Self-Interacting Asymmetric Dark Matter Coupled to a Light Massive Dark Photon

Self-Interacting Asymmetric Dark Matter Coupled to aLight Massive Dark Photon

Lauren Pearce

University of Minnesota

September 17th, 2014

Collaborators: Kalliopi Petraki and Alex Kusenko

JCAP 1407, 039 (2014)

Lauren Pearce (University of Minnesota) Self-Interacting Asymmetric DM September 17th, 2014 1 / 19

Motivation

The Standard Model

In the Standard Model:

Interactions are mediated by spin-1 gauge bosons.

The only spin-0 boson is the Higgs boson, which is involved inelectroweak symmetry breaking.

Matter is made of spin-1/2 fermions.

Global U(1) symmetries: baryon and lepton number.

What would a “similar” dark matter model look like?


Motivation

The Standard Model








Motivation

The Standard Model








Motivation

The Standard Model








Motivation

The Standard Model








Minimal “Similar” Dark Sector

Self-Interacting Dark Matter Model

Assume dark matter is also spin-1/2 fermions.

Has a self-interaction which is described by a UD(1) gauge group.

Carries a global quantum number: dark baryon number.














Further Motivations: Asymmetric Dark Matter

Asymmetric DM

Matter in the universe today carries a net baryon number.

We further assume that DM today has a nonzero dark baryon number.

The production of these asymmetries may be related.(Review: Petraki & Volkas, 2013)



Asymmetric DM






Asymmetric DM





Further Motivations: Self-Interaction

U(1) Gauge Self-Interaction

Long-range interaction, but strength ↓ as velocity ↑:

Can satisfy astrophysical bounds (Vogelsberger & Zavala, MNRAS 430(2013) 1722)......while being large enough for DM symmetric component to annihilatein early universe.

Eliminates cuspy profiles.

One way to resolve “Too-big-to-fail problem” (Boylan-Kolchin,Bullock, & M. Kaplinghat, 2011 & 2012)

Others: baryon effects, warm dark matter...




Long-range interaction, but strength ↓ as velocity ↑:Can satisfy astrophysical bounds (Vogelsberger & Zavala, MNRAS 430(2013) 1722)...

...while being large enough for DM symmetric component to annihilatein early universe.







Long-range interaction, but strength ↓ as velocity ↑:Can satisfy astrophysical bounds (Vogelsberger & Zavala, MNRAS 430(2013) 1722)......while being large enough for DM symmetric component to annihilatein early universe.


























If UD(1) is unbroken...

Dark Baryon Number

At high energies an asymmetry in dark baryon number is produced.

The particles that carry the dark baryon number also carry chargeunder the UD(1) gauge interaction (assume positive charge).

This asymmetry must be produced via UD(1) gauge-invariantoperators...

Hence an equal asymmetry is produced in some negatively-chargedparticle!

This negatively charged particle can’t be the antiparicle; otherwisethere’s no net asymmetry in dark baryon number.



Dark Baryon Number








Dark Baryon Number








Dark Baryon Number








Dark Baryon Number








Multiple Species

Need two species:

Positively charged dark protons which carry dark baryon number.

Negatively charged dark electrons.

An asymmetry of particles over antiparticles is produced in both species.

Like the Standard Model:

Somehow we have a baryon asymmetry, which corresponds to somenumber of positively charged protons.

Since electromagnetism is a good symmetry, this same process alsomade an equal number of negatively charged electrons.



Multiple Species

Need two species:









Multiple Species

Need two species:









Multiple Species

Need two species:









Multiple Species

Need two species:









Multiple Species

Need two species:








What About a Broken UD(1)?

Motiation to Break UD(1) Symmetry

Dark interactions cannot be infinitely long-ranged (e.g., would affectclustering at large scales).

One way to screen the interactions by giving the dark gauge mediatora nonzero mass through a dark Higgs mechanism.

This means that there is a phase transition above which the UD(1)symmetry is restored, and below which it is broken.














Multiple Species

As long as the asymmetry is generated before the dark phase transition inwhich the above argument still holds.

DM is multi-component in much of parameter space.

Ξ�ann =.5

Α D=Α D

,min

Α D=10

Α D,m

in

Below solid lines:Asymmetry generation

in pD and eD

Above solid lines:Asymmetry generationin pD only possible

Short-range scatte

ring Hv ~ 10 km�sL

Long-range scatterin

g Hv t10 km�sL

10-1 1 101 10210-6

10-5

10-4

10-3

10-2

10-1

mp @GeVD

MD

@GeV

D

ΑD > 4Π

ΑD> 4Π


in pD and eD

Above solidlines: Asymmetrygenerationin pD onlypossible

ΑD>Α

D, m

in

ΑD<Α

D, m

in

10-1 1 101 102 103 10410-6

10-5

10-4

10-3

10-2

10-1

mp @GeVD

MD@G

eVD

Σpp�mp = 1 cm2�g at v = 220 km�s

Σpp�mp = 0.5 cm2�g at v = 10 km�s

αD,min: minimum for sufficient annihilation of the thermal dark protons in the early universe.


Multiple Species

As long as the asymmetry is generated before the dark phase transition inwhich the above argument still holds.

DM is multi-component in much of parameter space.

Ξ�ann =.5

Α D=Α D

,min

Α D=10

Α D,m

in


in pD and eD

Above solid lines:Asymmetry generationin pD only possible

Short-range scatte

ring Hv ~ 10 km�sL

Long-range scatterin

g Hv t10 km�sL

10-1 1 101 10210-6

10-5

10-4

10-3

10-2

10-1

mp @GeVD

MD

@GeV

D

ΑD > 4Π

ΑD> 4Π


in pD and eD

Above solidlines: Asymmetrygenerationin pD onlypossible

ΑD>Α

D, m

in

ΑD<Α

D, m

in

10-1 1 101 102 103 10410-6

10-5

10-4

10-3

10-2

10-1

mp @GeVD

MD@G

eVD

Σpp�mp = 1 cm2�g at v = 220 km�s

Σpp�mp = 0.5 cm2�g at v = 10 km�s

αD,min: minimum for sufficient annihilation of the thermal dark protons in the early universe.


Dark Atoms

pD + eD → HD

Generically expect an asymmetric population of dark electrons anddark protons.

These can then form dark atoms (as long as dark photon massMD < αDµD).

Even in this simplistic model, we end up with multi-component darkmatter: dark protons, dark electrons, and dark atoms.

What Does This Mean?

What does the multicomponent nature of DM mean for:

Cosmology?

Halo shapes?


Dark Atoms

pD + eD → HD






Cosmology?

Halo shapes?


Dark Atoms

pD + eD → HD






Cosmology?

Halo shapes?


Dark Atoms

pD + eD → HD






Cosmology?

Halo shapes?


Dark Atoms

pD + eD → HD






Cosmology?

Halo shapes?


Dark Atoms

pD + eD → HD






Cosmology?

Halo shapes?


Implications for Cosmology...

Sample Sequence of Events

More involved cosmology due to multi-component nature:

Event Temperature ScaleDark asymmetry generation Tasy

Thermal decoupling of dark and SM sectors Tdec

Freeze-out of pD pD annihilations TD,p,fo ≈ mp/30Freeze-out of eD eD annihilations TD,e,fo ≈ me/30Dark recombination ∆ & TD,DR & ∆/50

UD(1)-breaking phase transition TD,PT ∼ MD/(8πq2φαD)1/2

Freeze-out of dark Higgs annihilations TD,φD ,fo ≈ mϕ/41

Dark photon chemical decoupling TD,γD ∼ MD/[40(8πq2φαD)1/2]

Big Bang Nucleosynthesis TV ,BBN ≈ 1 MeV

These events change number of d.o.f. in dark sector.Ratio of dark to SM d.o.f. ξ is time-dependent and may be > 1 or < 1.































Freeze-out of pD pD annihilations TD,p,fo ≈ mp/30

Freeze-out of eD eD annihilations TD,e,fo ≈ me/30Dark recombination ∆ & TD,DR & ∆/50












Freeze-out of pD pD annihilations TD,p,fo ≈ mp/30Freeze-out of eD eD annihilations TD,e,fo ≈ me/30

Dark recombination ∆ & TD,DR & ∆/50

























































































The UD(1)-breaking phase transition can occur before dark recombinationor freeze-out of dark proton and/or dark electron annihilations



Cosmological Constraints

Different cosmological histories lead to different constraints.

Time-dependence of ξ can affect constraints.

Several examples given in JCAP 1407, 039 (2014).

One example of constraints on dark photon mass:

qΦ 2Α

D»

0.1

qΦ 2

ΑD »

0.01

qΦ 2

ΑD »

10 -3

qΦ 2

ΑD »

10 -4

De

ca

yΓ

D®

e +e -

po

ssible

ifΕ

¹0

extra radiation at BBN

10-8 10-6 10-4 10-2 1

10-3

10-2

10-1

1

MD @GeVD

Ξ=

TD

�TV

Red: relic abundance of the dark photons may alterthe time of matter-radiation equality or dominate theDM density

Blue: Too much radiation at BBN








qΦ 2Α

D»

0.1

qΦ 2

ΑD »

0.01

qΦ 2

ΑD »

10 -3

qΦ 2

ΑD »

10 -4

De

ca

yΓ

D®

e +e -

po

ssible

ifΕ

¹0


10-8 10-6 10-4 10-2 1

10-3

10-2

10-1

1

MD @GeVD

Ξ=

TD

�TV










qΦ 2Α

D»

0.1

qΦ 2

ΑD »

0.01

qΦ 2

ΑD »

10 -3

qΦ 2

ΑD »

10 -4

De

ca

yΓ

D®

e +e -

po

ssible

ifΕ

¹0


10-8 10-6 10-4 10-2 1

10-3

10-2

10-1

1

MD @GeVD

Ξ=

TD

�TV










qΦ 2Α

D»

0.1

qΦ 2

ΑD »

0.01

qΦ 2

ΑD »

10 -3

qΦ 2

ΑD »

10 -4

De

ca

yΓ

D®

e +e -

po

ssible

ifΕ

¹0


10-8 10-6 10-4 10-2 1

10-3

10-2

10-1

1

MD @GeVD

Ξ=

TD

�TV










qΦ 2Α

D»

0.1

qΦ 2

ΑD »

0.01

qΦ 2

ΑD »

10 -3

qΦ 2

ΑD »

10 -4

De

ca

yΓ

D®

e +e -

po

ssible

ifΕ

¹0


10-8 10-6 10-4 10-2 1

10-3

10-2

10-1

1

MD @GeVD

Ξ=

TD

�TV




Implications for Halos

Self-Interaction and Dark Matter Halos

One motivation for introducing dark matter self-interaction is:

Interactions can modify the shape of small dark matter halos,potentially alleviating the disagreement between dark mattersimulations and observations.

However, if self-interactions are too large, than large halos may notbe elliptical.

Both of these questions must be revisited if dark matter ismulti-component, with different intra- and inter-species interactions.























Momentum-Transfer in Halos

Momentum-Transfer Rate

Define effective momentum transfer rate:

Γeff = hpΓp + heΓe + hHΓH

hi : mass fraction of species iΓi : momentum scattering rate of species i

Impose a cut-off on the contribution of each species:If the momentum-transfer rate for a given species is very large but this

species carries only a tiny fraction of the mass of the halo, the effect of the

momentum loss by this species on the halo dynamics is negligible.

Atom-atom interaction: Cline, Liu, Moore, & Xue (2014), Cyr-Racine & Sigurdson(2013)Atom-ion interactions: Cyr-Racine & Sigurdson (2013)

Ion-ion interactions: Khrapak, Ivlev & Morfill (2004)







Impose a cut-off on the contribution of each species:

If the momentum-transfer rate for a given species is very large but this




























Constraints on Momentum-Transfer Rate


To preserve ellipticity of large halos:

Γeff less than ∼ 17H0 at v ∼ 220 km/s, ρ ∼ 1 GeV/cm3.(σ/m . 1 cm2/g; Rocha, Bullock, & Kaplinghat (2012))

To modify smaller dwarf halos:

Γeff greater than ∼ 0.2H0 at v ∼ 10 km/s, ρ ∼ 0.5 GeV/cm3 .(σ/m & 0.5 cm2/g; Battaglia, Helmi, & Breddels (2013))





Γeff less than ∼ 17H0 at v ∼ 220 km/s, ρ ∼ 1 GeV/cm3.

(σ/m . 1 cm2/g; Rocha, Bullock, & Kaplinghat (2012))























Γeff greater than ∼ 0.2H0 at v ∼ 10 km/s, ρ ∼ 0.5 GeV/cm3 .

(σ/m & 0.5 cm2/g; Battaglia, Helmi, & Breddels (2013))









Sample Plots

Disfavored by ellipticityof large halos

Favored bygalactic

substructure

4ΜD > m H + D

Insufficientannihilation inearly universe

xD = 0.01

xD =0.99

1 101 102 103 104

10-2

10-1

mH @GeVD

ΑD

D = 500 keV, MD = 1 eV, ΞDR = 0.5

Favored by galactic substructure

Disfavored by ellipticity of large halos

xD =0.07

xD =0.01

D<

MD

<Μ

DΑ

D

MD

>Μ

DΑ

D

4ΜD >mH +D

10-11 10-9 10-7 10-5 10-3 10-110-1

1

101

102

MD @GeVD

ΜD

@GeV

D

m H = 250 GeV, ΑD = 0.05, ΞDR = 0.3

Regions where self-interaction can modify small halos withoutdestroying the ellipticity of large halos: due to velocity-dependence ofcross sections.

Can take mass of dark photon → 0; screening provided by boundstate formation.


Sample Plots


Favored bygalactic

substructure

4ΜD > m H + D


xD = 0.01

xD =0.99

1 101 102 103 104

10-2

10-1

mH @GeVD

ΑD

D = 500 keV, MD = 1 eV, ΞDR = 0.5



xD =0.07

xD =0.01

D<

MD

<Μ

DΑ

D

MD

>Μ

DΑ

D

4ΜD >mH +D

10-11 10-9 10-7 10-5 10-3 10-110-1

1

101

102

MD @GeVD

ΜD

@GeV

D

m H = 250 GeV, ΑD = 0.05, ΞDR = 0.3




Sample Plots


Favored bygalactic

substructure

4ΜD > m H + D


xD = 0.01

xD =0.99

1 101 102 103 104

10-2

10-1

mH @GeVD

ΑD

D = 500 keV, MD = 1 eV, ΞDR = 0.5



xD =0.07

xD =0.01

D<

MD

<Μ

DΑ

D

MD

>Μ

DΑ

D

4ΜD >mH +D

10-11 10-9 10-7 10-5 10-3 10-110-1

1

101

102

MD @GeVD

ΜD

@GeV

D

m H = 250 GeV, ΑD = 0.05, ΞDR = 0.3




Sample Plots


Favored bygalactic

substructure

4ΜD > m H + D


xD = 0.01

xD =0.99

1 101 102 103 104

10-2

10-1

mH @GeVD

ΑD

D = 500 keV, MD = 1 eV, ΞDR = 0.5



xD =0.07

xD =0.01

D<

MD

<Μ

DΑ

D

MD

>Μ

DΑ

D

4ΜD >mH +D

10-11 10-9 10-7 10-5 10-3 10-110-1

1

101

102

MD @GeVD

ΜD

@GeV

D

m H = 250 GeV, ΑD = 0.05, ΞDR = 0.3




Effect of Dark Atom Formation

Dark Atom Formation

Scattering rate in halos varies non-monotonically with αD and mH .

Very small αD : DM mostly ions, negligible DM self-interaction.Smaller αD : DM mostly ions, but more scattering. May affect smallhalos and eventually affect Milky-Way sized halos.Increasing αD : Dark recombination becomes more efficient; dark atomsform and scattering rate decreases.Large αD : atom-atom scattering cross section increases, may affectsmall halos and eventually larger halos.

Large mH suppresses the recomination rate in early universe (andscattering rate today).

This is the reason for the “wedge” shape.



Dark Atom Formation


Very small αD : DM mostly ions, negligible DM self-interaction.

Smaller αD : DM mostly ions, but more scattering. May affect smallhalos and eventually affect Milky-Way sized halos.Increasing αD : Dark recombination becomes more efficient; dark atomsform and scattering rate decreases.Large αD : atom-atom scattering cross section increases, may affectsmall halos and eventually larger halos.





Dark Atom Formation


Very small αD : DM mostly ions, negligible DM self-interaction.Smaller αD : DM mostly ions, but more scattering. May affect smallhalos and eventually affect Milky-Way sized halos.

Increasing αD : Dark recombination becomes more efficient; dark atomsform and scattering rate decreases.Large αD : atom-atom scattering cross section increases, may affectsmall halos and eventually larger halos.





Dark Atom Formation


Very small αD : DM mostly ions, negligible DM self-interaction.Smaller αD : DM mostly ions, but more scattering. May affect smallhalos and eventually affect Milky-Way sized halos.Increasing αD : Dark recombination becomes more efficient; dark atomsform and scattering rate decreases.

Large αD : atom-atom scattering cross section increases, may affectsmall halos and eventually larger halos.





Dark Atom Formation







Dark Atom Formation







Dark Atom Formation






Conclusions

Conclusions

Even with rather minimal assumptions, self-interacting asymmetricdark matter models generally have multi-component dark matter,with two species of ions and dark atoms.

This remains true for a light but not necessarily massless mediatorgauge boson.

Cosmological constraints may take very different forms depending onthe sequence of cosmological events.

There exist regions of parameter space in which DM self-scatteringcan affect clustering in small halos without endangering the ellipticityof larger halos.


Conclusions

Conclusions






Conclusions

Conclusions






Conclusions

Conclusions






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Self-Interacting Asymmetric Dark Matter Coupled to a Light Massive Dark Photon

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