The Hadrons — Question 7

Question 7

Inclusive scattering infers a hadronic mass without observing every fragment

A stationary target has rest energy 1.00 GeV. A probe transfers energy nu=.500 GeV and momentum magnitude q with qc=.800 GeV. Use $W^2=(mc^2+\nu)^2-q^2c^2$.

1. Find the invariant mass energy of the produced hadronic system.

2. Can a final state with minimum total rest energy 1.20 GeV be produced? Find its available center-of-mass kinetic energy.

Question 7 - Solution

Inclusive scattering infers a hadronic mass without observing every fragment

(a) Method and calculation

$$Q^2=q^2c^2-\nu^2=.640-.250=.390\,\mathrm{GeV^2}.$$$$\boxed{W=\sqrt{m^2c^4+2mc^2\nu-Q^2}=\sqrt{1.610}=1.26886\,\mathrm{GeV}}.$$

(b) Interpretation and further calculation

$$\boxed{W>1.20\,\mathrm{GeV}\Rightarrow\text{kinematically accessible}}.$$$$\boxed{K_{\mathrm{available}}=W-1.20=.068858\,\mathrm{GeV}}.$$

Physical check

The final invariant mass is not simply target rest energy plus transferred energy; net recoil momentum must be removed.