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

Suro Kim Kobe University w/Toshifumi Noumi, Keito Takeuchi(Kobe U.), Siyi Zhou(HKUST) based on arXiv:1906.11840 [hep-th]. Heavy Spinning Particles from Signs of Primordial Non-Gaussianities

Introduction: 
 Inflation as a particle collider

Cosmic Inflation

c.f. Previous Pimentel’s talk Inflation as High Energy Frontier c.f. LHC GeV (Cosmological Collider Physics) H ∼ 10 14 • Typical energy scale of Inflation GeV 
 ∼ 10 5 • It is natural to use inflation to probe high energy physics • Primordial non-Gaussiantiy as a particle collider Chen, and Wang[2010] Baumann and Green[2012] Noumi, Yamaguchi and Yokoyama[2013] Arkani-Hamed and Maldacena[2015] Lee, Baumann and Pimentel[2016] ≤ 10 $' ~10 $( ~10 $% ~10 $) String Planck scale Inflation GUT

Cosmological Collider Physics 1. on-shell Particle creation 
 by fluctuation @ de-Sitter temperature GeV ! ! ! " 10 14

Boltzmann factor Oscillating by fluctuation @ de-Sitter temperature GeV 1. on-shell Particle creation 
 Mass of Cosmological Collider Physics which can be observed by CMB 2. Decaying to scalar perturbation • Non-Gaussianity as Particle Collider Chen, and Wang[2010] ! ! ! Baumann and Green[2012] Noumi, Yamaguchi and Yokoyama[2013] Arkani-Hamed and Maldacena[2015] Lee, Baumann and Pimentel[2016] " 10 14 ⟨ ζ k 1 ζ k 2 ζ k 3 ⟩ m 2 H 2 − 9 ⟨ ζ k 1 ζ − k 1 ⟩⟨ ζ k 3 ζ − k 3 ⟩ ∝ e − πμ ( k 3 / k 1 ) 3/2 sin 4 log( k 3 / k 1 ) P s (cos θ ) Spin of σ σ ! $ ! # % m 2 H 2 − 9 μ = ! " 4

Oscillating Energy scale of target feature of non-Gaussianity ) (GeV) ~10 $% ~10 $( ≤ 10 $' String GUT Inflation

Energy scale of target What about this region feature of Oscillating Signal is suppressed by When non-Gaussianity Difficult with oscillating feature Boltzmann suppression ) (GeV) ~10 $% ~10 $( ≤ 10 $' String GUT Inflation m 2 H 2 − 9 ∝ e − πμ μ = 4 10 − 4 m = 3 H

When we want to see higher scale 
 1. Build a New Fancy Collider 
 
 
 
 2. Study effective interactions carefully 
 
 Prediction of Weak-bosons from 4-Fermi interaction LEP LHC ??? • @ Particle Collider 


When we want to see higher scale 
 1. Build a New Fancy Universe 
 
 
 
 2. Study effective interactions carefully • @ Cosmological Collider 


When we want to see higher scale 
 1. Build a New Fancy Universe 
 
 
 
 2. Study effective interactions carefully But we cannot So we focus on • @ Cosmological Collider 


Effective coupling @ Particle Collider Effective coupling Resonance part ex) Prediction of Weak boson Analytic part of Propagator from Fermi-interaction (on-shell particle creation) non-Analytic part of Propagator ϕ ϕ ϕ ϕ σ m 2 ≫ s 1 m 2 σ − s ϕ ϕ ϕ ϕ

Q. What are imprints of heavy particles on inflaton effective interactions?

Wilson-Coefficients we neglected massless pole assuming gravity is subdominant • Expand the scattering amplitude in Mandelstam variables = M ( s , t ) = ∑ a p , q s p t q = ∑ b p ( t ) s p p , q p s p a p , q t q = ∮ C b p ( t ) = ∑ ds M ( s , t ) • Coefficients of s p +1 2 π i ! q C

Wilson-Coefficients Deform the integral contour s p a p , q t q = ∮ C • Coefficients of b p ( t ) = ∑ ds M ( s , t ) s p +1 2 π i q = ( ∫ C ′ � + ∫ C ′ � + ∫ C ′ � 4 ) + ∫ C ′ � ds M ( s , t ) s p +1 2 π i 3 1 2 ! ! C ′ � 1 C ′ � C ′ � 4 3 C C ′ � 2

for Deform the integral contour Froissart-Martin bounds Wilson-Coefficients s p a p , q t q = ∮ C • Coefficients of b p ( t ) = ∑ ds M ( s , t ) s p +1 2 π i q 0 p ≥ 2 = ( ∫ C ′ � + ∫ C ′ � + ∫ C ′ � 4 ) + ∫ C ′ � ds M ( s , t ) s p +1 2 π i 3 1 2 M ( s , t ) < s 2 ! ! C ′ � 1 C ′ � C ′ � 4 3 C C ′ � 2

UV information in IR coefficient Continuous sum over to incorporate branch cuts from loops @ and Residue for each poles • For example, tree-level effects are a p , q t q = ( ∫ C ′ � + ∫ C ′ � b p ( t ) = ∑ 4 ) ds M ( s , t ) s p +1 2 π i q 3 n P ℓ n ( 1 + 2 t n ) n P ℓ n ( 1 + 2 t n ) g 2 g 2 n − t ) p +1 ] = ∑ n [ m 2 m 2 − ( m 2 n ) p +1 ( − m 2 ! ! m 2 − m 2 n − t n C ′ � C ′ � 4 3 − m 2 1 − t m 2 m 2 m 2 1 2 3 n

UV information in IR coefficient Continuous sum over to incorporate branch cuts from loops @ and Residue for each poles with mass and spin Propagation of on-shell particle • For example, tree-level effects are a p , q t q = ( ∫ C ′ � + ∫ C ′ � b p ( t ) = ∑ 4 ) ds M ( s , t ) s p +1 2 π i q 3 n P ℓ n ( 1 + 2 t n ) n P ℓ n ( 1 + 2 t n ) g 2 g 2 n − t ) p +1 ] = ∑ n [ m 2 m 2 − ( m 2 n ) p +1 ( − m 2 ! m 2 − m 2 n − t n m n l n − m 2 1 − t m 2 m 2 m 2 1 2 3 n

Positivity bounds on coefficient spins of the intermediate states is obscured at the cost for odd for even s 2 n t • Expanding in , we obtain each coefficients 𝒫 ( t 0 ) g 2 { ∑ n p ≥ 2 ( m 2 n ) p +1 n a p ,0 = 0 p ≥ 2 a 2 n ,0 a 2 n +1,0 = 0 • is always positive and s 2 n • The well-known positivity bounds on coefficients Adams, Arkani-Hamed, Dubovsky, Nicolis, Rattazzi .[2006] • Universal and elegant, but detailed information such as

Spin dependence of coefficient Otherwise for odd for even s p t 𝒫 ( t 1 ) g 2 { ∑ n p n ) p +1 ( 2 ℓ 2 n + 2 ℓ n − p − 1 ) ( m 2 a p ,1 = n g 2 ( p + 1) ∑ n p ( m 2 n ) p +1 n p • For even : Sign of coefficients depends on spins − 1 + 2 p + 5 a p ,1 > 0 l n > l ⋆ = 2 a p ,1 < 0 p • For odd : Always positive

Spin dependence of coefficient s 2 t g 2 a 2,1 = ∑ n n ) p +1 ( 2 ℓ 2 n + 2 ℓ n − 3 ) ( m 2 n where l n < l ⋆ ∼ 0.82 a 2,1 < 0 where l n > l ⋆ ∼ 0.82 a 2,1 > 0 l n

Spin dependence of coefficient scalar fields is dominant Spinning fields give a positive contribution to spinning fields is dominant The contribution from The contribution from Smoking Gun of massive spinning particle s 2 t g 2 a 2,1 = ∑ n ( m n ) p +1 ( 2 ℓ 2 n + 2 ℓ n − 3 ) • In general, Inflaton can couple to various fields. n a 2,1 where l n < l ⋆ ∼ 0.82 • Scalar fields give a negative contribution to 
 a 2,1 a 2,1 < 0 where l n > l ⋆ ∼ 0.82 a 2,1 < 0 a 2,1 > 0 a 2,1 ≥ 0

Implications to EFT of inflaton

Effective field theory of Inflaton Inflaton Focus on four point interaction, Derivative expansions slow-roll approximation, S = ∫ d τ d 3 x − g [ − 1 Λ 6 ( ∇ μ ∂ ν ϕ ) 2 ( ∂ ρ ϕ ) 2 + ⋯ ] 2 ( ∂ μ ϕ ) 2 + α Λ 4 ( ∂ μ ϕ ∂ μ ϕ ) 2 + β ϕ Λ ∼ Mass of intermediate state • Inflaton enjoys approximate shift symmetry under = 4 α Λ 4 ( s 2 + st + t 2 ) − 3 β Λ 6 ( s 2 t + st 2 ) + ⋯ a 2,0 a 2,1

Summary Can probe with sign of effective coupling!! feature of Oscillating non-Gaussianity ) (GeV) ~10 $% ~10 $( ≤ 10 $' String GUT Inflation σ 1 m 2 ≫ s m 2 σ − s

Summary is universally positive is dominant The contribution of spinning fields dominant The contribution of scalar fields is Smoking Gun of massive spinning particle = a 2,0 ( s 2 + st + t 2 ) + a 2,1 ( s 2 t + st 2 ) + ⋯ S = ∫ d τ d 3 x − g [ − 1 Λ 6 ( ∇ μ ∂ ν ϕ ) 2 ( ∂ ρ ϕ ) 2 + ⋯ ] 2 ( ∂ μ ϕ ) 2 + α Λ 4 ( ∂ μ ϕ ∂ μ ϕ ) 2 + β a 2,1 < 0 β > 0 a 2,1 ≥ 0 β ≤ 0 , α a 2,0

Summary Keito Takeuchi’s Poster session is dominant The contribution of spinning fields dominant The contribution of scalar fields is #32 is universally positive Phenomenological implication in Smoking Gun of massive spinning particle = a 2,0 ( s 2 + st + t 2 ) + a 2,1 ( s 2 t + st 2 ) + ⋯ S = ∫ d τ d 3 x − g [ − 1 Λ 6 ( ∇ μ ∂ ν ϕ ) 2 ( ∂ ρ ϕ ) 2 + ⋯ ] 2 ( ∂ μ ϕ ) 2 + α Λ 4 ( ∂ μ ϕ ∂ μ ϕ ) 2 + β a 2,1 < 0 β > 0 a 2,1 ≥ 0 β ≤ 0 , α a 2,0

Appendix

low-energy limit Open superstring amplitude higher spins M ( s , t ) = ( s 2 + t 2 + u 2 ) [ • Scalar amplitude in superstring theory ] B ( − s , − t ) + B ( − t , − u ) + B ( − u , − s ) s + t t + u u + s → π 2 ( s 2 + st + t 2 ) + π 4 2 + … 12 ( s 2 + st + t 2 ) B ( a , b ) = ∫ 1 dxx a (1 − a ) b = Γ ( a ) Γ ( b ) Γ ( a + b ) 0 s 2 t 0 • Coefficients of is • Exact cancellation between contributions of scalar and

Open superstring amplitude m max n +1 g 2 n ℓ ∑ ∑ n 4 ( 2 ℓ 2 n + 2 ℓ n − 3 ) a 2,1 = ϕ n ℓ =0 g n ℓ g n ℓ Is the coupling constant of m 2 σ = n Spin = ℓ 10 ϕ 8 6 4 Coefficient of s 2 2 Coefficient of s 2 t 0 - 2 - 4 0 20 40 60 80 100 n max ( n max + 1 = l max )

Energy scale of target ⟨ ζζ ⟩ 3/2 ∼ H 2 F NL = ⟨ ζζζ ⟩ • Typically 
 m 2 H ∼ 3 × 10 13 • For example, if 10 #( 10 #$ 1 % &' Ruled out Target! Gravitational Non-perturbative by Planck Interaction , (GeV) 10 )* 10 )+ String GUT

Fermion Loop k 1 k 4 y q 11 y 4 13 y 4 720 π 2 m 4 ( s 2 + st + t 2 ) − = 10080 π 2 m 6 st ( s + t ) k 2 k 3 • Scalar intermediate states dominate over spinning ones.