Multiple Extra Dimensions andCosmic Sources of KK Particles

Erin De Pree

June 22, 2015

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

Plan

1 General introduction to extra dimensions

2 Warped extra dimensions

3 Multiple extra dimensions

4 Involving students in high energy theory

5 Cosmic sources (if time)

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 2 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

S1: Wave function

Continuity requires:

Ψ (y) = Ψ (y + 2πR)

Ψ =1√

2πR

+∞∑n=−∞

ψ(n)e iny/R

E 2 = (pc)2 +(Mc2

)2De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 3 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

S1: Mass

E 2 = (pc)2 +(Mc2

)2= (p3Dc)2 + (pyc)2 +

(Mc2

)2= (p3Dc)2 +

( nR~c)2

+(Mc2

)2︸ ︷︷ ︸(mnc2)2

in particle physics, ~ = c = 1:

m2n =

n2

R2+ M2 Kaluza-Klein (KK) particles

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 4 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

S1: Mass

E 2 = (pc)2 +(Mc2

)2= (p3Dc)2 + (pyc)2 +

(Mc2

)2= (p3Dc)2 +

( nR~c)2

+(Mc2

)2︸ ︷︷ ︸(mnc2)2

in particle physics, ~ = c = 1:

m2n =

n2

R2+ M2 Kaluza-Klein (KK) particles

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 4 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

Randall-Sundrum Model

ds2 = e−2krc |φ|︸ ︷︷ ︸warp factor

ηµνdxµdxν − r 2c dφ

2︸ ︷︷ ︸extra dimension

Planck

AdS5

TeV

k

ke−πkrcπrc

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Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

Multiple Extra Dimensions

Fermions in Randall-Sundrum models with twoadditional unwarpped extra dimensions

Jeremy Perrin (2013 Apker Finalist)and Erin De PreearXiv:1310.1928 [hep-ph]

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 6 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

6D Models

ds2 = e−2krc |φ|ηµνdxµdxν − r 2c dφ

2 − R2dθ2︸ ︷︷ ︸new extra dim

ProblemNo bulk mass terms that are also 6D-chiral andhave four-components

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 7 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

6D Models

ds2 = e−2krc |φ|ηµνdxµdxν − r 2c dφ

2 − R2dθ2︸ ︷︷ ︸new extra dim

ProblemNo bulk mass terms that are also 6D-chiral andhave four-components

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 7 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

7D Warped Extra Dimensions

Instead we add two additional extra dimensions.

Choices

• Compactify on a torus (T2) or a sphere (S2)?

• Apply the warp factor to just the 4Ddimensions or all other dimensions?

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Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

AdS5 × T2

ds2 = e−2krc |φ|ηµνdxµdxν − r 2c dφ

2 − R2(dθ21 + dθ22

)Set of coupled differential equations for the KKwavefuntions.

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 9 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

AdS5 × S2

ds2 = e−2krc |φ|ηµνdxµdxν − r 2c dφ

2

− R2(dθ2 + sin2 θdω2

)ProblemNo zero-mode solutions without additional structure

General result for all manifolds of positive curvature.

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 10 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

AdS5 × S2

ds2 = e−2krc |φ|ηµνdxµdxν − r 2c dφ

2

− R2(dθ2 + sin2 θdω2

)ProblemNo zero-mode solutions without additional structure

General result for all manifolds of positive curvature.

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 10 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

AdS5 × S2

ds2 = e−2krc |φ|ηµνdxµdxν − r 2c dφ

2

− R2(dθ2 + sin2 θdω2

)ProblemNo zero-mode solutions without additional structure

General result for all manifolds of positive curvature.

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 10 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

Research Group

1 Start early

2 Work in small groups

3 Not every project results in a publication

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Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

Questions and Discussion

Thank you

ekdepree@smcm.eduarXiv:1505.00024 [astro-ph.HE]

arXiv:1310.1928 [hep-ph]

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 12 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

Possible sources of KK particles

Colliders

• Control the source (luminosity, ECM, etc)

• Expensive

Cosmic sources• Free

• No control over the source

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 13 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

Possible sources of KK particles

Colliders

• Control the source (luminosity, ECM, etc)

• Expensive

Cosmic sources• Free

• No control over the source

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 13 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

Gamma Ray Bursts (GRBs)

Ian Morgan, Ted Tao, De Pree, Kevin TennysonarXiv:1505.00024 [astro-ph.HE]

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Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

Observer’s frame

Earth

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 15 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

Beaming

Earth

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Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

Results

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 17 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

Questions and Discussion

Thank you

ekdepree@smcm.eduarXiv:1505.00024 [astro-ph.HE]

arXiv:1310.1928 [hep-ph]

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 18 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

S1: Momentum

p2 = p · p = p2x1+ p2x2

+ p2x3+ p2y = p23D + p2y

p̂ = −i~∇, p̂y = −i~ ∂∂y

p̂yΨ =−i~√2πR

ψ(n)e iny/R(in

R

)=

n~R

Ψ

Eigenvalue for p̂y : n~/R

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 19 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

S1: Momentum

p2 = p · p = p2x1+ p2x2

+ p2x3+ p2y = p23D + p2y

p̂ = −i~∇, p̂y = −i~ ∂∂y

p̂yΨ =−i~√2πR

ψ(n)e iny/R(in

R

)=

n~R

Ψ

Eigenvalue for p̂y : n~/R

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 19 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

S1: Fermion KK Spectrum

mass

0

1/R

2/R

ΨL

n ≥ 0 n < 0

ΨR

n ≥ 0 n < 0

For M = 0

De Pree Jun 2015 Multiple Extra Dimensions & Cosmic Sources 20 / 21

Introduction Warped Extra Dimensions Multiple Extra Dimensions Student Involvement Cosmic Sources

AdS7 Model

ds2 = e−2krc |φ|[ηµνdx

µdxν − R2(dθ21 + dθ22

)]−r 2c dφ2

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