Calculating Laboratory Energy in Neutral Pion Electroproduction

[GilboK]

I am a high school physics intern, trying to figure out how calorimeter accuracy affects the recoiled proton's mass in a collision, where an electron beam is aimed at a proton target. The electron beam emits a virtual photon and scatters off one of the virtual pions around the proton, and the pion becomes real due to the virtual photon energy and flies off to decay into two photons. The proton recoils.

I am interested in calculating the mass of the recoiled proton.

(should be the same as the initial proton, but I want it to vary based on detected quantities of the angle, momentum, energy of the pion, so I can build a Gaussian distribution of the proton' mass, affected by m,p, and angle of pion)

I know the proton momentum quantity, but am searching for a different equation for the proton energy to find recoiled proton mass through proton' mass= SQRT(Ep^2-Pp^2) because the one that I have for proton energy (laboratory):

Ep=SQRT(Pp^2+Mp)

makes it so that the proton' mass will always be 0.94 GeV because that is what I input in this equation (kind of a circular function)

I've tried Ep=(nu+Mp)-Epi, where Epi is energy of pion and nu is energy of the virtual photon..but am not sure if it is correct. Can someone suggest other ways to calculate energy of the recoiled proton?

I've also tried Ep=W-Epi...but I need Ep in laboratory frame and W, center of mass energy, is in center of mass frame...so it doesn't really work.

Thank you so much!

 

[AndyW]

Dear high school physics intern,

I am a fellow scientist with a background in particle physics and I would be happy to help you with your question. Calculating the mass of a recoiled proton in a collision can be a challenging task, but with the right equations and understanding of the physics involved, it is certainly possible.

First, let's review the basics of the collision you described. In this scenario, we have an electron beam colliding with a proton target. As a result of the collision, a virtual photon is emitted, which then scatters off a virtual pion around the proton. The energy of the virtual photon is transferred to the pion, making it real and causing it to fly off and eventually decay into two photons. This transfer of energy also causes the proton to recoil.

To calculate the mass of the recoiled proton, we need to use conservation of energy and momentum. This means that the total energy and momentum before the collision must be equal to the total energy and momentum after the collision.

Let's start with the total energy before the collision. We have the energy of the electron beam, which we will call Ee, and the mass of the proton, Mp. So the total energy before the collision is:

Et = Ee + Mp

After the collision, we have the energy of the recoiled proton, Ep, and the energy of the two photons produced by the decay of the pion, Eγ1 and Eγ2. So the total energy after the collision is:

Et = Ep + Eγ1 + Eγ2

Now, let's look at the total momentum before the collision. We have the momentum of the electron beam, Pe, and the momentum of the proton, Pp. So the total momentum before the collision is:

Pt = Pe + Pp

After the collision, we have the momentum of the recoiled proton, Pp, and the momentum of the two photons produced by the decay of the pion, Pγ1 and Pγ2. So the total momentum after the collision is:

Pt = Pp + Pγ1 + Pγ2

Now, we can use these equations to solve for the energy of the recoiled proton, Ep, in terms of the other variables. Rearranging the equation for total energy before the collision, we get:

Ee = Et - Mp

And rearranging the equation for total energy after the collision, we get:

Ep = Et - Eγ