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Exploring the Microworld
of Forces and Particles
The Particle Mandala
Arthur O. Williams Lecture April 10, 2006
Paul Grannis, Stony Brook
40 years ago we had four distinct forces,
governing different phenomena:
1. Electromagnetic – interactions of charged particles and
photons (unified by Maxwell in 19th century) responsible for
most of the phenemena seen in our laboratories.
2. Strong – responsible for the force between nucleons
(hadrons), and the binding of the nucleus.
3. Weak – decays of quasi-stable particles, interactions
involving neutrinos (e.g. powering the sun).
4. Gravity – the dominant long range force in the universe, of
negligible strength compared to all others on microscale at
low energy.
Electromagnetic force
Interaction between two charged vector currents
(electrons, positrons, protons etc), mediated by the
photon (spin 1) which couples (weakly, a=1/137) to
charge. The quantum theory QED is renormalizable, and
owing to the small coupling, susceptible to accurate
calculation by perturbation theory.
e+
e+
p
Massless photon → long
range interaction (~1/r2)
g
p
Weak force (beta decay is prototype)
p
n
en
Experiments initially showed ~zero range. This violates
unitarity (conservation of probability) at high energy so can’t be
correct. Structure seen to be combination of vector (V) and
axial vector (A) – parity violation.
Fermi introduced current form similar to EM; with charged
boson spin 1 force carriers (W±) this postponed the unitarity
problem. The observed short range means that W’s are very
massive.
p
 No neutral current analog observed
n
(e.g. K0 → p0 n n )
eW 2 charged leptons (e & m), 2 neutrinos
(ne & nm )
n
 Muon and electron number conserved
Weak force
The unitarity problem persists – WW scattering violates
probability conservation at TeV scale. And a renormalizable,
locally gauge invariant, theory requires massless force carriers.
Solution: (Higgs, Weinberg, Salam, Veltman, t’Hooft, …)
postulate a triplet of massless neutral gauge bosons (w+, w0, w-)
and a massless singlet (b0) that mediate the underlying weak
interaction. Introduce a set of 4 spin 0 Higgs fields (2 complex
doublets) that stimulate spontaneous symmetry breaking.
Gives mass to the charged bosons (W+ , W-), and causes a
rotation of the neutral states:
Z0 = cosqWw0 + sinqW b0
g = -sinqW w0 + cosqW b0
The W+, W- and Z acquire mass in this symmetry breaking. The
g remains massless. The longitudinal polarization states needed
for massive states ‘swallow’ 3 of the Higgs fields, leaving 1 Higgs
boson to be observed.
Weak force
This postulate combines the EM and Weak Interactions as
unified Electroweak theory. It requires neutral currents of fixed
strength relative to charged currents.
The Higgs field is responsible not only for giving mass to W and
Z, but also all the fermions (e, m, quarks). The weak mixing
angle qW was approximately determined by n scattering to yield
MZ ~ 90 GeV and MW ~ 80 GeV.
Spontaneous symmetry breaking
Spontaneous symmetry breaking – mass on
thin vertical wire. Ground
state minimizes
Ferromagnet
breaks the symmetry
total
energymechanism
of bent wire
gravitational
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The Higgs
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The Stong Force – the Quarks
By late 1960’s, a host of particles with
differing quantum numbers were
found – baryons (partners of proton
and neutron) and mesons like p, K, r,
w etc. ‘Strange’ particles produced in
pairs and decay by weak force.
etc. etc. !
Gell-Mann, Neeman, Zweig classify
these states with just 3 quarks:
strangeness
d
Three spin ½ quarks:
u
s
isospin
Two zero strangeness:
u (up) : Qu = +2/3
d (down): Qd = -1/3
One strangeness = -1
s (strange): Qs = -1/3
And corresponding
3 antiquarks
s
u
d
The Stong Force
The observed particles could be made from combinations of 3
quarks (baryons) or quark + antiquark (mesons) with differing
orbital angular momentum. “The Eightfold Way”
(proton = uud; neutron = udd; p+ = u d; K+ = u s; etc. )
Particles with quantum numbers not allowed by combining
quarks were not seen.
Predict new particles (e.g. W- = sss), observed in 1964 (Samios,
Shutt et al.)
 A statistics problem: baryons made of three identical quarks
in relative s-waves and spins aligned (e.g. W- = sss) have
wavefunctions symmetric in space and spin. Quarks are spin ½
fermions, so these states violate the Pauli Principle.
 Another problem: quarks not observed experimentally
 At this stage, quarks were considered to be useful but fictitious
memnonics for the particle zoo.
The Stong Force
Electron-proton scattering at high energy and momentum
transfer Q2 showed evidence for pointlike constituents with
charges of uds quarks (Friedman, Kendall, Taylor et al, Bjorken)
The approximate scaling (Q2 independence) would infer that
the proton is made only from quarks. But more precise
experiments show some Q2 dependence.
electron
g (carrying momentum Q)
proton
scattered
quark
x = fraction of proton momentum
carried by struck quark
Q2 = mom. transfer squared
(“microscope” resolution)
The Stong Force
The resolution comes with Quantum Chromodynamics (QCD)
– gauge theory of strong interactions involving matter particles
(quarks) and massless gauge bosons (gluons) responding to a
new type of ‘charge’ called ‘color’ (Yang, Mills, Gross, Politzer,
Wilczek … ). Unlike EM interaction where g has no charge, the
gluons have color-charge and thus interact with themselves.
 Solves statistics problem if there are three colors for quarks,
and wavefunction is antisymmetric in color.
Predicts non-scaling in ep scattering, since a single quark at low
Q2 can acquire structure through virtual gluon emission.
At low Q2, g from
electron sees only
a single quark
At high Q2, the
quark is resolved
into q and virtual g
QCD is a renormalizable gauge theory, like EW, (but fiendishly
difficult to calculate)
The dream of force unification
Magnetic
Electromagnetic
Electric
What about ‘grand unification’ of Electroweak
Electromagnetic
Weakaforces
unified into
Electroweak.
and Strongand
to make
single are
microscopic
force?
Maxwell !
Gravity
Unified
Force ??
Electroweak
Weak
??
?????
Strong
Our current theory does not quite permit this to
And then there is gravity … string theory could perhaps
happen, but if there were new particles, then such
bring it into the fold.
The
original 4could
forceshappen
of microscopic
matter
a unification
at very high
energy.
So, in the decade from 1965 – 1974 we passed from a view of
four distinct and very different forces among the 100’s of
hadrons and leptons to the:
STANDARD MODEL
Matter composed of a few quarks (u,d,s) and leptons (e, ne, m, nm)
 Unified Electroweak force with both charged and neutral gauge
boson force carriers. One surviving Higgs field.
 Strong force of QCD, with 8 colored gluons as carriers
(Gravity still outside the picture)
Symmetry structure:
SU(3) x ( SU(2) x U(1) )
QCD with 3 colors
EW with weak isospin and isosinglet pieces
QCD and EW just pasted together, no unification
Elementary matter particles and force bosons in 1974
?
Postulated in the SM;
not yet observed
 Both EW and QCD forces are gauge interactions with
fundamental zero mass bosons.
 Quarks feel the Strong and EW forces. Anything charged
feels the EM interaction. Leptons feel only the EW force.
Outstanding questions in 1974
 The 3 quark model gives far too large weak neutral current
effects, and has irredeemable divergences if #quarks ≠
#leptons. Need a fourth quark, partner to the strange quark.
 Higgs boson is not seen – no prediction for its mass.
 Few direct tests of EW model correctness existed.
 W±, Z not seen, but predicted at ~ 80, 90 GeV.
 No experimental evidence for the gluon, and only indirect
evidence for QCD.
The following ~20 years were devoted to resolving these
questions, and adding some unexpected surprises.
A whirlwind tour of the news headlines from 1974 to 2005
1974: Simultaneous observation of a narrow resonance
at 3.1 GeV, in e+e- collisions (Richter et al. at SLAC) and
in pN collisions (Ting et al. at BNL).
e+ e- → y
pN → J
The J/Y was quickly inferred to be an s-wave spin 1 bound
state of a new charm quark and its anti-charm partner. The c
quark (Qc = +2/3) is the isospin partner of the s quark.
1976: Charmed particles observed directly (Goldhaber,
Pierre et al) with expected properties.
Observation of the charm
quark restores the symmetry
between leptons and quarks
needed in theory and
necessary to suppress neutral
currents.
1976: New charged tau lepton observed (Perl et al.) in
e+e- → e m + missing energy. Its companion nt is
inferred from the missing energy. Who ordered this??
This discovery opens up a
third generation of leptons,
and again gives asymmetry in
number of quarks and leptons.
Where are the corresponding
quarks?
1977: the charge Q= -1/3 bottom quark is inferred from a
new narrow resonance at 9.5 GeV in pp collisions at Fermilab
(Lederman et al.) – a bb bound state. It is the first of the third
quark generation. Its mass is ~3x that of charm (and 5x
proton mass). The bottom hadrons themselves followed at
Cornell.
1979: The gluon is seen experimentally in e+e- → q q g
(experiments at PETRA storage ring at DESY), as events
where the radiated gluon is manifest as a third jet (jets =
collimated sprays of hadrons emerging from a single quark or
gluon progenitor). Quarks and gluons cannot seen directly
because the strong color force prevents un-matched color
particles from emerging alone.
3-jet event – gluon
discovery at PETRA
Measurements show the ‘running’
of strong coupling constant
1983: Discovery of the W± and Z bosons in UA1 and UA2
(Rubbia et al., Darriulat et al. at CERN proton-antiproton
collider). Masses and decay patterns are as predicted by EW
theory.
Then
Now
24 events
UA1 and UA2 Z to dilepton
invariant mass at discovery in
1983.
CDF Z → ee invariant
mass in 2006.
1995: Discovery of the top quark by CDF and DØ
experiments at the Fermilab proton-antiproton collider. The
top mass is about 175 GeV, over 50 times the mass of the next
most massive b quark (and ~ mass of Au nucleus).
Roster of SM matter particles
(quarks and leptons) and force
carrying bosons is complete.
World avg mass: 172.5 ± 2.3 GeV
~ 1985 – 2005: 100’s of precision studies of Z, W boson and
top quark properties at the CERN and SLAC e+e- colliders and
Fermilab proton-antiproton collider pin down the SM
Electroweak parameters to great accuracy. Although the Higgs
boson remains out of sight, these precision measurements tell us
what mass it would have in the SM context.
Virtual Higgs loops affect the top and W masses (logarithmically),
giving experimental sensitivity to Higgs mass
Favored SM
Higgs mass is
about 120 GeV.
LEP-2 rules out
Higgs < 114 GeV
W and top mass agree
with SM, but may hint
at something new
1990 – 2006: The weak quark eigenstates are rotations of the
strong quark states. The quark mixing rotation angle, and the
CP violation seen in K0 decays in 1964, have been studied in
both K and B decays (SLAC and KEK (Japan), BNL, CERN,
Fermilab). Unitarity constrains matrix elements.
1995
2005
Peanut shape is the error on closure
of unitarity constraint on quark
mixing matrix in SM.
Quark mixing and CP violation is seen to be consistent with the
3 generation of quarks in SM.
1998: Neutrino mass and mixing: nm produced by cosmic ray
collisions with upper atmosphere air molecules (and
subsequent p decay) disappear after traversing the earth’s
diameter (Superkamiokande experiment underground in
Japan, Koshiba et al.). This is interpreted as oscillation of nm
to (invisible) nt.
 Oscillation requires that neutrinos have different masses
and the mass eigenstates are mixtures of ne, nm, nt (mixing).
m/e (observed /
expected)
with no oscillation
cos qzenith →
upgoing
downgoing
Strictly speaking, n mass and
mixing is outside the SM, but is
analogous to what we see in the
quark sector.
The SM parameters:
• 6 quark masses
• 6 lepton masses
• 4 quark mixing matrix parameters
• 4 lepton mixing matrix parameters
• 3 force coupling `constants’
• 2 EWSB parameters (e.g. mH , sin2qW ),
• 1 phase for strong interaction CP violation
26 arbitrary parameters – to be determined by experiment
And if these parameters were different, our universe would be
dramatically changed: e.g. if down quark were lighter than the
up quark, the proton decays, hydrogen doesn’t exist, stars don’t
ignite, universe nearly transparent to light, chemistry vastly
changed …
The SM has been validated with 1000’s of measurements
showing agreement between theory and data
etc. etc.
The SM explains a vast array of experimental data –
so why don’t we like it?
1. Those 26 arbitrary parameters – SM has no explanation for
why they are as observed. Masses vary by 10 orders of
magnitude ! Why 3 generations?
2. SM shows CP violation, but not enough to explain why there
is the huge asymmetry between number of baryons and
antibaryons in the universe.
3. The Strong and EW interactions are just pasted together in
SM. If extrapolate the coupling constants to high energy,
they come close to a common value at ~ 1017 GeV –
but no cigar
g3
g2
g1
No unification
why we don’t like the SM …
4. Quantum corrections (loop diagrams) would cause the
Higgs, W, Z boson masses to diverge to Planck scale unless
there is some fantastic accidental tuning of couplings to
keep these at TeV scale. (hierarchy problem)
5. Galaxies show substantial dark matter, also evident in early
galaxy formation. DM seems to be massive particles, left
from the early universe. SM provides no candidate.
6. Dark energy, pushing the universe apart in the present
epoch, has no explanation in the SM.
7. The SM would give WL (energy density due to cosmological
constant) be O(10120). One might understand some new
symmetry causing it to be zero, but WL ~ 1. The biggest
fine tuning problem of them all !
8. Gravity is not included in SM
So, despite the successes of the SM, we strongly
believe it will be supplanted with new physics.
First one needs to find what serves the role of the Higgs boson
to break EW symmetry. Moreover, to solve the SM defects
(fine tuning of Higgs mass, DM particle, desire to unify the
forces … ) there needs to be new physics at few 100 – 1000
GeV – the Terascale.
The new theory must reproduce the successes of the SM while
adding new ingredients – much as Quantum Mechanics gives
Classical Mechanics in the correspondence limit.
There are several classes of theoretical models suggested for
the new paradigm:
 New symmetries of nature
 New forces and particles
 Extra space dimensions
Each model class has many variants
An experimentalists dream –
We know there is a new playing field at the Terascale, but
have no idea who the players are, or the rules of the game.
Go there and find out!
And there are two demonstrated new accelerator colliding beam
facilities that will give a complementary view of the new terrain:
The Large Hadron Collider (LHC), to be commissioned in 2007 at
CERN – proton-proton collisions at ECM = 14 TeV
The International Linear Collider (ILC) being designed in
international collaboration: e+e- collisions at ECM = 0.5 – 1 TeV.
Colliders for the energy frontier
 High energy reach
 Broad range of parton CM
energies at once
 Large event rate
 Large QCD backgrounds
 Pileup – spectator quarks &
other pp collisions
 Radiation damage issues
LHC
proton
proton
 Known initial quantum state
 Well-defined ECM and pol’zn
 low bkgd → ambitious
ILC
experimental techniques
 Event rates low; need
ee+
sequential runs at different
ECM and polarization
 Complex machine detector
LHC & ILC collider characteristics
interface; need exquisite
are highly complementary
control of beam optics
The LHC
Mt. Blanc
The 14 TeV (ECM), 27 km
circumference Large Hadron
proton-proton Collider at CERN on
the Swiss-French border – complete
in 2007. The LHC will be the
highest energy accelerator for many
years.
But …
Lake Geneva
The protons are bags of many
quarks and gluons (partons)
which share the proton beam
momentum. Parton collisions
have a wide range of energies –
up to ~2000 GeV. Initial
quantum state is not fixed.
The International Linear Collider
Collide beams with energy tuneable up to Ecm = 500 GeV
(upgrade to Ecm = 1000 GeV). Two identical linear 10 (20) km
long accelerators, bringing beams to head-on collision in 6 nm
high spot.
Fixed parton collison energy; polarized e+ and e- beams in JP=1initial state allow control of production processes.
International planning and design now underway for ILC.
pre-accelerator
few GeV
source
KeV
damping
ring
few GeV
few GeV
bunch
compressor
Layout of electron arm
250-500 GeV
main linac
extraction
& dump
final focus
IP
collimation
The physics program for the LHC and ILC:
The LHC should discover the
Higgs if it exists up to >1 TeV
(10 times higher than SM
e+ g,Z
Z
indicated value).
e-
interaction rate
Curves denote different Higgs
boson spins; ILC data cleanly
discriminate.
collision energy
significance
1. Find the agent for Electroweak symmetry breaking – in
the SM, the Higgs boson.
H
Higgs mass →
The ILC will tell us that if what LHC sees
is the SM Higgs or some other thing. It
can detect the Higgs even if it decays
into invisible particles. It can tell us the
Higgs quantum numbers, and its
couplings to different particles.
Yukawa coupling
1. Mapping the Higgs boson
In the SM, Higgs couplings are
directly proportional to mass.
Measuring these couplings to few
% level at ILC is a sensitive test of
whether we have the SM or some
new physics.
Particle mass →
Higgs
Z
W
top
charm
tau
bottom
glu on
The Higgs couplings to other particles is crucial for learning what
new physics is operating.
New symmetries
Extra dimensions
SM
value
2. Delineate the new physics:
New symmetries
Supersymmetry (SUSY) introduces new fermionic space-time
coordinates, resulting in a new boson for every existing SM
fermion and vice versa. (Partner of the spin ½ electron is a
spin 0 selectron). In exact SUSY, selectron mass = electron mass
etc. We know this is not true, so SUSY is a broken symmetry.
All the other properties of the selectron are like the electron
(charge, couplings). There are many model variants.
 SUSY boson and fermion higher order
contributions to Higgs mass cancel the SM pieces,
so the hierarchy problem is solved.
 SUSY has a natural DM candidate.
 SUSY could provide the CP violation needed.
 SUSY modifications to SM predictions are
small, so not in conflict with data.
2. Learning about Supersymmetry
The LHC and ILC have complementary strengths in mapping the
SUSY spectrum – LHC sees quark and gluon partners; ILC sees
lepton and W/Z/Higgs partners. Together they can extrapolate
to the scale where SUSY is broken and tell us how this works.
Mass unification pattern from
ILC & LHC in 2 different models
energy →
SUSY provides a good candidate for
DM (lightest SUSY particle). LHC
and particularly ILC can determine
its mass. Compare with CMB,
underground DM experiments to
see if the picture is consistent.
3. Delineate the new physics:
New forces
New forces and the particles they introduce provide a new
energy scale. This stabilizes the hierarchy problem of the SM.
The prototype candidate was a new interaction similar to QCD
(‘Technicolor’) with new particles at O(10 TeV). The simplest
of these models would produce deviations from the SM that
are not seen, but many more complex variants exist.
An example: a new higher
mass Z boson seen at LHC
production rate
All of these give new quarks and bosons that would be seen at
LHC and ILC.
dimuon mass
4. Delineate the new physics:
New dimensions
String theory requires at least 6 extra spatial
dimensions (beyond the 3 we already know).
The extra dimensions are curled up like spirals
on a mailing tube. If their radius is ‘large’ (~1
attometer = billionth of an atomic diameter)
or larger, they could lower the effective Planck
mass, eliminate the hierarchy problem and
unify all forces (including gravity?) at the new
Planck scale.
If a particle created in an energetic
collision goes off into the extra
dimensions, it becomes invisible in
our world and the event shows
missing energy and total momentum
imbalance.
production rate
4. Untangling New Dimensions
Combination of data from LHC and ILC allow the
determination of the reduced Planck scale and the number of
extra dimensions.
Wavefunctions trapped inside a ‘box’ of
dimuon mass
extra dimensions yields a series of
resonance states (like new heavy Z
bosons) – indistinguishable at LHC from
other sources of such states.
ILC measurements of the couplings (vector
and axial vector) allow us to distinguish what
new physics is operating.
Example of ILC and LHC complementarity
Observed final particles
4 ways to produce a ‘signal’ in jet ,
dilepton and missing energy at LHC
a) & b) SUSY with different choices
of dark matter particle (lightest
SUSY particle) = spin ½ partner
of photon partner or neutrino.
c) & d) Extra Dimensions models
with different character of
excited Z.
LHC can’t distinguish these interpretations. At ILC, the crosssections and angular distributions for different initial state
polarizations tell us which is happening.
This information can in turn be used by LHC to deduce the
heavy particle masses.
The important things to note about all the postulated models of
new physics:
 All known models have observable phenomena within reach
at the LHC and ILC.
 Each model class has many variants, each with a large degree
of freedom of parameters. The LHC and ILC are needed to give
complementary, binocular views of new phenomena. Together,
they will tell us much more than either alone.
“Pardon me, I thought you
were much farther away”
The outlook
The Standard Model and measurements in hand provide a vista
of new unity and interconnectedness of the microscopic world.
go here
sense whats happening here
The experimental tools to take us there are in hand. LHC will
start next year. The ILC prospects have improved steadily but
the project has yet to be approved by world governments.
The structure of the universe
The Particle Mandala
A gateway to
understanding
The eightfold way
to unification
The connectedness of things
Summary
 Over the course of 40 years, our
understanding of the fundamental
forces and constituents of matter has
been revolutionized.
 The SM paradigm is about to be
broken in ways that we cannot
predict. The next generation of
experiments will tell us a fascinating
new story.
 A truly exciting time for particle
physics !