Scalar Dark Matter from Grand Unified Theories T. Daniel Brennan Standard Model Dark Matter GUTs Babu- Mohapatra Model Conclusions Scalar Dark Matter from Grand Unified Theories T. Daniel Brennan November 24, 2014
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
Scalar DarkMatter from
Grand UnifiedTheories
T. DanielBrennan
StandardModel
Dark Matter
GUTs
Babu-MohapatraModel
Conclusions
1 Standard Model
2 Dark Matter
3 GUTs
4 Babu-Mohapatra Model
5 Conclusions
Scalar DarkMatter from
Grand UnifiedTheories
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)
Scalar DarkMatter from
Grand UnifiedTheories
T. DanielBrennan
StandardModel
Dark Matter
GUTs
Babu-MohapatraModel
Conclusions
Standard ModelWhat is the Standard Model?
Scalar DarkMatter from
Grand UnifiedTheories
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)
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
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.
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
T. DanielBrennan
StandardModel
Dark Matter
GUTs
Babu-MohapatraModel
Conclusions
Dark MatterExperiments
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
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.
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
T. DanielBrennan
StandardModel
Dark Matter
GUTs
Babu-MohapatraModel
Conclusions
Babu-Mohapatra ModelDark Matter Observations
LUX data from Feb 2014σSI ≈ 1.3× 10−45cm2
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
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
Scalar DarkMatter from
Grand UnifiedTheories
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+.