1. Lecture 10: Quarks III The November Revolution Heavy Quark States
Truth R
Useful Sections in Martin & Shaw:
Sections 6.4, 7.23, 7.3,

2. 1974

3. ABBA

4. e- e+

5. The November Revolution
Come The
Revolution...
(1974)
SPEAR
(Richter et al.)

6. The Psi e+ e
 + 
 
( )

7. The J
Brookhaven
(Ting et al.)

9. J/ u c d s CC ''Charmonium" e  e  Not entirely unexpected
the J/Psi
J/
CC ''Charmonium"
Not entirely unexpected
 had been some hints of
needing another quark
(Glashow, Bjorken, ...)
(“GIM” mechanism)
nicer parallel with the
(then known) leptons:
e 
e 
u c
d s
There are different energy
states of Charmonium, in
analogy to hydrogen atom:
There are different energy states of Charmonium, in analogy to hydrogen atom:

10. Hydrogen Different mechanisms which separate energy levels:
Hydrogen Splittings
Hydrogen
Different mechanisms
which separate energy
levels:
n  basic Bohr energy level
∝ 2
''Fine Structure"  spin-orbit
coupling
∝ 
''Hyperfine Structure" 
magnetic moment coupling
(very small in hydrogen)
∝ 

11. Charmonium & Positronium
Charmonium & Positronium Energy Levels
Note in charmonium the various splittings are all of the same order
 so S ~ 1 (best fit actually gives S ≃ 0.2)

12. Effective Quark Potential
At small distances, you might guess the potential for both would look
similar since both strong & EM forces are mediated by massless bosons.
But further out, of course, this potential will go ~linearly with r
V(r) ≃ a/r + br
So try a potential of the form:
''Coulomb" term
''Flux tube" term
In EM, V(r) = e2/4r
= /r (natural units)
b is basically the
flux tube energy
so, we’d expect a ≃ s
(≃0.18 GeV2)
Plug the potential into Schrodinger Equation and try to fit energy levels
 actually works suprisingly well !!

13. Charmonium Energy Levels
Another Way to Estimate Charmonium Energy Levels: (ala Bowler)
Take the total energy of the system to be
reduced mass
 = m/2
E ≃ 2m + p2/2 + V(r)
kinetic energy
rest masses
effective potential
2r = n
 p = nℏ/r
= n/r (natural units)
≃ h/p
V(r) ≃ s/r + r
En ≃ 2m + n2/(mrn2)  s/rn + rn

14. Comparison with Experiment
En ≃ 2m + n2/(mrn2)  s/rn + rn
find the values of rn which yield the minimum energy states:
dE/dr = 2n2/(mrn3) + s/rn2 + 
solve for rn numerically
then plug in to find En
n2/(mrn2) = 1/2 (s/rn + rn)
n rn En (GeV) E (exp)
s ~ 0.5
 ≃ 0.18 GeV2
mc≃ 1.5 GeV
(0.3 fm)
(0.56 fm)
(0.77 fm)
(1.11 fm)
(1.4 fm)
Among other things this means a non-relativistic approximation is
pretty good  so charmed quarks must indeed be very massive!

15. Naked Charm
''Naked" Charm:

16. But Wait! There’s More ! Get 2 Free !!! Buy 1 Quark, Special Offer:
More Quarks
But Wait! There’s More !
Special Offer:
Buy 1 Quark,
Get 2 Free !!!

17. Bottomonium ''Bottom" quark (aka ''Beauty") Even heavier than charm !
same simple calculation
of energy levels as before
n En (GeV) E (exp)

18. Naked Bottom

19. ''Meanwhile, back at the lab, Martin was
Discovery of the Tau
''Meanwhile, back at the lab, Martin was
about to make another unexpected discovery..."
e+ e  + e +''missing energy"
lepton number violation??
e+ e  + + 
+ +  + 
e + e +  
m = 1.78 GeV !

20. However       The  is heavy enough to decay into hadrons
Tau Decay
 decays weakly and we would naively expect the lifetime
to be roughly
T ≃ (m/m)5 T
= (0.106/1.78)5 (2.2x106s)
= 1.6x1012s
However
The  is heavy enough to decay into hadrons
as well as muons and electrons
(where as muon can only decay to electrons) s u W   
“Cabibo-mixing"
(only counts as 1) d u W   

21. So there is a relative phase-space factor of roughly:
Tau Decay
So there is a relative phase-space factor of roughly:
-decay
-decay
electron
electron
muon
quarks
versus
quark colours !! 3
Experiment:
T ≃ (1.6x10-12s) (1/5)
= 3.2x1013s
3.00.1 x1013s

22. And now back to our story...
Back to Quarks
And now back to our story...

23. Physicists find ''Truth" ! (Fermilab, 1995) (aka ''Top") Truth
naked bottom -page 3
(aka ''Top")

24. Fermilab

25. D0 and CDF
CDF D0

26. Collider Detector Configuration
High Energy Particle
Detectors in a Nutshell:

27. Top Production

28. Top Event

29. Top: Detector View

30. Top: Reconstruction

31. Top: Interpretation

32. Top: Quark View

33. Quark Masses

34. Standard Cork Model

35.  Nope, looks like that’s probably it !! (more on this later)
The Generations
Hey! The symmetry
is kinda interesting...
More to come ???
 Nope, looks like that’s probably it !! (more on this later)

36. R   R But is this real ? (e+e  hadrons) (e+e  +)
Reality of Quarks: R
But is this real ?
fragmentation e e+ q
hadrons
versus
Consider: e e+  +
Cross-sections for both processes should be basically the same
except for an additional phase-space factor for the number of
different quarks and different colour states that can be produced
R 
(e+e  hadrons)
(e+e  +)
(e+e  qq )
(e+e  +) =
For the CM energies we will look at, only the 5 lightest quarks can be produced.
= NC [ (qu/e)2 + (qd/e)2 + (qs/e)2 + (qc/e)2 + (qb/e)2 ]
 R
= NC [ 4/9 + 1/9 + 1/9 + 4/9 + 1/9 ] = (11/9) NC
(in fact, higher order corrections suggest a better estimate of R ≃ (11/9) NC (1+S/) )

37. Measurement of R
 NC = 3 !!

38. ( ) 0   u  0 + u  0 + u  0 +... if there are
Pi-Zero Decay
0  
More Evidence for Colour: 0 u  0 u  + 0 u  +
In this case, the amplitudes
add coherently and calculation
yields:
(0 2) =
NC 2 2 m3
3 f2
( )
+... if there are
other colours
= 7.73 (NC/3)2
(''pion decay constant" f = 92.4 MeV from charged pion decay rate)
NC = 2.99  0.12
Experimentally   = 7.7  0.6 eV