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• SUPERSYMMETRY:
– WHAT? WHY? WHEN? WHERE?
Gordy Kane, University of Michigan
Beijing, May 2014
• Introduction – the Standard Model(s) of particle physics
and cosmology
• What is supersymmetry (the supersymmetric Standard
Model)?
• Why do so many physicists think nature is
supersymmetric? (over 20,000 papers)
• When and where should the new particles predicted by
supersymmetry (“superpartners”) be discovered?
• Perspectives – briefly describe modern view of
supersymmetry as implied by M/string theory rather than
as an ad hoc electroweak scale theory
– final remarks
STANDARD MODEL OF PARTICLE PHYSICS
 Strong, Electromagnetic, Weak interactions + classical
gravity
o All we see is made up of electrons (e), up quarks (u), down
quarks (d)!
[quarks are particles like electrons, but with different electric
charge and mass, and having an additional, strong, interaction]
o Gauge theory, form of force determined -- Quarks interact via
gluons, bind to make protons (p), neutrons (n) – leakage of
the strong force outside p,n binds p,n to form nuclei
[gluons like photons, but in addition they have the strong interaction]
o Electrons bind to nuclei via photons to make atoms – leakage
of the electromagnetic force outside atoms binds atoms to
form molecules
o Not just metaphors, full quantitative relativistic quantum field
theory
o Essentially all e,u,d were produced in the Big Bang
o Higgs bosons
THERE ARE MORE PARTICLES
 MATTER:
-- charged “leptons” µ, τ – like e but heavier
-- quarks s,c,b,t – like u,d but heavier
-- neutrinos (ν) – one each for e,µ,τ – extremely light, no charge
Form 3 “families”
u,d,νe, e
s,c,νµ,µ
b,t,ντ,τ
NO IDEA WHY – all but e,u,d short-lived or do not bind – SM fully
accommodates them and describes their behavior – not
explained by supersymmetry
 DARK MATTER – not part of SM
• Always before found smaller constituents
• No more – we think these are the true constituents
• Why?
o Suggested by experiment – have looked 100,000 times deeper
than naïve expectation if there were structure
o For bound states, like atoms or the periodic table, usually many
such states, no end – here strong evidence just 3 families
o Have for first time a consistent theory that treats e,q as basic –
theory describes and relates many phenomena so if change it
whole structure collapses
o If e,q basic can unify description of forces
Description of e,q may change – e.g. may think of them as
strings instead of point particles, but still electrons and
quarks
HUGE PROGRESS IN UNDERSTANDING FORCES
o In SM, existence of particles implies forces (in q.th.)
electron  photon with correct interactions
 we understand light!
o All forces have same form
o Forces seem to have different strengths – can ask how
they behave if extrapolate them to high energies (short
distances) – strengths get similar in SM (become same
in supersymmetric Standard Model)
electrical
magnetic
weak
strong
electromagnetic
electroweak
“grand unified”?
gravity
string theory?
HIGGS PHYSICS – last piece of SM
• Accommodating parity violation in the Standard Model implies
electrons and quarks are massless
• That’s because electrons and quarks inhabit an “electroweak” space
– in that space, left-handed (L) electrons and quarks behave as if
they had “EWspin” ½, and right-handed (R) ones as if they had
“EWspin” 0
• Not explained in SM, that’s just how it is (this is one of the things we
would like to explain)
• Then if e,q have mass, can go to their rest frame, rotate ordinary
spin so L ↔ R, but then they have the wrong EW spin, so
inconsistent – only two ways out
o e, q massless
o Add Higgs field with EWspin ½, and claim that energy of
universe is lower when that higgs field has non-zero value than
when zero – allows RH electron to behave as if had EWspin ½
o Jargon – Higgs field has non-zero “vacuum expectation value”,
breaks the EW symmetry!
Interactions with Higgs bosons give mass to quarks,
leptons, W, Z, maybe some dark matter.
Mass of atom  1/(Melectron) so atoms become infinite in size
if no Higgs mechanism
Higgs field  Higgs bosons are quanta of Higgs field
Higgs mechanism is interaction of Higgs field with quarks,
leptons, gauge bosons
Over 99% of proton, neutron masses due to KE of motion
of quarks and gluons in proton, neutron, not to Higgs
interaction
STANDARD MODEL OF COSMOLOGY
• The universe begins tiny, contains some
(unstable) energy density, and 3 space
dimensions inflate
• After very short time energy density converts
into “radiation”, i.e. (massless) particles  Big Bang
• Universe cools and expands – today ~ 4%
neutrons and protons (ordinary matter), ~ 25%
dark matter, ~ 70% dark energy
• Description works from world around us to the
edge of the observable universe, back to 10-35
sec (or even earlier) after universe began
A little over a century ago it was not agreed that atoms exist, and
we had essentially no knowledge of weak and strong forces,
nor of the fundamental particles, nor did we know the universe
and the earth had histories!
• The Standard Model(s) of particle physics and cosmology
are wonderful, amazing – based on many remarkable
experiments, and powerful innovative theory – achieve
historical goals of physics, in a full theory
• Describe and explain many phenomena from a few basic
particles, forces, and rules – no contradictions in their domain
– SM consistent relativistic quantum field theory
• Many predictions correct, tests
• So why are we confident they will be extended?
Because the SMs do not seem compelling, inevitable
AND THERE IS MUCH THE STANDARD MODEL(S) CANNOT EXPLAIN
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Neither cosmology nor the SM can tell us what the dark matter is
Neither cosmology nor the SM can explain the matter asymmetry
Neither cosmology nor the SM can tell us what the dark energy is
Neither cosmology nor the SM can tell us the physical nature of the
inflaton field
The SM cannot tell us why there are 3 families of leptons and quarks
The SM cannot give us insight into how to unify gravity and the other
forces
The SM cannot explain the origin of the Higgs physics
The SM cannot allow calculation of the electron or muon or quark
masses
The SM cannot describe neutrino masses without adding a new mass
scale
The SM has a quantum hierarchy problem, very serious
The SM cannot explain parity violation
Remarkably, in past 2-3 decades, have learned
that if we hope to understand these things the
direction we need to go is to embed our 4D
world in additional space-time dimensions
Two approaches show great promise for explaining
what cosmology and the Standard Model(s)
cannot:
 Supersymmetry – for every space-time dimension add a
fermionic quantum dimension – focus here today since
this should be the next big discovery
 String theory – add 6(7) space dimensions like ours, except that ours
inflated, others didn’t– only known way to have consistent quantum
theory of gravity – all 10 D have a quantum dimension too
Imagine small particle – go around several times, returning wave
function to initial place – particles are bosons or fermions
n even → boson
n odd → fermion
[bosons are particles with integer spin, fermions with half integer]
This is tied to being in 3D – imagine a “superspace” dimension (of zero
length) for each of our space-time dimensions
Then can go into extra dimension and untwist fermion to get boson (or
vice versa) – spin changes by ½ unit
↔
↔
So every fermion gets a superpartner boson, and vice versa
Suggests the idea of supersymmetry (~1973):
THE LAWS OF NATURE DON’T CHANGE IF B ↔ F IN
THE EQUATIONS DESCRIBING THE LAWS
Originally very surprising – matter particles (e,u,d…) were
fermions, force particles (γ,g,W,Z) were bosons – in
quantum theory they were treated very differently – the
idea was studied just to see if it could work
Only idea in history of science that emerged purely from
theoretical study rather than from trying to understand
data, puzzles, observations – studied because it was a
beautiful idea
TURNED OUT IT MIGHT EXPLAIN MAJOR PROBLEMS
(SOME OF) WHAT SUPERSYMMETRY
MIGHT DO FOR UNDERSTANDING THE
NATURAL WORLD:
o 1979 Stabilize the quantum hierarchy
(like antiparticles for quantum electrodynamics)
o In quantum theory every particle spends time being all
other particles virtually ….
Explain the quantum hierarchy size (from electroweak
scale to unification or Planck scale) ??? – NO –
supersymmetry a broken symmetry, analogous to EW
symmetry – hierarchy explained if could prove masses of
superpartners close to those of SM particles
THEN CAN DERIVE MUCH:
o 1982 Explain Higgs mechanism
o 1983 Explain why the forces look different to us
in strength and properties, but become the same
at high energies
o 1983 Provide a dark matter candidate (the
lightest superpartner)
o 1991 Allow an explanation of the matter
asymmetry of the universe
o 1992 Explain why all LEP data is consistent with
the Standard Model(s) even though we expect
new physics
ALL SIMULTANEOUSLY
In addition there are theoretical motivations:
• If supersymmetry is a local symmetry it implies General
Relativity – if Einstein had not invented General
Relativity it would have been (i.e. it was) written in 1975
by studying supersymmetry
-- supersymmetry transformation affects spin – spin part of
angular momentum – generators of angular momentum
transformations part of Poincare group – connects to gravity
equations
• String theory probably requires supersymmetry if it is
relevant to understanding nature
IF SUPERSYMMETRY RELEVANT, SUPERPARTNERS
MUST BE DISCOVERED AT COLLIDERS, SUCH AS
TEVATRON, LHC
Selectron
photino
gluino
stop squark
sneutrino
etc
They differ by spin ±1/2 and mass from their SM partners
None of the existing particles can be superpartners of other existing
ones – no two have same quantum numbers and differ by half unit spin
– and must have consistent theory without anomalies
Supersymmetry is a full mathematical theory
Can summarize the perturbative SM by a set of vertices for
Feynman diagrams: let
fL =e,µ,τ,d,s,b,u,c,t l±=e±,µ±,τ± UR =u,c,t DR =d,s,b
ν=νe,νµ,ντ
Then all the phenomena in nature that we see involving fermions
are described by gravity plus the four vertices:
To make the theory supersymmetric, add the vertices with
particles turned into superpartners in pairs, all ways
Everything is known about the supersymmetric SM except
the masses of the particles – only string theory can
predict masses from first principles
The lightest superpartner (LSP) is very important
phenomenologically
o Superpartners produced in pairs at colliders
o LSPs at end of superpartner decay chains
o Can be partner of photon, Z boson, Higgs boson,
neutrino, gravitino (could calculate this if superpartner masses
known)
o Interacts at most weakly, electromagnetically
o Normally stable or long-lived
-- every event has 2 LSPs, both escape detector
o Missing energy a basic signature of superpartners
LSP may also be the dark matter of the universe!
• Big Bang, universe cools – after a while only
γ , e, u, d, , LSP remain
• Calculate relic density of LSPs – some annihilate, e.g.
• Need to know superpartner properties and cosmologicl
history to work out numbers – for reasonable choices,
answer about right
SOME QUESTIONS
√ addressed
√√ answered
What is matter?
What is light?
What interactions give our world?
Gravity
Stabilize quantum hierarchy?
Explain hierarchy?
Unify force strengths?
Higgs physics?
What is dark matter?
Baryon asymmetry?
More than one family? 3?
Values of quark, lepton masses?
Origin of CP violation?
What is the inflaton?
Dark energy?
Cosmological Constant Problem?
What is an electron? Electric charge?
Space-time?
Why quantum theory?
Origin of universe?
Standard
Model(s)
Supersymmetric
SM(s), light
superpartners
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M/String
Phenomenology
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WHAT DATA COULD SOON GIVE EVIDENCE FOR
SUPERPARTNERS?
• DIRECT observation of superpartners at LHC
• Indirect, expected from supersymmetry
–
–
o
–
–
Laboratory dark matter detectors
Electric dipole moments of e,n
(Muon anomalous magnetic moment)
Lepton flavor violation (µ→eγ…)
Bs→µµ at LHC
But indirect observation could be explained other ways
Units, energies, luminosities:
• E=mc2 so provide collisions of particles
• Cross sections in femptobarns (fb) – determined by nature
• Luminosity of collider integrated over time, fb-1 – limited by
Maxwell’s equations, cost
• Number of events = cross section x luminosity
• Energies
-- BEPC 4 GeV (G=giga=109eV)
-- CERN Large Hadron collider, total energy E=7,8 TeV,
(T=tera=103GeV)
o So far LHC about 20 fb-1 each detector at 7 TeV, being
upgraded, start again at 13-14 TeV
o Goal about 300 fb-1in 2-3 years, per detector
LHC
• Two large detectors, ATLAS, CMS
• Detectors amazing
Signatures of superpartners
e.g. Same-Sign (SS) dileptons
• g is the superpartner of the gluon g
• g a massless spin 1 boson, like photon, so 2 polarization
states – so g has 2 polarization states  Majorana fermion
• So g is its own antiparticle, can decay equally as gluinobar
or gluino, so produced pair of gluinos will give gluino
gluinobar, gluinobar gluino, gluino gluino, gluinobar gluinobar
• If g  l± + then
• Half of events have SS dileptons! None in SM!
Collider signatures of superpartners:
e.g.
Current status – no superpartner discoveries!
Interpretation? Very Model dependent
• Simplest models for masses  limits, gluinos and squarks
heavier than about 1.4 TeV
• Best motivated models  gluinos heavier than about 0.9 TeV
Implications?
• If want almost perfect solution of hierarchy problem, would
have guessed superpartner masses 100-200 GeV, like top
quark and W masses (“naturalness”)
• BUT
(A) Higgs boson found at LHC
-- higgs boson well motivated by supersymmetry –
effectively a superpartner – supersymmetry Lagrangian
allows derivation of higgs boson
-- with superpartner scalars of order 50 TeV, expect SMlike higgs boson, mass of 125 GeV
-- so discovery of higgs boson suggestive of
supersymmetry if scalars heavy
(B) Best motivated models from theories with “ultraviolet
completions” suggest gluinos 1 TeV, but squarks tens of
TeV(!), so should not have seen squarks yet, and gluinos need
luck to see so far – should see gluinos in 2015 at LHC
Look briefly at what M/string theories suggest for superpartners
If M/string theories are quantum theories of gravity, for
mathematical consistency they must have 11/10
dimensions (difference technical, ignore here)
So suppose M/string theory is a candidate framework for
nature -- then it must contain effectively 4D universe(s)
among its solutions, ones that are indistinguishable from
ours.
In such solutions the extra dimensions are “compactified” to
tiny scales comparable with the Planck size
“String phenomenology” studies such solutions, relates
their properties to data, and aims to answer many of the
outstanding questions of particle physics beyond the SM
New approach(es) to supersymmetry theory:
• Compactify M-Theory on G2 manifold
[Acharya, Kane, Bobkov, Kumar….]
• 7 small curled up dimensions, all also fermionic
• Full soft-breaking Lagrangian calculable
• Predicted summer 2011 higgs mass 125 GeV, higgs SM-like
• Gravitino mass about 50 TeV – natural scale for
supersymmetry
• Scalars heavy like gravitino, but gauginos generically
suppressed to TeV scale! – Meson F-term dominates moduli
F term but SM gauge kinetic function does not depend on
meson F term!
PAPERS ABOUT M-THEORY COMPACTIFICATIONS ON G2 MANIFOLDS
(11 D – 7 small D = our 4D)
Earlier work on compactified M theory(stringy, mathematical) : Witten 1995
• Papadopoulos, Townsend th/9506150, 7D manifold with G2 holonomy
preserves N=1 supersymmetry
• Acharya, hep-th/9812205, non-abelian gauge fields localized on singular
3 cycles
• Acharya, hep-th/0011289
Particles!
• Atiyah and Witten, hep-th/0107177
• Atiyah, Maldacena, Vafa, hep-th/0011256
• Acharya and Witten, hep-th/0109152, chiral fermions supported at points
with conical singularities
• Witten, hep-ph/0201018 – shows embedding MSSM probably ok
• Beasley and Witten, hep-th/0203061, Kahler form
• Friedmann and Witten, th/0211269
• Lukas, Morris hep-th/0305078, gauge kinetic function
• Acharya and Gukov, hep-th/0409101 – review – good summary of
known results about singularities, holonomy and supersymmetry, etc –
all G2 moduli geometric – gravity mediated because two 3-cycles
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won’t interact directly in 7D manifold
ASSUMPTIONS – note none closely related to results – string
phenomenology
• Compactify M-theory on G2 manifold (in fluxless sector)
• No principle yet to set gauge group and matter at
compactification scale – choose MSSM
• Assume CC problem orthogonal, and that can tune CC to
be small
• Assume no mathematical obstacles to ok G2 manifold even
though not yet known in detail – some predictions not
sensitive to details of manifold
• Keep approach fully generic, don’t fix any parameters or
parameter space regions, don’t introduce any parameters
• Assume can use generic Kahler potential (Beasley, Witten
2002).
• Assume generic gauge kinetic function (Lukas, Morris
2003).
Need two details about compactified string theories:
GRAVITINO
-- in theories with supersymmetry the graviton has a
superpartner, gravitino – when supersymmetry broken,
gravitino mass (M3/2 ) splitting from the massless graviton is
determined by the form of supersymmetry breaking
– gravitino mass sets the mass scale for the theory, for all
superpartners, for some dark matter
Also:
MODULI
-- to describe sizes and shapes and metrics of small manifolds
the theory provides a number of fields, called “moduli” fields
-- supersymmetry breaking generates a potential for all moduli
-- moduli fields have definite values in the ground state (vacuum)
– jargon is “stabilized” – then measurable quantities such as
masses, coupling strengths, etc, are determined in that
ground state
-- moduli fields like all fields have quanta (also called moduli),
with masses fixed by fluctuations around minimum of moduli
potential
Our M-theory papers --Review arXiv:1204.2795 , Acharya, Kane, Kumar
[Acharya, Kane, Vaman, Piyush Kumar, Bobkov, Kuflik, Shao, Lu, Watson, Zheng]
o M-Theory Solution to Hierarchy Problem th/0606262, PhysRevLett 97(2006)
 Stabilized Moduli, TeV scale, squark masses = gravitino mass, heavy;
gaugino masses suppressed 0701034
o Spectrum, scalars heavy, wino-like LSP, large trilinears (no R-symmetry)
0801.0478
o Study moduli, Nonthermal cosmological history– generically moduli 30 TeV so
gravitino 30 TeV, squarks gravitino so squarks 30 TeV 0804.0863
o CP Phases in M-theory (weak CPV OK) and EDMs 0905.2986
o Lightest moduli masses gravitino mass 1006.3272 (Douglas Denef 2004;
Gomez-Reino, Scrucca 2006)
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o
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o
Axions stabilized, strong CP OK, string axions OK 1004.5138
Gluino, Multi-top searches at LHC (also Suruliz, Wang) 0901.336
No flavor problems, (also Velasco-Sevilla Kersten, Kadota)
Theory, phenomenology of µ in M-theory 1102.0566 via Witten
Baryogenesis, ratio of DM to baryons (also Watson, Yu) 1108.5178
String-motivated approach to little hierarchy problem, (also Feldman) 1105.3765
 Higgs Mass Prediction 1112.1059 (Kumar, Lu, Zheng)
o R-parity conservation, EDMs, top yukawa, Neff , future colliders?
To take Higgs results fully seriously good to know other major physics
questions addressed OK in same theory
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Think of effective theories for Higgs sector, LHC,
superpartners, CPV both strong and weak, EDMs, rare b
decays, R-parity violation, axions, cosmological history,
dark matter, etc
In normal effective theory all operators
have independent coefficients – in
compactified M theory all coefficients
are determined, all are related to one
another, and calculable!
1112.1059, Kane,
Kumar, Lu, Zheng,
August 2011
M3/2=100
M3/2=50
M3/2=25
Points are
REWSB, no free
parameters,
gravatino= 50
TeV, µ=1 TeV,
This shows effect of doubling or halving
gravitino mass, Mh  1.5 GeV
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100
TeV
Final remarks:
Naturalness? Fine-tuning? Little hierarchy? Of course
compactified string theory is natural in some sense.
Opposite of naturalness is having a theory.
---------- Mpl  1018 GeV
susy (chiral fermion, gaugino
M/String theory:
condensation1014GeV)
Radiative
EWSB
---------- M3/2  30-60 TeV
TeV
String theory
gaugino
suppression
------------Mgluino
------------Mchargino, neutralino
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Why does supersymmetry provide explanations,
predictions?
• Dirac: Special Relativity + quantum theory
 antiparticles + explained spin (and QED renormalizable)
• Fermions + bosons
 superpartners + (possible) explanations
• Gravity + relativistic quantum field theory  M/string theory
 extra dimensions + (possible) explanations
Remember:
 The Standard Models of particle physics and cosmology provide a
very good description of all we see
 Supersymmetry relates matter particles, force particles – might
provide unification of understanding of forces, explanation of
Higgs physics, dark matter, matter asymmetry….
 Supersymmetry also provides essential window to connect
phenomena to underlying theory (such as string theory) at
fundamental scale
 If supersymmetry indeed explains what it might explain, then some
superpartners must be discovered at colliders
 Theories with ultraviolet completions suggest natural scale of
supersymmetry is gravitino mass  50 TeV – gauginos generically
suppressed to  TeV
Dirac ~ 1929, led by “beautiful” theory to unify relativity and quantum
theory  antiparticles, spin …
-- 1932 positron
-- 1956 antiproton (~ 27 years longer since
needed new accelerator)
Dirac, late 1970s “[supersymmetry] is indeed a beautiful theory, but if it
were a true symmetry of nature, those new fermions and bosons
would have been found long ago”
True – but we have learned broken symmetries are beautiful too –
breaking of EW symmetry and supersymmetry related
Supersymmetry idea discovered early 1970s – prematurely –
understood as effective theory early 1980s – indirect evidence
strong by early 1990s – hopefully direct evidence soon at LHC