Pseudo-Nambu-Goldstone dark matterfrom non-Abelian gauge symmetry
Yoshiki Uchida( South China Normal University 华南师范大学 )Collaborators：
Hajime Otsuka( Kyushu U. )Takashi Shimomura ( Miyazaki U. )Koji Tsumura( Kyushu U. )Naoki Yamatsu( National Taiwan U. )Based on Phys. Rev. D 106 (2022) 11, 115033 [2210.08696]“Kashiwa Dark Matter Symposium 2023” @ Univ. of Tokyo, Kashiwanoha Campus [hybrid]
2023/12/05-12/08

Pseudo-Nambu-Goldstone dark matterfrom non-Abelian gauge symmetry
Yoshiki Uchida( South China Normal University 华南师范大学 )Collaborators：
Hajime Otsuka( Kyushu U. )Takashi Shimomura ( Miyazaki U. )Koji Tsumura( Kyushu U. )Naoki Yamatsu( National Taiwan U. )Based on Phys. Rev. D 106 (2022) 11, 115033 [2210.08696]

w
Ne

C.W. Chang, K. Tsumura, YU, N Yamatsu,“Pseudo-Nambu-Goldstone Dark Matter in SU(7) Grand Uni cation” [2311.13753]

fi“Kashiwa Dark Matter Symposium 2023” @ Univ. of Tokyo, Kashiwanoha Campus [hybrid]
2023/12/05-12/08

・Unknown matter (Dark Matter) accounts for
26.8% of the total in the universe
・An attractive candidate for a DM is …
WIMP ( Weakly Interacting Massive Particle )・thermally produced in the early universe
・severely constrained by the direct detection

https://www.quora.com/What-is-the-percentage-of-dark-matter-in-the-universe

E. Aprile et al. [XENON],
Phys. Rev. Lett. 131 (2023) no.4, 041003, [2303.14729]

・Unknown matter (Dark Matter) accounts for
26.8% of the total in the universe
・An attractive candidate for a DM is …
WIMP ( Weakly Interacting Massive Particle )・thermally produced in the early universe
・severely constrained by the direct detection

Why is WIMP so constrained by direct detection ?

https://www.quora.com/What-is-the-percentage-of-dark-matter-in-the-universe

E. Aprile et al. [XENON],
Phys. Rev. Lett. 131 (2023) no.4, 041003, [2303.14729]

・Unknown matter (Dark Matter) accounts for
26.8% of the total in the universe
・An attractive candidate for a DM is …
WIMP ( Weakly Interacting Massive Particle )・thermally produced in the early universe
・severely constrained by the direct detection

annihilation ( thermal relic )Why is WIMP so constrained by direct detection ?

DM

DM

SM

SM

https://www.quora.com/What-is-the-percentage-of-dark-matter-in-the-universe

scattering ( direct detection )E. Aprile et al. [XENON],
Phys. Rev. Lett. 131 (2023) no.4, 041003, [2303.14729]

・Unknown matter (Dark Matter) accounts for
26.8% of the total in the universe
・An attractive candidate for a DM is …
WIMP ( Weakly Interacting Massive Particle )・thermally produced in the early universe
・severely constrained by the direct detection

annihilation ( thermal relic )Why is WIMP so constrained by direct detection ?

DM

DM

SM

SM

https://www.quora.com/What-is-the-percentage-of-dark-matter-in-the-universe

scattering ( direct detection )inevitably correlated

E. Aprile et al. [XENON],
Phys. Rev. Lett. 131 (2023) no.4, 041003, [2303.14729]

・Unknown matter (Dark Matter) accounts for
26.8% of the total in the universe
・An attractive candidate for a DM is …
WIMP ( Weakly Interacting Massive Particle )・thermally produced in the early universe
・severely constrained by the direct detection

annihilation ( thermal relic )Why is WIMP so constrained by direct detection ?

DM

DM

SM

SM

https://www.quora.com/What-is-the-percentage-of-dark-matter-in-the-universe

scattering ( direct detection )inevitably correlated

E. Aprile et al. [XENON],
Phys. Rev. Lett. 131 (2023) no.4, 041003, [2303.14729]

ti

Stronger DM-SM interac on helps DM to stay longer in thermal bath,leading to, but also increases DM-nucleon scattering.

・Unknown matter (Dark Matter) accounts for
26.8% of the total in the universe
・An attractive candidate for a DM is …
WIMP ( Weakly Interacting Massive Particle )・thermally produced in the early universe
・severely constrained by the direct detection

annihilation ( thermal relic )Why is WIMP so constrained by direct detection ?

DM

DM

SM

SM

https://www.quora.com/What-is-the-percentage-of-dark-matter-in-the-universe

scattering ( direct detection )inevitably correlated

E. Aprile et al. [XENON],
Phys. Rev. Lett. 131 (2023) no.4, 041003, [2303.14729]

ti

Stronger DM-SM interac on helps DM to stay longer in thermal bath,leading to, but also increases DM-nucleon scattering.

To realize viable WIMP model,
we must address this dilemma.

What type of WIMP model would solve this dilemma?

What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)

What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)

annihilation ( thermal relic )DM communicates with SM particles via derivative interaction

DM

DM

SM

SM

scattering ( direct detection )What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)

annihilation ( thermal relic )DM communicates with SM particles via derivative interaction

DM

DM

SM

SM

scattering ( direct detection )Small momentum transfer

What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)
symmetry：

new fields： complex

What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)
symmetry：

Origin for
pNGB mass

new fields： complex

What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)
new fields： complex

symmetry：

Origin for
pNGB mass,：pNGB DM

DM-quark scattering

What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)
new fields： complex

symmetry：

Origin for
pNGB mass,：pNGB DM

DM-quark scattering

Original pNGB DM model has several problems to be solved …

What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)
new fields： complex

symmetry：

Origin for
pNGB mass,：pNGB DM

Problems to be solved①

2023/12/05,,…

are dropped by hands

Kashiwa Dark Matter Symposium 2023

17

What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)
new fields： complex

symmetry：

Origin for
pNGB mass,：pNGB DM

Problems to be solved①,② DW Problem：

2023/12/05,…

are dropped by hands
symmetry () is spontaneously broken

Kashiwa Dark Matter Symposium 2023

18

What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)
new fields： complex

symmetry：

Origin for
pNGB mass,：pNGB DM

Problems to be solved①,② DW Problem：,…

are dropped by hands
symmetry () is spontaneously broken

To construct a feasible model, we need appropriate UV completions
2023/12/05

Kashiwa Dark Matter Symposium 2023

19

What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)

Problems：①,② DW problem, … are dropped by hands

What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)

Problems：①,, … are dropped by hands② DW problem

Solutions： gauged

model

Y. Abe, T. Toma, and K. Tsumura, JHEP 05 (2020) 057, [2001.03954]

fi

N. Okada, D. Raut and Q. Sha , Phys. Rev. D 103 (2021) no.5, 055024 [2001.05910]

What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)

Problems：①,, … are dropped by hands② DW problem

Solutions： gauged

model

Y. Abe, T. Toma, and K. Tsumura, JHEP 05 (2020) 057, [2001.03954]

fi

N. Okada, D. Raut and Q. Sha , Phys. Rev. D 103 (2021) no.5, 055024 [2001.05910]

What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)

Problems：,①, … are dropped by hands② DW problem

Solutions： gauged

model

Y. Abe, T. Toma, and K. Tsumura, JHEP 05 (2020) 057, [2001.03954]
N. Okada, D. Raut and Q. Sha , Phys. Rev. D 103 (2021) no.5, 055024 [2001.05910]①

fi

The other soft-breaking term are forbidden by

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)

Problems：,①, … are dropped by hands② DW problem

Solutions： gauged

model

Y. Abe, T. Toma, and K. Tsumura, JHEP 05 (2020) 057, [2001.03954]
N. Okada, D. Raut and Q. Sha , Phys. Rev. D 103 (2021) no.5, 055024 [2001.05910]①
The other soft-breaking term are forbidden byfi✔︎What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)

Problems：,①, … are dropped by hands② DW problem

Solutions： gauged

model

Y. Abe, T. Toma, and K. Tsumura, JHEP 05 (2020) 057, [2001.03954]
N. Okada, D. Raut and Q. Sha , Phys. Rev. D 103 (2021) no.5, 055024 [2001.05910]①
The other soft-breaking term are forbidden by
②
fi

✔︎

What type of WIMP model would solve this dilemma?

is embedded ingauge symmetry

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)

Problems：,①, … are dropped by hands② DW problem

Solutions： gauged

model

Y. Abe, T. Toma, and K. Tsumura, JHEP 05 (2020) 057, [2001.03954]
N. Okada, D. Raut and Q. Sha , Phys. Rev. D 103 (2021) no.5, 055024 [2001.05910]①
The other soft-breaking term are forbidden by
②
fi

✔︎✔︎

What type of WIMP model would solve this dilemma?

is embedded ingauge symmetry

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)
Invariant under

Problems：,①, … are dropped by hands② DW problem

Solutions： gauged

model

Y. Abe, T. Toma, and K. Tsumura, JHEP 05 (2020) 057, [2001.03954]
N. Okada, D. Raut and Q. Sha , Phys. Rev. D 103 (2021) no.5, 055024 [2001.05910]①
The other soft-breaking term are forbidden by
②
fi

✔︎✔︎

What type of WIMP model would solve this dilemma?

is embedded ingauge symmetry

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)
Invariant under

Problems：,①, … are dropped by hands② DW problem

Solutions： gauged

model

Y. Abe, T. Toma, and K. Tsumura, JHEP 05 (2020) 057, [2001.03954]
N. Okada, D. Raut and Q. Sha , Phys. Rev. D 103 (2021) no.5, 055024 [2001.05910]

No symmetryfor DM stability①

The other soft-breaking term are forbidden by
②
fi

✔︎✔︎

What type of WIMP model would solve this dilemma?

is embedded ingauge symmetry

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)
Invariant under

Problems：①,, … are dropped by hands② DW problem

Solutions： gauged

model

Y. Abe, T. Toma, and K. Tsumura, JHEP 05 (2020) 057, [2001.03954]
N. Okada, D. Raut and Q. Sha , Phys. Rev. D 103 (2021) no.5, 055024 [2001.05910]

No symmetryfor DM stability①

pNGB DM decays
fi

✔︎✔︎

What type of WIMP model would solve this dilemma?

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)
Invariant under

Problems：①,, … are dropped by hands② DW problem

Solutions： gauged

model

Y. Abe, T. Toma, and K. Tsumura, JHEP 05 (2020) 057, [2001.03954]
N. Okada, D. Raut and Q. Sha , Phys. Rev. D 103 (2021) no.5, 055024 [2001.05910]①

pNGB DM decays
：

fi

✔︎✔︎

What type of WIMP model would solve this dilemma?

gauge fieldC. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

pseudo Nambu-Goldstone Boson Dark Matter (pNGB-DM)
Invariant under

Problems：①,, … are dropped by hands② DW problem

Solutions： gauged

model

Y. Abe, T. Toma, and K. Tsumura, JHEP 05 (2020) 057, [2001.03954]
N. Okada, D. Raut and Q. Sha , Phys. Rev. D 103 (2021) no.5, 055024 [2001.05910]①“ hierarchy problem ”

HigherpNGB DM decays
breaking scale required to make DM long-lived

fi

✔︎✔︎

What type of WIMP model would solve this dilemma?

：gauge fieldBrief Summary● Problems for original pNGB-DM model①,②

DW Problem● Solution : gauged, … are dropped by hands

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

model

①
the only allowed soft-breaking term

Y. Abe, T. Toma, and K. Tsumura,
JHEP 05 (2020) 057, [2001.03954]
N. Okada, D. Raut and Q. Sha ,Phys. Rev. D 103 (2021) no.5, 055024[2001.05910]

symmetry is embedded in gauged②

breaking scale must be much high :Kashiwa Dark Matter Symposium 2023
fi

2023/12/05

32

Brief Summary● Problems for original pNGB-DM model①,②

DW Problem● Solution : gauged, … are dropped by hands

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

model

①
the only allowed soft-breaking term

Y. Abe, T. Toma, and K. Tsumura,
JHEP 05 (2020) 057, [2001.03954]
N. Okada, D. Raut and Q. Sha ,Phys. Rev. D 103 (2021) no.5, 055024[2001.05910]

symmetry is embedded in gauged②

breaking scale must be much high :Goal

UV completion of pNGB-DM model with no large hierarchy

Kashiwa Dark Matter Symposium 2023
fi

2023/12/05

33

Brief Summary● Problems for original pNGB-DM model①,②

DW Problem● Solution : gauged, … are dropped by hands

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

model

①
the only allowed soft-breaking term

Y. Abe, T. Toma, and K. Tsumura,
JHEP 05 (2020) 057, [2001.03954]
N. Okada, D. Raut and Q. Sha ,Phys. Rev. D 103 (2021) no.5, 055024[2001.05910]

symmetry is embedded in gauged②

breaking scale must be much high :Goal

UV completion of pNGB-DM model with no large hierarchy
We want to explain the origin of pNGB mass,
and want a stable DM so that we don’t need to introduce large hierarchy

Kashiwa Dark Matter Symposium 2023
fi

2023/12/05

34

Brief Summary● Problems for original pNGB-DM model①,②

DW Problem● Solution : gauged, … are dropped by hands

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

model

①
the only allowed soft-breaking term

Y. Abe, T. Toma, and K. Tsumura,
JHEP 05 (2020) 057, [2001.03954]
N. Okada, D. Raut and Q. Sha ,Phys. Rev. D 103 (2021) no.5, 055024[2001.05910]

symmetry is embedded in gauged②

breaking scale must be much high :Goal

UV completion of pNGB-DM model with no large hierarchy
Hint : SM scalar sector

Kashiwa Dark Matter Symposium 2023
fi

2023/12/05

35

Brief Summary● Problems for original pNGB-DM model①,②

DW Problem● Solution : gauged, … are dropped by hands

model

①
the only allowed soft-breaking term

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

Y. Abe, T. Toma, and K. Tsumura,
JHEP 05 (2020) 057, [2001.03954]
N. Okada, D. Raut and Q. Sha ,Phys. Rev. D 103 (2021) no.5, 055024[2001.05910]

symmetry is embedded in gauged②

breaking scale must be much high :Goal

UV completion of pNGB-DM model with no large hierarchy
Hint : SM scalar sectorfi

accidental global symmetry :Brief Summary● Problems for original pNGB-DM model①,②

DW Problem● Solution : gauged, … are dropped by hands

model

①
the only allowed soft-breaking term

C. Gross, O. Lebedev, and T, Toma
Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]

Y. Abe, T. Toma, and K. Tsumura,
JHEP 05 (2020) 057, [2001.03954]
N. Okada, D. Raut and Q. Sha ,Phys. Rev. D 103 (2021) no.5, 055024[2001.05910]

symmetry is embedded in gauged②

breaking scale must be much high :Goal

UV completion of pNGB-DM model with no large hierarchy
Hint : SM scalar sectorfi

accidental global symmetry :: custodial sym.

Our ModelGoal

2023/12/05

UV completion of pNGB-DM model with no large hierarchy

Kashiwa Dark Matter Symposium 2023

39

Goal

UV completion of pNGB-DM model with no large hierarchy
H. Otsuka, K. Tsumura, YU, N. Yamatsu, Phys. Rev. D 106 (2022) 11, 115033 [2210.08696]

We consider
and introduce

2023/12/05

symmetry,

under

Kashiwa Dark Matter Symposium 2023

40

Goal

UV completion of pNGB-DM model with no large hierarchy
H. Otsuka, K. Tsumura, YU, N. Yamatsu, Phys. Rev. D 106 (2022) 11, 115033 [2210.08696]

We consider
and introduce

symmetry,

under

Mass terms

4-point self-int.

4-point int.

2023/12/05

Kashiwa Dark Matter Symposium 2023

41

has “ Dark custodial symmetry ”
H. Otsuka, K. Tsumura, YU, N. Yamatsu, Phys. Rev. D 106 (2022) 11, 115033 [2210.08696]

We consider
and introduce

symmetry,

under

Mass terms

4-point self-int.

4-point int.

2023/12/05

Kashiwa Dark Matter Symposium 2023

42

has “ Dark custodial symmetry ”
H. Otsuka, K. Tsumura, YU, N. Yamatsu, Phys. Rev. D 106 (2022) 11, 115033 [2210.08696]

We consider
and introduce

symmetry,

underInvariant underglobal “ Dark custodial symmetry ”(

2023/12/05)

has “ Dark custodial symmetry ”
H. Otsuka, K. Tsumura, YU, N. Yamatsu, Phys. Rev. D 106 (2022) 11, 115033 [2210.08696]

We consider
and introduce

symmetry,

under

Explicitly breaks
global “ Dark custodial symmetry ”

2023/12/05()

has “ Dark custodial symmetry ”
H. Otsuka, K. Tsumura, YU, N. Yamatsu, Phys. Rev. D 106 (2022) 11, 115033 [2210.08696]

We consider
and introduce

symmetry,

under

Explicitly breaks
global “ Dark custodial symmetry ”
Even after
2023/12/05&, the exact

remains unbroken

ensures stability of pNGB-DMc.f.) T. Abe and Y. Hamada,
PTEP 2023 (2023) no.3, 033B04, [2205.11919]

H. Otsuka, K. Tsumura, YU, N. Yamatsu,
Phys. Rev. D 106 (2022) 11, 115033 [2210.08696]

Global symmetry breaking pattern

,

under

● Approximate symmetry
Total NGBs

＃ of broken generators = (3+3) - 1 = 5● Exact symmetry
would-be NGBs

＃ of broken generators = (3+1) - 1 = 3＃ of pNGB is 2 ( = 5 - 3 )2023/12/05

complex pNGB with

Kashiwa Dark Matter Symposium 2023

charge46

Benchmark

scalar mass :mixing angle :Reproduce

H. Otsuka, K. Tsumura, YU, N. Yamatsu,
Phys. Rev. D 106 (2022) 11, 115033 [2210.08696]

Benchmark

scalar mass :mixing angle :Direct detection

Higgs invisible decay

also becomes DM
(
)

ILC
CEPC

ATLAS
HL-LHC

Reproduce

H. Otsuka, K. Tsumura, YU, N. Yamatsu,
Phys. Rev. D 106 (2022) 11, 115033 [2210.08696]

Benchmark

scalar mass :mixing angle :Direct detection

Higgs invisible decay

also becomes DM
(
)

ILC
CEPC

opens

ATLAS
HL-LHC

Reproduce

H. Otsuka, K. Tsumura, YU, N. Yamatsu,
Phys. Rev. D 106 (2022) 11, 115033 [2210.08696]

Benchmark

scalar mass :mixing angle :Direct detection

Higgs invisible decay

also becomes DM
(
)

ILC
CEPC

opens

ATLAS
HL-LHCescape the direct detection
and reproduce a correct DM relic

Reproduce

H. Otsuka, K. Tsumura, YU, N. Yamatsu,
Phys. Rev. D 106 (2022) 11, 115033 [2210.08696]

Summary• In the original abelian pNGB DM model, particular soft-breaking
terms are included, and their origins are not addressed.

• UV completed models are proposed, but all of them predict
decaying DM. In order to make DM long-lived, we must
introduce large hierarchy in symmetry breaking scales.
• We construct pNGB-DM model with non-abelian gauge
symmetry. Unbroken dark custodial symmetry ensure stabilityof pNGB DM. We don’t need to introduce large hierarchy.

2023/12/05

Kashiwa Dark Matter Symposium 2023

51

Back Up

2023/12/05

Kashiwa Dark Matter Symposium 2023

52

Goal

UV completion of pNGB-DM model with no large hierarchy

But, this is not the end of the story …
Three-point breaking term may spoil the cancellation● Two-point breaking term

T. Abe and Y. Hamada, [2205.11919]

Origin of pNGBs’ mass

● Three-point breaking term

Our Model

Origin of pNGBs’ mass & interactions

We must make sure DM-nucleon scattering is suppressed enough53

Soft breaking terms● Soft-breaking = Quadratic

C. Gross, O. Lebedev, and T, Toma, Phys. Rev. Lett. 119 (2017) 19, 191801, [1708.02253]● Soft-breaking = Quadratic + tadpole

V. Barger, P. Langacker, M. McCaskey, M. Ramsey-Musolf and G. Shaughnessy, Phys. Rev. D 79 (2009), 015018, [0811.0393]
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Based on Idegawa-san’s slide