1. Adnan Bashir, UMSNH, Mexico
QCD: A BRIDGE BETWEEN
PARTONS & HADRONS
Adnan Bashir, UMSNH, Mexico
November 2017
CINVESTAV

2. Hadron Physics & QCD Part 1: From Hadrons to Quarks:
Mesons & Baryons - A historical preview
Particles and quantum numbers
Symmetries and cross-sections
The Quark Model – The eightfold way
SU(3) and hadrons, SU(4), SU(5)
Chiral symmetry and its breaking
Pions as Goldstone bosons
Linear sigma model
Explicit symmetry breaking
Non-linear sigma model

3. Hadron Physics & QCD Part 2: From Quarks to QCD: QCD as a gauge theory
Feynman rules
Higher orders and infinities
Regularization
Renormalization schemes
One loop renormalization
Anomalous dimensions
Running coupling
Beta function
Asymptotic freedom

4. Hadron Physics & QCD Part 3: From QCD back to Hadrons:
Deep inelastic scattering
Structure functions
Bjorken scaling
Callan-Gross relation
Parton model
Feynman’s partons versus Gell-Mann’s quarks
Parton distribution functions
Generalized parton distribution functions
Modern picture of proton’s internal structure

5. Hadron Physics & QCD
1: “Introduction to Elementary Particles”, D. Griffiths
“Quarks and Leptons”, F. Halzen & A. Martin
“Gauge Theory of Elementary Particles”, T. Cheng & L. Li
2: “Lecture Notes in Physics”, P. Pascual & R. Tarrach,
“Foundations of Quantum Chromodynamics”, T. Muta,
“An Introduction to Quantum Field Theory”, M. Peskin
& D. Schroeder.
3: “Gauge Theory of Elementary Particles”, T. Cheng & L. Li
“An Introduction to Quantum Field Theory”, M. Peskin
& D. Schroeder.
4: Theses, Reviews, Notes, Seminars

6. Adnan Bashir, IFM, UMSNH, Mexico
From Hadrons to Quarks
Adnan Bashir, IFM, UMSNH, Mexico
November 2017

7. Contents Probing the Structure Protons and Neutrons - Isospin Mesons
More Mesons
Particles and Quantum Numbers
Strangeness
Resonances
Isospin Revisited
What Next?

8. Probing the Structure
Scattering, Spectroscopy, Splitting-up experiments
Scattering: Compton scattering, Rutherford experiment,
cross-sections and interaction potentials.
Spectroscopy: Atomic spectroscopy: Lyman, Balmer and
Paschen series. Bohr model. Fine structure (spin-orbit
interaction). Hyperfine structure (electron spin – nuclear
spin interaction, Lamb shift)
Splitting up Experiments: Bombarding Beryllium with
alpha particles: discovery of neutrons. Modern
accelerators involving hadrons.

9. Probing the Structure
Nuclear degrees of freedom are frozen in atomic physics.
(Atomic excitations: ~eV, Nuclear excitations: ~MeV)

10. Probing the Structure
From Atom to Nucleus:

11. Probing the Structure
From Atom to Nucleus:

12. Protons and Neutrons
Until about 1930, atom was merely electrons and protons.
He is 4 times as heavy as H with only 2 electrons. Li has
3 electrons but 7 times as heavy as H. Why so heavy?
There could not be all protons in the nucleus with some
electrons necessary to cancel the additional charge.
Confining electrons in a nucleus of 5 Fermi requires
~ 250 MeV. Electromagnetic interaction of electrons with
nucleus provides much less energy.
Bothe & Becker bombarded beryllium with energetic alpha
particles in It produced neutral radiation which was
penetrating but non-ionizing. Led to discovery of neutrons.

13. Protons and Neutrons
Protons and neutrons are bound inside a nucleon through
strong interactions and have almost identical mass.
Strong interactions appeared independent of the electric
charge of p and n. Heisenberg proposed in 1932 that both
p and n are manifestations of the same state: Nucleon.
The symmetry relating them is called isospin, like spin.
Strong interactions are invariant under a transformation
which interchanges a proton and a neutron.
Heisenberg’s proposal is to identify:
and call this isospin. Spin can also be 1 etc. What about
isospin? We shall come to it later.

14. Protons and Neutrons
The group structure of the isospin generators Ti satisfies
the SU(2) Lie algebra.
The p and n form a doublet:
As isospin is a symmetry of the strong interaction with
Hamiltonian Hs:

15. Protons and Neutrons
Since the members of the isospin doublet have different
electric charge, it is not a symmetry of electromagnetic
interactions. Thus it is not an exact symmetry.
How good is it a symmetry of the total Hamiltonian H? If
it were exact, the members will be mass degenerate. Thus
difference in mass can provide an estimate:
Thus it is a fairly good symmetry and we can write:
Electromagnetic interactions belong to H1.

16. Mesons What holds the positively charged protons inside an atom
together in a close proximity within a nucleus?
There must be a force stronger than the electromagnetic
repulsion between protons and a short range one.
In SU(2) of spin, it is the photon which flips the up and
down electron spins. What happens in SU(2) of isospin?
Yukawa in 1934 proposed a massive boson being exchanged
between nucleons, explaining the short range of strong
forces. Yukawa estimated its mass: me.
It was called a meson, “the middle weight”. Baryons (e.g.,
protons and neutrons) are “the heavy weights” and
leptons (e.g., electrons) are the “light weights”.

17. Mesons Powell used photographic emulsions on mountain tops to
observe pions decaying into muons observed at sea level.
Pion was later found to come in three
versions: π+, π-, π0
The pions came out to have isospin 1:

18. Mesons Similarly, the compound states of n and p can in principle
be iso-triplet and iso-singlet. But no nn or pp states are
found in nature. Just an iso-singlet deuteron is found.
The quantum number of isospin is found to be conserved
in strong interactions.

19. More Mesons In 1947, Rochester and Butler observed the existence
of a new K0 particle decaying into a π+ and a π- in an
upside down V-pattern.
The mass of the K0 had to be at
least double that of pions.
They were like heavy pions but
lived much longer than pions.
π0 life time = sec
K0S-K0L life time=
(8.9 x – 5.12 x 10-8) s
Weak interactions?

20. More Mesons In 1949, Powel discovered charged Kaon in the decay.
It took till 1956 to figure
out K+ belonged to same
category as K0.
Its mass had to be more
than three times pion mass.
With time, more mesons
were discovered: η, φ, ω
and ρ mesons.

21. Particles & Quantum Numbers
In 1950 another strange particle was discovered in decay:
Λ was heavier than p. It was categorized as a baryon.
Other Baryons decay but
why is proton so stable?
We don’t observe:
Before lepton no. violation
was noticed, Stuckelberg
proposed Baryon quantum
number to explain this.

22. Particles and Quantum Numbers
The following assignments were made for the baryon no:
Beta-decay was allowed by baryon no. conservation:
Also the reaction which led to the discovery of anti-
proton was allowed:
Proton being the lightest baryon could not decay into
anything lighter.
No conserved number exists for mesons:

23. Strangeness It soon became clear that strange particles (kaons and
Lambdas) are produced copiously (time scale of sec)
but decay slowly (time scale of sec).
For strong interactions:
Electromagnetic decays
no more than around
10-16 sec:
It was observed:
Decay times of sec correspond to weak force:
It was obvious that strange particles were produced in
strong interactions and decayed through weak interactions.

24. Strangeness Strange particles were produced in pairs.
In 1953 Gell-Mann and Nishijima
coined another quantum number
strangeness and assigned:
Strangeness was seen to conserve in strong interactions
and hence strangers were never produced in ones:
Strange particles decay through weak
interactions and do not conserve
strangeness.

25. Strangeness Gell-Mann and Nishijima observed a
relation between quantum numbers:
For Baryons of B=1, it was seen:

26. Strangeness

27. Strangeness

28. Resonances Many particles have long life times to be observed directly
in the bubble chambers. (τ > sec).
Many other particles have much shorter lifetimes. Their
direct detection is impossible. Their existence must be
inferred indirectly.
These transient particles appear as intermediates states.
They are typically formed when colliding two particles and
decay very quickly.
They respect conservation laws. If, e.g., the isospin of
colliding particles is 3/2, the resonance must have isospin
3/2 ( Δ resonance).

29. Resonances Indication of their emergence is the strongly peaking cross
section (probability of the process a b -> c d to happen)
when plotting σ vs the centre of mass collision energy.
Cross-sections for the resonances are of the type:
where is the centre of mass energy squared of
incoming particles a & b. M is the mass of the resonance.
The width of the weak is given by ᴦ=1/τ, where τ is the
life time of the resonance.
A particle with super short lifetime has a huge width
meaning that it disappears. A particle with a very long time
has a small width (very sharp peak).

30. Resonances

31. Isospin Revisited
As the strong interaction is invariant in the isospin space,
the Hamiltonian commutes with all components of isospin.
This symmetry allows us to find ratios among scatterings:
Using Clebsch-Gordon coefficients, we find:

32. Isospin Revisited
If at a certain energy the scattering particles form a
bound state with I = 3/2.

33. Isospin Revisited
The cross-section is proportional to amplitude squared
H cannot connect states of different I & I3. Any member
of a given multiplet I has the same matrix element:
All this is satisfied near the I=3/2 resonance threshold,
i.e., M=1232 MeV.

34. Isospin Revisited

35. What next? In 1960s it was clear that hundreds of elementary
resonances existed. They all had definite quantum numbers
such as spin, isospin, strangeness, baryon number, etc.
There was a dire need for the classification of new
particles and resonances.
Were all these particles and resonances elementary or
they were composed of another layer of elementary
particles?

36. Comment Willis Lamb on receiving is Nobel prize:
When the Nobel prizes were first awarded in 1901, physicist knew something of just two objects which are now called “elementary particles”, the electron and the proton. A deluge of other “elementary” particles appeared after 1930; neutron, neutrino, μ meson, π meson, heavier mesons and various hyperons. I have heard it said that “the finder of a new elementary particle used to be rewarded by a Nobel prize, but such a discovery now ought to be punished by a $10,000 fine”.

37. What next?

38. What next?