Neutral naturalnessand (SIMP) dark matter
Hyun Min Lee
Chung-Ang University, Korea

Beyond the Standard Model
4th Kvali IPMU-IPPP-KEK-KIAS Workshop
Ikaho Onsen, Japan, Oct 1-4, 2018

Outline• Motivation• SIMP paradigm• Some stories on dark mesons• Conclusions

New physics beyond SM• New symmetry for solving the hierarchy problem
predicts new particles at weak scale.

No direct hint yet for new physics.

• Other good motivations for new physics: dark

matter, QCD axion, new forces, origin of baryon
asymmetry, neutrino interactions, etc.
But, we don’t have a good understanding
on how new physics is realized.
Extensive searches are needed.

DM number

WIMP dark matter
Dark matter abundance isdetermined by freeze-out.

time

DM

SM

DM

SM

[Lee,Weinberg(1977)]

Weak interaction with 100GeV~1TeV mass:
2⌦DM h = 0.1✓

1 pb · ch A vi◆

Predictive for direct, indirect and collider detections!

WIMP in challenge

No direct evidence for WIMP yet.

Light dark matter
Below typical WIMP masses: 1 keV . mDM . 10 GeV<latexit sha1_base64="gIXZRBSTkt5Uu5XeowGRRQbpMto=">AAACHnicbVDLSgMxFM3UV62vqks3wSK4kDIj4mMjBQXdCBXsAzrDkElv29BkZkgyQhn6J278FTcuVARX+jem7YDaeiBwOOdcbu4JYs6Utu0vKzc3v7C4lF8urKyurW8UN7fqKkokhRqNeCSbAVHAWQg1zTSHZiyBiIBDI+hfjPzGPUjFovBOD2LwBOmGrMMo0Ubyi8eOe5C6UuA+1IcuB6UUE1j4Y+3y5kdy7Cx4ZYLYL5bssj0GniVORkooQ9UvfrjtiCYCQk05Uarl2LH2UiI1oxyGBTdREBPaJ11oGRoSAcpLx/cN8Z5R2rgTSfNCjcfq74mUCKUGIjBJQXRPTXsj8T+vlejOqZeyME40hHSyqJNwrCM8Kgu3mQSq+cAQQiUzf8W0RySh2lRaMCU40yfPktph+azs3B6VKudZG3m0g3bRPnLQCaqga1RFNUTRA3pCL+jVerSerTfrfRLNWdnMNvoD6/Mb4IOhzw==</latexit>

2

2(Fermion DM)~q(mDM v)ER ==. keV : Small recoil energy
2mN
2mN<latexit sha1_base64="ATPh6cKNYiUx7dMu0/Xm+F0oFeQ=">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</latexit>

Challenging for lower detector threshold.

Status of DM models

US Cosmic Visions, 1707.04591

Light dark matter models have started being developed.
New production mechanisms call for detection strategies.

Beyond WIMP

[Spergel, Steinhardt, 2000; Weinberg et al, 2013]• Core-cusp problem: galaxy rotation curves favor cored
DM profile, in conflict with N-body simulations.

Baryons (SN feedback) erase small structures, butmany dwarf galaxies are lack of baryons.
self

May need Self-Interacting Dark Matter!
<latexit sha1_base64="QWQcRH+cfO9JIccebpgwxmZv8RE=">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</latexit>

mDM⇠ 1cm2 /s

cf. missing satellites, too-big-to-fail problems.

How to approach new physics• New physics not far from weak scale. [Chacko et al, 2005]“Neutral naturalness”

neutral top partners[W.Bardeen, 1995;• New physics couples too weakly. Shaposhnikov,
Zenhausern, 2008;“Scale invariance”
MP2 ⇠ ⇠h 2 i,<latexit sha1_base64="e5fTVyBZIaQOA5yXcPd7LIRzw7c=">AAACC3icbVDNSgMxGMzWv1r/qh69BIvgQcpuqX8XKXjxIlRwbaG7Ldk024Ym2SXJimXpA3jxVbx4UPHqC3jzbUy3PWjrQGAyMx/JN0HMqNK2/W3lFhaXllfyq4W19Y3NreL2zp2KEomJiyMWyWaAFGFUEFdTzUgzlgTxgJFGMLgc+417IhWNxK0exsTnqCdoSDHSRuoUS9ftSqfuKcqh90Chx5DoMeLFfdqueDK7HJmUXbaPqyeODQ3JAJ1ZUgJT1DvFL68b4YQToTFDSrUcO9Z+iqSmmJFRwUsUiREeoB5pGSoQJ8pPs2VG8MAoXRhG0hyhYab+nkgRV2rIA5PkSPfVrDcW//NaiQ7P/JSKONFE4MlDYcKgjuC4GdilkmDNhoYgLKn5K8R9JBHWpr+CKWFu5XniVsrnZeemWqpdTNvIgz2wDw6BA05BDVyBOnABBo/gGbyCN+vJerHerY9JNGdNZ3bBH1ifPxakmpU=</latexit>

Ghilencea, HML, 2018]

m2H ⇠

2
h
i:
H

<latexit sha1_base64="EQu70EGer4m90nap3KYeugHIk54=">AAACFnicbVDLSgMxFM34rPU16tJNsAiuykypz4UU3HRZwdpCpx0ymUwbmmSGJCOUoX/hxl9x40LFrbjzb0ynXWjrhcC559zDzT1BwqjSjvNtLS2vrK6tFzaKm1vbO7v23v69ilOJSRPHLJbtACnCqCBNTTUj7UQSxANGWsHwZqK3HohUNBZ3epSQLkd9QSOKkTaUb5d5r+LXPUU59JixhcjP6l4yoGPTij4jE9yreDJvrny75JSd0+qZ60AD8oLuPCiBWTV8+8sLY5xyIjRmSKmO6yS6myGpKWZkXPRSRRKEh6hPOgYKxInqZvldY3hsmBBGsTRPaJizvx0Z4kqNeGAmOdIDNa9NyP+0Tqqji25GRZJqIvB0UZQyqGM4CQmGVBKs2cgAhCU1f4V4gCTC2kRZNCEsnLwImpXyZdm9rZZq17M0CuAQHIET4IJzUAN10ABNgMEjeAav4M16sl6sd+tjOrpkzTwH4E9Znz+TDp/F</latexit>• New dynamics of early cosmology.
“Cosmological relaxion”<latexit sha1_base64="j/ML02/AwjmHKHg/mkdKLAv7p3U=">AAACDHicbVDLSsNAFJ3UV62vqEs3g1UQlJKU+gSl4KbLCtYWmlgm00k7dCYJMxOhhPyAG3/FjQsVt36AO//GSduFth64cDjnXu69x4sYlcqyvo3c3PzC4lJ+ubCyura+YW5u3ckwFpg0cMhC0fKQJIwGpKGoYqQVCYK4x0jTG1xnfvOBCEnD4FYNI+Jy1AuoTzFSWuqYe/y+3ElqR4kjOCS+n6aXTsRhptYOYc+J+vQCdsyiVbKOKye2BTUZAdrTpAgmqHfML6cb4piTQGGGpGzbVqTcBAlFMSNpwYkliRAeoB5paxogTqSbjL5J4b5WutAPha5AwZH6eyJBXMoh93QnR6ovp71M/M9rx8o/cxMaRLEiAR4v8mMGVQizaGCXCoIVG2qCsKD6Voj7SCCsdIAFHcLMy7OkUS6dl+ybSrF6NUkjD3bALjgANjgFVVADddAAGDyCZ/AK3own48V4Nz7GrTljMrMN/sD4/AGLWZoj</latexit><latexit sha1_base64="MLAhd2FyEYpeCCpUVpF7Uhemu40=">AAAB/3icbVC7TsMwFHXKq5RXgIGBxaJCYooSVF4LqsTSsUiEVmqiyHGc1qrjRLaDqKIs/AoLAyBWfoONv8F9DNByJEtH55yr63vCjFGpbPvbqCwtr6yuVddrG5tb2zvm7t69THOBiYtTlopuiCRhlBNXUcVINxMEJSEjnXB4M/Y7D0RImvI7NcqIn6A+pzHFSGkpMA88psMRCoqWlw1o6TEGvUdqBWbdtuyzxrljQ00mgM48qYMZ2oH55UUpzhPCFWZIyp5jZ8ovkFAUM1LWvFySDOEh6pOephwlRPrF5IASHmslgnEq9OMKTtTfEwVKpBwloU4mSA3kvDcW//N6uYov/YLyLFeE4+miOGdQpXDcBoyoIFixkSYIC6r/CvEACYSV7qymS1g4eZG4p9aV5dw26s3rWRtVcAiOwAlwwAVoghZoAxdgUIJn8ArejCfjxXg3PqbRijGb2Qd/YHz+AO7rlio=</latexit>

H

⌧ ⇠.

[D.E. Kaplan et al, 2015;
A. Hook, 2016]

m2H,e↵ = ±m2H + g :scanning stops at<latexit sha1_base64="frrs65NKgQwZ70FpjzU1tN9ctio=">AAACBXicbVDLSsNAFJ3UV62vqEsRBovgKiSlvjZScNNlBWMLTQyT6aQdOpOEmYlQQlZu/BU3LlTc+g/u/Bunj4W2HrhwOOde7r0nTBmVyra/jdLS8srqWnm9srG5tb1j7u7dySQTmLg4YYnohEgSRmPiKqoY6aSCIB4y0g6H12O//UCEpEl8q0Yp8TnqxzSiGCktBeahlw6oJymHHk+hFwmEc35fC5pF3i+swKzaln1aP3NsqMkE0JknVTBDKzC/vF6CM05ihRmSsuvYqfJzJBTFjBQVL5MkRXiI+qSraYw4kX4+eaOAx1rpwSgRumIFJ+rviRxxKUc81J0cqYGc98bif143U9GFn9M4zRSJ8XRRlDGoEjjOBPaoIFixkSYIC6pvhXiAdBRKJ1fRISy8vEjcmnVpOTf1auNqlkYZHIAjcAIccA4aoAlawAUYPIJn8ArejCfjxXg3PqatJWM2sw/+wPj8AUDZmIo=</latexit>

m2H
⇠⌥
.
g

True solutions might be combinations thereof.

Naturalness and dark QCD[Chacko,Goh,Harnik, 2005]• Double the SM gauge groups with twin Higgs and matter.
[SU (3)A ⇥ SU (2)A ] ⇥ [SU (3)B ⇥ SU (2)B ] ⇥ Z2✓
<latexit sha1_base64="fnwlD0Rx2yzzXJel8nGOiR4yfic=">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</latexit>

HA
HB

◆

0

1

0
1 B
0 C
B
C ei⇡/f
=p @
0 A
2
f

Z 2 : g A = g B , H A $ HB

: SU(4)

SU(3) “15 - 8 = 7 pNGBs”

Higgs = pBGBs on SU (4)/SU (3)• Neutral top partners cancel quadratic divergences of
Higgs mass at one-loop.
LY =yA HA qA ucAm2h =“Neutral naturalness”

yB HB qB ucB , yA = yB .

32
(y4⇡ 2 A2yB)⇤2 = 0.

WIMP from neutral partners[Craig et al; March-Russell et al, 2015]• U(1) loops to Higgs mass is about 100GeV for Λ ~ 5 TeV.
Y

No need of twin U(1)Y. (Also to avoid too large Neff.)
Similar arguments apply to twin light fermions.
“Fraternal” twin Higgs:,<latexit sha1_base64="mbn5Zw/UqD0oyvJgvjqc7gK/B+U=">AAAB53icbVBNS8NAEJ3Ur1q/qh69LBbBg5REBPUiBS8eWzC20Iay2U7btZtN2N0IJfQXePGg4tW/5M1/47bNQVsfDDzem2FmXpgIro3rfjuFldW19Y3iZmlre2d3r7x/8KDjVDH0WSxi1QqpRsEl+oYbga1EIY1Cgc1wdDv1m0+oNI/lvRknGER0IHmfM2qs1Djrlitu1Z2BLBMvJxXIUe+Wvzq9mKURSsME1brtuYkJMqoMZwInpU6qMaFsRAfYtlTSCHWQzQ6dkBOr9Eg/VrakITP190RGI63HUWg7I2qGetGbiv957dT0r4KMyyQ1KNl8UT8VxMRk+jXpcYXMiLEllClubyVsSBVlxmZTsiF4iy8vE/+8el31GheV2k2eRhGO4BhOwYNLqMEd1MEHBgjP8ApvzqPz4rw7H/PWgpPPHMIfOJ8/4HiMgA==</latexit><latexit• Twin taus can be WIMP dark matter.
m⌧ˆ ⇠ y⌧ˆ f ⇠ 100 GeV<latexit sha1_base64="ISG1RHKtjnKL9mRq13/gvO+LlPA=">AAACHHicbZDLSsNAFIYn9VbrLerSzWARXEhJpKBupOBClxXsBZpSJtNJO3QmCTMnQgh9ETe+ihsXKm5cCL6N0zaL2vrDwM93zuHM+f1YcA2O82MVVlbX1jeKm6Wt7Z3dPXv/oKmjRFHWoJGIVNsnmgkesgZwEKwdK0akL1jLH91M6q1HpjSPwgdIY9aVZBDygFMCBvXsquxl3pAA9oAkY09zidN5goMpcx3HO8s8JfEta457dtmpOFPhZePmpoxy1Xv2l9ePaCJZCFQQrTuuE0M3Iwo4FWxc8hLNYkJHZMA6xoZEMt3NpteN8YkhfRxEyrwQ8JTOT2REap1K33RKAkO9WJvA/2qdBILLbsbDOAEW0tmiIBEYIjyJCve5YhREagyhipu/YjokilAwgZZMCO7iycumcV65qrj31XLtOk+jiI7QMTpFLrpANXSH6qiBKHpCL+gNvVvP1qv1YX3OWgtWPnOI/sj6/gXjOaFT</latexit>

twin W/Z +0⌧ˆ⌧ˆ ! ⌫ˆ⌫ˆ, b̂b̂, Z Z<latexit sha1_base64="f5vHbteccyGfpvxkXnP+nOZJTJI=">AAACN3icbZDNSgMxFIUz/lv/qi7dBIvoopQZEdSNFNy4U8Gq2CnlTpq2oZnMkNxRytDHcuNjuBM3LlTc+gam7Qi19ZKQj3PuJckJYikMuu6LMzU9Mzs3v7CYW1peWV3Lr29cmyjRjFdYJCN9G4DhUiheQYGS38aaQxhIfhN0Tvv+zT3XRkTqCrsxr4XQUqIpGKCV6vnz1G8DUh8h6Y2gr0WrjaB19EAHsq8yvw9FvzhUadD7PYv0bteuer7gltxB0UnwMiiQrC7q+We/EbEk5AqZBGOqnhtjLQWNgkney/mJ4TGwDrR41aKCkJtaOvh4j+5YpUGbkbZbIR2ooxMphMZ0w8B2hoBtM+71xf+8aoLNo1oqVJwgV2x4UTORFCPaT5E2hOYMZdcCMC3sWylrgwaGNuucDcEb//IkVPZLxyXv8qBQPsnSWCBbZJvsEY8ckjI5IxekQhh5JK/knXw4T86b8+l8DVunnGxmk/wp5/sHwaqtDA==</latexit>

0[Craig et al, 2015]

SIDM from Dark QCD
Higgs mass from gluon loops“Dark QCD”

Dark light fermions
G=SU(Nf)LxSU(Nf)R

Dark mesons
SU(Nf)V flavor sym.
dark condensate<latexit sha1_base64="fAoMxgyl7roNV903gPG6mg3syDI=">AAACAnicbVDLSsNAFJ3UV62vqDvdDBbBhZakCOpGCm5cVmhsIUnDZDpph84kYWYilFBw46+4caHi1q9w5984bbPQ1gMXzpxzL3PvCVNGpbKsb6O0tLyyulZer2xsbm3vmLt79zLJBCYOTlgiOiGShNGYOIoqRjqpIIiHjLTD4c3Ebz8QIWkSt9QoJT5H/ZhGFCOlpcA8OOPdeuCl1DuFuSc4bImxq5/duh+YVatmTQEXiV2QKijQDMwvr5fgjJNYYYakdG0rVX6OhKKYkXHFyyRJER6iPnE1jREn0s+nN4zhsVZ6MEqErljBqfp7IkdcyhEPdSdHaiDnvYn4n+dmKrr0cxqnmSIxnn0UZQyqBE4CgT0qCFZspAnCgupdIR4ggbDSsVV0CPb8yYvEqdeuavbdebVxXaRRBofgCJwAG1yABrgFTeAADB7BM3gFb8aT8WK8Gx+z1pJRzOyDPzA+fwC2m5Z7</latexit>m2⇡ Tr[⇡ 2 ][Hochberg et al, 2014,2018; Seo, HML, 2015]

Dark mesons: self-interacting in dark ChPT
Massive “dark U(1)” decouples before dark condensate.
Mediator for kinetic equilibrium of dark mesons.

SIMP paradigm

SIMP interplay
DM

DM

DM

DM

DM
2
↵e↵

3
↵e↵

<latexit sha1_base64="BikNA0BQCK6Fl6lBc3FJPsJFEZQ=">AAAB+nicbVDLSsNAFJ3UV62vWJduBovgqiSlULuRghuXFYwtNDFMppN26MwkzEzEEvIrblyouPVL3Pk3Th8LbT1w4XDOvdx7T5QyqrTjfFuljc2t7Z3ybmVv/+DwyD6u3qskk5h4OGGJ7EdIEUYF8TTVjPRTSRCPGOlFk+uZ33skUtFE3OlpSgKORoLGFCNtpNCu+oilY/TQCHNfckjiuAjtmlN33Eaz1YaGzAHdVVIDS3RD+8sfJjjjRGjMkFID10l1kCOpKWakqPiZIinCEzQiA0MF4kQF+fz2Ap4bZQjjRJoSGs7V3xM54kpNeWQ6OdJjterNxP+8QabjyyCnIs00EXixKM4Y1AmcBQGHVBKs2dQQhCU1t0I8RhJhbeKqmBDWXl4nXqPerru3zVrnaplGGZyCM3ABXNACHXADusADGDyBZ/AK3qzCerHerY9Fa8lazpyAP7A+fwA7/JQc</latexit>

DM

DM

DM

DM

DM

DM

✏
LSM

DM
LSM

✏2

2

LSM

DM

LSM

SIMP production• Strongly Interacting Massive Particles (SIMP) in

chemical equilibrium by self-interactions (3→2).
[Carlson et al (1992); Hochberg et al (2014)]
DM

DM

DM

DM

DM
2
↵e↵

3
↵e↵

DM

<latexit sha1_base64="BikNA0BQCK6Fl6lBc3FJPsJFEZQ=">AAAB+nicbVDLSsNAFJ3UV62vWJduBovgqiSlULuRghuXFYwtNDFMppN26MwkzEzEEvIrblyouPVL3Pk3Th8LbT1w4XDOvdx7T5QyqrTjfFuljc2t7Z3ybmVv/+DwyD6u3qskk5h4OGGJ7EdIEUYF8TTVjPRTSRCPGOlFk+uZ33skUtFE3OlpSgKORoLGFCNtpNCu+oilY/TQCHNfckjiuAjtmlN33Eaz1YaGzAHdVVIDS3RD+8sfJjjjRGjMkFID10l1kCOpKWakqPiZIinCEzQiA0MF4kQF+fz2Ap4bZQjjRJoSGs7V3xM54kpNeWQ6OdJjterNxP+8QabjyyCnIs00EXixKM4Y1AmcBQGHVBKs2dQQhCU1t0I8RhJhbeKqmBDWXl4nXqPerru3zVrnaplGGZyCM3ABXNACHXADusADGDyBZ/AK3qzCerHerY9Fa8lazpyAP7A+fwA7/JQc</latexit>

DM

DM

DM

2
h
vi
=
n
h
v
i⌧
Large self-scattering vs small annihilation: e↵DM<latexit sha1_base64="N0huFxqrCOI6+GN3Nn2Gt+7dU1U=">AAAB/XicbVBNSwMxEJ31s9avqnjyEiyCp7IrgnqRghePFVxb6C5LNs22oUl2SbJCWQr+FS8eVLz6P7z5b0zbPWjrg4HHezPJzIszzrRx3W9naXlldW29slHd3Nre2a3t7T/oNFeE+iTlqerEWFPOJPUNM5x2MkWxiDltx8Obid9+pEqzVN6bUUZDgfuSJYxgY6WodhhwjgLN+gJHRaAEsk8l46hWdxvuFGiReCWpQ4lWVPsKeinJBZWGcKx113MzExZYGUY4HVeDXNMMkyHu066lEguqw2K6/hidWKWHklTZkgZN1d8TBRZaj0RsOwU2Az3vTcT/vG5uksuwYDLLDZVk9lGSc2RSNMkC9ZiixPCRJZgoZndFZIAVJsYmVrUhePMnLxL/rHHV8O7O683rMo0KHMExnIIHF9CEW2iBDwQKeIZXeHOenBfn3fmYtS455cwB/IHz+QONWpVq</latexit>

Relic density:⇣ m /35 MeV ⌘3/2
DM,
⌦DM h2 ' 0.1↵e↵<latexit sha1_base64="Jn08iRzcL15GOMNL5DQY8jO5wcM=">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</latexit>

self

mDM

⇠

⇣ 5 ⌘
↵e↵

cf. forbidden channels, coscattering, etc.

1cm2 /gself

SIMP in equilibrium• Equilibriate SIMP kinetic energy by kinetic equilibrium forthe structure formation.

[de Laix et al, 1995; Murayama, HML et al, 2017]

DM

DM

DM

DM
q2
Kscatt =2mDM

Kann ⇠ mDM

DM
3
↵e↵

✏2
LSM

DM

DM

K̇ + 2HK =

T2
⇠
mDM

m2DM HT

3→2

Kinetic equilibrium:
cf. WIMP:<latexit sha1_base64="FS+r0cEHFUWSe/0iIuh3Lm2toGA=">AAACFXicbVDLSsNAFJ34rPUVdelmsAhuLEkR1I0U7EIQoUJjC00sk+mkHTozCTMToYR8hRt/xY0LFbeCO//G6WOhrQcuHM65l3vvCRNGlXacb2thcWl5ZbWwVlzf2Nzatnd271ScSkw8HLNYtkKkCKOCeJpqRlqJJIiHjDTDweXIbz4QqWgsGnqYkICjnqARxUgbqWMf+zXCNILXncyXHCIhcl9RDv1IIpw17it5xidW7SbPO3bJKTtjwHniTkkJTFHv2F9+N8YpJ0JjhpRqu06igwxJTTEjedFPFUkQHqAeaRsqECcqyMZv5fDQKF0YxdKU0HCs/p7IEFdqyEPTyZHuq1lvJP7ntVMdnQUZFUmqicCTRVHKoI7hKCPYpZJgzYaGICypuRXiPjKBaJNk0YTgzr48T7xK+bzs3p6UqhfTNApgHxyAI+CCU1AFV6AOPIDBI3gGr+DNerJerHfrY9K6YE1n9sAfWJ8/a9ifHg==</latexit>1+ T (T ) ,✏2h el vi = 2
mDMD(T ) ⇠ nY

elastic scatt.
(T ) > H

T2
Kann ⇠
mDM

⇣m

DM

T

⌘2

LSM
T E
.
el vY
mDM

✏ > 10(T ) > H

8 1/2
↵e↵

SIMP direct detection• DM-nucleon scattering: cryogenic semi-conductors
e.g. CDMSlite: Ge, Eth=56eV

mDM & 1.6 GeV

mDM v 2 &[Hochberg et al (2015)]<latexit sha1_base64="W2nJF4tnbwzlZ4MufsWf0o/v4C8=">AAACCHicbVDLSsNAFJ34rPUVdelmsAguJCQiPjZSUNCNUMG0hSaEyXTSDp1JwsxEKCFbN/6KGxcqbv0Ed/6N07QLbT0wcDjnXO7cE6aMSmXb38bc/MLi0nJlpbq6tr6xaW5tN2WSCUxcnLBEtEMkCaMxcRVVjLRTQRAPGWmFg8uR33ogQtIkvlfDlPgc9WIaUYyUlgIT8iD3BIdXt4XXUzrHoWOdeIeleE2aRWDWbMsuAWeJMyE1MEEjML+8boIzTmKFGZKy49ip8nMkFMWMFFUvkyRFeIB6pKNpjDiRfl5eUsB9rXRhlAj9YgVL9fdEjriUQx7qJEeqL6e9kfif18lUdObnNE4zRWI8XhRlDKoEjmqBXSoIVmyoCcKC6r9C3EcCYaXLq+oSnOmTZ4l7ZJ1bzt1xrX4xaaMCdsEeOAAOOAV1cAMawAUYPIJn8ArejCfjxXg3PsbROWMyswP+wPj8ATaJmO8=</latexit>• DM-electron scattering: break Cooper-pairs and scatter<latexit sha1_base64="24aDAsPxVDrQ5vfRsWaOTmudG3c=">AAACEXicbVBNS8NAFNz4bf2qevSyWAS9lKQI6kUEPXgRFEwrNLVstq/t0t0k7L4IJfQ3ePGvePGg4tWbN/+Nm5qDVgcWhpl5vH0TJlIYdN1PZ2p6ZnZufmGxtLS8srpWXt+omzjVHHwey1jfhMyAFBH4KFDCTaKBqVBCIxyc5n7jDrQRcXSNwwRaivUi0RWcoZXa5T3VzgKt6NnF6O62FvTQRhUNzkAiC3I6dhXUR+1yxa26Y9C/xCtIhRS4bJc/gk7MUwURcsmMaXpugq2MaRRcwqgUpAYSxgesB01LI6bAtLLxSSO6Y5UO7cbavgjpWP05kTFlzFCFNqkY9s2kl4v/ec0Uu4etTERJihDx70XdVFKMad4P7QgNHOXQEsa1sH+lvM8042hbLNkSvMmT/xK/Vj2qelf7lZPjoo0FskW2yS7xyAE5IefkkviEk3vySJ7Ji/PgPDmvztt3dMopZjbJLzjvXzjcnWM=</latexit>⇠ meV

mDM & me :<latexit sha1_base64="+J7LkjXm+aduzo1ZiFlKDRr/pok=">AAAB/nicbVDLSsNAFJ34rPUVFdy4GSyCq5KI4GMhBV24ESpYW2hCmEwn7dCZJMzcCCV24a+4caHi1u9w5984bbPQ1gMDh3PO5d45YSq4Bsf5tubmFxaXlksr5dW19Y1Ne2v7XieZoqxBE5GoVkg0EzxmDeAgWCtVjMhQsGbYvxz5zQemNE/iOxikzJekG/OIUwJGCuxdGeSekvjqZuh1weQklgE7D+yKU3XGwLPELUgFFagH9pfXSWgmWQxUEK3brpOCnxMFnAo2LHuZZimhfdJlbUNjIpn28/H9Q3xglA6OEmVeDHis/p7IidR6IEOTlAR6etobif957QyiUz/ncZoBi+lkUZQJDAkelYE7XDEKYmAIoYqbWzHtEUUomMrKpgR3+suzpHFUPau6t8eV2kXRRgntoX10iFx0gmroGtVRA1H0iJ7RK3qznqwX6936mETnrGJmB/2B9fkD05aVhA==</latexit>

ER . 20 eV<latexit sha1_base64="zoYk4VDBide6ldoZRvjp4U4zH1g=">AAACAHicbVBNSwMxEM36WetX1YvgJVgED1J2i6BepCCCxypuW+iWkk1n29AkuyRZoSz14l/x4kHFqz/Dm//G9OOgrQ8GHu/NMDMvTDjTxnW/nYXFpeWV1dxafn1jc2u7sLNb03GqKPg05rFqhEQDZxJ8wwyHRqKAiJBDPexfjfz6AyjNYnlvBgm0BOlKFjFKjJXahf3r9l3AQWvNBC67wUkWKIGhNmwXim7JHQPPE29KimiKarvwFXRimgqQhnKiddNzE9PKiDKMchjmg1RDQmifdKFpqSQCdCsbfzDER1bp4ChWtqTBY/X3REaE1gMR2k5BTE/PeiPxP6+Zmui8lTGZpAYknSyKUo5NjEdx4A5TQA0fWEKoYvZWTHtEEWpsaHkbgjf78jzxy6WLknd7WqxcTtPIoQN0iI6Rh85QBd2gKvIRRY/oGb2iN+fJeXHenY9J64IzndlDf+B8/gCDjpXV</latexit>

e.g. Al: EF=11.7eV, vrel~vF=10-2

SIMP threshold

SIMP indirect detection
Galactic Center

CMB[Essig et al, 2013]• Gamma-ray & CMB can constrain SIMP DM.
• Need of velocity suppression: scalar SIMP ~ p-wave"2m⇡,<latexit sha1_base64="Z5eOw4AAfA9rlMdgwByN7TnmvSA=">AAACGXicbZBNS8MwGMfT+TbnW9Wjl+AQNpDZDkE9KANBPE6wbrCWkqbpFpa+mKSFMfY5vPhVvHhQ8agnv43p1oNOHwj58/s/D8nz9xJGhTSML620sLi0vFJeraytb2xu6ds7dyJOOSYWjlnMux4ShNGIWJJKRroJJyj0GOl4w8vc72SECxpHt3KUECdE/YgGFCOpkKubh/Z9inxoZ4iTRFCmYLOW1c/ngHtVr2VH+eXqVaNhTAv+FWYhqqCotqt/2H6M05BEEjMkRM80EumMEZcUMzKp2KkgCcJD1Cc9JSMUEuGMp6tN4IEiPgxirk4k4ZT+nBijUIhR6KnOEMmBmPdy+J/XS2Vw6oxplKSSRHj2UJAyKGOY5wR9ygmWbKQEwpyqv0I8QBxhqdKsqBDM+ZX/CqvZOGuYN8fV1kWRRhnsgX1QAyY4AS1wDdrAAhg8gCfwAl61R+1Ze9PeZ60lrZjZBb9K+/wGvSGfmQ==</latexit>"2 (v) = "2 (vF )(v/vF )SIMP in merging galaxies• DM subhalo can be separated from its boundedstars due to DM self-interactions.
DM stars“Drag force” between DM subhalo
and larger DM halo is greater than
“Gravity” between DM subhalo and star.

e.g. Abell 3827 cluster[Massey et al(2015)][Kahlhoefer et al(2015)]

Models of SIMP
• Fundamental scalars with Z

3[Bernal et al (2015); Choi, HML (2015)]• Composite scalars (dark mesons)[Hochberg et al (2014); Seo, HML (2015)]• Non-abelian vectors (minimal: SU(2))[Bernal et al (2015); Murayama, HML et al (2017)]• Fermions (assisted SIMP)[J. Cline et al (2017)]• 4→2 processes and more

• Generalizations[Choi, Seo, HML (2017)]

Scalar SIMP

[S.-M.Choi, HML, 2015]• Z is the minimal discrete symmetry from a dark
3

local U(1) and Z’ portal is built-in.
1 0
h i= p v
2

U (1)V ! Z3 .

" x

Z

0

B

l

l

• Correlation btw self-scattering and 3→2 annihilation.
4,
self ⇠m6
h v2 i ⇠ 5m↵e↵ ⇠ 2

Bounds on SIMP

[S.-M. Choi, HML, 2015]

gd =0.1, ΔZ' =4, Δh1 =0.5, λϕχ =0.4

2.5

2.0
Unitarity

1.5

0.1cm2 /g

R
1cm2 /g

1.0
Stability

10cm2 /g

0.5
Perturbativity

0.0
0

50

100

150

200

250

mχ (MeV)

Consistent self-interactions
for relic density & smallscale problems

Belle2, LHCb (Z’ production),
Beam dump exp, Meson decays,
DM-electron scattering, etc.

Some stories on darkmesonsDark meson dark matter• 5-point self-interactions from Wess-Zumino-Witten termfor π5(G/H)=Z (i.e. Nf ≥3).

[Wess, Zumino,1971;Witten, 1983]
NC : topological invariantof 5-sphere in SU(3)SIMP process:[Hochberg et al, 2014]

0⇤QCD ⇠ ⇤QCD

0
3
(⇤
)
QCD
2
2
m⇡˜ ⇠ mq̃
⇠
(100
MeV)
F2

Dark QCD

degenerate dark quarks

degenerate meson masses

Z’-portal for dark mesons
Dark mesons

SM

X

U(1)’

U(1)Y

Z’-portal

dark QCD.
• Vectorial Z’ with no chiral anomalies in [HML,
M. Seo, 2015]
Z’
Z’
0 1
3

QD = @ 0
0

0
1
3

0

1

SM

0
0 A
1
3

•Small meson mass splitting for SIMP process:Lm⇡ = ↵D ⇤4 Tr[QD U QD U

1

]

SM

m2⇡ ⇠ ↵D ⇤4 /F 2 . 0.01m2⇡ ,Dark meson relics
SIMP relicSelf-scatt.

Perturbativity

Bullet cluster[Hochberg, Kuflik, Murayama,Volansky, Wacker, 2014]

Bullet cluster, Halo shape
Perturbativity

Bullet cluster & perturbativity bounds favor large Nc.

Bounds on dark mesons[M.-S. Seo, HML, 2015]
EWPT

0
BaBar

BaBar

CMS7 DY
LHC8 DYmΠ "0.8GeV'4mΠ "0.29GeV

eV
G
9#ann$#3%2

SIMP
conditions

Log10 #ΕΓ $

'2

m

0.2
"
Π

"0

e
G
8
.

V

mΠ

#scat&#3%2'6

SU!10"

'8
'1

0

1

2

3

Log10 #mV !GeV"$• SIMP parameter space can be probed by Z’ searches.
(CMS 8TeV), Drell-Yan, dileptons.

cf. Hochberg et al, 2015

Perturbative mesons?

[Hansen et al, 2015]• 2→2: LO, 3→2: NLO, in SIMP meson scenarios.

NLO corrections enlarge 2→2 cross sections,making it harder to satisfy the Bullet cluster
bound within perturbativity.
Additional 3→2 annihilation channels?

Resonant annihilations[S.-M.Choi, HML, 2016]• Z is the minimal (gauged) discrete symmetry5

for 5-point interactions for SIMP.
1 0h i= v
2

0
@

S

1

0

A !@

DM

1
0
0

0
!
0

10

U (1)V ! Z5

1

0
A
0 A@
i 25 ⇡
3
!=e
!
S

DM

χ
χ

DM

χ∗
χ

DM

S

χ∗

DM

mR ⇠ 3mDM“3DM-Resonance”

Averaging on resonances[S.-M. Choi, HML, M.-S. Seo, 2017]• Thermal average of 3→2 cross section near resonances.
Breit-Wigner form for SIMP:

Thermal average with narrow width:
enhanced
at resonancemR & 3mDM<latexit sha1_base64="aULvqTSdjv1WXw6QbsA6lX2PjVk=">AAAB/nicbVBPS8MwHE3nvzn/VQUvXoJD8DRaFdSLDPTgRZhi3WAtJc3SLSxJS5IKo+7gV/HiQcWrn8Ob38Zs60E3HwQe770fv19elDKqtON8W6W5+YXFpfJyZWV1bX3D3ty6V0kmMfFwwhLZipAijAriaaoZaaWSIB4x0oz6FyO/+UCkoom404OUBBx1BY0pRtpIob3Dw1u/q02AwyMe5r7k8PJ6GNpVp+aMAWeJW5AqKNAI7S+/k+CME6ExQ0q1XSfVQY6kppiRYcXPFEkR7qMuaRsqECcqyMf3D+G+UTowTqR5QsOx+nsiR1ypAY9MkiPdU9PeSPzPa2c6Pg1yKtJME4Eni+KMQZ3AURmwQyXBmg0MQVhScyvEPSQR1qayiinBnf7yLPEOa2c19+a4Wj8v2iiDXbAHDoALTkAdXIEG8AAGj+AZvII368l6sd6tj0m0ZBUz2+APrM8fq42Vag==</latexit>

3 DM’s: higher dimensional phase space
cf. WIMP:Vector Meson resonances[S.-Choi, A. Natale, HML, P. Ko, 2018]

3→2 annihilation:

See also P. Ko’s talk!

Enhanced near resonances with 2π or 3π.
2→2 self-scattering:⇠v<latexit sha1_base64="/2Yv8rBAVakBoawXHOgdQCQ5RcU=">AAAB7nicbVBNSwMxEJ2tX7V+VT16CRbBU9ktQvUiBS8eK7i20K4lm2bb0CS7JtlCWfonvHhQ8erv8ea/MW33oK0PBh7vzTAzL0w408Z1v53C2vrG5lZxu7Szu7d/UD48etBxqgj1Scxj1Q6xppxJ6htmOG0nimIRctoKRzczvzWmSrNY3ptJQgOBB5JFjGBjpXZXM4HGj7VeueJW3TnQKvFyUoEczV75q9uPSSqoNIRjrTuem5ggw8owwum01E01TTAZ4QHtWCqxoDrI5vdO0ZlV+iiKlS1p0Fz9PZFhofVEhLZTYDPUy95M/M/rpCa6DDImk9RQSRaLopQjE6PZ86jPFCWGTyzBRDF7KyJDrDAxNqKSDcFbfnmV+LXqVdW7u6g0rvM0inACp3AOHtShAbfQBB8IcHiGV3hznpwX5935WLQWnHzmGP7A+fwB5CCPZQ==</latexit>

2⇠ v4<latexit sha1_base64="Rm03shcGjXO+DD/lswmMmCnfiqY=">AAAB7nicbVBNSwMxEJ2tX7V+VT16CRbBU9mVQvUiBS8eK7i20K4lm2bb0CS7JtlCWfonvHhQ8erv8ea/MW33oK0PBh7vzTAzL0w408Z1v53C2vrG5lZxu7Szu7d/UD48etBxqgj1Scxj1Q6xppxJ6htmOG0nimIRctoKRzczvzWmSrNY3ptJQgOBB5JFjGBjpXZXM4HGj7VeueJW3TnQKvFyUoEczV75q9uPSSqoNIRjrTuem5ggw8owwum01E01TTAZ4QHtWCqxoDrI5vdO0ZlV+iiKlS1p0Fz9PZFhofVEhLZTYDPUy95M/M/rpCa6DDImk9RQSRaLopQjE6PZ86jPFCWGTyzBRDF7KyJDrDAxNqKSDcFbfnmV+BfVq6p3V6s0rvM0inACp3AOHtShAbfQBB8IcHiGV3hznpwX5935WLQWnHzmGP7A+fwB5yaPZw==</latexit>

VM-induced self-scattering is velocitysuppressed at galaxies and galaxy clusters.

Perturbative mesons!
[S.-Choi, A. Natale, HML, P. Ko, 2018]10

c1-c2 = -1, ϵV = 0.1, mV ∼ 3mπ

2

se

(W
ZW

se
lf

10

π

2 〉 WZW

〈σv

)

/m

1

(W
ZW

10
2 〉 WZW

〈σv

)

1

10

Bullet cluster & SSP
m

mπ
〉 ,
〈σv V
2

2〉

〈σv

102

σ
lf /m
π

10

1

10

c1-c2 = -1, c3 = 1, ϵV = 0.1, mV ∼ 3mπ

2σ

Self-scatt.

fπ

10

2

σs

.1

a=0

10-1

elf /

1
= 0.0
a
,
V

σs

m

elf /

SIMP relic

π,

a=

0.1

10

σself

π

mπ

fπ

2〉 , a
〈σv V

-2

1

2〉 , a
〈σv V

m

π,

a=

Relic
1

0.0

10

10-1

= 0.1

σs

elf /

1
= 0.0
σs

m

elf /

-3

π,

m

π,

a=

a=

10-2
0.1

10-3
0.0

1

10

-1

10

10

2

10

10-4
104

3

mπ (MeV)<latexit sha1_base64="teRjYme/0/JLkh/G3zB7CbekUEs=">AAACB3icbVDLSsNAFJ3UV62vqEsXDhZBEErio7ULpeDGZQXTFpoQJtNJO3QmiTMToYQu3fgrblyouPUX3Pk3Th8LbT1w4XDOvdx7T5AwKpVlfRu5hcWl5ZX8amFtfWNzy9zeacg4FZg4OGaxaAVIEkYj4iiqGGklgiAeMNIM+tcjv/lAhKRxdKcGCfE46kY0pBgpLfnmPvcbl6eQ+25CoSvvhcrsY5ckkjJtN4a+WbRKVrlarpxDTcaA9iwpginqvvnldmKcchIpzJCUbdtKlJchoShmZFhwU0kShPuoS9qaRogT6WXjR4bwUCsdGMZCV6TgWP09kSEu5YAHupMj1ZOz3kj8z2unKrzwMholqSIRniwKUwZVDEepwA4VBCs20ARhQfWtEPeQQFjp7Ao6hLmX54lzUqqW7NuzYu1qmkYe7IEDcARsUAE1cAPqwAEYPIJn8ArejCfjxXg3PiatOWM6swv+wPj8AWgsmSs=</latexit>

10

p

-1

10

mV = 3m⇡ 1 + ✏V

102

103
mπ (MeV)

Vector mesons on-resonance improve perturbativity.
m⇡ /f⇡ . 6
for gV ⇡⇡ . 6 and m⇡ . 1 GeV.
cf. WZW terms only: m⇡ /f⇡ . 15.
Similar improvement at 2-meson resonance.
<latexit sha1_base64="kgCkJ97N2lHsBQJXb5c5C9ojDio=">AAAB/XicbVDLSsNAFL3xWesrKq7cDBbBVU1EfGyk4MZlBWMLTSiT6aQdOpOEmYlQQsFfceNCxa3/4c6/cdJmoa0H7uVwzr3MnROmnCntON/WwuLS8spqZa26vrG5tW3v7D6oJJOEeiThiWyHWFHOYupppjltp5JiEXLaCoc3hd96pFKxJL7Xo5QGAvdjFjGCtZG69r7o+ik7iYruc6qUYgKdd+2aU3cmQPPELUkNSjS79pffS0gmaKwJx0p1XCfVQY6lZoTTcdXPFE0xGeI+7RgaY0FVkE/OH6Mjo/RQlEhTsUYT9fdGjoVSIxGaSYH1QM16hfif18l0dBnkLE4zTWMyfSjKONIJKrJAPSYp0XxkCCaSmVsRGWCJiTaJVU0I7uyX54l3Wr+qu3dntcZ1mUYFDuAQjsGFC2jALTTBAwI5PMMrvFlP1ov1bn1MRxescmcP/sD6/AEsvJUp</latexit><latexit sha1_base64="p3BXbSbaJlDU832535dOLARt6qs=">AAAB/XicbVDLSsNAFJ3UV62vqLhyM1gEVyUR8bGRghuXFYwtNCFMpjft0MkkzEyEEgr+ihsXKm79D3f+jdM2C2093AuHc+5l7pwo40xpx/m2KkvLK6tr1fXaxubW9o69u/eg0lxS8GjKU9mJiALOBHiaaQ6dTAJJIg7taHgz8duPIBVLxb0eZRAkpC9YzCjRRgrtg35YPPgZMzX2OSilWILPQ7vuNJwp8CJxS1JHJVqh/eX3UponIDTlRKmu62Q6KIjUjHIY1/xcQUbokPSha6ggCaigmJ4/xsdG6eE4laaFxlP190ZBEqVGSWQmE6IHat6biP953VzHl0HBRJZrEHT2UJxzrFM8yQL3mASq+cgQQiUzt2I6IJJQbRKrmRDc+S8vEu+0cdVw787qzesyjSo6REfoBLnoAjXRLWohD1FUoGf0it6sJ+vFerc+ZqMVq9zZR39gff4AsCGVfQ==</latexit><latexit sha1_base64="p7qjOIx67hIZCCaMcKFDvRjIrjM=">AAAB/3icdVDLSsNAFJ3UV62vqgsXbgaL4ComfVk3UnDjsoKxhSaEyXTSDp1JwsxEKKEbf8WNCxW3/oY7/8ZJW0FFD9zL4Zx7mbknSBiVyrI+jMLS8srqWnG9tLG5tb1T3t27lXEqMHFwzGLRC5AkjEbEUVQx0ksEQTxgpBuML3O/e0eEpHF0oyYJ8TgaRjSkGCkt+eUD7rsJPQ3z7jIipaQc2g3TL1cs07JqtWoL5qTRbNg5qdWaVh3aWslRAQt0/PK7O4hxykmkMENS9m0rUV6GhKKYkWnJTSVJEB6jIelrGiFOpJfNDpjCY60MYBgLXZGCM/X7Roa4lBMe6EmO1Ej+9nLxL6+fqrDlZTRKUkUiPH8oTBlUMczTgAMqCFZsognCguq/QjxCAmGlMyvpEL4uhf8Tp2qem/Z1vdK+WKRRBIfgCJwAG5yBNrgCHeAADKbgATyBZ+PeeDRejNf5aMFY7OyDHzDePgFbr5XM</latexit>

10-4
104

σself
mπ

Conclusions• Naturalness of Higgs mass and dark matter need new

strategies beyond SM and will drive us in next generations.

• Dark mesons are natural candidates for dark matter inmodels of neutral naturalness where dark QCD and Z’
interactions exist by construction.

• SIMP dark matter is a sub-GeV SIDM produced via 3→2
freeze-out process, with testable signatures fromastrophysical and Earth-based experiments.

• SIMP meson scenarios may be valid solutions to smallscale problems.

Backup

Vector Mesons in dark ChPTSIMP mesons + Vector mesons in dark QCD:
G=SU(Nf)VxSU(Nf)/SU(Nf)V+ Hlocal=SU(Nf)V hidden local symmetry

Extra chiral-invariant term (in unitary gauge):

VM masses:
VM-pion couplings:

degenerate
cf. QCD: a ' 2<latexit sha1_base64="e9jMF2nnnBVdVVnkh37/3POrZvs=">AAAB73icbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoF6k4MVjBWMrbSib7bRdupvE3Y1QQn+FFw8qXv073vw3btsctPXBwOO9GWbmhYng2rjut1NYWV1b3yhulra2d3b3yvsH9zpOFUOfxSJWrZBqFDxC33AjsJUopDIU2AxH11O/+YRK8zi6M+MEA0kHEe9zRo2VHmhHc4mPpNYtV9yqOwNZJl5OKpCj0S1/dXoxSyVGhgmqddtzExNkVBnOBE5KnVRjQtmIDrBtaUQl6iCbHTwhJ1bpkX6sbEWGzNTfExmVWo9laDslNUO96E3F/7x2avoXQcajJDUYsfmifiqIicn0e9LjCpkRY0soU9zeStiQKsqMzahkQ/AWX14mfq16WfVuzyr1qzyNIhzBMZyCB+dQhxtogA8MJDzDK7w5ynlx3p2PeWvByWcO4Q+czx+iWI/S</latexit>

WZW with vector mesons
WZW terms
gauged
by
H
=SU(N
)
local
f
V
Z
anom

4

=

15(c1 L1 + c2 L2 + c3 L3 )]d x[LW ZW<latexit sha1_base64="RL3eWBdZSjwT9hJu94g6ifg4/Ic=">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</latexit>

FV = dV<latexit sha1_base64="8hSJE60mdxakxwt0J+EF5t8vuJU=">AAAB83icbVBNS8NAEJ34WetX1aOXxSJ4sSRFUA9KQRCPFUxaaGPZbLbt0s0m7m4KJfR3ePGg4tU/481/47bNQVsfDDzem2FmXpBwprRtf1tLyyura+uFjeLm1vbObmlv31NxKgl1Scxj2QywopwJ6mqmOW0mkuIo4LQRDG4mfmNIpWKxeNCjhPoR7gnWZQRrI/m3He8q9E5ZD3mP1U6pbFfsKdAicXJShhz1TumrHcYkjajQhGOlWo6daD/DUjPC6bjYThVNMBngHm0ZKnBElZ9Njx6jY6OEqBtLU0Kjqfp7IsORUqMoMJ0R1n01703E/7xWqrsXfsZEkmoqyGxRN+VIx2iSAAqZpETzkSGYSGZuRaSPJSba5FQ0ITjzLy8St1q5rDj3Z+XadZ5GAQ7hCE7AgXOowR3UwQUCT/AMr/BmDa0X6936mLUuWfnMAfyB9fkDbWyQwQ==</latexit>

4gC
Tr[Vµ @µ ⇡@⇢ ⇡@ ⇡],
3
f⇡

L1 =

L2 =

L3 =

2igC
Tr[@µ V⌫ (V⇢ @ ⇡f⇡<latexit sha1_base64="TcQBfsvHEVhLHJ8XSfDxlDMCSZg=">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</latexit><latexit sha1_base64="TApLA0oX+eqX3kvhDPU9LxAYH/M=">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</latexit>

cf. QCD:<latexit sha1_base64="Heh9QF2FdhsWnpWYX6lA9cFvh4s=">AAAB/nicbVDLSsNAFJ3UV62vqODGzWARXJVEBXUjBTcuKxhbaEKZTCft0HmEmYlSYhf+ihsXKm79Dnf+jdM2C209cOFwzr3ce0+cMqqN5307pYXFpeWV8mplbX1jc8vd3rnTMlOYBFgyqVox0oRRQQJDDSOtVBHEY0aa8eBq7DfvidJUilszTEnEUU/QhGJkrNRx90LJSQ+Fivb6BiklH+BJmNKOW/Vq3gRwnvgFqYICjY77FXYlzjgRBjOkddv3UhPlSBmKGRlVwkyTFOEB6pG2pQJxoqN8cv8IHlqlCxOpbAkDJ+rviRxxrYc8tp0cmb6e9cbif147M8l5lFORZoYIPF2UZAwaCcdhwC5VBBs2tARhRe2tEPeRQtjYyCo2BH/25XkSHNcuav7NabV+WaRRBvvgABwBH5yBOrgGDRAADB7BM3gFb86T8+K8Ox/T1pJTzOyCP3A+fwBwuZXp</latexit>igV 2! ! 3⇡

C=<latexit sha1_base64="AZ/0NIEehQwMrW/dedTTZwcT5G0=">AAACAHicbVBNS8NAEN34WetX1IvgZbEIXixJKagHpdCLJ6lgbKGJYbPdtEs3m7C7EUqIF/+KFw8qXv0Z3vw3btsctPXBwOO9GWbmBQmjUlnWt7GwuLS8slpaK69vbG5tmzu7dzJOBSYOjlksOgGShFFOHEUVI51EEBQFjLSDYXPstx+IkDTmt2qUEC9CfU5DipHSkm/uNy9O3FAgnNFrH+dZrW65Cb2v5b5ZsarWBHCe2AWpgAIt3/xyezFOI8IVZkjKrm0lysuQUBQzkpfdVJIE4SHqk66mHEVEetnkgxweaaUHw1jo4gpO1N8TGYqkHEWB7oyQGshZbyz+53VTFZ55GeVJqgjH00VhyqCK4TgO2KOCYMVGmiAsqL4V4gHSeSgdWlmHYM++PE+cWvW8at/UK43LIo0SOACH4BjY4BQ0wBVoAQdg8AiewSt4M56MF+Pd+Ji2LhjFzB74A+PzB3+5ldQ=</latexit>

iNc240⇡ 2@⇢ ⇡V )].

cf. QCD: VMphoton mixing
0⇡ !2<latexit sha1_base64="zCdWkrDnS/fr7W40jS1IOGydMOU=">AAACAHicbVBNS8NAEN34WetX1IvgZbEInkpSBPUiBS8eKxhbaGKZbDfp0t0k7G6UUurFv+LFg4pXf4Y3/43bNgdtfTDweG+GmXlhxpnSjvNtLSwuLa+sltbK6xubW9v2zu6tSnNJqEdSnspWCIpyllBPM81pK5MURMhpM+xfjv3mPZWKpcmNHmQ0EBAnLGIEtJE69r6fsTvHlyzuaZAyfcA1PwYhoGNXnKozAZ4nbkEqqECjY3/53ZTkgiaacFCq7TqZDoYgNSOcjsp+rmgGpA8xbRuagKAqGE4+GOEjo3RxlEpTicYT9ffEEIRSAxGaTgG6p2a9sfif1851dBYMWZLlmiZkuijKOdYpHseBu0xSovnAECCSmVsx6YEEok1oZROCO/vyPPFq1fOqe31SqV8UaZTQATpEx8hFp6iOrlADeYigR/SMXtGb9WS9WO/Wx7R1wSpm9tAfWJ8/k9yWhA==</latexit>

Dark photon case:
Berlin et al, 2018

2-meson resonance[S.-Choi, A. Natale, HML, P. Ko, 2018]10

c1-c2 = -1, ϵV = 0.1, mV ∼ 3mπ

2

Self-scatt.

2〉

〈σv

V,

se

se

lf /m
π

(W
ZW

lf /m
π

10
2 〉 WZW

〈σv

)

1

σs

.1

a=0

10-1

elf /

0.01
2〉 , a =
〈σv V

σs

m

elf /

SIMP relic
10-1
10

102

σ

Bullet cluster & SSP

mπ

1

10

c1-c2 = -1, c3 = 1, ϵV = 0.1, mV ∼ 2mπ

2

σ

10

fπ

10

2

102

π,

a=

0.1

10

σself

mπ

mπ

fπ

-2

a=

Relic
1

0.0

10

mπ (MeV)<latexit sha1_base64="AGC98wYS2sg2XEVrGaxynCW6GvY=">AAACBnicbVDLSgMxFM34rPU16lKQYBEEocwUa3WhFNy4rOC0hc4wZNK0DU0yY5IRytCdG3/FjQsVt36DO//G9LHQ1gMXDufcy733RAmjSjvOt7WwuLS8sppby69vbG5t2zu7dRWnEhMPxyyWzQgpwqggnqaakWYiCeIRI42ofz3yGw9EKhqLOz1ISMBRV9AOxUgbKbQPeFi/LPHQTyj01b3UmXvik0RRZtz6MLQLTtGplM/KZWjIGNCdJQUwRS20v/x2jFNOhMYMKdVynUQHGZKaYkaGeT9VJEG4j7qkZahAnKggG/8xhEdGacNOLE0JDcfq74kMcaUGPDKdHOmemvVG4n9eK9Wd8yCjIkk1EXiyqJMyqGM4CgW2qSRYs4EhCEtqboW4hyTC2kSXNyHMvTxPvFLxoujenhaqV9M0cmAfHIJj4IIKqIIbUAMewOARPINX8GY9WS/Wu/UxaV2wpjN74A+szx8E4Jj7</latexit>

)

〈σ

1
10-1

=2
2 〉V , av〈σ=12 〉V , a1v〈σ 2 , a = 0.
〉
〈σv V

1

σ

se
lf /

m

π,

σ

se
lf /

m

π,

σ

se
lf /

-3

m

10-4
104

103

10
v2 〉 WZW

10

m

π,

(W
ZW

10-1
10

p

mV = 2m⇡ 1 + ✏V

102

π,

a=

2

a=

1

a=

mπ (MeV)

Vector mesons on-resonance improve perturbativity.
m⇡ /f⇡ . 4
for gV ⇡⇡ . 1.3 and m⇡ . 1 GeV.
<latexit sha1_base64="yOnMgPf7u5lZyry8TEoNYuku1kM=">AAAB/3icbVC7TsMwFHXKq5RXgIGBxaJCYooSQAIWVImFsUiEVmqiyHGd1qrtRLaDVEVZ+BUWBkCs/AYbf4PbZoCWo3ulo3PulX1PnDGqtOt+W7Wl5ZXVtfp6Y2Nza3vH3t17UGkuMfFxylLZjZEijAria6oZ6WaSIB4z0olHNxO/80ikoqm41+OMhBwNBE0oRtpIkX0wiIqHIKOmyoARpRTl0HPOIrvpOu4UcJF4FWmCCu3I/gr6Kc45ERozpFTPczMdFkhqihkpG0GuSIbwCA1Iz1CBOFFhMT2ghMdG6cMklaaFhlP190aBuFJjHptJjvRQzXsT8T+vl+vkMiyoyHJNBJ49lOQM6hRO0oB9KgnWbGwIwpKav0I8RBJhbTJrmBC8+ZMXiX/qXDne3XmzdV2lUQeH4AicAA9cgBa4BW3gAwxK8AxewZv1ZL1Y79bHbLRmVTv74A+szx+WHpXt</latexit>

cf. WZW terms only:m⇡ /f⇡ . 15.
<latexit sha1_base64="p7qjOIx67hIZCCaMcKFDvRjIrjM=">AAAB/3icdVDLSsNAFJ3UV62vqgsXbgaL4ComfVk3UnDjsoKxhSaEyXTSDp1JwsxEKKEbf8WNCxW3/oY7/8ZJW0FFD9zL4Zx7mbknSBiVyrI+jMLS8srqWnG9tLG5tb1T3t27lXEqMHFwzGLRC5AkjEbEUVQx0ksEQTxgpBuML3O/e0eEpHF0oyYJ8TgaRjSkGCkt+eUD7rsJPQ3z7jIipaQc2g3TL1cs07JqtWoL5qTRbNg5qdWaVh3aWslRAQt0/PK7O4hxykmkMENS9m0rUV6GhKKYkWnJTSVJEB6jIelrGiFOpJfNDpjCY60MYBgLXZGCM/X7Roa4lBMe6EmO1Ej+9nLxL6+fqrDlZTRKUkUiPH8oTBlUMczTgAMqCFZsognCguq/QjxCAmGlMyvpEL4uhf8Tp2qem/Z1vdK+WKRRBIfgCJwAG5yBNrgCHeAADKbgATyBZ+PeeDRejNf5aMFY7OyDHzDePgFbr5XM</latexit>

10-3

0.1

103

<latexit sha1_base64="LIJLZZ911smXC8XS5Uq0Nxi67Qo=">AAAB/XicbVBNS8NAEJ34WetXVTx5WSyCp5pIQb1IwYvHCsYWmhA22027dDcJuxuhhIJ/xYsHFa/+D2/+GzdtDtr6YIbHezPs7AtTzpS27W9raXlldW29slHd3Nre2a3t7T+oJJOEuiThieyGWFHOYupqpjntppJiEXLaCUc3hd95pFKxJL7X45T6Ag9iFjGCtZGC2qEIvJSdRUX3OFVKMYGaQa1uN+wp0CJxSlKHEu2g9uX1E5IJGmvCsVI9x061n2OpGeF0UvUyRVNMRnhAe4bGWFDl59PzJ+jEKH0UJdJUrNFU/b2RY6HUWIRmUmA9VPNeIf7n9TIdXfo5i9NM05jMHooyjnSCiixQn0lKNB8bgolk5lZEhlhiok1iVROCM//lReKeN64azl2z3rou06jAERzDKThwAS24hTa4QCCHZ3iFN+vJerHerY/Z6JJV7hzAH1ifPym2lSc=</latexit>

10-2

10-4
104

σself
mπ