The Mysterious Standard Model of Elementary Particles

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The Mysterious Standard Model of Elementary
Particles
Paul Grannis Univ. Illinois/Chicago 3/8/00
The Standard Model of particle physics
successfully explains and predicts many observed
phenomena. But we believe it is fundamentally
flawed, and will be replaced by a more complete
theory. I review in this talk how we got the SM,
how/why we expect it to change, and the crucial
experiments of the near term future.
Based on M.K. Gaillard, P.D. Grannis, F.J.
Sciulli, Rev. Mod. Phys 71, S96 (1999) -- APS
Centenary Issue.
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Particle Physics SM in a Nutshell
At the smallest scale, all of matter is built
from quarks and leptons -- spin 1/2 fermions.
masses 5 to 174,000
MeV
ud
c s
t b
charge 2/3 e
charge -1/3 e
e ne
m nm
t nt
charge e
0.5 - 1976 MeV
neutral (nearly massless?)
6 flavors of quarks leptons in 3 doublets
(generations ) (and their antiparticles)
q,l
q,l
All fundamental forces of Nature (Strong, EM,
Weak (and Gravity) are transmitted by gauge
bosons which couple to specific properties of
matter particles.
coupling constant
boson
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3
Electromagnetic Interaction
Carried by photon (g), e.g. electron binding in
atom
g charge (q) 0 mass (m) 0
spin 1 In QED (Dyson, Feynman,
Schwinger, Tomonaga), g couples to electric
charge q just one type of electric charge.
Ze
Electromagnetism and Quantum Mechanics have gauge
symmetry -- classically, the freedom to redefine
the potentials and assign a global arbitrary
phase to potential fields. This gauge freedom
can be extended to higher symmetries (e.g.
isospin SU(2) symmetry) and the arbitrary phase
choice made locally at all space time points
(Yang, Mills), giving rise to more complex self-
couplings of massless gauge bosons. The
fundamental microscopic forces all appear to be
such local gauge theories.
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4
Strong Interaction (QCD)
Carried by gluon ( g ) spin 1 mg0 qg0
gluons have 3 types of charge -- colors
(R,Y,B) Strong Interaction coupling is to
color. quarks come in 3 colors (R,Y,B)
antiquarks ( R, Y, B ) (G,V,O) gluons
come in 8 colors (RB, RY, ...) (the SU(3)
analog of in spin SU(2) )
Leptons have no color, hence no strong
interaction. Observed hadrons have hidden
color p (uRdR) p
(uR,uY,dB) Strong interaction is local gauge
theory with structure SU(3) for 3 colors .
The resulting theory is called Quantum
Chromodynamics (QCD) .
q
q
gRB
q
q
Gluons have self coupling (to their color),
unlike photons
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5
Weak Int. -- EM/Weak Unification
Weak interaction responsible for nuclear b decay
etc. Processes like n p e n are parity
nonconserving (distinct L and R states) (Lee
Yang). Otherwise like EM interaction (spin 1
currents).
H a Jm J m (Fermi) (a
coupling) JmEM e gm e Jm Wk d gm
(1-g5) u e gm(1-g5) ne
(V-A charged currrent)
Unified EM Wk EW (Glashow, Salam, Weinberg)
has weak-isospin singlet and triplet of massless,
spin 1 gauge bosons (w , w 0, w -)
and ( b 0 ) This adds neutral currents (w 0, b0 )
leading to such reactions as n p n p,
observed in CERN and FNAL in 1973-74 But b
decay short range, requires massive
bosons. Invoke spontaneous symmetry breaking
(eigenstate rotation) by adding 2 spin 0 Higgs
boson doublets. 3 Higgs scalars absorbed as
longitudinal polarization states of massive
physical W,W-, Z0 , leaving 1 physical
(observable) Higgs.
(QW weak mixing angle)
charges of EW interaction are electric charge
(q), weak isospin (IW), and weak hypercharge
(YW). EW Intn SU(2) X U(1)
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Mass of Higgs boson is not predicted.
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A final note - quark mixing
Quarks have color, charge, IW, and YW, so feel
all the interactions. We observe that the quark
eigenstate basis is different for Strong and EW
(rotation).
This Unitary matrix (Cabibbo, Kobayashi, Maskawa)
has three real numbers and one complex phase.
Similar mixing can occur for neutrinos if
they have non zero masses.
Quark production by the strong interaction gives
the (ds ss bs) states weak decays employ the
(dew sew bew) states e.g. d u e n rate
(neutron b decay) less than m e nm ne
rate since dew(cosq ds sinq ss ) V11
cosq V12 sinq Studies such as b uen ,
c smn etc. determine Vij elements
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The Standard Model (SM) and its arbitrary
parameters
The Standard Model is the pasting together of the
SU(3) strong interaction with the SU(2) x U(1)
electroweak interaction, with all the associated
assignments of couplings, charges and mixings.
SM SU(3) x SU(2) x U(1)
The arbitrary parameters

• 6 quark masses
• 6 lepton masses
• 4 quark mixing matrix parameters
• 4 lepton mixing matrix parameters
• 3 force coupling constants
• (Coupling constant varies with momentum
  transfer (q 2 ) due to virtual structure.)
• 2 Higgs parameters (mH , sin2qW ),
• 1 phase for strong interaction CP violation

26 arbitrary parameters that can only be
determined from experiment !
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How do we know all this ?? A sampling of results
Leptons observed -- electron (Thomson/1898) muon
Anderson Neddermeyer/1936) tau (Perl et
al./1976) Quarks not seen in nature, but seem to
exist inside hadrons. Particle patterns are
suggestive (Gell-Mann/Zweig) e.g. the JP 3/2
baryon decuplet
ddd udd uud uuu dds dus uus
dss uss sss
D-,0,, Y-,0, X -,0 W -
m 1232 1385 1530 1672 (GeV)
Baryon decuplet
sss
predicted
Regularity of the mass and quantum number
pattern, observation of the predicted W - ,
suggested the existence of the light u,d,s quarks.
A similar story for mesons for example, s-wave,
spin-singlet combinations of (qq ) states of
(u,d,s) quarks exactly reproduce the octet of
observed mesons (p , p0, p- ) ,h0, ( K, K0 ),
( K-, K0 ). We need the (u,d,s)
quarks! (masses 5, 10, 150 MeV)
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Dynamical evidence for quarks in hadrons
Scattering processes involving the proton reveal
pointlike particles with quark properties (spin
1/2 charges 2/3 or -1/3) (Friedman, Kendall,
Taylor et al.)
q q q
e
e
p
g
g
e-p scattering
or
pp scattering
q q q
q q q
p
p
Experiments similar to Rutherford scattering
showing pointlike nucleus! See pointlike
constituents with essentially 1/sin4( q / 2)
behavior (with spectator quarks not
participating)
Color charge exists
The W - particle noted above is an S-wave bound
state of three identical s-quarks (fermions).
This would violate the Pauli principle (overall
antisymmetric wavefunction for fermions) unless
there is an additional quantum number. Color
provides this -- the sss combination is
antisymmetric color singlet.
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10
Running of strong coupling constant
SU(3) gauge coupling constant ( aS ) varies with
q2, decreasing as q2 increases 1/aS log(q2).
This arises as a result of 3 (or more) color
charges.
(Gross, Politzer, Wilczek )
aS
Compilation of many experiments
Measurements of the strong coupling are made in
many processes at different q2, clearly
establishing the running of aS. (aEM,,
aWk also run)
q2
Asymptotic freedom (aS 0 as q2 )
Infrared slavery (aS as q2
0 )
No free quarks or gluons jets
Increase of aS as q2 0 means that color
force becomes extremely strong when a quark or
gluon tries to separate from the region of
interaction (large distance small q2 ). A
quark cannot emerge freely, but is clothed with
color-compensating quark-antiquark pairs. The
colorless states condense into a spray of roughly
collinear hadrons along the quark or gluon
direction, called a jet.
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Sighting quark and gluon jets
e e - collisions proceed through an
intermediate state of a photon (or Z) such
collisions lead to quark antiquark. Presence of
3rd jet signals gluon radiation
quark jet
e
g
(gluon jets are broader than quark jets)
gluon jet
e
quark jet
Typical ee event with 2 quarks and one gluon.
(Gluons exist and are manifested as jets). (OPAL
expt at LEP)
Quark-quark collisions produce clear jets as
well two 500 GeV ET quark jets from q q
scattering in D0. (color indicates energy
deposit)
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Establishing QCD
Scattering of electrons from quarks in protons
probes structure of proton at scale of photon q
2. At larger q 2, see more substructure and
scattering strength decreases.
e
e
g
q q q
p
e-p data from HERA/ Hamburg Germany
Causes observable departure from simple
Rutherford scattering due to aS variation,
internal structure -- tests QCD. More internal
structure as resolution improves.
Electron scattering gives quark gluon composition
of proton vs. momentum fraction carried by quarks
and gluons
q2 mom. transfer squared
(microscope resolution)
x q or g fraction of proton momentum
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13
Tests of QCD
jet
Scattering of proton antiproton at large q2
proceeds through q-q, q-g, g-g scattering. Cross
section calculated from knowledge of proton
structure and known QCD matrix elements.
p
g
p
D0 expt cross section for inclusive
production of jets
jet
QCD prediction (line) agrees excellently with
data (points) for jets out to 450 GeV (half of
beam energy), over 7 orders of magnitude !
theory
D0 experiment at Fermilab
Angular distribution of di-jets is very similar
to Rutherford scattering 1/sin4(q/2) here
mapped into flat in variable c . Small
modifications to Rutherford needed from quark
exchange in and aS variation QCD (solid line).
Dotted lines show the effect of quark
substructure (limit on size of quarks at about 1
am (10-18 m)
D0 expt
Rutherford
Many other tests of perturbative QCD -- it works!
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The heavy quarks
By 1970, three light quarks (u,d,s) were
established four leptons were known (e,ne,m ,
nm ). EW theory fails if unequal numbers of
quarks and leptons ! Suppression of decays in
which s d (flavor changing neutral current
decays) (Glashow, Iliopoulos, Maiani) also
required a new quark species. In 1974,
dramatic discovery in SLAC BNL (Richter/Ting.
et al.) of J/Y resonance in e e- -- quickly
interpreted as (c c) bound state.
s
CESR/Cornell data mU 9460 MeV
In 1976, new leptons t, nt , calling for more
quarks. In 1979, U discovered at Fermilab
(Lederman et al.) and studied at Cornell. U
composed of bb. Mass of b is 5 GeV, 1000 x
mass of u !
(radial excitations of 3S1 U state)
mee
U (U, U, U ) resonances
In 1995, CDF and D0 experiments at Fermilab
discovered the top quark with decay t W b.
The top decays before making hadrons.
The top mass is 174 GeV, 3 x 104 times the u
quark mass ( MAu ! ). Maybe it has something to
do with EW symmetry breaking that occurs at same
mass scale?
mWb
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Mtop 174 GeV
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Electroweak Interaction Verification
The EW interaction with spontaneous symmetry
breaking predicts massive Z boson that mediates a
new Neutral Current weak interaction
(e.g. nm u nm u ), differing from
previous (Fermi) Charge Current (e.g. nm u
m- d ). These Neutral Current interactions were
first seen in CERN and Fermilab in 1973 - 74,
verifying the basic tenets of the EW theory.
The cross sections indicate the value of mixing
angle, sin2qW 0.2.
A n beam enters from the left striking (the
quarks in) an iron target. Top picture shows a
Charged Current event (m track exits to right.
Bottom picture shows a Neutral Current event
with an invisible n. The recoil quark jets
leaves localized hadron activity in the detector.
The red bars indicate the energy deposition as
a function of depth.
CC event
m
n
Iron plate target/calorimeter magnetized
toroids
NC event
n
n
CCFR (Fermilab) data
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W and Z boson discovery
The W and Z bosons were discovered in 1983 at the
masses predicted by the EW model (Rubbia et al.)
in the p p collider at CERN (van der Meer), whose
energy ECM 540 GeV was sufficient to make them
directly. More recent measurements allow
precision study.
The CERN LEP collider (e e -) has beautifully
confirmed the Z boson. The Z decays into ee -,
mm-, t t-, and q q precisely studied. Mass(Z)
91,187 2 MeV ! (after calibrating earth
tidal effects and the passage of the Paris train
!)
The Fermilab collider (pp) and LEP at CERN have
made precision studies of the W boson. Its mass
is 80,394 42 MeV.
mT2 2ETe ETn (1-cosfne)
Both Z and W masses agree to great precision with
EW theory and the other precision measurments.
Transverse mass,
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Electroweak Verification
EW interaction relates Z and g , hence predicts
interference of the two. The asymmetry in ee-
mm- production is sensitive to this
interference.
Z
Higher order EW corrections are required by
the data. Self couplings of W, Z , g are as
specified by the theory.
(SU(2) x U(1) Std. Model S T 0)
The worlds data can be used to confront the
basic validity of the SU(2)xU(1) structure of the
interaction. The bands represent constraints
from various measurements. Chevron is SM theory
allowed region.
Combined data fit
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Where is the Higgs boson?
The W mass depends upon both the Higgs and top
masses due to virtual loops.
Direct mW, mt
indirect from Z studies
t
W
W W
W W
Higgs
b
mtop
Measure MW and Mtop to get indirect prediction of
Mhiggs . Result favors SM Higgs with mass below
230 GeV, within reach of experiments in
coming several years.
Direct searches for the Higgs at LEP have been
unsuccessful (Mhiggs below 105 GeV is ruled
out). The full set of precision measurements
limits the SM Mhiggs to be below 180 GeV ( at 1
s). Finding the Higgs (or ruling it out) in this
range will be a crucial step for SM verification
or evidence for new physics.
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Quark Mixing and CP Violation
K0 - K0 mixing well established requires quark
mixing. (Produce K0 at t0 observe K0 at
later time.)
s u d
Moreover, K0 and K0 show violation of CP
consistent with complex phase in the Mixing
matrix
K0
K0
W
W
d t s
Rate (K0 p p) (K0 p p)
(Fitch, Cronin 1964).
There is recent evidence for a similar
phenomenon in the B0/ B0 mesons (unequal rates
for B0/ B0 J/Y KS ).
K, B decays show that mixing matrix does have a
CP violating phase. The universe requires CP
violation to accommodate the observed matter
-antimatter asymmetry. But the observed Mixing
Matrix phase seems unable to explain the matter-
antimatter asymmetry in the universe !
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Neutrino mass and mixing
Standard solar model predicts 1.0
Experiments over 30 years have found fewer nes
from Sun than predicted by solar model nuclear
physics data.
SuperKamiokande others see 1/2 of the
ne n e p reaction rate expected.
En (MeV)
Postulate ne produced in sun oscillates to nm (or
nt ) enroute to earth (nm , nt are unobservable
since their energy is below mm , mt threshold).
Oscillation nj(t) Vij ni(0) e i
Dmij t Vij are elements of neutrino
mixing matrix . n 1,2,3 are mass
eigenstates n e,m, t
Need both mass difference between species and
neutrino eigenstate mixing for oscillations to
occur. (3 independent neutrinos
2 independent mass differences.)
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More neutrino oscillations
Atmospherically produced ns (cosmic ray
collisions in air) should give nm /ne 2. (p
m nm m e nm ne ) Observations
underground show deficit of nm with variation
with zenith angle.
Cosmic ray
n
air
SuperK detector (Japan)
n
earth
m/e (observed / expected)
SuperKamiokande data
with no oscillation
Deficit of nm variation with zenith angle
(different n flight paths) suggests nm
nt oscillation.
upgoing
downgoing
cos qzenith
World data favor nm - nt mixing with Dm2 2
x10-3 eV2 and q p / 2 nm - ne mixing
with Dm2 10-5 - 10-10 eV2 . LSND expt at
Los Alamos finds nm ne signal at Dm2 1 eV2
. If verified, and the solar and atmospheric
effects persist as n oscillation signals, we
would need more than 3 neutrino species !
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The SM works very well --So why dont we like it?
Too many arbitrary parameters with a weird
pattern (mtop / mup 3 x 104 mt / me 4 x
103 ). The quark and lepton masses mixing
parameters are unexplained. Strong and EW
interactions just pasted together (SU(3) x SU(2)
x U(1) independent couplings all vary with
energy scale, but SM does not give force
unification. The Higgs mechanism is ugly.
Inserted in ad hoc manner to reproduce the
observed massive W and Z . In EW theory there
are necessarily quantum loop corrections to the
Higgs mass that naturally drive the Higgs mass to
something like 1016 GeV/c2 ! (Quadratic
divergence in the Higgs mass unless there is a
very unnatural fine tuning of parameters)
and Why CP violation ?
Why 3 flavor generations and such different
masses ? Cosmological constant
(L 0) should be O(10100 GeV)
How to get gravity into the picture? etc.
New Physics at TeV scale needed to stabilize
Higgs
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Supersymmetry -- possible cure for some ills
Postulate a new set of particles --
Supersymmetric partners. For every fermion there
is a boson, and for each boson a fermion.
(e.g. Susy spin 0 selectron) . Susy is
extension of Poincare group to include
boson-fermion symmetry. boson-fermion
partners stabilize Higgs mass. Susy must be
broken (e.g. no selectron with mass of electron).
But, there must be Susy partners below 1000
GeV to make symmetry breaking work.
Susy provides at least 1 Higgs lt 150 GeV.
Susy could provide dark matter candidate.
Susy makes the three couplings become equal at a
common value of energy !
g3
g2
g1
With Susy
Unification of forces at energy scale 1016
GeV.
Coupling unification in Susy
No Susy
g3
g2
g1
If Susy, many new particles in 1000 GeV range
next round of experiments should find them.
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Progress in next several years?
New experiments (LEP ee- at 200 GeV -- will
conclude in 2000 ) Tevatron upgraded to 2 TeV,
x20-40 in luminosity upgraded D0 and CDF
detectors. Start in early 2001 B- factories -
high luminosity ee- at BdBd threshold (SLAC,
Japan Cornell ) and a f factory just starting
at KK threshold (Frascati) LHC at CERN -- 14 TeV
pp collisions 2006 Several new experiments
around the world studying rare K, B decays, n
oscillations.
These experiments are essentially assured of
making fundamental progress on the big questions
concerning Electroweak Sym breaking.
Beyond these, planning and discussion for future
accelerators
Linear ee- collider at TeV scale (incisive study
of Higgs and Susy) mm- colliders at multi-TeV
scale also possible muon storage ring for
intense n source Very large hadron collider (
100 TeV)
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Find the Higgs Boson
LEP should find the SM Higgs up to 105 GeV
CDF/D0 can search for SM Higgs up to 180 GeV
q
W (Z)
b
q
H
b
SM Higgs discovery reach with 5 yrs of data is
180 GeV at Tevatron includes the present
allowed SM region. Susy Higgs can be discovered
over much of allowed parameter space.
Indirect constraints on Higgs mass from precision
top quark W boson mass measurements will be
very good -- overall test of model.
Now
Run II
LHC should find any Higgs
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Supersymmetry Searches
Supersymmetry is motivated by string models, but
for present energy scales, it is a model
dependent phenomenology.
If there is no Higgs below 150 GeV, the Susy
models for EW symmetry breaking fail. This
limit is within reach of near term experiments.
The search for the partners to the ordinary
particles is more model dependent. In some
models, there are clear signatures (long-lived
heavy particles, direct photon production).
CDF D0 should be able to search in roughly half
the parameter space. Many interesting signatures
(trileptons, g missing ET, multijets missing
ET ). LHC will find Susy if it
exists !
Proposals are being developed (in US, Japan,
Germany) for new ee- colliders at the TeV scale.
Such linear colliders have the potential to
fully delineate the Susy particles and the
underlying symmetry breaking mechanism and force
unification.
Linear Colliders have great potential to
understand Susy and its origin.
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Advances in understanding flavor
The B factories and dedicated K and B decay
experiments can measure all the parameters of the
mixing matrix, thus illuminating the source of
the CP violation and quark mixing
Mixing matrix unitarity gives triangle constraints
e.g.
K p0 nn measures the height (h)
(BNL/FNAL) Bd vs. Bd Y KS asymmetry
measures b (B factories, CDF/D0) Bd
rare decays measure side opposite g (Cornell)
etc. can overconstrain
The questions of why there are three quark and
lepton generations, and the pattern of fermion
masses and couplings are further from
understanding.
Some progress may be possible through study of
Higgs boson couplings to fermions at ee- linear
colliders. Since the Higgs generates all masses,
it has some way to distinguish different fermions
!
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Neutrino Mixing and Mass

• Neutrino masses, oscillations between species
  seem established, but not the detailed pattern.
• What are the oscillating ns in solar,
  atmospheric data?
• Why the pattern of mixing?
• 3 or more n types?

Experimental situation now is confused! Too many
indications of n mixing to be accommodated with 3
generations !
K2K expt in Japan, future expts at FNAL/CERN,
and future experiments underground or at a muon
storage ring should sort out this picture. Is it
possible for muon storage ring n beams to allow
determination of CP violation for neutrinos? The
low masses of neutrinos seem to be telling us
something about very high mass scales.
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Conclusions
The Standard Model, evolved over the past 30
years, has explained and predicted a vast body of
experimental data. It must be a good
approximation to Nature.

The SM has many arbitrary features and
shortcomings we are confident that a more
general model must emerge.
Experiments and theoretical advances in the next
10 years should give dramatic insights into the
nature of the more complete model.
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Sample stuff
e
Y Y y Uu
t
W
W W
W W
b
Higgs
s u d
K0
K0
d t s
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Charged current interaction of form
L WK GF J m J m
with Jm u c t gm (1-g5 ) VCKM
d b s
Vud Vus Vub Vcd Vcs Vcb Vtd Vts Vtb
VCKM

and
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LEP measurements can be used to constrain qW
other observables, modulo Higgs and top quark
masses. Current measurements agree well with
SU(2) x U(1) EW, but not with a theory without
the EW quantum corrections.
from LEP measurements
EW model for various mHiggs , mtop
Without EW corrections
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D0 experiment at Fermilab
Rutherford scattering ds/dcosq 1/sin4(q/2)
define (1 cosq )
(1- cosq ) so that ds/dc
const. Angular distribution for scattering of
quarks in proton/antiproton collisions is nearly
Rutherford.
Rutherford
Strength of scattering gives quark charges near
constant distribution says they are pointlike
(the deviations are interesting too !)