Download Overview of Neutrino Physics Issues and Opportunities Andr´ e de Gouvˆ

André de Gouvêa
Northwestern
Overview of Neutrino Physics Issues
and Opportunities
André de Gouvêa
Northwestern University
The 9th ICFA Seminar
SLAC National Accelerator Laboratory, October 28–31, 2008
October 28, 2008
ν Overview
André de Gouvêa
Northwestern
Outline
1. What We Have Learned About Neutrinos;
2. What We Know We Don’t Know;
3. What We Are Trying to Understand;
4. Where Do We Go From Here? Conclusions.
October 28, 2008
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(By Now Old) News from ν Flavor Oscillations
Neutrino oscillation experiments have revealed that neutrinos change
flavor after propagating a finite distance. The rate of change depends on
the neutrino energy Eν and the baseline L.
• νµ → ντ and ν̄µ → ν̄τ — atmospheric experiments
[“indisputable”];
• νe → νµ,τ — solar experiments
[“indisputable”];
• ν̄e → ν̄other — reactor neutrinos
[“indisputable”];
• νµ → νother from accelerator experiments
[“indisputable”].
The simplest and only satisfactory explanation of all this data is that
neutrinos have distinct masses, and mix.
October 28, 2008
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[Gonzalez-Garcia, PASI 2006]
October 28, 2008
ν Overview
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October 28, 2008
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[Gonzalez-Garcia, PASI 2006]
October 28, 2008
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Previous fits shown assuming two-flavor mixing. Of course, there are three neutrinos. . .
Phenomenological Understanding of Neutrino Masses & Mixing

νe


Ue1

 
 νµ  =  Uµ1

 
ντ
Uτ 1
Ue2
Ue3
Uµ2
Uµ3
Ueτ 2
Uτ 3

ν1



  ν2 


ν3
Definition of neutrino mass eigenstates (who are ν1 , ν2 , ν3 ?):
∆m213 < 0 – Inverted Mass Hierarchy
• m21 < m22
∆m213 > 0 – Normal Mass Hierarchy
• m22 − m21 |m23 − m21,2 |
tan θ12 ≡
2
October 28, 2008
|Ue2 |2
|Ue1 |2 ;
tan θ23 ≡
2
|Uµ3 |2
|Uτ 3 |2 ;
Ue3 ≡ sin θ13 e−iδ
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André de Gouvêa
Putting It All Together:
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[absent: new MINOS results]
[Gonzalez-Garcia, PASI 2006]
October 28, 2008
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(including new MINOS result – better ∆m213 measurement)
[from Gonzalez-Garcia, Maltoni]
October 28, 2008
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What We Know We Don’t Know (1): Missing Oscillation Parameters
2
2
(m3)
(m2)
(m1)2
(∆m2)sol
• Is CP-invariance violated in neutrino
oscillations? (δ 6= 0, π?)
νe
2
(∆m )atm
νµ
(∆m2)atm
2
normal hierarchy
(m2)2
(m1)2
• Is ν3 mostly νµ or ντ ? (θ23 > π/4,
θ23 < π/4, or θ23 = π/4?)
• What is the neutrino mass hierarchy?
(∆m213 > 0?)
ντ
(∆m )sol
• What is the νe component of ν3 ?
(θ13 6= 0?)
⇒ All of the above can “only” be
(m3)2
addressed with neutrino oscillation
inverted hierarchy
experiments.
Ultimate goal not just to measure parameters → test formalism (over-constrain parameters?)
October 28, 2008
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The “Holy Graill” of Neutrino Oscillations – CP Violation
In the old Standard Model, there is only onea source of CP-invariance
violation:
⇒ The complex phase in VCKM , the quark mixing matrix.
Indeed, as far as we have been able to test, all CP-invariance violating
phenomena agree with the CKM paradigm:
• K ;
• 0K ;
• sin 2β;
• etc.
Neutrino masses and lepton mixing provide strong reason to believe that
other sources of CP-invariance violation exist.
a modulo
October 28, 2008
the QCD θ-parameter, which will be “willed away” as usual.
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CP-invariance Violation in Neutrino Oscillations
The most promising approach to studying CP-violation in the leptonic
sector seems to be to compare P (νµ → νe ) versus P (ν̄µ → ν̄e ).
where ∆1i =
Aµe =
∗
Ue2
Uµ2
e
∆m21i L
2E ,
i = 2, 3.
i∆12
∗
i∆13
− 1 + Ue3 Uµ3 e
−1
The amplitude for the CP-conjugate process is
Āµe =
∗
Ue2 Uµ2
e
i∆12
∗
i∆13
− 1 + Ue3 Uµ3 e
−1 .
∗
∗
∗
[remember: according to unitarty, Ue1 Uµ1
= −Ue2 Uµ2
− Ue3 Uµ3
]
October 28, 2008
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In general, |A|2 6= |Ā|2 (CP-invariance violated) as long as:
∗
• Nontrivial “Weak” Phases: arg(Uei
Uµi ) → δ 6= 0, π;
• Nontrivial “Strong” Phases: ∆12 , ∆13 → L 6= 0;
• Because of Unitarity, we need all |Uαi | =
6 0 → three generations.
All of these can be satisfied, with a little luck: given that two of the three
mixing angles are known to be large, we need |Ue3 | =
6 0.
The goal of next-generation neutrino experiments is to determine the
magnitude of |Ue3 |. We need to know this in order to understand how to
study CP-invariance violation in neutrino oscillations!
[talks by Y. Wang, M. Messier, E. Kearns]
October 28, 2008
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In the real world, life is much more complicated. The lack of knowledge
concerning the mass hierarchy, θ13 , and θ23 , for example, leads to several
degeneracies and ambiguities.
Note that, in order to see CP-invariance violation, we need the
“subleading” terms (and need to make sure that the leading atmospheric
terms do not average out)!
In order to ultimately measure a new source of CP-invariance violation,
we will need to combine different measurements:
– oscillation of muon neutrinos and antineutrinos,
– oscillations at accelerator and reactor experiments,
– experiments with different baselines (or broad energy spectrum),
– etc.
[talk by Y. Wang, M. Messier, E. Kearns]
October 28, 2008
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What We Know We Don’t Know (2): How Light is the Lightest Neutrino?
(m3)2
(m2)2
2
So far, we’ve only been able to measure
2
(∆m )sol
(m1)
The lightest neutrino mass is only poorly
νe
(∆m2)atm
neutrino mass-squared differences.
νµ
(∆m2)atm
ντ
constrained: m2lightest < 1 eV2
qualitatively different scenarios allowed:
• m2lightest ≡ 0;
(m2)2
——————
↑
(∆m2)sol
(m1)2
(m3)2
normal hierarchy
• m2lightest ∆m212,13 .
inverted hierarchy
m2lightest = ?
m2 = 0
• m2lightest ∆m212,13 ;
↓
——————
October 28, 2008
Need information outside of neutrino oscillations:
β-decay, cosmology, neutrinoless double β-decay
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What We Know We Don’t Know (3) – Are Neutrinos Majorana Fermions?
A massive charged fermion (s=1/2) is
described by 4 degrees of freedom:
+
(e−
L ← CPT → eR )
νL
l Lorentz
+
(e−
R ← CPT → eL )
you
A massive neutral fermion (s=1/2) is
described by 4 or 2 degrees of freedom:
(νL ← CPT → ν̄R )
__
νR? νL?
l Lorentz
“DIRAC”
(νR ← CPT → ν̄L )
you
(νL ← CPT → ν̄R )
How many degrees of freedom are required
to describe massive neutrinos?
October 28, 2008
“MAJORANA”
l Lorentz
(ν̄R ← CPT → νL )
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Why Don’t We Know the Answer?
If neutrino masses were indeed zero, this is a nonquestion: there is no
distinction between a massless Dirac and Majorana fermion.
Processes that are proportional to the Majorana nature of the neutrino
vanish in the limit mν → 0. Since neutrinos masses are very small, the
probability for these to happen is very, very small: A ∝ mν /E.
The “smoking gun” signature is the observation of LEPTON NUMBER
violation. This is easy to understand: Majorana neutrinos are their own
antiparticles and, therefore, cannot carry “any” quantum numbers —
including lepton number.
October 28, 2008
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Search for the Violation of Lepton Number (or B − L)
Best Bet: search for
Neutrinoless Double-Beta
×
Decay: Z → (Z + 2)e− e−
1
disfavoured by 0ν2β
←(next)
Helicity Suppressed Amplitude ∝
∆m223 < 0
10− 2
←(next-next)
∆m223 > 0
10− 3
90% CL (1 dof)
−4
10
10− 4
10− 3
10− 2
10− 1
lightest neutrino mass in eV
October 28, 2008
disfavoured by cosmology
| mee | in eV
10− 1
Observable: mee ≡
P
i
mee
E
2
Uei
mi
Are other probes competitive?
1
[see talk by G. Gratta]
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mass (eV)
André de Gouvêa
10
12
10
11
10
10
Northwestern
TeV
t
τ
b
10
9
10
8
µ
s
10
7
10
6
10
5
10
4
10
3
10
2
c
d
What We Are Trying To Understand:
GeV
⇐ NEUTRINOS HAVE TINY MASSES
u
MeV
e
keV
⇓ LEPTON MIXING IS “WEIRD” ⇓
10
10
-1
-2
ν2
10
-3
10
10

eV
1
ν3
meV
ν1
-4
VM N S



∼




0.8 0.5 0.2 
0.4 0.6 0.7 
0.4 0.6 0.7
VCKM
1



∼
 0.2

0.001
0.2
1
0.01




0.01 


0.001
1
-5
10
0
1
October 28, 2008
2
3
4
generation
What Does It Mean?
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Who Cares About Neutrino Masses: Only∗ “Palpable” Evidence
of Physics Beyond the Standard Model
The SM we all learned in school predicts that neutrinos are strictly
massless. Massive neutrinos imply that the the SM is incomplete and
needs to be replaced/modified.
Furthermore, the SM has to be replaced by something qualitatively
different.
——————
∗
There is only a handful of questions our model for fundamental physics cannot
explain properly. These are, in order of “palpability” (my opinion):
• What is the physics behind electroweak symmetry breaking? (Higgs or not in SM).
• What is the dark matter? (not in SM).
• Why does the Universe appear to be accelerating? Why does it appear that the
Universe underwent rapid acceleration in the past? (not in SM – is this “particle
physics?”).
October 28, 2008
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What is the New Standard Model? [νSM]
The short answer is – WE DON’T KNOW. Not enough available info!
m
Equivalently, there are several completely different ways of addressing
neutrino masses. The key issue is to understand what else the νSM
candidates can do. [are they falsifiable?, are they “simple”?, do they
address other outstanding problems in physics?, etc]
We need more experimental input, and it looks like it may be coming in
the near/intermediate future!
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Options include:
• modify SM Higgs sector (e.g. Higgs triplet) and/or
• modify SM particle content (e.g. SU (2)L Triplet or Singlet) and/or
• modify SM gauge structure and/or
• supersymmetrize the SM and add R-parity violation and/or
• augment the number of space-time dimensions and/or
• etc
Important: different options → different phenomenological consequences
October 28, 2008
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[Albright and Chen, hep-ph/0608137]
Flavor Theories Bottom Line– “We can’t compute what |Ue3 | is – must measure it!”
(same goes for the mass hierarchy, δ)
October 28, 2008
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Comments On Current Flavor Model-Building Scene:
• VERY active research area. Opportunity to make bona fide prediction
regarding parameters that haven’t been measured yet but will be
measured for sure in the near future → θ13 , δ, mass hierarchy, etc;
• For flavor symmetries, more important than determining the values of
the parameters is the prospect of establishing non-trivial relationships
among several interesting unkowns;
e.g.,
sin2 θ13 ∼ ∆m212 /|∆m213 | if hierarchy is normal,
sin2 θ13 ∼ (∆m212 /|∆m213 |)2 if hierachy is inverted
is common “prediction” of many flavor models (often also related to
cos 2θ23 ).
October 28, 2008
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How Do We Learn More?
In order to learn more, we need more information. Any new data and/or
idea is welcome, including
• searches for lepton number violation (neutrinoless double
beta decay, etc);
• precision measurements of the neutrino oscillation
parameters;
• searches for charged lepton flavor violation (µ → eγ, etc);
• searches for fermion electric/magnetic dipole moments (electron edm,
muon g − 2, etc);
• searches for new physics at the TeV scale – we need to understand the
physics at the TeV scale before we can really understand the physics
behind neutrino masses (is there low-energy SUSY?, etc).
October 28, 2008
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mass (eV)
Only Palpable Evidence of Physics Beyond the Standard Model!
10
12
10
11
10
10
TeV
NEUTRINOS HAVE MASS
t
τ
b
10
9
10
8
µ
s
10
7
10
6
10
5
10
4
10
3
10
2
c
d
GeV
– are neutrinos their own antiparticles?
u
MeV
e
keV
– we may run into more surprises!
Discovery → intriguing theoretical questions:
eV
1
-1
-2
-3
10
meV
ν1
-4
0
– lepton mixing 6= quark mixing: why?
– how do neutrinos acquire mass? Too many choices!
-5
10
– neutrino masses charged fermion masses: why?
ν3
ν2
10
10
– how light is the lightest neutrino?
– is the three neutrino + mixing paradigm complete?
10
10
Discovery → well-defined experimental questions:
1
October 28, 2008
2
3
4
fermion
– how do we learn more about this new physics?
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Backup Slides . . .
October 28, 2008
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What I Mean By the Standard Model
The SM is a quantum field theory with the following defining
characteristics:
• Gauge Group (SU (3)c × SU (2)L × U (1)Y );
• Particle Content (fermions: Q, u, d, L, e, scalars: H).
Once this is specified, the SM is unambiguously determined:
• Most General Renormalizable Lagrangian;
• Measure All Free Parameters, and You Are Done! (after several
decades of hard experimental work. . . )
If you follow these rules, neutrinos have no mass. Something has to give.
October 28, 2008
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Candidate νSM
SM as an effective field theory – non-renormalizable operators
1
Li HLj H
LνSM ⊃ −λij 2Λ + O Λ2 + H.c.
There is only one dimension five operator [Weinberg, 1979]. If Λ 1 TeV, it
leads to only one observable consequence...
after EWSB LνSM ⊃
mij i j
2 ν ν ;
mij =
v2
λij Λ .
• Neutrino masses are small: Λ v → mν mf (f = e, µ, u, d, etc)
• Neutrinos are Majorana fermions – Lepton number is violated!
• νSM effective theory – not valid for energies above at most Λ/λ.
• What is Λ? First naive guess is that M is the Planck scale – does not
work. Data require Λ < 1015 GeV (anything to do with the GUT
scale?).
What else is this “good for”? Depends on the ultraviolet completion!
October 28, 2008
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Another νSM
Why don’t we just enhance the fermion sector of the theory?
One may argue that it is trivial and simpler to just add
LYukawa = −yiα Li HN α + H.c.,
and neutrinos get a mass like all other fermions: miα = yiα v
• Data requires y < 10−12 . Why so small?
• Neutrinos are Dirac fermions. B − L exactly conserved.
• νSM is a renormalizable theory.
This proposal, however, violates the rules of the SM (as I defined them)!
The operator M2N N N , allowed by all gauge symmetries, is absent. In
order to explain this, we are forced to add a symmetry to the νSM. The
simplest candidate is a global U (1)B−L .
U (1)B−L is upgraded from accidental to fundamental (global) symmetry.
October 28, 2008
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Old Standard Model, Encore
The SM is a quantum field theory with the following defining
characteristics:
• Gauge Group (SU (3)c × SU (2)L × U (1)Y );
• Particle Content (fermions: Q, u, d, L, e, scalars: H).
Once this is specified, the SM is unambiguously determined:
• Most General Renormalizable Lagrangian;
• Measure All Free Parameters, and You Are Done.
This model has accidental global symmetries. In particular, the anomaly
free global symmetry is preserved: U (1)B−L .
October 28, 2008
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New Standard Model, Dirac Neutrinos
The SM is a quantum field theory with the following defining
characteristics:
• Gauge Group (SU (3)c × SU (2)L × U (1)Y );
• Particle Content (fermions: Q, u, d, L, e, N , scalars: H);
• Global Symmetry U (1)B−L .
Once this is specified, the SM is unambiguously determined:
• Most General Renormalizable Lagrangian;
• Measure All Free Parameters, and You Are Done.
Naively not too different, but nonetheless qualitatively different →
enhanced symmetry sector!
October 28, 2008
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Hint for Non-Zero θ13 in the Current Data?
G.L. Fogli et al, arXiv:0806.2649 [hep-ph]
October 28, 2008
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|
|
|
[C. Galbiati, Nu2008]
October 28, 2008
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