Neutrino Mass (Inverse Seesaw ) and Dark - Copy

8/16/2019 Neutrino Mass (Inverse Seesaw ) and Dark - Copy

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By Mallika Priyadarshini ShivamPHY14002

M.Sc Fourth Semester .


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1.A neutral lepton, (an elementary particle with half-integerspin), that interacts only via the weak force and gravity.

2. Comes in three flavors: , ,

3 Neutrinos have long been thought to be to be massless ,aspredicted by the Standard Model.

4. Neutrinos are the most frequent particles in the Universe.(no. exceeds the count of all atoms)

5. The 2015 physics Nobel Prize went to the discoverery of thestrange ability of neutrinos to transform among three “flavors.”


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Are neutrinos Dirac or Majorana particles?

Are there sterile neutrinos?

What is the absolute neutrino mass scale?

If the Neutrino spectrum follows normal or invertedmass hierarchy…?


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The Standard Model is notcomplete.

Convincing evidence-:Neutrino oscillates among itsflavour and mass eigen statesas it propagates.

These conversions can onlyoccur via a quantum-mechanical effect thatrequires neutrino mass to benon-zero.


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Survival Probability

E

Lm

P ee

2sin)2(sin1

)(22122

2

1

2

2

2

21 mmm

In order to have neutrino oscillations:

1)at least one neutrino must have mass.

1)the neutrinos must mix.

Since the oscillation depends on m2 the mass of the neutrinos.


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Right handed neutrinos are inserted by hand

We get three neutrino mass terms —

1.Dirac Mass Term —

= ( + ) + h.c

2.Majorana Mass term —

= + h.c

= + h.c


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L = + +

=

The above mass matrix is

After diagonalizing the following mass eigen statesare obtained ..

≈ ≈ Gev.

≈

− = × ≈ .


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Here small neutrino masses arise as a result ofnew physics at Tev scale.

May be probed at LHC, unlike TYPE I

3 right handed neutrinos + the 3 extra SMgauge singlet neutral fermions S + the 3 activeneutrinos

=


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A diagonalization of the above 9 × matrix leads to the effective light neutrinomass matrix i.e.

= ( )− µ( ) −

. = −

Thus we see that Standard neutrinos with

mass at sub ev scale are obtained for at electroweak scale and at Tev scale.ISS is also called DOUBLE SEESAW


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10

onnecting Neutrinophysics with Dark Matter


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Mass eigen states that are dominantly linear combinations of RHneutrinos.A potential candidate for Dark MatterSterile Neutrino decays into Xray photon and neutrino, aspredicted by Dodelson Widrow Mechanism.

Recent Detection of a 3.5 KeV xray emission line…active areaof research


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Extension of the Standard Model by 2 righthanded neutrinos and 3 sterile states.

, a 8 × mass matrix

Block Diagonalisation gives the the effectiveneutrino mass matrix:

=d − µ−

or − µ−

= d + m + n S +µ S


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THE TEXTURE OF THE MATRICES ARE TAKENAS:

− = =−

= Identity matrix.

µ matrix as a TBM ( Tribimaximal mixing) .

being the product of two identity matrices and aTBM matrix; is also a TBM matrix.

We get light neutrino mass matrix of TBM Type, namely

= t ++

; where t is the

Yukawa coupling.


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Subsequent Proceedings :

The well known neutrino mixing matrix TBM

predict the mixing angle angle = 0.

The non zero and relatively large mixing anglehave already been reported by MINOS, Double

Chooz,, Daya Bay, and RENO collaborations.

For non zero mixing angle , we modify theTribimaximal mixing matrix (TBM) by introducing asimple perturbation matrix.

We proceed with the calculations for studying theneutrino phenomenology in both normal andinverted hierarchy from the modified TBM matrix.


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Our Working Matrix is t ++

It predicts the mixing angles ≅ . °, =45 ° = 0.

Apart from , the other two angles arewithin the 3 σ range of neutrino mixing angle.

To generate non zero , the neutrino massmatrix arising from type II Seesaw is taken as

PERTURBATION , =


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The modified TBM matrix becomes = +

= +

+ + ( )+ ( ) +

For each value of t = 0.1 to 0.5, we diagonalize the abovematrix; the elements of the diagonalized matrix arerelated to the parameters of the model.

By varying the strength w from − to 0.01, we compute10000 values of the neutrino oscillation parameters.

Next we see whether the computed parameters fall in the3σ range ; thereby making our concept of sterile neutrino arelevant parameter of neutrino and Dark Matterphenomenology.


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The variation of Type IIstrength w with thenon vanishing

Parameter bfp 3σ

0.0218 (.0186,.0250)

NH

Parameter bfp 3σ

0.0219 (.0188,.0251)

IH


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Other oscillation parameters as a function of non zero

Parameters bfp 3σ

--- .381 to.643

0.0218 . 0186 to.0250

NH

Parameters bfp 3σ

--- .388to.644

0.0219 . 0188to.0251

IH


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Parameters BFP 3σ

sin2

θ12 0.304 .270 to.344

sin 2 θ13 0.0218 .0186 to.0250

NH

Parameters BFP 3σ

sin 2 θ12 0.304 .270 to

.34 sin 2 θ13 0.0219 .0188 to

.0251

IH


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Parameters Bfp 3 σ

∆

[−

]

2.457 (2.317 ,2.607)

213 0.0218

.0186 to

.0250

Parameters Bfp 3 σ

∆[ − ]

-2.449 (-2.590 ,-2.307)

213 0.0219

.0188 to

.0251

NH

IH


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Parameters Bfp 3 σ

∆[ − ]

7.5 (7.02 ,8.07)

213 0.0218

.0186 to

.0250

NH

Parameters Bfp 3 σ

∆[ − ]

7.5 (7.02 ,8.07)

213 0.0219

.0188 to

.0251

IH


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MODEL ∆ 212 ∆m 31 or2 ∆m 232 θ12 θ13 θ23

TBM( NH)

TBM(IH) ×

The symbol (×)

the column can (cannot) be realised within the model given by the

row .


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The non zero value of has been found tobe consistent with the variation of Type IIseesaw strength.

All the oscillation parameters are beinggenerated in the correct 3σ by the workingmatrix for any value of Yukawa couplingranging from 0.1 to 0.5 in the NH case.

However the matrix is unable to generate ∆ 122 for the IH case; other parameters aregenerated in the 3σ range for the IH case.


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Thus we have studied the prospect of producing nonzero by introducing a perturbation to the lightneutrino mass matrix using Type II seesaw.

We have also determined the strength of the Type IIseesaw term which is responsible for generating nonzero in the correct 3σ range .

This model may have high relevance for future study sofar as dark matter phenomenology and sterile neutrinois concerned.


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[1 ] D. Borah and M. K. Das, Phys. Rev. D90 , 015006 (2014).

[2] S. F. King and N. N. Singh, Nucl. Phys. B596 (2), 26 (2001).

[3] M. Borah, D. Borah, M. K. Das and S. Patra, Perturbations to the -symmetry, Leptogenesis and Lepton flavour violation with Type II Seesaw

Mechanism, Phys. Rev. D90 , 095020 (2014)

[4] M.Taoso, G.Bertone and A. Masiero, Dark Matter Candidates: A ten pointtest, A journal of Cosmology and Astroparticle Physics 2014 , no 10 (October 1,2014)

[5] B. Adhikari, M.Chakrabarty and A. Ghosal, Phys. Rev. D86 , 013015 (2012)

[6] A. Abada, S. Davidson, M. Losada and A. Riotto, JHEP 0601, 164 (2006).

Neutrino Mass (Inverse Seesaw ) and Dark - Copy

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