The Hadrons — Question 9

Question 9

A hypothetical proton-decay channel tests more than electric charge

Examine $p\to e^++\pi^0$. Assign B=1, L=0 to the proton; B=0, L=-1 to the positron; and B=L=0 to the pion. Charges are +e, +e and 0 respectively.

1. Calculate changes in B, L and B-L.

2. With supplied rest energies 938, .511 and 135 MeV, find the released rest energy and explain why energetic allowance does not establish ordinary proton decay.

Question 9 - Solution

A hypothetical proton-decay channel tests more than electric charge

(a) Method and calculation

$$\boxed{\Delta B=0-1=-1,\quad\Delta L=-1-0=-1}.$$$$\boxed{\Delta(B-L)=0,\quad Q_{\mathrm{charge}}:\ +e=+e+0}.$$

(b) Interpretation and further calculation

$$\boxed{Q_{\mathrm{energy}}=938-.511-135=802.489\,\mathrm{MeV}>0}.$$$$\boxed{\Delta B\ne0}\quad\text{violates baryon-number conservation in ordinary hadronic reactions}.$$

Physical check

This is a proposed beyond-standard-process channel, not an observed decay asserted here. Passing energy and charge tests is necessary but not sufficient.