight Sterile Neutrinos in the Minimal Radiative Inverse Seesaw Model P. S. Bhupal Dev Consortium for Fundamental Physics, University of Manchester PSBD, A. Pilaftsis, Phys. Rev. D86, 113001 (2012) [arXiv:1209.4051 [hep-ph]]; Phys. Rev. D87, 053007 (2013) [arXiv:1212.3808 [hep-ph]]. Baryon and Lepton Number Violation 2013 MPIK, Heidelberg April 08, 2013 P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 1 / 18
Transcript of Light and Superlight Sterile Neutrinos in the Minimal Radiative Inverse Seesaw Model · 2018. 9....
Light and Superlight Sterile Neutrinos in the Minimal Radiative
Inverse Seesaw ModelLight and Superlight Sterile Neutrinos in the
Minimal Radiative Inverse Seesaw Model
P. S. Bhupal Dev
Consortium for Fundamental Physics, University of Manchester
PSBD, A. Pilaftsis, Phys. Rev. D86, 113001 (2012) [arXiv:1209.4051 [hep-ph]]; Phys. Rev. D87, 053007 (2013) [arXiv:1212.3808 [hep-ph]].
Baryon and Lepton Number Violation 2013 MPIK, Heidelberg
April 08, 2013
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 1 / 18
Outline
Neutrino Mass and Seesaw Mechanism Inverse Seesaw Minimal Radiative Inverse Seesaw Model (MRISM) Light and Superlight Sterile Neutrinos Conclusion
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 2 / 18
Neutrino Mass and Seesaw Mechanism
Neutrino oscillation data require at least two nonzero neutrino masses.
Massless neutrinos in the SM because of no RH neutrino (no Dirac mass) and a global (B − L)-symmetry (no Majorana mass).
Add νR : for Dirac mass term yνLΦνR alone, require yν <�∼ 10−12.
A more natural way is to break (B − L) by extra fields.
Can be parametrized within the SM by Weinberg’s dimension-5 operator.
The simplest tree-level realization: (type-I) seesaw mechanism.
Observed baryon asymmetry can be explained by leptogenesis.
Supersymmetrization gives an extra DM candidate (mixed sneutrino).
Thus could provide all the missing features of the SM in a single testable framework.
Could be directly probed at colliders if the seesaw scale is < O(TeV).
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 3 / 18
Neutrino Mass and Seesaw Mechanism
Neutrino oscillation data require at least two nonzero neutrino masses.
Massless neutrinos in the SM because of no RH neutrino (no Dirac mass) and a global (B − L)-symmetry (no Majorana mass).
Add νR : for Dirac mass term yνLΦνR alone, require yν <�∼ 10−12.
A more natural way is to break (B − L) by extra fields.
Can be parametrized within the SM by Weinberg’s dimension-5 operator.
The simplest tree-level realization: (type-I) seesaw mechanism.
Observed baryon asymmetry can be explained by leptogenesis.
Supersymmetrization gives an extra DM candidate (mixed sneutrino).
Thus could provide all the missing features of the SM in a single testable framework.
Could be directly probed at colliders if the seesaw scale is < O(TeV).
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 3 / 18
Light Sterile Neutrinos?
There exist a few “anomalies" –can be explained by additional neutrino(s) with ∆m2 ∼ eV2. (See talk by T. Lasserre)
Cannot be active neutrinos due to the LEP invisible Z -decay width constraint.
Must be SM gauge singlets – sterile.
Planck data has put stringent constraints for thermalized light steriles. (See talk by S. Hannestad)
Neff = 3.30+0.54 −0.51 and
∑ mν < 0.23 eV (Planck+WP+highL+BAO). [Ade et al.
’13]
However, light steriles favored by SBL can still be made compatible with cosmology. [Mirizzi et al ’13]
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 4 / 18
Light Sterile Neutrinos?
There exist a few “anomalies" –can be explained by additional neutrino(s) with ∆m2 ∼ eV2. (See talk by T. Lasserre)
Cannot be active neutrinos due to the LEP invisible Z -decay width constraint.
Must be SM gauge singlets – sterile.
Planck data has put stringent constraints for thermalized light steriles. (See talk by S. Hannestad)
Neff = 3.30+0.54 −0.51 and
∑ mν < 0.23 eV (Planck+WP+highL+BAO). [Ade et al.
’13]
However, light steriles favored by SBL can still be made compatible with cosmology. [Mirizzi et al ’13]
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 4 / 18
Canonical (Type-I) Seesaw Add one set of SM singlet RH Majorana neutrinos (νRα
). [ Minkowski ’77; Yanagida ’79;
−LY = yνLΦνR + 1 2 νC
RMRνR + H.c.,
R MT D, Mheavy
ν ' MR
Seesaw Limit: Small (sub-eV) M light ν for large Majorana mass MR .
TeV scale MR possible if MD <�∼ O(me) (barring fine-tuning).
Hard for colliders. /
SO(10)-GUT embedding =⇒ relates MD to charged fermion sector.
Predicts the seesaw scale MR ∼ 1010−14 GeV. /
Light steriles not so natural in type-I seesaw.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 5 / 18
Canonical (Type-I) Seesaw Add one set of SM singlet RH Majorana neutrinos (νRα
). [ Minkowski ’77; Yanagida ’79;
−LY = yνLΦνR + 1 2 νC
RMRνR + H.c.,
R MT D, Mheavy
ν ' MR
Seesaw Limit: Small (sub-eV) M light ν for large Majorana mass MR .
TeV scale MR possible if MD <�∼ O(me) (barring fine-tuning).
Hard for colliders. /
SO(10)-GUT embedding =⇒ relates MD to charged fermion sector.
Predicts the seesaw scale MR ∼ 1010−14 GeV. /
Light steriles not so natural in type-I seesaw.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 5 / 18
Inverse Seesaw Add two sets of SM singlet fermions (νRα
and SLρ ). [Mohapatra ’85; Mohapatra, Valle ’86]
−LY = yνLΦνR + SLMNνR + 1 2 νC
RµRνR + 1 2
SLµSSC L + H.c.,
M light ν '
)T , Mheavy
ν ' MN
TeV scale inverse seesaw easily possible (even with large Dirac Yukawa coupling) due to the smallness of Majorana mass.
( Mν
Smallness of µS is “technically natural”.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 6 / 18
Inverse Seesaw Add two sets of SM singlet fermions (νRα
and SLρ ). [Mohapatra ’85; Mohapatra, Valle ’86]
−LY = yνLΦνR + SLMNνR + 1 2 νC
RµRνR + 1 2
SLµSSC L + H.c.,
M light ν '
)T , Mheavy
ν ' MN
TeV scale inverse seesaw easily possible (even with large Dirac Yukawa coupling) due to the smallness of Majorana mass.
( Mν
Smallness of µS is “technically natural”.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 6 / 18
Inverse Seesaw Add two sets of SM singlet fermions (νRα
and SLρ ). [Mohapatra ’85; Mohapatra, Valle ’86]
−LY = yνLΦνR + SLMNνR + 1 2 νC
RµRνR + 1 2
SLµSSC L + H.c.,
M light ν '
)T , Mheavy
ν ' MN
TeV scale inverse seesaw easily possible (even with large Dirac Yukawa coupling) due to the smallness of Majorana mass.
( Mν
Smallness of µS is “technically natural”.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 6 / 18
Rich Phenomenology
Inverse Seesaw models have very rich phenomenology, e.g.,
A natural way to explain heavy neutrino mass splitting required for resonant leptogenesis. [Blanchet, PSBD, Mohapatra ’10]
Mixed sneutrino DM candidate. [Arina et al. ’08; An, PSBD, Cai, Mohapatra ’11]
Trilepton+ET/ signal for the LHC. [Chen, PSBD ’11; Das, Okada ’12]
Observable non-unitarity and LFV effects. [Malinsky, Ohlsson, Xing, Zhang ’09; PSBD,
Mohapatra ’09; Abada, Das, Vicente, Weiland ’12]
Modifications to SM Higgs signal strength. [PSBD, Franceschini, Mohapatra ’12]
Higgs vacuum stability. [Khan, Goswami, Roy ’12]
Neutrinoless double beta decay. [Mitra, Senjanovic, Vissani ’11; Lopez-Pavon, Pascoli, Wong ’12;
Parida, Patra ’13]
Light sterile neutrinos. [Barry, Rodejohann, Zhang ’11; Zhang ’12; PSBD, Pilaftsis ’13] –This talk.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 7 / 18
Inverse Seesaw with µR 6= 0
Consider the possibility: µR 6= 0, µS = 0 in inverse seesaw mass matrix.
Might arise in models where the Majorana mass term for S-field forbidden due to specific flavour symmetries. [Chun, Joshipura, Smirnov ’95; Barry,
Rodejohann, Zhang ’11]
The light neutrinos are exactly massless at tree-level.
To see this, cast the inverse seesaw mass matrix into a type-I seesaw-like structure:
Mν =
S MT D +O(||MDM−1
S ||2) = 0
L L νCRνR
〈Φ〉 〈Φ〉
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 8 / 18
Inverse Seesaw with µR 6= 0
Consider the possibility: µR 6= 0, µS = 0 in inverse seesaw mass matrix.
Might arise in models where the Majorana mass term for S-field forbidden due to specific flavour symmetries. [Chun, Joshipura, Smirnov ’95; Barry,
Rodejohann, Zhang ’11]
The light neutrinos are exactly massless at tree-level.
To see this, cast the inverse seesaw mass matrix into a type-I seesaw-like structure:
Mν =
S MT D +O(||MDM−1
S ||2) = 0
L L νCRνR
〈Φ〉 〈Φ〉
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 8 / 18
Minimal Radiative Inverse Seesaw
L L νR νCR
k
p− k p
Small νL mass can be generated at one-loop level from SM electroweak radiative corrections. [Pilaftsis ’92]
M1−loop νL
)] MT
D
Minimal Radiative Inverse Seesaw since does not require any extra (scalar, gauge, or fermion) fields. [PSBD, Pilaftsis ’12]
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 9 / 18
Light Sterile Neutrinos in MRISM
Consider the limit ‖µR‖ � ‖MD‖, ‖MN‖. Integrate out the three heavy singlet states ν1,2,3R with masses of order ‖µR‖. Left with six light states: three active neutrinos νiL, and three sterile ones SρL.
One sterile state in the eV-range can explain the LSND+MiniBooNE+reactor neutrino data.
One sterile state in the keV-range to account for a Dark Matter candidate.
Third sterile state could be in:
keV-range [extra DM candidate]. eV range [(3+2)-sterile model]. sub-eV range [superlight sterile neutrino].
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 10 / 18
Light Sterile Neutrinos in MRISM
Consider the limit ‖µR‖ � ‖MD‖, ‖MN‖. Integrate out the three heavy singlet states ν1,2,3R with masses of order ‖µR‖. Left with six light states: three active neutrinos νiL, and three sterile ones SρL.
One sterile state in the eV-range can explain the LSND+MiniBooNE+reactor neutrino data.
One sterile state in the keV-range to account for a Dark Matter candidate.
Third sterile state could be in:
keV-range [extra DM candidate]. eV range [(3+2)-sterile model]. sub-eV range [superlight sterile neutrino].
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 10 / 18
Two Benchmark Scenarios
ν1
ν5
ν2
ν3
ν4
ν6
B. The (4+1+1) Case
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 11 / 18
Effective Neutrino Mass Matrix
eff
N MNµ
N
D 03 03 03
f (xR) = αW
Z /m2 W , assuming µR = µ̂R13 for simplicity.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 12 / 18
Effective Neutrino Mass Matrix
eff
N MNµ
N
D 03 03 03
f (xR) = αW
Z /m2 W , assuming µR = µ̂R13 for simplicity.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 12 / 18
Diagonalization
)
Use available global-fit results for the mass and mixing parameters. Best-fit values for the active sector: [Gonzalez-Garcia et al. ’12]
θ12 = 33.3◦ , θ23 = 40.0◦ , θ13 = 8.6◦ , ϕ13 = 1.67π, ∆m2
21 = 7.50× 10−5 eV2 , ∆m2 31 = 2.47× 10−3 eV2
For the sterile sector, [Conrad et al. ’12]
∆m2 41 = 0.92 eV2, ∆m2
51 = 17 eV2,
|Ue4| = 0.15 , |Uµ4| = 0.13 , |Ue5| = 0.069 , |Uµ5| = 0.16 , φ54 ≡ arg(Ue5U∗µ5U∗e4Uµ4) = 1.8π
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 13 / 18
Fitting Procedure
−1 R
∥∥∥
with respect to the unknown mixing angles, and predict their values.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 14 / 18
3+2+1 Case
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P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 15 / 18
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P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 16 / 18
Conclusion
Seesaw mechanism is a simple paradigm for understanding some of the outstanding issues in the SM.
Can be tested directly if the heavy neutrinos are accessible at the LHC.
Inverse Seesaw is an attractive low-scale seesaw mechanism.
We prposed the minimal radiative inverse seesaw model.
Can have light sterile neutrinos to explain all existing neutrino data.
In addition, might have some interesting effects for a superlight sterile state.
Thank You.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 17 / 18
Conclusion
Seesaw mechanism is a simple paradigm for understanding some of the outstanding issues in the SM.
Can be tested directly if the heavy neutrinos are accessible at the LHC.
Inverse Seesaw is an attractive low-scale seesaw mechanism.
We prposed the minimal radiative inverse seesaw model.
Can have light sterile neutrinos to explain all existing neutrino data.
In addition, might have some interesting effects for a superlight sterile state.
Thank You.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 17 / 18
νe Survival Probability
(3) For large !m2 01 and relatively small !, the survival
probability as function of the neutrino energy has wiggles (see Fig. 3). The wiggles are a result of the interference of the two amplitudes in the first term of (21) which develops over finite space interval. Indeed, according to (21), there are two channels of transition of "e to "1:
(i) "e has admixture Um e1 in "1m, the latter adiabatically
evolves to "1: "e ! "1m ! "1, and the amplitude equals Um
e1A11. (ii) "e has admixtureUm
e0 in "0m; this state transforms to "1 due to nonadiabatic transition: "e ! "0m ! "1. The corresponding amplitude is Um
e0A01. The two contributions to the amplitude interfere
leading to the oscillatory dependence of the probability on energy (wiggles). Introducing P01 ! jA01j2, so that jA11j2 " 1# P01, we can rewrite the probability (21) as
Pee $ jUe1j2%jUm e1j2&1# P01' ( jUm
e0j2P01
that Um e1 and U
m e0 are real. The oscillatory behavior follows
from the energy dependence of the phase #. The key point is that the phase is collected over restricted space interval, L, and therefore is not averaged out even after integration over the production region. Indeed, the phase# is acquired from the neutrino production point to the second (low density) resonance. Below the second resonance (in den- sity) both ‘‘trajectories’’ (channels of transition) coincide. Appearance of the wiggles requires the adiabaticity viola- tion. In the adiabatic case, A01 " 0, only one channel exists. Unfortunately, it will be difficult, if possible, to observe experimentally these wiggles. Some more details concerning the wiggles are presented in Appendix A.
If "s mixes in "2, then
U! " cos!0 0 sin!0
0 @
1 A (30)
and the Hamiltonian can be obtained from (28) by sub- stitutions
cos&$12 # $m12' ! sin&$12 # $m12'; sin&$12 # $m12' ! # cos&$12 # $m12';
!m2 01 ! !m2
02:
(31)
The state "2m decouples and the "s # "LMA 1m mixing is
given by
2E &1# R!' sin&$12 # $m12': (32)
Notice that this mixing appears due to the matter effect and it is absent in vacuum when $m12 ! $12. It happens that for values of R! we are considering &1# R!'+ sin&$12 # $m12' $ R! cos&$12 # $m12', and therefore the probabilities in this case are very similar to those shown in Figs. 3 and 4.
III. SOLAR NEUTRINO DATA AND STERILE NEUTRINO EFFECT
In what follows, we will consider scenario with m1
A. Borexino measurements of the Be-neutrino line
The results of Borexino experiment [10] are in a very good agreement with prediction based on the LMA solu- tion and thestandard solar model. Within the error bars, no additional suppression of the flux has been found on the top of PLMA
ee . In Borexino (and other experiments based on the "e-scattering), the ratio of the numbers of events with and without conversion can be written as
RBorexino " Pee&1# r' ( r# rPes; (33)
where r ! %&"&e# "&e'=%&"ee# "ee' is the ratio of cross sections. Using Eq. (33), we find an additional sup- pression of the Borexino rate in comparison with the pure LMA case [13]:
!RBorexino ! RLMA Borexino # RBorexino " &1# r'!Pee ( rPes
$ !Pee&1( rtan2$12': In Fig. 5, we show dependence of the survival probability at E " EBe as a function of R! for two different values of
0
0,2
0,4
liy
0 2 4 6 8 10 12 14 neutrino energy (MeV)
0
0,2
0,4
R"=0.08
R"=0.2
R"=0.25
FIG. 4 (color online). The same as in Fig. 3 for higher values of mixing angle !.
P. C. DE HOLANDA AND A.YU. SMIRNOV PHYSICAL REVIEW D 83, 113011 (2011)
113011-6
[de Holanda, Smirnov ’10]
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 18 / 18
Fitting Borexino Data
reproduced by the proposed dip, although with the dip the description is better.2 Also, the Borexino spectrum (Fig. 10) can be fitted better in the presence of sterile neutrino mixing.
C. Fit of spectra
As follows from Figs. 6–10, the mixing with sterile neutrino improves description of the data. It is also clear that, with the present data, it is not possible to make a conclusion about existence of !s-mixing. Further experi- mental studies of the solar neutrino spectrum in the inter- mediate energy range are needed. In view of this for
illustrative purposes, we have performed a simplified "2-fit of the energy spectra shown in Figs. 6–10. This will allow us to quantify somehow the improvement of the description and to determine plausible values of parameters of !s. For the best fit values of !s parameters, we have the
following improvements in individual experiments: !"2 ! 1:94 (SK-I), 0.81 (SK-III), 3.52 (SNO), 0.63 (Borexino) 0.56 (SNO-NC), 7.45 (Total). In our "2 analysis, we use the spectra from SK-I (21 data
points), SK-III (21 points), SNO-LETA (16 points), Borexino (6 points), and SNO-LETA neutral current result (1 point)—altogether 65 degrees of freedom. Recall that all these experiments are sensitive to the same 8B-neutrino flux. We use # and !m2
01 as the fit parameters and fix $12 and !m2
21 to their best fit values from the 2!- LMA analysis. Since oscillations to sterile neutrinos change the neutral current event rate, we cannot use the SNO-LETA neutral currentresult to fix the boron neutrino flux in the model independent way. Therefore, we have performed fit of the spectra employing two different procedures. In the first approach, we use the boron neutrino flux
predicted in the solar neutrino model GS98 [25]: FSSM B !
5:88" 10#6 cm#2 s#1. We computed the difference of "2
obtained in the fits without sterile neutrinos "2 and with sterile neutrinos "2
s :!" 2 $ "2 # "2
s (see Table I). We find that the strongest improvement,!"2 ! 7:5, is obtained for
!m2 01 % 1:6" 10#5 eV2; sin22# % 10#3:
For 65 degrees of freedom and two fit parameters, this!"2
corresponds to an increase of goodness of the fit from 16% to 25%. The fit with !"2 > 6 can be obtained in the range
R! ! 0:12–0:22; sin22# ! &0:6–1:3' " 10#3: (34)
The range of R! in (34) corresponds to !m2 01 (
&0:9–1:8' " 10#5 eV2 and therefore
2 4 6 8 10 12 14
Energy (MeV)
-3
FIG. 10 (color online). The predicted energy spectrum of events due to the 8B-neutrinos at Borexino versus the experi- mental data [17]. The neutrino parameters and the solar model are the same as in Fig. 6.
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ee - (MeV)
Su ri
vi al
P ro
ba bi
lit y,
P ee
FIG. 8 (color online). The predicted Super-Kamiokande-III energy spectrum versus the experimental data [15]. The neutrino parameters and the solar model as well as the normalization factor for pure LMA spectrum are the same as in Fig. 6 (left).
2 4 6 8 10 12
T eff (MeV)
R /R
SS M
FIG. 9 (color online). Prediction for the SNO-LETA electron spectrum versus experimental data [16]. The neutrino parameters and the solar model are the same as in Fig. 6.
2Too sharp a decrease of signal in the lowest energy bins is probably statistical fluctuations or some systematics.
P. C. DE HOLANDA AND A.YU. SMIRNOV PHYSICAL REVIEW D 83, 113011 (2011)
113011-8
[de Holanda, Smirnov ’10]
P. S. Bhupal Dev
Consortium for Fundamental Physics, University of Manchester
PSBD, A. Pilaftsis, Phys. Rev. D86, 113001 (2012) [arXiv:1209.4051 [hep-ph]]; Phys. Rev. D87, 053007 (2013) [arXiv:1212.3808 [hep-ph]].
Baryon and Lepton Number Violation 2013 MPIK, Heidelberg
April 08, 2013
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 1 / 18
Outline
Neutrino Mass and Seesaw Mechanism Inverse Seesaw Minimal Radiative Inverse Seesaw Model (MRISM) Light and Superlight Sterile Neutrinos Conclusion
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 2 / 18
Neutrino Mass and Seesaw Mechanism
Neutrino oscillation data require at least two nonzero neutrino masses.
Massless neutrinos in the SM because of no RH neutrino (no Dirac mass) and a global (B − L)-symmetry (no Majorana mass).
Add νR : for Dirac mass term yνLΦνR alone, require yν <�∼ 10−12.
A more natural way is to break (B − L) by extra fields.
Can be parametrized within the SM by Weinberg’s dimension-5 operator.
The simplest tree-level realization: (type-I) seesaw mechanism.
Observed baryon asymmetry can be explained by leptogenesis.
Supersymmetrization gives an extra DM candidate (mixed sneutrino).
Thus could provide all the missing features of the SM in a single testable framework.
Could be directly probed at colliders if the seesaw scale is < O(TeV).
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 3 / 18
Neutrino Mass and Seesaw Mechanism
Neutrino oscillation data require at least two nonzero neutrino masses.
Massless neutrinos in the SM because of no RH neutrino (no Dirac mass) and a global (B − L)-symmetry (no Majorana mass).
Add νR : for Dirac mass term yνLΦνR alone, require yν <�∼ 10−12.
A more natural way is to break (B − L) by extra fields.
Can be parametrized within the SM by Weinberg’s dimension-5 operator.
The simplest tree-level realization: (type-I) seesaw mechanism.
Observed baryon asymmetry can be explained by leptogenesis.
Supersymmetrization gives an extra DM candidate (mixed sneutrino).
Thus could provide all the missing features of the SM in a single testable framework.
Could be directly probed at colliders if the seesaw scale is < O(TeV).
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 3 / 18
Light Sterile Neutrinos?
There exist a few “anomalies" –can be explained by additional neutrino(s) with ∆m2 ∼ eV2. (See talk by T. Lasserre)
Cannot be active neutrinos due to the LEP invisible Z -decay width constraint.
Must be SM gauge singlets – sterile.
Planck data has put stringent constraints for thermalized light steriles. (See talk by S. Hannestad)
Neff = 3.30+0.54 −0.51 and
∑ mν < 0.23 eV (Planck+WP+highL+BAO). [Ade et al.
’13]
However, light steriles favored by SBL can still be made compatible with cosmology. [Mirizzi et al ’13]
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 4 / 18
Light Sterile Neutrinos?
There exist a few “anomalies" –can be explained by additional neutrino(s) with ∆m2 ∼ eV2. (See talk by T. Lasserre)
Cannot be active neutrinos due to the LEP invisible Z -decay width constraint.
Must be SM gauge singlets – sterile.
Planck data has put stringent constraints for thermalized light steriles. (See talk by S. Hannestad)
Neff = 3.30+0.54 −0.51 and
∑ mν < 0.23 eV (Planck+WP+highL+BAO). [Ade et al.
’13]
However, light steriles favored by SBL can still be made compatible with cosmology. [Mirizzi et al ’13]
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 4 / 18
Canonical (Type-I) Seesaw Add one set of SM singlet RH Majorana neutrinos (νRα
). [ Minkowski ’77; Yanagida ’79;
−LY = yνLΦνR + 1 2 νC
RMRνR + H.c.,
R MT D, Mheavy
ν ' MR
Seesaw Limit: Small (sub-eV) M light ν for large Majorana mass MR .
TeV scale MR possible if MD <�∼ O(me) (barring fine-tuning).
Hard for colliders. /
SO(10)-GUT embedding =⇒ relates MD to charged fermion sector.
Predicts the seesaw scale MR ∼ 1010−14 GeV. /
Light steriles not so natural in type-I seesaw.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 5 / 18
Canonical (Type-I) Seesaw Add one set of SM singlet RH Majorana neutrinos (νRα
). [ Minkowski ’77; Yanagida ’79;
−LY = yνLΦνR + 1 2 νC
RMRνR + H.c.,
R MT D, Mheavy
ν ' MR
Seesaw Limit: Small (sub-eV) M light ν for large Majorana mass MR .
TeV scale MR possible if MD <�∼ O(me) (barring fine-tuning).
Hard for colliders. /
SO(10)-GUT embedding =⇒ relates MD to charged fermion sector.
Predicts the seesaw scale MR ∼ 1010−14 GeV. /
Light steriles not so natural in type-I seesaw.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 5 / 18
Inverse Seesaw Add two sets of SM singlet fermions (νRα
and SLρ ). [Mohapatra ’85; Mohapatra, Valle ’86]
−LY = yνLΦνR + SLMNνR + 1 2 νC
RµRνR + 1 2
SLµSSC L + H.c.,
M light ν '
)T , Mheavy
ν ' MN
TeV scale inverse seesaw easily possible (even with large Dirac Yukawa coupling) due to the smallness of Majorana mass.
( Mν
Smallness of µS is “technically natural”.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 6 / 18
Inverse Seesaw Add two sets of SM singlet fermions (νRα
and SLρ ). [Mohapatra ’85; Mohapatra, Valle ’86]
−LY = yνLΦνR + SLMNνR + 1 2 νC
RµRνR + 1 2
SLµSSC L + H.c.,
M light ν '
)T , Mheavy
ν ' MN
TeV scale inverse seesaw easily possible (even with large Dirac Yukawa coupling) due to the smallness of Majorana mass.
( Mν
Smallness of µS is “technically natural”.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 6 / 18
Inverse Seesaw Add two sets of SM singlet fermions (νRα
and SLρ ). [Mohapatra ’85; Mohapatra, Valle ’86]
−LY = yνLΦνR + SLMNνR + 1 2 νC
RµRνR + 1 2
SLµSSC L + H.c.,
M light ν '
)T , Mheavy
ν ' MN
TeV scale inverse seesaw easily possible (even with large Dirac Yukawa coupling) due to the smallness of Majorana mass.
( Mν
Smallness of µS is “technically natural”.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 6 / 18
Rich Phenomenology
Inverse Seesaw models have very rich phenomenology, e.g.,
A natural way to explain heavy neutrino mass splitting required for resonant leptogenesis. [Blanchet, PSBD, Mohapatra ’10]
Mixed sneutrino DM candidate. [Arina et al. ’08; An, PSBD, Cai, Mohapatra ’11]
Trilepton+ET/ signal for the LHC. [Chen, PSBD ’11; Das, Okada ’12]
Observable non-unitarity and LFV effects. [Malinsky, Ohlsson, Xing, Zhang ’09; PSBD,
Mohapatra ’09; Abada, Das, Vicente, Weiland ’12]
Modifications to SM Higgs signal strength. [PSBD, Franceschini, Mohapatra ’12]
Higgs vacuum stability. [Khan, Goswami, Roy ’12]
Neutrinoless double beta decay. [Mitra, Senjanovic, Vissani ’11; Lopez-Pavon, Pascoli, Wong ’12;
Parida, Patra ’13]
Light sterile neutrinos. [Barry, Rodejohann, Zhang ’11; Zhang ’12; PSBD, Pilaftsis ’13] –This talk.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 7 / 18
Inverse Seesaw with µR 6= 0
Consider the possibility: µR 6= 0, µS = 0 in inverse seesaw mass matrix.
Might arise in models where the Majorana mass term for S-field forbidden due to specific flavour symmetries. [Chun, Joshipura, Smirnov ’95; Barry,
Rodejohann, Zhang ’11]
The light neutrinos are exactly massless at tree-level.
To see this, cast the inverse seesaw mass matrix into a type-I seesaw-like structure:
Mν =
S MT D +O(||MDM−1
S ||2) = 0
L L νCRνR
〈Φ〉 〈Φ〉
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 8 / 18
Inverse Seesaw with µR 6= 0
Consider the possibility: µR 6= 0, µS = 0 in inverse seesaw mass matrix.
Might arise in models where the Majorana mass term for S-field forbidden due to specific flavour symmetries. [Chun, Joshipura, Smirnov ’95; Barry,
Rodejohann, Zhang ’11]
The light neutrinos are exactly massless at tree-level.
To see this, cast the inverse seesaw mass matrix into a type-I seesaw-like structure:
Mν =
S MT D +O(||MDM−1
S ||2) = 0
L L νCRνR
〈Φ〉 〈Φ〉
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 8 / 18
Minimal Radiative Inverse Seesaw
L L νR νCR
k
p− k p
Small νL mass can be generated at one-loop level from SM electroweak radiative corrections. [Pilaftsis ’92]
M1−loop νL
)] MT
D
Minimal Radiative Inverse Seesaw since does not require any extra (scalar, gauge, or fermion) fields. [PSBD, Pilaftsis ’12]
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 9 / 18
Light Sterile Neutrinos in MRISM
Consider the limit ‖µR‖ � ‖MD‖, ‖MN‖. Integrate out the three heavy singlet states ν1,2,3R with masses of order ‖µR‖. Left with six light states: three active neutrinos νiL, and three sterile ones SρL.
One sterile state in the eV-range can explain the LSND+MiniBooNE+reactor neutrino data.
One sterile state in the keV-range to account for a Dark Matter candidate.
Third sterile state could be in:
keV-range [extra DM candidate]. eV range [(3+2)-sterile model]. sub-eV range [superlight sterile neutrino].
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 10 / 18
Light Sterile Neutrinos in MRISM
Consider the limit ‖µR‖ � ‖MD‖, ‖MN‖. Integrate out the three heavy singlet states ν1,2,3R with masses of order ‖µR‖. Left with six light states: three active neutrinos νiL, and three sterile ones SρL.
One sterile state in the eV-range can explain the LSND+MiniBooNE+reactor neutrino data.
One sterile state in the keV-range to account for a Dark Matter candidate.
Third sterile state could be in:
keV-range [extra DM candidate]. eV range [(3+2)-sterile model]. sub-eV range [superlight sterile neutrino].
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 10 / 18
Two Benchmark Scenarios
ν1
ν5
ν2
ν3
ν4
ν6
B. The (4+1+1) Case
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 11 / 18
Effective Neutrino Mass Matrix
eff
N MNµ
N
D 03 03 03
f (xR) = αW
Z /m2 W , assuming µR = µ̂R13 for simplicity.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 12 / 18
Effective Neutrino Mass Matrix
eff
N MNµ
N
D 03 03 03
f (xR) = αW
Z /m2 W , assuming µR = µ̂R13 for simplicity.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 12 / 18
Diagonalization
)
Use available global-fit results for the mass and mixing parameters. Best-fit values for the active sector: [Gonzalez-Garcia et al. ’12]
θ12 = 33.3◦ , θ23 = 40.0◦ , θ13 = 8.6◦ , ϕ13 = 1.67π, ∆m2
21 = 7.50× 10−5 eV2 , ∆m2 31 = 2.47× 10−3 eV2
For the sterile sector, [Conrad et al. ’12]
∆m2 41 = 0.92 eV2, ∆m2
51 = 17 eV2,
|Ue4| = 0.15 , |Uµ4| = 0.13 , |Ue5| = 0.069 , |Uµ5| = 0.16 , φ54 ≡ arg(Ue5U∗µ5U∗e4Uµ4) = 1.8π
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 13 / 18
Fitting Procedure
−1 R
∥∥∥
with respect to the unknown mixing angles, and predict their values.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 14 / 18
3+2+1 Case
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P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 15 / 18
4+1+1 Case
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P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 16 / 18
Conclusion
Seesaw mechanism is a simple paradigm for understanding some of the outstanding issues in the SM.
Can be tested directly if the heavy neutrinos are accessible at the LHC.
Inverse Seesaw is an attractive low-scale seesaw mechanism.
We prposed the minimal radiative inverse seesaw model.
Can have light sterile neutrinos to explain all existing neutrino data.
In addition, might have some interesting effects for a superlight sterile state.
Thank You.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 17 / 18
Conclusion
Seesaw mechanism is a simple paradigm for understanding some of the outstanding issues in the SM.
Can be tested directly if the heavy neutrinos are accessible at the LHC.
Inverse Seesaw is an attractive low-scale seesaw mechanism.
We prposed the minimal radiative inverse seesaw model.
Can have light sterile neutrinos to explain all existing neutrino data.
In addition, might have some interesting effects for a superlight sterile state.
Thank You.
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 17 / 18
νe Survival Probability
(3) For large !m2 01 and relatively small !, the survival
probability as function of the neutrino energy has wiggles (see Fig. 3). The wiggles are a result of the interference of the two amplitudes in the first term of (21) which develops over finite space interval. Indeed, according to (21), there are two channels of transition of "e to "1:
(i) "e has admixture Um e1 in "1m, the latter adiabatically
evolves to "1: "e ! "1m ! "1, and the amplitude equals Um
e1A11. (ii) "e has admixtureUm
e0 in "0m; this state transforms to "1 due to nonadiabatic transition: "e ! "0m ! "1. The corresponding amplitude is Um
e0A01. The two contributions to the amplitude interfere
leading to the oscillatory dependence of the probability on energy (wiggles). Introducing P01 ! jA01j2, so that jA11j2 " 1# P01, we can rewrite the probability (21) as
Pee $ jUe1j2%jUm e1j2&1# P01' ( jUm
e0j2P01
that Um e1 and U
m e0 are real. The oscillatory behavior follows
from the energy dependence of the phase #. The key point is that the phase is collected over restricted space interval, L, and therefore is not averaged out even after integration over the production region. Indeed, the phase# is acquired from the neutrino production point to the second (low density) resonance. Below the second resonance (in den- sity) both ‘‘trajectories’’ (channels of transition) coincide. Appearance of the wiggles requires the adiabaticity viola- tion. In the adiabatic case, A01 " 0, only one channel exists. Unfortunately, it will be difficult, if possible, to observe experimentally these wiggles. Some more details concerning the wiggles are presented in Appendix A.
If "s mixes in "2, then
U! " cos!0 0 sin!0
0 @
1 A (30)
and the Hamiltonian can be obtained from (28) by sub- stitutions
cos&$12 # $m12' ! sin&$12 # $m12'; sin&$12 # $m12' ! # cos&$12 # $m12';
!m2 01 ! !m2
02:
(31)
The state "2m decouples and the "s # "LMA 1m mixing is
given by
2E &1# R!' sin&$12 # $m12': (32)
Notice that this mixing appears due to the matter effect and it is absent in vacuum when $m12 ! $12. It happens that for values of R! we are considering &1# R!'+ sin&$12 # $m12' $ R! cos&$12 # $m12', and therefore the probabilities in this case are very similar to those shown in Figs. 3 and 4.
III. SOLAR NEUTRINO DATA AND STERILE NEUTRINO EFFECT
In what follows, we will consider scenario with m1
A. Borexino measurements of the Be-neutrino line
The results of Borexino experiment [10] are in a very good agreement with prediction based on the LMA solu- tion and thestandard solar model. Within the error bars, no additional suppression of the flux has been found on the top of PLMA
ee . In Borexino (and other experiments based on the "e-scattering), the ratio of the numbers of events with and without conversion can be written as
RBorexino " Pee&1# r' ( r# rPes; (33)
where r ! %&"&e# "&e'=%&"ee# "ee' is the ratio of cross sections. Using Eq. (33), we find an additional sup- pression of the Borexino rate in comparison with the pure LMA case [13]:
!RBorexino ! RLMA Borexino # RBorexino " &1# r'!Pee ( rPes
$ !Pee&1( rtan2$12': In Fig. 5, we show dependence of the survival probability at E " EBe as a function of R! for two different values of
0
0,2
0,4
liy
0 2 4 6 8 10 12 14 neutrino energy (MeV)
0
0,2
0,4
R"=0.08
R"=0.2
R"=0.25
FIG. 4 (color online). The same as in Fig. 3 for higher values of mixing angle !.
P. C. DE HOLANDA AND A.YU. SMIRNOV PHYSICAL REVIEW D 83, 113011 (2011)
113011-6
[de Holanda, Smirnov ’10]
P. S. Bhupal Dev (Univ. of Manchester) Light and Superlight Sterile Neutrinos BLV’13, MPIK, Heidelberg 18 / 18
Fitting Borexino Data
reproduced by the proposed dip, although with the dip the description is better.2 Also, the Borexino spectrum (Fig. 10) can be fitted better in the presence of sterile neutrino mixing.
C. Fit of spectra
As follows from Figs. 6–10, the mixing with sterile neutrino improves description of the data. It is also clear that, with the present data, it is not possible to make a conclusion about existence of !s-mixing. Further experi- mental studies of the solar neutrino spectrum in the inter- mediate energy range are needed. In view of this for
illustrative purposes, we have performed a simplified "2-fit of the energy spectra shown in Figs. 6–10. This will allow us to quantify somehow the improvement of the description and to determine plausible values of parameters of !s. For the best fit values of !s parameters, we have the
following improvements in individual experiments: !"2 ! 1:94 (SK-I), 0.81 (SK-III), 3.52 (SNO), 0.63 (Borexino) 0.56 (SNO-NC), 7.45 (Total). In our "2 analysis, we use the spectra from SK-I (21 data
points), SK-III (21 points), SNO-LETA (16 points), Borexino (6 points), and SNO-LETA neutral current result (1 point)—altogether 65 degrees of freedom. Recall that all these experiments are sensitive to the same 8B-neutrino flux. We use # and !m2
01 as the fit parameters and fix $12 and !m2
21 to their best fit values from the 2!- LMA analysis. Since oscillations to sterile neutrinos change the neutral current event rate, we cannot use the SNO-LETA neutral currentresult to fix the boron neutrino flux in the model independent way. Therefore, we have performed fit of the spectra employing two different procedures. In the first approach, we use the boron neutrino flux
predicted in the solar neutrino model GS98 [25]: FSSM B !
5:88" 10#6 cm#2 s#1. We computed the difference of "2
obtained in the fits without sterile neutrinos "2 and with sterile neutrinos "2
s :!" 2 $ "2 # "2
s (see Table I). We find that the strongest improvement,!"2 ! 7:5, is obtained for
!m2 01 % 1:6" 10#5 eV2; sin22# % 10#3:
For 65 degrees of freedom and two fit parameters, this!"2
corresponds to an increase of goodness of the fit from 16% to 25%. The fit with !"2 > 6 can be obtained in the range
R! ! 0:12–0:22; sin22# ! &0:6–1:3' " 10#3: (34)
The range of R! in (34) corresponds to !m2 01 (
&0:9–1:8' " 10#5 eV2 and therefore
2 4 6 8 10 12 14
Energy (MeV)
-3
FIG. 10 (color online). The predicted energy spectrum of events due to the 8B-neutrinos at Borexino versus the experi- mental data [17]. The neutrino parameters and the solar model are the same as in Fig. 6.
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ee - (MeV)
Su ri
vi al
P ro
ba bi
lit y,
P ee
FIG. 8 (color online). The predicted Super-Kamiokande-III energy spectrum versus the experimental data [15]. The neutrino parameters and the solar model as well as the normalization factor for pure LMA spectrum are the same as in Fig. 6 (left).
2 4 6 8 10 12
T eff (MeV)
R /R
SS M
FIG. 9 (color online). Prediction for the SNO-LETA electron spectrum versus experimental data [16]. The neutrino parameters and the solar model are the same as in Fig. 6.
2Too sharp a decrease of signal in the lowest energy bins is probably statistical fluctuations or some systematics.
P. C. DE HOLANDA AND A.YU. SMIRNOV PHYSICAL REVIEW D 83, 113011 (2011)
113011-8
[de Holanda, Smirnov ’10]
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