JHW, Budapest - July 4, 2017

Baryonic Dark Matter

Michele RediBased on: arxiv 1503.08749 +1707.xxxx

with Antipin, Mitridate, Smirnov, Strumia, Vigiani

MotivationIn the SM, all observed global symmetries arise

as accidental symmetries of the renormalizable Lagrangian. This explains why the proton is stable.

We need at least one more stable particle for Dark Matter…

New gauge theory:DM is an accidentally stable “dark”-baryon

g

yGµ

ij

SM including elementary Higgs couples to the strong sector with renormalizable couplings:

SM +HQi

↵

Confining gauge theory with fermions vectorial under SM

L = LSM + Qi(i�µDµ �mi)Qi �

GA2µ⌫

4g2DC

+✓DC

32⇡2GAµ⌫ GA

µ⌫ + [HQi(yLijPL + yRijPR)Qj + h.c.]

Accidental symmetries:

• Dark-Baryon number

• Dark-Species number

• G-parity

B = ✏i1i1...inQ{↵1

i1Q↵2

i2. . . Q↵n}

in

Qi ! ei↵iQi

Q ! e�i⇡J2Qc

M = QiQj

M = (QQ)triplet

Qi ! ei↵Qi

1

MQQHH ,

1

MQ�µ⌫QBµ⌫

Baryon number broken by dimension 6 operators:

Species symmetry and G-parity can be broken by Yukawa couplings, hypercharge and dim 5 operators

⌧ ⇠ 8⇡M4

M5DM

⇠ 1026 sec⇥✓

M

MPl

◆4 ✓100TeV

MDM

◆5

Dark baryons robustly cosmologically stable.

Majorana vs. Dirac

- Q-complex (SU(N))

Baryons are Dirac particles that can be produced thermally or asymmetrically. Strong direct detection constraintsfrom tree level Z-couplings.

- Q-real (SO(N))

Baryon and anti-baryons are the same particle so 2 DM particles can annihilate. Only thermally produced. Direct detections constraints avoided.

Effective coupling is perturbative.Cosmology non-standard and model dependent:

rDC ⇠ (↵DCmQ)�1

Strongly coupled dynamics, DM simple.

- Light Dark Quarks:

- Heavy Dark Quarks:

(mQ < ⇤DC)

(mQ > ⇤DC)

• rDC < ⇤�1DC

• rDC > ⇤�1DC

“Coulomb”

“Quarkonium”

⇤DC ⇠ mQexp

� 6⇡

11C2(G)↵DC(mQ)

�

Light Quarks

- with O. Antipin, A. Strumia, E. Vigiani ‘15

SU(N) gauge theory with NF light flavors.Dark-quarks are vectorial with respect to SM.

Fermions SM SU(n)TC

LP

i ri n R

Pi ri n

X

i

d[ri] = NF

SU(NF )⇥ SU(NF )

SU(NF )

Nambu-Goldstone bosons:

h i ji ⇠ 4⇡f3�ij

AdjSU(NF ) =KX

i=1

ri ⇥KX

i=1

ri � 1

Vacuum does not break electro-weak symmetry.

SU(N)

• Dark-Baryons

Lightest multiplet has minimum spin. Flavor rep:

DM candidate: I=0,1,2,...

NDC = 3 NDC = 4

QDB = T 3DB + YDB = 0

YDB = 0

Pions behave as elementary minimal dark matter candidates.

• Dark-Pions

Strumia, Cirelli ’05

mI=1 ⇠ 2.5TeV �SI = 0.12± 0.03⇥ 10�46 cm2

0

{ ⇠ 100MeV

�m = ↵2Q2mW sin2

✓W2

⇠ m2⇡

mB

mD⇡

mDb

mDb0

mQ

Flavor multiplets are split by fermion masses and gauge interactions:

⇤DC

Classification:

R = (N,SM)� (N , ¯SM)

- SU(N) asymptotically free - No Landau poles below the Planck scale.- Lightest dark-baryon with Q=Y=0- No unwanted stable particles

Golden models:

Relic abundance:

DB

SMg2

g2

h�ANNBB vi ⇠ 4⇡

m2B

THERMALABUNDANCE

geff ⇠ 4⇡

D⇡

DM could also be produced asymmetrically.

mB ⇠ 100TeV

If DB has SM charges it interacts as WIMPS.

�3SI = 0.12⇥ 10�46 cm2

Yukawa couplings very constrained.

d�

dER⇡ e2Z2

16⇡m2B ER

✓g2M +

g2Ev2

◆g2M + 107g2E <

⇣ mB

5TeV

⌘3

Dipole interactions:

LUX 90% CL SI bound

ν background

*pion 30

gE =0.005

gM=1or g

E =0.0003

100 101 102 103 104 105

10-47

10-46

10-45

10-44

10-43

10-42

Dark Matter mass in GeV

DMcrosssectionσ S

Iincm

2

Dirac baryon DM

gM = O(1) gE ⇠ e ✓TC min[mQ]

MDM

With NF flavors in the vector rep: SU(NF )

SO(NF )

- No difference between baryons and anti-baryons. Two baryons can annihilate into N pions

✏i1i2...iN ✏j1j2...jN = (�i1j1�i2j2 . . . �iN jN ± permutations)

h0|qai qbi |0i ⇠ 4⇡f3�ab

Fermions are in a real dark color rep:

- Real SM fermions have Majorana masses

NN V V GG

SO(N)

SO(N) DM candidates are Majorana fermions or real scalars:

• production

• detection

Cannot be produced through an asymmetry.Thermal abundance:

There are no vector couplings with Z eliminating spin independent bounds. No dipole interactions.

After electro-weak symmetry breaking neutral mass eigenstates are Majorana particles. Analogous to SUSY neutralinos.

mB ⇠ 100TeV

Golden models:

Q=L+N

Lightest baryon is a quintuplet of SO(5) containing “Higgsino" + “bino” states

• “Higgsino DM”

mLLL+mN

2NN + yLH

†LN + y⇤RHLN + h.c

�mM ⇠ y2v2

mN

mL ⌧ mN

0

BBBBB@

10 21/2 2�1/2 · · ·10 m10 yLv yRv · · ·21/2 y⇤Lv 0 m21/2 · · ·2�1/2 y⇤Rv m21/2 0 · · ·...

......

.... . .

1

CCCCCA

Heavy quarks

- with A. Mitridate, J. Smirnov, A. Strumia, to appear

⇤DC

7⇤DC

2mQ

NDC mQ

Dark glueballs

Dark mesons

Dark baryons

mQ

Non-relativistic bound states N fermions:

� �� ��� ��� ����

�

�

�

�

��/��

���

��(���)

�/�� ≪ Λ�� ��≪ Λ�� ≪ �/�� Λ�� ≪ �� ≪ �/��

α ��=���

α ��=���

α ��=���

V ⇠ �↵DC

r+ ⇤2

DCr

Lightest baryons are naturally made of a single specie.

= N � . . .

DM = V V V , I(JP ) = 1

✓1

2

+◆DM = NNN , I(JP ) = 0

✓3

2

+◆

= V � . . .

• SU(3)

• SO(3)

= L�N � V + . . . DM = LLL I(JP ) =1

2

✓1

2

+◆

Static properties of bound states:

mB ⇡ NDCmQ EB ⇠ ↵2DCN

3DCmQ

M0++ ⇡ 7⇤DC

Q

Q

QQQ

Q

Q

Q

G

GG G

G

�

�

�

Q Q

f

f

Glueballs:

Glueballs need to decay before BBN:

⌧DG + t⇤DC < 1s

⌧��DG ⇠ 10sec

✓10GeV

mDG

◆9✓ mQ

TeV

◆8

⌧ bbDG ⇠ 10�3sec

✓0.1

y

◆4 ✓10GeV

mDG

◆7✓ mQ

TeV

◆4

Non standard cosmological histories:

•⇤DC >mQ

25

•⇤DC <mQ

25

Baryons form before thermal free-out.

Dark quarks free-out in the perturbative regime. A fraction recombines into baryons after dark confinement.

h�vi =4⇡↵2

eff

m2B

+ h�viSM

⌦DM = pB⌦Q+Q pB = O(1)

Glueball decays may dilute abundance, late time annihilations, thermal excitement…

mQ < 100TeV

��-� ��� ��� ������

���

���

���� ������������ ����� �� �� ���

��������������

������

��→

γγ

��→�

�=�

τ�� < �Λ��

���� > �����

���� < �����

��≫Λ�

�

��≪

��

In the non-relativistic regime thermal abundance of DM can be obtained for masses up to few TeV.

(QNDC ) + (QNDC ) ! (QQ) + (QNDC�1) + (QNDC�1)

�BBvrel ⇠1

↵DC

⇡

m2Q

Indirect detection:

At low energies annihilation cross-section can be huge for extended objects:

- SU(N): Z and Higgs mediated SI scatterings

�� �/��

=��

�� �/��

=�� �� �

/��=�

��� ��� ��� ��� �����-�

��-�

��-�

��-�

���

�� �� ���

�(=�� )

��(�) �⊕� �����

�� �/�

�=�

�� �/�

�=���� �

/��=��

��� ��� ��� ��� �����-�

��-�

��-�

���

�� �� ���

�(=�� )

��(�) �⊕� ������ ����� ��������

Z+h

Inelastic DM

- SO(N): Higgs SI x-sec and Z inelastic transitions.

h

Direct detection:

CONCLUSIONS• Stability of DM suggests the existence of accidental symmetries

beyond the SM. DM can be simply realised as baryons of a new gauge theory.

• Dark color could be accessible to collider and DM experiments. Interesting effects include: long lived glueballs, bound states, EDMs, gravitational waves, unification…

• SU(N) models generate complex DM while SO(N) models give real DM with very different phenomenology depending on confinement scale.

• Thermal abundance of DM is obtained for masses 1-100 TeV. With heavy quarks cosmology is highly non standard.

OTHER PHENO(O. Antipin, MR, arxiv:1508.01112

Agugliaro, Antipin, Becciolini, De Curtis, MR 1609.07122)

+q

q

Goldstone bosons and vector bosons with SM charges:

g2SM

g⇢

Kilic, Okui, Sundrum ’09

COLLIDER SIGNATURES

⇢

h0| �µT a |⇢bi = ��ab m⇢f⇢✏µ

h0| �µ�5T a |⇡bi = �i�ab f pµ

Heavy vectors mix with SM gauge bosons

m⇢ ⇠ g⇢f

Unlike composite Higgs fermions are elementary.

•mQ < ⇤DC

Decay to hidden pions and back to SM gauge bosons through anomalies or quarks

Pions can also be collider stable or long lived.

⇢⇡

⇡

⇢

q

q

Br(⇢ ! qq) / g42g4⇢

Pions can also be produced through SM interactions

pp ! W± ! ⇡±3 ⇡

03 ! 3� + W±

Only search from CDF!m⇡3 > 230GeV

New features arise with Yukawa couplings

HQi(yLijPL + yRijPR)Qj ym⇢f H⇡2 + . . .

✏ ⇠ ym⇢f

m2⇡2

MIXING :

⇢

⇡

⇢

- Pions with species number decay through Higgs:⇡21/2 ! H⇡10 , ⇡11 ! HH⇡10

- Small effects in precision tests, Higgs couplings etc…

BR(⇢ ! WW ) ⇠ ✏4BR(⇢ ! ⇡W ) ⇠ ✏2

W W

W

�T ⇠ v2

f2✏4 �S ⇠ m2

W

m2⇢

✏2�hWW

hSMWW

⇠ v2

f2✏3

Antipin, MR’15

����� ��������

����� ���������=���

�=����

�=����

�=���

��� ��� ��� ��� ��� ��� ��� �������

���

���

���

���

�� �� ���

σ(��→

)����

�=����

�=�����=���

�=���

����� ��������

��� ���� ���� ������-�

��-�

���

���

���

�� �� ���

σ(��→�→ℓℓ)����

Single Hadronization

•mQ > ⇤DC

Mesons can be produced singly or through hadronization. Spin-0 resonances decay to SM gauge bosons and spin-1 to fermions and scalars.

Most significant bound from spin-1particles decaying to leptons.

Mitridate, MR, Smirnov, Strumia ’17

EDM for SM particles generated with complex Yukawas:

de < 8.7⇥ 10�29 e cm @90%C.L.

WEAK STRONG

de t 10�27 e · cm⇥ Im(yLyR)⇥NDC

3⇥

✓TeV

m⇡,⌘

◆2

⇥⇣⇤DC

TeV

⌘2

ELECTRIC DIPOLE MOMENTS

Phase transition :

fpeak = 3.3⇥ 10�3 Hz⇥⇣ T

10TeV

⌘⇥⇣ �

10H

⌘Peak frequency:

Amplitude of the GW signal :

h2�GW ⇠ 10�9

P. Schwaller 15’

X

Confinement phase transition often 1st order:

T ⇠ ⇤DC

3 NF 4N and N > 3

GRAVITATIONAL WAVES

Incomplete SU(5) reps modify SM running

1

↵i(MZ)=

1

↵GUT+

bSMi2⇡

log

MGUT

MZ+

�bi2⇡

log

MX

⇤TC+

�b

2⇡log

MGUT

MX

lnMX

⇤TC=

68

�b21 � 1.9�b32, ln

MGUT

MX=

35.3�b21 � 49.2�b32�b21 � 1.9�b32

UNIFICATION

102 104 106 108 1010 1012 1014 10160

10

20

30

40

50

60

Energy in GeV

1êa

3HQ+DL 3HU+L+EL1êa3

1êa2

1êa1

Ex:

Q+ D DM = QQD

MX ⇡ 2⇥ 1011 GeV

↵GUT ⇡ 0.06

MGUT ⇡ 2⇥ 1017 GeV

⇤DC = 100TeV

SHIP

O6 =↵DC

4⇡H†HGA

µ⌫Gµ⌫A sin↵ ⇡ c6↵DC

4⇡

vf0SM2

h