The Mysterious Standard Model of

Elementary Particles

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.

Particle Physics SM in a Nutshell

At the smallest scale, all of matter is built from quarks and leptons -- spin 1/2 fermions.

All fundamental forces of Nature (Strong, EM, Weak (and Gravity) are transmitted by gauge bosons which couple to specific properties of matter particles.

ud

c s

t b

e

e

charge 2/3 e

charge -1/3 e

charge eneutral (nearly massless?)

6 `flavors ’ of quarks & leptons in 3 doublets (`generations ‘) (and their antiparticles)

masses 5 to 174,000 MeV

0.5 - 1976 MeV

q,ll

q,l

boson

coupling `constant’

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Electromagnetic Interaction

Carried by photon e.g. electron binding in atom:

Ze

: charge (q) = 0; mass (m) = 0; spin 1;

In QED (Dyson, Feynman, Schwinger, Tomonaga), couples to electric charge q; just one type of electric charge.

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.27

Ze

ee

Atomic binding

Strong Interaction (QCD)

Carried by gluon ( g ); spin 1; mg=0; qg=0; 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:

= (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) .

qq

q qgRB

26

Gluons have self coupling (to their color), unlike photons

Weak Int. -- EM/Weak Unification

H = JJ (Fermi) ( = coupling)

J = e e + … ; JWk = d u + e e + … (V-A charged currrent)

Weak interaction responsible for nuclear decay etc. Processes like n p e are parity nonconserving (distinct L and R states) (Lee & Yang). Otherwise like EM interaction (spin 1 currents).

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 p p, observed in CERN and FNAL in 1973-74

But 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.

25

Z = cosWsinW

sinWcosW

b0

w0(W = weak mixing angle)

`charges’ of EW interaction are electric charge (q), weak isospin (IW), and weak hypercharge (YW).

EW Int’n = SU(2) X U(1) Mass of Higgs boson is not predicted.

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).

dew sew

bew

ds ss

bs

V11 V12 V13 V21 V22 V23 V31 V32 V33

=

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 rate (neutron decay) less than e e rate since dew=(cos ds+ sin ss ) [V11 cosV12 sin

Studies such as b ue, c s etc. determine Vij elements

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The Standard Model (SM) and its 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 , sin2W ), • 1 phase for strong interaction CP violation

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.

The arbitrary parameters:

SM = SU(3) x SU(2) x U(1)

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26 arbitrary parameters that can only be determined from experiment !

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

Y-,0,+

Baryon decuplet

m= 1232

1385

1530

1672 (GeV)

ssspredicted

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: ()(K+, K0 ), ( K-, K0 ).

We need the (u,d,s) quarks! (masses 5, 10, 150 MeV)

22

Regularity of the mass and quantum number pattern, observation of the predicted ,

suggested the existence of the light u,d,s quarks.

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.)

e e

pq q q

pq q q

pq q q

g or

Experiments similar to Rutherford scattering showing pointlike nucleus! See pointlike constituents with essentially 1/sin42) behavior: (with spectator quarks not participating)

21

e-p scattering

pp scattering

Color charge exists

The 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.

`Running’ of strong coupling `constant’SU(3) gauge coupling constant ( S ) varies with q2, decreasing as q2 increases: 1/S log(q2). This arises as a result of 3 (or more) color charges.

Measurements of the strong coupling are made in many processes at different q2, clearly establishing the running of S.

(EM,, Wk also ‘run’)

Asymptotic freedom (S 0 as q2 )

Infrared slavery (S as q2 0 )

Compilation of many experiments

S

q2

20

(Gross, Politzer, Wilczek )

No free quarks or gluons : jets

Increase of S 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.

quark jet

quark jet

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

gluon jet

e

e

Quark-quark collisions produce clear jets as well: two 500 GeV ET quark jets from q q scattering in D0. (color indicates energy deposit)

Typical ee event with 2 quarks and one gluon. (Gluons exist and are manifested as jets). (OPAL expt at LEP)

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(gluon jets are broader than quark jets)

Sighting quark and gluon jets

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

pq q q

q qq q

g g

Causes observable departure from simple `Rutherford’ scattering due to S 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

x= q or g fraction of proton momentum

e-p data from HERA/ Hamburg Germany

18

q2 = mom. transfer squared(“microscope” resolution)

Tests of QCD

p

g

p

jet

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.

QCD prediction (line) agrees excellently with data (points) for jets out to 450 GeV (half of beam energy), over 7 orders of magnitude !

Angular distribution of di-jets is very similar to Rutherford scattering [1/sin4(here mapped into flat in variable ]. 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

17

D0 expt cross section for inclusive production of jets

theory

D0 experiment at Fermilab

Rutherford

Many other tests of perturbative QCD -- it works!

The heavy quarks

By 1970, three light quarks (u,d,s) were established; four leptons were known (e,e,). 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/resonance in e+ e- -- quickly interpreted as (c c) bound state.

In 1976, new leptons , calling for more quarks.

In 1979, discovered at Fermilab (Lederman et al.) and studied at Cornell. composed of bb. Mass of b is 5 GeV, 1000 x mass of u !

’’’’’’ ) resonances

CESR/Cornell data m= 9460 MeV

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?

mee

mWb 16

(radial excitations of 3S1 state)

Mtop = 174 GeV

Electroweak Interaction Verification

The EW interaction with spontaneous symmetry breaking predicts massive Z boson that mediates a new `Neutral Current’ weak interaction (e.g. u u ), differing from previous (Fermi) `Charge Current’ (e.g. u 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, sin2W ~ 0.2.

A beam enters from the left striking (the quarks in) an iron target.

Top picture shows a Charged Current event (track exits to right.

Bottom picture shows a Neutral Current event with an invisible .

The recoil quark jets leaves localized hadron activity in the detector. The red bars indicate the energy deposition as a function of depth.

CCFR (Fermilab) data

Iron plate target/calorimeter magnetized toroids

CC event

NC event

15

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 e+e -, +-, +-, 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.

Both Z and W masses agree to great precision with EW theory and the other precision measurments.

14

mT2 = 2ET

e ET (1-cose)

Transverse mass,

Electroweak Verification

EW interaction relates Z and , hence predicts interference of the two. The asymmetry in e+e- +- production is sensitive to this interference.

Z

13

The world’s 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.

(SU(2) x U(1) Std. Model S = T = 0)

Combined data fit

Higher order EW corrections are required by the data.

Self couplings of W, Z , are as specified by the theory.

Where is the Higgs boson?

The W mass depends upon both the Higgs and top masses due to virtual loops.

W WW

Higgs

t

b

W W

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 ).

Finding the Higgs (or ruling it out) in this range will be a crucial step for SM verification or evidence for new physics.

mto

p

12

Direct mW, mt

indirect from Z studies

Quark Mixing and CP Violation

K0 - K0 mixing well established; requires quark mixing. (Produce K0 at t=0 & observe K0 at later time.)

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 !

s u d

d t s

K0 K0WW

11

Moreover, K0 and K0 show violation of CP consistent with complex phase in the Mixing matrix:

Rate (K0 (K0

(Fitch, Cronin 1964).

There is recent evidence for a similar phenomenon in the B0/ B0 mesons (unequal rates for B0/ B0 J/KS ).

Neutrino mass and mixing

Experiments over 30 years have found fewer e’s from Sun than predicted by solar model & nuclear physics data.

SuperKamiokande & others see ~ 1/2 of the e n e p reaction rate expected.

Postulate e produced in sun oscillates to (or )enroute to earth ( , are unobservablesince their energy is below m , m threshold).

Oscillation: j(t)Vij i(0)e i mij t

Vij are elements of neutrino mixing

matrix . 1,2,3 are mass eigenstates

e, Need both mass difference between species and neutrino eigenstate mixing for oscillations to occur. (3 independent neutrinos 2 independent mass differences.)

10

Standard solar model predicts 1.0

E (MeV)

More neutrino oscillations

Atmospherically produced ’s (cosmic ray collisions in air) should give /e = 2.

(e e )

Observations underground show deficit of with variation with zenith angle.

earth

air

SuperK detector (Japan)

Deficit of variation with zenith angle (different flight paths) suggests oscillation.

downgoing

upgoing

with no oscillation

cos zenith

/e (observed / expected)

SuperKamiokande data

World data favor mixing with m2 2 x10-3

eV2 and e mixing with m2 10-5 - 10-10 eV2 . LSND exp’t at Los Alamos finds e

signal at m2 ~ 1 eV2 . If verified, and the solar and atmospheric effects persist as oscillation signals, we would need more than 3 neutrino species !

9

Cosmic ray

The SM works very well --So why don’t we like it?

Too many arbitrary parameters with a weird pattern (mtop / mup ~ 3 x 104 ; m/ 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 ( ~ 0) should be O(10100

GeV) How to get gravity into the picture? etc.

8

New Physics at TeV scale needed to stabilize Higgs

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 < 150 GeV. Susy could provide dark matter candidate.

With Susy

Susy makes the three couplings become equal at a common value of energy !

g1

g2

g3

No Susy

If Susy, many new particles in 1000 GeV range; next round of experiments should find them.

g1

g3

Coupling unification in Susy

g2

7

Unification of forces at energy scale ~ 1016

GeV.

Progress in next several years?

New experiments:

(LEP e+e- 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 e+e- at BdBd threshold (SLAC, Japan & Cornell ); and a 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, 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:

6

Linear e+e- collider at TeV scale (incisive study of Higgs and Susy)

colliders at multi-TeV scale; also possible muon storage ring for intense source

Very large hadron collider (~ 100 TeV)

Find the Higgs Boson

LEP should find the SM Higgs up to ~ 105 GeVCDF/D0 can search for SM Higgs up to 180 GeV; q

q HW

We

q

q

q

qH

b

b

W (Z)

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 5

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, + missing ET, multijets + missing ET … ).

LHC will find Susy if it exists !

Proposals are being developed (in US, Japan, Germany) for new e+e- 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. 4

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

K measures the height BNL/FNAL)

Bd vs. Bd KS asymmetry measures (B factories, CDF/D0)

Bd rare decays measure side opposite (Cornell)

e.g.

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.

3

Some progress may be possible through study of Higgs boson couplings to fermions at e+e- linear colliders. Since the Higgs generates all masses, it has some way to distinguish different fermions !

Mixing matrix unitarity gives triangle constraints

Neutrino Mixing and Mass

Neutrino masses, oscillations between species seem established, but not the detailed pattern.• What are the oscillating ’s in solar, atmospheric data?

• Why the pattern of mixing? • 3 or more types?

2

K2K exp’t in Japan, future exp’ts 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 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.

Experimental situation now is confused! Too many indications of mixing to be accommodated with 3 generations !

Conclusions

Experiments and theoretical advances in the next 10 years should give dramatic insights into the nature of the more complete model.

1

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.

Sample stuff

~

W Wt

b

W WW

Higgs

s u d

d t s

K0 K0

24

e

Vud Vus Vub Vcd Vcs Vcb Vtd Vts Vtb

=

Charged current interaction of form:

L WK ~ GF J J

with J ~ {u c t}(1-5 ) VCKM { }d b s

VCKMand

D0 expt

100 200pT(W) (GeV/c)

LEP measurements can be used to constrain W & 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 , mtopWithout EW

corrections

Rutherford scattering: ddcos 1/sin42) : define coscosso that ddconst.

Angular distribution for scattering of quarks in proton/antiproton collisions is nearly Rutherford.

D0 experiment at Fermilab

Rutherford

Strength of scattering gives quark charges; near constant distribution says they are pointlike (the deviations are interesting too !)