PX156 - H2 - the strong force

• boson: gluons ($g$)

  • rest mass: $0$
  • technically infinite range
  • but carry colour charge themselves

• conserves all quantum numbers

• a gluon carries a colour, and an anti-colour

  • eg: $g:r\overline{b}$

• needed to conserve colour at vertices

  • eg: $q_r\to q_b+g_{r\overline{b}}$

• there are 8 gluons in the strong force

• there is one gluon that cannot be seen: a colourless gluon

  • eg: $g\sim r\overline{r}$ cannot exist

• so, some decays cannot happen

  • eg: ${\pi }^0(u\overline{u})\to g?:$ no! as ${\pi }^0$ is colourless

• gluons can interact with other gluons

• this is the defining difference with the EM interaction
  

• large distances: constant, very strong, restoring force with the form:

• at a small distance, $k\approx 1GeV/fm$

• ${\alpha }_S\approx 140\times {\alpha }_{EM}$

• as $r\to \mathrm{\infty }:F_{strong}\sim -k$

• small distances (within nucleons): acts like the EM force, but is very weak

• small distances between quarks: coulomb force dominates

• eg:

  • within a nucleus, $\frac{1}{r^2}$ force
  • long distances: $F\sim -k⟹$ constant attractive force

• this drives the behaviour of the strong force at large distances

• acts like a rubber band

• two distinct types of behaviours at different distance scales

• small distances: ends can move independently and freely

• large distances: energy stored as it 'stretches'

• eventually energy stored is enough to break the bond and the band snaps

hadronization & the principle of confinement

• quarks can never be separated from nuclei to get a lone quark

• as quarks separate, more energy needs to be donated and this energy is stored in the colour field between the quarks

• at some point, the energy density in the field is greater than the mass of two quarks

• at this point, the colour tube snaps and creates two new quarks

• this process is called hadronization

• the fact that quarks are locked in hadrons is called the 'principle of confinement'
  

• in experiments, this gives rise to jets of hadrons that are clustered around the direction of one of the initial quarks