PHY323:Lecture 11
SUSY and UED
••••
Higgs and Supersymmetry The Neutralino Extra Dimensions How WIMPs interact
Candidates for Dark Matter III
The New Particle Zoo
Here are a few of the candidates on a plot showing cross section vs. mass. An enormous range. We will focus on WIMPs
thanks to L. Roszkowski (Sheffield)
Freeze Out of Thermal DM Particles
WIMP Candidate 1
Supersymmetric Dark Matter
Each particle gets a “sparticle” counterpart. Bosons get fermions and vice versa.
e.g. Photon Photino
W
Z
Wino Zino etc
The Lightest Supersymmetric Particle (LSP) is predicted to be stable. This is called the NEUTRALINO.
Supersymmetry Theory
What we are aiming to do, e.g.: At higher energies, where symmetries are unbroken, you might expect a unified theory should have a single coupling constant
Supersymmetry Theory and the Higgs
To make things simpler, it would be nice if all the forces of nature were unified under the same theoretical framework. The energy at which this is likely called the Planck energy (1019 GeV).
This was started in the 1970s - the result is the electroweak theory. The theory is intricate and complicated, partly because the photon is massless, but the W & Z are heavy.
The electroweak theory posits that the very different carriers, and therefore properties, of these forces at energy scales present in nature today are actually the result of taking a much more symmteric theory at higher energies, above the ‘electroweak scale’ of 90GeV (the W and Z rest energy) and ‘spontaneously breaking’ it. The theoretical mechanism for spontaneous symmetry breaking requires yet another new particle, a spin zero particle called the HIGGS BOSON.
Massive Force Carriers
Extra Note
The carrier of the electromagnetic force is a massless photon.
The carriers of the weak force are heavy, having a rest energy of roughly 90GeV. They are weakly interacting massive particles.
Can these things be dark matter ? No, actually, because they are unstable. A
Are there other weakly interacting, massive particles which ARE stable, and therefore could be a candidate for dark matter ? Yes, but not within the standard model.
The “Higgs” is unstable, so it can’t be the dark matter itself
The Higgs endows the carriers of the weak force with their high mass, resulting in a feeble force with a short range. But now the standard model contains another particle, and when you look in to the properties of the Higgs, you hit problems. For example, the Higgs in electroweak theory has a coupling to two electrons and a four Higgs self-coupling.
Because of the Higgs mechanism, the standard model of particle physics is internally inconsistent. To remove the inconsistencies, extensions to the theory are needed.
SUPERSYMMETRY is a popular candidate extension.
Higgs Self
Energy
The quantum mechanical amplitude for a Higgs to travel from A to B, summed over all contributing processes is...
H
Notes
Fixing Higgs Self Energy Problem
In supersymmetry, each particle in the standard model has a supersymmetric partner with spin angular momentum differing by hbar/2. So for every fermion there is a supersymmetric partner boson and vice-versa.
The extra diagrams for the Higgs self energy where virtual superpartners are formed and destroyed cancel the divergent diagrams in the standard model sector, rendering the Higgs selfenergy finite.
In fact, it’s more complicated than this. The supersymmetric partners, none of which have been detected, mix together quantum mechanically, so that the actual supersymmetric objects we might detect in the LHC will be MIXTURES of the supersymmetric partners of the known particles.
A Lot to Buy Into ?
Supersymmetry is a lot to swallow. Twice the number of particles we have already found, and none of the superpartners detected yet ? To solve one puny Higgs self-energy problem?
Well, supersymmetry could do much more than this. (1) Some supersymmetric extensions, particularly supergravity, allow the possibility of quantizing the gravitational force, the biggest unsolved problem in quantum mechanics.
(2) Supersymmetry eases extrapolation to high energy unification
(3) The lightest supersymmetric particle might be stable. Lots of supersymmetric theories conserve something called R-parity, in which case a supersymmetric particle cannot decay into a set of non-supersymmetric particles.
Supersymmetric Partner Mixing
Lots of very clever people are working very hard on detecting the supersymmetric partners of ordinary particles, and if they do then they will sort out the mess of what supersymmetric states are actually observed in nature, and what their properties are.
Possibility of very exciting new physics if supersymmetry is detected at the LHC. Dan Tovey, Stathes Paganis, Davide Costanzo here at Sheffield.
SUSY and R Parity
SUSY introduces a new quantun number called R parity, in order to prevent proton decay and make distinguishable some states otherwise identical.
Introducing R parity and giving the value of 1 and -1 to the SM particles and their supersymmetric partners respectively, the two states become distinguishable.
The R parity is defined as
where B, L are the baryon and lepton number operators and S is the spin. R parity is a multiplicative symmetry, so sparticles are produced in pairs.
If R parity is broken, then there are no special selection rules to prevent the decay of those supersymmetric particles in the spectrum with masses of order of few GeV. In particular, the theory would possess no natural candidate for cold dark matter particles.
The Neutralino
The neutralino is a possibility for the lightest supersymmetric particle, and hence WIMPs. What is it? Well, it’s quite complicated.
The neutralino is a quantum mechanical superposition of the bino, wino and two higgsinos
SUSY DM Summary
• Supersymmetry first formulated in the 1970s. • Symmetry between fermions and bosons. • Each SM particle has a ‘superpartner’ • R-Parity introduced to prevent rapid proton decay - must be conserved. • Leads to existence of a stable Lightest Supersymmetric Particle (LSP)
For SUSY to agree with
Standard Model:
• Most important SUSY particle for
DM is the Neutralino.
10GeV < Mχ <104 GeV
Searches for charginos and squarks at LEP and Tevatron:
• If this is the LSP, it is an ideal
WIMP candidate.
• In most realistic SUSY models (i.e. no charged LSP), Neutralino IS LSP
Mχ > 50GeV
A natural candidate not invented to solve Dark Matter
Notes
WIMP Candidate 2
Kaluza-Klein Dark Matter
This important candidate comes from the theory of Universal
Extra Dimensions (UED) where all standard model particles
propagate into flat dimensions. It produces a WIMP called the
Lightest Kaluza-Klein particle (LKP).
Extra Dimensions
Extra dimensions is used to lower the fundamental Planck scale, MP ~ 1019 GeV, close to the electroweak scale by allowing gravity to propagate in (3 + 1) + n dimensions whilst confining the Standard Model particles to the 3 + 1 (Minkowski subspace)
In this case, the apparent Planck scale is related to the
MP ~ MF (RMF )n/2 fundamental scale MF via
size of the extra dimensions
As these extra dimensions modify the usual inverse-square law of gravity at distances < R, their size must be < 1mm in order not to conflict with the results from current short range gravitational experiments.
Any extra dimensions must therefore be compactified, and so R represents their compactification radius. A significant feature of extra dimensional theories is heavy ‘KaluzaKlein’ particles that can propagate in the extra dimensions.
KK Dark Matter Candidate
For 1 dimension plus 1 extra compact dimension, the compactification can be visualised as an infinite garden hose with a small but finite radius. At large distances only the length of the wire can be perceived, but sufficiently close to the wire the finite distance around the wire can also be resolved.
Consider 1 extra spatial dimensions curled up in a small circle
Particles moving in extra dimensions appear as a set of copies of normal particles.
LKP (lightest KK particle) is stable –dark matter!
KK Dark Matter Relic Density
Some predictions from UED for KK dark matter particles, showing that they could make up all the dark matter
Rather like R-parity in SUSY there is KK-parity (−1)KK in UED
Summary on DM particles
We like CDM and WIMPs and Neutralinos
(1) CDM favours structure formation (2) Such particles match well generic arguments about freeze-out in the Big Bang
(3) There are well motivated candidates predicted independently from particle physics
So WIMPs are the best generic candidate and of these we like Neutralinos from SUSY
Standard Model Particle Physics
Extra Note
This is a model that accounts for the vast majority of the known behaviour of the known particle types, either present in nature or discovered in accelerators. It supercedes older classical field theories like classical electromagnetism, which means that it explains all the phenomena explained by these theories and then also explains some outside the context of those theories.
It does NOT superscede classical gravitation !
The basic idea is that there is a set of fundamental spin-1/2 particles that interact with each other by the exchange of some fundamental spin-1 particles.
The word particle is used loosely here - these are quantum mechanical objects having both particle and wave-like properties.
EG: Quantum Electrodynamics - The quantum theory of electromagnetism
Extra Note
We know that electromagnetic radiation is emitted and absorbed by electrically charged particles being accelerated. What is the quantum foundation of this classical theory?
The quantum theory of electromagnetic interactions is called quantum electrodynamics. It was invented by Julian Schwinger, Richard Feynmann, and others in the 1950s.
Quantum electrodynamics is integral to the standard model of particle physics.
Classical vs. Quantum
Electrodynamics
Extra Note
fundamental coupling Scattering of charged particles by each other (Moller scattering)
scattering of light by charged particles (Compton scattering)
The Weak Interactions
Extra Note
Defining characteristics: (a) Much feebler than the electromagnetic interactions, at least when the energies of the interacting particles are much less than 90GeV. At 90GeV, they dominate over the electromagnetic interactions, and above 90GeV the strengths of the two interactions are compatible.
Hence the name...
(b) Short range - particles separated by more than the size of roughly an atomic nucleus will not be affected.
Because of these characteristics, weak interactions were not noticed until the latter half of the 20th century, and there was never any call for a classical theory of weak interactions.
So how do you make an interaction feeble and short range ?
Summary on SUSY
Particle theorists like supersymmetry because they could solve the higgs self energy problem, the problem of quantizing gravity and the problem of unifying the fundamental forces at high energies (in the early Universe) in one go!
Particle experimentalists like supersymmetry because
supersymmetric particles can be searched for in machines we can (just about) afford to build and run, and finding them may allow experiment to jump ahead of theory by providing sorely needed experimental data.
Particle Astrophysicists like supersymmetry because it yields a
class of dark matter candidates of about the right mass to close the universe with standard astrophysics phenomenology based on the standard model.
BUT making supersymmetric particles in accelerators does not prove they are dark matter !
Basic Neutralino/WIMP Properties
Main characteristics of the particles
•
••
Mass in the range Number density in the range De Broglie wavelength in the range per litre
Main characteristics of the collisions
•••
Short range Elastic - same particles come out as go in to collision.
-[7,8]
Rare - cross section upper limits are currently ~10 pb
Rare processes mean that we need as many ‘detectors’ as possible. Use solid matter, where each nucleus is a potential detector. Look for materials having CHARACTERISTIC SIGNATURES that are detectable by existing technology.
Notes
e.g. describe the relationship between the terms CDM, WIMP, Neutralino, LSP and LKP.
Neutralino Dark Matter Properties
REST ENERGY:
Lower limit because at this mas they would have been
Upper limit is that if the energy scale for supersymmetric detected in accelerators but partners is this high, they no
- in fact have not been.
- longer rid the standard model
of infinities. Thye may also over-close the Universe.
