(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For the following theory: ##\mathcal{L}=\frac{1}{2}[(\partial \phi)^2-m^2\phi^2+(\partial\Phi)^2-M^2\Phi^2]+g\phi^2 \Phi^2##

Compute s-channel amplitude for process ##\phi\phi \rightarrow \phi\phi##. Interpret result for ##M>2m##.

2. Relevant equations

Scattering amplitude: ##\mathcal{iA}=(ig)^2\frac{i}{s-M^2}##

##s=(p_1+p_2)^2##

3. The attempt at a solution

Choosing to work in center-of-mass frame: ##\vec{p_1}+\vec{p_2}=0##.

##s=(E_1+E_2)^2## in CoM.

$$E_1=E_2$$, because ##|\vec{p_1}|=|\vec{p_2}|## and masses are same.

Then ##s=4E^2##

We get in CoM:##\mathcal{A}=(ig)^2\frac{1}{4E^2-M^2}=(ig)^2\frac{1}{4(\vec{p}^2+m^2)-M^2}##

Applying ##M>2m## we get ##\mathcal{A}> (ig)^2\frac{1}{4|\vec{p}|^2}##

So far it is hard for me to interpret this result. Could anyone give me some hints how to think about this constraint?

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# Homework Help: Interpret constraints on scattering amplitude

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