Hadron Physics & Quantum Chromodynamics Adnan Bashir, IFM, UMSNH, Mexico August 2013 Hermosillo Sonora

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2 Hadron Physics & Quantum Chromodynamics Adnan Bashir, IFM, UMSNH, Mexico August 2013 Hermosillo Sonora

3 Hadron Physics & QCD Part 1: First Encounter With Hadrons: Introduction to Mesons & Baryons, The Quark Model, Goldstone Theorem & Goldstone Bosons, Sigma Model, Part 2: From Hadrons to QCD: QCD Lagrangian and its Symmetries, QCD as a Gauge Theory, Feynman Rules, Asymptotic Freedom Part 3: From QCD Back to Hadrons: Symmetries, Their Breaking, Current Algebra and Low Energy Results Part 4: Modern Challenges: Transition From Low to High Energies. Lattice, Chiral Perturbation Theory, Schwinger-Dyson Equations, etc.

4 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

5 First Encounter With Hadrons Adnan Bashir, IFM, UMSNH, Mexico August 2013

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

7 Probing the Structure Scattering, Spectroscopy, Splitting-up experiments Scattering: Compton scattering, Rutherford experiment, cross-sections 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.

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

9 From Atom to Nucleus: Probing the Structure

10 From Atom to Nucleus: Probing the Structure

11 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 ionizing. Led to discovery of neutrons.

12 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.

13 Protons and Neutrons The group structure of the isospin generators T i satisfies the SU(2) Lie algebra. The p and n form a doublet: As isospin is a symmetry of the strong interaction with Hamiltonian H s :

14 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 H 1.

15 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. Yukawa in 1934 proposed a massive boson being exchanged between nucleons, explaining the short range of strong forces. Yukawa estimated its mass: m e. 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.

16 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 -, π 0 The pions came out to have isospin 1:

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

18 More Mesons In 1947, Rochester and Butler observed the existence of a new K 0 particle decaying into a π + and a π - in an upside down V-pattern pattern. The mass of the K 0 had to be at least double that of pions. They were like heavy pions but lived much longer than pions. π 0 life time = sec K 0 S-K 0 L life time= (8.9 x x 10-8 ) s Weak interactions?

19 More Mesons In 1949, Powel discovered charged Kaon in the decay. It took till 1956 to figure out K + belonged to same category as K 0. Its mass had to be more than three times pion mass. With time, more mesons were discovered: η, φ, ω and ρ mesons.

20 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.

21 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:

22 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: The electromagnetic decays are expected to be in times no more than around sec: Decay times of sec correspond to weak force: It was obvious that strange particles were produced in strong interactions and decayed through weak interactions.

23 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.

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

25 Strangeness

26 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).

27 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 energy of the collision. The mean lies at E cm (ab ab) with a width given by ΔE=1/τ /τ, where τ is the life time of the resonance. Cross-sections sections for the resonances are of the type: where is the centre of mass energy squared of the incoming particles a and b, M is the mass and Г=1/τ is the width of the resonance.

28 Resonances

29 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:

30 Isospin Revisited Let T be the operator whose matrix elements <f T i f T i> give us the scattering amplitude for i -> f. Then: T cannot connect states of different I & I 3. Any member of a given multiplet I has the same matrix element T I : Thus:

31 Isospin Revisited If T 1/2 << T 3/2,: This condition is satisfied near the I=3/2 resonance threshold, i.e., M=1232 MeV. This corresponds to the well-known Δ resonance. Experimentally, the total threshold is easier to measure:

32 Isospin Revisited Isospin invariance:

33 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. Typically, widths increased with mass or lifetimes decreased with the mass of the resonance. 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?

34 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 10, fine.

35 What next?

36 What next?