open questions in physics : mechanism & eft iii. neutrinos
TRANSCRIPT
• Open questions in physics
• : mechanism & EFT
III. Neutrinos
New “Periodic Table”
Courtesy: R.D. McKeown
Not physical states
Missing Solar Neutrinos…
Courtesy: R.D. McKeown
Neutrino Oscillations: What We’ve Learned & What’s Unknown
The status of the present knowledge of the neutrinooscillation
phenomenais schematicallydepicted in this slide.Three quantities areunknown at present:a) The mass m1
b) The angle 13
c) Whether the normal or
inverted hierarchy is
realized.Courtesy: P. Vogel
Neutrino Masses and Mixing: Scales
Courtesy: R.D. McKeown
Maki – Nakagawa – Sakata Matrix
CP violation
Future ReactorExperiment!
Courtesy: R.D. McKeown
νL νR( )mD
mD M
⎛
⎝ ⎜
⎞
⎠ ⎟
νL
νR
⎛
⎝ ⎜
⎞
⎠ ⎟
mν =mD
2
M<<mD
“Seesaw mechanism”
M
The Mass Puzzle
Courtesy: R.D. McKeown
Very heavy neutrino
}Familiar light neutrino
{
The Mixing Angle Puzzle
Why so different???Why so different???
Courtesy: R.D. McKeown
• What is the absolute value of m ? Why is m so tiny ?
• What is the mass hierarchy ?
• Is the neutrino its own antiparticle?
• What is 13 ?
• Do neutrinos violate CP?
• How do neutrinos affect/reflect astrophysical phenomena ?
Open Questions
-Decay: LNV? Mass Term?
€
e−
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e−
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M
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W −
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W −
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A Z,N( )
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A Z − 2,N + 2( )0.1
1
10
100
1000
Effective
( )Mass meV
12 3 4 5 6 7
12 3 4 5 6 7
12 3 4 5 6 7
1 ( )Minimum Neutrino Mass meV
U1e=.866δm2
sol=7meV
2
U2e=.5δm2
atm=2meV
2
U 3e =
Inverted
Normal
Degenerate
Dirac Majorana
-decayLong baseline
?
?
Theory Challenge: matrix elements+ mechanism
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mν
EFF= Uek
2mk e2iδ
k
∑
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e−
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e−
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χ 0
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˜ e −
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u
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u
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d
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d
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˜ e −€
e−
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e−
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M
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W −
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W −
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u
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u
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d
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d
mEFF & neutrino spectrum
Normal Inverted
See-saw mechanism
Leptogenesis
L LR
H H
Lepton Asym -> Baryon Asym
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
GERDA CUORE
EXO Majorana
Majorana or Dirac
Or equivalently, is the total lepton number conserved?
Courtesy: P. Vogel
& Lepton Number Violation
0e– e–
u d d u
()R L
W W
Whatever processes cause , its observation would imply the existence of a Majorana mass term:
Schechter and Valle,82
By adding only Standard model interactions we obtain
()R ()L Majorana mass term Courtesy: P. Vogel
Decay vs. 2 Decay
virtual state of the intermediate nucleus virtual state of the intermediate nucleus
Courtesy: P. Vogel
Decay vs. 2 Decay
2.0
1.5
1.0
0.5
0.01.00.80.60.40.20.0
Ke/Q
30
20
10
0
1.101.000.90Ke/Q
assumed 2%resolution
2
ratio 1:100
ratio1:106
Courtesy: P. Vogel
-Decay: Theoretical Challenges
Dirac Majorana
Theory Challenge: matrix elements+ mechanism
€
mν
EFF= Uek
2mk e2iδ
k
∑
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e−
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e−
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χ 0
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˜ e −
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u
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u
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d
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d
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˜ e −€
e−
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e−
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M
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W −
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W −
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u
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u
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d
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d
Light M exchange: can we determine m
Shell Model vs. QRPA
Configs near Fermi surface
Levels above Fermi surface
Vogel et al: reduce QRPA spread by calibrating gPP to T2
Decay Matrix Elements
Why it is difficult to calculatethe matrix elements accurately?
Contributions of differentangular momenta J of theneutron pair that is transformed in the decay into the proton pair with the same J.
Note the opposite signs, and thus tendency to cancel, between the J = 0 (pairing) and the J 0(ground state correlations) parts.
The same restricted s.p. space is used for QRPA and NSM. There is a reasonable agreement between the two methodsCourtesy: P. Vogel
Decay Matrix Elements
Full estimated range of M within QRPA framework and comparison with NSM (higher order currents now included in NSM) Courtesy: P. Vogel
-Decay: Theoretical Challenges
Dirac Majorana
Theory Challenge: matrix elements+ mechanism
€
mν
EFF= Uek
2mk e2iδ
k
∑
€
e−
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e−
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χ 0
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˜ e −
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u
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u
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d
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d
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˜ e −€
e−
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e−
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M
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W −
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W −
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u
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u
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d
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d
Mechanism: does light M exchange dominate ?
How to calc effects reliably ? How to disentangle H & L ?
O(1) for ~ TeV
-Decay: Mechanism & m
0.1
1
10
100
1000
Effective
( )Mass meV
12 3 4 5 6 7
12 3 4 5 6 7
12 3 4 5 6 7
1 ( )Minimum Neutrino Mass meV
U1e=.866δm2
sol=7meV
2
U2e=.5δm2
atm=2meV
2
U 3e =
Inverted
Normal
Degeneratesignal equivalent to degenerate hierarchy
Loop contribution to m of inverted hierarchy scale
-Decay: Theoretical Challenges
Dirac Majorana
Theory Challenge: matrix elements+ mechanism
€
mν
EFF= Uek
2mk e2iδ
k
∑
€
e−
€
e−
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χ 0
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˜ e −
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u
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u
€
d
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d
€
˜ e −€
e−
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e−
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M
€
W −
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W −
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u
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u
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d
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d
Mechanism: does light M exchange dominate ?
How to calc effects reliably ? How to disentangle H & L ?
O(1) for ~ TeV
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u
€
d€
u
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d
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e−
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e−
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N
€
N€
π
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π€
e−
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e−
Prezeau, R-M, Vogel: EFT
Does operator power counting suffice?
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n
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n
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p
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p
€
ˆ O 0νββL
- decay Mechanism: EFT
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e−
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e−
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M
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W −
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W −
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u
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u
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d
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d
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e−
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e−
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χ 0
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˜ e −
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u
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u
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d
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d
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˜ e −
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e−
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e−
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A Z,N( )
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A Z + 2,N − 2( )€
u
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d€
u
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d
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e−
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e−
4 quark operator: low energy EFT
How do we compute & separate heavy particle exchange effects?
- decay in EFT I
We have a clear separation of scales
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>>>χ >> kF
L-violating new physics
Non-perturbative QCD
Nuclear dynamics
Effective Field Theory
Systematically and effectively organizing our ignorance
Weak: MW
Hadronic: χ
Nuclear: kF
Scale separation
€
LEFF =GF
2C j
j
∑ (Λχ ) p Λχ( )j
“Low-energy constants” parameterizing non-perturbative QCD
Nuclear operators reflecting symmetries of short distance physics
Power counting
- decay in EFT II
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N
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N€
π
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π€
e−
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e−
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N
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N€
π€
e−
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e−
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N
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N
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e−
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e−
Tractable nuclear operators
Systematic operator classification
- decay in EFT III
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N
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N€
π
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π€
e−
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e−
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N
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N€
π€
e−
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e−
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N
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N
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e−
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e−
€
Kππ p−2
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KπNN p−1
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KNNNN p0
Kππ, KπNN , KNNNN can be O ( p0 ), O ( p1 ), etc.
- decay in EFT IV
Operator classification
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μ =MWEAK
€
μ =M HAD
Spacetime & chiral transformation properties
L(q,e) Lπ,N,e
- decay in EFT V
Operator classification
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μ =MWEAK
L(q,e) =
€
GF2
Λββ
C j (μ) ˆ O j++ e Γ je
c + h.c.j=1
14
∑
€
ˆ O 1+ab = q Lγ μτ aqL q Rγ μτ bqR e.g.
- decay: a = b = +
- decay in EFT VI
Operator classification
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μ =MWEAK
€
ˆ O 1+ab = q Lγ μτ aqL q Rγ μτ bqR
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qL → LqL
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qR → RqR
€
L
R= exp i
r θ L
R
⋅r τ
2PL
R
⎛
⎝ ⎜
⎞
⎠ ⎟
Chiral transformations: SU(2)L x SU(2)R
€
ˆ O 1+ab ∈ (3L , 3R )
Parity transformations: qL qR
- decay: a = b = +
€
ˆ O 1+++ ↔ ˆ O 1+
++
- decay in EFT VI
Hadronic basis
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XRa = ξ τ a ξ +
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XLa = ξ + τ a ξ
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ξ =exp ir τ ⋅
r π 2( ), ,
Chiral transformations
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ˆ O 1+++ ~ Tr XR
+ XL+
( ) ~2
Fπ2
π − π − +L
No derivatives Kππ ~ O (p0)
- decay in EFT VIII
Hadronic basis
Chiral transformations
€
ˆ O 3+++ ~ Tr Dμ XL
+ Dμ XL+ + L ↔ R( )[ ] ~
2
Fπ2
∂ μπ − ∂μπ − +L
Two derivatives Kππ ~ O (p2)
€
ˆ O 3+++ = q Lτ +γ μqL q Lτ +γ μqL + q Rτ +γ μqR q Rτ +γ μqR
€
5L ,1R( )⊕ 1L ,5R( )
- decay in EFT: Implications
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N
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N€
π
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π€
e−
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e−
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N
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N€
π€
e−
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e−
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N
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N
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e−
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e−
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KNNNN p0
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KπNN p−1
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Kππ p−2
Prezeau, R-M, & VogelL(q,e) =
€
GF2
Λββ
C j (μ) ˆ O j++ e Γ je
c + h.c.j=1
14
∑
Chiral properties of Oj++
determine p-dependence of KππKπNN , KNNNN
€
ˆ O 1+++ ∈ (3L , 3R ) Kππ ~ O (p0)
€
ˆ O 3+++ ∈ (5, 1)⊕ (1, 5) Kππ ~ O (p2)
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e−
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e−
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χ 0
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˜ e −
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u
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u
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d
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d
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˜ e −
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ˆ O 1+++ ∈ (3L , 3R )
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ˆ O 3+++ ∈ (5L , 1R )⊕ (1L , 5R )
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ˆ O 1+++ ∈ (3L , 3R )
No WR - WL
mixing
WR - WL mix
RPV SUSY
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M
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W −
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W −
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u
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u
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d
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d
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e−
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e−
An open question
Is the power counting of operators sufficient to understand weak matrix elements in nuclei ?
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n
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n
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p
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p
€
ˆ O 0νββL
76Ge76Se€
g9 2ν
( )2
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p3 2π
( )2, f5 2
π( )
2
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l =0,K ,9
€
′l =0,K ,5
An open question
Is the power counting of operators sufficient to understand weak matrix elements in nuclei ?
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l =0,K ,9
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′l =0,K ,5
€
ˆ O 0νββL
e.g.
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M fi ~ p0
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l = ′l =0
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ˆ O 0νββL= 0
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M fi ~ p0
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l =2, ′ l = 0
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ˆ O 0νββL= 2
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M fi ~ p4
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l =0, ′ l = 2
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ˆ O 0νββL= 2
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M fi ~ p0
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l =4, ′ l = 0
€
ˆ O 0νββL= 4
etc.
-Decay: Interpretation
0.1
1
10
100
1000
Effective
( )Mass meV
12 3 4 5 6 7
12 3 4 5 6 7
12 3 4 5 6 7
1 ( )Minimum Neutrino Mass meV
U1e=.866δm2
sol=7meV
2
U2e=.5δm2
atm=2meV
2
U 3e =
Inverted
Normal
Degenerate
Dirac Majorana
Theory Challenge: matrix elements+ mechanism
€
mν
EFF= Uek
2mk e2iδ
k
∑
€
e−
€
e−
€
χ 0
€
˜ e −
€
u
€
u
€
d
€
d
€
˜ e −€
e−
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e−
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M
€
W −
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W −
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u
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u
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d
€
d
If the existence of the decay is established:
• What mechanism?
• Which additional isotopes ?
-Decay: Mechanism & m
- SM extensions with low ( TeV) scale LNV **
** In absence of fine-tuning or hierarchies in flavor couplings. Important caveat! See: V. Cirigliano et al., PRL93,231802(2004)
Left-right symmetric model,R-parity violating SUSY, etc.possibly unrelated tom
2
R ~ O(π1312
R = Bμe/Bμe» 10-2
Bμe = (μe)/(μeμe) μ(Z,A) e- + (Z,A))
μ(Z,A) μ + (Z,A))Bμe =
Lepton Flavor & Number Violation
Present universe Early universe
Weak scale Planck scale
log10(μ / μ0)
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S−1
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L−1
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Y−1
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μ
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e
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μ
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e
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A Z,N( )
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A Z,N( )
MEG: Bμ->e ~ 5 x 10-14
Mu2e: Bμ->e ~ 5 x 10-17
??
R = Bμ->e
Bμ->e
Also PRIME
Lepton Flavor & Number Violation
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μ
€
e
€
€
μ
€
e
€
A Z,N( )
€
A Z,N( )
MEG: Bμ!e ~ 5 x 10-14
Mu2e: Bμ!e ~ 5 x 10-17
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μ
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e
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*
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e
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e
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˜ ν
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μ
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e
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*
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e+
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e+
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Δ−−
Logarithmic enhancements of R
Low scale LFV: R ~ O(1) GUT scale LFV: R ~ O
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e−
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e−
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M
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W −
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W −
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u
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u
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d
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d
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e−
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e−
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χ 0
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˜ e −
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u
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u
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d
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d
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˜ e −
0decay
Light M exchange ?
Heavy particle exchange ?
Raidal, Santamaria; Cirigliano, Kurylov, R-M, Vogel
k11/ ~ 0.09 for mSUSY ~ 1 TeV
μ->e LFV Probes of RPV:
k11/ ~ 0.008 for mSUSY ~ 1 TeV
μ->e LFV Probes of RPV:
• What is the absolute value of m ? Why is m so tiny ?
• What is the mass hierarchy ?
• Is the neutrino its own antiparticle?
• What is 13 ?
• Do neutrinos violate CP?
• How do neutrinos affect/reflect astrophysical phenomena ?
Open Questions
Precision Neutrino Property Studies
Neutrino Mass: Terrestrial vs Cosmological
WMAP & BeyondKATRIN, Mare
0.1
1
10
100
1000
Effective
( )Mass meV
12 3 4 5 6 7
12 3 4 5 6 7
12 3 4 5 6 7
1 ( )Minimum Neutrino Mass meV
U1e=.866δm2
sol=7meV
2
U2e=.5δm2
atm=2meV
2
U 3e =
Inverted
Normal
Degenerate
Energy Density Power Spectrum
Beacom, Bell, Dodelson
New interactions
Precision Neutrino Property Studies
Mixing, hierarchy, & CPV
€
U =
Ue1 Ue2 Ue 3
Uμ1 Uμ 2 U μ 3
Uτ 1 Uτ 2 Uτ 3
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
=
1 0 0
0 cosθ23 sinθ23
0 −sinθ23 cosθ23
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟×
cosθ13 0 e−iδ CP sinθ13
0 1 0
−e iδ CP sinθ13 0 cosθ13
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟×
cosθ12 sinθ12 0
−sinθ12 cosθ12 0
0 0 1
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟×
1 0 0
0 e iα / 2 0
0 0 e iα / 2+iβ
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
Mini Boone
Long baseline oscillation studies:
CPV?
Normal or Inverted ?
Daya Bay
Double Chooz
T2K
Precision Neutrino Property Studies
Solar Neutrinos
KamLAND Borexino SNO+ LENS
Ice Cube
High energy solar s
DM + EWB
EM vs. luminosity: MNSP unitarity? Solar model?