Leptogenesis
Takehiko Asaka (Niigata Univ.)
Flavor Physics workshop 2021 (FPWS2021)
2021/09/27̶30
OnlineOnline (2021/09/30)

Contentsn2

Introduction¤ Baryon asymmetry of the universe (BAU)¤ Baryogenesis in the Standard Modeln

Leptogenesis¤ Motivation¤ Some scenarios of leptogenesisnExperimental tests of leptogenesis scenariosnSummary2021/09/21

Baryon Asymmetryof the Universe(BAU)

Baryon v.s. antibaryonn4BaryonAntibaryon

proton （𝐵 = +1)
neutron （𝐵 = +1)

antiproton （𝐵 = −1)
antineutron （𝐵 = −1)

We find baryons mostly, not antibaryons !
¤ Existence of antiproton

In cosmic rays, 𝑝 + 𝑝 → 𝑝 + 𝑝 + 𝑝 + 𝑝̅At TEVATRON, 𝑝 + 𝑝̅ →XnAsymmetry between baryons and antibaryons in our Universe

How large ???
2021/09/21

Baryon Asymmetry of the Universe (BAU)nObservational value

5

Planck 2018 [1807.06209]𝑛!
𝑌! == (0.872 ± 0.004)×10"#$𝑠𝑛! ∶ baryon number density, 𝑠 ∶ entropy density

CMBR

BBN

[Strumia 06][PDG]

2021/09/21

Brief history of the universe

𝐵=0

Inflation

Generate
BAU !

temperature

~MeV

6

BBN

~0.3 eV

Recombination~10!" eV

Today

CMB

Baryogenesis

𝐵≠0𝐵≠04He, D,…
2021/09/21

BaryogenesisnSakharov

7（１９６７）（１）Baryon number B is violated“According to our hypothesis, the occurrence of C asymmetry is theconsequence
violationof CP invariancethe nonstationary expansion of（２）CofandCP symmetries
are inviolated
the hot Universe during the superdense stage, as manifest in the difference
betweenthe partialof the charge-conjugate reactions.”（３）Outofprobabilities
thermal equilibrium

Let us see whether the SMsatisfies these conditions

2021/09/21

B violation in the MSMn

At classical level, 𝐵 and 𝐿 are conserved
𝜕! 𝑗" = 0!

Baryon number: 𝐵 = ∫ 𝑑 ( 𝑥 𝑗")!

Lepton number: 𝐿 = ∫ 𝑑 ( 𝑥 𝑗#)

𝜕! 𝑗# = 0
accidental symmetriesn8both charges are conserved

At quantum level, 𝐵 and 𝐿 are violated
by non-perturbative anomaly effect𝑔%!
!
' 0 '!&
𝜕! 𝑗" = 𝜕! 𝑗# = 𝑁$
𝑊
𝑊
!&
%
32𝜋
𝑁" : number of generations (families)##
𝜕# (𝑗$ − 𝑗% ) = 0

𝐵 and 𝐿 are violated, but (𝐵 − 𝐿) is conserved !
2021/09/21

DB and DLn

9Chern-Simons number (integer)&+#∆𝐵 = 0 𝑑𝑡 0 𝑑 ' 𝑥 𝜕# 𝑗$ = 𝑁( ∆𝑁)*
&*

𝑔+
2
'
,-.
𝑁)* =
0 𝑑 𝑥 𝜀 𝑡𝑟 𝐴, 𝜕- 𝜕. + 𝑖𝑔 𝐴, 𝐴- 𝐴.
+
32𝜋
3
Energy2021/09/21

DB and DLn

10

At the vacuum (at temperature 𝑇 = 0)
EnergyInstanton[G. ʻｔ Hooft ʼ76]

The transition rate
16 𝜋 %
Γ~ exp −𝑔%= 𝒪(10,-.) )B+L breaking effect is negligible
2021/09/21

DB and DLn11

For high temperatures (at temperature 𝑇 > 𝒪(10% ) GeV)
EnergySphaleron
The transition rate

( per unit volume )1
Γ~𝜅 𝛼0
𝑇1[Moore ʻ00]

∆𝐵 = ∆𝐿 = 𝑁(
Sphaleron process is in equilibrium

10/+ GeV > 𝑇 > 10+ GeV[Kuzumin, Rubakov, Shaposhnikov ʼ85]

Buchmuller
2021/09/21

Sphaleron conversionn

12

Initial (𝐵 − 𝐿) asymmetry is converted into 𝐵

8𝑁( + 4𝐵2 =𝐵 − 𝐿 , = 0.35 𝐵 − 𝐿 ,22𝑁( + 13[Khlebnikov, Shaposhnikov ʻ88, Harvey, Turner ʻ90]n

𝐵 − 𝐿 / = 0 initially leads to 𝐵 = 0 universe
à Initial asymmetries 𝐵/ and 𝐿/ are washed out if 𝐵 − 𝐿 / = 0nWe have to generate 𝐵 − 𝐿 / > 0 initiallyin order to explain 𝐵 > 0 universe !

2021/09/21

Baryogenesis in the Standard Modeln

13

B and L violations¤ Sphaleron for T>100GeVn

CP violation¤ 1 CP phase in the quark-mixing (CKM) matrix

𝐽#$ 𝑚%& − 𝑚'& 𝑚%& − 𝑚(& 𝑚'& − 𝑚(& 𝑚)& − 𝑚*& 𝑚)& − 𝑚+& 𝑚*& − 𝑚+&CPV~~10/.0.&𝑇,-à too smalln

Out of equilibrium[Kajantie, Laine, Rummukainen, Shaposhnikov]¤ Strong 1st order phase transition if

but 𝑚3 = 125 GeVà not satisfied

𝑚0 < 72 GeV
We have to go
beyond the SM !
2021/09/21

Various baryogenesis scenarios

14¤ GUT baryogenesis, GUT baryogenesis after preheating,

Baryogenesis from primordial black holes, String scale
baryogenesis, Affleck-Dine (AD) baryogenesis, Hybridized AD
baryogenesis, No-scale AD baryogenesis, Single fieldbaryogenesis, Electroweak (EW) baryogenesis, Local EW
baryogenesis, Non-local EW baryogenesis, EW baryogenesis
at preheating, SUSY EW baryogenesis, String mediated EW
baryogenesis, Inflationary via baryogenesis, Baryogenesis
without ground unification (leptogenesis), Resonant
leptogenesis, Spontaneous baryogenesis, Coherent
baryogenesis, Gravitational baryogenesis, Defect mediatedbaryogenesis, Baryogenesis from cosmic strings, B-ballbaryogenesis, Baryogenesis via neutrino oscillations,Monopole baryogenesis, …
See, for example, talk by M. Shaposhnikov @COSMO 2012
2021/09/21

Leptogenesis

LeptogenesisーMotivation

Neutrino properties
n

n

17

Mixing angles and mass squared differences are measured very
precisely
sin& 𝜃.& = 0.30831.1.4/1.1.&&/7 eV &
Δ𝑚&.
= 7.4931..0/1..5 ×10

sin& 𝜃&4 = 0.44031.1&4/1.1.0&/4 eV &
Δ𝑚4.
= 2.52631.1&0/1.145 ×10

sin& 𝜃.4 = 0.0216331.11156/1.11156

Gonzalez-Garcia, Maltoni and Schwetz(𝜈-fit, August ʼ16)

(NH case)

Unknown properties¤ Absolute masses of neutrinos (𝑚& 12345675 ?
¤ CP violations (Dirac phase ?

Mass ordering ?)Majorana phase(s) ?)¤ Dirac or Majorana fermions

2021/09/21

𝜈!

Right-handed neutrinos

18

2021/09/21

Why 𝝂𝑹 ?
n

Chiral structure of fermions in the SMn

Hierarchical patterns of fermion masses

19¤ neutrino masses << masses of quarks and leptons(𝑚8%9 ≃ 50 meV ≪ 𝑚: ≃ 0.5 MeV)nInteresting phenomena by right-handed neutrinos¤ Baryogenesisl Leptogenesis / Mechanism by oscillations¤ Dark matterl keV mass right-handed neutrino is a candidate of WDM(it may be irrelevant in the seesaw mechanism)¤ etc.

2021/09/21

Standard Model
Higgs
Boson

ℎ

20

Quarks and Leptons

Gauge
Bosons(left-handed)(right-handed)æu ö æcö æ t ö
ç d ÷ ç s ÷ çb÷è øL è øL è øLu R cR t R

𝑔d R sR bR

𝑍KeR µ R t R𝑊±æ e ö æ µ ö æt öçn ÷ çn ÷ çn ÷
è e øL è µ øL è t øL𝛾2021/09/21

Three right-handed neutrinos
Higgs
Boson

ℎ

Quarks and Leptons

21

Gauge
Bosons(left-handed)(right-handed)æu ö æcö æ t ö
ç d ÷ ç s ÷ çb÷è øL è øL è øLu R cR t R

𝑔d R sR bR

𝑍KeR µ R t R𝑊±𝜈&# 𝜈&' 𝜈&(𝛾æ e ö æ µ ö æt öçn ÷ çn ÷ çn ÷
è e øL è µ øL è t øL

2021/09/21

Extension by right-handed neutrinos 𝝂𝑹
𝑀9!
Q
𝛿ℒ = 𝑖𝜈; 𝛾 𝜕! 𝜈; − 𝐹 𝐿𝜈; Φ +𝜈; 𝜈;< + ℎ. 𝑐.
2n22Minkowski ʼ77, Yanagida ʼ79
Gell-Mann, Ramond, Slansky ʻ79
Glashow ʼ79,
Mohapatra, Senjanovic ʻ79

Seesaw mechanism (𝑀8 = 𝐹 Φ ≪ 𝑀9 )01c æ
- L = (n L ,n R ) ç T
2
èMD

M D ö æn Lc öMn1c æç ÷ + h.c = (n , N ) ç÷M M ø èn R ø2è 0

0 ö æn c öç ÷ + h.c.
÷
M M øè N ø

𝝂¤ Light active neutrinos
𝑀8:
𝑀& = −
×𝑀8 ⟸ tiny neutrino masses !
𝑀9→ explain neutrino oscillations¤ Heavy neutral leptons

l Mass 𝑀9l Mixing Θ = 𝑀8 /𝑀9𝑵 (≃ 𝜈& )Neutrino mixing𝜈) = 𝑈 𝜈 + Θ 𝑁 *2021/09/21

Yukawa coupling and Majorana mass
𝑀=
𝐹& Φ &
𝑚; =
×𝑀= =
𝑀>
𝑀<

23

𝐹=

𝑚; 𝑀<
Φ

𝑚; = 5×10/.. GeV
Seesaw
does
notwork !

2021/09/21

Mixing and mass of heavy neutral lepton
&
𝑀
𝑚;
=
&
Θ = &=𝑀< 𝑀<

24𝑚; = 5×10/.. GeV

2021/09/21

Range of parameter space

25

TA, Tsuyuki ʻ15

1
10-5

10-15
See
saw

10-20

1
=M
M2

|1|2

10-10

10-25
10-30

1

102 104 106 108 1010 1012 1014 1016 1018
M1 [GeV]
2021/09/21

Bound from seesaw mechanism
n

n

26

Mixings of HNL must be sufficiently large
to explain masses of active neutrinos !
Bound on the mixing of the lightest HNL 𝑁/

Θ/

+

𝑚4
≥
𝑀/

TA, Tsuyuki ʻ15

Θ- % ≡ V Θ=- %=>?,!,A

𝑚. 𝑚4 in the NH (IH) for 3RHN (𝒩 = 3)𝑚B =𝑚& 𝑚. in the NH (IH) for 2RHN (𝒩 = 2)

NOTE: Θ. & can be zero for 𝒩 = 3(No lower bound for 𝒩 > 3)
2021/09/21

Range of parameter space
TA, Tsuyuki ʻ15

Direct search1

Too large
neutrino Yukawa
couplings
𝐹 & > 4𝜋

10-15

𝒩=2
10-20

Too smallneutrino masses

10-25
10-30

See
saw

1
=M
M2

10-10

|1|2

10-5

Cosmology
(BBN)

27

1

102 104 106 108 1010 1012 1014 1016 1018
M1 [GeV]
2021/09/21

RH neutrinos and baryogenesis
Extension by 𝝂𝑹 (seesaw)

28

Sakharovʼs 3 conditions

L violationby Majorana mases

C1
B, L violations

CP violationin neutrino sector

C2
CP violation

New particles

C3
Out of equilibrium(HNL/RH neutrinos )𝝂𝑹 in the seesaw mechanism can satisfy
all three conditions for baryogenesis
2021/09/21

Baryogenesis regions

29

TA, Tsuyuki ʻ15

1
Baryogenesis via neutrino oscillation(Akhmedov, Rubakov, Smirnov ʼ98,
TA, Shaposhnikov ʼ05)

10-5

Resonant Leptogenesis(Pilaftsis ʻ97, Pilaftsis, Underwood ʻ05)

10-15
See
saw

10-20

1
=M
M2

|1|2

10-10

Leptogenesis(Fukugita, Yanagida ʻ86)

10-25
10-30

1

102 104 106 108 1010 1012 1014 1016 1018
M1 [GeV]
2021/09/21

Thermal Leptogenesis[Fukugita, Yanagida ʼ86]

Leptogenesisn31

𝜈; (𝑁) can into LH leptons and also their anti-particles𝑁.

n[Fukugita, Yanagida ʼ86]

O
𝐿? + Φ
𝐿? + Φ

When CP is violated in neutrino sector,
O − Γ 𝑁. → 𝐿? + ΦΓ 𝑁. → 𝐿? + Φ
𝜀. =O + Γ 𝑁. → 𝐿? + Φ ≠ 𝟎 !
Γ 𝑁. → 𝐿? + Φ⟹ generate asymmetry Δ𝐿? between #𝐿? and #𝐿?
nAsymmetry in 𝐿# is partially converted into baryon asymmetry
by EW sphaleron process (𝑇 ≳ 10% GeV)

28
28
𝐵=
𝐵 −𝐿 6= ー𝐿6
79
79

2021/09/21

Out of Equilibrium Decayn

For 𝑻 ≫ 𝑴𝟏 , 𝑵𝟏 is in thermal equilibriumn

For 𝑻 < 𝑴𝟏

32

EQ

à Out of equilibrium decay of 𝑵𝟏
2021/09/21

Leptogenesisn[Fukugita, Yanagida ʼ86]( − Γ 𝑁! → 𝐿" + Φ
Γ 𝑁! → 𝐿" + Φ
𝜀! =( + Γ 𝑁! → 𝐿" + Φ
Γ 𝑁! → 𝐿" + Φ

Yield of BAU𝑛"∝ 𝜀- ∝ 𝑀𝑠

33

𝑀. ≪ 𝑀&,4,…

[Giudice et al ʻ03]

Lower bound on Majorana
mass in order to explain theobserved BAU

𝑀/ > 𝑂 107 GeV→ impossible to test
directly such a heavy
particle by experiments

2021/09/21

Resonant leptogenesisnPilaftsis ʼ97
Pilaftsis, Underwood ʼ04

34

Resonant production of lepton asymmetry occurs
if right-handed neutrinos are quasi-degenerate( − Γ 𝑁! → 𝐿" + Φ
Γ 𝑁! → 𝐿" + Φ
𝜀! =( + Γ 𝑁! → 𝐿" + Φ
Γ 𝑁! → 𝐿" + Φ

Δ𝑀 ≪ 𝑀E
Δ𝑀 = 𝑀& − 𝑀.
𝑀< = (𝑀& +𝑀. )/2

𝑀8+
𝜀/ ∝
Δ𝑀 +

（for Δ𝑀& > 𝑂(𝑀< Γ< )）huge enhancement⟹ Leptogenesis is possible even for 𝑀. ≪ 100 GeV
Note that 𝑀! ≳ 10# GeV in this case in order to convert lepton asymmetry
into baryon asymmetry by EW sphaleron process (𝑇 ≳ 10# GeV)
2021/09/21

Resonant Leptogenesis

35

Degenerate RH neutrinos（𝑴𝟏,𝟐 = 𝟏𝟎𝟑 GeV）
Maximum values of YB
IH
Contour of 𝑌"
Contour of 𝑌"

2.0-1. ¥ 10-602.01.0 0

1.5

1.50.5

2. ¥ 10-6-6

2. ¥ 10-6-2. ¥ 100
-2. ¥ 10-6
1. ¥ 10-6

0.5

1. ¥ 10-6-0.5-1. ¥ 10-6

-9

8. ¥ 10
0

0

-8-6
1.2
¥¥
1010
-2.

1. ¥ 10-8

2. ¥ 10-6

1.00.0-0.5
0.5-2. ¥ 10

0.0
-1.0

4. -6
¥ 10
2. ¥ 10

6. ¥ 10-9

1.2 ¥ 10-8

1. ¥ 10-6-1. ¥ 10-6

1. ¥ 10-8-6-1. ¥ 10-6

2. ¥ 10-9-9cp-1. ¥ 10-6

1.0

1. ¥ 10-6

ad21êpêpHa21-a31Lêp

Majorana Phase-2. ¥ 10-6

-2. ¥ 10-60

1. ¥ 10

0.0

dcpêp

0.5

Dirac Phase

1.0

-1.0
0.0

2. ¥ 10-9-

8. ¥ 10-9-6-910-62. ¥6. ¥ 10-1. ¥ 10-6

dcpêp

NH

-6
-2.
10-9
4. ¥¥10-6-1.
0 ¥ 10-1.0 -0.4-0.5-0.2 0.00.0

0.2
0.5

-

0.4
1.0

êp
dRew
cp êp23
TA, Yoshida [arXiv:1812.11323]

MAX
Figure 1: Contour plots of YBMAX in the NH case. YBFigure
is positiveor negative
inMAX
the inregionwithbright2: Contour
plots of Y
the IHcase.
Y MAX is laB

B

2021/09/21
or dark color. In the left or right panel the plot is shownin the δ-(αleft) plane
when
= π/4
21 −α
23 is
dark color.
InCPtheor31right
panel
theReω
plot
shown in thBaryogenesis via
neutrino oscillation
Akhmedov, Rubakov, Smirnov ’98
TA, Shaposhnikov ‘05

Baryogenesis via Neutrino Oscillation

37

Akhmedov, Rubakov, Smirnov (ʼ98) / TA, Shaposhnikov (ʻ05)

Shaposhnikov (ʼ08), Canetti, Shaposhnikov (ʻ10)
TA, Ishida (ʻ10), Canetti, Drewes, Shaposhnikov (ʼ12), TA, Eijima, Ishida (ʻ12)
Canetti, Drewes, Shaposhnikov (ʻ12), Canetti, Drewes, Frossard, Shaposhnikov (ʻ12)...

¤ Oscillation starts at 𝑻𝒐𝒔𝒄 ~ 𝑴𝟎 𝑴𝑵 𝜟𝑴

𝑁%
𝑁(

𝟏/𝟑

Medium effects

𝑇% N
𝑉E =
𝐹 𝐹
8𝑘

N

L

N

¤ Asymmetries are generated since evolution rates of 𝐿= and𝐿0 are different due to CPV
𝐿=

𝐿9

𝐿=

∗
𝐹,'

𝑁+

𝑁'

𝐿9

𝐹,(
2021/09/21

Evolution of each asymmetries
LH leptons

38

RH neutrinos

2021/09/21

Baryogenesis via neutrino osc.

39

Oscillation of heavy neutrinos can be a source of BAU¤ CPV in oscillation and production generates asymmetries¤ Asymmetries are separated into LH and RH leptons¤ Asymmetry in LH leptons is converted into BAU

Yield of BAU depends on
Yukawa couplings 𝐹BC and masses
Especially, CP violating parametersand mass difference

𝑇:;< ~ 𝑀6 𝑀8 𝛥𝑀 //'2021/09/21

Key Point40

Baryogenesis via Leptogenesis
B

B

L

L

sphaleron

Baryogenesis via Neutrino Oscillation
B

L

B

L

sphaleron

2021/09/21

Analytical Formula of BAU

TA, Shaposhnikov ʻ05
TA, Ishida ʼ10

41

7/3
5/3 5/2 1/2
M
M
nB
-11
0
N matm msol
= 1.8 ´ 10 k
´ d CP62
2 2/3s
TW ( DM 32 / M N ) F
5/3=4.7 ´ 10
n

-10

ö
10
æ MN ö æ
ç
÷ ç
2
2 ÷
5GeV
D
M
/
M
è
ø è
32
N ø
-8

2/3

´ d CP

RH neutrinos N2 and N3 must be quasi-degenerate
to get a sizable BAU !

n

CP asymmetry parameter for BAU

d CP µ ååa µt

I = 2,3 = e , ,2

FIa Im éë Fa 3 ( F † F )32 Fa*2 ùû
CPV in neutrino Yukawa couplings
2021/09/21

Baryogenesis Region
Region accounting for

>O
?

42

= (8.55-9.00)×10/..
TA, Eijima ʻ13

Canetti, Shaposhnikov ʻ10
IH

IH
NH

𝑀8 > 2.1 MeV (NH)NH

𝑀8 > 0.7 MeV (IH)
2021/09/21

Constraints on HNL

43TA, Eijima, Takeda ʻ14

Direct Search

Cosmology

𝜏< < 1 sec

𝑀8 > 122 MeV (NH)𝑀8 > 136 MeV (IH)
2021/09/21

Baryogenesis region

44

31

FIG. 9. The range of the total mixing angle
U 2 Shaposhnikov,
consistent withTimiryasov
both the seesaw
mechanism andKlaric,ʻ21 [2103.16545]
leptogenesis as a function of HNLs’ mass MN . The black solid lines show the results obtainedwith the full kinetic equations and vanishing initial conditions for HNLs. The blue, dashed lines
correspond to thermal initial conditions. In this regime the freeze-in does not2021/09/21
contribute to theLeptogenesis scenarios

45

TA, Tsuyuki ʻ15

1
Baryogenesis via neutrino oscillation(Akhmedov, Rubakov, Smirnov ʼ98,
TA, Shaposhnikov ʼ05)

10-5

Resonant Leptogenesis(Pilaftsis ʻ97, Pilaftsis, Underwood ʻ05)

10-15
See
saw

10-20

1
=M
M2

|1|2

10-10

Leptogenesis(Fukugita, Yanagida ʻ86)

10-25
10-30

1

102 104 106 108 1010 1012 1014 1016 1018
M1 [GeV]
2021/09/21

Experimental tests for
leptogenesis scenarios

RH neutrinos and baryogenesis
Extension by 𝝂𝑹 (seesaw)

47

L violationby Majorana mases•••

Neutrinoless double beta
decay
Inverse neutrinolessdouble beta decay
LNV meson decay…

CP violationin neutrino sector•••

CPV neutrino oscillation
EDM…

New particles•••

Peak searches
Beam dump experiments…

(HNL/RH neutrinos )•Experimental tests are crucial !!
2021/09/21

48

Lepton number violation in
the seesaw mechanism
1) Neutrinoless double beta decay2) Inverse neutrinoless double beta decay
3) LNV meson decay

2021/09/21

Neutrinoless double beta (0ν𝛽𝛽) decayn49

W.H. Furry 1939

Neutrinoless double beta (0ν𝛽𝛽 ) decay

𝑍, 𝐴 → 𝑍 + 2, 𝐴 + 2𝑒 !

¤ LNV (Δ𝐿 = +2) process mediatedby Majorana massive neutrinos¤ Half-life of 0𝜈𝛽𝛽 decay

+
𝑚
+
E
!/
𝑇//+ = 𝐴 + + 𝑚@AA
𝑝

𝑈D,
𝑚,
𝑈D,

+
𝑚@AA = Z 𝑚, 𝑈D,,B/,+,'

2021/09/21

Future prospects

50

Slide by J. Shirai@Neutrino2016

2021/09/21

Effective mass in low-scale seesawnEffective mass%
𝑚6QQ = V 𝑚/ 𝑈?/+/>-,%,(

𝑓$ 𝑀% =

V 𝑓S 𝑀R 𝑀R Θ%?RR

active neutrinos 𝝂2
G
𝑚@AA

n

51

Λ#$
Λ#$ + 𝑀%#Λ$ ~ 200 MeV

HNLs 𝑁P
8𝑚@AA

𝑁P may give a significant
contribution to 𝑚6QQ !
𝑒/𝑊/

𝑀R Θ%?R
E
𝑚6QQ
=

ΛS %

%
𝑀
Θ
R
?R
𝑀R%

𝑁F

(𝑀R ≪ ΛS )(𝑀R ≫ ΛS )

𝑁F
𝑊/

×

ΘD,
𝑀F
ΘD,

𝑒/

2021/09/21

HNL may hide NDBD (𝒎𝐞𝐟𝐟 = 𝟎)
Range of mixing element |Θ?- |% is predicted
10-7

10-7

10-8

10-8

10

| e1|2| e1|2

n

52

-9

10-10

10

-9

10-10
NH

10-11
10-1

100

101
M1[GeV]

IH
102

10-11
10-1

100

101

102

M1[GeV]gure 6: The region of the mixing element |£e1 |2 for the vanishing effective neutrino mass (between td lines) in the NH (left panel) or IH (right panel) case. TA,
HereIshida,we vary
the Majorana
phase ¥ = 0 to º. T
TanakaarXiv:2012.13186
aded regions are excluded by the direct searches for HNL. The dotted lines shows the sensitivities2
e1 | by future search experiments.
2021/09/21

HNL may enhance NDBD (𝒎𝐞𝐟𝐟 > 𝒎𝝂𝐞𝐟𝐟 )n53

Range of mixing element |Θ?- |% is predicted
FGH
𝑚DEE=100meV (red), 50meV (blue), 10meV (green)

10-7

10-7

10-8

10-8

1

10

MN[GeV]

2

10-9

|

e1|

10-9

|

e1|

2

100

-10

10

10
NH
M2=200GeV

10-11
10-1

100

101
M1 [GeV]

-1

10

-10

IH
M2=200GeV
102

10-11
10-1

100

101

102

M1 [GeV]TA, Ishida, 2Tanaka arXiv:2101.12498
FIG. 2: Upper and lower bounds on|⇥e1 | for the NH (left)
2021/09/21
and IH (right) cases. We take mobse↵ =100 meV (red sold lines),

-2

10

1

FIG

2

NDBD in different nuclein54

Effective mass
¤ Active neutrino contribution&%
𝑚6QQ= V 𝑚/ 𝑈?/

independent on decay nuclei/¤ HNL contribution
E
𝑚6QQ= V 𝑓S 𝑀R 𝑀R Θ%?R
R

𝑓S 𝑀R =

dependent on decay nuclei !

Λ%S
Λ%S + 𝑀R%

Multiple detection/non-detection by NDBD using different nuclei
is crucial to reveal the properties of HNLs in the seesaw mechanism

2021/09/21

55

Another example of LNV:
𝒆" 𝒆" → 𝑾" 𝑾"
𝑒/

𝑊/

𝑒/

𝑊/
×

×
𝑊/

𝑒/

0𝜈𝛽𝛽 decay𝑒/𝑊/

Inverse 0𝜈𝛽𝛽 decay
2021/09/21

Inverse neutrinoless double beta (i𝟎𝝂𝜷𝜷) decayn𝑒 , 𝑒 , → 𝑊 , 𝑊 , offers test for LNVn𝑒 , 𝑒 , collision is option of ILC, CLICn56

[T. G. Rizzo 1982]

Advantages over 0𝜈𝛽𝛽 decayl Signal is cleanl Free from uncertainty in nuclear matrix elementsl Can occur even if 0𝜈𝛽𝛽 decay is absent

à Inverse 0𝜈𝛽𝛽 decay and 0𝜈𝛽𝛽 decay are complementary tests
for LNV in the seesaw mechanism

2021/09/21

Inverse 𝟎𝝂𝜷𝜷 decay in the seesawnSensitivity of mixing(@100 fb,- )57

TA, Tsuyuki ʻ15

2021/09/21

58

Lepton number violation
in meson decays

2021/09/21

Lepton number violation by heavy
Majorana neutrino in B decays
Takehiko Asaka (Niigata Univ.)
In collaboration with

Hiroyuki Ishida (NCTS, Taiwan)
Ref: arXiv:1609.06113
to appear in Physics Letters B
Flavor Physics Workshop 2016
@Iwamuro, Niigata (26-28 October, 2016)

Contents

60

GeV scale right-handed (RH) neutrinos 𝝂𝑹nWhy are such particles interesting?
¤ Seesaw mechanism for neutrino masses¤ Oscillation mechanism for baryon asymmetry of the universe¤ Direct tests by (near) future experimentsn

How do we test such particles?
¤ Lepton number violating decays of B mesons,induced by Majorana properties of such particlesµ+Search for 𝐵 → 𝜇 𝜇 𝜋
at Belle II and …
H

H H !

B+

µ+
W+

N
W−

π−

2021/09/21

Sensitivity limits on 𝚯𝝁
FCC-ee ( 𝑠 = 𝑚T )

-3

AR

M

10

-5

b
LHC
Belle

|Θµ |

2

-4

II

10

Sensitivity by using
𝐵3 → 𝜇3𝜇3𝜋 /310TA, Ishida [arXiv:1609.06113]

NA

-2
CH

10

61

LHC
b (Bc
)

n

𝟐

Belle II with 𝑁! = 5×10.1

(W)
e
e
FCC

FCC-ee (B) with 𝑁I = 10.4
(𝑍 → 𝑏 𝑏d ⇒ 𝑁! ≃ 6×10.. )Belle II

10-6

FCC-ee (B)
BE

10

-7

10

-8

10

Cf. Sensitivity by using

BC

NuTeV

𝑊 3 → 𝜇3𝜇3𝜋 /0MN [GeV]

10

1

FCC-ee (W)with 𝑁- = 2×10J

2021/09/21

62

CPV and Leptogenesis

2021/09/21

Decay rate asymmetryn63

LeptogenesisO − Γ 𝑁. → 𝐿? + ΦΓ 𝑁. → 𝐿? + Φ
𝜀. =O + Γ 𝑁. → 𝐿? + ΦΓ 𝑁. → 𝐿? + Φ
1
=
f
8𝜋

KL.

&

Im 𝐹 M 𝐹 .K
𝐹 M 𝐹 ..
𝑓 𝑥

!
= 𝑥#

𝑓

𝑀K&
𝑀.&

+𝑔

𝑀K&
𝑀.&

𝑥
1 + 1 + 𝑥 log
𝑥+1

!

𝑥#
𝑔 𝑥 =
1−𝑥

𝜀. is determined by Yukawa couplings
and Majorana masses of RH neutrinos

CPV in neutrino Yukawa couplings is important !!
2021/09/21

BAU and CPV in neutrino sectorn64

Neutrino Yukawa couplings/.
𝑀; = −𝑀=O 𝑀<,PQRS
𝑀=

Casas, Ibarra (ʻ01)

𝑖
//+
//+
𝐹=
𝑈 𝑀G,IJKL Ω 𝑀8,IJKLΦIn mixing matrix 𝑈of active neutrinos
Dirac phase

In mixing matrix Ωof RH neutrinos
Phase(s) for 𝜈N

Majorana phase(s)These phases are essential for BAU !
2021/09/21

CPV in active neutrino sectorn65

PMNS mixing matrix of active neutrinos𝑐.& 𝑐.4
𝑈 = −𝑠.& 𝑐&4 − 𝑐.& 𝑠&4 𝑠.4 𝑒 TU
𝑠.& 𝑠&4 − 𝑐.& 𝑐&4 𝑠.4 𝑒 TU

𝑠.& 𝑐.4𝑐.& 𝑐&4 − 𝑠.& 𝑠&4 𝑠.4 𝑒 TU
−𝑐.& 𝑠&4 − 𝑠.& 𝑐&4 𝑠.4 𝑒 TU

𝑠.4 𝑒 /TU
𝑠&4 𝑐.4𝑐&4 𝑐.4

1
0
0

0

𝑒

0

B
T &!"

0

0

𝑒

B
T &#"

¤ Dirac phase 𝛿¤ Majorana phases 𝛼%- and 𝛼(-n

CPV in PMNS matrix can be source of BAU¤ Decay rate asymmetry 𝜀- does NOT depend on 𝑈-(
¤ But, the flavor effects (for 𝑀- ≲ 𝑂(10 )GeV) give theconnection between CPV in PMNS matrix and BAU→ Dirac and Majorana phases in PMNS matrix can bea source of BAU !!
2021/09/21

Thermal Leptogenesisn66

𝑀- = 10-) GeV (Hierarchical masses for RH neutrinos)
NH

IH

Moffat, Pascoli, Petcov, Turner ’19
2021/09/21

Resonant Leptogenesis
𝑀-,% = 1 TeV (quasi-degenerate)!2. " 10

!6

1. " 10

2. " 10!1. " 10!6

1.0

!2. " 10!6
!6

1. " 10!6

0.0
!1.0

!0.5

"8
!6
1.2
!"
1010
!2.

1. " 10

2. " 10!6

0.5
!0.5

1. " 10!6

2. ! 10"9

0.0

∆cp!Π

0.5

1.0

0

!0

0
8. ! 10"9"9
6. ! 10
2. " 10!6!1. " 10!60

1. " 10!6!1. " 10!6

1. ! 10!6

1. ! 10"8

1.2 ! 10"8"8

!2. " 10!6
!1. " 10!6

8. ! 10"9!1. " 10001.00.00

0.5

6. ! 10"91.50.5

!6

4.!6
! 10
2. " 101

2. ! 10"9"9!6

2. " 10!6!2. " 10!6

!2. " 10!6

cp

"Α21!Α31#!Π

1.5

2.01.0 0!1. " 10!6

0

∆cp!Π

2.0

Α
!Π
∆ 21!Π

n

67

!6
!2.
4. !" 10"9!6

!1.
0 " 100.0!1.0"1.0 !0.4"0.5!0.2 0.00.0 0.5
0.2

∆ReΩ
cp !Π23 !Π

1.0
0.4

!1

MAX
Yoshida’19plots
Figure 1. Contour plots of YBMAX in the NH
case. TA,Y2.
is positiveor negative
FigureContourof YBMAXininthe
theregion
IH case.
B
with bright or dark color. In the left or right panel
plotoris darkshownin theInδCP
21 −31 ) planewith thebrightcolor.
the-(αleft
or αright
panel thewhen Reω23 = π/4 or the Reω23 -δCP plane when
α2112−=α31= orπ, therespectively.
green
lines
shows
2021/09/21
Reω
π/4
Reω12 -δCPThe
plane
when
α21
= π, respe
the central value of δ from the global neutrino oscillation analysis.

Baryogenesis via RH neutrino oscillationn68𝑀-,% = 5 GeV (quasi-degenerate)

TA, Ishida’10asymmetry
Figure 2: Parameter regions in the δ-η plane accounting for the observed
baryonthe NH case are shown by lines. The red solid lines are for ξ = +1 while the blue dashed lin
2
are for ξ = −1. Here we take M3 = 5 GeV, ∆M32
/M32 = 10−8 , Reω = π/4, and sin2 θ13 = 0.05
We take sin2 θ23 = 0.5 (left) and 0.36 (right), respectively.
2021/09/21

BAU and CPV in neutrino sectorn69

T2K and NOνA indicate CPV in neutrino sector
week ending
14 APRIL 2017
T2K, PRL 118, 151801 (ʻ17)

REVIEW LETTERS

ions
ong[46]

Allowed 90% CL
Normal Ordering

14
12

Inverted Ordering

Non-zero Dirac phase
𝜋
3𝜋
𝛿~ −
𝑜𝑟
2
2

-2 ∆ lnL

10
8
6
4
2
0

-3

-2

-1

0

δCP (radians)

1

2

3

FIG. 7. −2Δ ln L as a function of δCP for the normal (black)
Important
step
to understandby RH neutrinos !
and inverted(yellow) massordering.
The vertical lines baryogenesis
show thecorresponding allowed 90% confidence intervals, calculatedusing the Feldman-Cousins method. sin2 θ13 is marginalizedusing the reactor measurement as prior probability.
2021/09/21

Electric dipole moments of charged leptons

70

JHEP

JHEP02(

JHEP02(201Abada, Toma ʻ16[1511.03265]

2021/09/21

Search for HNL (𝝂𝑹 )Search for Heavy Neutral Leptonsn72

Production by meson decays

𝐾 H → 𝑒 H 𝑁, 𝐾 H → 𝜇 H 𝑁, …
¤ Peak search experimentsl Measure 𝐸? in 𝐾 U → 𝑒 U 𝑁+
𝑚M− 𝑚D+ − 𝑀8+
𝐸D =
2 𝑚M
¤ Beam dump experiments

𝐾H → 𝑒H 𝑁[Shrock ʼ80]

events𝐾3 → 𝑒3 ν

𝐾3 → 𝑒3 𝑁𝐸:𝑁 ⟶ ℓH ℓ! 𝜈 + 𝑐. 𝑐.

CERN
PS191

2021/09/21

Search for HNLs at T2K
Production of 𝑵

𝐾 H → ℓH + 𝑁

TA, Eijima, Watanabe[JHEP1303 (2013) 125]73

Detection of 𝑵

𝑁 → ℓ! +ℓH + 𝜈

0.86×10!" POT

PS191
T2K
10#! POT𝑉 = 61.25m$ (9m$ )2021/09/21

Yamamoto, S. Yamasu, C. Yanagisawa,
G. Yang, T. Ya
51, ‡
54
66
14
v,25 M.
Yokoyama,
T.
Yoshida,M.
Yu,
A.
Zalewska,
74 J. Z
Following the selection from section
III
B, no events
Searchfor heavy neutrinos with the T2K near detector ND280
were observed in any of the di↵erent signal regions, which
61 with the background-only hypothesis, allow7
6
41
is consistent
Ziembicki,
E.D.
Zimmerman,
M.
Zito,
S.
Zsoldos,and A.2 Zy52
53
2350, 31
31
18
28
ing
upper
limits
on
U
,
U
and
U
to
be
placed.
K. Abe, R. Akutsu, A. Ali, C. Andreopoulos,
L. Anthony, M. Antonova, S. Aoki, A. Ariga,
An
exampleofresultsfromthesingle-channel
approachaY.
channelA 29 Y. Awataguchi,55 Y. Azuma,38 S. Ban,29 M. Barbi,42 G.J. Barker,62 G. Barr,39 C. Barry,31
Ashida,is presentedT2K
in Figure 5. Collaboration)
It shows the comparison of thel B and the (The31give similar upper
21limits
4, 58
2
54
66
three methods14(A, B, C), which
IV.

2
e

RESULTS

2
µ

2
⌧

U2e

via the factor} where ↵ isn of the heavy
ved in its dees, several for

10−6

for MN > 388 MeV/c2 , the correlations b
Uµ2 (as seen in Figure 7) would give lim
T2K, profilingside T2K’s reach. However, profiling lea
PS191 (2-body)the sensitivity on Ue2 with respect to thePS191 (3-body)as it forcefully suppresses the contributio
modes involving Uµ2 or U⌧2 .
It is worth mentioning that the limits
230
choice 12of prior on U↵2 . The limits on Ue52arobust with respect to a change of prior a
directly sensitive to these mixing
21
18 eleme⇡U 2 (U↵2 ) = U↵2 varies the limit by less th2
the limit on U⌧ is strongly a↵ected (mor31
23
It is also possible to define 2D
contou400
450
500
Ue2 Uµ2 plane, allowing the correlations b
MN [MeV/c2]
ing31
elements to be visualised. Figure50
7p
such contours for di↵erent heavy neutrin
T2K
of behaviour at MN = 388 MeV/
PS191 (2-body)
49 change
20
to the kinematic cut-o↵ for K ± ! µ± N p
PS191 (3-body)inFigure
3.
E949
T2K

10−7

A

10−8

10−9

K. Abe,52 R. Akutsu,53 A. Ali,23 C. Andreopoulos,50, 31 L. Anthony,31 M. Antonova,18
Y. Ashida,29 Y. Awataguchi,55 Y. Azuma,38 S. Ban,29 M. Barbi,42 G.J. Barker,62 G.
M. Batkiewicz-Kwasniak,14 F. Bench,31 V. Berardi,21 S. Berkman,4, 58 R.M. Berner,2 L
S. Bienstock,49 A. Blondel,12, ⇤ S. Bolognesi,6 B. Bourguille,17 S.B. Boyd,62 D. Brailsford,30
M. Buizza Avanzini,10 J. Calcutt,33 T. Campbell,7 S. Cao,15 S.L. Cartwright,46 M.G. Ca
A. Chappell,62 C. Checchia,23 D. Cherdack,16 N. Chikuma,51 G. Christodoulou,31, ⇤ J. Co
D. Coplowe,39 A. Cudd,33 A. Dabrowska,14 G. De Rosa,22 T. Dealtry,30 P.F. Denner,62 S.R
F. Di Lodovico,41 N. Dokania,36 S. Dolan,10, 6 O. Drapier,10 K.E. Du↵y,39 J. Dumar
S. Emery-Schrenk,6 A. Ereditato,2 P. Fernandez,18 T. Feusels,4, 58 A.J. Finch,30 G.A. Fio
C. Francois,2 M. Friend,15, † Y. Fujii,15, † R. Fujita,51 D. Fukuda,37 Y. Fukuda,34 K. Ga
F. Gizzarelli,6 T. Golan,64 M. Gonin,10 D.R. Hadley,62 L. Haegel,12 J.T. Haigh,62 P. H
M. Hartz,58, 27 T. Hasegawa,15, † N.C. Hastings,42 T. Hayashino,29 Y. Hayato,52, 27 A. H
J. Holeczek,47 N.T. Hong Van,19, 26 F. Hosomi,51 F. Iacob,23 A.K. Ichikawa,29 M. Ikeda,52 T
T. Ishida,15, † T. Ishii,15, † M. Ishitsuka,56 K. Iwamoto,51 A. Izmaylov,18, 25 B. Jamieson,6
S. Johnson,7 P. Jonsson,20 C.K. Jung,36, ‡ M. Kabirnezhad,39 A.C. Kaboth,44, 50 T. Ka
J. Kameda,52 D. Karlen,59, 58 T. Katori,41 Y. Kato,52 E. Kearns,3, 27, ‡ M. Khabibullin
H. Kim,38 J. Kim,4, 58 S. King,41 J. Kisiel,47 A. Knight,62 A. Knox,30 T. Kobayashi,15, †P.P. Koller,2 A. Konaka,58 L.L. Kormos,30 Y. Koshio,37, ‡ K. Kowalik,35 H. Kubo,2
R. Kurjata,61 T. Kutter,32 M. Kuze,54 L. Labarga,1 J. Lagoda,35 M. Lamoureux,6 P. La
M. Lawe,30 M. Licciardi,10 T. Lindner,58 Z.J. Liptak,7 R.P. Litchfield,13 X. Li,36 A. Lo
T. Lou,51 L. Ludovici,24 X. Lu,39 T. Lux,17 L. Magaletti,21 K. Mahn,33 M. Malek,46 S.
A.D. Marino,7 J.F. Martin,57 P. Martins,41 T. Maruyama,15, † T. Matsubara,15 V. Matve
W.Y. Ma,20 E. Mazzucato,6 M. McCarthy,66 N. McCauley,31 K.S. McFarland,43 C. McG
C. Metelko,31 M. Mezzetto,23 A. Minamino,65 O. Mineev,25 S. Mine,5 M. Miura,52, ‡S. Moriyama,52, ‡ J. Morrison,33 Th.A. Mueller,10 S. Murphy,11 Y. Nagai,7 T. Nakadaira
Y. Nakajima,52 A. Nakamura,37 K.G. Nakamura,29 K. Nakamura,27, 15, † K.D. Nakamu
S. Nakayama,52, ‡ T. Nakaya,29, 27 K. Nakayoshi,15, † C. Nantais,57 K. Niewczas,64 K. Nishik
T.S. Nonnenmacher,20 P. Novella,18 J. Nowak,30 H.M. O’Kee↵e,30 L. O’Sullivan,46 K. Oku
W. Oryszczak,60 S.M. Oser,4, 58 R.A. Owen,41 Y. Oyama,15, † V. Palladino,22 J.L. Palo
W.C. Parker,44 P. Paudyal,31 M. Pavin,58 D. Payne,31 L. Pickering,33 C. Pidcott,46 E.S. Pin
B. Popov,49, ⇤⇤ K. Porwit,47 M. Posiadala-Zezula,60 A. Pritchard,31 B. Quilain,27 T. Rader
B. Radics,11 P.N. Rato↵,30 E. Reinherz-Aronis,8 C. Riccio,22 E. Rondio,35 B. Rossi,22 S
A.C. Ruggeri,22 A. Rychter,61 K. Sakashita,15, † F. Sánchez,12 S. Sasaki,55 E. Scantambu
K. Scholberg,9, ‡ J. Schwehr,8 M. Scott,20 Y. Seiya,38 T. Sekiguchi,15, † H. Sekiya,52, 27, ‡ D. S
A. Shaikhiev,25 F. Shaker,63 D. Shaw,30 A. Shaykina,25 M. Shiozawa,52, 27 A. Smirnov,25 M
H. Sobel,5, 27 Y. Sonoda,52 J. Steinmann,45 T. Stewart,50 P. Stowell,46 Y. Suda,51 S. Suv
S.Y. Suzuki,15, † Y. Suzuki,27 A.A. Sztuc,20 R. Tacik,42, 58 M. Tada,15, † A. Takeda,52 Y. Ta
H.K. Tanaka,52, ‡ H.A. Tanaka,48, 57 T. Thakore,32 L.F. Thompson,46 W. Toki,8 C. Tour
T. Tsukamoto,15, † M. Tzanov,32 Y. Uchida,20 W. Uno,29 M. Vagins,27, 5 Z. Vallari,36 D.
C. Vilela,36 T. Vladisavljevic,39, 27 V.V. Volkov,25 T. Wachala,14 J. Walker,63 Y. Wa
M.O. Wascko,20 A. Weber,50, 39 R. Wendell,29, ‡ M.J. Wilking,36 C. Wilkinson,2 J.R. W
C. Wret,43 Y. Yamada,15, ¶ K. Yamamoto,38 S. Yamasu,37 C. Yanagisawa,36, †† G. Y
K. Yasutome,29 S. Yen,58 N. Yershov,25 M. Yokoyama,51, ‡ T. Yoshida,54 M. Yu,66 A. Za
K. Zaremba,61 G. Zarnecki,35 M. Ziembicki,61 E.D. Zimmerman,7 M. Zito,6 S. Zsoldo(The T2K Collaboration)
U2µ

U2e

10−10

150

200

250

300

350

10−6

−6

10−7

10−9

−8

U2τ

10−10

−9

10

150

200

250

−3

10−4

10−5

10−6

150

200

250

2
⌧

2

ous experiments such
as PS191 [6, 7], 65
E949 [5] and
23

31

25

5 mixing elements.
two other

Search for heavy neutrinos with the T2K near detector

10−8

−7

U2µ

M.
F. Bench, V. Berardi, S. Berkman,
R.M. Berner, L. Berns, S. Bhadra,
nt Batkiewicz-Kwasniak,
production
withmethodA
givingslightly
moreconservative
limits12, ⇤6
nstock,49 A.arXiv:1902.07598v1
Blondel,S. Bolognesi,
B. Bourguille,
S.B.
Boyd,62 D.28049
Brailsford,Madrid,
A. Bravar, Spain
C. Bronner,[hep-ex]
20 Feb172019
asDepartment
expected.
Madrid,ofTheoretical
Physics,. Buizza Avanzini,10 J. Calcutt,33 T. Campbell,7 S. Cao,15 S.L. Cartwright,46 M.G. Catanesi, A. Cervera,
62 Albert Einstein
16
⇤
)⇥
(3)
i.
Bern,
Centerfor 51Fundamental
Chappell,C. Checchia,23 D. Cherdack,N. Chikuma,
G. Christodoulou,31, Physics,
J. Coleman, G. Collazuol,
39
33
14 K → eN → e(eπ), analysis A 2230
62plowe,A.
Cudd,
A.
Dabrowska,
G.
De
Rosa,
T.
Dealtry,
P.F.
Denner,S.R. Dennis, C. Densham,forEnergy Physics(LHEP),Bern,
Switzerland
dered inHigh
this
10 41
6 B
K → eN → 10,e(eπ), analysis
F. Di
Lodovico, N. Dokania,36 S. Dolan,
O. Drapier,10 K.E. Du↵y,39 J. Dumarchez, P. Dunne,using
a PoisK → eN → e(eπ), 18
analysis C
62Physics,
58
66
vents
in
ty, nobs
DepartmentofMassachusetts,
U.S.A.
Emery-Schrenk,
A. Ereditato,
P. Fernandez,Boston,
T. Feusels,4,
A.J. Finch,30 G.A. Fiorentini,
G. Fiorillo,22A
PS191 (2-body)
10
A:. Francois,2 M. Friend,15, † Y. Fujii,15, †PS191R.(3-body)
Fujita,51 D. Fukuda,37 Y. Fukuda,34 K. Gameil,4, 58 C. Giganti,49
Departmentof Physics
Vancouver,
BritishColumbia,
C
64
10
12
45
F. Gizzarelli,6 T.10Golan,
M. Gonin,and
D.R.Astronomy,
Hadley,62 L. Haegel,
J.T. Haigh,62 P.
Hamacher-Baumann,(4) 2758,†
29
52, 2729
8M.
Hartz,
T. Hasegawa,15,ofN.C.
Hastings,42
T. Hayashino,
Y. Hayato,
A. Hiramoto,M. Hogan,vine, 47Department
Physics
andAstronomy,
Irvine,California,
U.S.A
M [MeV/c ]leczek, N.T. HongVan,19, 26 F. Hosomi,51 F. Iacob,23 A.K. Ichikawa,29 M. Ikeda,52 T. Inoue,38 R.A. Intonti,21
10
ncy are taken
15, †15, https://www.overleaf.com/15589043frvbsssdxxrxFrance†
56
51
18, 25f-sur-Yvette,shida,priors
T. Ishii,150
M. Ishitsuka,
B. Jamieson,63 C. Jesus,17 M. Jiang,29
200
250
300
350K. Iwamoto,400
450
500 A. Izmaylov,
aussian
2
39
N [MeV/c ]e. Johnson,background 7 P. Jonsson,20 C.K. Jung,36, ‡ M.M
Kabirnezhad,
A.C. Kaboth,44, 50 T. Kajita,53, ‡ H. Kakuno,55
and standard 52
FIG. 7. 2D contours in the59, 5841522
3, 27, ‡25
25U U planover U (U = 0). Each line corresponds toJ.
Kameda,D.
Karlen,T.
Katori,Y.
Kato,E.
Kearns,M.
Khabibullin,A.
Khotjantsev,
FIG.
5.
90%
upper
limitsonthemixingelementUase
nd and its unneutrino mass hypothesis.
a function
mass using
38
4, 58 of heavy neutrino
41
47 the single-channel
62
30
15, †
xing
elements. Kim, J. Kim,
King, onlyJ. theKisiel,A. Knight,
T. Kobayashi,
L. Koch,50 T. Koga,51
approach, S.
considering
contribution
from K ± ! A. Knox,
2N, N ! e± ⇡ ⌥ , with
30 B and C. The 37, ‡
25, §
e±
three
methods A,
P.P.
Koller,A. Konaka,58 theL.L.
Kormos,Y. Koshio,
K. Kowalik,35 H. Kubo,29M [MeV/c
Y. Kudenko,
V. CONCLUSION
p is then de]limits are comparedto the onesof PS191 experiment[6, 7].
61
32
54
1
35
6
41
nd
the priors, T. Kutter,. Kurjata,
M. Kuze, L. Labarga, J. Lagoda, M.FIG.Lamoureux,
P. Lasorak, AM.
Laveder,23
selection of events with two tracks
6. 90% upper limits on the mixing elements U (top), U(middle),13
U (bottom) as a functionof heavy neutrino mass, 23
charges originating from theers (flux, effi1058
736
7 ND280 TP
obtained with the
combined
approach.
The
blue solid lines
M. Lawe,30 M. Licciardi,
T. Lindner,
Z.J. Liptak,
R.P. Litchfield,
X.
Li,
A.
Longhin,
J.P.
allowsheavy Lopez,
neutrino decays to be effi
The results of the
combined approach
are shown inare obtained after marginalisation over the two other mixing
from expected background coming from
Figure 6. They
provideby a factor of 21
51
24
39an improvement
17
33 In the top plot, the additional
46 blue dashed line 43
12 No evenelements.
trino interactions
with matter.
T. Lou, L. Ludovici,
X.
Lu,
T.
Lux,
L.
Magaletti,
K.
Mahn,
M.
Malek,S.
L.
Maret,
corresponds tothe case
where profiling is used
(U Manly,= U = 0).
inthedefinedsignalregions,
which is con
2-3 with respect to the single-channel approach, thanks
The limits are compared to the ones of other experiments:
background-only hypothesis.
7
57
41
15, †
15
25
31
PS191 [6, 7], E949 [5], CHARM[25].
D. Marino, J.F.
Martin,P. Martins,
T. Matsubara,
V. Matveev,
K. Mavrokoridis,
to theincreased statisticalpower of T.
theMaruyama,
combination.
Limits on the mixing elements U , U⇡B ⇡U . (5)using a combined Bayesian approa
6
66 those of previ- 31
43
36 tained
25
The limits arewith2021/09/21
ply
to anymodel with heavy neutrinos w
W.Y. Ma,20 E. Mazzucato,
M.competitive
McCarthy,N. McCauley, K.S. McFarland,
C.
McGrew,A.
Mefodiev,
The limits are obtained after marginalisation over thetween 140 MeV/c and 493 MeV/c such
10−4

10−5

10−6

−7

10
10

350

10−9

2

N

200
250

−8

300

150

48

42

0

0

300
350

10−10

T2K

10−11

CHARM

10−12

10−13 −13 −12 −11 −10
10 10 10 10
10−9 10−8 10−7 10−6 1

2
⌧

300

2
e

2
⌧

2
µ

350

2

N

2
e

2
µ

2
µ

2
⌧

‡ limits after
For52,
U 2 , the

2
e

2

2
µ

2

11 as constraint
in particular, be interpreted

SHiP
n

arXiv:1310.1762

75

A new fixed-target experiment at the CERN SPS accelerator is
proposed that will use decays of charm mesons to search for
Heavy Neutral Leptons

2021/09/21

Limits on mixing of HNL
nLimits on mixing ΘDF

76

Deppisch, Dev, Pilaftsis ʻ15

2021/09/21

Summary
n

n

n

77

Leptogenesis
à Connection between neutrino masses and BAU is
attractive and important idea
à Various scenarios are possible depending on RH
neutrino masses
Conventional seesaw scenario (𝑀8 >109GeV)[Seesaw + Leptogenesis]
à natural framework of SUSY GUT …
à Exp. test for RH neutrinos is impossible
Connection can be obtained even lighter mass region[Seesaw + Baryogenesis via RH neutrino osc.]à Such RH neutrinos might be tested!
2021/09/21