Dark matter heavyweights SUSY and Q-balls Inflation+SUSY Q-balls - - PowerPoint PPT Presentation

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Dark matter heavyweights SUSY and Q-balls Inflation+SUSY Q-balls - - PowerPoint PPT Presentation

Dec 20, 2022 293 likes •1.54k views

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015 Dark matter heavyweights SUSY and Q-balls Inflation+SUSY Q-balls stable Q-balls as dark matter interactions with matter, detection, constraints The IceCube discovery and

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Dark matter heavyweights

  • SUSY and Q-balls

– Inflation+SUSY⇒ Q-balls – stable Q-balls as dark matter – interactions with matter, detection, constraints

  • The IceCube discovery and

very heavy dark matter

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Echoes of supersymmetry in the early universe

baryons baryonic Q−balls unstable stable dark matter Affleck−Dine condensate gravity waves

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

SUSY and Q-balls

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

SUSY and Q-balls

Why would one suspect that SUSY ⇒ Q-balls?

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

SUSY and Q-balls

Why would one suspect that SUSY ⇒ Q-balls?

SUSY SUSY Bose−Einstein nucleus SUSY

Q−ball

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Q-balls

Let us consider a complex scalar field φ(x, t) in a potential that respects a U(1) symmetry: φ → eiθφ.

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Q-balls

Let us consider a complex scalar field φ(x, t) in a potential that respects a U(1) symmetry: φ → eiθφ. vacuum: φ = 0

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Q-balls

Let us consider a complex scalar field φ(x, t) in a potential that respects a U(1) symmetry: φ → eiθφ. vacuum: φ = 0 conserved charge: Q =

1 2i

φ† ↔ ∂0 φ

  • d3x

4

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Q-balls

Let us consider a complex scalar field φ(x, t) in a potential that respects a U(1) symmetry: φ → eiθφ. vacuum: φ = 0 conserved charge: Q =

1 2i

φ† ↔ ∂0 φ

  • d3x

Q = 0 ⇒ φ = 0 in some finite domain

4

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Q-balls

Let us consider a complex scalar field φ(x, t) in a potential that respects a U(1) symmetry: φ → eiθφ. vacuum: φ = 0 conserved charge: Q =

1 2i

φ† ↔ ∂0 φ

  • d3x

Q = 0 ⇒ φ = 0 in some finite domain

⇒ Q-ball [Rosen; Friedberg, Lee, Sirlin; Coleman]

4

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Minimize energy E =

  • d3x
  • 1

2| ˙

φ|2 + 1

2|∇φ|2 + U(φ)

  • under

the constraint Q = const. Introduce Lagrange multiplier:

5

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Minimize energy E =

  • d3x
  • 1

2| ˙

φ|2 + 1

2|∇φ|2 + U(φ)

  • under

the constraint Q = const. Introduce Lagrange multiplier:

E = E + ω

  • Q − 1

2i

  • φ∗ ↔

∂ t φ d3x

  • 5
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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Minimize energy E =

  • d3x
  • 1

2| ˙

φ|2 + 1

2|∇φ|2 + U(φ)

  • under

the constraint Q = const. Introduce Lagrange multiplier:

E = E + ω

  • Q − 1

2i

  • φ∗ ↔

∂ t φ d3x

  • =
  • d3x 1

2

  • ∂

∂tφ − iωφ

  • 2 +
  • d3x
  • 1

2|∇φ|2 + ˆ

Uω(φ)

  • + ωQ,

where ˆ Uω(φ) = U(φ) −

1 2 ω2 φ2.

5

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Minimize energy E =

  • d3x
  • 1

2| ˙

φ|2 + 1

2|∇φ|2 + U(φ)

  • under

the constraint Q = const. Introduce Lagrange multiplier:

E = E + ω

  • Q − 1

2i

  • φ∗ ↔

∂ t φ d3x

  • =
  • d3x 1

2

  • ∂

∂tφ − iωφ

  • 2 +
  • d3x
  • 1

2|∇φ|2 + ˆ

Uω(φ)

  • + ωQ,

where ˆ Uω(φ) = U(φ) −

1 2 ω2 φ2.

  • Minimize blue by setting φ = eiωt ¯

φ(x)

5

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Minimize energy E =

  • d3x
  • 1

2| ˙

φ|2 + 1

2|∇φ|2 + U(φ)

  • under

the constraint Q = const. Introduce Lagrange multiplier:

E = E + ω

  • Q − 1

2i

  • φ∗ ↔

∂ t φ d3x

  • =
  • d3x 1

2

  • ∂

∂tφ − iωφ

  • 2 +
  • d3x
  • 1

2|∇φ|2 + ˆ

Uω(φ)

  • + ωQ,

where ˆ Uω(φ) = U(φ) −

1 2 ω2 φ2.

  • Minimize blue by setting φ = eiωt ¯

φ(x)

  • Minimize red by choosing ¯

φ(x) to be the bounce for tunneling in ˆ Uω(φ) = U(φ) −

1 2 ω2φ2.

5

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Minimize energy E =

  • d3x
  • 1

2| ˙

φ|2 + 1

2|∇φ|2 + U(φ)

  • under

the constraint Q = const. Introduce Lagrange multiplier:

E = E + ω

  • Q − 1

2i

  • φ∗ ↔

∂ t φ d3x

  • =
  • d3x 1

2

  • ∂

∂tφ − iωφ

  • 2 +
  • d3x
  • 1

2|∇φ|2 + ˆ

Uω(φ)

  • + ωQ,

where ˆ Uω(φ) = U(φ) −

1 2 ω2 φ2.

  • Minimize blue by setting φ = eiωt ¯

φ(x)

  • Minimize red by choosing ¯

φ(x) to be the bounce for tunneling in ˆ Uω(φ) = U(φ) −

1 2 ω2φ2.

  • Finally, minimize E with respect to ω.

5

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Q-balls exist whenever ˆ Uω(φ) = U(φ) −

1 2 ω2φ2 is not positive definite

for some value of ω.

small , large Q ω ω

2

large , small Q

2

ω=0

ϕ

ϕ(0)

U( )

1

ϕ − − ω ϕ

2

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Q-balls exist if U(φ)

  • φ2 = min,

for φ = φ0 > 0 [Coleman]

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Q-balls exist if U(φ)

  • φ2 = min,

for φ = φ0 > 0 [Coleman] Finite φ0: M(Q) ∝ Q

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Q-balls exist if U(φ)

  • φ2 = min,

for φ = φ0 > 0 [Coleman] Finite φ0: M(Q) ∝ Q Flat potential (U(φ) ∼ φp, p < 2); φ0 = ∞:

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Q-balls exist if U(φ)

  • φ2 = min,

for φ = φ0 > 0 [Coleman] Finite φ0: M(Q) ∝ Q Flat potential (U(φ) ∼ φp, p < 2); φ0 = ∞:

✓ ✒ ✏ ✑

M(Q) ∝ Qα, α < 1

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Q-balls exist in (softly broken) SUSY because

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Q-balls exist in (softly broken) SUSY because

  • the theory has scalar fields

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Q-balls exist in (softly broken) SUSY because

  • the theory has scalar fields
  • the scalar fields carry conserved global charge (baryon and lepton

numbers)

8

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Q-balls exist in (softly broken) SUSY because

  • the theory has scalar fields
  • the scalar fields carry conserved global charge (baryon and lepton

numbers)

  • attractive scalar interactions (tri-linear terms, flat directions) force

(U(φ)

  • φ2) = min for non-vacuum values.

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

MSSM, gauge mediated SUSY breaking Baryonic Q-balls (B-balls) are entirely stable if their mass per unit baryon charge is less than the proton mass.

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

MSSM, gauge mediated SUSY breaking Baryonic Q-balls (B-balls) are entirely stable if their mass per unit baryon charge is less than the proton mass. M(Q) = MSQ3/4 ⇒

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

MSSM, gauge mediated SUSY breaking Baryonic Q-balls (B-balls) are entirely stable if their mass per unit baryon charge is less than the proton mass. M(Q) = MSQ3/4 ⇒

M(QB) QB

∼ MSQ−1/4 < 1GeV

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

MSSM, gauge mediated SUSY breaking Baryonic Q-balls (B-balls) are entirely stable if their mass per unit baryon charge is less than the proton mass. M(Q) = MSQ3/4 ⇒

M(QB) QB

∼ MSQ−1/4 < 1GeV for QB ≫ MS 1 TeV 4

> ∼ 1012

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

MSSM, gauge mediated SUSY breaking Baryonic Q-balls (B-balls) are entirely stable if their mass per unit baryon charge is less than the proton mass. M(Q) = MSQ3/4 ⇒

M(QB) QB

∼ MSQ−1/4 < 1GeV for QB ≫ MS 1 TeV 4

> ∼ 1012

✓ ✒ ✏ ✑

Such B-balls are entirely stable.

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Baryon asymmetry

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Baryon asymmetry

✗ ✖ ✔ ✕

η ≡

nB nγ =

  • 6.1 +0.3

−0.2

  • × 10−10

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Baryon asymmetry

✗ ✖ ✔ ✕

η ≡

nB nγ =

  • 6.1 +0.3

−0.2

  • × 10−10

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

What happened right after the Big Bang?

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

What happened right after the Big Bang?

  • Inflation probably took place

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

What happened right after the Big Bang?

  • Inflation probably took place
  • Baryogenesis – definitely after inflation

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

What happened right after the Big Bang?

  • Inflation probably took place
  • Baryogenesis – definitely after inflation

Standard Model is not consistent with the observed baryon asymmetry (assuming inflation)

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Affleck–Dine baryogenesis

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Affleck–Dine baryogenesis

  • Natural if SUSY+Inflation

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Affleck–Dine baryogenesis

  • Natural if SUSY+Inflation
  • Can explain matter

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Affleck–Dine baryogenesis

  • Natural if SUSY+Inflation
  • Can explain matter
  • Can explain dark matter

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Affleck–Dine baryogenesis

  • Natural if SUSY+Inflation
  • Can explain matter
  • Can explain dark matter
  • Predictions can be tested soon

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Inflation

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Inflation All matter is produced during reheating after inflation.

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Inflation All matter is produced during reheating after inflation. SUSY ⇒ flat directions. During inflation, scalar fields are displaced from their minima.

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Affleck – Dine baryogenesis

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Affleck – Dine baryogenesis at the end of inflation a scalar condensate develops a large VEV along a flat direction

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Affleck – Dine baryogenesis at the end of inflation a scalar condensate develops a large VEV along a flat direction

14

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Affleck – Dine baryogenesis at the end of inflation a scalar condensate develops a large VEV along a flat direction

14

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Affleck – Dine baryogenesis at the end of inflation a scalar condensate develops a large VEV along a flat direction CP violation is due to time-dependent background.

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Affleck – Dine baryogenesis at the end of inflation a scalar condensate develops a large VEV along a flat direction CP violation is due to time-dependent background. Baryon asymmetry: φ = |φ|eiωt

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Affleck – Dine baryogenesis: an example [Dine+AK, Rev.Mod.Phys.]

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Affleck – Dine baryogenesis: an example [Dine+AK, Rev.Mod.Phys.] Suppose the flat direction is lifted by a higher dimension operator Wn =

1 MnΦn+3. The expansion of the universe breaks SUSY and introduces mass

terms m2 ∼ ±H2.

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Affleck – Dine baryogenesis: an example [Dine+AK, Rev.Mod.Phys.] Suppose the flat direction is lifted by a higher dimension operator Wn =

1 MnΦn+3. The expansion of the universe breaks SUSY and introduces mass

terms m2 ∼ ±H2. The scalar potential: V = −H2|Φ|2 + 1 M 2n|Φ|2n+4

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Affleck – Dine baryogenesis: an example [Dine+AK, Rev.Mod.Phys.] Suppose the flat direction is lifted by a higher dimension operator Wn =

1 MnΦn+3. The expansion of the universe breaks SUSY and introduces mass

terms m2 ∼ ±H2. The scalar potential: V = −H2|Φ|2 + 1 M 2n|Φ|2n+4 Assume the inflation scale E ∼ 1015 GeV The Hubble constant HI ≈ E2/Mp ≈ 1012 GeV. TR ∼ 109 GeV

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

In this example, the final baryon asymmetry is nB nγ ∼ nB (ρI/TR) ∼ nB nΦ TR mΦ ρΦ ρI ∼ 10−10

  • TR

109GeV Mp m3/2 (n−1)

(n+1) 16

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

In this example, the final baryon asymmetry is nB nγ ∼ nB (ρI/TR) ∼ nB nΦ TR mΦ ρΦ ρI ∼ 10−10

  • TR

109GeV Mp m3/2 (n−1)

(n+1)

Correct baryon asymmetry for n = 1.

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

✓ ✒ ✏ ✑

Fragmentation of the Affleck-Dine condensate

t x

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

✓ ✒ ✏ ✑

Fragmentation of the Affleck-Dine condensate

t x

[AK, Shaposhnikov]

17

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

✓ ✒ ✏ ✑

Fragmentation of the Affleck-Dine condensate

t x

[AK, Shaposhnikov] small inhomogeneities can grow

17

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

✓ ✒ ✏ ✑

Fragmentation of the Affleck-Dine condensate

t x

[AK, Shaposhnikov] small inhomogeneities can grow unstable modes: 0 < k < kmax =

  • ω2 − U ′′(φ)

17

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

✓ ✒ ✏ ✑

Fragmentation of the Affleck-Dine condensate

t x

[AK, Shaposhnikov] small inhomogeneities can grow unstable modes: 0 < k < kmax =

  • ω2 − U ′′(φ)

⇒ Lumps of baryon condensate

17

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

✓ ✒ ✏ ✑

Fragmentation of the Affleck-Dine condensate

t x

[AK, Shaposhnikov] small inhomogeneities can grow unstable modes: 0 < k < kmax =

  • ω2 − U ′′(φ)

⇒ Lumps of baryon condensate ⇒ Q-balls

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

✓ ✒ ✏ ✑

Fragmentation ≈ pattern formation Familiar example:

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Numerical simulations of the fragmentation

20 40 60 20 40 60 20 40 60 20 40 60 20 40 60

[Kasuya, Kawasaki]

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Two-dimensional charge density plots [Multamaki].

10 20 30 40 10 20 30 40

(a) mt = 0

10 20 30 40 10 20 30 40

(b) mt = 75

10 20 30 40 10 20 30 40

(c) mt = 150

10 20 30 40 10 20 30 40

(d) mt = 375

10 20 30 40 10 20 30 40

(e) mt = 525

10 20 30 40 10 20 30 40

(f) mt = 675

10 20 30 40 10 20 30 40

(g) mt = 825

10 20 30 40 10 20 30 40

(h) mt = 900 20

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Three-dimensional charge density plots [Multamaki].

(i) mt = 900 (j) mt = 1050 (k) mt = 1200 (l) mt = 1350 21

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

✓ ✒ ✏ ✑

Fragmentation of AD condensate can produce Q-balls

t x

22

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

✓ ✒ ✏ ✑

Fragmentation of AD condensate can produce Q-balls

t x

SUSY Q-balls may be stable or unstable

22

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

✓ ✒ ✏ ✑

Fragmentation of AD condensate can produce Q-balls

t x

SUSY Q-balls may be stable or unstable if stable ⇒ dark matter

22

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

✓ ✒ ✏ ✑

Fragmentation of AD condensate can produce Q-balls

t x

SUSY Q-balls may be stable or unstable if stable ⇒ dark matter

baryons baryonic Q−balls unstable stable dark matter Affleck−Dine condensate

Dark matter in the form of stable SUSY Q-balls?

22

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Stable Q-balls as dark matter

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Stable Q-balls as dark matter Q-balls can accommodate baryon number at lower energy than a nucleon ⇒ B-Balls catalyze proton decay [AK,Kuzmin,Shaposhnikov,Tinyakov] Signal:

23

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Stable Q-balls as dark matter Q-balls can accommodate baryon number at lower energy than a nucleon ⇒ B-Balls catalyze proton decay [AK,Kuzmin,Shaposhnikov,Tinyakov] Signal:

✛ ✚ ✘ ✙

dE dl ∼ 100

  • ρ

1 g/cm3

  • GeV

cm

23

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Stable Q-balls as dark matter Q-balls can accommodate baryon number at lower energy than a nucleon ⇒ B-Balls catalyze proton decay [AK,Kuzmin,Shaposhnikov,Tinyakov] Signal:

✛ ✚ ✘ ✙

dE dl ∼ 100

  • ρ

1 g/cm3

  • GeV

cm

Heavy ⇒ low flux

23

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Stable Q-balls as dark matter Q-balls can accommodate baryon number at lower energy than a nucleon ⇒ B-Balls catalyze proton decay [AK,Kuzmin,Shaposhnikov,Tinyakov] Signal:

✛ ✚ ✘ ✙

dE dl ∼ 100

  • ρ

1 g/cm3

  • GeV

cm

Heavy ⇒ low flux ⇒ experimental limits from Super-Kamiokande and other large detectors

23

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Present experimental limits [Arafune et al.];

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

A “candidate event” [Lattes, Fujimoto and Hasegawa, Phys.Rept. 65, 151 (1980)]

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Unstable B-balls

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Unstable B-balls Gravity mediated SUSY breaking typically produces potentials which grow as ∼ φ2 up to the Planck scale. Hence, Q-balls are unstable.

26

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Unstable B-balls Gravity mediated SUSY breaking typically produces potentials which grow as ∼ φ2 up to the Planck scale. Hence, Q-balls are unstable. Decay of Q-balls results in late non-thermal production of LSP.

26

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Unstable B-balls Gravity mediated SUSY breaking typically produces potentials which grow as ∼ φ2 up to the Planck scale. Hence, Q-balls are unstable. Decay of Q-balls results in late non-thermal production of LSP. Ordinary and dark matter arise from the same process. Hence, one may be able to explain why Ωmatter and Ωdark are not very different. [AK;Fijii,Yanagida; Enqvist, McDonald; Laine, Shaposhnikov]

26

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Ωdark/ Ωmatter ∼ 6

27

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Ωdark/ Ωmatter ∼ 6

  • Dark matter is stable Q-balls [AK; Laine, Shaposhnikov]

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Ωdark/ Ωmatter ∼ 6

  • Dark matter is stable Q-balls [AK; Laine, Shaposhnikov]
  • Dark matter is LSP produced non-thermally from decay of unstable

Q-balls [Enqvist, McDonald; Fujii, Hamaguchi; Fujii, Yanagida]

27

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SLIDE 86

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Ωdark/ Ωmatter ∼ 6

  • Dark matter is stable Q-balls [AK; Laine, Shaposhnikov]
  • Dark matter is LSP produced non-thermally from decay of unstable

Q-balls [Enqvist, McDonald; Fujii, Hamaguchi; Fujii, Yanagida]

  • Dark matter is gravitino produced non-thermally from decay of unstable

Q-balls [Fujii, Yanagida; Kawasaki et al.; AK, Shoemaker]

27

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SLIDE 87

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

ΩB−ball/ Ωmatter ∼ 6

28

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SLIDE 88

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

ΩB−ball/ Ωmatter ∼ 6

  • Gauge-mediated SUSY breaking

28

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SLIDE 89

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

ΩB−ball/ Ωmatter ∼ 6

  • Gauge-mediated SUSY breaking
  • QB ∼ 1026±2 (in agreement with numerical simulations)

28

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SLIDE 90

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

ΩB−ball/ Ωmatter ∼ 6

  • Gauge-mediated SUSY breaking
  • QB ∼ 1026±2 (in agreement with numerical simulations)

More specifically, ΩB−ball/Ωmatter ∼ 6 implies ηB ∼ 10−10 MSUSY

TeV QB 1026

−1/2

28

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SLIDE 91

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

ΩB−ball/ Ωmatter ∼ 6

29

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SLIDE 92

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

ΩB−ball/ Ωmatter ∼ 6

30

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SLIDE 93

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Astrophysical constraints

31

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SLIDE 94

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Astrophysical constraints

  • Q-balls pass through ordinary stars and planets

31

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SLIDE 95

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Astrophysical constraints

  • Q-balls pass through ordinary stars and planets
  • SUSY Q-balls accumulate inside white dwarfs and neutron stars

31

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SLIDE 96

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Astrophysical constraints

  • Q-balls pass through ordinary stars and planets
  • SUSY Q-balls accumulate inside white dwarfs and neutron stars
  • SUSY Q-balls can convert nuclear matter into squark condensate

31

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SLIDE 97

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Astrophysical constraints

  • Q-balls pass through ordinary stars and planets
  • SUSY Q-balls accumulate inside white dwarfs and neutron stars
  • SUSY Q-balls can convert nuclear matter into squark condensate

– first published estimates underestimated the rates

31

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SLIDE 98

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Astrophysical constraints

  • Q-balls pass through ordinary stars and planets
  • SUSY Q-balls accumulate inside white dwarfs and neutron stars
  • SUSY Q-balls can convert nuclear matter into squark condensate

– first published estimates underestimated the rates – new rates too high, unless the flat direction is lifted by baryon number violating operators.

31

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SLIDE 99

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Interactions of SUSY Q-balls with matter (old picture)

x x

Q−ball

quark quark χ

∝

1 m2

χ, slow

This process was thought to limit the rate at which the Q-balls could process baryonic matter. Lifetimes of neutron stars were though to be greater than the age

  • f the universe

32

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SLIDE 100

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Interactions of SUSY Q-balls with matter (correct picture)

x

Q−ball

antiquark quark

There is a Majorana mass term for quarks inside coming from the quark-squark-gluino vertex. Probability ∼ 1 for a quark to reflect as an antiquark. Very fast! [AK, Loveridge, Shaposhnikov].

33

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SLIDE 101

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Interactions of SUSY Q-balls with matter The MSSM Lagrangian contains terms describing interactions of quarks ψ with squarks φ and gluinos λ: L = −g √ 2T a

ij(λaσ2ψjφ∗ i) + C.C. + ...

and also the Majorana mass terms for gluinos: LM = Mλaλa. Of course, the quarks also have Dirac mass terms.

34

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SLIDE 102

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

In the basis {ψL, ψR, λ}, the mass matrix has a (simplified) form:   m ϕL m ϕR ϕL ϕR M   The squark fields φ grow large inside the Q-ball. This mass term causes a quark to scatter off a Q-ball as an antiquark, with probability of order 1.

35

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SLIDE 103

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

In the basis {ψL, ψR, λ}, the mass matrix has a (simplified) form:   m ϕL m ϕR ϕL ϕR M   The squark fields φ grow large inside the Q-ball. This mass term causes a quark to scatter off a Q-ball as an antiquark, with probability of order 1. Interaction rates are not limited by weak-scale cross section.

35

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SLIDE 104

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

In the basis {ψL, ψR, λ}, the mass matrix has a (simplified) form:   m ϕL m ϕR ϕL ϕR M   The squark fields φ grow large inside the Q-ball. This mass term causes a quark to scatter off a Q-ball as an antiquark, with probability of order 1. Interaction rates are not limited by weak-scale cross section. Signatures in detectors do not change significantly

35

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SLIDE 105

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Neutron stars: can they survive long enough? Pulsars ages: oldest pulsars have ( ˙ P /P ) ∼ (0.3 − 3) × 10−10yr−1 Some pulsars are also known to be (at least) as old as 10 Gyr based on the cooling ages of their white dwarf companions

36

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SLIDE 106

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Neutron stars: can they survive long enough? Pulsars ages: oldest pulsars have ( ˙ P /P ) ∼ (0.3 − 3) × 10−10yr−1 Some pulsars are also known to be (at least) as old as 10 Gyr based on the cooling ages of their white dwarf companions Inside a neutron star Q-ball VEV grows fast and reaches values at which the flat direction is lifted by higher-dimension operators

36

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Generally, the lifting terms can be written in the form V n(φ)lifting ≈ λnM 4 φ M n−1+m φ∗ M n−1−m

37

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SLIDE 108

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Generally, the lifting terms can be written in the form V n(φ)lifting ≈ λnM 4 φ M n−1+m φ∗ M n−1−m

  • If m = 0, the baryon number is broken. Q-balls inside a neutron star

reach some maximal size and stop growing in size. The rate of conversion

  • f matter into condensate stabilizes at a small value. This is allowed.

37

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SLIDE 109

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Generally, the lifting terms can be written in the form V n(φ)lifting ≈ λnM 4 φ M n−1+m φ∗ M n−1−m

  • If m = 0, the baryon number is broken. Q-balls inside a neutron star

reach some maximal size and stop growing in size. The rate of conversion

  • f matter into condensate stabilizes at a small value. This is allowed.
  • If m = 0, Q-balls change the way they grow after reaching a certain

size Qc.

37

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SLIDE 110

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Q-balls along ”Flat” and ”Curved” directions

FD CD ϕ

1 √ 2ΛQ1/4

ϕmax ω π √ 2ΛQ−1/4 Λ2ϕ−1

max = π

√ 2ΛQc−1/4 = ωc M 4π

√ 2 3 ΛQ3/4

ωQ R

1 √ 2ΛQ1/4

  • 3

8π 1 Λ2ϕmaxQ

1/3 = (3

2)1/3(Q/Qc)1/12RF D

The change from FD to CD makes the Q-ball grow faster and neutron star is destroyed: FD Q-balls CD Q-balls t 1010 years 1500 years Q-balls that go from FD to CD for Q < 1057 are ruled out, unless the lifting terms can break the baryon number.

38

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

White Dwarfs White dwarfs can also accumulate SUSY Q-balls. The rate of consumption is lower because of the lower density. Nevertheless, one should consider a possible limit coming from the fact that some very old (10 Gyr) white dwarfs are known to have cooled down to very low temperatures; they emit Lwd = 3 × 10−5L⊙ = 7 × 1028 erg/s. Q-balls must not produce more heat than this.

39

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

White Dwarfs White dwarfs can also accumulate SUSY Q-balls. The rate of consumption is lower because of the lower density. Nevertheless, one should consider a possible limit coming from the fact that some very old (10 Gyr) white dwarfs are known to have cooled down to very low temperatures; they emit Lwd = 3 × 10−5L⊙ = 7 × 1028 erg/s. Q-balls must not produce more heat than this. No new limits arise. For m = 0, Q-balls are ruled out by stability of neutron

  • stars. For m = 0, the rate of heat release is much less than Lwd.

39

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Another caveat: electric charge While the flat directions are gauge-invariant, a small number of scalar quanta can decay until kinematically forbidden. [AK,Shoemaker] This makes DM Q-balls electrically charged. Different signature: small ionization instead of massive pion production. Difficult to detect in Super-K, HAWC, and other large detectors.

40

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

IceCube detector

41

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SLIDE 115

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

PeV neutrinos discovered by IceCube

10-1 100 101 102 Events per 988 Days 102 103 Deposited EM-Equivalent Energy in Detector (TeV)

Background Atmospheric Muon Flux

  • Bkg. Atmospheric Neutrinos (π/K)

Background Uncertainties Atmospheric Neutrinos (90% CL Prompt Limit) Signal+Bkg. Best-Fit Astrophysical E−2 Spectrum Data

Features: no events at the Glashow resonance; apparently, a peak at 1 − 2 PeV;

42

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SLIDE 116

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

An astrophysical explanation

43

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SLIDE 117

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

A more exciting possibility: decaying dark matter Dark matter with mass >

∼ 2 PeV

X → ν+ SM particle [Feldstein, AK, Matsumoto, Yanagida]

44

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SLIDE 118

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Models of very heavy dark matter decaying into PeV neutrinos

  • Gravitino with R-parity violation
  • Hidden sector gauge boson
  • A singlet in extra dimension
  • A right-handed/sterile neutrino
  • ...

Case Spin SU(2)L U(1)Y Decay Operator 1. 3 1 ¯ LcφL 2. 1/2 ¯ LHcψ 3. 1/2 3 ¯ LψaτaHc 4. 1/2 2 −1/2 ¯ LF ψ 5. 1/2 3 −1 ¯ LψaτaH 6. 1 ¯ LγµV µL 7. 3/2 (¯ LiDµHc)γνγµψν

[Feldstein, AK, Matsumoto,Yanagida] Models/discussion: Feldstein et al., Esmaili & Serpico, Bhattacharya et al., Ahlers

45

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SLIDE 119

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Model-dependent gamma-ray constraints The dark matter explanation is consistent with multimessenger

  • bservations

and limits. These constraints are model- dependent, but common features exist in the spectra.

  • [Murase et al.]

Need more data, especially from IceCube-Gen2 !

46

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SLIDE 120

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Conclusions

47

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Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Conclusions

  • Very heavy dark matter is a well-motivated possibility.

47

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SLIDE 122

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Conclusions

  • Very heavy dark matter is a well-motivated possibility.
  • SUSY + Inflation ⇒ Q-balls, some may be stable, may be dark matter

47

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SLIDE 123

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Conclusions

  • Very heavy dark matter is a well-motivated possibility.
  • SUSY + Inflation ⇒ Q-balls, some may be stable, may be dark matter
  • Typical size large ⇒ typical density small ⇒ need large detectors to

search for relic Q-balls

47

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SLIDE 124

Alexander Kusenko (UCLA/Kavli IPMU) ICTP, 2015

Conclusions

  • Very heavy dark matter is a well-motivated possibility.
  • SUSY + Inflation ⇒ Q-balls, some may be stable, may be dark matter
  • Typical size large ⇒ typical density small ⇒ need large detectors to

search for relic Q-balls

  • IceCube discovery of PeV neutrinos could point to a very heavy relic

particle decay. (However, astrophysical explanations are possible and plausible.)

47