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 sin213 < 0.032 (at 2).
The theoretical prediction of 13 is not sharp:
Present
bound
sin213
(
)
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 sin213 > (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
sin213
3
m2atm
(Mass)2
2
1
}m
2
sol
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.
6
Complementary Approaches
Reactor Experiments
Reactor e disappearance while traveling L ~
1.5 km. This process depends on 13 alone:
P(e Disappearance) =
= sin2213 sin2[1.27m2atm(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 213 sin 2 23 sin 2  31
 sin 213 cos 13 sin 223 sin 212 sin  31 sin  21 cos( 32   )
 sin 2 212 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  2cos13 sin213 sin212 sin2 23 sin 
 2
L   2
L   2
L 
 sinm 31
sinm 32
sinm 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 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 >> 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 mmN  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 223 sin 2  atm
Here atm lies between the (very nearly equal) 31 and 32.
This measurement determines sin2223, 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
sin2223 =
.95  .01
23
Sensitive
to sin2213
= 0.01
(McConnel, Shaevitz)
29