The Neutrino World

1
Neutrino Phenomenology
Boris Kayser Scottish Summer School August 11,
2006
2
Are There Sterile Neutrinos?
Rapid neutrino oscillation reported by LSND
? 1eV2
in contrast to
?m2atm 2.7 x 103 eV2
gt
?m2sol 8 x 105 eV2
Measured ?(Z???) only 3 different
active neutrinos.
At least 1 sterile neutrino.
3
Is the so-far unconfirmed oscillation reported
by LSND genuine?
MiniBooNE aims to definitively answer this
question.
4
What Is the Pattern of Mixing?

• How large is the small mixing angle ?13?

We know only that sin2?13 lt 0.032 (at 2?). The
theoretical prediction of ?13 is not sharp
Present bound
(
)
Albright Chen
sin2?13
5
The Central Role of ?13

• Both CP violation and our ability to tell
  whether the spectrum is normal or inverted depend
  on ?13.

If sin2?13 gt (0.0025 0.0050), we can study both
of these issues with intense but conventional ?
and ? beams.
Determining ?13 is an important stepping-stone.
6
How ?13 May Be Measured

• sin2?13 ?Ue3?2 is the small ?e piece of ?3.
• ?3 is at one end of ?m2atm.
• ?We need an experiment with L/E sensitive to
  ?m2atm (L/E 500 km/GeV) , and involving ?e.

7
Complementary Approaches
Reactor Experiments
Reactor ?e disappearance while traveling L
1.5 km. This process depends on ?13 alone
P(?e Disappearance)
sin22?13 sin21.27?m2atm(eV2)L(km)/E(GeV)
8
Accelerator Experiments
Accelerator ?? ? ?e while traveling L gt Several
hundred km. This process depends on ?13, ?23, on
whether the spectrum is normal or inverted, and
on whether CP is violated through the phase ?.
9
Neglecting matter effects (to keep the formula
from getting too complicated)
()
The accelerator long-baseline ?e appearance
experiment measures
The plus (minus) sign is for neutrinos
(antineutrinos).
10
The Mass Spectrum or ?
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.
11
How To Determine If The Spectrum Is Normal Or
Inverted
This changes both the spectrum and the mixing
angles.
12
Matter effects grow with energy E. At E 1 GeV,
matter effects ? sin2 2?M sin2 2?13 1 S
. Signm2( ) - m2( ) At
oscillation maximum, P(??? ?e) gt1 P(???
?e) lt1

()
()

Note fake CP violation.
In addition,

(
)
PHi E(??? ?e) gt1 PLo E(??? ?e)
lt1
Mena, Minakata, Nunokawa, Parke
13
CP Violation and the Matter-Antimatter Asymmetry
of the Universe
14
Leptonic CP Violation

• Is there leptonic CP, or is CP special to quarks?
• Is leptonic CP, through Leptogenesis, the origin
  of the Matter-antimatter asymmetry of the
  universe?

15
How To Search for Leptonic CP
?? ? ?? is a different process from ?? ? ??
even when ?i ?i
?e ? ??
e-
?-
?
Source
Detector
?e ? ??
?
e
?
Source
Detector
16
CPT P(??? ??) P(???? ??) ?
P(??? ??) P(???? ??) No CP violation in a
disappearance experiment. But if ? is present,
P(?????e) ? P(???? ?e)
Note that all mixing angles must be nonzero for
CP.
17
Separating CP From the Matter Effect
Genuine CP and the matter effect both lead to a
difference between ? and ? oscillation.
But genuine CP and the matter effect depend quite
differently from each other on L and E. To
disentangle them, one may make oscillation
measurements at different L and/or E.
18
What Physics Is Behind Neutrino Mass?
19
The See-Saw Mechanism A Summary
This assumes that a neutrino has both a Majorana
mass term mR?Rc ?R and a Dirac mass term mD?L?R.
No SM principle prevents mR from being extremely
large. But we expect mD to be of the same order
as the masses of the quarks and charged
leptons. Thus, we assume that mR gtgt mD.
20
When ? ? ? We have 4 mass-degenerate states
This collection of 4 states is a Dirac neutrino
plus its antineutrino.
21
When ? ?
We have only 2 mass-degenerate states
This collection of 2 states is a Majorana
neutrino.
22
What Happens In the See-Saw?

• The Majorana mass term splits a Dirac neutrino
  into two Majorana neutrinos.

Note that m?mN ? mD2 ? mq or l2 . See-Saw
Relation
23
The See-Saw Relation
24
Predictions of the See-Saw

• 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
Coincidence??
25
A Possible Consequence of the See-Saw
Leptogenesis
The heavy see-saw partners N would have been made
in the hot Big Bang. Then, being very heavy,
they would have decayed. The see-saw model
predicts N ? l- and
N ? l If there was CP in these leptonic
processes, then unequal numbers of leptons and
antileptons would have been produced. Perhaps
this was the origin of todays
matter-antimatter asymmetry.
26
Enjoy The Rest Of The School!
27
Backup Slides
28

• What is the atmospheric mixing angle ?23?

29
Assumes sin22?23 .95 ? .01
?23
Sensitive to sin22?13 0.01
(McConnel, Shaevitz)