The Neutrino World
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Transcript The Neutrino World
Neutrino
Phenomenology
Boris Kayser
Scottish Summer School
August 11, 2006 +
1
Are There Sterile Neutrinos?
Rapid neutrino oscillation reported by LSND —
1eV2
in contrast to
m2atm = 2.7 x 10–3 eV2
> m2sol = 8 x 10–5 eV2
At least 4 mass eigenstates, hence at least 4 flavors.
Measured (Z)
only 3 different active neutrinos.
At least 1 sterile neutrino.
2
Is the so-far unconfirmed oscillation
reported by LSND genuine?
MiniBooNE aims to definitively
answer this question.
3
What Is the Pattern of Mixing?
How large is the small mixing angle 13?
We know only that sin213 < 0.032 (at 2).
The theoretical prediction of 13 is not sharp:
Present
bound
sin213
(
)
Albright
& Chen
4
The Central Role of 13
Both CP violation and our ability to
tell whether the spectrum is normal or
inverted depend on 13.
If sin213 > (0.0025 – 0.0050), we can
study both of these issues with intense
but conventional and beams.
Determining 13 is an
important stepping-stone.
How 13 May Be Measured
sin213
3
m2atm
(Mass)2
2
1
}m
2
sol
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
m2atm (L/E ~ 500 km/GeV) , and involving e.
6
Complementary Approaches
Reactor Experiments
Reactor e disappearance while traveling L ~
1.5 km. This process depends on 13 alone:
P(e Disappearance) =
= sin2213 sin2[1.27m2atm(eV2)L(km)/E(GeV)]
7
Accelerator Experiments
Accelerator e while traveling L > 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
.
8
Neglecting matter effects (to keep the
formula from getting too complicated):
(—)
The accelerator long-baseline e appearance
experiment measures —
(—)
(—)
P[ e ] sin 2 213 sin 2 23 sin 2 31
sin 213 cos 13 sin 223 sin 212 sin 31 sin 21 cos( 32 )
sin 2 212 cos 2 23 cos 2 13 sin 2 21
ij mij 2 L 4E
The plus (minus) sign is for neutrinos (antineutrinos).
9
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.
10
How To Determine If The
Spectrum Is Normal Or Inverted
Exploit the fact that, in matter,
e
( )
e
( )
W
e
e
raises the effective mass of e, and lowers that of e.
This changes both the spectrum and the mixing angles.
11
Matter effects grow with energy E.
At E ~ 1 GeV, matter effects
(—)
2
sin 2 =~ sin2 2 [ 1 (+—) S
M
Sign[m2(
13
) - m2(
E
].
6 GeV
)]
At oscillation maximum,
P( e)
P( e)
{
>1 ;
Note fake CP
violation.
<1 ;
In addition,
PHi E( e)
PLo E( e)
{
>1 ;
<1 ;
(
Mena, Minakata,
Nunokawa, Parke
12
)
CP Violation and the
Matter-Antimatter Asymmetry
of the Universe
13
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?
14
How To Search for Leptonic CP
Look for P( ) P( )
“ ” is a different process from even
when i = i
eSource
e+
Source
e
-
Detector
“ e ”
+
Detector
15
CPT: P( ) = P( )
P( ) = P( )
No CP violation in a disappearance experiment.
But if is present, P( e) P( e):
P e P e 2cos13 sin213 sin212 sin2 23 sin
2
L 2
L 2
L
sinm 31
sinm 32
sinm 21
4 E
4 E
4 E
Note that all mixing angles must be nonzero for CP.
16
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.
17
What Physics
Is Behind
Neutrino Mass?
18
The See-Saw Mechanism
— A Summary —
This assumes that a neutrino has both
a Majorana mass term mRRc R
and a Dirac mass term mDLR.
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 >> mD.
19
When
We have 4 mass-degenerate states:
This collection of 4 states is a Dirac
neutrino plus its antineutrino.
20
When =
We have only 2 mass-degenerate states:
This collection of 2 states is a Majorana neutrino.
21
What Happens In the See-Saw?
The Majorana mass term splits a Dirac
neutrino into two Majorana neutrinos.
N
Dirac
neutrino
mN ~
– mR
Splitting due to mR
m ~– mD2 / mR
Note that mmN mD2 mq or l2 . See-Saw Relation
22
The See-Saw Relation
Very
heavy
neutrino
}
{
Familiar
light
neutrino
N
23
Predictions of the See-Saw
–
Each i = i
(Majorana neutrinos)
The light neutrinos have heavy partners N
How heavy??
m2top
m2top
mN ~ ––––– ~ –––––– ~ 1015 GeV
m
0.05 eV
Near the GUT scale.
Coincidence??
24
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 today’s
matter-antimatter asymmetry.
25
Enjoy The Rest
Of The School!
26
Backup Slides
27
What is the atmospheric mixing angle 23?
P[ Not ] sin 2 223 sin 2 atm
Here atm lies between the (very nearly equal) 31 and 32.
This measurement determines sin2223, but if
23 45°, there are two solutions for 23:
23 and 90° – 23.
A reactor experiment may be able to
resolve this ambiguity.
28
Assumes
sin2223 =
.95 .01
23
Sensitive
to sin2213
= 0.01
(McConnel, Shaevitz)
29