# Invariance Principles and Conservation Laws

### Recall from last lecture:

• The proton is I=1/2, I3=1/2
• The neutron is I=1/2, I3=-1/2
• The deuteron is an isosinglet, I=0
• The pions form an isotriplet, I=1, I3=pion charge.
• Application of isospin symmetry to strong interactions.

## Isospin Symmetry

#### Example: 3H and 3He

At a given CM energy, what is the ratio of cross-sections for the reactions

(a) p d --> 3He π0 (b) p d --> 3H π+

3H and 3He are an isodoublet, I=1/2, I3=+1/2 (-1/2) for 3He (3H). The initial state has |I=1/2, I3=1/2>. The final states are sqrt{2/3}|3/2,1/2> - sqrt{1/3}|1/2,1/2> for (a) and sqrt{1/3}|3/2,1/2> + sqrt{2/3}|1/2,1/2> for (b). Since the reaction can proceed through the I=1/2 channel only, the ratio of cross sections is σ(pd --> 3Heπ0)/σ(pd --> 3+) = 1/2.

# Chapter 4: Quarks in Hadrons

## The Discovery of the J/ψ and υ

### J/ψ

[slide of "1974 Standard Model"] The Standard Model is our picture of particle physics now, but in 1974, things looked quite different. I hope you will allow me a little leeway on the historical facts in the interest of time and simplicity.

In early 1974, we knew of the three light quarks, up, down, and strange. We knew of the electron, muon, and their corresponding neutrinos. We knew of the photon, graviton, gluon, and W's (at least their low energy effects). The Z0 and Higgs were proposed in the theory of Weinberg and Salam, but still far from general acceptance. Despite the way this slide looks, the full organization of quarks and leptons was not yet apparent.

[slide of the J/psi signals of the two experiments] In October 1974, two experiments observed the J/ψ particle, an e+e- experiment at SLAC called MarkI, and a proton-nucleus experiment at Brookhaven.

It took a little time to sort out exactly what this new particle was, but it soon became clear that this particle was the bound state of a new quark called charm, and it's anti-particle.

### υ

In 1977 another resonance was observed with characteristics similar to the J/ψ but heavier. This new resonance was dubbed the Upsilon (υ) and is now understood as the bound state of bottom and anti-bottom.

### Energy levels in bound particle-anti-particle systems

[Refer to Figure 4.8 of Perkins] An important factor in the charm quark conclusion is the set of related states. The bound state of a charm quark and its antiparticle has a set of energy levels each characterized by a set of quantum numbers, similar to the hydrogen atom, or, maybe more accurately, positronium. The J/ψ particle is the n=1 state with J=1, L=0, ml = 0; it is an S-wave state with the quark spins in an antisymmetric state, a triplet S-state, 3S. States of higher radial excitation are called ψ' (2S), ψ'' (3S), and so on.

The S-wave states with the quark spins anti-aligned (in a symmetric state) are called ηc (1S), ηc' (2S), and so on. These states are harder to find because

• they are not readily produced in e+e- annihilation, and
• they decay most readily to complex multi-hadron states that are difficult to discern from background interactions.

Another set of important states are the p-wave states with anti-aligned quark spins, the χc's. The lowest mass chic states form a triplet known as χc0, χc1, and χc2. The last two of these decay readily to a J/ψ plus a photon.

The process of identifying the states of this system goes on to this day, and the study of these states is used to probe low energy QCD. However, most of the work involving ccbar states, the J/ψ in particular, has turned to using them to get access to other physics.