Cosmological Production of Dark Nuclei [arXiv:1812.08784 with - - PowerPoint PPT Presentation

Cosmological Production of Dark Nuclei

IAS program HKUST — 14 Jan 2019

Andrea Tesi

[arXiv:1812.08784 with Michele Redi]

Visible Matter Dark Matter

χ

*OK, but also less minimal scenarios can be simple and give interesting dark physics

Outline

• Introduction to Baryonic Dark Matter
• Dark Big Bang Nucleosynthesis
• Example: nucleon triplet of SU(2)
• Example: nucleon singlet with dark photon
• Outlook

Introduction to Baryonic Dark Matter

Stability of Dark Matter

robust property if it is related to an accidental symmetry

q → eiα/3q

in the SM, stability of matter thanks to U(1)B

• proton

What’s accidentally stable? What’s not?

• wino in the MSSM

fixed by gauge structure of the theory at renormalizable level

Introduction to Baryonic Dark Matter Cosmological Production of Dark Nuclei

how to build model based on accidental stability?

Minimalistic approach: A bit of theory bias:

[Cirelli, Strumia]

• Consider new ‘dark’ sectors, with QCD-like interactions
• Just a twist on the minimalistic approach

L = LSM + LDM + X

i

Oi MPl

Cosmological Production of Dark Nuclei Introduction to Baryonic Dark Matter

χ

part of an SU(2) multiplet w/o hypercharge (quintuplet)

Vector-like confinement

• SU(N) gauge theory confines at scale
• Valid up to the Planck scale
• Fundamental fermions have electroweak charges

[Kilic, Okui, Sundrum]

Ψ → eiαΨ

accidental dark baryon number conservation

Λ

We have: We also assume:

• Fermion masses much smaller than confinement scale m ⌧ Λ,

Λ & TeV

Cosmological Production of Dark Nuclei Introduction to Baryonic Dark Matter

L = LSM − Ga

µνGa µν

4g2

DC

+ ¯ Ψ(i / D − mΨ)Ψ + y ¯ ΨHΨ

Spectrum of the theory

it depends on the representation dimension of the fermions flavor symmetry as in ordinary QCD

SU(NF )×SU(NF ) → SU(NF )

Cosmological Production of Dark Nuclei Introduction to Baryonic Dark Matter

Concretely, we will consider NF = 3

• dark pion octect, decomposed under the SM
• dark baryon octect, decomposed under the SM

π, N

G, Ψ

energy

Λ

Dark Matter candidates in VLC

Good candidates among dark baryons N ∼ ΨΨΨ... ∼ 30, 50, 70, ...

under SU(2) U(1)

Cosmological Production of Dark Nuclei Introduction to Baryonic Dark Matter

Ψ

simplest model: triplet of SU(2)

N = ΨΨΨ, N = 8

SM

→ 3 + 5

cosmological stability dimension 5 dimension 6 dark pions × – dark baryons – X

[Antipin, Redi, Strumia, Vigiani]

Constraint from the LHC

even for only weakly charged states, constraints are around TeV this sets O( TeV) scale also for Dark Matter in related models

Cosmological Production of Dark Nuclei Introduction to Baryonic Dark Matter

[1805.12578/JHEP08(2018)017 with Barducci, De Curtis, Redi]

Dark Big Bang Nucleosynthesis

[Krnjaic, Sigurdson] [Hardy, Lasenby, March-Russell, West] [Detmold, McCullough, Pochinsky]

Residual strong forces and binding energies

Cosmological Production of Dark Nuclei Dark Big Bang Nucleosynthesis

nuclear physics affected by unnaturally large scattering lenghts

Ed/mp ≈ 0.0022

[see later]

a

howevere, we restrict to the the scenario

• nucleons splitting

∆MN ∼ α2 4π MN

splitting of nuclei

∆EB ∼ α2 a

&

• dominance of nuclear binding energy over weak binding

for the dark sector we consider

0.001 . EB MN . 0.1

EB & α2

2MN/4

BBN, cornerstone of cosmological history

many detailed codes, what are the structural properties?

[PRIMAT]

Cosmological Production of Dark Nuclei Dark Big Bang Nucleosynthesis

BBN, structural and accidental facts

Structural:

• Time scale set by deuterium
• Need to produce deuterium first
• Need emission of light quanta (weak process)

Accidental (typical of SM):

• Overall mass scale ~GeV
• Neutron decay
• Binding energy bottlenecks after 4He

ηb ∼ 10−10

in the SM deuterium formation is at saturation

σ(NN → Dγ)

precise knowledge of not crucial EB

Cosmological Production of Dark Nuclei Dark Big Bang Nucleosynthesis

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→

T

EB

what about dark BBN?

The discussion is simplified assuming asymmetric abundance we only track the redistribution of dark baryon number*

YDM ≈ 10−13 ✓TeV MN ◆ , 1 = X

Ai

AYAi YDM ≡ X

Ai

XAi

evolution of dark deuterium number

˙ nD + 3HnD = hσDvi  n2

N (neq N )2

neq

D

nD

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Cosmological Production of Dark Nuclei Dark Big Bang Nucleosynthesis

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→

T

EB

accidental facts of dark BBN

An approximate solution to the dark deuterium density dark deuterium is rarely at saturation (dark tritium even less abundant)

σ(NN → Dγ)

knowledge of crucial

XD = 5% ✓3TeV M ◆2✓EB/MN 0.05 ◆✓ hσDvi α/M 2

N

◆✓ g? 106.75 ◆1/2✓25 zf ◆

Cosmological Production of Dark Nuclei Dark Big Bang Nucleosynthesis

Dark Deuterium production rate

precise predictions for dark BBN

exploiting the universal properties of short range nuclear forces in modern language we use non-relativistic EFT for NN-scattering

[Kaplan, Savage, Wise 1996]

Dark Deuterium Production Rate Cosmological Production of Dark Nuclei

dark nucleon EFT

L = N † iDt + ~ D2 2MN + D2

t

2MN ! N + L4 +  MN g2N †Ja(~ · ~ Ba)N

L4 = − X

channel

Cchannel 4 (NPchannelN)†(NPchannelN)

Cosmological Production of Dark Nuclei Dark Deuterium Production Rate

minimal interactions, magnetic dipole operator and 4-fermi interactions elastic scattering per spin/isospin given by the above lagrangian fully determine the bound state formation under the assumption of ‘shallow’ bound states let’s see how…

Matching to elastic scattering

A = 4π MN 1 p cot δ − ip, p cot δ|s−wave ≈ −1/a, p = p MNE

Cosmological Production of Dark Nuclei Dark Deuterium Production Rate

A ∼ Cchannel

scattering lenght L4 poles of A bound state SM case a ! 0 irrelevant – ⇥ – a ⌧ 0 relevant E = |✏| ⇥ (nn): a(1S0) = 23.75fm a 0 relevant E = |✏| X = pMNEB = 1/a d(pn): a(3S1) = 5.38fm

effects of need to be included at all order when is large

L4

|a|

N

N

[see lectures by Iain Stewart]

Matching to elastic scattering

Cosmological Production of Dark Nuclei Dark Deuterium Production Rate

E → −EB

=

1 E+EB

2

coupling to the bound state read off from the residue N

N

D

by matching the EFT to the measured/given scattering lenghts/ binding energies alone we fully determine the ingredients needed for the BSF rate analog of the wave function overlap in Coulombian bound state formation (BSF)

gNND = √8πγ MN = p 8π√MNED MN

Validity of the EFT

appropriate description in presence of shallow bound states it obviously fails in the Coulombian case

Cosmological Production of Dark Nuclei Dark Deuterium Production Rate

[see original works by Kaplan, Savage, Wise from the ‘90s]

−|V0|

a

• nly one bound state close to zero energy

r

V (r)

[for SM deuterium: Kaplan, Savage, Scaldeferri, Wise; Rupak]

Magnetic transitions

everything in terms of scattering lenght and binding energies K, group factor calculable case by case

Cosmological Production of Dark Nuclei Dark Deuterium Production Rate

enhancement from initial state in the SM , slow neutrons are captured via magnetic dipole interactions a(1S0)γ ≈ −5

σvrel

• magnetic = KM

πα M 2

N

✓EBfinal MN ◆ 3

2

(1 − ainitialγfinal)2

+

Electric transitions (aka dipole approximation)

Cosmological Production of Dark Nuclei Dark Deuterium Production Rate

no enhancement from initial state (initial state is p-wave) everything in terms of scattering lenght and binding energies K, group factor calculable case by case

σvrel

• electric = KE

πα M 2

N

✓ MN EBfinal ◆ 1

2

v2

rel

Example: nucleon triplet of SU(2)

Cosmological Production of Dark Nuclei Example: nucleon triplet of SU(2)

Dirac triplet of SU(2),

dark nuclei with dark baryon number two live in the product name r of SU(2) Spin D1 1 D3 3 1 D5 5

V × V

V

in the symmetric limit, absence of Coulomb barrier for singlet and triplet, we have Sommerfeld enhancement quintuplet is repulsive, also we do not consider bound state there

⊗

N

N

ED1 > ED3

Cosmological Production of Dark Nuclei Example: nucleon triplet of SU(2)

Boltzmann equation

we consider symmetric Sommerfeld effect (SU(2) preserved)

dXD dz = 2cpg?MPlEBhσDvieff z2 YDM  (1XD)2β

• g2

N

geffg? z3/2e−z YDM MN EB 3/2 XD 2

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transition between bound states are faster than dissociation rates, we can sum:

(σvrel)eff = X

i

(σvrel)i , geff

D (T) =

X

i

gDi exp  −EB1 − EBi T

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Cosmological Production of Dark Nuclei Example: nucleon triplet of SU(2)

Cross sections

many rates contributes to hσvieff

20 40 60 80 100 10-4 10-3 10-2 10-1 1 10 10-4 10-3 10-2 10-1 1 10 z=B1/T 〈σv〉/σ0 〈σv〉/σ0

Triplet of SU(2)L EB1/MN=0.05, EB3/EB1=0.1 MN =3 TeV (3→1)M (3→1)E (1→3)M (1→3)E

20 40 60 80 100 10-4 10-3 10-2 10-1 1 10 10-4 10-3 10-2 10-1 1 10 z=B1/T 〈σv〉/σ0 〈σv〉/σ0

Triplet of SU(2)L EB1/MN=0.05, EB3/EB1=0.5 MN =3 TeV (3→1)M (3→1)E (1→3)M (1→3)E

E, Electric M, Magnetic E, Electric M, Magnetic

• Effect of less bind D3 can be important
• Important effect of Sommerfeld enhancement for the electric (p-wave) rates

Cosmological Production of Dark Nuclei Example: nucleon triplet of SU(2)

Abundance of Dark Deuterium D1

2000 4000 6000 8000 10000 10-3 10-2 10-1 1 10-3 10-2 10-1 1 MN [GeV] XD

EB1/MN=0.1 EB1/MN=0.05 EB1/MN=0.01 EB3/EB1=0.5 Triplet of SU(2)L w/ Sommerfeld (solid) w/o Sommerfeld (dashed)

2000 4000 6000 8000 10000 10-3 10-2 10-1 1 10-3 10-2 10-1 1 MN [GeV] XD

EB1/MN=0.1 EB1/MN=0.05 EB1/MN=0.01 EB3/EB1=0.1 Triplet of SU(2)L w/ Sommerfeld (solid) w/o Sommerfeld (dashed)

• Large effect only for very large binding energies
• Fraction of O(10%) recombined into dark deuterium

Indirect detection signals

can happen today from annihilation of residual V0

possible even in presence of totally asymmetric component Sommerfeld effects allow for the transition:

Cosmological Production of Dark Nuclei Example: nucleon triplet of SU(2)

we can reuse the results for the Wino

Indirect detection signals

Cosmological Production of Dark Nuclei Example: nucleon triplet of SU(2)

1000 1500 2000 2500 3000 10-26 10-25 10-24 10-23 10-22 10-21 10-26 10-25 10-24 10-23 10-22 10-21 MN [GeV] 〈σD+γv〉 [cm3s-1]

Triplet of SU(2)L EB3/EB1=0.5 EB3/MN=0.01, a5γ3=3 FERMI-LAT

NFW profile [R4]

1000 1500 2000 2500 3000 10-26 10-25 10-24 10-23 10-22 10-21 10-26 10-25 10-24 10-23 10-22 10-21 MN [GeV] 〈σD+γv〉 [cm3s-1]

Triplet of SU(2)L EB3/EB1=0.5 EB3/MN=0.05, a5γ3=3 FERMI-LAT

NFW profile [R4]

Example: nucleon singlet with dark photon

Cosmological Production of Dark Nuclei Example: nucleon singlet with dark photon

Mimicking the SM

different results with previous studies [Krnjajic, Sigurdson] input for studies that focus on large atomic numbers [Hardy et al] new Dirac fermions Q±

Q × Q = 11 + 30

→

3S1 + 1S0

2 4 6 8 10 10-1 1 10-1 1 MN [GeV] XD

EB1/MN=0.05 EB1/MN=0.01 EB1/MN=0.005 EB3/EB1=0.5 dark photon αD=10-4

200 400 600 800 1000 10-4 10-3 10-2 10-1 1 10-4 10-3 10-2 10-1 1 MN [GeV] XD

EB1/MN=0.1 EB1/MN=0.01 solid (w/ magnetic) dashed (w/o magnetic) EB3/EB1=0.5 dark photon αD=10-3

Outlook

Cosmological Production of Dark Nuclei Outlook

Conclusions Future Directions

• Rich phase in the dark sector, if it is similar to the SM
• Dark BBN can be computed from first principles
• Improvement on existing treatments
• A strongly-coupled analogy of BSF widely studied in the literature
• Clarify better the implications for indirect detection
• Sommerfeld from strong interactions?
• Explore the dark sector in more extreme condition (large density)

Thank You!

BACKUP (calculation of enhancement from initial state)

BACKUP (group theory factors)

BACKUP (dark tritium abundance)