two-loop neutrino masses with large r-parity violating...
TRANSCRIPT
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Two-loop neutrino masses with large R-parityviolating interactions in supersymmetry
Paramita Dey
Regional Center for Accelerator-based Particle PhysicsHarish-Chandra Research Institute, Allahabad, India
Work done with Anirban Kundu, Biswarup Mukhopadhyaya and Soumitra Nandi
JHEP12(2008)100, [arXiv:0808.1523]
Paramita Dey HRI NuHoRIzons09 – p. 1
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Basic ideas behind our work
It is an inescapable fact that neutrinos are massive andtheir physical states are mixtures of flavour eigenstates.
Paramita Dey HRI NuHoRIzons09 – p. 2
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Basic ideas behind our work
It is an inescapable fact that neutrinos are massive andtheir physical states are mixtures of flavour eigenstates.
In standard model (SM) neutrinos are massless to allorders in perturbation theory (without νR and L-violation).
Paramita Dey HRI NuHoRIzons09 – p. 3
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Basic ideas behind our work
It is an inescapable fact that neutrinos are massive andtheir physical states are mixtures of flavour eigenstates.
In standard model (SM) neutrinos are massless to allorders in perturbation theory (without νR and L-violation).
SM has to be extended; there are several possibilities(including introduction of νR).
Paramita Dey HRI NuHoRIzons09 – p. 4
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Basic ideas behind our work
It is an inescapable fact that neutrinos are massive andtheir physical states are mixtures of flavour eigenstates.
In standard model (SM) neutrinos are massless to allorders in perturbation theory (without νR and L-violation).
SM has to be extended; there are several possibilities(including introduction of νR).
One possibility (without νR) is a supersymmetric (SUSY)extension of SM with renormalizable R-parity violating( 6Rp) terms in the Lagrangian.
Paramita Dey HRI NuHoRIzons09 – p. 5
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Basic ideas behind our work
It is an inescapable fact that neutrinos are massive andtheir physical states are mixtures of flavour eigenstates.
In standard model (SM) neutrinos are massless to allorders in perturbation theory (without νR and L-violation).
SM has to be extended; there are several possibilities(including introduction of νR).
One possibility (without νR) is a supersymmetric (SUSY)extension of SM with renormalizable R-parity violating( 6Rp) terms in the Lagrangian.
Rp = (−1)3B+L+2S can be violated either by L-orB-violation, but not both simultaneously.
Paramita Dey HRI NuHoRIzons09 – p. 6
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Basic ideas...The MSSM superpotential is:
WMSSM = µH1H2 + huijQ
iU jH2 + hdijQ
iDjH1 + hℓijL
iEjH2
The complete 6Rp-superpotential is:
W 6Rp= λijkLiLjE
ck + λ′
ijkLiQjDck + λ′′
ijkUci D
cjD
ck + ǫiLiH2
Paramita Dey HRI NuHoRIzons09 – p. 7
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Basic ideas...The MSSM superpotential is:
WMSSM = µH1H2 + huijQ
iU jH2 + hdijQ
iDjH1 + hℓijL
iEjH2
The complete 6Rp-superpotential is:
W 6Rp= λijkLiLjE
ck + λ′
ijkLiQjDck + λ′′
ijkUci D
cjD
ck + ǫiLiH2
L violation results in small Majorana mass terms forneutrinos (∆L = 2).
Paramita Dey HRI NuHoRIzons09 – p. 8
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Basic ideas...The MSSM superpotential is:
WMSSM = µH1H2 + huijQ
iU jH2 + hdijQ
iDjH1 + hℓijL
iEjH2
The complete 6Rp-superpotential is:
W 6Rp= λijkLiLjE
ck + λ′
ijkLiQjDck + λ′′
ijkUci D
cjD
ck + ǫiLiH2
L violation results in small Majorana mass terms forneutrinos (∆L = 2).
We consider the trilinear λ′ijk-type couplings only.
Paramita Dey HRI NuHoRIzons09 – p. 9
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Basic ideas...The MSSM superpotential is:
WMSSM = µH1H2 + huijQ
iU jH2 + hdijQ
iDjH1 + hℓijL
iEjH2
The complete 6Rp-superpotential is:
W 6Rp= λijkLiLjE
ck + λ′
ijkLiQjDck + λ′′
ijkUci D
cjD
ck + ǫiLiH2
L violation results in small Majorana mass terms forneutrinos (∆L = 2).
We consider the trilinear λ′ijk-type couplings only.
λ′ijk
[
νiLdk
RdjL + dj
LdkRνi
L + (dkR)∗(νi
L)cdjL − ei
LdkRuj
L
−ujLdk
ReiL − (dk
R)∗(eiL)cuj
L
]
+ h.c.
Paramita Dey HRI NuHoRIzons09 – p. 10
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Neutrino mass from λ′ijk-terms
Relevant terms : λ′ijk
[
djL dk
R νiL + (dk
R)∗ (νiL)c dj
L
]
+ h.c.
⊗dp d∗
p
νi dk νcj
(m1−loopν )ij ≃
3
8π2md
k mdp M
SUSY
1
m2q
λ′ipk λ′
jkp
Observed pattern of neutrino masses ⇒ λ′ ∼ 10−5 − 10−4 fora SUSY breaking mass scale ∼ 500 GeV.
Paramita Dey HRI NuHoRIzons09 – p. 11
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Basic ideas...
Q: Does this mean
All trilinear 6Rp-couplings are destined to be so small?
Observation of any process, requiring large values(∼ 0.1 − 1.0) of some λ′-terms, necessarily indicate weneed additional mechanism to explain neutrino masspattern?
Paramita Dey HRI NuHoRIzons09 – p. 12
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Basic ideas...
Q: Does this mean
All trilinear 6Rp-couplings are destined to be so small?
Observation of any process, requiring large values(∼ 0.1 − 1.0) of some λ′-terms, necessarily indicate weneed additional mechanism to explain neutrino masspattern?
A: No, so long as we can
Eliminate one-loop contributions, but
Allow two-loop ones,
through a limited number of large (∼ 0.1 − 1.0) λ′-terms.
Paramita Dey HRI NuHoRIzons09 – p. 13
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Indications(?) of some large λ′’sLarge leptonic branching ratio of the Ds meson:
Expts : fDs= 273 ± 10 MeV. (Dobrescu and Kronfeld, arXiv:0803.0512
[hep-ph])
Lattice : fDs= 250 ± 15 MeV. (HPQCD Collab, arXiv:0706.1726
[hep-lat], Lubicz and Tarantino, arXiv:0807.4605 [hep-lat])
⇒ Large λ′223 for Ds → µν, λ′
323 for Ds → τν
(Kundu and Nandi, arXiv:0803.1898 [hep-ph])
Paramita Dey HRI NuHoRIzons09 – p. 14
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Suppose such a hint comes insome other expt, even if Ds-data donot stay?
Paramita Dey HRI NuHoRIzons09 – p. 15
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What we have to fit
sin2(2θ12) = 0.86+0.03−0.04, sin2(2θ23) > 0.92, sin2(2θ13) < 0.19
Normal hierarchy: m3 >> m2 & m1
m22 = (7.60 ± 0.35) × 10−5 eV2,
∣
∣m23 − m2
2
∣
∣ = (2.50 ± 0.27) × 10−3 eV2
Inverted hierarchy: m2 & m1 >> m3
m22 − m2
1 = (7.60 ± 0.35) × 10−5 eV2,∣
∣m22 − m2
3
∣
∣ ≃∣
∣m21 − m2
3
∣
∣ = (2.50 ± 0.27) × 10−3 eV2
Degenerate neutrinos: m1 ≃ m2 ≃ m3 ≃ O(10−1) eV
Paramita Dey HRI NuHoRIzons09 – p. 16
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What we need?
A ‘minimal’ set of ‘large’ λ′’s so thatthere are no one-loop neutrinomasses.
Paramita Dey HRI NuHoRIzons09 – p. 17
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Minimal set of λ′’s: PropertiesNo less than three λ′ type couplings, each with a differentleptonic index, for the three neutrinos.
Paramita Dey HRI NuHoRIzons09 – p. 18
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Minimal set of λ′’s: PropertiesNo less than three λ′ type couplings, each with a differentleptonic index, for the three neutrinos.
Couplings like λ′ijj =⇒ generate diagonal entries of
neutrino mass matrix at one-loop.
Paramita Dey HRI NuHoRIzons09 – p. 19
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1-loop masses from λ′ijj
Relevant terms : λ′ijj
[
djL dj
R νiL
]
and λ′ijj
[
(djR)∗ (νi
L)c djL
]
⊗dj d∗
j
νi dj νci
(m1−loopν )ii ≃
3
8π2md
j mdj M
SUSY
1
m2q
λ′ijj λ′
ijj
Paramita Dey HRI NuHoRIzons09 – p. 20
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Minimal set of λ′’s: PropertiesNo less than three λ′ type couplings, each with a differentleptonic index, for the three neutrinos.
Couplings like λ′ijj =⇒ generate diagonal entries of
neutrino mass matrix at one-loop =⇒ forbidden.
Paramita Dey HRI NuHoRIzons09 – p. 21
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Minimal set of λ′’s: PropertiesNo less than three λ′ type couplings, each with a differentleptonic index, for the three neutrinos.
Couplings like λ′ijj =⇒ generate diagonal entries of
neutrino mass matrix at one-loop =⇒ forbidden.
Combinations like λ′ilkλ
′jkl =⇒ generate diagonal (i = j)
and off-diagonal (i 6= j) entries of neutrino mass matrix atone-loop.
Paramita Dey HRI NuHoRIzons09 – p. 22
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1-loop masses from λ′ilkλ
′jkl comb.
Relevant terms : λ′ilk
[
dlL dk
R νiL
]
and λ′jkl
[
(dlR)∗ (νj
L)c dkL
]
⊗dl d∗
l
νi dk νcj
(m1−loopν )ij ≃
3
8π2md
k mdl M
SUSY
1
m2q
λ′ilk λ′
jkl
Paramita Dey HRI NuHoRIzons09 – p. 23
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Minimal set of λ′’s: PropertiesNo less than three λ′ type couplings, each with a differentleptonic index, for the three neutrinos.
Couplings like λ′ijj =⇒ generate diagonal entries of
neutrino mass matrix at one-loop =⇒ forbidden.
Combinations like λ′ilkλ
′jkl =⇒ generate diagonal (i = j)
and off-diagonal (i 6= j) entries of neutrino mass matrix atone-loop =⇒ forbidden.
Paramita Dey HRI NuHoRIzons09 – p. 24
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Minimal set of λ′’s: PropertiesNo less than three λ′ type couplings, each with a differentleptonic index, for the three neutrinos.
Couplings like λ′ijj =⇒ generate diagonal entries of
neutrino mass matrix at one-loop =⇒ forbidden.
Combinations like λ′ilkλ
′jkl =⇒ generate diagonal (i = j)
and off-diagonal (i 6= j) entries of neutrino mass matrix atone-loop =⇒ forbidden.
Combinations like λ′ilkλ
′jkm =⇒ generate one-loop masses
with the mass insertion δLRlm .
Paramita Dey HRI NuHoRIzons09 – p. 25
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1-loop masses from λ′ilkλ
′jkm comb.
Relevant terms : λ′ilk
[
dlL dk
R νiL
]
and λ′jkm
[
(dmR )∗ (νj
L)c dkL
]
⊗dl d∗
m
νi dk νcj
(m1−loopν )ij ≃
3
8π2md
k mdl M
SUSY
1
m2q
λ′ilk λ′
jkm ∆LRlm
where ∆LRlm = δLR
lm /mlMSUSY.
Paramita Dey HRI NuHoRIzons09 – p. 26
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Minimal set of λ′’s: PropertiesNo less than three λ′ type couplings, each with a differentleptonic index, for the three neutrinos.
Couplings like λ′ijj =⇒ generate diagonal entries of
neutrino mass matrix at one-loop =⇒ forbidden.
Combinations like λ′ilkλ
′jkl =⇒ generate diagonal (i = j)
and off-diagonal (i 6= j) entries of neutrino mass matrix atone-loop =⇒ forbidden.
Combinations like λ′ilkλ
′jkm =⇒ generate one-loop masses
with the mass insertion δLRlm =⇒ Cannot avoid having at
least one element of neutrino mass matrix with l = m =⇒
forbidden.
Paramita Dey HRI NuHoRIzons09 – p. 27
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Minimal set of λ′’s: PropertiesNo less than three λ′ type couplings, each with a differentleptonic index, for the three neutrinos.
Couplings like λ′ijj =⇒ generate diagonal entries of
neutrino mass matrix at one-loop =⇒ forbidden.
Combinations like λ′ilkλ
′jkl =⇒ generate diagonal (i = j)
and off-diagonal (i 6= j) entries of neutrino mass matrix atone-loop =⇒ forbidden.
Combinations like λ′ilkλ
′jkm =⇒ generate one-loop masses
with the mass insertion δLRlm =⇒ Cannot avoid having at
least one element of neutrino mass matrix with l = m =⇒
forbidden.
The chosen non-zero λ′’s can lie in the range 0.1 − 1.
Paramita Dey HRI NuHoRIzons09 – p. 28
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What we need?
We need at least 3 λ′’s, each with adifferent leptonic index, and 2 ∆LR’sin a minimal set.
Paramita Dey HRI NuHoRIzons09 – p. 29
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The minimal set chosen
Choose λ′223 and λ′
323 in the minimal set =⇒ partially motivated byexplanation of results on Ds decays.
Paramita Dey HRI NuHoRIzons09 – p. 30
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The minimal set chosen
Choose λ′223 and λ′
323 in the minimal set =⇒ partially motivated byexplanation of results on Ds decays.
Possible choices for the third λ′ are: λ′112, λ′
121, λ′113, λ′
131, λ′123.
Paramita Dey HRI NuHoRIzons09 – p. 31
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The minimal set chosen
Choose λ′223 and λ′
323 in the minimal set =⇒ partially motivated byexplanation of results on Ds decays.
Possible choices for the third λ′ are: λ′112, λ′
121, λ′113, λ′
131, λ′123.
Cannot choose λ′112
One-loop contributions to Mν(1, 2) and Mν(1, 3) driven by ∆LR13 .
Phenomenological constraints don’t allow it to be large.
Paramita Dey HRI NuHoRIzons09 – p. 32
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The minimal set chosen
Choose λ′223 and λ′
323 in the minimal set =⇒ partially motivated byexplanation of results on Ds decays.
Possible choices for the third λ′ are: λ′112, λ′
121, λ′113, λ′
131, λ′123.
Cannot choose λ′112
One-loop contributions to Mν(1, 2) and Mν(1, 3) driven by ∆LR13 .
Phenomenological constraints don’t allow it to be large.
Similarly, cannot choose λ′131.
Paramita Dey HRI NuHoRIzons09 – p. 33
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The minimal set chosen
Choose λ′223 and λ′
323 in the minimal set =⇒ partially motivated byexplanation of results on Ds decays.
Possible choices for the third λ′ are: λ′112, λ′
121, λ′113, λ′
131, λ′123.
Cannot choose λ′112
One-loop contributions to Mν(1, 2) and Mν(1, 3) driven by ∆LR13 .
Phenomenological constraints don’t allow it to be large.
Similarly, cannot choose λ′131.
If λ′123 is chosen, we have
No one-loop contributions.
A set of four independent parameters: λ′223, λ′
323, λ′123 and ∆LR
23 .
Difficult to fit Mν with experimental data.
Paramita Dey HRI NuHoRIzons09 – p. 34
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The minimal set...
If λ′113 is chosen, we have
No one-loop contributions.
A set of five independent parameters: λ′223, λ′
323, λ′113, ∆LR
23 and∆LR
13 .
=⇒ We could fit Mν with experimental data.
Paramita Dey HRI NuHoRIzons09 – p. 35
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The minimal set...
If λ′113 is chosen, we have
No one-loop contributions.
A set of five independent parameters: λ′223, λ′
323, λ′113, ∆LR
23 and∆LR
13 .
=⇒ We could fit Mν with experimental data.
λ′121 could also be chosen
No one-loop contributions.
A set of five independent parameters: λ′223, λ′
323, λ′121, ∆LR
23 and∆LR
21 .
=⇒ But this choice is severely restricted by absence of leptonic flavorviolating decays π0 → eµ, φ → eµ, B → e(µ)τ etc.
Paramita Dey HRI NuHoRIzons09 – p. 36
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Constraints: [ λ′223 λ′
323 λ′113 ∆LR
13 ∆LR23 ]
λ′223 and λ′
323 . 1.
Recent CLEO constraint on Υ → µτ consistent with this upper
limit (arXiv:0807.2695 [hep-ex]).
|λ′113| ≤ 0.15 at 99% confidence level.
charged current universality, processes like π+ → e+νe
(V.D. Barger, G.F. Giudice and T. Han, Phys. Rev. D 40, 2987 (1989)).
∆LR13 < 5.2
From B0-B0 mixing.
∆LR23 < 1
From inclusive b → sγ branching ratio.
Paramita Dey HRI NuHoRIzons09 – p. 37
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Two-loop diagrams: 1⊗
dp d∗p′
νi dk un dk′ νcj
W+, φ+, H+
Overall vertex factors: λ′ipk λ′
jk′p′ ∆LRpp′ Vundk
V ∗undk′
[Mν ]11 ∼mbMSUSY
(m2d − m2
b)∆LR
13 V ∗tsVtb md
[Mν ]ij ∼mbMSUSY
(m2s − m2
b)∆LR
23 V ∗tdVtb ms i, j = 2, 3
Paramita Dey HRI NuHoRIzons09 – p. 38
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Two-loop diagrams: 2⊗dp d∗
p′
νi dk uk′ ℓcj νc
j
φ+, H+
Overall vertex factors: λ′ipk λ′
jk′p′ ∆LRpp′ Vuk′dk
[Mν ]11 ∼ Vub
mbMSUSY
m2W
∆LR13
m2u
m2W
m2e
m2W
md
[Mν ]ii ∼ Vcb
mbMSUSY
m2W
∆LR23
m2c
m2W
m2ℓi
m2W
ms i = 2, 3
Paramita Dey HRI NuHoRIzons09 – p. 39
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Two-loop diagrams: 3
dk d∗p′
νi ℓci
up dk′ νcj
W+, φ+, H+
Overall vertex factors: λ′ipk λ′
jk′p′ ∆LRkp′ Vupdk′
We chose [λ′223 λ′
323 λ′113] =⇒ k = p′ = 3 =⇒ ∆kp′ = 1
[Mν ]11 ∼ V ∗ud
m2u
m2W
me [Mν ]ii ∼ V ∗cs
m2c
m2W
mℓii = 2, 3
Paramita Dey HRI NuHoRIzons09 – p. 40
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Diagrams contributing...
Based on lepton/quark mass dependence
of loop integrals
For a given element of Mν, contributions
of diagrams of type 1 > type 3 > type 2.
For a given diagram, contribution to the
(i, j)-elements (i, j = 2, 3) of Mν are
more than the rest of the elements.
Paramita Dey HRI NuHoRIzons09 – p. 41
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Diagrams not contributing: 1
νi χ0k
νcj
νi νj
×
×
×
bL
bR
bR
bL
bL,R
bL,R
×
×
bL
bR
bR
bL
Paramita Dey HRI NuHoRIzons09 – p. 42
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Diagrams not contributing: 1
These diagrams contribute only when there is amass-splitting between CP-even and CP-odd sneutrinos(F. Borzumati and J.S. Lee, Phys. Rev. D 66, 115012 (2002) [arXiv:hep-ph/0207184]).
We choose a mass ≃ 500 GeV for all sleptons.
Paramita Dey HRI NuHoRIzons09 – p. 43
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Diagrams not contributing: 2
×
×
×
νi νjc
ν
χ0j
bL
bRbR
bL
bL
νi νjc
dp
dk dn
ν
d∗p′
These diagrams involve λ′ilkλ
′jkl combination, one which
generates one-loop masses.
Some are induced by trilinear L-violating soft SUSYbreaking terms.
Paramita Dey HRI NuHoRIzons09 – p. 44
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Values of parameters used
tan β = 10
Charged Higgs mass = 500 GeV
Squark mass (all) = 500 GeV
mt = 172.5 GeV
|Vtd| = (8.12 ± 0.88) × 10−3
|Vts| = (40.67 ± 1.3) × 10−3
|Vcb| = (40.8 ± 0.6) × 10−3
sin 2β = 0.755 ± 0.040 where β = arg(V ∗td)
Paramita Dey HRI NuHoRIzons09 – p. 45
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Mixing matrix, θ23 = π/4, θ13 = 0
m1c2 + m2s
2 cs√2(−m1 + m2)
cs√2(m1 − m2)
cs√2(−m1 + m2)
1
2(m1s
2 + m2c2 + m3)
1
2(−m1s
2 − m2c2 + m3)
cs√2(m1 − m2)
1
2(−m1s
2 − m2c2 + m3)
1
2(m1s
2 + m2c2 + m3)
Paramita Dey HRI NuHoRIzons09 – p. 46
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Mixing matrix, θ23 = π/4, θ13 = 0
m1c2 + m2s
2 cs√2(−m1 + m2)
cs√2(m1 − m2)
cs√2(−m1 + m2)
1
2(m1s
2 + m2c2 + m3)
1
2(−m1s
2 − m2c2 + m3)
cs√2(m1 − m2)
1
2(−m1s
2 − m2c2 + m3)
1
2(m1s
2 + m2c2 + m3)
Look at (2, 2) and (3, 3) elements
Recall the dominant contributions;
[Mν ]22
∼ λ′223 λ′
223
mbMSUSY
(m2s − m2
b)
∆LR
23 V ∗tdVtb ms
[Mν ]33
∼ λ′323 λ′
323
mbMSUSY
(m2s − m2
b)
∆LR
23 V ∗tdVtb ms
Paramita Dey HRI NuHoRIzons09 – p. 47
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Mixing matrix, θ23 = π/4, θ13 = 0
m1c2 + m2s
2 cs√2(−m1 + m2)
cs√2(m1 − m2)
cs√2(−m1 + m2)
1
2(m1s
2 + m2c2 + m3)
1
2(−m1s
2 − m2c2 + m3)
cs√2(m1 − m2)
1
2(−m1s
2 − m2c2 + m3)
1
2(m1s
2 + m2c2 + m3)
Look at (2, 2) and (3, 3) elements
Recall the dominant contributions;
[Mν ]22
∼ λ′223 λ′
223
mbMSUSY
(m2s − m2
b)
∆LR
23 V ∗tdVtb ms
[Mν ]33
∼ λ′323 λ′
323
mbMSUSY
(m2s − m2
b)
∆LR
23 V ∗tdVtb ms
=⇒ λ′223 ≈ λ′
323.
Paramita Dey HRI NuHoRIzons09 – p. 48
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Correlation plots for NH, θ13 = 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5
∆ 23
λ’223
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 0.1 0.2 0.3 0.4 0.5
∆ 13
λ’113
0
0.1
0.2
0.3
0.4
0.5
0 0.1 0.2 0.3 0.4 0.5
λ’11
3
λ’223
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
∆ 13
∆23
Paramita Dey HRI NuHoRIzons09 – p. 49
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Correlation plots for IH, θ13 = 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
∆ 23
λ’223
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
∆ 13
λ’113
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
λ’11
3
λ’223
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
∆ 13
∆23
Paramita Dey HRI NuHoRIzons09 – p. 50
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Correlation plots for DN, θ13 = 0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
∆ 23
λ’223
0.5
1
1.5
2
2.5
3
3.5
4
0.4 0.5 0.6 0.7 0.8 0.9 1
∆ 13
λ’113
0.4
0.5
0.6
0.7
0.8
0.9
1
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
λ’11
3
λ’223
0.5
1
1.5
2
2.5
3
3.5
4
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
∆ 13
∆23
Paramita Dey HRI NuHoRIzons09 – p. 51
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Correlation plots for NH, θ13 = 10◦
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5
∆ 23
λ’223
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 0.1 0.2 0.3 0.4 0.5
∆ 13
λ’113
0
0.1
0.2
0.3
0.4
0.5
0 0.1 0.2 0.3 0.4 0.5
λ’11
3
λ’223
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
∆ 13
∆23
Paramita Dey HRI NuHoRIzons09 – p. 52
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ConclusionsLarge trilinear R-parity violating interactions are notnecessarily an impediment to the explanation of neutrinomasses and mixing.
Paramita Dey HRI NuHoRIzons09 – p. 53
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ConclusionsLarge trilinear R-parity violating interactions are notnecessarily an impediment to the explanation of neutrinomasses and mixing.
One can reconcile large R-parity violating couplings andneutrino masses, if only a subset of all possible couplingsof such nature exist.
Paramita Dey HRI NuHoRIzons09 – p. 54
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ConclusionsLarge trilinear R-parity violating interactions are notnecessarily an impediment to the explanation of neutrinomasses and mixing.
One can reconcile large R-parity violating couplings andneutrino masses, if only a subset of all possible couplingsof such nature exist.
If there is indication of large couplings, the subset mustfurther be determined by the impossibility of generatingone-loop neutrino masses.
Paramita Dey HRI NuHoRIzons09 – p. 55
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ConclusionsLarge trilinear R-parity violating interactions are notnecessarily an impediment to the explanation of neutrinomasses and mixing.
One can reconcile large R-parity violating couplings andneutrino masses, if only a subset of all possible couplingsof such nature exist.
If there is indication of large couplings, the subset mustfurther be determined by the impossibility of generatingone-loop neutrino masses.
Two-loop contributions are tenable in such situations, andthey can fit the entire neutrino mass matrix answering tothe experimental constraints.
Paramita Dey HRI NuHoRIzons09 – p. 56
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ConclusionsFor our choice of the minimal set with three λ′-couplingsand two squark flavour violating parameters, we couldreproduce the NH scenario.
Paramita Dey HRI NuHoRIzons09 – p. 57
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ConclusionsFor our choice of the minimal set with three λ′-couplingsand two squark flavour violating parameters, we couldreproduce the NH scenario.
IH and DN cases could be reproduced either withadditional R-parity violating terms in the superpotential,or including the bilinear R-parity violating terms.
Paramita Dey HRI NuHoRIzons09 – p. 58
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Thank You
Paramita Dey HRI NuHoRIzons09 – p. 59