Quark Soup

Elementary Particles?? (circa 1960)(pions),K, , etc

proton neutron c,b,Etc

www-pnp.physics.ox.ac.uk/~huffman/

Long before the discovery of quantum

m

echanics, the Periodic table of the E

lements

gave chemists a testable m

odel with enough

predictive power to search for the m

issing ones.

Re su

l t:D

is c ov e r y of Ge a n

d G

a(am

ong o th

e r s)

Examples of Similarities among ‘elementary’ particles

Total Spin 1/2: p+ n 938, 939 (all masses in MeV)0 1116

+ 0 - 1189,1192, 1197 0 - 1315, 1321

++, +, 0, - 1231, 1235, 1234, 1235(?)

Total Spin 0: 0 139, 134 (all masses in MeV) 0 547

K K0L

K0S

494, 497 ’ 0 958 D D0 1869, 1864 c

0 2980

These similarities are what has led to the quark model of particle bound states.

Quark Model Botany lessons:

Quarks: up charm top down strange bottom

Hadrons: Everything that is a bound state of the quarks which are

spin 1/2 (Fermions). Held together by the strong nuclear force.

Hadrons split into two sub-classes:Mesons: bound quark- antiquark pairs.

Bosons; none are stable; copiously produced in interactions involving nuclear particles.

Baryons: bound groups of 3 quarks or 3 antiquarks. Fermions; proton is stable; neutron is almost stable;

copiously produced in interactions involving nuclear particles.

Conservation of Baryon number conservation of quark number

Meson

Baryon

More Botany lessons:

Leptons: electron muon tau e neutrinos

Each individual Lepton number is conserved exactly in all interactionselectron number, muon number, and tau number are all conserved. (But New Discovery of Neutrino oscillations at SNO!)

You will learn about this later in the course.Leptons do not form any stable bound states with themselves, only with hadrons (in atoms).

Since Leptons also do not interact with the strong nuclear force,we will not discuss them much further in this part of the course.

The Fermions of the Standard Model• The Hadrons -

composite structures• The Leptons -

‘elementary’• What does ‘elementary’

mean?• ANS: an exact

geometric point in space.

• Are the quarks and leptons black holes?

• ANS: Beats me!

What Makes a Theory “Good”?

Any theory … not just a theory of matter and Energy.

Falsifiable!

Baryon Octet:

I3

JP = 1/2+The only Example There is also a complete octet where L = 1 but you will never see it.

pn

0

0 1190

13200

0

S

0 1/2-1/2-1 1

-2

-1

udd uud

udsdds uus

dss uss

Notes:U+D-S = 3for all Baryon states.

Quark compositions are NOTthe same as quark wave functions

Baryon Decuplet:

I3

JP = 3/2+The only Example

0

15300

S

0

0 1/2-1/2 1

-1

udd

-2

-1

-3

-3/2 3/2

ddd uud uuu

dds uds uus

dss uss

sss

13850

1673

Meson Nonets:

I3

1

S

0 1/2-1/2-1 1

-1

0

Pseudoscalars JP = 0-

Vector Mesons JP = 1-

Q = 0

Q = 1

Q = -1

Examples

ssdduu ,,

sd su

us ds

ud du

KK 0

0

0KK

*0* KK

**0 KK

0

0

Much Ado about Isospin(apologies for revealing my bias)

Before we get much deeper into Isospin though, it would be a good idea to divert somewhat and revision on spin 1/2 particles and introduce the Special Unitary group in Two dimensions (the infamous SU(2)).

Talk about ad hoc! First we make ‘upness’ and ‘downness’ and then proceed to make this Isospin quantum number, the ‘z’ component of which is really just 1/2 times up-ness or down-ness.

Legitimate question:Is this useful at all?

Why is there no uuu or ddd state in the spin 1/2 Baryon chart?

1/2 x 1/2

1 x 1/2

1 +1 1 0+1/2 +1/2 1 0 0 +1/2 -1/2 1/2 1/2 1 -1/2 +1/2 1/2 - 1/2 - 1 -1/2 -1/2 1 3/2

+3/2 3/2 1/2+1 +1/2 1 +1/2 + 1/2 +1 -1/2 1/3 2/3 3/2 1/2 0 +1/2 2/3 -1/3 -1/2 -1/2 0 -1/2 2/3 1/3 3/2 -1 +1/2 1/3 -2/3 -3/2 -1 -1/2 1

Note: A square-root sign is to be understood over every coefficient, e.g., for -8/15, read -(8/15).

Notation: J J M Mm1 m2

m1 m2

. . . .

coefficient

3/2 x 1

5/2 +5/2 5/2 3/2+3/2 +1 1 +3/2 +3/2 +3/2 0 2/5 3/5 5/2 3/2 1/2 +1/2 +1 3/5 -2/5 +1/2 +1/2 +1/2 +3/2 -1 1/10 2/5 1/2 +1/2 0 3/5 1/15 -1/3 5/2 3/2 1/2 -1/2 +1 3/10 -8/15 1/6 -1/2 -1/2 -1/2 +1/2 -1 3/10 8/15 1/6 -1/2 0 3/5 -1/15 -1/3 5/2 3/2 -3/2 +1 1/10 -2/5 1/2 -3/2 -3/2 -1/2 -1 3/5 2/5 5/2 -3/2 0 2/5 -3/5 -5/2 -3/2 -1 1

J J M Mm1 m2

m1 m2

. . . .

Notation:

coefficient

Note: A square-root sign is to be understood over every coefficient, e.g., for -8/15, read -(8/15).