Introduction to the SPAN Project
SPAN group, Okayama University
January 9, 2014
1 What is neutrino and what we know about neutrino?
1.1 What is neutrino?
Neutrino and its family Neutrinos belong to a family of leptons; the family in which elec-
trons, muons and tau belong. Neutrinos come in three types referred to as “flavors” or “gen-
erations”. Neutrinos interact with other particles via only weak interaction; neither strong
nor electromagnetic interactions acts on neutrinos. This fact makes neutrinos very illusive and
difficult to detect. Figure 1 summarizes all the elementary particles observed experimentally.
Particle universe It might be surprising to know that neutrinos are the second most abundant
particle in the universe. Figure 2 shows the average number density of various particles in the
universe. The most abundant particle is photons: there are about 400 particles per cm
3
.The
second one is neutrino, and there are more than 300 particles per cm
3
. The third group, protons
and electrons, are down by 9-10 order of magnitude.
Figure 1: Elementary particles included in the Standard
Model. The three generations of fermions (quarks and
leptons) in the 1st-3rd columns, gauge bosons in the 4th
and the Higgs boson in the 5th. Quarks and leptons are
building block of matters (atoms and molecules) while
the gauge bosons are force carriers. Recently observed
Higgs particle is a source-field of mass. [1]
Figure 2: Particles in the uni-
verse. The vertical scale shows
the average number of particles
per cm
3
.
1
1.2 What we know about neutrino?
Recent advance in neutrino physics Recently neutrino physics has advanced considerably.
The progress has been brought by a type of experiments called oscillation experiments. The
oscillation experiments ask “Is neutrino produced at some place the same type (or flavor) at
different place?” The answer is found to be “NO” in general. Fig.3 shows an example of exper-
imental layouts. In this example, muon-type neutrino beam is produced at Tsukuba. Purity
of the beam is guaranteed by selecting a π
+
beam decaying into ν
μ
and μ
+
.AtKamioka,
about 250 km away from Tsukuba, you observe neutrino and ask “Are the detected neutrinos
all muon-type neutrino as were produced? ”. The answer we have found by the experiments is
NO. In fact, some of them are found to turn into electron-type neutrinos. Here an important
remark is that flavor is distinguished by interactions (in a detector) and that mass is measured
by velocity (during the flight).
( p m n )
m
n
m
n
t
n
e
n
m
?
?
?
Figure 3: The principle of neutrino oscillation experiments. Neutrinos are produced at Tsukuba
as a pure ν
μ
state, and travel about 250 km to Kamioka where they are caught by a detector
and their species are examined.
How do we interpret this fact? Let’s consider a simple model consisting only two flavors and two
mass eigenstates. Let’s also suppose neutrino avor eigenstate is a linear combination of mass
eigenstates. Then the two types of neutrinos, say ν
a
and ν
b
, are described by linear combinations
of mass eigenstate neutrinos ν
1
and ν
2
;
flavor state

|ν
a
|ν
b
=
mixing matrix

cos θ sin θ
sin θ cos θ|ν
b
×
mass state

|ν
1
|ν
2
. (1)
Here the mixing angle (θ) represents the degree of “mixing” of two neutrinos. Now let’s suppose
that a neutrino is produced as a pure flavor eigenstate ν
a
at the production point x =0. Then
its wave function can be represented by
ψ(x =0)=|ν
a
=cosθ|ν
1
+sinθ|ν
2
. (2)
Note that it is a super-position of the mass-eigenstate neutrinos denoted by |ν
1
and |ν
2
with
masses of m
1
,andm
2
, respectively. During the ight, each of the mass eigenstate oscillates
according to its own frequency. This can be described by (in units of c h =1)
ψ(x)=cosθ|ν
1
e
i(E
1
tp
1
x)
+sinθ|ν
2
e
i(E
2
tp
2
x)
,E
i
=
m
2
i
+ p
2
i
(3)
2
Then at x = L where neutrinos are detected, they are distinguished by flavor again. As shown
in Appendix, it is a straight-forward matter to calculate the probability of finding as ”b” which
is produced as ”a”;
P
ab
=
ν
b
|ψ(x = L)
2
=sin
2
(2θ)sin
2
Δm
2
21
L
4E
Δm
2
21
= m
2
2
m
2
1
,E=
E
1
+ E
2
2
(4)
The oscillation experiments found P
ab
= 0, establishing that neutrinos have finite mass-squared
differences m
2
21
= 0), and that neutrinos are mixed (θ =0).
Figure 4 summarizes what we found by the oscillation experiments up to now. Let’s look at
the left panel. There are 3 horizontal boxes, each representing mass-eigenstate neutrinos. The
mass of the neutrinos is shown by the vertical axis while their flavor contents by the colors. For
example, the top horizontal box, the heaviest neutrino, consists of muon- and tau-types almost
equally, with a tiny bit of electron type. The second heaviest one is divided into 3 types with
approximately equal weights. The mass difference between the heaviest and the second heaviest
neutrinos is about 50 meV. Compared to other particle, electrons for example, the neutrino’s
mass scale is surprisingly small. One important remark here is that the oscillation experiments
are sensitive only to mass-squared difference, not to mass itself. Therefore, we cannot determine
the absolute mass of neutrinos nor its mass pattern, namely which is the lightest one. Actually
there are two mass patterns emerged from the measurements, they are called normal or inverted
hierarchy, as shown in Fig.4.
mass
flavor
m3
m2
m1
Normal Hierarchy
50 meV
10 meV
mass
flavor
m2
m1
m3
Inverted Hierarchy
50 meV
10 meV
n
m
n
t
n
e
Figure 4: Summary of neutrino flavor mixing. The left (right) panel shows a mass pattern called normal
(inverted) hierarchy, which has been emerged from a series of oscillation experiments. The vertical scale
shows mass of mass eigenstate neutrinos, and the horizontal axis shows flavor contents. Note that only
mass-squared differences can be measured with oscillation experiments.
1.3 Universe and its hitory
Composition of Universe Observational cosmology has made a remarkable advance recently
thanks to the space technology. The pie-chart shown in Fig. 5 is the current (energy) composition
of the universe established by various observations. Surprisingly three-quarter of them are
filled with unknown energy source, dubbed “dark energy”. We do not know what it really is.
Another 22% is so-called dark matter. Its existence itself is rmly established by observing
their gravitational interaction with other astronomical objects. However it cannot be observed
3
Figure 5: Composition of Universe: Universe is
found to be composed of dark energy, dark matter
and visible matter (atoms and molecules). Why
“matteranti-matter” now while “matter=anti-
matter” at its beginning (Big-Bang)?
Figure 6: Majorana vs Dirac. Like the elec-
tron and positron, a particle is different en-
tity from its anti-particle in the Dirac theory.
However, a particle is its own anti-particle in
the Majorana theory. Whether neutrino is
Dirac or Majorana must be determined ex-
perimentally.
directly by telescopes of any wavelengths (optical, microwave, X-rays etc.), thus the name “dark
matter”. The rest of 4% is familiar atoms. However, there are virtually no anti-atoms (or
anti-matters). From view point of the particle physics, the fact is surprising because exactly the
same amount of matter and anti-matter should have existed at the beginning of the universe
(Big Bang). We somehow lost our partner in the course of the 14-billion-year history. Thus the
fact demands physics explanation.
The most promising theory is called “lepto-genesis”. According to the theory, when the
universe was much hotter than today, a gigantic neutrino (a hypothetical partner of the standard
neutrino, yet to be confirmed) made tiny imbalance between matter and anti-matter: all anti-
matters annihilated away with matters but small portion of the matter survived. There are two
key features for this theory to be viable: one is Majorana nature of neutrinos, and the other
is violation of CP-symmetry. Let’s explain these key words one by one below. All the charged
leptons and quarks are known to be the Dirac particles. In this case, a particle and its anti-
particle is a totally different entity. The electron, for example, has a negative charge while its
anti-particle, the positron, has positive charge, and they are different each other. In the case of
Majorana particle, however, there is no distinction between particle and anti-particle. In another
words, a particle’s anti-particle is a particle itself. See Fig.6. That neutrino is Majorana particle
is prerequisite for the “lepto-genesis” scenario. There is another reason to believe neutirnos are
Majorana. As shown in Fig.7, neutrino’s masses are exceptionally light compared with other
fundamental particles. Again the Majorana nature of neutrinos can explain this fact very well.
Energy cale
1GeV1MeV1keV1eV1meV1µeV 1TeV1neV
t
H
u c
μ
s
τ
b
e
d
ν
1
ν
2
ν
3
Quarks
Leptons
Neutrino
Higgs
Masses
?
Figure 7: Masses of elementary particles in the Stadard Model. Neutrino masses are exception-
ally small compared with the others.
4
h
Figure 8: RENP Diagram
Xe
Energy Level [eV]
0
1
8
9
10
5p S
6 1
0
5p ( P )6s [3/2]
52 2
3/2 2
5p ( P )6s [3/2]
52 2
3/2 1
5p ( P )6s [1/2]
52 2
1/2 0
5p ( P )6s [1/2]
52 2
1/2 1
|g>
|e>
|p>
Figure 9: Xe energy levels relevant to the
RENP process.
The other key feature is the CP-symmetry nature, which is the symmetry between particle
and its anti-particle times the space inversion symmetry (parity symmetry). Quarks are known
to violate this symmetry; it is explained by the Kobayashi-Maskawa CP-violation mechanism
(by the CP-violating phase δ). At present, whether or not the CP-violation exits in the neutrino
sector is unknown. If neutrinos are Majorana type, there are other CP-violation sources (by CP-
violation phases α, β) in addition to a similar CP-violation phase δ to the Kobayashi-Maskawa
mechanism in the quark sector. The question whether neutrino is Dirac or Majorana has a
profound impact on the elementary particle physics as well as cosmology, and it must be answered
by experiments.
2 Spectroscopy with Atomic Neutrino
2.1 Basic Principle of SPAN
The SPAN project aims to determine neutrino’s most important properties such as their ab-
solute masses, mass type (Majorana/Dirac nature), CP-violating phases etc. SPAN stands for
SPectroscopy with Atomic Neutrino. As the name suggests we employ atoms or molecules as a
source of neutrinos instead of more traditional nuclear/particle decays. Why do we use atoms,
instead of more traditional and popular particle/nuclear decays? How do we do actual experi-
ments with atoms? How sensitive are the experiments to the neutrino properties of interests?
We will answer these questions below. (See reference [2] for more details.)
RENP process We focus on the process |e→|g + γ + ν¯ν,where|e and |g represent
an excited and a ground state of atoms, γ is a photon, and ν ¯ν is a pair of neutrinos. It is a
radiative emission of neutrino pair process, and we call it “RENP” in short. Actually we detect
the emitted photons and measure their energies (neutrinos are impossible to detect). The photon
spectra contain information on the neutrino’s absolute masses, the mass type (Majorana/Dirac
distinction), and CP phases, as shown below. Use of atoms as neutrino sources has disadvantages
as well as advantages. One advantage is closeness of two energy scales between atomic levels
( 1eV) and neutrino masses (< 1eV). This fact permits us to determine all desired neutrino
properties. On the other hand the biggest disadvantage is smallness of rate. We plan to overcome
this disadvantage by a new amplification mechanism called “macro-coherent amplification”. This
amplification is the most crucial concept in our project, and will be explained in §2.2.
5
RENP rate and spectrum The rate of the RENP process is conveniently factorized by three
terms, and is expressed by [2]
Γ
γ2ν
0
I(ω)η
ω
(t), Γ
0
G
2
F
n
3
V. (5)
The first factor, Γ
0
, is an over all rate. It is proportional to the product of the Fermi weak
coupling constant (G
F
), and target parameters such as its number density (n)andvolume(V )
etc. The second one, I(ω), represents photon energy spectrum containing the physics information
about neutrinos: it can be calculated reliably with the Standard Model. The last factor, η
ω
,is
a product of the target coherence and field energy stored in the atomic system. Below we show
RENP spectra of Xe target as an example, assuming the macro-coherent amplification functions
as expected. The Xe state in interests is the metastable state of 5p
5
(
2
P
3/2
)6s[
2
3
2
]
2
(see Fig. 9).
It is an E1-forbidden state, and has a natural life time of 40 seconds. Figure 10 shows the
over all spectrum. The spectrum starts at the half of the energy gap between the metastable
and ground states ( 8.4 eV). Real physics information exists near threshold. Figure 11 shows
an expanded view around the threshold region. Now many structures can be seen clearly. In
particular, the sudden rises (kinks) in the spectrum indicate that new channels are opening for
a particular combination of neutrino pairs. For example, the largest rise, on the left, comes
from the heaviest neutrinos m
3
and m
3
. The threshold positions are expressed by (in units of
c h =1)
ω
ij
=
E
eg
2
(m
i
+ m
j
)
2
2E
eg
(6)
where E
eg
is the energy gap between |e and |g. In this plot, the lightest neutrino mass is
assumed to be 2 (in blue) and 20 meV (in red). The solid line or dashed line show normal
or inverted hierarchy mass pattern. In real experiment, we turn the argument around. We
determine the photon spectrum, or locate the threshold position, and then infer the neutrinos
absolute mass from it. In a similar way, we will be able to determine Majorana/Dirac mass
type, as well as CP-violating phases. These are, however, much more difficult tasks because the
differences in spectra are more subtle. In summary, SPAN project provides us with a systematic
approach to studying neutrino properties that are undetermined at present.
1 2 3 4
eV
0.05
0.10
0.15
0.20
0.25
Xe NH and IH,m020meV
Figure 10: Xe RENP spectrum I(ω).
4.1570 4.1571 4.1572 4.1573 4.1574 4.1575 4.1576
eV
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Xe, Dirac NH vs IH: m02,20meV
Figure 11: Xe RENP spectrum I(ω)inthe
the threshold region. The smallest neutrino
massisassumedtobe2and20meVfortwo
cases of mass patterns, IH (in dashed curves)
and NH (in solid).
6