- #1
RicardoMP
- 49
- 2
- Homework Statement
- I want to show for the following process that, except for the angle [tex]\theta[/tex], all momenta and energies are fixed by energy-momentum conservation.
- Relevant Equations
- [tex]p_A=\frac{1}{2\sqrt{s}}(s+m^2_A-m^2_B\space,\space 0\space,\space 0\space,\space\sqrt{\eta_i})[/tex]
[tex]p_B=\frac{1}{2\sqrt{s}}(s-m^2_A+m^2_B\space,\space 0\space,\space 0\space,\space -\sqrt{\eta_i})[/tex]
[tex]p_C=\frac{1}{2\sqrt{s}}(s+m^2_C-m^2_D\space,\space \sqrt{n_f}sin(\theta)\space,\space 0\space,\space\sqrt{n_f}cos(\theta))[/tex]
[tex]p_D=\frac{1}{2\sqrt{s}}(s-m^2_C+m^2_D\space,\space -\sqrt{n_f}sin(\theta)\space,\space 0\space,\space-\sqrt{n_f}cos(\theta))[/tex]
, where [tex]\eta_i=4s|\vec{p_i}|^2[/tex] and [tex]\eta_f=4s|\vec{p_f}|^2[/tex].
That said, my approach was to determine the energies and 3-momenta at the center of momentum reference frame for each particle, with a fixed s, and check it corresponds to each one of the above, but I'm having some trouble proving that, for example, [tex]E_A=\frac{s+m^2_A-m^2_B}{2\sqrt{s}}[/tex]. I've been playing around with [tex](p_A+p_B)^2=(E_A+E_B)^2=s[/tex] but I'm failing to determine [tex]E_A[/tex]. How should I do it?