Heavy Spinning Particles from Signs of Primordial Non-Gaussianities - - PowerPoint PPT Presentation

Heavy Spinning Particles from Signs of Primordial Non-Gaussianities

Suro Kim Kobe University

w/Toshifumi Noumi, Keito Takeuchi(Kobe U.), Siyi Zhou(HKUST) based on arXiv:1906.11840 [hep-th].

Introduction:
 Inflation as a particle collider

Cosmic Inflation

• Typical energy scale of Inflation GeV


c.f. LHC GeV

• It is natural to use inflation to probe high energy physics
• Primordial non-Gaussiantiy as a particle collider

(Cosmological Collider Physics)

Inflation as High Energy Frontier

~10$% ≤ 10$' ~10$( String Inflation GUT ~10$) Planck scale

H ∼ 1014

∼ 105

Chen, and Wang[2010] Baumann and Green[2012] Noumi, Yamaguchi and Yokoyama[2013] Arkani-Hamed and Maldacena[2015] Lee, Baumann and Pimentel[2016]

c.f. Previous Pimentel’s talk

Cosmological Collider Physics

! ! ! "

• 1. on-shell Particle creation


by fluctuation @ de-Sitter temperature GeV

1014

! ! ! "

Chen, and Wang[2010] Baumann and Green[2012] Noumi, Yamaguchi and Yokoyama[2013] Arkani-Hamed and Maldacena[2015] Lee, Baumann and Pimentel[2016]

σ

• Non-Gaussianity as Particle Collider
• 2. Decaying to scalar perturbation

which can be observed by CMB

Cosmological Collider Physics

⟨ζk1ζk2ζk3⟩ ⟨ζk1ζ−k1⟩⟨ζk3ζ−k3⟩ ∝ e−πμ(k3/k1)3/2sin m2 H2 − 9 4 log(k3/k1) Ps(cos θ)

!" !# !$ %

Mass of Spin ofσ

• 1. on-shell Particle creation


by fluctuation @ de-Sitter temperature GeV

1014

μ = m2 H2 − 9 4 Oscillating

Boltzmann factor

Energy scale of target

~10$% ≤ 10$' ~10$( String Inflation GUT )(GeV)

Oscillating feature of non-Gaussianity

Energy scale of target

What about this region

Difficult with oscillating feature Boltzmann suppression

∝ e−πμ

~10$% ≤ 10$' ~10$( String Inflation GUT )(GeV)

μ = m2 H2 − 9 4

When Signal is suppressed by

m = 3H

10−4

Oscillating feature of non-Gaussianity

When we want to see higher scale

• @ Particle Collider


• 1. Build a New Fancy Collider


• 2. Study effective interactions carefully



 Prediction of Weak-bosons from 4-Fermi interaction

LEP LHC ???

When we want to see higher scale

• @ Cosmological Collider


• 1. Build a New Fancy Universe


• 2. Study effective interactions carefully

When we want to see higher scale

• @ Cosmological Collider


• 1. Build a New Fancy Universe


• 2. Study effective interactions carefully

But we cannot So we focus on

Effective coupling @ Particle Collider

Resonance part non-Analytic part of Propagator (on-shell particle creation)

Effective coupling Analytic part of Propagator ex) Prediction of Weak boson from Fermi-interaction

m2 ≫ s

ϕ ϕ ϕ ϕ σ ϕ ϕ ϕ ϕ

• Q. What are imprints of

heavy particles on inflaton effective interactions?

Wilson-Coefficients

• Expand the scattering amplitude in Mandelstam variables

= M(s, t) = ∑

p,q

ap,qsptq = ∑

p

bp(t)sp

we neglected massless pole assuming gravity is subdominant

• Coefficients of

bp(t) = ∑

q

ap,qtq = ∮C ds 2πi M(s, t) sp+1

sp

C

!

• Coefficients of

Wilson-Coefficients

Deform the integral contour

sp

bp(t) = ∑

q

ap,qtq = ∮C ds 2πi M(s, t) sp+1

+∫C′

3

+ ∫C′

4 )

ds 2πi M(s, t) sp+1

= (∫C′

1

+ ∫C′

2

C′

1

C′

2

C′

3

C′

4

!

C

!

• Coefficients of

Wilson-Coefficients

Deform the integral contour Froissart-Martin bounds

M(s, t) < s2

sp

C′

1

C′

2

C′

3

C′

4

for p ≥ 2

bp(t) = ∑

q

ap,qtq = ∮C ds 2πi M(s, t) sp+1

+∫C′

3

+ ∫C′

4 )

ds 2πi M(s, t) sp+1

= (∫C′

1

+ ∫C′

2

!

C

!

UV information in IR coefficient

• For example, tree-level effects are

!

m2

1

m2

2

m2

3

= ∑

n [

g2

nPℓn (1 + 2t m2

n )

(m2

n)p+1

− g2

nPℓn (1 + 2t m2

n )

(−m2

n − t)p+1 ]

bp(t) = ∑

q

ap,qtq = (∫C′

3

+ ∫C′

4 )

ds 2πi M(s, t) sp+1

Residue for each poles @ and

m2

n

−m2

1 − t

−m2

n − t

Continuous sum over to incorporate branch cuts from loops

n

!

C′

3

C′

4

• For example, tree-level effects are

UV information in IR coefficient

!

m2

1

m2

2

m2

3

= ∑

n [

g2

nPℓn (1 + 2t m2

n )

(m2

n)p+1

− g2

nPℓn (1 + 2t m2

n )

(−m2

n − t)p+1 ]

bp(t) = ∑

q

ap,qtq = (∫C′

3

+ ∫C′

4 )

ds 2πi M(s, t) sp+1

m2

n

−m2

1 − t

−m2

n − t

Propagation of on-shell particle with mass and spin

mn ln

Residue for each poles @ and Continuous sum over to incorporate branch cuts from loops

n

Positivity bounds on coefficient

ap,0 =

∑

n

g2

n

(m2

n)p+1

• is always positive and
• The well-known positivity bounds on coefficients
• Universal and elegant, but detailed information such as

spins of the intermediate states is obscured at the cost

{

𝒫(t0)

for even for odd

p ≥ 2 p ≥ 2

Adams, Arkani-Hamed, Dubovsky, Nicolis, Rattazzi .[2006]

a2n,0

• Expanding in , we obtain each coefficients

t

s2n

s2n

a2n+1,0 = 0

• For odd : Always positive

𝒫(t1)

ap,1 =

∑

n

g2

n

(m2

n)p+1(2ℓ2 n + 2ℓn − p − 1)

(p + 1)∑

n

g2

n

(m2

n)p+1

• For even : Sign of coefficients depends on spins

{

for even for odd

p p p p

ln > l⋆ = −1 + 2p + 5 2

ap,1 > 0

Otherwise

ap,1 < 0

Spin dependence of coefficient

spt

Spin dependence of coefficient

a2,1 = ∑

n

g2

n

(m2

n)p+1 (2ℓ2 n + 2ℓn − 3)

where ln < l⋆ ∼ 0.82

a2,1 > 0 a2,1 < 0

s2t

where ln > l⋆ ∼ 0.82

ln

Spin dependence of coefficient

a2,1 = ∑

n

g2

n

(mn)p+1(2ℓ2

n + 2ℓn − 3)

where ln < l⋆ ∼ 0.82

a2,1 > 0 a2,1 < 0

s2t

where ln > l⋆ ∼ 0.82

The contribution from scalar fields is dominant The contribution from spinning fields is dominant

a2,1 ≥ 0 a2,1 < 0

• In general, Inflaton can couple to various fields.
• Scalar fields give a negative contribution to 


Spinning fields give a positive contribution to

a2,1 a2,1

Smoking Gun of massive spinning particle

Implications to EFT

• f inflaton

Effective field theory of Inflaton

S = ∫ dτd3x −g[ − 1 2 (∂μϕ)2 + α Λ4 (∂μϕ∂μϕ)2 + β Λ6 (∇μ∂νϕ)2(∂ρϕ)2 + ⋯]

Λ ∼ Mass of intermediate state

Focus on four point interaction, Derivative expansions

• Inflaton enjoys approximate shift symmetry under

slow-roll approximation,

ϕ

Inflaton

= 4α Λ4 (s2 + st + t2) − 3β Λ6 (s2t + st2) + ⋯

a2,0 a2,1

Summary

Can probe with sign of effective coupling!!

~10$% ≤ 10$' ~10$( String Inflation GUT )(GeV)

1 m2

σ − s

σ

m2 ≫ s

Oscillating feature of non-Gaussianity

Summary

S = ∫ dτd3x −g[ − 1 2 (∂μϕ)2 + α Λ4 (∂μϕ∂μϕ)2 + β Λ6 (∇μ∂νϕ)2(∂ρϕ)2 + ⋯]

, α

is universally positive = a2,0 (s2 + st + t2) + a2,1 (s2t + st2) + ⋯

a2,0

The contribution of scalar fields is dominant The contribution of spinning fields is dominant

a2,1 < 0 β > 0 a2,1 ≥ 0 β ≤ 0

Smoking Gun of massive spinning particle

Summary

S = ∫ dτd3x −g[ − 1 2 (∂μϕ)2 + α Λ4 (∂μϕ∂μϕ)2 + β Λ6 (∇μ∂νϕ)2(∂ρϕ)2 + ⋯]

= a2,0 (s2 + st + t2) + a2,1 (s2t + st2) + ⋯

Phenomenological implication in Keito Takeuchi’s Poster session #32

, α

is universally positive

a2,0

The contribution of scalar fields is dominant The contribution of spinning fields is dominant

a2,1 < 0 β > 0 a2,1 ≥ 0 β ≤ 0

Smoking Gun of massive spinning particle

Appendix

• Scalar amplitude in superstring theory

Open superstring amplitude

M(s, t) = (s2 + t2 + u2) [ B(−s, − t) s + t + B(−t, − u) t + u + B(−u, − s) u + s ]

→ π2 (s2 + st + t2) + π4 12 (s2 + st + t2)

2 + …

• Coefficients of is
• Exact cancellation between contributions of scalar and

higher spins

s2t

B(a, b) = ∫

1

dxxa(1 − a)b = Γ(a)Γ(b) Γ(a + b)

low-energy limit

Open superstring amplitude

20 40 60 80 100

• 4
• 2

2 4 6 8 10 nmax Coefficient of s2 Coefficient of s2t

a2,1 =

mmax

∑

n n+1

∑

ℓ=0

g2

nℓ

n4 (2ℓ2

n + 2ℓn − 3)

(nmax + 1 = lmax)

gnℓ Is the coupling constant of

ϕ ϕ gnℓ

m2

σ = n

Spin = ℓ

Energy scale of target

• Typically

• For example, if

FNL = ⟨ζζζ⟩ ⟨ζζ⟩3/2 ∼ H2 m2

H ∼ 3 × 1013

Ruled out by Planck

Target!

Gravitational Interaction 10#$ %

&'

1 10#( 10)* 10)+ String GUT Non-perturbative ,(GeV)

Fermion Loop

• Scalar intermediate states dominate over spinning ones.

q k1 k2 k3 k4

= 11y4 720π2m4 (s2 + st + t2) − 13y4 10080π2m6 st(s + t)

y