Osaka City University Advanced Mathematical Institute (OCAMI)MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics

OCAMI Reports Vol. 6 (2021)
doi: 10.24544/ocu.20210605-006

Workshop for Particle and Phenomenology 2020

Organized by
Masato Yamanaka
Hiroshi Itoyama
Nobuhito Maru

November 26 - 28, 2020

Abstract. The domestic workshop on the “Workshop for particle and phenomenology 2020” is reported. The workshop covers all major areas and developments in high energy and particle physics, (finite temperature) field theory,
astroparticle physics, cosmology, and related areas.

2020 Mathematics Subject Classification.
70S15, 81T13, 81T30, 81T60, 81V05, 81V10,
81V15, 81V17, 81V22, 83C56, 83E15, 83F05

Key words and Phrases.
High energy and particle physics, field theory, astroparticle physics, cosmology© 2021 OCAMI.
OCAMI. Workshop for Particle and Phenomenology 2020. OCAMI Reports. Vol. 6, Osaka City
University Advanced Mathematical Institute. 2021, 487pp. doi: 10.24544/ocu.20210605-006

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Preface
The domestic workshop on the “Workshop for particle and phenomenology 2020”
will be held at Osaka City University, in honor of the second anniversary of the founding the Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP).
The workshop features review and short-talk sessions covering all major areas anddevelopments in high energy and particle physics, (finite temperature) field theory,
astroparticle physics, cosmology, and related areas. The workshop welcomes contribution talks for not only a recent/ongoing topic but also for your lifework, flagship workwithin a few years, and so on.
Invited speakers:
Kazunori Kohri
Jisuke Kubo
Shun’ya Mizoguchi
Yuji Sugawara
Satoshi Uetake

Primordial black holes
Classically scale invariant extension to SM
From string to phenomenology
Super string theory and cosmological constant problem
Precise muonium spectroscopy experimentDue to the situation of the COVID-19, the workshop will be a hybrid-type (i.e., on-line
and on-site, simultaneously). All of the talks are given by on-line, and participants canalso join the workshop on-cite if they hope.

The workshops in this series:
Workshop for particle and phenomenology 2019https://sites.google.com/view/nitep-workshop-2019/
Workshop for particle and phenomenology 2020
https://indico.nitep.osaka-cu.ac.jp/event/66/

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Organizers
Masato Yamanaka
Nambu Yoichiro Institute of Theoretical and Experimental Physics, Osaka City University,
Osaka 558-8585, Japan
E-mail address: yamanaka@osaka-cu.ac.jp

Hiroshi Itoyama
Nambu Yoichiro Institute of Theoretical and Experimental Physics, Osaka City University,
Osaka 558-8585, Japan
E-mail address: itoyama@sci.osaka-cu.ac.jp

Nobuhito Maru
Nambu Yoichiro Institute of Theoretical and Experimental Physics, Osaka City University,
Osaka 558-8585, Japan
E-mail address: nmaru@osaka-cu.ac.jp

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Table of Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Organizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2
3Jisuke Kubo
Classically scale invariant extension to SM . . . . . . . . . . . . . . . . . . .

6Seishi Enomoto
Matter-antimatter production due to oscillating background field . . . . . . .

38

Masaki Jung Soo Yang
Reflection symmetries and universal four-zero texture . . . . . . . . . . . . .

56

Takahiro Yoshida
Lepton flavor model with modular A4 symmetry in large volume limit . . . .

86

Nagisa Hiroshima
Dark matter search in dwarf spheroidal galaxies combined with structure formation models of halo . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Koji Ishiwata
Probing heavy dark matter decays with multi-messenger astrophysical data . . 120
Kazunori Kohri
Primordial black holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
Etsuko Itou
Phenomenology of QCD-like theory in low-temperature and high-density regions204
Shin Suzuki
Typical Features of the Triple Higgs Boson Coupling in Flat Gauge-Higgs
Unification Models with a Bulk-Brane Mixing . . . . . . . . . . . . . . 223
Atsuyuki Yamada
To be, or not to be finite? The Higgs potential in Gauge-Higgs Unification . 234
Shun’ya Mizoguchi
From string to phenomenology . . . . . . . . . . . . . . . . . . . . . . . . . . 248
Yu HamadaTopological Nambu monopole in two Higgs doublet models . . . . . . . . . . . 277
Takayuki Hirayama
Classical Statistical simulation of Quantum Field Theory . . . . . . . . . . . 309
Naoto Kan
From 3d dualities to hadron physics . . . . . . . . . . . . . . . . . . . . . . . 315
Satoshi Uetake
Precise muonium spectroscopy experiment . . . . . . . . . . . . . . . . . . . 338
Joe Sato
Low Scale models for U (1)Lµ −Lτ gauge symmetry. . . . . . . . . . . . . . . 361

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Naoki Yamatsu
Is Symmetry Breaking into Special Subgroup Special? . . . . . . . . . . . . . 403
Yoshihiko Abe
Electroweak axion string and superconductivity . . . . . . . . . . . . . . . . . 424
Yuji Sugawara
Super string theory and cosmological constant problem . . . . . . . . . . . . . 450
Issei Koga
Catalytic Creation of Bubble Universe Induced by Quintessence in Five Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
Hiroshi Itoyama
Stability, enhanced gauge symmetry and suppressed cosmological constant inheterotic interpolating models . . . . . . . . . . . . . . . . . . . . . . . 479

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Matter-antimatter production due tooscillating background field
Enomoto, Seishi [(Sun Yat-sen University []])Based on:Int. Jour. Mod. Phys. A 33 (2018) 1850146 (arXiv:1707.05310 [hep-ph])Phys. Rev. D 99 (2019) 036005 (arXiv:1811.06197 [hep-ph])Eur. Phys. J. C XX XX, XXXX [accepted] (arXiv:2005.08037 [hep-ph])2020/11/26@, Zoom

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Outlook
1. Introduction
2. Asymmetric particle production
1. Demonstration in a simple model
2. Application to Type-I seesaw model

3. Summary

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1. Introduction

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, Zoom- 1. Introduction -History of the Universe

Reheating

Inflation(Baryogenesis)

EW

s

BBN
s

Recombination

time

s

s

1. Slow roll [Inflation]
Inflaton:

3. Decay [Reheating](

2. Oscillation [Preheating]2020/11/26@, Zoom4/32

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OCAMI Reports Vol. 6 (2021)- 1. Introduction +)[J. H. Traschen and R. H. Brandenberger (1990), L. Kofman, A. D. Linde, A. A. Starobinsky (1994, 1997)]

Preheating ( =Parametric resonance: background(classical field)( http://www.nicovideo.jp/watch/sm14518057 ): real scalar(quantum field)[ http://www.riken.jp/pr/press/2014/20140725_1/ ]Equation of motion forMathieu equation+

2020/11/26@, Zoom5/32- 1. Introduction +)[J. H. Traschen and R. H. Brandenberger (1990), L. Kofman, A. D. Linde, A. A. Starobinsky (1994, 1997)]

Preheating ( =Parametric resonance: background(classical field)(wave func.): real scalar(quantum field)

Non-adiabatic region :(occupation #): frequency of(parametric resonance)(massless point
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- 1. Introduction -Backreaction

shrinkEnergy loss

Trapped!

production!
Non-adiabatic region

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Number density

stop

trapped

time
10.0
9.0

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8.0
7.0
6.0
5.0
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3.0
2.0
1.0

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1.E+000.06

1.E-020.04

1.E-040.02

1.E-060

Number density|Amplitude| /(1.E-080

5

1015# of oscillation

20

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15
20
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2530

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1.E+02
1.E+00
1.E-02
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1.E-06
1.E-08

Inflaton

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2-1. Demonstration in a simple model
2-2. Application to Type-I seesaw model

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- 2. Asymmetric particle production -Baryogenesis through preheating
Inflation

Reheating(Baryogenesis)

EW

s

BBN
s

2. Oscillation [Preheating]

Recombinationss

2.5. Heavy particle production[ Possible even if
!]

time

4. Decay, scattering[Baryogenesis]
Asymmetry

3. Decay [Reheating]

Asymmetry

3. Asymmetry generation in preheating[K. Funakubo, A. Kkuto, S. Otsuki, F. Toyoda[R. Rangarajan, D. V. Nanopoulosetc.
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Minimal

CPV model:

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Contents : 1 complex scalar + 1 real scalar ( + oscillating mass)

1

(CP

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EOMs:

Total number density of:[ (kinetic energy

Net number density of
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OCAMI Reports Vol. 6 (2021)- 2. Asymmetric particle production -Numerical results 1,

Number densities

1.0E-02,(matter)

1.0E-03(antimatter)

1.0E-04(net density)

1.0E-05
0

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200

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500

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(Berry connection
c.f.

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EOM :

c.f. Berry connection :Chemical potential: (net number) x
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Type-I seesaw# violating process- Heavy particle production- Non-thermal leptogenesis- Direct production ofasymmetric LH

Situation(RH mass scale) >> (Higgs oscillation energy)
RH: RH

Sakharov

LH

asymmetric

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1.

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Mass of RH : taken to be real

2.

Operator EOMs

3.

Operator EOMs
2

(RH

integrate out )

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Case A:

Inflation
VD

2.

Case B:

Higgs oscillation(leptogenesis)

MD

Entropy fixing
RD(ex. Higgs inflation)

Preheating
Inflation
VD

W, Z(= leptogenesis

Higgs oscillation(leptogenesis)
MD

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Higgs oscillation(leptogenesis))

Entropy fixing@

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Inflation

Inflaton decay- 2. Asymmetric particle production -)Inflaton decay

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GeV ,

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Higgs oscillation(leptogenesis)

Parametric resonanceW

Entropy fixingZ:

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Case A
Higgs inflation

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Preheating

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Type-I
GeV
GeV
Higgs inflation
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Okayama-U Group

10 staff
9+2 students

SPAN: SPectroscopy with Atomic Neutrino
Energy [keV]

Energy [eV]

Xe

8.315

18.6
two-photon
emission
RENP

0

0
0.1 0
Freq. [GHz]Endpoint Spectrum

m0=1 meV
m0=10 meV
m0=50 meV
NH/
IH

0.08
0.06

Rate [Hz]Endpoint Spectrum

2

E

0.04

1

0.02

1

2

3

Photon Energy [eV]44.1565

4.15704.1575 eV0

10

18 keV340

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two-photon
emission
RENP

0.1 0
Freq. [GHz]Workshop for Particle and Phenomenology 2020

341

R. H. Dicke

N. Skribanowitz et al (1973) HF molecule
HF molecule
200 ns

pump

SR
Pump
2.5 µm (Natural lifetime ~10 s)

Nd:YAG
532 nm369

H2 gas

436
436

532

Nonlinear
Frequency
conversion

532

683

5 mJ + 5 mJ
~ 200 m beam
(peak intensity:
9 GW/cm2 total)

+7
209

+6
228

PPSLT

CW684 nm

CW864 nm

+5+4 +3
252 282 320

+1 -1
-3
435 683 1586

Y. Miyamoto, SU, et al., Prog. Theor. Exp. Phys. 2014, 113C01 (2014)

532
nm

ECLD

ECLD+TA

955

+2
0
-2
-4
369 532 953 4665

+8
192

Nd:YAG

Nd:YAG SHG

683

Damper

684
nm

LBO

p-H2

1064

KTA
532

PPLN

1386

LBO

4.59
µm
5.05 µm
LPFs

4.59 µm

MCT
Detector

Monochromator

684 nm532 nm

4.59 µm
5.05 µm

Y. Miyamoto, SU, et al., Prog. Theor. Exp. Phys. 2015, 081C01 (2015)

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goal
tool

80
60
40
20
0

340 nK~Tc

40
20
0
-60

New!!

~140 nK

-40

-20
0
20
Frequency [kHz]40

Workshop for Particle and Phenomenology 2020

343

Willis Lamb

n=2

n=1

Schrödinger

Hans Bethe

n=2

n=1

Bohr

Dirac

QED

344

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34 Hz: Lamb
Shift

44 kHz

3, 0
0.4
0.3
0.2
0.1
0.0
0

5

10

15

20

T. W. Hänsch, Nobel Lecture Slides (2005),
with recent results[1] Phys. Rev. Lett. 110, 230801 (2013) [2] Eur. Phys. J. 172, 109 (2009)

1S Lamb Shift
Term of the Lamb shift
Self-energy (one-loop)
Vacuum polarization (one-loop)
Recoil corrections
Proton size
Two-loop corrections
Radiative recoil corrections
Vacuum polarization (muon)
Vacuum polarization (hadron)Proton self-energy
Three-loop corrections
Nuclear size corrections to SE and VP
Proton polarization
1S Lamb shift

Value for the 1S level
8 383 339 .466 kHz
214 816.607 kHz
2 401.782 kHz
1 253.000 kHz
731.000 kHz
12.321 kHz
5.068 kHz3.401 kHz4.618 kHz
1.800 kHz
0.149 kHz0.070 kHz8 172 894(51) kHz

Uncertainties
0 .083 kHz
0 .005 kHz
0 .010 kHz
50 kHz3 .300 kHz
0 .740 kHz< 0.001 kHz
0 .076 kHz
0 .160 kHz
1 .000 kHz
0 .011 kHz
0 .013 kHz1105 kHz for 1S level)
RN[2] Eur. Phys. J. 172, 109 (2009)[3] Rev. Mod. Phys. 77, 1 (2005): eq. A42

Workshop for Particle and Phenomenology 2020

345

e

+ –

-65 Hz
PRA 53, 2953 (1996)+232.7(1.4) Hz
Sov. J. Nucl. Phys. 53, 626(1991)

long-range force–0.028 mHz

arXiv: 1810.05429

1S-2S Laser Spectroscopy

Mu Energy Levelu[(]Theo. : 1.4 MHz

120 ppb): 1.2 THz (0.48%)

Laser Spectroscopy

QED error:[3]1S-2S
muon mass
mass uncertainty
CODATA 2014

1S-HFS microwave
spectroscopyu[(]Theo. : 515 Hz [2]120 ppb)

Microwave

Electroweak Frequency shift: -65 Hz
Hadronic vacuum polarizaiton: +232.7 Hz[2] M. I. Eides, Phys. Lett. B 795, 113 (2019)[3] M. I. Eides, Phys. Rept. 342, 63 (2001)

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1S-2S Laser Spectroscopy

Mu Energy Levelu[(]Theo. : 1.4 MHz

120 ppb

)

1S-2S
u[
]exp.: 10 kHz

Laser Spectroscopy(RAL 1999: 9.8 MHz[1])

CODATA 2014

Microwave

22 ppb8 ppb
0.8 ppb(a) : 1S-2S
120 ppb[1] V. Meyer et al., PRL 84, 1136 (2000)

mass uncertainty

263 kHz100 kHz
10 kHz

1 ppb

1S-HFS microwave
spectroscopyu[(]Theo. : 515 Hz [2] 4 Hz

120 ppb

MuSEUMu[]exp.: 8 Hz)(b) : 1S-HFS(LAMPF1998: 53 Hz)

Electroweak Frequency shift: -65 Hz
Hadronic vacuum polarizaiton: +232.7 Hz[2] M. I. Eides, Phys. Lett. B 795, 113 (2019)[3] M. I. Eides, Phys. Rept. 342, 63 (2001)

Slide by T. Mibe

Workshop for Particle and Phenomenology 2020

Spin-independent Forces

Spin-dependent Forces

010Phys. Rev. D 100,
015010 (2019)arXiv:1902.08585

10- 3

347

Phys. Rev. D 82, 113013 (2010)

-2

10

10-4

10- 5

Ps

10-6

10- 7

-8

10

-10

10- 11 (

H

10

10- 9

-12

10

Mu 1S–2S
9.8 MHz)10- 13 Mu 1S–2S (
10-5

(*)

-14

10

10 kHz)

10-3

10-1

101

Mu 1S-HFS
120 ppb

10-16
10-18

Mu 8 Hz
-8

10

-6

10

-4

10

-2

10

0

10

2

10

4

10

6

10

(*) Constraints from astrophysics: J. High Energy Phys. 02, 033 (2017)

History of Muonium Laser Spectroscopy
Japan

1987

The first laser excitation of
1S-2S transition
S. Chu, A.P. Mills, Jr. A.G. Yodh,
K. Nagamine, Y. Miyake, T. Kuga
Laser spectroscopy of
1S-2S transition (RAL)
V. Meyer et al.

1999

before 2017

World wide

Good facility for 1S-2S laser
spectroscopy of Mu
No proposal of experiment

Mu-MASS (PSI)

KAKENHI type-S: approved

2019

2020

S. Uetake (PI), K. Shimomura, M. Yoshida,
T. Yamazaki, M. Yoshimura

S type research project of J-PARC
MLF: approved
Two different KAKENHI was approved:
type-S (1S-HFS, PI: K. Shimomura)Specially Promoted Research (g-2, PI: T. Mibe)

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1S-HFS: Previoius Measurement

Phys. Rev. Lett. 82, 711 (1999)
W. Liu et al., “High Precision Measurements of the Ground State Hyperfine
Structure Interval of Muonium and of the Muon Magnetic Moment”

Workshop for Particle and Phenomenology 2020

HFS

349

Zeeman Splitting
HFS

positrondetector
(b)

Pi
ck
up

An
t

en
na

(a)
Tuning Bar
Input Antenna

Piezo Positioner

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1.7T

400 mmWorkshop for Particle and Phenomenology 2020

351

Previous Muonium Laser Spectroscopy
VOLUME 84, NUMBER 6

PHYSICAL REVIEW LETTERS

7 FEBRUARY 2000

p.1136

Measurement of the 1s-2s Energy Interval in Muonium

V. Meyer,1 S. N. Bagayev,5 P. E. G. Baird,2 P. Bakule,2 M. G. Boshier,4 A. Breitrück,1 S. L. Cornish,2 S. Dychkov,5G. H. Eaton,3 A. Grossmann,1 D. Hübl,1 V. W. Hughes,6 K. Jungmann,1 I. C. Lane,2 Yi-Wei Liu,2 D. Lucas,2Y. Matyugin,5 J. Merkel,1 G. zu Putlitz,1 I. Reinhard,1 P. G. H. Sandars,2 R. Santra,1 P. V. Schmidt,1 C. A. Scott,3
W. T. Toner,2 M. Towrie,3 K. Träger,1 L. Willmann,1 and V. Yakhontov 1

Alexandrite
Tripler
Laser 732 nm

Fast Beam
Diagnostics

Cavity Control
Electronics

MCP

Uncerntainty from Residual
Doppler
3.4 MHz
Pulse laser was used
linewidth ~ 10 MHz
Events per Laser Pulse 10-4

244 nmVacuumApparatus
Retroreflector!

1.4
Muonium

1.2

F=1

1

Signal

F=1

Theory0.8~20 MHz

0.6
0.4
0.2
0
640

660

680

700

Laser- Iodine

720

MHz

1S-2S Result of RAL 1999 Experiment
Result: 2 455 528 941.0(9.8) MHz[V. Meyer et al., PRL84,1136(2000)]Conclusion of the paper:µ+ intensity
3500 50 Hz
Mu yield
600 cpsnum. of Mu in Laser
1.5 /pulse
Laser / Linewidth pulsed / ~8 MHz
Number of signals
99
Uncertainty
Statistics
9.1 MHz
Residual doppler
3.4 MHz
Freq. calibration
0.8 MHzLine shape
1.2MHzTotal
9.8 MHz

Solutions for improvement:
Larger number of Muonium
CW laser with optical cavity
Freq. measurement by opt. comb

Events per Laser Pulse 10-4

RAL(1999)

1.4
1.2
1

Muonium
F=1

Signal

F=1

Theory0.8~20 MHz

0.6
0.4
0.2
0
640

660

680

700

Laser- Iodine

720

MHz

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Requirements for Mu Laser Spectroscopy
1S-2S Signal Rate: (for CW laser, I < 1 MW/cm2): Number of Muonium: Mu-Laser Interaction time

: Laser intensity: Two-photon Rabi frequency

Laser beam diameter of 1 mm:
4 W laser power
300 K Mu (8.1 km/s)

I = 1 kW/cm2
t0 = 123 ns

Large number of Mu
Higer laser power
Lower Mu temperature(longer interaction time)

Natural linewidth of the 1S-2S transition (1.2 PHz x2)<1 kHz laser linewidth,
Radiative width 1.3 Hz
long-term stability
muon lifetime
72 kHzaccuracy

Result: 2 455 528 941.0(9.8) MHz
RAL(1999)µ+ intensity
3500 50 Hz
Mu yield
600 cpsnum. of Mu in Laser
1.5 /pulse
Laser / Linewidth pulsed / ~8 MHz
Number of signals
99
Uncertainty
Statistics
9.1 MHz
Residual doppler
3.4 MHz
Freq. calibration
0.8 MHzLine shape
1.2MHzTotal
9.8 MHz

Solutions for improvement:
Larger number of Muonium
CW laser with optical cavity
Freq. measurement by opt. comb

Workshop for Particle and Phenomenology 2020

Result: 2 455 528 941.0(9.8) MHz
RAL(1999)µ+ intensity
3500 50 Hz
Mu yield
600 cpsnum. of Mu in Laser
1.5 /pulse
Laser / Linewidth pulsed / ~8 MHz
Number of signals
99
Uncertainty
Statistics
9.1 MHz
Residual doppler
3.4 MHz
Freq. calibration
0.8 MHzLine shape
1.2MHzTotal
9.8 MHz

Solutions for improvement:
Larger number of Muonium
CW laser with optical cavity
Freq. measurement by opt. comb

353

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OCAMI Reports Vol. 6 (2021)

10 ns

1/25 = 40 ms

Result: 2 455 528 941.0(9.8) MHz
RAL(1999)µ+ intensity
3500 50 Hz
Mu yield
600 cpsnum. of Mu in Laser
1.5 /pulse
Laser / Linewidth pulsed / ~8 MHz
Number of signals
99
Uncertainty
Statistics
9.1 MHz
Residual doppler
3.4 MHz
Freq. calibration
0.8 MHzLine shape
1.2MHzTotal
9.8 MHz

Solutions for improvement:
Larger number of Muonium
CW laser with optical cavity
Freq. measurement by opt. comb

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355

Doppler Broadening

Doppler width (FWHM)

Transmittance

Velocity distribution at temperature T(Maxwell-Boltzmann distribution)laser frequency
Doppler shift

Doppler width of 1-photon transition, e.g.
Lyman- ( =121 nm, 0=2.4 PHz), T=300 K
HydrogenMuonium

Doppler Cancellation: Two-photon Absorption
Two-photon excitation by counter-propagating plane-waves

Doppler shift can be canceled
Doppler-free spectroscopy

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OCAMI Reports Vol. 6 (2021)

Residual Doppler Broadening
Gauss beam propagation
Imperfect
counter-propagating
beams:

Cavity Control
Electronics

MCP
VacuumApparatus

Retroreflector!

Events per Laser Pulse 10-4

Muonium 1S-2S spectroscopy at RAL (1999)
Uncerntainty from Residual
Fast BeamAlexandrite
Doppler
3.4 MHz
Tripler
Diagnostics
Laser 732 nm
Pulse laser was used
244 nmlinewidth ~ 10 MHz
1.4
1.2
1

Muonium
F=1

Signal

F=1

Theory0.8~20 MHz

0.6
0.4
0.2
0
640

660

680

700

Laser- Iodine

720

MHz

1st Order Doppler Cancellation in Optical Cavity+

A stable resonant-cavity mode (standing wave):
Consists of perfectly counter-propagating laser beams
1st-order Doppler shift is always cancelled
Beam intensity can be enhanced in the cavity tofor a typical 1S-2S cavity
Beam diameter for the stable mode is ~1 mm
2nd-order Doppler shift / broadening cannot be cancelled

Workshop for Particle and Phenomenology 2020

357

Result: 2 455 528 941.0(9.8) MHz
RAL(1999)µ+ intensity
3500 50 Hz
Mu yield
600 cpsnum. of Mu in Laser
1.5 /pulse
Laser / Linewidth pulsed / ~8 MHz
Number of signals
99
Uncertainty
Statistics
9.1 MHz
Residual doppler
3.4 MHz
Freq. calibration
0.8 MHzLine shape
1.2MHzTotal
9.8 MHz

Solutions for improvement:
Larger number of Muonium
CW laser with optical cavity
Freq. measurement by opt. comb

Transit Time Broadening
RMS Thermal velocity

W. Demtröder,“Laser Spectroscopy,” Fig. 3.19
[rad/s]Transit
time

width

2nd-order
Doppler

Hydrogen366 ns

1.1 MHz

0.1 MHz

Muonium

123 ns 3.2 MHz
Beam diameter

0.9 MHzTo decrease the muonium temperature(i.e. increase the interaction time)

Reduction both oftransit time
2nd-order doppler

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OCAMI Reports Vol. 6 (2021)

for their contributions to thedevelopment of laser-based
precision spectroscopy, including
the

1
0.8

0.1

Intensity

Normalized power

FWHM 97.9 fs

0.01

0.5

0.6
0
0.4
-0.5

0.2

0.001
1500 1525 1550 1575 1600 1625 1650
Wavelength [nm]10-300 -200 -1000-1
100 200 300

Time [fs]Phase [rad]Amplified: FWHM 56.8 nm
1Workshop for Particle and Phenomenology 2020

359

976 nmcw, 30 mW

3000
2500
2000
1500
1000
500
0

G. A. Beer et al., Prog. Theor. Exp. Phys. 2014, 091C01

Region 1
10 < z < 20 (mm)360

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361

Low scale seesaw models for low scale
U(1)L -L symmetry

Joe Sato (Saitama U.)
Based on PRD91, 037301 and PRD93, 013014 PRD100, 095012.
Collaboration with T. Araki, K.Asai, F. Kaneko, Y. Konishi, T. Ota, T. Shimomura.

OutlineIntroduction
IceCube Gap and U(1)L-L

PRD 91 & 93
UV completion of U(1)LPRD 100
Summary

-L

model

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Introduction

Motivations of U(1)New U(1) force acting on.

e,others

e

U(1)L

0

+1

-1

0

Motivated by
Muon g-2 problem,
Energy spectrum of cosmic neutrinos (IceCube),
Flavor puzzles in the lepton sector,
etc.

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363

Muon g-2
Longstanding discrepancy between experiments and theory:[ Hagiwara, Liao, Martin, Nomura, Teubner, JPG38, 085003 (2011) ]In themodel, we have an additional contribution:

Muon g-2
The red band is consistent with g-2 within

g-2

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Motivations of U(1)New U(1) force acting on.

e,others

e

U(1)L

0

+1

-1

0

Motivated by
Muon g-2 problem,
Energy spectrum of cosmic neutrinos (IceCube),
Flavor puzzles in the lepton sector,
etc.

IceCube Gap
PRD91&93

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365

High energy cosmic neutrinos
Our target: neutrinos produced in cosmic-ray interactions
with gas ( p ) or radiation ( ), followed by pion decays.
@ Source@ Earthoscillation

High energy cosmic neutrinos
Our target: neutrinos having energies of O( TeV PeV ) .

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Three-year data
Neutrino flux () as a function of its energy.

[ PRL 113 (2014), 101101 ]1. It rejects a purely
atmospheric explanation
at 5.7 sigma.
2.

The data are consistent
with equal (1:1:1) flavor
ratios and isotropic
arrival directions.
The best-fit power low is

3.

[ Astrophys. J. 809 (2015) 1, 98 ]

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367

Impacts of IceCube
The IceCube data have a great impact on
not only astrophysics

the origin of high energy cosmic neutrinos,
an acceleration mechanism of cosmic rays

but also particle physics.

Gap or fluctuation?
Neutrino flux () as a function of its energy.

[ PRL 113 (2014), 101101 ]Gap !?

1. It rejects a purely
atmospheric explanation
at 5.7 sigma.
2.

The data are consistent
with equal (1:1:1) flavor
ratios and isotropic
arrival directions.
The best-fit power low is

3.

400 TeV

1 PeV[ Astrophys. J. 809 (2015) 1, 98 ]

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Gap or fluctuation?
Neutrino flux () as a function of its energy.
1. It rejects a purely
atmospheric explanation
at 5.7 sigma.

[ PRL 113 (2014), 101101 ]Gap !?

2.

The data are consistent
with equal (1:1:1) flavor
ratios and isotropic
arrival directions.

New
New
interactions
interactionsof neutrinosof neutrinos?? ?
The best-fit power low is
3.

400 TeV

1 PeV[ Astrophys. J. 809 (2015) 1, 98 ]Secret neutrino interaction

Ioka, Murase, PTEP2014, 061E01
Ng, Beacom, PRD90, 065035 (2014)
Ibe, Kaneta, PRD90, 053011 (2014)

The Gap may indicate.

Cross section is enhanced as

500 TeV10

eV

Workshop for Particle and Phenomenology 2020

Secret neutrino interaction
Rough estimation of the mass of X and its coupling.

center-of-mass energy
Newphysics at the MeV scalemass of X
X
is a possible candidate
forrequires:the IceCube gap!!
(1) Resonant condition(2) To attenuate sufficient amount of cosmic neutrino:

Explanation by

369

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A new gauged U(1): mu - tau
We introduce a new U(1) gauge symmetry associated withthe muon number minus tau number:

New gauge boson

New gauge coupling

1. No quantum gauge anomalies.
2. No LFV couplings.
3. Large atm. and small reactor mixing:
4. A possible solution for muon anomalous magnetic moment.

Kinetic mixing is forbidden in

limit

In
limit, we cannot distinguish between
Then, a discrete symmetry appears.

andTherefore,

is forbidden in.

model.
20

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A new gauged U(1): mu - tau
We introduce a new U(1) gauge symmetry associated withthe muon number minus tau number:

New gauge boson

New gauge coupling

1. No quantum gauge anomalies.
2. No LFV couplings.
3. Large atm. and small reactor mixing:
4. A possible solution for muon anomalous magnetic moment.

Muon g-2
The interaction between the electron/muon spin and magnetic field,
Magnetic moment,

g-factor
The prediction of Dirac equation,
Due to the field theory, a small difference with Dirac value appers.

Consistent with SM

22
K. Hagiwara et al., J. Phys. G 38, 0850003 (2011). Marc Knecht, arXiv:1412.1228

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Muon g-2
Longstanding discrepancy between experiments and theory:[ Hagiwara, Liao, Martin, Nomura, Teubner, JPG38, 085003 (2011) ]In themodel, we have an additional contribution:

Muon g-2
The red band is consistent with g-2 within

g-2.

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Neutrino trident production
The model is constrained by the neutrino trident production.

New

in good agreement with SM[ CCFR collaboration, PRL66, 3117 (1991) ]( This confirmed the destructive interference of W-Z, and thus SM. )Other constraints
one-loop mixing
It contributes to

The model is constrained by Borexino.
[ Harnik, Kopp, Machado, JCAP 1207, 026 (2012) ]BBN
Such a lightincreases the effective number.

Directly
Indirectly[ Kamada, Yu, 1594.00711 ]374

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Parameter region

Parameter region

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Secret neutrino interaction
RoughChallenge
estimation of the mass of X and its coupling.

g-2 and IceCube gap
simultaneously??
center-of-massenergymass of X

X(1) Resonant condition requires:(2) To attenuate sufficient amount of cosmic neutrino:

Calculation of neutrino flux
and model parameter

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Propagation of neutrinos
A propagation equation for cosmic neutrino:

c: speed of lightz: redshift parameter: number density of CnB

Propagation of neutrinos
A propagation equation for cosmic neutrino:

1. Energy loss via redshift

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Propagation of neutrinos
A propagation equation for cosmic neutrino:

2. Source term
: normalization of flux
: spectral index: cut-off energyStar formation rate

Propagation of neutrinos
A propagation equation for cosmic neutrino:

3. Scattering with CnB

center-of-mass energy

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Propagation of neutrinos
A propagation equation for cosmic neutrino:

4. Regeneration term

Parameter setting
Neutrino mixing[ Forero, Tortola, Valle, PRD90, 093006 (2014) ]We use best-fit values for the normal (inverted) mass hierarchy:

andPropagation equation: normalization of flux
: cut-off energy

Adjust to fit the IceCube data.

We calculate diffuse neutrino flux for several values offor NH and IH.

Workshop for Particle and Phenomenology 2020

Gap: Spectral index
Diffuse neutrino flux for several spectral indices.

Normal hierarchy( quasi-degenerate )The gap can successfully be reproduced , but not completely.
Some events are expected in IceCube in the future. Indeed now appearing !

Gap: Source distribution
Diffuse neutrino flux for several types of source distribution.

Normal hierarchy( quasi-degenerate )Source distributions have a small impact on the flux.

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Parameter region

A Concrete Model
PRD100Workshop for Particle and Phenomenology 2020

381

Motivation
Extra U(1) models are often studied as an effective theory
Really it exists ?
Including scalar potentials ? Say, extra matter(s) in low energy ?
Predictive or just parameter physics ?
For example,
In cosmic neutrino attenuation,
if there were more light particles , prediction would have differed,
Neutrino masses and lepton mixings are predictive?
For latter zero texture is a key.

Zero textures
Zeros in neutrino mass matrix gives constraint = prediction

One zero yields two conditions.
Zero textures

Zero-minor textures

One can check the consistency of the conditions.

Testable !

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Mass matrix in U(1)U(1)

charges of a Dirac mass matrix.
U(1)L - symmetric,
allowed.

Thus, the mass
matrix is given by

Not U(1) - symmetric,
forbidden.

(ex.)

U(1)L

Mass matrix in U(1)U(1)

charges of a Majorana mass matrix.

Thus, the mass(ex.)

matrix is given by
U(1)LWorkshop for Particle and Phenomenology 2020

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Neutrino masses & mixing in U(1)(Majorana) neutrino masses and mixing in U(1).

U(1)L must be
broken.

VS exps.
predictions

From the first , though
the symmetry must be broken, since there is no massless gauge other than photon.
How to break ?

Breaking of U(1)U(1)-

With U(1)L -symmetry must be broken in the neutrino sector.
charge 1 scalars.

Many possibilities,
we will focus on this.

With U(1)L -charge 2 scalars.

12
13 remain
vanishing, unrealistic.

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Zero textures

Zero textures
One zero yields two conditions.
Zero textures

Zero-minor textures

One can check the consistency of the conditions.

Testable !

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Two-zero textures
Simple models give often two zeros
The number of parameters in two-zero textures.

9

4 = 5 parameters

Three masses,
three angles
three CP phases.

Two zeros yieldfour conditions(four constraints).

One can predict 4 observables with 5 input parameters.
(ex.)

Possible two-zero textures before Planck
Two-zero textures

Two-zero-minor textures[ S. Zhou, Chin. Phys. C40 (2016) ]Equivalent

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Checking the consistencyoftwo-zero textures

Two-zero textures vs Planck[ I. Esteban, et al, JHEP01, 106 (2019). ]Outputs: sin223

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387

Two-zero textures vs Planck
Should be inside

NO

IO

Planck2018 + low E + lensing + BAO:
[ Planck Callaboration, arXiv1807.06209 ]Two-zero-minors vs Planck

Planck2018 + low E + lensing + BAO:
[ Planck Callaboration, arXiv1807.06209 ]388

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New model

Our model

SU(2)L

2

U(1)L2 generations

Particle contents

1

1

1

2

2

1

U(1)L -

1

Model

A:

( NRe, NR )=(0, 1)( NLe, NL )=(0, 1)

Model

B:

( NRe, NR )=(0, -1)( NLe, NL )=(0, -1)

Workshop for Particle and Phenomenology 2020

389

Our model
The 7 by 7 effective neutrino mass matrix is obtained, after thescalars develop VEVs.

<<SL>, it triggers Inverse seesaw.
U(1)L -by <S>.

Our model

Model A

Model B390

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Our model
The 7 by 7 effective neutrino mass matrix is obtained, after thescalars develop VEVs.

<<SL>, it triggers Inverse seesaw.
U(1)L -by <S>.

Our model
After block diagonalization, the active neutrino mass
Linearmatrix is obtained.
InverseTiny neutrino masses can be realized.
Small U(1)LWorkshop for Particle and Phenomenology 2020

391

Our model
One-zero textures are obtains.
Model

A:

( NRe, NR )=(0, 1)
LinearModel

B:( NLe, NL )=(0, 1)

Inverse( NRe, NR )=(0, -1)( NLe, NL )=(0, -1) One zero

One-zero textures
The number of parameters in two-zero textures.

9
Three masses,
three angles
three CP phases.

2 = 7 parameters
One zero yields
two conditions(two constraints).

One can predict 2 observables with 7 input parameters.

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One-zero textures
Model - A

Model - B

Normal ordering (NO) is disfavored,
inverted ordering (IO) is allowed.

nEXO

Workshop for Particle and Phenomenology 2020

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Scalar potential
The scalar potential is given by

The U(1)L term is necessary.
VEVs

Small U(1)L[ E. Ma, PRL86, 2502 (2001) ]Light Scalar(s)? Majoron

Summary
Extension of SM with U(1)Lattractive.

-Lgauge is very

Not only g-2, here we show
It explains the gap observed at IceCube around 500 TeV.
We also construct a UV completion of such model which
explains neutrino physics with predictions.

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BackupThree-years vs four-years

In four-years data, the gap
has been somewhat filled,
but there still exists a dip.

Workshop for Particle and Phenomenology 2020

395

Event topology (flavors)
IceCube can distinguish flavors by observing event topology.

Charged Current (CC)track,
double-bang

Neutral Current (NC)

hadronic shower
forall flavors[ K. Mase, KEK-PH2014 ]Energy cut-off
Diffuse neutrino flux for several spectral indices.
Inverted hierarchy( hierarchical )Without setting

Excluded by trident.
We needand the CnuB momentum effects.

396

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Calculation of mean free path(
( Inverted hierarchy )(1) Positions of the gaps.

Calculation of mean free path(
( Inverted hierarchy )Workshop for Particle and Phenomenology 2020

397

Calculation of mean free path(
( Inverted hierarchy )(3) Larger red-

Secret neutrino interaction
The gap may indicate
CosmicneutrinosX

Cosmic Neutrino Background ()

A gap at a particular energy could be realized by a resonantinteraction mediated by a new particle
X.
[ Ioka, Murase, PTEP2014, 061E01 ][ Ng, Beacom, PRD90, 065035 (2014) ][ Ibe, Kaneta, PRD90, 053011 (2014) ]398

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U(1)Breaking-

in
Seesaw mechanisms

Breaking of U(1)(ex.) Type-I seesaw
Without symmetry breaking.

A SM singlet scalar having U(1)-Two zero minors.

charge 1 or -1.

Workshop for Particle and Phenomenology 2020

399

Breaking of U(1)(ex.) Type-I seesaw
An SU(2) doublet scalar having U(1)-charge 1.

An SU(2) doublet scalar having U(1)-charge -1.

Two-zero textures are obtained.

Breaking of U(1)(ex.) Inverse seesaw
Without symmetry breaking.

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Breaking of U(1)(ex.) Inverse seesaw
A SM singlet scalar having U(1)-An SU(2) doublet scalar having U(1)Breaking of U(1)(ex.) Linear seesaw
Without symmetry breaking.

charge 1.

-

charge 1or -1.

Workshop for Particle and Phenomenology 2020

401

Breaking of U(1)(ex.) Linear seesaw
An SU(2) doublet scalar having U(1)Two SU(2) doublet scalar having U(1)charge 1 or -1.

--

Two-zero textures vs PlanckNO

IO

charge 1, -1.

402

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Two-zero textures vs Planck<mee> = 0<mee> = 0

Planck2018 + low E + lensing + BAO:
[ Planck Callaboration, arXiv1807.06209 ]Workshop for Particle and Phenomenology 2020

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23/11/2020@

(

2020

)
,
(

)

Ref. arXiv:2010.02834[hep-ph]2Workshop for Particle and Phenomenology 2020

425

CP
QCD Lagrangian-term

non-zero
EDM

EDM[P. G. Harris et al.

3

PQ[Peccei-

Peccei-Quinn(PQ)
SSB

KSVZ modelNGanomalous U(1)(axion)Shifman-Vainshtein-Zakhrov

Extra heavy quark + singlet PQ scalar
DFSZ model[Zhitnitsky-Fischler-Srednicki

Two Higgs doublets + singlet PQ scalar
4426

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global string

Field profile

5

String Reconnection
String string
String 1

dynamics
String 2

Reconnection

Scaling behavior[Hiramatsu-

-17]

6

Workshop for Particle and Phenomenology 2020

427

Y-(Shaped) Junction

String string[Betterncourt-

Betterncourt-Laguna-

dynamics

String 1

String 2

Reconnection

Stringbound state
Reconnection
string network

Y-junction = bound state

7

Superconducting String
Stringsuperconducting string
EM current
stringString
EM current string
Y-junction

Cf.
[JakiwShafi

superconducting string
Lazarides

Ganoulis-Lazarides

Lazarides8

428

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DFSZ modelaxion string

Electroweak axion string
EW axion string superconducting string
current
Y-junction
DFSZ modelreconnection

9

Model

10

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DFSZ Model[Zhitnitsky

Particle contents-Fischler-Srednicki

Two Higgs doublet model + SM singlet scalar

Scalar potential

Charge relation
11

PQ Charge

current Z-boson

PQ

PQ charge

12

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Electroweak Axion String

13

Strings2

Characterized by NGB
form Higgs boson

Characterized by axion
(NGB)
14

Workshop for Particle and Phenomenology 2020

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Strings
2

Anomaly inflow

Characterized by NGB
form Higgs boson

Characterized by axion
(NGB)
15

Strings2

Characterized by NGB
form Higgs boson

Characterized by axion
(NGB)
16

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Electroweak Axion String
Axion string core(Core)

Electroweak flux tube
17

Electroweak Axion String

Electroweak
Axion String
Electroweak flux tube
(Frankfurt)Frankfurt(Delicious smell)Axion string core
(Stick)18

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Axion String in DFSZ Model
breaking

unbroken phase

PQ

19Electroweak Axion Strings

2

Higgs doublet non-zero VEV
EW flux

EW sym.
String core
Axion string

Electroweak axion string

Higgs winding pattern
stringType-A, B, C
Superconducting string

EW axion
20

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Electroweak Axion Strings
Assumptions:Field profiles Type-A

Type-C

Type-B

21

Type-A EW Axion String
Type-A EW axion string

22

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Type-A EW Axion String
Type-A EW axion string

winding

NB:

winding

winding23

Type-A EW Axion String
Non-zero Z-boson fieldZ fluxString coreZ-flux

NB:
24

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Type-B EW Axion String
Type-A EW axion string

winding

winding

Z-boson and Z-flux

25

Type-B EW Axion String
Type-B EW axion string

profileBoundary condition

Z fluxStringcore

26

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Type-C EW Axion String
Type-C EW axion string

Z-flux and W-flux

winding

winding

winding
Z and W flux

Core

27

Type-C EW Axion String
String:EW sym.

spontaneously broken
Superconducting
Current carrier: Higgs charged components

W-boson28

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String Tension
3

EW axion strings

tensionLength unit:

Type-C string
EW phase transition

favoredaxion string type-C string
29

Superconductivity

30

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Type-C String
EW axion string

439

Supercurrent
current[Alford-Benson-Coleman-March-Russell-Wilczek

Background
Z, W flux
String coreaxion string
zero mode

Cf.
Type-C
electroweak axion string
31

Type-C String Supercurrent
dependent zero mode
type-C backgrounds[YA-Hamada-

EOMs

32

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Type-C String

Supercurrent

Linearized EOM at large
is massless excitation along the string

Static solution

with a constantEM field strength and electric current

33

Type-C String
Zero mode

Current

Higgs:

superconducting state
Current
negative mass terms(current quenching)
Higgs potential

current
34

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StringStringcurrent

axion
Stringstringnet
Y-junction?
35

EW phase transition
DFSZ axion string
electroweak gauge flux
Electroweak axion string

Type-C EW axion string
carriersuperconducting string
StringCurrent
axion stringbosonic

current

Y-junction

DFSZ model
36

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Backup
37

Superconducting String
Axion string[Lazarides-Shafi

fermion zero modes
Lazarides-Panagiotakopoulos-Sfafi

Ganolis-Lazarides

Iwazaki

JackiwCallan-zero mode EM current
superconducting string
current

Phenomenology, cosmology
see

Fukuda-Manohar-Murayama-TelemarXiv:2010.02763 [hep-ph]38

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443

Higgs Bi-linear Formalism
Higgs matrix:[Grzadkowki-Maniastis-Wudka

Covariant derivative

Higgs potential

39

Higgs Bi-linear Formalism
Scalar potential[Grzadkowki-Maniastis-Wudka

Parameter relations

40

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Unbroken
where
Positive normalization factor

defined to satisfy

subgroup

NB:

Higgs matrix.
41

Z-boson photon[Eto-Hamada-

Higgs doublet

42

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EOMs of Type-A String

Boundary conditions

43

EOMs of Type-B String

Boundary conditions

44

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EOMs of Type-C String

Boundary conditions

45

Profile of Strings
Type-A46

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Profile of Strings
Type-B

47

Profile of Strings
Type-C

48

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String Tension

Parameters

Length unit:
49

Supercurrent of Type-C String
EOMs

Linearized EOM for
Zero mode solutions:50

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Supercurrent of Type-C String
Static zero mode solution
background

EOMs

Long-range force

51

Current Quenching
String
Lagrangian:mass terms

Determinant of the mass matrix:

Quenchingregion where

52

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2020

11

28
2020

Contents
Introduction : Cosmological Constant inSuperstring
Asymmetric Orbifolds as Non-SUSY
String Vacua with Vanishing CC
Non-SUSY Vacua with Vanishing CC :Part 22

Workshop for Particle and Phenomenology 2020

Introduction :Cosmological Constant inSuperstring3

Whats cosmological constant?
Cosmological const.

vacuum energy density

no interaction

4

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Whats cosmological constant?
Point particle

UV-cut off

Schwinger parameter(moduli)5Whats cosmological constant?
String theory

Torus partition
function
Torus, moduli

6Workshop for Particle and Phenomenology 2020

453

Whats cosmological constant?
Modular invarianceintegration region :7

Whats cosmological constant?
CC for string is formally identified as that of a particle theory withan infinite number of mass spectrum:(

But, the integration region is different.
8

)

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Integration region of moduli(Schwinger parameter)

StringParticle

9

cosmological constant problem

suggests a vacuum with (nearly)
vanishing cosmological constant
without SUSY?

10

Workshop for Particle and Phenomenology 2020

Non-SUSY with455?

Two possibilities, but no supercharges exist.

, but

11

Asymmetric Orbifolds
asNon-SUSY String Vacua with
Vanishing Cosmological Constant

12

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How to break SUSY?

(

Orbifolding by: left-moving space-time

fermion number

Removes massless Ramondstates in the untwisted sector.
(break SUSY?)
But, new massless Ramondstates emerge in the twisted
sector. (eventually, SUSY)
13

How to break SUSY?
Orbifolding by
Scherk-Schwarz
Compactification(see also Prof. Itoyamas talk)

shift
operator

Lightest Ramond states in the twisted sectors
get massive. (No supercharge can appear.)
SUSY breaking
14)

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457

Non-SUSY Model with
Non-SUSY string vacua (type II)with vanishing
1-loop cosmological constant[Kachru, Kumar, Silverstein 1998],[Kachru, Silverstein 1998][Kachru, Silverstein 1998],

Asymmetric orbifold defined by the orbifold group:,

do not commute.

Non-abelianorbifold15

includesand (chiral) shift op.

break all the right-moving SUSY
includesand (chiral) shift op.

break all the left-moving SUSY

Totally Non-SUSY
16

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Nevertheless, the 1-loop cosmological constant(torus partition function) strictly vanishes.
Bose-fermi cancelation
without SUSY
Crucial point :is well-defined, only whencommutes with

Clever, but looks complicated17

Closely related studies :[Harvey 1998][Shiu, Tye 1998][Blumenhagen, Gorlich 1998][Angelantonj, Antoniadis, Forger 1999][Aoki, DHoker, Phong 2003 ]18

Workshop for Particle and Phenomenology 2020

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Non-SUSY Model withMy studies[Satoh,Y.S, Wada 2015][Y.S, Wada 2016][Satoh, Y.S, Uetoko 2017][Y.S, Uetoko 2018][Aoyama, Y.S 2020][Aoyama, Y.S to appear]19

Non-SUSY Model with
[Satoh,Y.S, Wada 2015]

Realized by simpler (asymmetric) orbifold actions.
(only single generator in the orbifold group)
Each building block

separately vanishes.

(bose-fermi cancellation in each sector)
No supercharges (globally defined on the total
Hilbert space) exist.
20

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Non-SUSY Model withmodular covariance21

Non-SUSY Model with
[Aoyama, Y.S 2020][Aoyama, Y.S to appear]

Asymmetric orbifolds of Gepner models
Each building block
does notnecessarily vanish.
(bose-fermi cancellation among different
twisted sectors)

22

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461

Non-SUSY Vacua with Vanishing
Cosmological Constant : part 2[Satoh,Y.S work in progress]
23

Non-SUSY Model with: part 2

Two possibilities, but no supercharges exist.

, but
no bose-fermi cancellation
24

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Non-SUSY Model with
[Moore 1987]

If: part 2

Atkin-Lehner Symmetry,

have opposite parity,

should vanish.
Beautiful idea, but difficulty in concretemodel building . . .
25

Non-SUSY Model with: part 2

Our idea :Modular invariant: winding numbers(

26-doublet )Workshop for Particle and Phenomenology 2020

Polchinskis trick[Polchinski 1986]( assume

27

Assume the situation :
, but

but

Correct integration region
for the particle theory !
28

463

)

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interpretable as a particle theory with,without the bose-fermi cancellation(including infinite number of mass spectrum)

29

Starting with various SUSY string vacua,
we can realize this situation by implementing
asymmetric orbifolding~ untwisted sector~ twisted sector

30

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Summary
Non-SUSY stirng vacua withcan be constructed byasymmetric ( non-geometric )orbifold
Vanishing CC withvery difficult in string theory,can be realized as particle vacua
31

32

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Stability, enhanced gauge symmetry and suppressedcosmological constantin heterotic interpolating models
with S. Nakajima

On nonsusy hetero

H. Itoyama, Nambu Yoichiro Institute of Theoretical andExperimental Physics (NITEP), OCU
arXiv: 1905.10745, PTEP INkjm1
arXiv: 2003.1121, NPB INkjm 2
INkjm3, in preparation
I-Koga-Nakajima, in progressI) Some background materials
Q : What is string theory?
A : Nobody knows.

cf. point particle vs. field (wave)

began with the construction based on a single string:

quantization

many body problem

quantization

2nd quantization

waviclebegan as a candidate for unified theory that must include quantum gravity

1997

2015

decoupling of gravity by D brane

direct connection to Planck scale: paradigm shift

UV finite, but couplings run in real world, so need a big help from QFT.
Ironically, more successful in stimulating LEEF construction at IR

only to begin with, but all marginal deformations of worldsheet action need to betaken into accounttranslates into undetermined V.E.V. (moduli) of LEEF
energetic consideration needed & nonsusy hetero helps

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just do the two simple things:
i)

partition function used for state countingii)
To elaborate little morei) using

can derivebycf. Nambu 1950 @OCU

up toii) just one diagram/amplitude
leave the rest to QFT
and/ori)(tension) limit, interesting in the presence of, WLii) possibility of UV-IR separation in

Heterotic string & history
Closed string only & inherently chiral with matter rep

Idea of Heterotic strings
adopt the lightcone coordinates
Right mover: 10d superstring
Left mover: 26d bosonic string out of whichinternal 16d realize rank 16 current algebra(or fermions)fanatically investigated during
got bored during
got converted to D-braners or quitIn

, modular inv (tachyon free) non SUSY hetero. found

SUSY-non SUSY interpolating model upon comp. foundDixon-Harvey
Alvarez-Gaume et.al.
H.I.-T.Taylor

resurgence of interest since around 2015 as nothing found beyond Higgs at LHC so far

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Cosmological constant in string with broken SUSY
Due to the cosmological observation up until around 2000, the cosmological const

obs

was thought to be exactly zero.
should havesuperstring

string

The goal was to predict SUSY scales in multi TeV region and superpartners

Now in 2020, about 70% of the mass of our universe is attributed to something called
dark energy whose leading candidate is
nonSUSY hetero is fine,
The issue is how to makeobs.

s can be as large as
string small

Planck.

obs upon compactification while keeping

nonaberian gauge group.
#(theories with SUSY) < #(theories without SUSY)
Heterotic
Type IIB
Type 0B
Type IIAHeterotic
Type 0A
Type I
Heterotic
Heterotic
Heterotic
Heterotic
Heterotic
call M1
call M2
today
interpolation by a radius () or in general radii interpolation of M1 and M2
upon compactification-Taylorgauge symmetry enhancement
Simplest example: bosonic strings on
Mass formula :
boost

( )

gauge sym.
is enhanced() forms SO(1,1) Lorentzian lattice:(momentum) (winding) = a indep.

In QFT, we can regard more or lessHiggsing
unHiggsing

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Our choice
M2 = SO(16) x SO(16) tachyon free
IDixon, Alvarez-GaumeINkjm 1, 2

warning: consider all marginal deformation of the world sheet action
full set of Wilson lines should be turned on
generally spoil the nonabelian gauge groupextremapoints of sym. enhancement &the stable 9D perturbative vacuum can be determined

Our results and ongoing work
completed the above analysis in the case ofin susy restoring region
a few
models foundthe minimum is SO(32)/E8 E8 gauge sym., massless bosons only
AdS spacetime
dilaton tadpole is small to this order & will be made harmlessa general analysis at and study of interactions are in progress

The rest of my talkII) 9D interpolating models
III) 9D interpolating models with WL

II)formula for one-loop cosm. const in SUSY res. region:
H.I.M1

M2

nB, nF; # of massless bosons & fermions in D dim.
sketch of the proof:
The integrand of theintegration involves

SUSY restoring factor
apply the Jacobi imaginary transf.
nB=nF models (by now more than several existing)enjoy exponential suppression of
In this setup, mass splitting due to broken SUSY ise.g.
interesting possibility

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State counting & characters
counts #(states) at level m as coeff. in
It takes the form of

expansionand involves spacetime &internal SO(2n), n=4, 8 characters

expressible in termsof the four theta constants and the Dedekind eta fn

SO(32) hetero
E8 x E8 hetero

Construction
The starting point is a supersymmetric heterotic strings on

:

with

: 16D Euclidean even self-dual lattice
Projection by

spacetime fermion number: half translation acting on: half translation acting on

Adding twisted sectors+ (twisted sectors)

consist ofnonzero winding

suppressed intheregion

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Example: SUSY
Partition function
splitting byContribution fromContribution fromThe contribution from the internal directions is
The one-loop partition function istwisted sectors

Endpoint limits
contribution from the states with

only

The partition function of SUSY
contribution from the states with

The partition function of

only

model

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Marginal deformations

III)

The marginal deformations of the world-sheet action:: Wilson lines: metric, anti-sym tensor

The boosts of the momentum lattice forming the coset

In thecase,

Narain, Sarmadi, Witten, (1986)

Deformed by
Wilson lines

Let us consider these deformations for interpolating models
and study the massless spectra!

Enhanced gauge symmetry
Mass formula:
Massless states (NS)Sector1:
D.O.F (sector1)

8 ( 8 + 16 )10D gravity multiplet

Sector2:

NOT depend on moduli

Gauge bosons ofdepend on moduli
nonzero roots of a simply laced Lie algebra

At generic points in moduli space, the gauge symmetry is.

However, there are special points satisfying
for,where the gauge symmetry is enhanced to a simply laced Lie group.

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Example: SUSY
Enhanced gauge symmetry
The gauge symmetry is enhanced to
There is no massless fermion.

The massless spectrum at this point is
The gauge bosons of
The spinors in the bi-fund rep of.

))

We can find a variety of symmetry enhancements depending on
the Wilson lines.
Are there points where?
In this model, the cosmological constant is suppressed when the gauge
symmetry is enhanced toor.

Example: SUSY
Stability

1-loop effective potential:

Up to exponentially suppressed terms (in theregion),Stability analysis of Wilson lines
solve
Maximally enhanced gauge symmetry

How about the points with

Negative cosmological constant
Saddle points?
(Extrema with someunstable directions)

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Our choice
M2 = SO(16) x SO(16) tachyon free
IDixon, Alvarez-GaumeINkjm 1, 2

warning: consider all marginal deformation of the world sheet action
full set of Wilson lines should be turned on
generally spoil the nonabelian gauge groupextremapoints of sym. enhancement &the stable 9D perturbative vacuum can be determined

Our results and ongoing work
completed the above analysis in the case ofin susy restoring region
a few
models foundthe minimum is SO(32) gauge sym., massless bosons only
AdS spacetime
dilaton tadpole is small to this order & will be made harmlessa general analysis at and study of interactions are in progress

The rest of my talkII) 9D interpolating models
III) 9D interpolating models with WL