The Neutrino World

1
Majorana Neutrinos
Boris Kayser Venice February 23, 2005
2
What other kind of neutrino is there?
Lincoln Wolfenstein
3
Questions

• Why do we think neutrinos are Majorana particles
  (? ?)?
• How can we test whether ? ?? Is neutrinoless
  double beta decay the only way?
• If ? ?, what electromagnetic properties do
  neutrinos have?
• What are Majorana CP phases? What CP effects can
  they produce?

4
We will assume CPT invariance.
(Barenboim, Beacom, Borissov, BK)
5
Majorana Neutrinos or Dirac Neutrinos?

• The S(tandard) M(odel)
• and
• couplings conserve the Lepton Number L defined
  by
• L(?) L(l) L(?) L (l) 1.
• So do the Dirac charged-lepton mass terms
• mllLlR

l
?
W
Z
?
?


ml
6

• Original SM m? 0.
• Why not add a Dirac mass term,
• mD?L?R
• 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.
• To add the Dirac mass term, we had to add ?R to
  the SM.

7

• Unlike ?L, ?R carries no Electroweak Isospin.
• Thus, no SM principle prevents the occurrence of
  the Majorana mass term
• mR?R ?R
• But this does not conserve L, so now
• ?i ?i (Majorana neutrinos)
• No conserved L to distinguish ?i from ?i
• We note that ?i ?i means
• ?i(h) ?i(h)
• helicity

c




8

• In the See-Saw Mechanism,
• Lmass
• with mR gtgt mD mq or l .

N mN mR

Splitting due to mR
Dirac neutrino
? m? mD2 / mR

One of the ?i.
9
Predictions

• Each ?i ?i (Majorana neutrinos)
• The light neutrinos have heavy partners N
• How heavy??
• mN 1015 GeV
• Near the GUT scale.

m2top m2top m? 0.05 eV
10
How Can We Demonstrate That ?i ?i?
We assume neutrino interactions are correctly
described by the SM. Then the interactions
conserve L. An Idea that Does Not Work and
illustrates why most ideas do not work Produce
a ?i via
Spin
Pion Rest Frame
?
?i
?
?
Give the neutrino a Boost
??(Lab) gt ??(? Rest Frame)
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• The SM weak interaction causes

?
?

?i
Target at rest
Recoil
?i ?i means that ?i(h) ?i(h).
helicity
?
?

??????i
,
????i
?
??????i
will make ? too.
12
Minor Technical Difficulties

• ??(Lab) gt ??(? Rest Frame)
• E?(Lab) E?(? Rest Frame) m? m?
• ? E?(Lab) gt 105 TeV if m? 0.05 eV
• Fraction of all ? decay ?i that get helicity
  flipped
• ? ( )2 10-18 if m??? 0.05 eV
• Since L-violation comes only from Majorana
  neutrino masses, any attempt to observe it will
  be at the mercy of the neutrino masses.
• (BK Stodolsky)

? gt
i

i
m? E?(? Rest Frame)
i
i
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The Idea That Can Work Neutrinoless Double
Beta Decay 0???
e
e
?i
?
i
W
W
Nuclear Process
Nucl
Nucl
By avoiding competition, this process can cope
with the small neutrino masses.
Observation would imply L and ?i ?i , making
the neutrinos very different from the charged
leptons and quarks.
14
In
SM vertex
e
e
?i
?
Mixing matrix
Uei
Uei
i
W
W
Nuclear Process
Nucl
Nucl
Mass (?i)
the ?i is emitted RH Omi/ELH. Thus, Amp ?i
contribution ? mi Amp0??? ? ?? miUei2?? m??
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 mass terms.
16
Whatever diagrams cause 0???, its observation
would imply the existence of a Majorana mass term
Schechter and Valle
17
Majorana mass terms either directly involve New
Physics not in the Standard Model, or else imply
its existence.
Observation of 0??? would imply that The
origin of neutrino mass involves physics
different from that which gives masses to the
charged leptons, quarks, nucleons, humans, the
earth, and galaxies.
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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

or
19

• If the spectrum looks like
• then
• m?? ? m01 - sin22?? sin2()½ .
• Solar mixing angle
• m0 cos 2?? ? m?? ? m0
• At 90 CL,
• m0 gt 43 meV (SuperK) cos 2?? gt 0.33 (SNO),
• so
• m?? gt 14 meV .

m0
?2?1 2
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• If the spectrum looks like
• then
• 0 lt m?? lt Present Bound (0.31.0) eV .
• (Petcov et al.)
• Analyses of m?? vs. Neutrino Parameters
• Barger, Bilenky, Farzan, Giunti, Glashow, Grimus,
  BK, Kim, Klapdor-Kleingrothaus, Langacker,
  Marfatia, Monteno, Murayama, Pascoli, Päs,
  Peña-Garay, Peres, Petcov, Rodejohann, Smirnov,
  Vissani, Whisnant, Wolfenstein,
• Review of ?? Decay Elliott Vogel

Evidence for 0??? with m?? (0.05 0.84)
eV? Klapdor-Kleingrothaus
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Electromagnetic Properties and Lifetimes

• Majorana neutrinos are very neutral.
• No charge distribution

CPT

?



But for a Majorana neutrino,




?i
?i

CPT
22
No magnetic or electric dipole moment




?
?

e
e
But for a Majorana neutrino,
?i
?i

Therefore,
?i
?i
0

?
?
23
Transition dipole moments are possible.
Hence, either a Majorana or a Dirac neutrino can
decay radiatively ?2 ? ?1 ? But in
the (extended) SM, radiative decays are extremely
slow, since
? GF2m(?2)5
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For m(?2) 0.05 eV, ?? ?2 ? ?1 ?
1049yr. Looking for visibly fast decays is
looking for very new physics. For years, the
SuperKamiokande atmospheric ??disappearance data
were consistent with disappearance due to decay,
rather than oscillation. (Barger,
Learned, Pakvasa, Weiler) Decay is now excluded
by SuperKamiokande results, including the L/E
(Distance/Energy) dip.
25
Transition dipole moments make possible
One can look for them this way. To be visible,
they would have to vastly exceed Standard Model
predictions.
26
Majorana CP-Violating Phases

• The 3x3 quark mixing matrix 1 CP phase
• When ?i ?i The 3x3 lepton mixing matrix 3 CP
  phases
• The 2 extra phases, ?1 and ?2, are called
  Majorana phases.
• Each Majorana phase is associated with a
  particular ? mass eigenstate ?i

Bilenky, Hosek, and Petcov Schechter and Valle,
Doi et al.
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An L-conserving process AmpeW ? ? ? ?W
?i ??W?H??i? Propagator(?i) ??i?H?eW?
An L-nonconserving process AmpeW ? ? ?
?W ?i ??W?H??i? Propagator(?i)
??i?H?eW? CTP ??i?H?eW? ??i?H?eW?
Uei So Amp L ?i U?i Propagator(?i) Uei This
is sensitive to Majorana phases.

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• Majorana phases have physical consequences, but
  only in physical processes that involve violation
  of L.
• They do not affect ? flavor oscillation, but they
  do affect 0???
• m?? ?? miUei2?
• clearly depends on the relative phase of Ue12
  and Ue22.

i
29
Can Majorana Phases Lead to Manifest CP?

• Manifest CP
• Rate Process ? Rate Process
• The Dirac CP phase in the quark mixing matrix
  causes such inequalities.
• Can Majorana phases cause them too?

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• Yes, they can cause them in heavy neutrino decay
  in the early universe (leptogenesis).
• (Fukugita Yanagida)
• But can they cause rate inequalities in
  present-day processes?
• Yes, although only in processes that are
  extremely difficult to observe.
• (de Gouvêa, BK, Mohapatra)

An example is
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Amp eW ? ? ? ?W S ?i UeiU?i mi/E
exp-imi2 (L/2E)

Distance

Kinematics
Has Maj. phases
??? propagator
Helicity suppression
Amp eW ? ? ? ?W S ?i UeiU?i mi/E
exp-imi2 (L/2E)
Suppose only 2 generations matter
c ? cos ? s ? sin ? ? ? a Majorana phase.
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(Schechter Valle)
Here, K irrelevant constant S2 m1,2
masses of ?1,2 ?m2 m22 - m12 Note the two
rates are not the same.
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When Mixing is Meaningful

• In the quark sector, the mixing matrix loses its
  meaning when all quarks of a given charge are
  degenerate.
• What happens here when m1 m2 ? m?

When Majorana phases are present, the mixing
matrix is still meaningful even when the neutrino
masses are of equal size.
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Why?

• The Majorana phase ? associated with neutrino ?1
  may be viewed as the phase of its mass
• mass(?1) m1 ei?

Real
Even when m1 m2, ? distinguishes ?1 from ?2.
Thus, the mixing matrix still has meaning.
35
Can G0?ßß Reveal Majorana Phases?

• If the spectrum looks like
• then
• m?? ? m01 - sin22?? sin2()½ .
• With ?2?1 ? ??,
• CP ?? ? 0, p. sin2(??/2) ? 0, 1.

?2?1 2
?
36

• Experimentally, 1/sin2 2?? ? 1.2 .
• Thus,
• Establishing that sin2(??/2) ? 0, 1 requires
• A knowledge of m0 Tritium?
• Shrinking the present (factor of three)2
  theoretical uncertainty in G0?ßß?? m??2
• Studies of Observability of ?? ? 0, p
• Barger, Glashow, Langacker, MarfatiaPascoli,
  Petcov, Rodejohann Pascoli, Petcov

37
Why Are There 3 Generations?

• If the preponderance of Matter over antimatter in
  the universe arose from CP in quark mixing, we
  could argue that
• It takes ? 3 generations to have CP in quark
  mixing.
• It takes CP in quark mixing to have Matter gtgt
  antimatter.
• It takes Matter gtgt antimatter to have us.
• But CP in quark mixing is completely inadequate
  for Matter gtgt antimatter.

38

• Majorana phases can produce the manifest CP
• ?N ? l Higgs ? ?N ? l Higgs
• in the early universe. This may be the origin of
  Matter gtgt antimatter.
• It takes only 2 generations to have manifest CP
  from Majorana phases.
• So why are there 3??

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Backup Slides
40
If ? ?, How Is Neutrino CP Affected?
CP in neutrino oscillation is not affected at
all. We can still have P(??????????????)
P(????????????????? even if ?i ?i??
41
???????????????????
??
e-
?
?i

i
Source
Detector
U?i
exp(-imi2L/2E)
Uei
????????????
??
e
?i
?
Source

i
Detector
Uei
U?i
exp(-imi2L/2E)
The probabilities can be different!
42
Movable Phase

• In the flavor basis (where the charged-lepton
  mass matrix is diagonal),
• LLight ?LcM ?L ,
• where M U D U
• Write U VP, where P ( )
• Then
• M??

Light ? mass matrix
? mass