Elementary Particle Physics III
(素粒子物理学III)
Satoru Yamashita (山下) and Junichi Tanaka (田中)
•
E-mail
– satoru@icepp.s.u-Tokyo.ac.jp for Yamashita
– Junichi.Tanaka@cern.ch for Tanaka
•
Website for materials (to be uploaded after each lecture)
– http://www.icepp.s.u-tokyo.ac.jp/~satoru/lecture/pp3/
– http://www.icepp.s.u-tokyo.ac.jp/~jtanaka/lecture/pp3/
1
Schedule of the Course
Monday 14:55-16:40
•
•
•
4/11 Introduction, High Energy Physics, The Standard Model (SY)
4/18 QCD, Weak and Electroweak unification (SY)
4/25 QCD, Weak and Electroweak unification (JT)
– Short Report (I)
•
•
•
•
•
•
•
•
•
5/2
5/9
5/30
6/6
6/13
6/20
6/27
7/4
7/11
Higgs Mechanism, Higgs Search and Measurements (JT)
Higgs Mechanism, Higgs Search and Measurements (JT)
CKM Matrix and CP Violation (JT)
Neutrino Physics (JT)
Supersymmetry (SY)
New Physics Search at the Energy Frontier Experiments (JT)
New Physics Search at the Energy Frontier Experiments (SY)
Grand Unified Theories (SY)
Search for LFV and Summary of this Course (SY)
– Final report
Note: other 2 or 3 “short report”s will be announced later.
2
3
Neutrino Physics
4
“Neutrino” hypothesis
Electron energy from particles
does not have a sharp peak
but a board distribution.
(Z, N) -> (Z+1, N-1) + e2-body decay -> a sharp peak
(Z, N) -> (Z+1, N-1) + e- + “n”
3-body decay -> a board dist.
(Phosphorus = 燐)
W. Pauli introduced “n” in 1930.
5
Neutrino Discovery
at Nuclear Reactor in 1956 by Reines and Cowan
Inverse b-decay
n e  p  n  e
(Reines got Novel Prize in 1995.)
O(ns)
Neutron capture by cadmium
-> Excited state -> emit gs
6
(Revisited) Neutrino in the SM
–
–
–
–
–
Lepton, Spin 1/2
3 generations … Electron neutrino, muon neutrino and tau neutrino n e n  n 
Massless
Neutral particle -> Only neutrinos are the neutral “matter” particles in the SM
Interact via only the weak interaction: W->ln, Z->nn
• Left-handed neutrino and right-handed anti-neutrino
– Left-handed neutrino: helicity – Right-handed anti-neutrino: helicity + = “Left-handed neutrino with E<0”
• No “right-handed neutrino and left-handed anti-neutrino” (=massless)
– Such particles (nR) have no charge (T3=Y=Q=0) in the SM
EM, weak and strong
-> Even if they exist, we cannot observe them with the SM interactions.
But in principal we can use Yukawa interaction to observe them.
7
Neutrino Mass Measurements
•
Information from the PDG web site (http://www-pdg.lbl.gov/)
Each measurements
3
3

m(ne) < 2 eV (95%CL) … Tritium (三重水素) beta-decay T  He
1
m(n) < 190 keV (90%CL) …
m(n) < 18.2 GeV (95%CL) …
2
 e  n e
     n 
           n 
Total mass … constraints from cosmology (many results/calculations exist. See PDG.)
Sm < 0.23eV (95%CL) (The present PDG does not quote any number officially.)
• Constraints the total mass of neutrinos from Planck CMB data along with WMAP
polarization, high L, and BAO(baryon acoustic oscillations) data (arXiv:1303.5076
[astro-ph.CO])
-> The absolute values have not been measured yet because of its smallness.
8
Observation of Neutrino Oscillation
•
We observed neutrino oscillation in many experiments.
– Several experiments will be shown later.
Anyway,
it means that neutrinos have finite mass!!!
5
3
m  10  10 (eV )
2
2
- How do we describe such massive neutrino in theories?
- Why does the neutrino oscillation indicate “massive” neutrino?
9
Dirac vs Majorana mass term
Dirac mass
Add nR to the SM like a quark part.
We can get the next mass term from Lyukawa.



mD n Rn L n Ln R  mD  R L  L R

To avoid confusion of “-” on neutrinos (some of you may
think this is anti-neutrino but this is wrong. This is a Dirac conjugate.),
we use  instead of n for neutrino’s spinor.
Majorana mass
Use anti-particle instead of different chiral particle.
-> This type of form can be Lorentz invariant. (also Hermite)

m 


mL  L   L  L  L 
R
c
  R  R  R
c
R
c
c
10
Dirac mass

mD  R L  L R

Y
Y
L
m
R
Y
m
L
Left-handed particle and right-handed particle have the
same lepton number.
 No lepton number violation
Majorana mass

mL  L   L  L  L 
c

c
 mL   L  L
c
R
 L c   Rc
See the next page.
c
R


Yc
Y
L
m
R
Y
m
L
Particle and anti-particle have different lepton number.
 Lepton number violation
11
おまけ
Charge conjugate of Y can be written by the Charge conjugate operator C as follows.
 c  C 
 L 
c
T
   C   g 
1
1
 C 1  g   g   C 
2
2
CL
T
T
†
5

L
0
†
T
0
1  g 5  g 0 

T
†
†

T
1
1
T
 C  †g 0 1  g 5   C 1  g 5   †g 0
2
2
T
1
1
 1  g 5 C   1  g 5  c   Rc
2
2

T

  g 0
†
 
* T
A  A
†
12

mD  R L  L R
Dirac mass

This type of mass is not preferred by many physicists. Why?
We can generate this term from the Higgs mechanism
by adding the right-handed neutrino to the SM.
(Personally) in term of uniqueness of theory approach,
this term looks to be OK except for the fact that there is
“no interaction with other particles” (=all the charges are ZERO).
However, when we looked at the measured/known masses of fermions,
the values of Yukawa couplings are much different among them even in
a single generation.
Such differences must be explained.
Too small!!!
BTW, concerning the right-handed neutrinos, since they cannot
interact with the SM interactions, we call such particles “sterile”.
The right-handed neutrino is one of the “sterile neutrinos”.
13
Majorana mass

mL   L  L
c
R
c
R

Write a “general” mass term,
which is a Lorentz invariant (+Hermite)
Lmass  mD   mD 
c
 mL   L  L
c
R
c

➀
➁
c
R
 m  
R
c
L
R
 R
c
L

   g 0   

†
    g 0  C
c
i
 e 
 … (any) charge
c†

g 0  
T†
We can have conserved charges in ➀ but not in ➁.
Let’s consider “electronic charges”
 ➀ … for all fermions, ➁ … only for neutral fermions
14
Majorana mass

mL   L  L
c
R
c
R

Write a “general” mass term,
which is a Lorentz invariant (+Hermite)
Lmass  mD   mD 
c
 mL   L  L
c
R
c

c
R
 m  
R
c
L
R
 R
c
L

N1   L   L    L  Rc
c
N 2   R   R    R  Lc
c
N1 N1   L Rc  Rc L
N1 N 2   L R  Rc Lc
N 2 N 2   R   R
N 2 N1   R L  
c
L
c
L
c
L
c
R
15
Lmass  mD N1 N 2  N 2 N1   mL N1 N1  mR N 2 N 2
N1   L   L    L  Rc
c
N 2   R   R    R  Lc
c
 N1 and N2 are Majorana neutrinos
“Majorana” means “particle = anti-particle” (identical).
16
Lmass  mD N1 N 2  N 2 N1   mL N1 N1  mR N 2 N 2
 N1
 mL
N 2  
 mD
m D   N1 
  
mR   N 2 
mR  mL mR  mL
m 

2
2
4mD2
1
2
mR  mL 
mR  mL mR  mL
mD2
~


2
2
mR  mL
mD2
mD2
m  mL 
~
mR  mL
mR
mD2
m  mR 
~ mR
mR  mL
(mR  mL , mD )
mD2
(mR 
 mL ~ 0)
mR
17
N1  N1 
mD
N2
mR
mD
N 2  N 2 
N1
mR
Lmass
2
D
m
~
N1N1  mR N 2 N 2
mR
 Two majorana neutrinos mass
mD2
mn 
mR
… observed small mass
2
D
See-saw mechanism
m
and mR
mR
mR … heavy mass
mn  10 3 [eV], mD  0.1 [GeV]  m R  1010 [GeV]
-> Need a new physics in this scale
18
PMNS Matrix
•
Neutrino oscillation -> mixture of neutrino flavors like quarks
•
Pontecorvo-Maki-Nakagawa-Sakata matrix (PMNS or MNS Matrix) was
introduced.
Weak eigenstates
n e 
n e 
 
 
n    U PMNS n  
n  
n 
 
 
Mass eigenstates
=VCKM (exactly the same parameterization)
-> 3 real parameters/angles and 1 complex phase (Dirac neutrino)
-> CP-violation is possible!
If neutrinos are majorana, we need two additional phases, which might cause CPV.
-> 3 real parameters/angles and 3 complex phases (Majorana neutrino)
19
PMNS vs CKM
(d=0 is used.)
(I calculated elements by using the following values,
which are obtained from PDG web site)
2
0.024
sin 2 12  0.307 00..018
016 , sin  23  0.386  0.021 ,
sin 213  0.0241  0.0025 (m1  m 2  m 3 )
12  33.6 ,  23  38.4 , 13  8.9
The mixing size of the neutrinos are relatively larger.
(but we don’t know this reason.)
20
Oscillation
For simplicity, we consider a two-generation oscillation.
weak
mass
See the evolution of a neutrino created as n at t=0
Two mass states can travel with different frequencies.
Then get the transition n(t=0)  nb
The probability of n(t=0)  nb
21
Oscillation/transition probability of n to nb
Survival probability of n
We should optimize the parameters of experiments
to get the maximum oscillation/transition/survival probability.
22
L  180km
m 2  7 10 5 eV 2
sin 2 2  0.84
(PDG)
1.27m 2 L 3

 E  3.3 [MeV]
E
2
1.27m 2 L 
  E  10 [MeV]
E
2
23
Neutrino Experiments
 m232 and 23 : n -> n
 Atmospheric neutrino and accelerator neutrino experiments
 m122 and 12 : ne -> n
 Solar neutrino and reactor neutrino experiments
 13 : ne -> n
 Reactor neutrino and accelerator neutrino experiments
m 2 [eV 2 ]L[km]
~1
E[GeV]
PDG
24
Neutrino Experiments
(a part of them…)
 m232 and 23 : n -> n
 Atmospheric neutrino and accelerator neutrino experiments
Atmospheric exp: (Super-)Kamiokande, Soudan-2, MACRO,
MINOS, … -> 23
Accelerator exp: K2K, MINOS, T2K, … -> m232
 m122 and 12 : ne -> n
 Solar neutrino and reactor neutrino experiments
Solar exp: Homestack, (Super-)Kamiokande, Gallex, SAGE, SNO,
Borexino, … -> 12
Reactor neutrino exp: KamLAND, … -> m122 and 12
 13 : ne -> n
 Reactor neutrino experiments and accelerator neutrino experiments
Reactor exp: Daya Bay, Chooz, Double Chooz, RENO, …
Accelerator exp: T2K, …
25
Atmospheric n
Atmospheric Neutrino
So-called “atmospheric neutrinos”
are produced from cosmic rays.
()
   n 


()
()
  e n e n 


n  :n e  2 : 1
is naively expected.
A nominal n energy range is 1-100GeV.
(-> The flux is maximum around 1GeV.)
In 1988, Kamiokande reported
a kind of anomaly in the atmospheric
neutrinos. (See the next slide)
26
Atmospheric n
Phys.Lett.B 205 (1988) 416
Kamionkande
Muon-like events 85/144 = 59%
Historically they (including other experiments in 1980’s) would observe “Proton decay”.
-> They observed many atmospheric neutrinos, which are background for the proton
decay search.
 0

p  e   e gg
p  K n
27
Atmospheric n
Kamiokande and Super-K
Kamiokande
1983~1996
1996~
15.5m
3000 ton (~1032 proton)
1000 PMT
28
29
1
cos  c 
nb
nwater  1.33 (T  20o C)
c Emit Cherenkov light (300 photons/cm of λ=300-600nm)
① cos  c  1 v 
n (this is very small comparing to MIP.)
1
mc 2
mc 2
nmc 2
No Cherenkov light E 
 Eth 

②b 
2
2
n
1 b
11 n
n2 1
Eth = 0.77MeV for electron, 158MeV for muon
30
Atmospheric n
n
“Fully contained” neutrino events
with single Cherenkov ring
(“partially contained” -> not discussed)
(“multi rings” -> not discussed)
Electron-like
Single Cherenkov ring
A ring can be observed but
due to EM shower, it is not so clear.
(e)
(e)
lepton
Muon-like
Single Cherenkov ring
A clear ring can be observed.
31
Atmospheric n
Atmospheric Neutrino
 zenith angle
Diameter=~104km
32
Atmospheric n
n
Result of 1489-day SK exposure
n at SK
PRL81 (1998) 1562
“Evidence for oscillation of
atmospheric neutrinos”
 Kajita-san Nobel Prize in 2015
PRD71 (2005) 112005
“Measurement of atmospheric neutrino oscillation parameters by SK I”
Non-oscillation
Δm23  2.110-3 eV 2 , sin 2 2θ23  1.00
33
Solar n
Solar Neutrino
Standard Solar Model (SSM)
Main chain
0.26MeV
1.44MeV
0.86MeV (90%)
0.38MeV (10%)
7.2MeV
4 p  4He  2e   2n e  27[MeV]
Solar neutrino observation  “nuclear fusion in the Sun”
34
Solar n
Solar Neutrino Energy
35
Solar n
1968
Homestake
37Cl
(Chlorine)
PRL 20 (1968) 1205
Half-life of Argon = 35days
- Keep the detector (C2Cl4) at least
35 days
-> The number of Ar becomes
stable.
- Count Ar by using X-ray from Ar.
-> Can calculate neutrino flux
Measured = 2.56±0.23 SNU
SSM predictions
9.3±1.3 SNU
6.36 SNU
7.64 SNU
C2Cl4 615ton
APJ 496 (1998) 505
36
Solar n
•
Solar Neutrino Problem/Puzzle
The Homestake result shows a deficit of solar neutrino.
~1/3 of SSM predictions
•
At that time one did not understand this result.  “Solar Neutrino Problem/Puzzle”
Did some mistake in the Homestake experiment ?
SSM is wrong ?
or anything else  Oscillation ?
(Gallium)
Similar type of experiments with Ga
37
Solar n
Solar neutrino at Super Kamiokande
1496 days
(1996-2001)
n e  e n e  e
22400±230 events
46.5% of the SSM prediction
-> Confirm the deficit of the Solar neutrinos
but no one understood its reason.
38
Solar n
Canada
SNO experiment
“Heavy” water is used.
(deuterium oxide)
 CC and NC are measured
at the same experiment.
We observed the deficit of ne. We need to show such neutrinos
are converted into other neutrinos (n/n). SNO exp can test it.
39
Solar n
SNO exp.
6
-2 1

CC n e   1.68  0.06 00..08

10
cm
s
09
ES n X   2.35  0.22  0.15106 cm -2 s 1
38
106 cm-2 s 1
 NC n X   4.94  0.2100..34
Phys. Rev. C 72, 055502 (2005)
Why so important?
① CC
n e   ES n X 
ne (solar neutrino) 
Something(n, n?)
This shows still only the “deficit”.
② Three measurements are consistent
in term of e and other n flux.
CC n e , ES n X    NC n X 
Solar neutrinos really change
into other neutrinos.
“Solar neutrino puzzle” was
solved.
A.B.McDonald Nobel Prize in 1995 with Kajita-san
40
The Nobel Prize in Physics 2015
For the discovery of neutrino oscillations, which shows that neutrinos have mass
41
Matter effect
•
Neutrino oscillation in matter is different from that in the vacuum:
Light in a matter has different wave length due to the refraction (屈折).
Neutrino also has a similar effect in matter.
This is called “MSW effect”.
(Mikheyev–Smirnov–Wolfenstein)
m2 n
m2n
m2ne
Surface
Center
Electron Density in the Sun
Electron neutrinos produced
in the center of the Sun is changed
into muon neutrinos due to the matter
effect when they are emitted from the Sun.
We need to take into account this effect
properly in our calculations.
This is the case for the earth etc.
(T2K etc  See it later)
42
Survival probability of electron neutrinos in the Sun
(θ, Δm2) measurement  not a point but a contour
43
Solar n
Large Mixing Angle
Electron recoil energy at SK
Small Mixing Angle
Low Δm2
Quasi-Vaccum
Still LMA and LOW solutions
4 possibilities from solar neutrino exp.
 Wait for KamLAND!
44
Reactor n
Reactor Neutrino exp. KamLAND
1000tons Liquid Scintillator ( low energy neutrino)
Inverse b-decay reaction

n
n e  p  e  n (E th  1.806 MeV)
 Take coincidence
45
Reactor n
Reactors around KamLAND (~2002)
Ln  180km (with ~70GW)
En  a few MeV
m 2 ~ 10 5 [eV 2 ]
46
Reactor n
Evidence of reactor anti-neutrino disappearance (2002)!
47
Reactor n
Determination of Solution
Without KamLAND results, we had still a few regions for parameters of m
2
12
, 12 .
 By combining both solar and KamLAND we selected one of them.
PRL 94 (2005) 081801
LMA
m 2  7.9 00..65 10 5 [eV 2 ] , tan 2   0.40 00..10
07
48
Reactor n
Oscillation observed at KamLAND
At that time, some of reactors were turned off for the maintenance etc.
 A “effective distance” L0 En between KamLAND and neutrino
e
sources are changed.
49
Neutrino Mass Hierarchy
So far what we have measured is relative mass size.
We cannot measure the absolute values.
Note: cosmology
Sm < 0.23eV (95%CL)
+
reactor
+
reactor
50
13
The last phase to be observed (expect CP phase) is 13.
There are (at least) two ways to measure this phase:
① ne disappearance
Reactor neutrino experiments
② ne appearance
(please see 3-generation oscillation formula.)
Accelerator neutrino experiments
(Atmospheric neutrino experiments)
51
Reactor n
NuFact2013 Talk
Daya Bay Experiment
GPS and modern theodolites
-> relative detector-core positions ~ 3cm
52
Reactor n
Daya Bay
53
Why can Daya Bay measure 13?
Short baseline
Reactor neutrino En~MeV
m2~10-3 with L~km
Long baseline
m2~10-5 with L~100km
54
Reactor n
NuFact2013 Talk by Soeren Jetter
Daya Bay
(mee~m13  A term for the short baseline is
more complicated.)
55
Reactor n
NuFact2013 Talk by Soeren Jetter
March 2012
DC=Double Chooz
56
Accelerator n
T2K Experiment
Long baseline neutrino experiment
Muon neutrino beam produced by accelerators
57
Accelerator n
Normal
hierarchy
Inverted
hierarchy
2
sin 2 213  0.140 00..038
(

m
032
32  0)
045
2
sin 2 213  0.170 00..037
(m 32
 0)
2
(| m32
| 2.4 10 3 [eV 2 ],
sin 2 23  0.5, d CP  0)
PRL 112 (2014) 061802
58
Future Neutrino Experiments
•
What we need to understand in (near) future is
–
–
–
–
–
Mass Hierarchy
CP phase(s)
Dirac vs Majorana
Absolute mass size
Existence of other neutrinos
• More than 3 flavors
• “Sterile” neutrino  eV mass scale?
59
Reactor n
MC simulation for RENO-50 exp.
Reactor Experiment for Neutrino Oscillations in Korea
We can observe small differences in, for example, P(nene).
(see PLB 533 (2002), 94)
Solid … Normal Hierarchy
Dashed … Inverted Hierarchy
@1MeV
Require better energy resolution  3% or better
(also need statistics)
60
Accelerator n
CP Violation at Neutrino Sector
More complete ne appearance probability including the matter effects
Leading term
Matter
effects
2

 E 



a  7.56  10 5 eV 2 
3 
 [g cm ]   [GeV] 
 
By measuring this probability precisely with n beam, we can extract CP phase.
Ideally it is better to measure this probability with both n and n beam.
In addition, we may separate the mass hierarchy with this measurement.
(see the next)
61
Accelerator n
ne appearance probability including the matter effects at the oscillation maximum
(sin2213=0.1 and sin2223=1)
(Ichikawa-san’s slide)
This value can
be obtained
from the 1st term
of the expression
shown in the
previous page
with the present
measurements.
62
Hyper Kamiokande
Previous proposal: size : 48m(W) x 54m(H) x 250m(L) x 2
Current proposal (2016) : size : Diameter 74m x Height 60m x 2
Fiducial volumn
190k ton per one tank
~ 8 x SK
Operate from ~202x
Don’t forget the “proton decay”…
63
Double b-decay
2n mode : Z   Z  2   2e   2n e
0n mode : Z   Z  2   2e
n
en p
e-
n p
bb2n
n
e-

Must be n=n
e-
n
n
n p
n p
bb0n
2n mode is possible in the SM (with both Dirac and Majorana neutrino).
0n mode is possible in case of Majorana neutrino.
Also this mode violates the lepton number: 0  2
The search for 0n mode is very interesting.
 If we’ll observe it, it means that neutrino is not “Dirac” but “Majorana”.
64
Normalized “sum of two electron energy”
In case of the “neutrino double beta decay”, ideally we can observe
a peak instead of a broad energy distribution.
65
The type of isotopes is limited.
~ 30 kinds of isotopes could be candidates. Why?
Because the next type of “Energy level structure” is required.
76As
76Ge
2.04 MeV
Double b-decay
ヒ素
76Se
セレン
The bb2n decay itself is rare. Typical half-life of bb2n is 1018-1024 or longer.
-> We have observed bb2n decay, for example,
76
Ge76 Se  2e   2n e
2n
T1/2
 (1.5  0.1) 10 21 year
For the bb0n decay, we have not observe such decay yet (except one?).
The Heidelberg-Moscow group set a limit on it with 1.9x1025 year
with a limit on <mn> of 0.3-0.6 eV by using 76Ge. But a part of
the same collaboration also claimed the observation of bb0n decay,
that is, 1.5x1025 year and <mn> of 0.39 eV in 2001.
-> In the final paper (2006), this observation is still supported.
76
0n
25
Ge76 Se  2e  T1/2
 (2.2300..44
31 )  10 year
Also we see a kind of hints on
136Xe.
MPLA Vol21 No20 (2006) 1547
One need to check them in future.
66
Many experiments are on-going and also planed.
CUORICINO … 130Te
EXO-200 … 136Xe
KamLAND-Zen … 136Xe
NEMO3 … 48Ca, 82Se, 100Mo, 116Cd, 130Te
etc
(Not MeV but meV)
m(majorana)<140-380meV
EXO-200
EXO-200 (SLAC, US)
Signal region arXiv:1205.5608
2nbb … grey region
232Th … dotted magenta
>1.6x1025 year
67