neutrino mixing at the tev scale and the recent results · t2k is a long-baseline neutrino...
TRANSCRIPT
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
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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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
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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)
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Neutrino mass types
2L
13 Lt
03 Lt
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See-saw model
Neutrinos can have simultaneous Dirac and Majorana mass terms.
Neutrino mass
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Neutrino mass types
Introduction to neutrino mixing 8
Flavor and mass eigenbases
Charged current of the weak interaction
Physical lepton mixing matrix
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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 × …
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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 × …
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Bimaximal mixing (BM)
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: 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
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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)
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Recent T2K results 14
The result
Appearance of in a beam. (E ~ 0.6 GeV)
CP-Violation
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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.
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
1 32
What we know?, and what we don’t know?
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We know:
Goal of next generation experiments:
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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)
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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 .
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Symmetric Limit
“Approximated angles” Lagrangian
Symmetry Breaking
Numerical Results
“Realistic angles” Charged Leptons
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)
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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.
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
The Lagrangian of the model:
1. Yukawa Lagrangian
2. Majorana Lagrangian
3. Scalar Potential (Є1 Є2 )
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Lagrangian
The VEVs of the scalar fields can be parameterized in this way
By minimizing the potential
with
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Lagrangian
Symmetry breaking, deviations from the symmetric limit.
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Symmetric Limit
“Approximated angles” Lagrangian
Symmetry Breaking
Numerical Results
“Realistic angles” Charged Leptons
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)
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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.
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
For example; (δ=π)
which leads to
The charged lepton contribution can accommodate the recent results from the T2K experiment.
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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).
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
“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.
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Neutrino sector
Symmetry breaking; Full picture
We obtain the lepton mixing matrix
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Numerical results. 33
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Symmetric Limit
“Approximated angles” Lagrangian
Symmetry Breaking
Numerical Results
“Realistic angles” Charged Leptons
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
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Numerical results.
im
M
eeM
35
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Numerical results.
For z=2.0, we have (s12L , s23L , s13L) = (-0.34 ,-0.059 ,-0.0011), with τ=0.1
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Numerical results.
37
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Numerical results.
For z=2.06, we have (s12L , s23L , s13L) = (-0.3 ,-0.061 ,-0.001), with τ=0.1
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Numerical results.
.35.0,,17.006.0 eVMMMeVm eeeei
Our model treats the TBM in the symmetric limit
40
Neutrino mass matrix,
Symmetry,
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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Lagrangian
Scalar potential (S3)
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Our model treat TBM.
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Future Work
45
Study the CP-violating parameters.
Study the phenomenology of the model; masses and new couplings of the new fields.
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
46
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Thank you
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Extra slides
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Using the seesaw mechanism, the generated neutrino mass matrix can be obtained as,
48
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Neutrino sector
Parameterization of the mixing matrix up to the first order
Up to the first order, we obtain the mixing angles as
50
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Symmetry breaking; Full picture
Numerical results.
We obtain the lepton mixing matrix
The experimental constraints on the deviation parameters (r, s, a)
51
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
The Model 55
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
Symmetric Limit
“Approximated angles” Lagrangian
Symmetry Breaking
Numerical Results
“Realistic angles” Charged Leptons
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
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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),
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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.
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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.
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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.
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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.
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
ATM. & SOLAR NEUTRINOS 64
Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
eHeep 224 4
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi
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Ahmed Rashed COLLOQUIUM 2011, University of Mississippi