neutrinos: results and future
DESCRIPTION
Neutrinos: Results and Future. Boris Kayser DESY March 4, 2008. Evidence For Flavor Change. Neutrinos Solar Reactor (L ~ 180 km) Atmospheric Accelerator (L = 250 and 735 km) Stopped + Decay LSND L 30 m. Evidence of Flavor Change Compelling Compelling Compelling - PowerPoint PPT PresentationTRANSCRIPT
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Neutrinos: Neutrinos: Results and Results and
FutureFutureBoris KayserBoris KayserDESYDESY
March 4, 2008March 4, 2008
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Evidence For Flavor ChangeNeutrinos
Solar Reactor
(L ~ 180 km)
AtmosphericAccelerator
(L = 250 and 735 km)
Stopped Decay LSND
L 30 m
Evidence of Flavor Change
CompellingCompelling
CompellingCompelling
Unconfirmed by MiniBooNE
( )
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Neutrinos have nonzero masses
Leptons mix.
The neutrino flavor-change observations imply that —
and that —
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What We What We Have LearnedHave Learned
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(Mass)2
12
3
or
123
}m2so
l
m2atm
}m2so
l
m2atm
m2sol = 7.6 x 10
–5 eV2, m2
atm = 2.4 x 10–3 eV2
~ ~
Normal
Inverted
The (Mass)2 Spectrum
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Are There MoreMore Than 3 Mass Eigenstates?
Rapid oscillation reported by LSND —
1eV2
in contrast to
> m2sol = 7.6 x
10–5 eV2
m2atm = 2.4 x
10–3 eV2
At least 4 mass eigenstates.
When only two neutrinos count,
€
P ν α → ν β( ) = sin 2 2θ sin2 1.27Δm2 eV 2( )
L km( )
E GeV( )
⎡
⎣ ⎢
⎤
⎦ ⎥
€
→ e
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MiniBooNE Search for e
•No excess above background for energies E > 475 MeV.
•Unexplained excess for E < 475 MeV.
•Two-neutrino oscillation cannot fit LSND and MiniBooNE.
•More complicated fits are possible.
R.Tayloe at LP07
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MiniBooNE in the NuMI Beam
The MiniBooNE detector is illuminated by both
the MiniBooNE beam, and the NuMI beam pointed at MINOS.Distance to MiniBooNE —
L (from NuMI source) 1.4 L (from MiniBooNE source)
Neutrino oscillation depends on L and E only through L/E.
Therefore, if an anomaly seen at some E in the MiniBooNE-beam data is due
to oscillation, it should appear at 1.4 E in the
NuMI-beam data.
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Outgoing electron angular Outgoing electron angular distributiondistribution
ee CCQE sample: CCQE sample: Reconstructed energy Reconstructed energy EE of of
incoming incoming
All
All e
PRELIMINARY
PRELIMINARY
(Z. Djurcic, Dec. 11, 2007)
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To be continued …
Meanwhile, we will assume there are
only 3 neutrino mass eigenstates.
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This has the consequence that —
|i > = Ui |> .
Flavor- fraction of i = |Ui|2 .
When a i interacts and produces a charged lepton, the probability that this charged lepton will be of flavor is |Ui|2 .
Leptonic Mixing
PMNS Leptonic Mixing Matrix
Mass eigenstate
Flavor eigenstate
e, , or
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e [|Uei|2]
[|Ui|2] [|Ui|2]
Normal Inverted
m2atm
(Mass)2
m2sol}
m2atm
m2sol}
or
sin213
sin213
The spectrum, showing its approximate flavor content, is
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The Mixing Matrix
€
U =
1 0 0
0 c23 s23
0 −s23 c23
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥×
c13 0 s13e−iδ
0 1 0
−s13eiδ 0 c13
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥×
c12 s12 0
−s12 c12 0
0 0 1
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
×
eiα1 /2 0 0
0 eiα 2 /2 0
0 0 1
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
12 ≈ sol ≈ 34°, 23 ≈ atm ≈ 37-53°, 13 < 10°
would lead to P( ) ≠
P( ). CP
But note the crucial role of s13 sin 13.
cij cos ijsij sin ij
Atmospheric
Cross-Mixing
Solar
Majorana CP phases~
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“Atmospheric” m2 and mixing angle
from MINOS, Super-K, and K2K.
From talk by
N. Saoulid
ou
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“Solar” m2 and mixing angle from KamLAND and solar
experiments.
Presented by
KamLAND, a reactor
e experiment
.
m sol
2eV2
€
tan2 θsol
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KamLAND Evidence for Oscillation
L0 = 180 km is a flux-weighted average travel distance.
P(e e) actually oscillates!
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7Be Solar Neutrinos
Until recently, only the 8B solar neutrinos,
with E 7 MeV, had been studied in detail.
The Large Mixing Angle MSW (matter) effect boosts the
fraction of the 8B solar e that get transformed into neutrinos of
other flavors to roughly 70%.
At the energy E = 0.862 MeV of the 7Be solar neutrinos, the matter effect is expected to be very
small. Only about 45% of the 7Be solar e are expected to change into neutrinos of other flavors.
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Borexino —
Detects the 7Be solar neutrinos via e e elastic scattering.
Event rate (Counts/day/100 tons)
Observed: 47 7(stat) 12(syst)
Expected (No Osc): 75 4
Expected (With 45% Osc): 49 4
Expected (With 70% Osc): ~ 31
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QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.The Open The Open QuestionsQuestions
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•What is the absolute scale
of neutrino mass?
•Are neutrinos their own antiparticles?
•Are there “sterile” neutrinos?
We must be alert to surprises!
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•What is the pattern of mixing among
the different types of neutrinos?
What is 13?
•Do neutrino – matter interactions violate CP?
Is P( ) P( ) ?
•Is the spectrum like or ?
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• What can neutrinos and the universe tell us about one
another?
• Is CP violation involving neutrinos the key to understanding the matter – antimatter asymmetry
of the universe?
•What physics is behind neutrino mass?
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QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
The The Importance of Importance of
Some Some Questions, Questions,
and How They and How They May Be May Be
AnsweredAnswered
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That is, for each mass eigenstate i does —
• i = i (Majorana neutrinos)
or• i ≠ i (Dirac neutrinos) ?
Does = ?
Equivalently, do neutrinos have Majorana masses? If they do, then the mass eigenstates are Majorana
neutrinos.
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Majorana Masses
mLL Lc
Out of, say, a left-handed neutrino field, L, and its charge-conjugate, Lc, we can build a Majorana mass term —
XmL
L()R
Quark and charged-lepton Majorana masses are forbidden by electric charge conservation.
Neutrino Majorana masses would make the neutrinos very distinctive.
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The objects L and Lc in mLL Lc are not the mass eigenstates, but just the neutrinos in terms of which the model is constructed.
mLL Lc induces L Lc
mixing.
As a result of K0 K0 mixing, the neutral K mass eigenstates are —
KS,L (K0 K0)/2 . KS,L = KS,L .
As a result of L Lc
mixing, the neutrino mass eigenstate is —
i = L + Lc = “ + ”. i = i .
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To Determine To Determine If Neutrinos If Neutrinos Have Majorana Have Majorana
MassesMasses
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The Promising Approach —
Neutrinoless Double Beta Decay [0]
We are looking for a small Majorana neutrino mass. Thus, we will need a lot of parent nuclei (say, one ton of them).
e–
e–
Nucl Nucl’
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0e– e–
u d d u
()R L
W W
Whatever diagrams cause 0, its observation would imply the
existence of a Majorana mass term:Schechter and Valle
()R L : A Majorana mass term
0 i = i
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The Central Role of 13
Both CP violation and our ability to tell whether the spectrum is normal or inverted depend on 13.
Determining 13 is an important step.
If sin2213 > 10–(2-3), we can study both
of these issues with intense but conventional accelerator
and beams, produced via + + + and – – + .
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How 13 May Be Measured
Reactor neutrino experiments are the cleanest way.
Accelerator neutrino experiments can also probe 13 . Now it is entwined
with other parameters.
In addition, accelerator experiments can probe
whether the mass spectrum is normal or inverted,
and look for CP violation.
All of this is done by studying e and e
while the beams travel hundreds of kilometers.
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Generically, grand unified models (GUTS) favor —
GUTS relate the Leptons to the Quarks.
is un-quark-like, and would probably involve a lepton symmetry with no quark analogue.
The Mass Spectrum: or ?
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How To Determine If The Spectrum Is Normal Or
InvertedExploit the fact that, in matter,
W
e
e
e( )
e( )
affects and oscillation (differently), and leads to —
P( e)P( e)
> 1 ;< 1 ;
Note fake CP
Note dependence on the mass ordering
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Q : Does matter still affect and differently when = ?
A : Yes!
“”
e+ W+
e– W–
“”
Spin
Spin
The weak interactions violate parity. Neutrino – matter interactions depend
on the neutrino polarization.
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Is leptonic CP, through Leptogenesis, the origin of the Baryon Asymmetry of the universe?
The observed CP in the weak interactions of quarks cannot explain the Baryon Asymmetry of the universe.
Do Neutrino Interactions Violate CP?
(Fukugita, Yanagida)
Wilfried Buchmueller
Leading contributor
( )
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See-Saw Mechanism
NVery heavy neutrino
Familiar light neutrino}
{
The very heavy neutrinos N would have been made in the hot Big Bang.
Leptogenesis In BriefThe most popular theory of why neutrinos are so light is the —
(Yanagida; Gell-Mann, Ramond, Slansky; Minkowski)
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If neutrino oscillation violates CP, then quite likely so does N decay. In the See-Saw, these two CP violations have a common origin.
Then, in the early universe, we would have had different rates for the CP-mirror-image decays –
N l + … and N l + …
This would have led to unequal numbers of leptons and antileptons (Leptogenesis).
Then, Standard-Model Sphaleron processes would have turned 1/3 of this leptonic asymmetry into a Baryon Asymmetry.
The heavy neutrinos N, like the light ones , are Majorana particles. Thus, an N can decay into l or l+.
+
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Look for P( ) P( )
How To Search for CP In Neutrino Oscillation
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Q : Can CP violation still lead to P( e) P( e) when = ?
Detector
e+
“ e ”
–
Detector
e–+ e
+
–
Compare
with
A : Certainly!
Ui*
Ui Uei*
Uei
€
i∑
€
i∑
i
i
€
exp −imi2 L 2E( )
€
exp −imi2 L 2E( )
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Separating CP From the Matter Effect
But genuine CP and the matter effect depend quite differently from each other on L and E.
One can disentangle them by making oscillation measurements
at different L and/or E.
Genuine CP and the matter effect
both lead to a difference between
and oscillation.
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Accelerator Oscillation Probabilities
( )
€
P ν μ →ν e[ ] ≅ sin 2 2θ 13 T1 − α sin 2θ 13 T2 + α sin 2θ 13 T3 + α 2 T4€
≡m212 Δm31
2
€
≡m31
2 L
4E
€
x ≡2 2GF Ne E
Δm312
€
T4 = cos2 θ23 sin2 2θ12sin2 xΔ( )
x2€
T1 = sin2 θ23
sin2 1− x( )Δ[ ]
1− x( )2
€
T2 = sinδ sin 2θ12 sin 2θ23 sin Δsin xΔ( )
x
sin 1− x( )Δ[ ]
1− x( )
€
T3 = cosδ sin 2θ12 sin 2θ23 cosΔsin xΔ( )
x
sin 1− x( )Δ[ ]
1− x( )
With , , and —
,
,
,
;
€
P ν μ → ν e[ ]
€
P ν μ → ν e[ ]= with – and x – x.
(Cervera et al., Freund, Akhmedov et al.)
Atmospheric
CP-odd interference
CP-even interference
Solar
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The matter-effect parameter x has E/12 GeV.
€
x
At L/E of the 1st “atmospheric” oscillation peak, and E 1 GeV, the effect of matter on the neutrino atmospheric oscillation term (sin2213 T1) is —
€
1 1− x( )2 ≅ 1± E 6GeV( )
Strategies
At fixed L/E, genuine CP effects do not change with E, but the matter effect grows, enhancing (suppressing) the oscillation if the hierarchy is Normal (Inverted).
Normal
Inverted
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If E E/3 at fixed L, we go from the
1st atmospheric oscillation peak to the 2nd one.
When E E/3 at fixed L, CP is tripled, but
the matter effect is reduced by a factor of 3.
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Neutrino Vision Neutrino Vision at Fermilabat Fermilab
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Develop a Develop a
phased approach withphased approach with
ever increasing beam ever increasing beam
intensitiesintensities
and ever increasing and ever increasing
detector capabilitiesdetector capabilitiesProbe Mixing, Mass Ordering, Probe Mixing, Mass Ordering,
CP ViolationCP ViolationY-K Y-K KimKim
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NuMI (NOvA)8 GeV ILC-like Linac
Project X = 8 GeV ILC-like LinacProject X = 8 GeV ILC-like Linac+ Recycler+ Recycler
+ Main Injector+ Main Injector
Main Injector: 2.3 MW (120 GeV) for neutrinosRecycler: 200 kW (8 GeV) for kaons, muons, …
The Intensity Frontier With The Intensity Frontier With Project XProject X
National Project with International Collaboration
DUSEL
Y-K Kim
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Project X: Properties
~2.3 MW at 120 GeV for Neutrino ScienceInitially NOvA, Possibly DUSEL later
200 kW at 8 GeV for Precision Physics
8 GeV H- Linac with ILC Beam Parameters (9mA x 1msec x 5Hz)
v = c (ILC Linac)v < c
(Young-Kee Kim)
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(Y-K Kim)
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Booster
AccumulatorDebuncher
RecyclerMain Injector
Tevatron
MiniBooNESciBooNE
MINOS(200 kW, 120 GeV)
Present:MINOS: • best measurement of m2
23
• provide an early glimpse on 13
MiniBooNE, SciBooNE:• probe neutrino parameters• measure neutrino x-sections
Y-K Kim
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Booster
RecyclerMain Injector
Phase 1:MINOSMINERvANOvA(700 kW, 120 GeV)
NOvA: • provide the first glimpse of the mass hierarchy for large 13 - the only near term probe of hierarchy in the world
• excellent sensitivity to 13
MINERvA:• measure neutrino x-sections (above 1 GeV) to high precision
Y-K Kim
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The NOA Experiment
Gary Feldman
810 km
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NOA
•A study of e and e
• 15 kton liquid scintillator detector
• Off the axis of Fermilab’s NuMI neutrino beamline
•L = 810 km; E 2 GeV (L/E near 1st
osc. peak)
•Main goal: Try to determine whether the spectrum is Normal or Inverted
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Booster
RecyclerMain Injector
Phase 1.5:
neutrinosFrom Booster
NOvALAr 5 kton at Soudan(700 kW, 120 GeV)
LAr 5 kton:• if small scale R&D / experiments are successful.
NOvA + LAr 5 kton: • enhancing the NOvA sensitivity• enabling a new detector technology
Y-K Kim
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RecyclerMain Injector
Project X Linac
Phase 2:NOvALAr 5 kton at Soudan(2.3 MW, 120 GeV)
NOvA w/ Project Xor NOvA + LAr 5 kton w/ Project X:
• enhancing sensitivity even further
Project XBeam Power (kW)
Y-K Kim
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RecyclerMain Injector
Project X Linac
Phase 3
DUSEL (WC or/and LAr)(>2 MW, 50 – 120 GeV)
( Detector = Proton Decay Detector)
Project X beam to DUSEL:
• enhancing the sensitivity markedly
Project XBeam Power (kW)
Y-K Kim
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The 3The 3 Reach of the Reach of the Successive PhasesSuccessive Phases
sin2213 Mass Ordering
CP Violation
N. Saoulidou
€
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Project X Linac Upgrade
4 GeV Factory
2 MW Target
DUSEL
Toward “Proton Intensity Upgrade”Evolutionary Path to a Neutrino Factory
Neutrino Beam to DUSEL
Y-K Kim
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We have learned a lot about the neutrinos in the last
decade.
What we have learned raises some very interesting
questions.
We look forward to answering them.
SummarySummary
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Backup Slides
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U.S. Long Baseline Neutrino Study
Explored two approaches:
1.Add detector mass, beyond NOA, in Fermilab’s NuMI beamline
2.Build at Fermilab a new, wide-band beam aimed at a very large ( and p-decay) detector more than 1000 km away, possibly in a Deep Underground Science and Engineering Laboratory (DUSEL) The 2nd approach has greater
physics reach, particularly for determining whether the spectrum is Normal or Inverted, and greater
cost.
(Brookhaven & Fermilab)
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ILC Decision Timelines
Possible ILC Decision Timelines
LHC discoveries
International
Agreements
ILC
2010 ILC DecisionSite
selec
ted
US collidersShutdownGreat Opportunityfor ILC
EPP2010 & P5 Assumption
ILC
2010 ILC Decision
ILC RDR with Cost Estimate in Feb. 2007
(Young-Kee Kim)
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Steering Group Report(Points relevant to
neutrinos)If ILC remains near the proposed timeline, the Fermilab neutrino program will focus on NOA and several small experiments.
If ILC start is delayed a couple of years, Fermilab should undertake SNuMI, an upgrade of the NuMI beamline.
If ILC postponement would accommodate an interim major project, the laboratory should undertake Project X, an ILC-related high-intensity proton source.
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(Y2K)
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(Y2K)
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(Y2K)
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(Young-Kee Kim)
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Planning Backup Slides
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NOA Timeline
Construction: 2008 – 2012 (US$36.5M requested in President’s budget for 2008)
Data taking : 2012 – 2021, evenly
split between and
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Sensitivity reach of different long baseline experiments
(U.S. Long Baseline Neutrino Study)
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Neutrino Scientific Assessment Group (NuSAG)
(A subpanel of HEPAP and NSAC)
Recommends preparation for a U.S. long baseline neutrino program, including R&D on both of the approaches explored by the U.S. Long Baseline Neutrino Study.
Detector R&D should include both water Cerenkov and liquid argon detectors.
Points out that, because of the different matter effects in Japan and the U.S., a cooperative program with T2K could help determine the mass ordering.
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Project X would make possible a high-intensity, flexible-energy, neutrino
beam aimed at a distant (L > 1000 km) large
detector.
It would also be a high-intensity source of muons and quarks for experiments in precision physics.
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If the ILC is constructed outside of the U.S., Fermilab should pursue additional neutrino science with SNuMI at a minimum, and Project X if possible.In all scenarios —
R&D on Project X should start now
R&D on future accelerator options, concentrating on a Neutrino Factory and a Muon Collider, should be increased
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Backup Slides
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Why Many Theorists Think Majorana Mass Terms Are
LikelyThe Standard Model (SM) is defined by the fields it contains, its symmetries (notably Weak Isospin Invariance), and its renormalizability.
Anything allowed by the symmetries occurs in nature.
The SM contains no mass, and no R field, only L.
Now that we know the neutrino has mass, we must somehow extend the SM to accommodate it. In doing this, we can either add R, or not add it.
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If we do not add R, then the only neutrino mass term we can construct is , a Majorana mass term.
If we do add R, then we can construct the Dirac mass term mDLR. If this term is all there is, the neutrino gets its mass the same way that a quark or charged lepton does. No Majorana neutrino masses.
However —
Unlike L , R carries no Weak Isospin.
Thus, once R has been added, no SM symmetry prevents the occurrence of the Majorana mass term mRRc R.
mLLc L
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If anything allowed by the extended SM occurs in nature, then neutrinos
have Majorana masses.
Hence, the neutrino mass eigenstates are their own antiparticles.
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ii
W– W–
e– e–
Nuclear Process
Nucl Nucl’
Uei
Uei
SM vertex
i
Mixing matrix
We anticipate that 0 is dominated by
a diagram with Standard Model vertices:
Then —
Amp[0] miUei2 m
Mass (i)
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How Large is m?
How sensitive need an experiment be?
Suppose there are only 3 neutrino mass eigenstates. (More might help.)
Then the spectrum looks like —
sol < 21
3atm
3
sol < 12
atmo
rNormal
hierarchy Inverted hierarchy
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m
Smallest
95% CLTakes 1 ton
Takes 100 tons
m For Each Hierarchy
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How Large Is 13?We know only that sin213 < 0.032
(at 2). The theoretical prediction of 13 is not sharp:
Albright & Chen( )
Present
bound
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sin213 = Ue32 is the small e piece of 3.
3 is at one end of m2atm.
We need an experiment with L/E sensitive to m2
atm (L/E ~ 500 km/GeV) , and involving e.
m2atm
(Mass)2
m2sol}
sin213
How 13 May Be Measured
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P(e Disappearance) =
= sin2213 sin2[1.27m2
atm(eV2)L(km)/E(GeV)]
Reactor Experiments
Looking for disappearance of reactor e while they travel L ~
1.5 km with energy E ~ 3 MeV is the cleanest way to
determine 13 .
(Possible experiment in Japan?)
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Does Leptogenesis Require Neutrino Mass?
Could leptogenesis occur even if
the light neutrinos were massless??
(André de Gouvêa, B.K., and Paul Langacker)
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Leptogenesis is an outgrowth of the see-saw picture.
In a straightforward (i.e., Type I) see-saw picture,
€
L new = −Mi2
NiRcNiR
i=1
3∑ − yαi ναL ϕ 0 − l αLϕ − ⎡
⎣ ⎢ ⎤ ⎦ ⎥NiR
α , i=1
3∑ + h.c.
SM Higgs doublet
Yukawa couplings
The Yukawa couplings yi play two roles:
They cause the heavy neutrinos to decayThey give masses to the light neutrinos
The light neutrino masses can have implications for Leptogenesis.
Real, positive
Diagonal basis
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€
L new = −Mi2
NiRcNiR
i=1
2∑ − yi ν L ϕ 0 − l Lϕ − ⎡
⎣ ⎢ ⎤ ⎦ ⎥NiR
i=1
2∑ + h.c.
SM Higgs doublet
Yukawa couplings
Leptogenesis In a Minimal Model
A minimal model:
Two heavy RH neutrinos, N1R and N2R
One light LH lepton doublet, (L, lL) In the basis where the Majorana mass term is diagonal, with real positive eigenvalues,
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Long ago —
N1 l– + +
+
+
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The decay rates were —
(N1 l– + +) = ay1 + by1*y2
22and
(N1 l+ + –) = ay1* + by1y2*22
These rates produced a matter – antimatter asymmetry if —
(N1 l– + +) – (N1 l+ + –)
m(ab*)
m(y1*2y22) 0.
(LeptogeneLeptogenesissis)
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Today —
0vac v 0
The light neutrino now has a nonzero mass unless —
Det(M) = 0 .
Mass matrix
The product P of all the heavy and light neutrino eigenmasses satisfies —
P2 = Det(MM*) = |Det(M)|2 .
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The only natural solution to this constraint is —
y1 = y2 = 0.
Then N1 and N2 do not decay, and there is no Leptogenesis.
Det(M) = 0
€
y12
M1+
y22
M2= 0
Masses of N1, N2
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The loophole —
€
y12
M1+
y22
M2= 0
can be satisfied by a cancellation between the terms.
This requires a conspiracy between the Yukawa sector and the Majorana sector of the theory.
But suppose this conspiracy happens:
Then y12 and y2
2 must be relatively real, so that —
m(y1*2y22) = 0
Thus, there is still no Leptogenesis!
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In the minimal model that can give
Leptogenesis, the light neutrino
must have a nonzero mass
or Leptogenesis cannot occur.
Perhaps neutrino mass is
essential to our existence.
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When There Are Three Light Doublets and Three Heavy
Neutrinos
€
L new = −Mi2
NiRcNiR
i=1
3∑ − yαi ναL ϕ 0 − l αLϕ − ⎡
⎣ ⎢ ⎤ ⎦ ⎥NiR
α , i=1
3∑ + h.c.
The condition that all 3 light neutrinos be massless is —
The only natural solution to these 6 constraints is —The Yukawa coupling
matrix y = 0.Then the Ni do not decay, and there is
no Leptogenesis.
.
€
yαi1
M i
yβii=1
3∑ ≅ 0 ; α , β =1, 3
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The loophole —
can be satisfied by a cancellation between the terms.
This requires a conspiracy between the Yukawa sector and the Majorana sector of the theory.
In addition, the Yukawa coupling matrix y must be singular.
While mathematically possible, these circumstances are quite unnatural.
€
yαi1
Miyβi
i=1
3∑ = 0 ; α , β =1, 3
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However, suppose they occur:
For hierarchical heavy neutrino masses (M2, 3 >> M1) —
(N1 l– + +) – (N1 l+ + –)
(Dutta & Mohapatra)
Then there is still no Leptogenesis.€
∝ℑm yα 1* yβ1
* yαi1
M i
yβii=1
3∑ ⎛
⎝ ⎜
⎞
⎠ ⎟
α ,β =1
3∑
⎡
⎣ ⎢
⎤
⎦ ⎥yi yiy1 y1
* *
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If the three light neutrinos are all
massless, Leptogenesis is possible, but quite
unlikely.
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Double beta decay backup
slides
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This leads many theorists to expect
Majorana masses, hence L and i = i.
The Standard Model (SM) is defined by the fields it contains, its
symmetries (notably Electroweak Isospin Invariance), and its
renormalizability.
Leaving neutrino masses aside, anything allowed by the SM symmetries
occurs in nature.
If this is also true for neutrino masses,
then neutrinos have Majorana masses.
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Do We Expect That i = i?
How can the S(tandard) M(odel) be
extended to include neutrino masses?
How does the SM become the SM?
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The S(tandard) M(odel)
and
couplings conserve the Lepton Number L.
So do the Dirac charged-lepton mass terms
mllRlL
–
Wl–
Z
l +(—) l
+(—)
Xml
R(L) Right(Left) Handed
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• Original SM: m = 0.
• Why not add a Dirac mass term,
mDRL
Then everything conserves L, so for each mass eigenstate i,
i ≠ i (Dirac neutrinos)
[L(i) = – L(i)]
• The SM contains no R field, only L. (Only Left-Handed fermions couple to the W boson.)
XmD
(—)
(—)—
But to add the Dirac mass term, we had to add R to the SM.
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Unlike L, R carries no Electroweak Isospin.
Thus, no SM principle prevents the occurrence of the Majorana mass term
mRRc R
Charge-conjugate fields:
c = (Particle Antiparticle)
The Majorana mass does not conserve L, so
now
i = i (Majorana neutrinos)
[No conserved L to distinguish i from i]
XmR
—
Charge conjugate
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This leads many theorists to expect
Majorana masses, hence L and i = i.
The Standard Model (SM) is defined by the fields it contains, its
symmetries (notably Electroweak Isospin Invariance), and its
renormalizability.
Leaving neutrino masses aside, anything allowed by the SM symmetries
occurs in nature.
If this is also true for neutrino masses,
then neutrinos have Majorana masses.
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• The presence of Majorana masses
• i = i (Majorana neutrinos)
• L not conserved— are all equivalent
Any one implies the other two.
(Recent work: Hirsch, Kovalenko, Schmidt)
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the i is emitted [RH + O{mi/E}LH].
Thus, Amp [i contribution] mi
Amp[0] miUei2 m
i
ii
W– W–
e– e–
Nuclear Process
Nucl Nucl’
In
Uei
Uei
SM vertex
i
Mixing matrix
Mass (i)
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The proportionality of 0 to mass is no surprise.
0 violates L. But the SM interactions conserve L.
The L – violation in 0 comes from underlying Majorana neutrino mass terms.
The 0 amplitude would be proportional to neutrinomass even if there were no helicity mismatch.
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Possible Information From Neutrino Magnetic
MomentsBoth Majorana and Dirac neutrinos can have transition magnetic dipole moments :
i j
For Dirac neutrinos, < 10–
15 Bohr
For Majorana neutrinos, < Present bound Present
bound =
7 x 10–11 Bohr ; Wong et al. (Reactor)
3 x10–12 Bohr ; Raffelt (Stellar E loss)
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An observed below the present bound
but well above 10–15 Bohr would imply that neutrinos are Majorana
particles.
However, a dipole moment that large requires
L-violating new physics below 100 TeV.
Bell, Cirigliano, Davidson, Gorbahn, Gorchtein,
Ramsey-Musolf, Santamaria, Vogel, Wise, Wang
( )Neutrinoless double beta decay at the planned level of sensitivity only requires this new physics at 1015 GeV, near the Grand Unification scale.