The document discusses potential theories to explain the nature of dark matter, including supersymmetry (SUSY) and theories with extra dimensions. SUSY proposes that every standard model particle has a supersymmetric partner, and if R-parity is conserved, the lightest supersymmetric particle could be a dark matter candidate. Theories with extra dimensions suggest that gravity appears weaker over large distances because it propagates in more dimensions, and the lightest particle that can move in the extra dimensions would be stable and could explain dark matter. Both SUSY and extra dimensions could help reconcile problems with the standard model and general relativity, but direct evidence is still needed to confirm these theories.
2. 2!
• What we know:
– Dark matter exists
– It can’t be moving relativistic speeds (‘cold
dark matter’)
• But we don’t know what dark matter
actually is
18/11/2014!
Joel Klinger - University of Sheffield –
j.klinger@sheffield.ac.uk!
s the baryonic matter density is only ⌦Bh2 = 0.02. T
of matter in the universe is dark matter.
ll this evidence is indirect - based on gravitational e↵e
.
• Our best two theoretical frameworks could
offer an insight:
– General relativity (‘big things’)
• A geometric theory of gravity on
macroscopic scales
– The Standard Model of particle
physics (‘small things’)
• A quantum theory of electromagnetic and
nuclear interactions on microscopic scales
3. 3!18/11/2014!
Joel Klinger - University of Sheffield –
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The ‘Standard Model’ is a
quantum field theory
The SM summarises our best
understanding of the forces
of nature (except gravity)
and all known particles.
4. 4!18/11/2014!
Joel Klinger - University of Sheffield –
j.klinger@sheffield.ac.uk!
The ‘Standard Model’ is a
quantum field theory
The SM summarises our best
understanding of the forces
of nature (except gravity)
and all known particles.
According to the Standard
Model, the only stable
particles are:
• Electrons
• Up/down quarks
• Neutrinos
5. 5!18/11/2014!
Joel Klinger - University of Sheffield –
j.klinger@sheffield.ac.uk!
Could up/down quarks or
electrons explain dark matter?
No:
• Quarks interact via the strong
force
• Quarks and electrons interact via
the weak force and the
electroweak force
What properties would a dark matter
particle have?
⇒ Very weak interactions
⇒ Very massive OR very abundant
⇒ No EM charge (otherwise it wouldn’t be dark)
Could neutrinos explain dark
matter?
Maybe…
• They interact very weakly (only
weak interaction)
• They have no EM charge
• They are the highly abundant
But neutrinos have tiny masses:
⇒ They travel at the speed of light
⇒ ‘Too fast’ to cause galactic scale
clumping
6. 6!
Doesn’t predict dark matter
Incompatible with General Relativity
Can’t account for the weakness of gravity
Can’t account for the huge energy scale between
the SM interactions and Planck scale
18/11/2014!
Joel Klinger - University of Sheffield –
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7. 7!
One framework in which to reconcile these problems is
Supersymmetry (SUSY)
Give all SM fermions a bosonic partner and
all SM bosons a fermionic partner
18/11/2014!
Joel Klinger - University of Sheffield –
j.klinger@sheffield.ac.uk!
8. 8!
SUSY introduces a partner particle to each SM particle with spin differing by ½:
• Quarks (spin-½ fermions) → squarks (spin-0 bosons)
• Leptons (spin-½ fermions) → sleptons (spin-0 bosons)
• Gluon, photon,
W, Z bosons
• Higgs (spin-0 bosons) → higgsinos (spin-½ fermions)
The SUSY partners of the photon, Z boson and the Higgs have indistinguishable
properties (other than mass) and so they mix to form a set of neutralino states.
Neutralinos are phenomenologically similar to neutrinos- but won’t they decay?
18/11/2014!
Joel Klinger - University of Sheffield –
j.klinger@sheffield.ac.uk!
(spin-1 bosons) → gauginos (spin-½ fermions)
9. 9!
• All Standard Model interactions conserve ‘Baryon number’ B, ‘Lepton number’ L
and ‘Spin’ S
• Therefore, the following quantity ‘R-parity’ is also conserved in SM interactions:
• If SUSY is consistent with the Standard Model, the SUSY interactions
should also conserve R-parity.
• Note:
– SM particles have R = +1
– SUSY particles have R= - 1
– R-parity is a multiplicative quantum number therefore the total product is
conserved
18/11/2014!
Joel Klinger - University of Sheffield –
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10. 10!
If R-parity is conserved in SUSY interactions then:
• Only even numbers of SUSY particles can be
produced in SM interactions
• The lightest SUSY particle (‘LSP’) must be stable
Therefore if the LSP is a neutralino, then SUSY
provides a candidate for dark matter
18/11/2014!
Joel Klinger - University of Sheffield –
j.klinger@sheffield.ac.uk!
11. 11!
• By colliding high energy protons at the LHC we can create high mass states
• The collisions take place in large detectors like ATLAS and CMS
• Detectors are capable of measuring:
– Charged tracks
– Hadronic energy deposits
– Electromagnetic energy deposits
• The detectors are capable of identifying:
– Hadronic ‘jets’
– Electrons
– Photons
– Muons
18/11/2014!
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13. 13!18/11/2014!
Joel Klinger - University of Sheffield –
j.klinger@sheffield.ac.uk!
(d)
High energy
protons collide
Proton
constituents
interact
Even number of
heavy sleptons
produced
Each slepton
decays via a
charged lepton
and a neutralino
In the detector we
would look for:
• Two charged
tracks (from the
two leptons)
• Large momentum
imbalance (from
the neutralinos,
which are
undetectable)
16. 16!
Galilean relativity tells us that any
position in a 3-dimensional space is a
dynamic quantity
Special relativity tells us that any
position in a 4-dimensional spacetime is a
dynamic quantity
General Relativity tells us that
spacetime itself is a dynamical object
18/11/2014!
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Why can’t there be more than 4 dimensions?
What would extra dimensions that even mean?
What would be the point of extra dimensions?
17. 17!18/11/2014!
Joel Klinger - University of Sheffield –
j.klinger@sheffield.ac.uk!
Why can’t there be more than 4 dimensions?
⇒ There’s no good reason
What does a dimension even mean?
⇒ Dimensions are independent spaces in which a single value is required to
specify a position in that dimension
What would be the point of extra dimensions?
⇒ General Relativity can be extended to any number of extra dimensions- and
this changes the strength of gravity in our dimensions
⇒ Extra-dimensions can be used to incorporate additional forces into
General Relativity
18. 18!18/11/2014!
Joel Klinger - University of Sheffield –
j.klinger@sheffield.ac.uk!
If there are extra-dimensions, they must be different to the ‘every day’ infinitely long
dimensions
They could be compact extra-dimensions, which are too small to see.
In the 1920s/30s, the Kaluza-Klein theory incorporated one compact extra-
dimension into General Relativity, in order to unify electromagnetism and gravity.
For N extra-dimensions which are visible on the scale of radius R then gravity is
modified (eg Newtonian gravity):
F = G
Mm
r2
r < R
! →!! G
Mm
r2+N
r > R
! →!! G''
Mm
r2
where G'' =
G
RN
So the gravitational coupling G
could appear very small at large
distances, but is in fact the similar to
the SM forces if we consider all the
dimensions relevant to gravity.
19. 19!
Consider a the energy of a single particle
moving in an extra-dimension of size R:
18/11/2014!
Joel Klinger - University of Sheffield –
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E2
= pc( )
2
+ mc2
( )
2
E2
= pxc( )
2
+ pyc( )
2
+ pzc( )
2
+ mc2
( )
2
and in extra-dimensions:
E2
= pxc( )
2
+ pyc( )
2
+ pzc( )
2
+ pextrac( )
2
+ mc2
( )
2
E2
= pxc( )
2
+ pyc( )
2
+ pzc( )
2
+ m''c2
( )
2
where m''c2
( )
2
= pextrac( )
2
+ mc2
( )
2
Particles which exist in extra-
dimensions can be very massive
20. 20!18/11/2014!
Joel Klinger - University of Sheffield –
j.klinger@sheffield.ac.uk!
From quantum mechanics (‘particle in a box’):
⇒ The momentum of the an excitation (‘particle’) over a length
R is given by
⇒ Recalling that
means that every particle moving in the extra dimension has
an infinite number (n) of higher mass partners.
⇒ Unlike SUSY partners, these partners would be identical to
the SM particles, only with higher mass.
pextra =
nh
R
m''c2
( )
2
= pextrac( )
2
+ mc2
( )
2
21. 21!
• As with our familiar large spatial dimensions, you have to
conserve momentum in interactions
• Kaluza-Klein particles have momenta in units of n so for
example (considering neutral particles):
⇒ when n = 3, the particle can decay to:
⇒ two partner particles with n = 1 and n = 2
⇒ three partner particles each with n = 1
⇒ when n = 2, the particle has to decay to two partner particles
each with n = 1
⇒ when n = 1, the particle can’t decays
So - in order to conserve momentum in the extra-dimensions,
the lightest Kaluza-Klein particle (LKP) must be stable
18/11/2014!
Joel Klinger - University of Sheffield –
j.klinger@sheffield.ac.uk!
Dark matter candidates could be the partners of
photons, Z-bosons, neutrinos or gravitons
23. 23!18/11/2014!
Joel Klinger - University of Sheffield –
j.klinger@sheffield.ac.uk!
(a)
q
¯q
γ
GKK
Quarks and
anti-quarks
from inside
the proton
Quark and anti-
quark annihilate
to produce a
photon
Photon
radiates a
graviton
The graviton
escapes
undetected
In the detector we would look for:
• No charged tracks
• A photon depositing energy
• Large momentum imbalance (from the
undetectable graviton)
26. 26!18/11/2014!
Joel Klinger - University of Sheffield –
j.klinger@sheffield.ac.uk!
• We know dark matter exists, but we don’t know what it is
• Extending the SM to include SUSY fixes lots of problems:
– The LSP is a dark matter candidate
– New physics is introduced between the SM interactions and the
Planck scale
• Extending General Relativity to include extra-dimensions
also fixes lots of problems:
– The LKP is a dark matter candidate
– The weakness of gravity is explained
– The Planck scale is ‘reduced’ to the SM scale
But – we have no evidence yet
