camilo garcia cely, ulb · 2017. 10. 6. · camilo garcia cely, ulb self-interacting dark matter...

From spin-1 to spin-2 SIMPs

Camilo Garcia Cely, ULB

Self-interacting Dark Matter WorkshopCopenhagen, Denmark

The Neils Bohr International Academy

August 3rd, 2017

In collaboration with N. Bernal, X. Chu, T. Hambye and B. ZaldivarBased on JCAP 1603 (2016) no.03, 018 and arXiv:1708.xxxxx

MotivationSpin-1 caseSpin-2 case

1 Motivation: Self-interacting DM without light mediators

2 Spin-1 case

3 Spin-2 case

Camilo Garcia Cely, ULB From spin-1 to spin-2 SIMPs


How to produce self-interacting DM

Solution to small-scale problems: σSImDM∼ 0.1− 10 cm2/g

σSI ∼ 1011-1013 pb for mDM ∼ 1 GeV

If σvannihilation ∼ 1 pb : ΩDMh2 ∼ 0.1 (WIMP miracle)

If σvannihilation ∼ σSI : ΩDMh2 1

One option

Keep pb cross sections in the Early Universe but enhance theinteractions in DM halos today

Invoke a light mediator and consider non-perturbative effects






If σvannihilation ∼ 1 pb : ΩDMh2 ∼ 0.1 (WIMP miracle)If σvannihilation ∼ σSI : ΩDMh2 1

One option

Keep pb cross sections in the Early Universe but enhance theinteractions in DM halos today

Invoke a light mediator and consider non-perturbative effects






If σvannihilation is of the same order of magnitude: ΩDM 1

Another option: Suppress the interactions in the Early Universe.

Consider annihilations of three DM particles into two of them.

SIMPs (Strongly Interacting Massive Particles)

Hochberg, Kuflik, Volansky, Wacker (PRL 2014)



Similar processes occur in the Sun

Bahcall et al. , ( ApJ, 2005)



Concrete Implementations

Basic requirements

An underlying principle for having 3-to-2 processes

Dark Matter Stability

Examples:

Z3 dark matter Bernal et al. (2015), Soo-Min Choi (2015)

QCD-like theories of dynamicalchiral symmetry breaking Hochberg et al, 2014

Dark Matter in a hidden gauge theory Yamanaka et al (2015)

...

This talk

Warm-up: spin-1 case (vector SIMPs) Bernal, Chu, GGC, Hambye, Zaldivar (JCAP 2016)

Spin-2 case Preliminary



Spin-1 case: Hidden Vector DM model

Field SU(3) SU(2) U(1)Y SU(2)XH 1 2 1

2 0φ 1 1 0 2A′µ 1 1 0 3

Local SU(2)X → Global SO(3)Gauge Fields A′µ → Massive Fields Aµ Stable (DM Candidate)Doublet φ → Higgs-like η It mixes with the Higgs

Hambye (JHEP 2009)



Vector SIMPs


Bernal, Chu, GGC, Hambye, Zaldivar (JCAP 2016)

Dark Matter

Self-Interactions

3-to-2 process

Annihilationsinto SM particlesare naturally

suppressed

A

A

A

AA

AA

A A

A

A

A A

A

A

A

η, hA

A

Aη, h

A

A A

A

A

A

AA

A

AA

A

A

A A

A

A

A

A AA

A

AA

A

AA

A A

A

A

AA

A A

A

A

A

A

A

A

A

A

η, h

A

A AA

A

AA

A

η, hA

A A

A

A

η, hA

A A

A

A

A

AA

η, h A

A

A

A

A

Aη, h

A

A


Production Regimes

For fixed mη and mA

10-12 10-10 10-8 10-6 10-4 10-2 10010-10

10-8

10-6

10-4

10-2

100

λm

αX

Phase diagram (mA=10 GeV, mη≪mA)

Regime4

Regime3BRegime2&3A

Regime1


etaetaetaetaeta


Freeze-in regime

SIMPs in kinetic equilibriumSIMPs not in kinetic equilibrium


Production Regimes


10-12 10-10 10-8 10-6 10-4 10-2 10010-10

10-8

10-6

10-4

10-2

100

λm

αX


Regime4

Regime3BRegime2&3A

Regime1


etaetaetaetaeta


Freeze-in regime

SIMPs in kinetic equilibrium

SIMPs not in kinetic equilibrium


Production Regimes


10-12 10-10 10-8 10-6 10-4 10-2 10010-10

10-8

10-6

10-4

10-2

100

λm

αX


Regime4

Regime3BRegime2&3A

Regime1


etaetaetaetaeta


Freeze-in regime

SIMPs in kinetic equilibriumSIMPs not in kinetic equilibrium


Regime 3A for 3-to-2 processes

mA = 100 MeV, mη = 300 MeV, αX = 0.08 and λm = 4.3 × 10−12

0.001 0.010 0.100 1 10 100

2.× 10-9

5.× 10-9

1.× 10-8

2.× 10-8

x = mA / T

YA

a b c d

actualthermal

ΩAh2=0.12

0.001 0.010 0.100 1 10 100

1

10

100

1000

104

105

x = mA / T

Temperature

[MeV

]

a b c d

mA

T'

T

In (c), T ′/T ∼ a/log(a)

Carlson, Machacek, Hall (Astrophysics J 1992)




Regime 3A

10-3 10-2 10-1 100 101 102 103

10-7

10-5

10-3

10-1

101

mA [MeV]

αX

Lyman-α

Dark freeze-out

Freeze-in

Reanni.

Log10[T'/T]

-2.5

-2.0

-1.5

-1.0

-0.5

Figure: Parameter space for self-Interactions




How about spin-2 dark matter?

Classical theory of free massive spin-2 fields. Fierz and Pauli (1939)

Interactions → Very hard!.Until very recently, it seemed that any interacting theory had ghosts.

Boulware, Deser (PRD 1972)

Ghosts are absent for very restrictive interaction terms inbimetric theories. Hassan, Rosen (PRL 2012), Hassan, Rosen, Schmidt-May (JHEP 2012)



What is a bimetric theory?

A massive spin-2 particle will generally mix with the gravitron.

Gravitron: fluctuation of the metric→ Write down a theory with 2 metrics and have them interact.

S = m2g

∫d4x

(√−gR(g) + α2

√−f R(f )

)+ Sint + Smatter .



No ghosts are present if

Sint = −2α2m4g

∫d4x√−g V (

√g−1f )

V (S) = β0 + β1 Sµ1

µ1 + β2 Sµ1

[µ1Sµ2

µ2] + β3 Sµ1

[µ1Sµ2

µ2Sµ3

µ3] + β4 detS

Consistent theory with few parameters

√−gV (g−1f )

∣∣∣βn

=√−f V (f −1g)

∣∣∣β4−n

The metrics are treated symmetrically in Sint.

Smatter =

∫d4x√−gLmatter(g ,Φmatter)



Quadratic Lagrangian:

Spin-2 particles are fluctuations of the metrics around the same background

gµν = gµν +1

mPl(δGµν − αδMµν) , fµν = gµν +

1

mPl

(δGµν + α−1δMµν

)

S ⊃∫

d4x√−g(Lkin

2 (δG ) + Lkin2 (δM)− m2

FP

4

(tr(δM2)− tr(δM)2

)− 1

mPl(δGµν − αδMµν)Tµν + LΛ

)

Fierz-Pauli mass: mFP = mPl√β1 + 2β2 + β3

Reduced Planck mass: mPl = mg

√1 + α2

Λ = α2m2g (β0 + 3β1 + 3β2 + β3) = m2

g (β4 + 3β3 + 3β2 + β1)


Babichev, Marzola, Raidal, Schmidt-MayUrban, Veermae, Von Strauss (PRD 2016, JCAP 2016)

Two spin-2 particles:

one massless, one massive.




gµν = gµν +1


1

mPl


)S ⊃

∫d4x

√−g(Lkin

2 (δG ) + Lkin2 (δM)− m2

FP

4


)− 1


)

Fierz-Pauli mass: mFP = mPl√β1 + 2β2 + β3


√1 + α2

Λ = α2m2g (β0 + 3β1 + 3β2 + β3) = m2

g (β4 + 3β3 + 3β2 + β1)








gµν = gµν +1


1

mPl


)S ⊃

∫d4x

√−g(Lkin

2 (δG ) + Lkin2 (δM)− m2

FP

4


)− 1


)Fierz-Pauli mass: mFP = mPl

√β1 + 2β2 + β3


√1 + α2

Λ = α2m2g (β0 + 3β1 + 3β2 + β3) = m2

g (β4 + 3β3 + 3β2 + β1)






Dark Matter

This theory modifies GR → The laws of gravity change

Make sure that the predictions are in agreement with those ofGR where this has been tested.

Simplest possibility : take α 1

In this limit, δM is a dark matter candidate

Vertex δMδGδG = 0 → Γ (δM → δGδG ) = 0

δM responds to δG (gravity) in the same way as the SMfields.




Heavy spin-2 DM



Γ (δM → SMSM) ∼ α2m3FP

m2Pl

Perturbativity condition:typical energy < αmPl

Production via Freeze-in


Second surprise

gµν = gµν +δGµν

mPl+O(α1) , fµν = gµν +

1

α

δMµν

mPl+O(α1)

Loosely speaking, the self-interactions of δM are the same as thoseof δG but enhanced by powers of 1/α.

Figure: Bimetric theories naturally give rise to self-interacting spin-2 DM

Very predictive! Lengthy calculations


PRELIMINARY


Self-interaction cross section

gµν = gµν +δGµν

mPl+O(α1) , fµν = gµν +

1

α

δMµν

mPl+O(α0)

Loosely speaking, the self-interactions of δM are the same as thoseof δG but enhanced by powers of 1/α.

Figure: Bimetric theories naturally give rise to self-interacting spin-2 DM

Very predictive! But calculations are very lengthy


PRELIMINARY

σSI =(β1 + 2β2 + β3)2

m2FPα

4F (r) , with r =

β1 − β3

β1 + 2β2 + β3

Perturbativity condition: typical energy < αmPl

β1 + 2β2 + β3 < α2


How can we produced them? + no thermal equilibrium

(Regime 3A)


PRELIMINARY


How can we produced them? + no thermal equilibrium

(Regime 3A)Camilo Garcia Cely, ULB From spin-1 to spin-2 SIMPs

PRELIMINARY


- -

≡ (β-β)/(β+β+β)

[

]-


PRELIMINARY

Conclusions

In bimetric theories, requiring negligible interactions betweenthe second metric and ordinary particles naturally leads tospin-2 SIDM capable of addressing the small-scale problems.

SIDM without light mediators can be produced via 3-to-2annihilations. The corresponding increase of temperature isnot problematic if the two sectors have a large temperatureratio before freeze-out.

10-3 10-2 10-1 100 101 102 103

10-7

10-5

10-3

10-1

101

mA [MeV]

αX

Lyman-α

Dark freeze-out

Freeze-in

Reanni.

Log10[T'/T]

-2.5

-2.0

-1.5

-1.0

-0.5

camilo garcia cely, ulb · 2017. 10. 6. · camilo garcia cely, ulb self-interacting dark matter...

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