Scalar Dark Matter from Grand Unified Theoriestdanielbrennan/Scalar... · Grand Uni ed Theories T. Daniel Brennan Standard Model Dark Matter GUTs Babu-Mohapatra Model Conclusions

Scalar DarkMatter from

Grand UnifiedTheories

T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Scalar Dark Matter from Grand Unified Theories

T. Daniel Brennan

November 24, 2014



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

1 Standard Model

2 Dark Matter

3 GUTs

4 Babu-Mohapatra Model

5 Conclusions



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Standard ModelWhat is the Standard Model?

Gauge theory that explains strong weak, andelectromagnetic forces

SU(3)C × SU(2)W × U(1)YEach generation (3) has 2 quark flavors (each comes inone of three colors) and 2 leptons

Each type of quark and lepton can have either left or rightchirality except the neutrinoEach left pair forms a doublet which transforms underSU(2) (couples to the weak force)Each quark flavor forms a triplet which transforms underSU(3) (couples to strong force)

There is also a Higgs boson doublet (which transformsunder SU(2))

Y = 2(Q − I3)



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Standard ModelWhat is the Standard Model?



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Standard ModelMathematics of the Standard Model

Standard Model Multiplets

Q(c)|L =

(u(c)

d (c)

)L

EL =

(νee−

)L

φ =1√2

(φ+

φ0

)u

(c)R d

(c)R e−R

Standard Model Lagrangian

L =QL(i /∂ + gWσA /W

A+ gST

A /GA

+gY3/A)QL

+ EL(i /∂ + gWσA /W

A − gY /A)EL + ...

+1

2

∣∣∣(∂µ + igWσAW A

µ + igYAµ)φ∣∣∣2

− 1

4W aµνW

aµν + ...+ LYukawa + V (φ)



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Standard ModelElectroweak Symmetry Breaking

At observable energies, the standard model breaks toSU(3)C × U(1)EMAt some energy level (standard model breaks around 246GeV) Higgs boson gains value expectation value

Reparametrize φ = v + σ



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Standard ModelResults of Electroweak Symmetry Breaking

After Electroweak Symmetry Breaking:

Weak force propagators gain mass (part that breakssymmetry)Higgs boson mass changesMass of particles coupled to Higgs boson by Yukawa termchange



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Standard ModelRunning Gauge Coupling

In the effective action of QFT, gauge couplings havequantum corrections given by higher order processes

In renormalizing the gauge couplings, introduce aparameter µ (renormalization scale) with dimensions ofenergy. It describes how couplings change with energyscale of interactions.



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Standard ModelProblems with the Standard Model

No quantum description of gravity

Matter/anti-matter asymmetry

Neutrino Mass

Landau Pole

Strong CP Problem

Hierarchy Problem-Cancellation of quantum corrections toHiggs mass

L-R Asymmetry/Irreducible representation of gauge group

Gauge group structure unexplained

Dark Matter



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Dark MatterWhat is Dark Matter?

Cold

Non-relativistic at some comparable era of the universeHot dark matter smooths out over density fluctuations∼ 1keV

Collisionless

No scatters on average ⇒ nσvτuniv ≈ 1 or σ10−24cm ≤

1TeVMDM

Dark

Does not couple to Photons

Matter

uDM ∼ T 3(1+w) with w ≈ 0



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Dark MatterEvidence

Rotation Curves

CMB

Fluctuation density not enough to form structure

Gravitational Lensing

Bullet Cluster



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Dark MatterProperties

Interacts through Gravity ⇒ Massive

Makes up ∼ 85% of matter in Universe

Is non-luminous ⇒ neutral charge

Does not react very much with normal baryonic matter ⇒unlikely to interact through the strong force

WIMPs (Weakly Interacting Massive Particles) are an obviouschoice for candidates



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Dark MatterCosmological Production

WIMPs are theorized to have been created in their currentabundance by Thermal Relic model

Characteristic length scale of universe a ∼ T−1

nrel ∼ T 3

nnon−rel ∼ T 3/2e−mX /T

n =∫ d3p

eE(p)/T±1



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Dark Matter

Panoply of theories attempt to model dark matter observations.Several popular theories include:

Neutralino - Supersymmetry

Combination of photino, zino, and neutral higgsinoProtected by R-Symmetry- lightest supersymmetric particle(LSP)

Axion - Solution to Strong CP Problem

LAxion = g2θ32π2 ε

µνσρG aµνG

aσρ = g2θ

32π2 GµνGµν

Sterile Neutrino - Giving up on life

Neutral leptons which only couple to gravity



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Dark MatterExperiments

Particle Accelerator SearchesLHC

Look for missing energy/momentum in measurements

Direct DetectionLarge Underground Xenon experiment (LUX)

Detect photons and electrons ⇒ electroluminescence



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Dark MatterExperiments



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Grand Unified TheoriesWhat are Grand Unified Theories?

Grand Unified Theories (GUTs) extend standard model to alarger semisimple gauge group with single fundamental force byusing spontaneous symmetry breaking as in electroweaksymmetry breaking. Can be used to explain

Matter/antimatter asymmetry

Neutrino Mass

L-R Asymmetry/Irreducible representation of gauge group

Landau Pole

Dark Matter?????

Common GUTs are SU(5) and SO(10)

GUTs predict Proton Decay



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Grand Unified TheoriesHiggs Sector

To extend the standard model to a larger gauge group,need to add new scalar higgs multiplet to break gaugegroup down to standard model.Common Higgs multiplets are5, 10, 16, 45, 54, 126, 144, 210 dimensional.



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Grand Unified TheoriesFavorable Models

Neutrino Mass

Suppressed Proton Decay

L-R Symmetry

Irreducible Representation

As few symmetry breaking steps as possible

Suggests SO(10) model containing 10⊕ 126⊕? Higgs sector.Also want to try to incorporate Dark Matter candidates



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Grand Unified TheoriesDark Matter Candidate

Decomposition of a couple Higgs multiplets under varioussubgroups of SO(10)

45 Higgs 126 Higgs



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Babu-Mohapatra ModelSpecifics

Single step symmetry breaking MU ≈ 1015.5GeV

Higgs Sector 10⊕ 45⊕ 45⊕ 126Produces Seesaw mechanism which gives proper neutrinomass and mixing

Highly suppressed Proton Decay

Lifetime on order of 1034 − 1035 yearsCurrent limit from Super-Kamiokande is 5.9× 1033 yearsCurrently working on calculating to 2-loop order

At low energies, has color sextet and 2 identical weaktriplets which transform under SM as (6, 1, 2/3) and(1, 3, 0) respectively

Mass scale approx 1-10 TeV



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Babu-Mohapatra ModelScalar Dark Matter

2006 Cirelli, Fornengo, and Strumia characterized scalar andfermionic 2-4 WIMP multiplets. First order approximation to

this model.

Total LHC Luminocity:44.2 pb−1+6.1 fb−1+23.3 fb−1

=29.4 fb−1



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Babu-Mohapatra ModelDark Matter Observations

LUX data from Feb 2014σSI ≈ 1.3× 10−45cm2



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Babu-Mohapatra ModelDark Matter Observations

To complete the first order approximation need to check tomake sure mass fits observation. Used to fix unification scale:

Mω = 2 TeV

M∆ = 12 TeV

MU ≈ 1015.2GeV



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

ConclusionsFuture Directions and Applicability

Future Directions

Calculate Proton decay rate to 2-loopVerify StabilityFormulate dynamical thermal relic modelLook for observable effects

Applicability

Provides a newly motivated theory of dark matterWill rule out or provide strong constraints on GUTs



T. DanielBrennan

StandardModel

Dark Matter

GUTs

Babu-MohapatraModel

Conclusions

Proton Decay

Given:

ψ0 = νcL ψi =

dc

1

dc2

dc3

e−

ν

L

ψij =

0 uc3 −uc2 u1 d1

0 uc1 u2 d2

0 u3 d3

0 e+

0

L

the gauge bosons couple ψ0 to ψij and ψij to εijklmψk and ψij

to either ψik or ψkj .So we can have a boson X which takes d3 → X + e+ andu2 + X → uc1 . This takes p → π0e+.

Documents

Scalar Dark Matter from Grand Unified Theoriestdanielbrennan/Scalar... · Grand Uni ed Theories T. Daniel Brennan Standard Model Dark Matter GUTs Babu-Mohapatra Model Conclusions