Four Lectures Leading to the Standard Model of Particle Physics

Four Lectures Leading to the Standard Model of Particle

Physics

• Particles, Light, and Special Relativity

• Quantum Mechanics, Atoms and Particles

• Particles, Forces, and the Electroweak Interaction

• Hadrons, Strong Force and the Standard Model Illustrate, hopefully, that Physics (Science) has as ultimate

arbitrator

NATURE ! ! ! !

Some Comments re Yesterday

• Wave functions a bit more complicated:

in general functions () are COMPLEX!

• Probabilities given by * - modifying the function e

doesn’t change prob.

• Math used in Quantum Mechanics Complex Algegra

Calculus

Matrix Algebra Group Theory

….

Intrinsic Particle Properties

• Mass

• Electric Charge, magnetic moments, +

• Angular momentum (Spin)

• Fermion or Boson

• Fundamental ( eg, electron) or composite ( eg, nuclei)

• Antiparticles

Basics of Atomic/Nuclear Physics

But Much More to Come!!

The Measurements:

Decay Rates (lifetimes) and

Cross Sections (interaction rates)

• Most familiar atoms stable

• Many atoms found that were unstable

• The instability invariably found to be in the nucleus

• Huge range of lifetimes for these nuclides

• Soon other unstable “particles”, not just nuclei hit the scene

• Some particles live long enough to make beams

The Cross Section ()- a Measure of How Often Particles Scatter (aside)

Range of some forces will be found to be

finite, so the cross section () is finite.

Rutherford saw EM

scattering (infinite

range, so infinite ).

Forces between Particles

Electromagnetic (EM) Forces

• Gravity

• Electromagnetism

Inconsequential at atomic level and smaller

Carried by real and virtual photons

EM: Virtual Photon Exchange

2 2 2

gives the approximate momentum required to keep electron bound in orbit.

No energy is required (though actual virtual photons can have either + or - energies)

so for atom case:

W

E

0

v q r

q q

v q

e e



  

 

 hen

, the photon is (Alternative statement of H. Uncert vi

ainty Pr.) rtual!

0

q 

N

Feynman Diagrams

• A bit ahead of ourselves, but …

• Powerful calculational tools for interactions between particles where the force strength is not too large

• Calculations incorporate essentials of Quantum Mechanics, E&M, and Special Relativity (called Quantum Electrodynamics or QED)

• But also a language to describe particle

interactions

Quantum Picture of Interactions

Classical picture Quantum picture

“Feynman Diagram”

Charge and Interaction Coupling

2

1

137 e

  c 



• Strength of electromagnetic interactions characterized by a dimensionless coupling constant,  :

QED brought a different way of viewing EM interactions:

• Particles interact if they have

charge, Q=  1,  2, …. (and most

elementary objects seem only

to have Q=0,  1)

Feynman Diagrams of EM Interactions

e

e

e

e









 

2

Exch. has 0

e e

e e q













2

Above diagram plus one at the left:

Exch. has 0

e e

q

e e

2



"Real" photons have q 0

But New Forces between Particles Required in the Nucleus

But the nucleus contains only positive (protons) and neutral (neutrons)

particles. A NEW FORCE need to hold it together.

Nuclear Strong or

Force





15

1/3

) mA 10 .3 ~(1 r

All below held together by EM

r ~ 10

m

Hypothesized Carrier of Strong Force - the pion (Yukawa 1935)

Range of Strong Force implies carrier ~ 200m

or 105 MeV/c

2 ~

force force

carrier range

m c r  c

N

Range of EM infinite:

implies zero mass photon





15

1/3

) mA 10 .3 ~(1 r

Return to strong force later !!!

The Pion Would Become A Unique Object

• First nonbaryonic hadron

• Weak Interaction Decays Hints from

1933

Observations of “Mesotrons”

by 1937 intermediate in Mass View 1 View 2

Curvature and range provide mass ~ 240m

N

Unfortunately, interactions were not strong!

Unlikely to be Yukawa’s “meson”! Wait - WWII!

Another Force: Radioactive Decay Needs to be Produced by some Force









   

  

232 90

's from Strong interactions (eg, Thorium )

( , ) ( 4, 2) 's from EM interactions

e's from nucleus, but How to get electrons without positrons?

Exampl

Streng e:

th weak!

A Z A Z

n p e ?

Angular

momentum and momentum missing??

32

P

Pauli Hypothesis (1930) The Neutrino

Fermi & collaborators (1934-8) Dozens of new radioactive

elements with e

in decay

New force: “weak interaction”



 ( , )  (  1, )  (  1,   1)



n A Z A Z A Z e

Always unobserved

=Rare (or weak) interactions

The Neutrino partakes of only the Weak Interaction

• Weak Interaction produces electrons and antineutrinos or positrons and neutrinos

• Names of forces reflect relative strengths:

Strong, EM, Weak, gravity. Unlike strong force, calculations possible for the weak force!

N

• Weak interaction has a finite range

… implies that this

force carrier has a

nonzero mass.

Elementary Particles Thought to Exist as of WWII

Nuclear

• protons

• neutrons

Leptons

• electrons

• neutrinos

Force fields

• photons

• pions?

• +????

Good reason to believe that every particle had an antiparticle, though only positrons had been seen.

N

• (1947) The prewar “mesotron” found to be compicated

• the expected pion (+-) of mass 140 MeV/c

decaying promptly to the muon of mass 106 MeV/c

…

• Rabi: wrt muon …”who ordered THAT?”

• (1950) Steinberger finds neutral pion (mass at 135 MeV/c

)

• (1950-65) Many “hadronic” particles!

• Some very strange!

Postwar revolution 1946 - 1970

“Chaotic” Discovery Period



   

Emulsion photos

Production and Decay of  Pions

Prolific

production when

enough energy is available:

28 ’s at left made by high energy

cosmic ray 

stop

 product of  decay has unique range

 stops and

decays to

electron

Bubble Chamber Picture of

Many e Decays

Pion mass 140 MeV

Muon mass 106 MeV

Two-body  decay

Three-body  decay

Pions made in Strong Interactions and Decay by Weak Interactions

0

( nt g I tron S by ion uct Prod

... ):

eg  

 

  p  p  p  p



8

eak by W ay Dec

Int se 10 2.6 (

c):



 











  



6

odu pr ay of Dec

ct m

uon : sec) 10 .2 (=2

e

e



 











 





Note that muons, electrons, and

neutrinos NOT made by S. I.

Why do we label the

neutrinos???

N

Distinct Neutrino Types:

Direct Evidence







Absorb all

particles except neutrinos

?

Interactions

Find ONLY and NO !!!

n e p

e



 











      

 

1964 Nobel Prize experiment:

Schwarz, Lederman, Steinberger

BNL AGS 30 GeV p

Later Version of High Energy Neutrino Detection

meters of steel



 N  

 X

FNAL p-acc

200 - 800 GeV

Leptons… by 1975, THREE families all with spin 1/2

• Lepton Family number conserved

• Note range of charged lepton masses

• Neutrino masses only known small

e e

e e





 

  

  

   

 

 

 

  

  

  

N

Leptons and The Weak Interaction

Leptons all engage in weak interactions

Charged leptons engage in EM interactions

Contrast hadrons, which engage in these but also in the Strong Interactions

Strong and EM Interactions preserve important global symmetries:

• same for particle-antiparticle reversal ( C )

• same for reversal of time ( T )

• same for inversion of left and right ( P )

• QED+ Proofs that combination ( CPT ) preserved

Weak Interaction and Parity

•Until 1956, generally assumed that ALL

symmetries observed by ALL interactions

• Early 1950’s:

perplexing phenomena of “strange” particles motivated question of this assumption

1956: Lee & Yang: maximal violation of parity violation in weak interactions; discovered by

C.S.Wu and corroborated by Lederman, Garwin, ...

Maximal Parity Violation in Weak Interactions

Illustrated by spin-oriented muons from pion decay.

What should happen (for P -invariance) and what does

Real world

Reflected world:

should occur with equal frequency

Never Happens

Always

happens

For Antiparticles, Opposite Occurs





  



Never Happens Always

happens

In Pion Decays:

•Parity Always Violated

• Particle-antiparticle symmetry Always Violated

• Product ( CP ) appears valid!

Implications of Parity Violation

• Not just violated, but couldn’t be more violated (maximal)

• Many similarities to EM, but this a major dis- similarity

• Made everyone question ALL the assumptions!

• Found that particle-antiparticle symmetry ( C ) also maximally violated, so that product CP

preserved!

• In 1964, even this found violated (Fitch,

Cronin,…) but at small level ~ 2/10

Particle Classification by Spin

Charged leptons have magnetic moments

characteristic of point-like particles, hadrons have very different magnetic moments!

max

called ( 0, 1 , 1,..) 2

( 1) and (2

"Intrinsic ang. momentum"

or SPIN

Half-integer spin particles are fermions In

1) s

teger spin particles are boson

s

s tate

z z

J m S m

s m

J s s s

   



  



 

Isospin - Important Classification Property

 

  

 

  

        

              

 1/2  

  1

/2 2

1

e

Q I

e L

• Isospin Space - Analogous to the properties of Spin

• Leptons comprise three families with individual conserved lepton family numbers: L

, L

, and L

.

• L

, L

, and L

conserved in all known processes!

• Q conserved in all known processes!

• Different family members differentiated by isospin component.

• “Weak charge” of leptons correlated with I .

N

Weak Interactions and Isospin

 

  

 

  

     

     



     e

• Interesting feature of Leptons: Spin 1/2 and Isospin ½

• Wk Int change I

• Lifetimes and cross- sections depend on G



 

   

   

 

 

   

   

2 2

2

1/

Dimensions of are 1/Energy

e F

e F

F

e G

e G mE

G

Hypothesis of Weak Boson of Finite Mass Carrying Weak Force







2

2 but unclear what these are Natural hypothesis:

but the devil in the details

F W

EM

G g

M

g

Electroweak Synthesis by Weinberg, Salaam

Specific Theory based on Electromagnetic and Weak Forces characterized in simplest case by

• massless force particles

• massless matter particles

• same couplings

Hypothesize that mass acquired through a

NEW force: “Higgs” field ---- see E. Weinberg Specific and clear predictions:

• W

bosons carry known (charged current) weak int.

• Z

boson carries new (neutral current) weak int.

Predictions of New Neutral Current Weak Interaction

First evidence (GGM,1973) for Neutral Current processes seen in CERN experiment using

neutrinos with E ~ 2 GeV - but some questions ...

Counter Expt at Fermilab

Announced Clear Observation of Neutral Currents: 1974

~ 100 GeV 

~ 100 GeV 

1 m Steel



 N  

 X

 

  N    X

~ 20%

~80%

Particle Properties Useful for Detectors:

Different Particles Interact Differently in Materials

SLD (SLAC) Detctr

Planned

LHC Detector

Known W.I. parameters permitted prediction of the masses of the

W

and Z

bosons

 

   

 

0 0

p p Z X X '

Z e e

 

   

   



 

2 2 2

Reconstruct Mass

( ) ( )

Huge excess at _Z e e

M E E p p

M M

1983: UA1 colliding beam at CERN

Present values:

M_Z=91.19 GeV M_W=80.4 GeV

N

Electroweak Unification an Essential Feature of the Standard Model

• Weak and EM Coupling Strengths

intimately connected and unify at high energies

• Q is the charge of Electromagnetism

• I

is the charge of Charged Current Weak

• Both I

and Q provide the charge for the Neutral Current Weak … in predictable way

• Masses of the Force Carriers predicted from EM and Weak Interaction constants

• These Masses verified with incredible

precision

Meanwhile, there were the hadrons (particles with S. Int.)

• More particles discovered than could be handled!

• But important differences:

• leptons were point-like

• hadrons had spatial extent





15 1/

3

) mA 10 .3 ~(1 r

Point-like

Isospin - Important Classification Property

 

  

 

  

        

              

 1/2  

  1

/2 2

1

e

Q I

e L

• Isospin Space - Analogous to the properties of Spin

• Leptons comprise three families with individual conserved lepton family numbers: L

, L

, and L

.

• L

, L

, and L

conserved in all known processes!

• Q conserved in all known processes!

• So I

also conserved. Picture with different

family members differentiated by isospin property.

• “Weak charge” of leptons correlated with I .

N

Isospin and Baryon Number of Hadrons

So far, we have proton, neutron, and pions.

The proton and neutron obviously related.

    ^ _ ^ _

      

          

   

3 2

3

particle mass(MeV/c ) 938.3

1/2 1 939.6 2

1/2 Q I

I

p

n B

• The free neutron is not stable, but decays to proton (and e and ) by Weak Interaction.

• The free proton is stable!!! (>10

years)

• Baryon number is conserved!

N

Isospin in Nuclei It works!

    



    

3

3

1 1

( ) ( )( )

2 2

1 1

2 2

( ) QED

I Z A Z

Q Z

Q I Z Z A A

A nucleus consists of Z protons, each with I

=+1/2, and (A-Z) neutrons, each with I

=-1/2.

Does this relation work? 

 1

Q I 2 B

Collision of 300 GeV proton with stationary

nucleon





    28  ?

p p p p

New kinds of particles made out of kinetic energy: mesons (pions) with mass of 140 MeV each.

These particles made prolifically, by the Strong Interactions.

Clearly they are not nucleons.

But they are hadrons!



   

And then the

with lifetime of ~10 sec

It works!!!

Isospin for Pions…Works?

+ 0 -

3

Three states:

3 states, so 1 (2 1) 3

Since 0 for pions, then we should have

I I

B

Q I







 

     

 

 







Lifetimes Important

Particles decay when they can !

(That is, the decay is not forbidden!) The lifetime gets shorter (or decay rate gets larger) with increase of either

• energy release

• strength of the responsible force

2 /

mc 

  

The uncertainty principle requires that

the mass of the particle be uncertain by

How Uncertain are particle masses?

2

c 2 10 Mev-cm

mc  c  c 



     

proton neutron





???????

Mass (MeV)

Decay Force

Lifetm

 (sec)

c

(cm)

Mass Uncert.

p 938 None   0 MeV

n 940 Weak 890 2.6 10¹³ 7.7 10^-25

^ ₁₄₀ Weak 2.6 10^-8 780 2.6 10^-14

⁰ 135 EM 8.4 10^-17 2.5 10^-6 8.0 10^-6 .33 10^-23 1.0 10^-13 200 MeV

Strong

The Pion - The First of Many New Strongly Interacting

Particles

• All “easily” produced, but decay through all three forces!

• Stay tuned tomorrow for the rest!

• And the completion of the Standard Model

with Quarks and Gluons