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SUPERSYMMETRY
FYS 4560
Lecture #1, April 6, 2015
Eirik Gramstad
Based on lectures by
Børge Kile Gjelsten
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Outline
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Intro I: Standard Model (SM); deficiencies
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Intro II: Models Beyond the SM (BSM)
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Supersymmetry (SUSY): principles
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SUSY: constructing viable models (MSSM)
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SUSY: “successes”
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SUSY: Phenomenology
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SUSY: Experimental status
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Standard Model
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Force fields:
–
Determined by gauge structure SU(3) x
SU(2) x U(1)
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spin-1: force carriers: g,W,Z,photon
Matter particles (fermions):
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Quarks and leptons
–
3 generations
–
SU(2) doublets: (u d), (nu, e), ..
–
L/R structure (SU(2))
Problem of mass:
–
gauge invariance allows only massless
fields
–
Higgs mechanism: allows mass
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Standard Model: deficiencies
1. Problem of cosmological constant
2. Dark energy: no SM explanation
3. Inflation: no SM mechanism (field)
4. Matter/antimatter asymmetry: no
SM mechanism
5. Dark matter: no SM candidate
6. Origin of the Higgs potential
7. Hierarchy problem
8. Gravity not included
9. Mass values not explained
10.Why three generations?
Kane: The Dawn of PHYSICS BEYOND THE STANDARD MODEL
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http://home.slac.stanford.edu/pressreleases/2006/20060821.htm
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Beyond SM: some considerations
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Why?
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Address contradiction of SM
with experiment (~none)
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Add features to address things
currently outside of SM
(a la “deficiencies”)
–
Address (theoretically)
inelegant features of SM
(a la “deficiencies”)
–
Good ideas which can be
implemented
–
Ideas which can be
implemented
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How?
Prefere not to break structure of
SM (gauge, Lorentz, renorm., ..)
–
Forces? (Gauge groups)
–
Particles? (new families)
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Space? (new dim, ...)
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Unification...
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New interpretation
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Beyond the Standard Model
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Grand Unification (GUT)
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Technicolor
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Compositeness
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String Theory
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Extra Dimensions
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Supersymmetry (SUSY)
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Grand Unified Theories (GUT)
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Is SU(3) x SU(2) x U(1) part of a larger structure?
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The SM coupling constants seems to meet around 10 15 GeV
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Ex.: Unified group SU(5), one coupling constant [Georgi-Glashow, 1974]
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Leptons and quarks are organized into multiplets
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At some high GUT scale SU(5) is spontaneously broken down to the SM groups (3 coupling
constants)
SU(5) Has 52-1=24 gauge fields
–
8+3+1 = 12 of the SM
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12 superheavy X and Y bosons (leptoquarks)
Leptoquarks can transform quarks into leptons, leading to proton decay
–
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~ 1030 years
Current experimental limit > 1033 years
More elaborate theories can be put in
agreement with experiment
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Technicolor
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Main idea: There is no fundamental Higgs field
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Instead: Have additional asymptotically free gauge interaction: technicolor
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Plus technifermions feeling this force
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Technicolor interactions become strong around 100 GeV, leading to technifermion condensates
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Effect is similar to vacuum-expectation-value of Higgs:
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W and Z obtains masses
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Problems:
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–
To give masses to fermions
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EW precision measurements
So more elaborate models built
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Compositeness
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Historically successful strategy: the atom is divisible
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Assumption: Quarks and leptons made up of smaller constituents: preons
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Quarks and leptons related (in SM only by 'accident')
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Experimentally: would see deviation in cross-section at energies close to the
binding energies (a la Rutherford scattering)
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Will have excited states of quarks and leptons
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No experimental evidence
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String Theory
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Assumption: Fundamental object is not point particles but strings
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History
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197x: First version 25 dim, tachyons, new massless parti.,
no fermions
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197x: Supersymmetry invented: 10 dim, removes tachyons,
get fermions, get graviton!
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1984: First revolution: shown to be finite & consistent
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1995: Second revolution: 5 theories joined in 1 M-theory
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1995: not just 1D strings, but n-dim branes
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The landscape: >10500 theories, anthropic principle?
(from different ways of compactifying up the extra dimensions)
Current status: no experimental tests in sight, but SUSY might be a first hint
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Extra Dimensions
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Inspiration: string theory needs (curled up) extra dimensions
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In string theory the extra dim are of Planck length (~10 -34 m): undetectable
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But exp. limit is only: ~0.1 mm for a curled up (flat) extra dimension
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Particles moving in ex. dim get extra mass term in 4 dim
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Planck scale can be much closer (may dissolve hierarchy problem)
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ADD models: Gravity appears weak because it goes into extra dimensions
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Actual Planck scale:
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Quantum gravity accessible at LHC? Mini black holes?
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RS model: curved extra (small) dim., graviton resonance at LHC?
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Universal Extra Dimensions: SM fields too in ex.dims, excitations, CDM
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and finally supersymmetry!
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Supersymmetry
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SM: clear distinction between spin-1 and spin½: force and matter
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Idea and development not motivated by SM
deficiencies
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Spin 1: g,W,Z,gamma
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1970s: SUSY discovered (theoretically)
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Spin 1/2: quarks, leptons
–
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Spin 0: Higgs
Developed in string theory context,
applied as theoretical concept in several
fields (makes Lagrangians more wellbehaved)
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1981: Realistic SUSY model constructed
(MSSM: Minimal Supersymmetric SM)
Supersymmetry is a symmetry between
fermions and bosons
Q |F> = |B>, Q |B> = |F>
A highly constrained extension of Poincare
spacetime symmetry
For each fermion degree of freedom, there must
be a boson degree of freedom
Superpartners: particles come in multiplets
containing fermions and bosons
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But does address many of the important items
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Hierarchy problem
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GUT unification
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Cold Dark Matter
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“Unnatural” Higgs potential
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Gravity
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Field content of Minimal SUSY SM
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Particle comes in supermultiplets
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Early, failed attempt:
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SM spin-½ get spin-0 partners
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multiplet Hd and L have same q-numbers.
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SM spin-1 or spin-0 get spin ½ partners
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Why not assume Higgs/neutrino
partners? The sneutrino would then be
Higgs
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Fails
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Partners have identical quantum numbers
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Naming convention
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Add an 's' (for 'scalar', spin-0) in front
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So: SUSY needs a doubling(+) of particles
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Or an 'ino' at the end (spin-1/2)
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Plus: SM 1 Higgs doublet -> 2 Higgs doublets
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MSSM mass states
higgsinos
squarks
the colour shows the spin:
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blue: spin-0
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red: spin-1/2
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green: spin-1
charginos
gauginos
gluino
gravitino
neutralinos
Neutralino mixing matrix:
Neutralinos are mixtures of
bino (B), wino (W) and higgsino.
The exact mixture is
relevant for the LSP relic density.
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The SUSY Higgs sector
In the SM the Higgs field consists of one left-handed scalar doublet. In
the MSSM this doublet is promoted to a doublet of left-handed superfields
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In SM:
Weak hypercharge, Y = 1, mass to up-type fermions
Not
al
lowe
d in
In SM:
supe
rpot
e
ntial
Weak hypercharge, Y = -1, mass to down-type fermions
With the two doublets we get the following Higgs potential in SUSY:
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The SUSY Higgs sector cont'd
With two doublets we have 8 degrees
of freedom, thus we get 5 Higgs
bosons:
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MSSM: building
(MSSM=Minimal Supersymmetric Standard Model)
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Superpotential, Lagrangian
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Interactions
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Proton decay, R-parity
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SUSY breaking
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Lagrangian, superpotential
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Notation:
= (SM fermion, SUSY scalar)
= (SM vector, SUSY fermion)
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(see Table on slide 23 for the supermultiplets
def.)
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For the MSSM (1. generation only):
The (unbroken) MSSM lagrangian is given by
a kinetic, chiral and scalar part
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[sketchy]
1) The kinetic part is fully determined by SM
parameters and gives the gauge interactions
(between SM part. and SM and SUSY part.)
2) The chiral part can be derived from a
superpotential W of general form
via
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ye, yu,yd are 3x3 matrices in generation space
containing the Yukawa couplings (Higgsfermion couplings)
3) The scalar potential V
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relates to EW symmetry breaking
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gives trilinear scalar couplings
Full supersymmetrisation of SM achieved
with
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Particle content doubled
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But no new parameters introduced
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Interactions
(SM)
(SUSY)
(SUSY)
(SM)
(SUSY)
Roughly speaking:
MSSM couplings are
generated from SM
couplings by exchanging
two SM particles with
their SUSY partners
Gauge interactions
in general dominate
yukawa interactions
(SM)
(SUSY)
(SUSY)
Exception is 3. gen.
(top, bottom, tau) where
yukawas are relevant
= (SM fermion, SUSY scalar)
= (SM vector, SUSY fermion)
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Proton decay, R-parity
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The superpotential given earlier is not
exhaustive, one can also have terms like:
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(L,E:sleptons, Q,D,U: squarks, H:Higgses)
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Define R-parity by
R= +1: SM-particles (and Higgses)
R= -1 : SUSY partners
If interactions are required to conserve Rparity, then all dangerous terms are removed
MSSM is defined with R-parity conservation
These violate lepton (ΔL = 1) or baryon
number (ΔB = 1)
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Also makes the lightest SUSY particle
stable (Dark Matter candidate?)
Experimentally no such observations
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And in collider experiments sparticles
have to be pair produced
Proton decay most obvious case.
To satisfy lifetime bound of >1033 years,
coupling must be ridiculously small:
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Origin of R-parity ... ?
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Breaking SUSY
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Fields in the same multiplet have identical
mass
–
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But there are no selectrons of 0.5 MeV !!
Supersymmetry cannot be an exact symmetry,
it must be spontaneously broken
So: For MSSM the drastic and heroic path is
taken: put in by hand all allowed terms, i.e.
which
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respect SM gauge inv., renormalisable
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are 'soft', i.e. coupling constants should
have pos. mass-dim. [to still solve
hierarchy prob.]
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involve gauginos and scalars only (not
SM)
Lots of work on SUSY breaking mechanisms
Typically SUSY breaking is assumed to occur
in a hidden sector, then mediated to our sector
by some weak interaction [more later]
Many models. All involve extended structures
(fields, ...) None dominantly persuasive.
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Introduces 105 new parameters ! (Masses++)
(But remember: have chosen the elaborate
path of full generality.)
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Models of SUSY breaking
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Assume a “hidden” sector which interacts with
our sector (MSSM) only very weakly
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Super-Higgs mechanism : massive gravitino
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Assume SUSY is a local symmetry
(is then a supergravity theory)
(i.e. includes general relativity)
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The spontaneous breaking of SUSY gives
mass to the spin-3/2 gravitino
(it “eats” the massless goldstino)
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Gravitational interactions of gravitino are
negligible, but inherits goldstino couplings
The more uniform the breaking & mediating is,
the fewer “free” parameters will appear in the
resulting MSSM
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Interaction strength and mass of goldstino
depends strongly on the breaking
scenario
Examples: SUGRA, GMSB, AMSB
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Relevant to Dark Matter considerations
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and collider phenomenology
SUSY is broken in the hidden sector
–
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typically by scalar (or a gaugino
condensate) acquiring a non-zero VEV
A messenger sector mediates the SUSY
breaking to our sector
Several models exist for breaking & mediating
SUSY breaking: two popular mech.
Gauge-mediated SUSY breaking (GMSB)
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Ex. minimal GMSB (mGMSB)
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Hidden sector: field VEV ~ 10^5 GeV
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Messenger sector: supermultiplet with lepton and quark q-numbers: get masses from VEV
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Then couple to MSSM via ordinary gauge couplings
(gravity mediation is also present, but negligible)
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m(gravitino) ~ eV (<< 100 GeV): is LSP
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5 free parameters (+ a sign):
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SUSY breaking: two popular mech.
Gravity-mediated SUSY breaking (SUGRA):
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Ex. mSUGRA (minimal SUperGRAvity)
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Hidden sector: scalar field VEV ~ 10^10 GeV
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Messenger: gravity; mediates directly between hidden
sector and visible sector (MSSM)
m(gravitino) ~ 10 TeV
(Of little importance to colliders & DM)
High degree of uniformity is assumed
(partly convincing, partly constructed)
Only 4 free parameters (+ a sign), all set at GUT scale
(2 x 1016GeV):
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mSUGRA
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Renormalisation group evolution: from
common GUT values to certain EW scale
hierarchies
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Depends on all relevant couplings
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One Higgs parameter usually driven
negative by the large top mass (EWSB)
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Gluino > wino > bino
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Squarks > sleptons
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Certain mass structure results at EW
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Gluino and/or squarks heaviest
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In hadron collider mainly these will be
produced since they have SU(3) coupling
Then will have so-called cascade decay down
to the LSP (lifetime?)
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A few MSUGRA mass spectra
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Simplified models
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SUSY Successes
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Having met with some of the “set-backs”
(R-parity, SUSY breaking),
Let's regain optimism with a few of the
“successes” of SUSY ....
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Hierarchy problem
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With SUSY the same number of bosons and fermions are running in loops
(giving Higgs mass contribution of opposite sign)
If couplings are related
and
:
With broken SUSY, cancellation is not exact,
though still tolerable if SUSY masses < 1 TeV:
So: logarithmic instead
of quadratic divergence
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Grand Unification w/SUSY
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In SM gauge couplings nearly meet at very
high scale. Embed in larger group?
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in 1970s couplings met within exp. precision
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later they were found to only nearly meet
In SUSY the gauge couplings meet exactly
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if SUSY masses around 1 TeV (again)
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If no other particles in between
Unification not very sensitive to m(SUSY)
though; 100 GeV < m(SUSY) < 10 TeV
Nevertheless; same range as solution to the
hierarchy problem requires
SM:
MSSM:
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Higgs sector becoming natural
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In SM the Higgs field is the only scalar
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And a potential is constructed as needed
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with positive λ and negative µ²
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In SUSY a light Higgs is required, just like
global SM fits predict
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In SUSY scalars are automatically present
A Higgs potential comes out naturally from the
structure
If GUT is assumed, µ² is driven negative by
running of the couplings down to El.Weak
scale
As an aside, SUSY breaking is a blessing,
without it µ² would stay positive definite
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Cold Dark Matter
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The type of dark matter needed from
astrophysics and cosmology
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Cold (massive)
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Weakly interacting
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of mass around 100-1000 GeV
(debatable)
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is exactly the type suggested by most SUSY
scenarios (neutralino)
–
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Provided R-parity is conserved
Not only does SUSY provide a candidate :
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Dark Matter constraints limit SUSY
parameter space considerably
With T≫m() in the early hot and dense universe the LSP is in thermal equilibrium Universe expands and cools down. When T< m() only LSP annihilation occurs
Number density n() ~ exp(­m()/T) Eventually density becomes too low: ­ Collision rate too small, annihilation stops ­ Freeze out of the LSP: relic density
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Experimental bounds
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Astrophysical, Cosmological
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WMAP constraints on Dark Matter
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Searches for Dark Matter
Indirect Searches (loop effects)
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Ongoing searches:
Strongly constrain the internal structure
(flavour, FCNC, CP)
Direct Collider Searches (old & ongoing)
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Higgs sector ...
–
Sparticle mass bounds
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Sto
len
slid
e
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Cold Dark Matter
The type of dark matter needed from
astrophysics and cosmology:
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Cold (massive)
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Weakly interacting
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of mass around 100-1000 GeV
(well, depends on particle type)
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is exactly the type suggested by most SUSY
scenarios (neutralino)
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Provided R-parity is conserved
Not only does SUSY provide a candidate :
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Dark Matter constraints limit SUSY
parameter space considerably
With T≫m() in the early hot and dense universe the LSP is in thermal equilibrium: Universe expands and cools down. When T< m() only LSP annihilation occurs
Number density n() ~ exp(­m()/T) Eventually density becomes too low: ­ Collision rate too small, annihilation stops ­ Freeze out of the LSP: relic density
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mSUGRA Dark Matter
Usually too high LSP relic density in mSUGRA
(since LSP is mostly bino, hence small coupling)
Need special conditions to get within strong WMAP bounds
mSUGRA
4 regions where LSP annihilation cross section is increased and relic density reduced: bulk region
light sleptons (or squarks)
Green: 0.094<Dh2<0.129
co­annihilation region
m(NLSP)  m(LSP)
rapid­annihilation funnel region
m(A/H)  2m(LSP)
focus point region
non­negligible higgsino­
component to LSP
Different annihilation processes
are enhanced and dominate in
the different regions
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( NB: less constrained models can accomodate WMAP bounds with more ease )
Low-energy constraints
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Stringent limits on contributions from SUSY
particles in loops for a number of quantities :
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oscillations
–
–
b -> s + gamma
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Other Flavour-Changing Neutral Currents
(FCNC)
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g-2 measurement
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Lepton-flavour violating decays
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CP-violation
–
...
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In the minimal models, mSUGRA, mGMSB,
most of these constraints are already taken
care of (by construction)
In less constrained MSSM models, they
constrain parameter space considerably
(provided sparticle masses are not sufficiently
high)
Serious candidates for SUSY breaking had
better provide good reasons why the
dangerous parameters are absent or
sufficiently small
SM
SUSY
SUSY
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Examples of low-energy constraints:
Ex.1:
additional
SUSY
diagrams
bound to compare with exp. value
Ex.2: Mass difference between KS and KL (exp.: 3.5x10-12 MeV)
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bound to compare with exp. value
Measured Higgs mass: 125 GeV
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Is consistent with SUSY
–
Many take this as good news for SUSY
(could have been game over for the MSSM)
–
We already had good hints that the Higgs
should not be above, say 200 GeV (from EW
precision measurements)
125 GeV Higgs puts considerable constraints
on some of the SUSY parameters
Higgs couplings: are they fully compatible with
(minimal) SM?
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The measured
production
strengths
for Higgs
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Sparticle limits pre-LHC
(Mainly LEP + TEVATRON)
( Limits always some model dependence ... )
( Usually mSUGRA is assumed )
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SUSY production at pp-colliders I
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SUSY production at pp-colliders II
se!
e
t th
a
ok
o
l
t's
e
L
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Schematic SUSY event at LHC
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Initially produced: squark and gluino
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Gives two cascades
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(Many) quarks(jets) and leptons hit the
detector
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LSPs interact too weakly to be detected
Longitudinal direction (along beam):
- hard collision between partons, not protons
- have an unknown boost,
Transverse direction: Should sum up to zero
Missing transverse momentum is a prime
signature of (R-parity conserving) SUSY
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How to discover SUSY (at LHC)
Mass reach (in mSUGRA)
Main discovery channels:
If SUSY is to
- address the hierarchy problem
- and/or give gauge unification
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ETmiss + n hard jets + m leptons
Ex.: 0-lepton channel
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Then should have sparticle masses ≲ 1 TeV
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pT of 4 leading jets > 100,50,50,50 GeV
ETmiss > 100 GeV
And thus normally within early ATLAS reach.
mSUGRA
benchmark
points SUx
only
1 fb-1
Pr
ex e-LH
pe C
c te
dr
ea
ch
preliminary
Pr
e
e
xp - L HC
preliminary
ec
te d
rea
ch
Comfortable discovery at lum < 1 fb-1 for most of
the considered mSUGRA benchmarks
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Some regions may be more tricky, e.g. SU2.
Other channels (e.g. trilepton) help out.
LHC: we have already excluded good parts of this parameter space.
Squarks & gluinos need to be a little heavier than the most optimistic hopes.
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How to discover SUSY (at LHC)
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SUSY contains very many possible
cascades & signatures
Search channels range from very
inclusive (general) to very
exclusive (particular)
–
–
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Inclusive channels pick up
many cascade types
Exclusive channels pick
up a few or one
cascade type
Channel examples:
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0 lep + 1 jet
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0 lep + 2 jets
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...
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1 lep + 1 jet
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1 lep + 2 b-jets
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...
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3 lep + 0 jets
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...
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etc.
Observables:
–
–
Particle types: e, mu, tau,
jet, b-jet, (c-jet), top
Kinematic properties of
(combination of)
particles
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SUSY Measurements
If a discovery of something SUSY-like is being made (in inclusive analysis, a-la
previous page),
then need more detailed measurements
- to confirm that it is SUSY
- to describe the model (open decay channels, masses, branching ratios)
- and obtain underlying model parameters, SUSY breaking scenario
- and e.g. calculate Dark Matter
One example of such measurements: endpoint measurements to determine masses
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Endpoints (-> masses)
Consider the mass hierarchy:
LSP undetected => No mass
peaks
●
But invariant mass of the
visible particles, m(lnlf),
m(lnlfqf), m(lnqf), etc. will have
kinematic endpoints given by
the masses of the sparticle
involved in the decay
●
4-5 endpoints for 4 masses
from lf, ln and qf
=> solvable for the
masses
●
10-11 endpoints for 5
masses from lf, ln, qf and qn
=> solvable for the
masses
●
etc.
64
Endpoint measurements
P re
ex -LH
pe C
cte
dr
ea
ch
“First year”
10 years
●
●
For favourable scenarios
But LHC will do a good job
on TeV-scale SUSY
65
State-of-the-art 2015 limits
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a few examples ...
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(model dependencies: interpretation is usually somewhat involved)
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More limits available from here:
https://twiki.cern.ch/twiki/bin/view/AtlasPublic/SupersymmetryPublicResults
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Stop limits
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Neutralino and chargino limits
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SUSY: 2015-202x
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From june 2015 the CoM energy will increase from 8 to 13 TeV: more parameter
space becomes available for testing
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Final words
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●
●
●
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SUSY seems to be the BSM theory which
addresses most of the deficiencies of the SM
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- 8 TeV running has excluded the lower parts
of the allowed parameter space
This is however partly due to the large
freedom, large parameter space given by
SUSY breaking
It is not given that all topics can be addressed
with one SUSY scenario
- 13 TeV running will exclude more – or
discover
●
SUSY has been searched for for many years,
at many different facilities, no luck so far
Nevertheless, SUSY remains (for many) the
most promising BSM still
LHC searches are ongoing:
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If SUSY is discovered, a multitude of relevant
measurements will be performed at LHC, then
more precise measurements in some sectors
will be made at a Linear Collider
However: If SUSY is not discovered at the
LHC, ...
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References
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Gordon Kane
–
The Dawn of Phyiscs Beyond the Standard Model
–
Supersymmetry: what? Why? When?
Luc Pape and Daniel Treille:
–
●
Much ado (already) about nothing (yet)
Stephen Martin
–
A Supersymmetric Primer
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https://fliptomato.wordpress.com/2008/03/20/supersymmetry-literature-for-the-perplexed/
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Recent Supersymmetry results from ATLAS
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BACKUP
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NON-SUSY BSM
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Non-mSUGRA (like) scenarios
●
●
Split-SUSY
●
MSSM105
–
Scalars very heavy, gauginos below 1 TeV
–
Lots of low-energy constraints
–
Gluino can then be sufficiently long-lived
that it hadronises into
and interacts with the detector
–
Difficult to set limits
Gauge-mediated SUSY breaking
–
●
●
Gravitino is LSP
R-parity non-conserving scenarios
–
No Dark Matter candidate
–
At collider also single sparticle production
–
No missing transverse energy signature
–
But can reconstruct full event, mass peaks
Next-to MSSM (NMSSM):
–
Add a Higgs singlet
–
Increases theoretical upper bound on
lightest Higgs mass to ~150 GeV
84