observable gravitational waves in minimal scotogenic modelseminar/pdf_2020_zenki/... · 2020. 7....

Observable Gravitational Waves in Minimal Scotogenic Model

Kohei Fujikura (TokyoTech)

Debasish Borah (IIT Guwahati)This work in collaboration with:

Sin Kyu Kang (SeoulTech)Arnab Dasgupta (SeoulTech)

Devabrat Mahanta (IIT Guwahati)

Based on arXiv:2003.02276 1

The Standard Model

CMS (2012)

✓ The SM is in agreement with collider experiments.

✓ In 2012, the SM-like Higgs boson was discovered by the LHC.

2

・Dark matter

・Neutrino massesSM does not have DM candidate.

SM cannot explain tiny neutrino masses.

Problems in the SMThe SM cannot explain following phenomena:

We need a beyond standard model physics!3

The subject today

Collider searches Gravitational wave

Scotogenic Model

4

Outline・Minimal Scotogenic Model

・A First-Order Electroweak Phase Transition

・Results

5

SM + additional SU(2)w doublet + 3 right-handed neutrinos can explain following phenomena:

・Dark matter

・Neutrino masses

[E. Ma (2006)]

Scotogenic Model

6

The Scalar Potential

Invariant under the Z2 symmetry: S ! �S

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Suppose that S does not acquire VEV. (Inert scalar doublet)

S is stable, i.e., cannot decay into the SM particles.7

V = �SM

✓|H|2 �

v2SM

2

◆2+ m21|S|2 + �1|H|2|S|2

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+�2|H†S|2 + [�3(H†S)2 + h.c.] + �S|S|4

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SM Higgs potential

S : SU(2)W doublet

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H : SM Higgs doublet

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Three Right-handed Neutrinos

Lint �1

2(MN)ijNiNj + (YijL̄i eSNj)

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Ni ! �Ni

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S ! �S

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Interactions with new particles preserve Z2 symmetry!

Interactions with SM particles:

•The inert scalar S: SU(2)W×U(1)Y gauge interactions and scalar-Higgs couplings!•Right-handed neutrinos: Yukawa couplings with SM leptons!

L̄ : SM leptons

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Ni : right � handed neutrino

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8

Two DM candidates

•A neutral component of the inert scalar.

•The lightest right-handed neutrino.

9

S =

✓H

+

H0

◆

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Charged component

Neutral component(WIMP dark matter)

H0 =H + iA

p2

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H: CP-even scalar

A: CP-odd scalar

Scalar masses

m±

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mA

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mH

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

Chargedscalar

CP-oddscalar

CP-evenscalar

Stable

Scalar Masses

10

m2± = m21 +

1

2�1v

2SM

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m2A = m21 +

1

2(�1 + �2 � 2�3) v2SM

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

m2H

= m21 +1

2(�1 + �2 + 2�3) v

2SM

AAACynichVFLaxRBEK6Mj8TxkVUvAS+NSyQiDDWTDe4KQoiXHBSSrJsEMskwM9u7adLzoKd3YR3mlpN/IAdPCiLiz/AiePaQnyCeJIKgHqydnSAeojVMV9VX9VV/3R2kUmQa8XjKOHf+wsXpmUvm5StXr83Wrt/YzJKBCnknTGSitgM/41LEvKOFlnw7VdyPAsm3goNH4/rWkKtMJPFTPUr5buT3Y9EToa8J8mrcDRLZzUYRudyMvNU9hz1kkWeTv+f2lB/mdpE7BXMl7+kFV9Loru/ZVKxC6mPOabLIXCX6+/ru0MtdFbH2k2LPMQuvVker1cJGY4mhtYSO4zQpwEWn2bKZbWFpdahsLam9ARe6kEAIA4iAQwyaYgk+ZPTtgA0IKWG7kBOmKBJlnUMBJnEH1MWpwyf0gNY+ZTsVGlM+npmV7JB2kfQrYjKYx0/4Fk/wA77Dz/jrzFl5OWOsZUQ+mHB56s0+n2t//y8rIq9h/w/rn5o19KBZahWkPS2R8SnCCX/47Oik/WBjPr+Dr/AL6X+Jx/ieThAPv4Wv1/nGCzDpAU5vmZ0dbDqW3bBa64368kr1FDNwC27DAt33fViGVViDDu37Eb7CD/hpPDaUMTLySasxVXFuwl9mHP4GvYyvDg==

Weakly Interacting Massive Particle (WIMP)

11

H (or A) scalar can be a DM candidate!

DM

DM

SM

SM

DM annihilation

•DM is thermally produced.•Freeze-out occurs when

�(T ) ' H(T )

<latexit sha1

_base64="k9tnt4ooluKAJsE

YkRyEObhnri8=">AAACiXich

VHLLgRBFD3aa7TXYCOx6RiEz

eSOSAwrYcHSa5AYmXS3Mir6p

btnkjHxA37AwopERGxs2dr4A

QufIJYkNhZu94yICG6n6546dc

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NJGama0/RQIDGMQo3/ckZrCAR

eR43yNc4wa3SruSUbLKdK1Ua

ahr+vAtlLkP2FSWTQ==</lat

exit>

Reaction rate Hubble parameter

•A correct DM abundance can be obtained with weak scale DM mass.mDM ⇠ O(1 ⇠ 100)GeV

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

Scalar DM

High DM mass regime

Low DM mass regimemDM < 80GeV

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

Assumption: 100% DM mDM > 550GeV

AAACh3ichVE9TxtBEH0cJMARghOaSDQnLBDVMT7sxKaICEGCBokvGySMrLtjgRP3pbuzJXNyj/gDKaiIhBBCooWehj9AwU9AlCDRpMj4bBSlAGa1O7Nv582+nTV82wojotsOqbPr3fvunl6570P/x4HUp8+l0KsGpiianu0Fa4YeCttyRTGyIlus+YHQHcMWq8buz+b5ak0EoeW5K1HdFxuOvu1aW5apRwxVUsNlw7M3w7rDLpadSjwz3/iey1FcDhxlVpQacqOSSpNaKFA2m1NIzZGmaXkOaELLFzJKRqXE0mjbgpc6QRmb8GCiCgcCLiKObegIeawjA4LP2AZixgKOrORcoAGZuVXOEpyhM7rL6zbv1tuoy/tmzTBhm3yLzTNgpoIRuqFTeqBrOqM7+vNirTip0dRSZ2+0uMKvDBx8WX56k+Wwj7Dzj/Wq5ghbyCdaLdbuJ0jzFWaLX9v79bA8uTQSj9Jvumf9R3RLV/wCt/ZoHi+KpUPI/AHPXVZeDkqamsmqhcVsemq6/RU9GMIwxrjf3zCFOSygyPfu4xwXuJR6pXHpq5RvpUodbc4g/jPpx1/lspZy

12[micrOMEGAs: arXiv:1305.0237]

The Direct Detection Constraint

13

DM

DM

SM

SM

Direct detection

•DM interacts with SM particles (Nucleon) via the SM Higgs.•Spin-independent (SI) cross-section with nucleon:

mh : SM Higgs mass

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

mn : Nucleon mass

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

µ = mnmDM/(mn + mDM)

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

�H = �1 + �2 + 2�3

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

m2DM

= m21 +1

2�Hv

2SM

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

�SI ⇠ �2Hµ2m2

n

m4hm2

DM

AAACtHichVFNb9NAEH01X8V8NIULEheLqIhTNImiAj1VwKEcEG1D2kp1Y9mbTbrqrm3ZTqRg+Q/wBzhwAgkhxJlfwIU/wKHiCgfEsUhcODB2ghBChVntzpu382Znd4NYqzQjOpyzTpw8dfrM/Fn73PkLFxdqi5e20miUCNkVkY6SncBPpVah7GYq03InTqRvAi23g4O75f72WCapisJH2SSWe8YfhmqghJ8x5dUeukGk++nEsMttN1VD43t5537B0Diu5kp9JtaKXstxB4kvcteMGBsv7LWK3Hj7vTYH+b0HnFHYhVerU6NFpTl/g2aj8lTHzNaj2iu46COCwAgGEiEyxho+Uh67aIIQM7eHnLmEkar2JQrYrB1xluQMn9kDXocc7c7YkOOyZlqpBZ+ieSasdLBEH+g1HdF7ekNf6MextfKqRtnLhH0w1crYW3hypfP9vyrDPsP+b9U/e84wwK2qV8W9xxVT3kJM9ePHT486K5tL+XV6QV+5/+d0SO/4BuH4m3i5ITefweYP+PXKzvFgq9Vothu3N9r11Tuzr5jHVVzDDX7vm1jFGtbR5XPf4iM+4bO1bLmWsOQ01ZqbaS7jD7PCnwjoqQs=

Direct Detection Constraint (Scalar DM)

14

0 < m1 < 50 GeV

m1 > 50 GeV

Xenon1T (2018)

20 40 60 8010-11

10-10

10-9

10-8

10-7

10-6

mDM (GeV)

SI(pb)

Ruled out!

A small dark matter coupling is needed!

(A small m1 is ruled out!)

�H = �1 + �2 + 2�3

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

m2DM

= m21 +1

2�Hv

2SM

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

Two DM candidates

•A neutral component of the inert scalar.

•The lightest right-handed neutrino.The direct detection constraint is stringent.H (or A) boson should be the lightest state.

15

Fermion DM (1)

16

Masses for Z2 odd particles

m±

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mA

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cHuqZLuqOXT2s14hpNLXX2Rosr/PLQ4cjK07csh32EvXfWl5oj

VDATa7VYux8jzVeYLX7t79HDyuzyRGOSzuie9Z/SLV3xC9zao/l

vSSwfQ+YPeOty5vNgLaeomqItadm5hfZXJDGKcUxxvwuYw28so

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it>

mH

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cZbgDIPRfV53ebfRQD3e12pGCdviWxyeITMzGKUHuqEXuqdbeq

KPX2tVkxo1LRX2Zp0rgmLv8eDy278sl32MvW/Wn5pj7CCXaLVZ

e5AgtVdYdX758ORleXpptDpGF/TM+s/pke74BV751bpcFEunkPk

Dvrqc+T1Y1RRVV/RFPTsz2/iKdgxhBOPc7ynMYB4LKPC9BzjDF

a5T79KwNCaN11OlVIMzgB8mqZ89R5Fe</latexit>

Chargedscalar

CP-oddscalar

CP-evenscalar

MN

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

Right-handed neutrino

There is no restriction on scalar masses!

(The charged scalar can be light.)

DM

DM

SM

SM

DM annihilation

N1

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

N1

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

Fermion DM (2)

The direct detection constraint is not relevant!

(The fermion DM does not couple to the SM Higgs at tree level!)

The charged scalar can be lighter than neutral component.

Assumption: 100% DM

17

Scalar VS Fermion DMScalar DM Fermion DM

18

Two DM candidates

•A neutral component of the inert scalar

•The lightest right-handed neutrinoThe direct detection constraint is not relevant.

The direct detection constraint is stringent.H (or A) boson should be the lightest state.

The charged scalar can be lighter than neutral component.

19

Two DM candidates

•A neutral component of the inert scalar

•The lightest right-handed neutrinoThe direct detection constraint is not relevant.

The direct detection constraint is stringent.H (or A) boson should be the lightest state.

The charged scalar can be lighter than neutral component. However, Yukawa interactions with SM leptons are sources of

lepton flavor violation processes. (Discuss later) 20

SM + additional SU(2)w doublet + 3 right-handed neutrinos can explain following phenomena:・Dark matter

・Neutrino masses

The inert (scalar) dark matterThe lightest right-handed neutrino

[E. Ma (2006)]

Scotogenic Model

21

DM

DM

SM

SM

DM annihilation

Neutrino massesNeutrino masses are generated radiatively!

22

Lint �1

2(MN)ijNiNj

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

+(YijL eSNj + h.c.)

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

Yukawa interaction and Majorana mass

Lint � �3(H†S)2 + h.c.

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

Higgs-scalar doublet interaction hHi

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

hHi


H0

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

H0


⌫i

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

⌫j

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

Nk

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

�3

<latexit sha1_base64="atz8+bhMSezpMrw6mkYRFIpyyZ

4=">AAACfXichVFLbhpBEH1Mfs7kA443SN4gI6wsolENAYOyQs7GS/8ASwahmaGNR/R8NDMgEWQfwBfwwitbiSwrii/hTS

6QBUeIsiRSNpbsYiCKsiCpVndVv65X/bra9KUdRkSjhPLg4aPHTxaeqs+ev3iZTC2+qoVeL7BE1fKkF+yZRiik7YpqZEdS

7PmBMBxTirrZfT85r/dFENqeuxsNfNF0jI5rH9iWETHUSqUbpifb4cBhN1Qbkplto/VWPWqlsqTRWrGglzOkFUkv60UO8kW

dKJ/RNYoti5lteqlLNNCGBws9OBBwEXEsYSDksQ8dBJ+xJoaMBRzZ8bnAEVTm9jhLcIbBaJfXDu/2Z6jL+0nNMGZbfIvkG

TAzgxx9oysa01f6TN/pdm6tYVxjomXA3pxyhd9KnqR3fv2X5bCPcPiH9U/NEQ5QjrXarN2PkckrrCm//+F0vPNuOzdcpQv

6wfrPaUQ3/AK3/9P6tCW2z6DyB/zucmZ+UMtrekErbBWylfXZVyxgGSt4zf0uoYINbKLK9x7jI77gOnGn5JQ3ijZNVRIzzh

L+MqV0D6DWk8I=</latexit>

Yik

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

Ykj

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

23

hHi


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GLmA

EwEJZ

ATcjz

EjP0

ETPJN

BE2cE

JGhU

cDNIM

Sgwa

wPA2Z

3Bg8G

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gF2tv

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SZDJm

OIUi

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hBhTA

ZAMA

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late

xit>

One-loop suppression!

Thanks to the one-loop suppression, tiny neutrino masses are generated with TeV scale Majorana masses!

e.g.)�3 = 0.01

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

M ⇠ 1TeV

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

m⌫ ⇠ 1eV

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

[E. Ma 2006]

Neutrino masses

Y ⇠ O(0.1)

AAACi3ichVHPSxtBFP7cVqvrr1QvgpfQoNhLeNsKrdKDKII3EzVqMRJ210kcnP3B7iQQl/wD0nsPniyUUrz12t566T/Qg39C6VHBiwdfNgtFpe1bdt4337zvzTczTqhkrIku+oxHj/sHngwOmcMjo2PjuacT23HQjFxRcQMVRLuOHQslfVHRUiuxG0bC9hwldpyjle76TktEsQz8Ld0Oxb5nN3xZl66tmarlZqtOoA7itscpMd/mq7H08lXP1oeurZL1zhwVredmp5YrUJHSyD8EVgYKyKIU5D6higMEcNGEBwEfmrGCjZi/PVgghMztI2EuYiTTdYEOTNY2uUpwhc3sEY8Nnu1lrM/zbs84Vbu8i+I/YmUeM/STPtMl/aBz+kU3f+2VpD26XtqcnZ5WhLXxk6nN6/+qPM4ah39U//SsUcfr1Ktk72HKdE/h9vSt4/eXm4sbM8ksfaDf7P+MLug7n8BvXbkfy2LjFCY/gHX/uh+C7RdFa764UJ4vLC1nTzGIaTzDHN/3KyxhDSVUeN93+IKv+GaMGi+NReNNr9ToyzSTuBPG6i1WVpdq

Lepton Flavor Violation (LFV)

0e

)/BR

exp(->e

)

LFV constraint can be evaded with small Yukawa couplings!A correct DM abundance is obtained by coannihilation

with the charged scalar.

In the SM, LFV is generated at one-loop which is suppressed by tiny neutrino masses.

5

η+

η+

Ni

"α

"β

γ

Ni "β

η+

"α

"β

γ

"αNi

η+"α

"β

γ

FIG. 1: 1-loop Feynman diagrams leading to #α → #βγ.

III. ANALYTICAL RESULTS

In this section we present our analytical results for the LFV processes #α → #βγ, #α → 3 #β and

µ− e conversion in nuclei. Before we proceed to the analytical discussion a comment is in order. It

is well-known that the rates for LFV processes get greatly enhanced in models with right-handed

neutrinos at the electroweak scale [34–42]. This is due to the fact that the GIM suppression at

work in the SM contribution is spoiled by the mixing between left- and right-handed neutrinos.

One could naively think that this is also the case in the scotogenic model. However, the unbroken

Z2 symmetry forbids this mixing, (see footnote 2), and thus the enhancement in the W − ν loops

is not present. We will show that the enhancement is still possible, but with η±−N loops instead.

A. #α → #βγ

The most popular searches for LFV have focused on the radiative process #α → #βγ. This is

described by the effective Lagrangian

Leff =(µβα

2

)

#βσµν#αFµν , (12)

where µβα is a transition magnetic moment. It proves convenient to define it in terms of the

dipole form factor AD as µβα = emαAD/2, where terms proportional to mβ have been neglected

and e is the electromagnetic coupling, related to the electromagnetic fine structure constant as

αem = e2/(4π). In the model under consideration, AD gets contributions at the 1-loop level from

the Feynman diagrams in Fig. 1. They lead to the following expression

AD =3∑

i=1

y∗iβyiα

2(4π)21

m2η+F2 (ξi) , (13)

H+

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

H+

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

Yi↵

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

Y�i

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

24[arXiv:1312.2840]

[SPheno 3.1: arXiv:1104.1573]

Fermion DM (3)

25

Scotogenic Model

・Dark matter

・Neutrino massesRight-handed neutrino

hHi


hHi


H0


H0


⌫i


⌫j


Nk


�3

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

Yik


Ykj


DM

DM

SM

SM

SM + additional SU(2)w doublet + 3 right-handed neutrinos can explain following phenomena:

26

The inert (scalar) dark matterThe lightest right-handed neutrino

Summary of Scotogenic Model

•The minimal scotogenic model can explain the DM and tiny neutrino masses.•The lightest neutral inert scalar or the right-handed neutrino can be a DM candidate.•In the scalar DM scenario, the direct detection constraint is stringent.•In the fermion DM scenario, LFV processes give a stringent constraint (depending the size of Yukawa coupling).

27

Outline・Minimal Scotogenic Model

・A First-Order Electroweak Phase Transition

・Results

28

First-order phase transition proceeds through bubble nucleation.

Three sources of the Gravitational Wave:

Bubble collisions

Sound Waves of the plasma

Turbulence of the plasma

First-order Phase Transitions

Tunneling!

[Kosowski et al. 1992]

[Hindmarsh et al. 2014]

[Kamionkowski et al. 1993]29

Detections of Gravitational Wave (GW)

http://gwplotter.com 30

31

Electroweak Phase Transition (EWPT)

•EWPT in the SM is not of first order.

•EWPT in the inert doublet model can be of strong first order.

[M. LAINE (2000)]

[arXiv:1204.4722]

[arXiv:9510020]

The scalar potential

V = �SM

✓|H|2 �

v2SM

2

◆2+ m21|S|2 + �1|H|2|S|2


+�2|H†S|2 + [�3(H†S)2 + h.c.] + �S|S|4


SM Higgs potential

32

S : SU(2)W doublet




The tree level potential is same as SM.

How is the strength of the phase transition changed?

�SM

4�4

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

M2(T )

2�2

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

Ve↵ =M2(T )

2�2 � ET�3 +

�SM

4�4

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

Thermal fluctuation

�ET�3

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

Potential barrier comes from bosons!(Matsubara zero-modes)

Standard Model: SU(2)W ⇥ U(1)Y

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

This model: SU(2)W ⇥ U(1)Y

AAACiHichVE9TxtBEH2+EOIcX07SRKKxsIxMY40tSySpLNJQ+oPDINuy7o6FrLgv3a0tORY/IPkDKVIFKYqiFLRJnSZ/gIKfgChBoqFg7uwoipBhVrsz+3be7NtZK3BkpIjOUtqjmcezT9JP9bn5hcWlzLPn25HfD21h2L7jhzuWGQlHesJQUjliJwiF6VqOaFmHb+Pz1kCEkfS9LTUMRNc1Dzy5L21TMdTL5DqW7+xFQ5fdSG8ahfJar9VR0hVR1iiU1nq7+hFnUbFMsWXvBqVi4imHidX8zDd0sAcfNvpwIeBBcezARMSjjRIIAWNdjBgLOZLJucARdOb2OUtwhsnoIa8HvGtPUI/3cc0oYdt8i8MzZGYWeTql73RJf+gHndPN1FqjpEasZcjeGnNF0Fv6+LJ5/SDLZa/w7h/rXs0K+3iVaJWsPUiQ+BX2mD94/+my+aaRH63SMV2w/i90Rr/5Bd7gyv5aF43P0PkD/nY5Oz3YLhdLlWKlXslVNyZfkcYyVlDgfq+jik3UYPC9H3CCn/il6Rpp69rrcaqWmnBe4D/TNm4Bo2CVwA==

+ one scalar doublet

A Potential BarrierThermal effective potential at one-

loop order

�

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33

Overview of Calculation Method

Quantum and Thermal effects

GW spectrum

Solve bounce eq.

Fix a model

Bubble dynamicsBubble wall velocity:

Efficiency factor:

etc..

34

Important parameters for GWGW amplitude is related to two important parameters.

Vacuum energy difference:

Duration of phase transition:

Vacuum decay rate

Linde.(1983)

Bubble nucleation rate per unit time per unit volume

Tunneling occurs at

35

GW amplitude

Quadra-pole formula:

Bubble size at collision:

Bubble volume

Large vacuum energy and long-duration enhance the GW amplitude.⌦GW ⇠

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1 + ↵

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efficiency factor:

36

EGW ⇠Z

dtPGW ⇠ ��1PGW

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The Scalar Potential

V = �SM

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SM Higgs potential

S : SU(2)W doublet




No couplings between SM Higgs and the additional scalar!

m1 ! 1

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S is heavy so that it does not contribute to the thermal effective potential. 37

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Effective Potential and Tunneling Rate

39

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observable gravitational waves in minimal scotogenic modelseminar/pdf_2020_zenki/... · 2020. 7....

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