Tuesday, 17 November 2020

particle physics - Pion production in proton-proton collision



Why is π0 created in the high-energy collision p+pp+p+π0?



Answer



Just summing together all the comments and providing some more explicit calculations, we have conservation of four-momentum (which is the amalgamation of the conservation of energy and conservation of momentum), we have:


pμ1+pμ2=pμ1+pμ2+pμπ


Taking the inner product of each side with itself, we get:


pμ1|pμ1+2pμ1|pμ2+pμ2|pμ2=pμ1|pμ1+2pμ1|pμ2+2pμ1|pμπ+pμ2|pμ2+2pμ2|pμπ+pμπ|pμπ


We note that pμpμ=pμ|pμ is invaraiant in all frames of reference and that pμpμ=m2c2, we can therefore simplify:


2m2pc2+2pμ1|pμ2=4m2pc2+4mpmπc2+m2πc2


If we consider that the second proton is initially at rest we have: pμ1=(Ec,p) and therefore:


2mpE=2m2pc2+4mpmπc2+m2πc2



Rearranging we get:


E=mpc2+2mπc2+m2πc22mp


Using the constants mp=938 MeV/c2 and mπ=139.6 MeV/c2, we get:


E=1.228 GeVT=289 MeV


So if a proton with 289 MeV of kinetic energy collided with a stationary proton, there is a chance that a pion will be produced.


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