neutrino mixing at the tev scale and the recent results · t2k is a long-baseline neutrino...

AHMED RASHED

UNIVERSITY OF MISSISSIPPI

O C T O B E R 2 5 , 2 0 11

C O L L O Q U I U M

A R X I V : 11 0 9 . 2 3 2 0 [ H E P - P H ]

A . R A S H E D A N D A . D A T T A

Neutrino Mixing at the TeV Scale and the

Recent Results

Ahmed Rashed COLLOQUIUM 2011, University of Mississippi

Outlines


Neutrino in and beyond the Standard Model

Introduction to neutrino mixing: TBM and BM.

T2K results and neutrino mixing experiments.

The model: BM from flavor symmetry.

The Lagrangian in the symmetric limit.

Symmetry breaking and deviations from the BM limit.

Numerical results.

Our model can treat the TBM in the symmetric limit.

Summary.

Future work.

2

Neutrinos in the Standard Model:

Neutrino is massless in the SM (no right-handed neutrinos)

Neutrinos do not oscillate.

They are companions of charged leptons which come in 3 flavors

νe νµ ντ

e µ τ

Neutrino in and beyond the Standard Model

3


Neutrino is massive (mν ≠ 0)

It could be either Dirac or Majorana.

Neutrinos do oscillate:

vacuum oscillation probability for two neutrinos

P (να νβ) = sin2 2θ sin2 {1.27 δm2 (eV/c4)2 [L(km)/E(GeV)]}

δm2 = m22 - m1

2

Neutrinos beyond the Standard Model

4


5

Dirac mass

Transition between right and left Weyl spinors.

Dirac neutrino field

Dirac neutrino mass (connect 2 distinct Weyl spinors)

Conserves lepton number

Violates weak isospin


Neutrino mass types

ψL ψR

0L

2

13 Lt

6

Majorana mass Neutrinos are Majorana field

(Particle “υ” = Its antiparticle “υc”)

Majorana mass (connect Weyl spinor with itself)

Violate lepton number

Weak isospin:

oActive : (triplet)

o Sterile : (singlet)


Neutrino mass types

2L

13 Lt

03 Lt

7

See-saw model

Neutrinos can have simultaneous Dirac and Majorana mass terms.

Neutrino mass


Neutrino mass types

Introduction to neutrino mixing 8

Flavor and mass eigenbases

Charged current of the weak interaction

Physical lepton mixing matrix


U~

lUl l~

UUl

lJ

l)1(

~)1(~

5

5

IUUUUUU lPMNS )(),()( 121213132323 †

†

Neutrino mixing

Mass-squared differences (m2 > m1)

Δm212 = (7.59±0.2)×10-5 , |Δm23

2|= (2.43±0.13)×10-3

Three neutrinos oscillation

9


076.0008.0 2

13 s

8.055.0)74.055.0(38.025.0

79.06.066.031.0)53.046.0(

28.009.059.051.085.076.0

Tri-Bimaximal mixing (TBM)

In Tri-Bimaximal mixing matrix;

Sin2 θ23 = 1/2 ; Sin2 θ12 = 1/3 ; θ13 = 0

Here ν2 is tri-maximally mixed, whereas

ν3 is bi-maximally mixed.

Extension of the SM symmetry group

SU(3)c × SU(2)L × U(1)Y × …

10


In Bimaximal mixing matrix;

Sin2 θ23 = 1/2 ; Sin2 θ12 = 1/2 ; θ13 = 0

Here ν3 is bi-maximally mixed.

Extension of the SM symmetry group

SU(3)c × SU(2)L × U(1)Y × …

11


Bimaximal mixing (BM)

12

: Majorana mass only

Decay rate

: decay rate

G : two-body phase-space factor

M: the nuclear matrix element

mee : so-called effective

Majorana neutrino mass


Neutrinoless Double Beta Decay ( ) 0

2L22

MG eem

eepn

Recent Results

13

T2K is a long-baseline neutrino oscillation experiment between the Japan Proton Accelerator Research Complex (J-PARC) and the Super-Kamiokande detector. The goal of T2K is to measure

the neutrino mixing angle θ13 by observing

oscillations of muon neutrinos into

electron neutrinos. (υµ υe appearance)


Recent T2K results 14

The result

Appearance of in a beam. (E ~ 0.6 GeV)

CP-Violation


e

0,104.2,0.12sin

)5.2(..%90)(

)34.0(28.02sin)04.0(03.0

232

2323

2

13

2

CPeVmfor

LCatIHNHfor

sin2sin)()( 13

2

2

23

2

12

m

mPPP ee

Experimental results; mixing parameters 15

Best-fit values with errors, and and intervals for the three-flavor neutrino oscillation parameters from global data including solar, atmospheric, reactor (KamLAND and CHOOZ) and accelerator (K2K and MINOS) experiments.


1 32

What we know?, and what we don’t know?

16

We know:

Goal of next generation experiments:


132312

2

23

2

12 ,,|,|, mm

2313

2

23 ,,,?,0 imm (maximal)

Future Experiments. 17

Solar neutrino (S), Low-energy solar neutrino (LS), Reactor neutrino (R), Atmospheric neutrino (ATM), Accelerator neutrino (AC), Elastic scattering (ES), Neutral current (NC), Charged current (CC), Double beta decay (BB)


Abv. Sensetivi

ty Induced reaction Detector

Type of detector

Thre. energy

Location

RENO R (CC) Gd-doped LOS Scintillation 1.8 MeV South Korea

UNO S, ATM (ES) Water

(440 kt H2O) Cherenkov Colorado

Daya Bay R (CC) Gd-doped LOS Scintillation 1.8 MeV Daya Bay,

China

Dbl. Chooz R (CC) Gd-doped LOS Scintillation 1.8 MeV France

HERON LS (NC) Superfluid He Rot. excitation 1 MeV

HOMESTAKE-IODINE S (ES,CC) Nal in water Radiochemical 789 keV S. Dakota

Majorana BB (BB) HPGe Semiconductor 2039 keV S. Dakota

NOυA AC (CC) Liquid scintillator Scintillation 0.1 GeV IL & Minn

ee ee

nepe

nepe

ee xx

XeeI

ee

e

127127

eeAsGe 7676

Xenucle

nepe

The model 18


Symmetric Limit

“Approximated angles” Lagrangian

Symmetry Breaking

Numerical Results

“Realistic angles” Charged Leptons

Neutrino Sector

BM from flavor symmetry

Charged lepton Sector:

In the decoupled 2-3 flavor

symmetric limit, the charged

lepton Yukawa couplings leads

to zero muon mass. It is symmetric under Z2 .

It is diagonalized by the unitary

matrix

19


Cont.

Neutrino Sector:

We can assume a certain form for

This mass matrix can be

diagonalized by

where

Requiring the mass matrix to

be diagonalized by pure numbers.

It is symmetric under Z2 .

20


21


Symmetric Limit


Symmetry Breaking

Numerical Results


Neutrino Sector

The Lagrangian in the Symmetric Limit.

Particle Content:

1. Three left-handed lepton doublets (DαL)

2. Three right-handed charged lepton singlets (αR)

3. Three right-handed neutrino singlets (ναR)

4. Two Higgs doublets (φj)

5. Two real singlet scalar fields (Єj)

22


Lagrangian

The symmetries of the lagrangian:

Z223 : generates the 2-3 symmetry.

Z2e : leads to decoupling in the charged lepton sector .

Z2D : neutrino Dirac mass comes from the second

Higgs only.

23


The Lagrangian of the model:

1. Yukawa Lagrangian

2. Majorana Lagrangian

3. Scalar Potential (Є1 Є2 )

24


Lagrangian

The VEVs of the scalar fields can be parameterized in this way

By minimizing the potential

with

25


Lagrangian

Symmetry breaking, deviations from the symmetric limit.

26


Symmetric Limit


Symmetry Breaking

Numerical Results


Neutrino Sector

“Charged lepton sector”

We break the decoupled 2-3 symmetry by the higher dimensional operators

to generate the muon mass in the full Yukawa matrix (zμ = mμ /mτ)

27


Charged lepton sector

In order to diagonalize the Yukawa matrix

we have to introduce a correction to the unitary matrix

By satisfying the Yukawa matrix elements to the three relations, one can obtain solutions to the three correction angles.

28


For example; (δ=π)

which leads to

The charged lepton contribution can accommodate the recent results from the T2K experiment.

29


Charged lepton sector

Symmetry breaking term for (Є1 Є2 ) in the scalar potential

under the condition

The SB slightly shifts the VEVs of the two singlet scalars ω1 ≠ ω2 (or, cos 2γ ≠ 0).

30


“Neutrino sector”

In order to diagonalize the neutrino mass matrix

we have to introduce a correction to the unitary matrix

By satisfying the mass matrix

elements to the two relations,

one can obtain a solution

to the two correction

angles.

31


Neutrino sector

Symmetry breaking; Full picture

We obtain the lepton mixing matrix

32


Numerical results. 33


Symmetric Limit


Symmetry Breaking

Numerical Results


Neutrino Sector

34

Three mass-dependent neutrino observables:

: sum of absolute masses, probed in cosmology

: kinetic electron neutrino mass, probed in direct

search for neutrino masses (e.g. Troitsk Exp.)

: effective mass for neutrinoless double beta decay


Numerical results.

im

M

eeM

35


Numerical results.

For z=2.0, we have (s12L , s23L , s13L) = (-0.34 ,-0.059 ,-0.0011), with τ=0.1

36


Numerical results.

37


Numerical results.

For z=2.06, we have (s12L , s23L , s13L) = (-0.3 ,-0.061 ,-0.001), with τ=0.1

38


Numerical results.

1. The results accommodate the recent T2K data θ13 =9.70 2. The experimental constraints on the mixing angles

support the normal hierarchy of neutrino masses. 3. The case of degenerate neutrino masses are excluded in

the symmetric and SB limit. 4. The scale of the neutrino masses are expected to be in the

few meV to ~ 50 meV. 5. From the graphs, the see-saw scale (M, M′) are in the TeV 6. The VEV of the second Higgs that couples to the right-

handed neutrinos is in the MeV scale. 7. The graphs indicate that the VEV of the singlet scalar

fields vω is in the TeV scale. 8. We found that

39


Numerical results.

.35.0,,17.006.0 eVMMMeVm eeeei

Our model treats the TBM in the symmetric limit

40

Neutrino mass matrix,

Symmetry,


41

Lagrangian

Scalar potential (S3)


Our model treat TBM.

42


Our model treat TBM.

43

Comparison BM TBM

Sin θ12 1/2 1/3

Symmetry group

Particle content

Charged lepton sector Accommodate Doesn’t accommodate

θ13 , θ12 , θ23 13 , 27 , 38 7 , 31 , 44

m1 , m2 , m3 (eV) 3 , 9 , 50 2 , 9 , 50

M, M’ (TeV) 2.0 , 0.2 2.0 , 0.2

A, vw (MeV/TeV) 0.1 , 2.0 0.1 , 2.0


Comparison between TBM and BM

De ZZZ 22

23

2 )1(4

23

2 UZZ

21,,, jR 321 ,,,, jR

We considered the decoupled 2-3 symmetry to be the flavor symmetry in the charged lepton sector.

The SM symmetry group is extended by the product of symmetries

The Lagrangian includes right-handed neutrinos, two real singlet scalar fields, and an additional Higgs field.

The model accommodates the experimental results.

Our model can treat both the TBM and BM patterns.

Summary

44


Future Work

45

Study the CP-violating parameters.

Study the phenomenology of the model; masses and new couplings of the new fields.


46


Thank you

47

Extra slides


Using the seesaw mechanism, the generated neutrino mass matrix can be obtained as,

48


Lagrangian

We introduce an additional invariant term to violate the almost degeneracy of the neutrino masses

which leads to the Majorana mass matrix and the neutrino mass matrix

49


Neutrino sector

Parameterization of the mixing matrix up to the first order

Up to the first order, we obtain the mixing angles as

50


Symmetry breaking; Full picture

Numerical results.

We obtain the lepton mixing matrix

The experimental constraints on the deviation parameters (r, s, a)

51


J-PARC/T2K status (Earthquake) 52

J-PARC and surrounding area were affected by the March 11 earthquake roads and buildings have suffered visible damage

The tsunami did not reach the lab

No T2K collaborators or J-PARC staff were injured

all foreign collaborators left Tokai area safely within a few days of the disaster

The reactors at the JAEA site in Tokai are fine

Electricity is still limited and no drinking water

Preliminary inspection has been carried out, but no thorough survey yet until power is restored


53


54


The Model 55


Symmetric Limit


Symmetry Breaking

Numerical Results


Neutrino Sector

OPERA 56

The OPERA neutrino experiment at the underground Gran Sasso Laboratory (LNGS) was designed to perform the first detection of neutrino oscillations in direct appearance mode in the νμ→ντ channel, the signature being the identification of the τ− lepton created by its charged current (CC) interaction.

For CNGS neutrino energies, <Eν> = 17 GeV, the relative

deviation from the speed of light c of the neutrino velocity due to its finite rest mass is expected to be smaller than 10-19, even assuming the mass of the heaviest neutrino eigenstate to be as large as 2 eV


OPERA (Cont.) 57

Researchers on the OPERA experiment recorded the arrival times of the neutrinos sent from CERN on a 730 km journey through the Earth to the LNGS. The trip would normally take a beam of light 2.4 milliseconds to complete, but after running the experiment for three years the scientists discovered that the particles arrived at Gran Sasso sixty billionths of a second (60 nsec) earlier. The measurement amounts to the neutrinos traveling 7.4 km/sec faster than the speed of light. This anomaly correspond to a relative difference of the neutrino velocity (v) with respect to the speed of light (c),


OPERA (Cont.) 58

The PDF (the probability density function of the time of emission of the neutrinos within the duration of extraction) can then be compared with the time distribution of the interactions detected in OPERA, in order to measure TOFν.

The deviation

δt = TOFc - TOFν

is obtained


OPERA (Cont.) 59

The total statistics used for the analysis reported in this paper is of 16111 events detected in OPERA, corresponding to about 1020 protons on target collected during the 2009, 2010 and 2011 CNGS runs. This allowed estimating δt with a small

statistical uncertainty, presently comparable to

the total systematic uncertainty.


OPERA (Cont.) 60

The momentum and energy combine into a covariant 4-vector:

The invariant magnitude of the momentum four vector is:

Since it is a scalar, it doesn't matter which reference frame we calculate it, and then by transforming to a frame where the total momentum is zero.


z

y

x

p

p

p

cE

P

/

222 )/( pcEP

222 )()/( cmcEP rest

OPERA (Cont.) 61

G. Cohen and L. Glashow (arXiv:1109.6562v1)

They showed that such superluminal neutrinos would lose energy rapidly via the bremsstrahlung of electron-positron pairs (υ υ+e−+e+). For the claimed superluminal neutrino velocity and at the stated mean neutrino energy, they found that most of the neutrinos would have suffered several pair emissions en route, causing the beam to be depleted of higher energy neutrinos. Thus they refuted the superluminal interpretation of the OPERA result.


OPERA (Cont.) 62

Xiao-Jun Bi, Peng-Fei Yin, Zhao-Huan Yu, and Qiang Yuan (arXiv:1109.6667)

They found that such a large Lorentz invariance violation (LIV) implied by OPERA data will make the neutrino production process π→ μ + υμ kinematically forbidden for neutrino energy greater than about 5 GeV. The OPERA detection of neutrinos at 40 GeV can constrain the LIV parameter to be smaller than 3 × 10−7.


Neutrinoless double-beta decay 63

More than 60 naturally occurring isotopes are capable of undergoing double-beta decay

48Ca, 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128Te, 130Te, 130Ba, 136Xe, 150Nd, and 238U.

Completed experiments: Gotthard TPC, Heidelberg-Moscow, IGEX, NEMO1 and 2

Current and proposed experiments COBRA, CUORICINO and CUORE, EXO, GERDA,

MAJORANA

MOON, NEMO-3 and SuperNEMO, NEXT, SNO+, KamLAND-Zen

mββ between ~ 0.2-0.5 eV


http://en.wikipedia.org/wiki/Calcium-48



http://en.wikipedia.org/wiki/Germanium-76

http://en.wikipedia.org/wiki/Germanium-76

http://en.wikipedia.org/wiki/Selenium-82

http://en.wikipedia.org/wiki/Selenium-82

http://en.wikipedia.org/wiki/Zirconium-96

http://en.wikipedia.org/wiki/Zirconium-96

http://en.wikipedia.org/wiki/Molybdenum-100

http://en.wikipedia.org/wiki/Molybdenum-100

http://en.wikipedia.org/wiki/Cadmium-116

http://en.wikipedia.org/wiki/Cadmium-116

http://en.wikipedia.org/wiki/Tellurium-128




http://en.wikipedia.org/wiki/Barium-130

http://en.wikipedia.org/wiki/Barium-130

http://en.wikipedia.org/wiki/Xenon-136

http://en.wikipedia.org/wiki/Xenon-136

http://en.wikipedia.org/wiki/Neodymium-150

http://en.wikipedia.org/wiki/Neodymium-150

http://en.wikipedia.org/wiki/Uranium-238

http://en.wikipedia.org/wiki/Uranium-238

http://www.unine.ch/phys/corpus/Gothard/got_art.html

http://www.klapdor-k.de/



http://www.unizar.es/lfnae/ipaginas/ip0400.html

http://nemo.in2p3.fr/




http://cobra.physik.uni-dortmund.de/

http://crio.mib.infn.it/wig/Cuoricinopage/CUORICINO.php

http://crio.mib.infn.it/wig/Cuorepage/CUORE.php

http://en.wikipedia.org/wiki/EXO

http://www.mpi-hd.mpg.de/ge76/

http://majorana.npl.washington.edu/

http://ewiserver.npl.washington.edu/moon/

http://en.wikipedia.org/wiki/Neutrino_Ettore_Majorana_Observatory



http://nemo.in2p3.fr/supernemo/

http://next.ific.uv.es/

http://en.wikipedia.org/wiki/SNO+

http://www.awa.tohoku.ac.jp/kamlande/



ATM. & SOLAR NEUTRINOS 64


eHeep 224 4

65


66


neutrino mixing at the tev scale and the recent results · t2k is a long-baseline neutrino...

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