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Phase space element calculation

  1. Jul 1, 2010 #1
    Can anyone see whats not right?

    In the phase space calculation of a 2 to 2 process I get to
    [tex]I=\int dp_1d\Omega \frac{1}{(2\pi)^2}\frac{p_1^2}{2E_12E_2}\delta(E_1+E_2-E)[/tex]

    then I use
    [tex]p_1=\sqrt{E_1^2+m_1^2} \Rightarrow dp_1=\frac{E_1}{\sqrt{E_1^2+m_1^2}}dE_1[/tex]

    thus
    [tex]I = \int dE_1d\Omega \frac{1}{(2\pi)^2}\frac{E_1^2-m_1^2}{2E_12E_2}\frac{E_1}{\sqrt{E_1^2-m_1^2}}\delta(E_1+E_2-E) [/tex]
    [tex]=\int d\Omega \frac{\sqrt{E_1^2-m_1^2}}{16\pi^2E_2}[/tex]

    [tex]=\int d\Omega \frac{|p_1|}{16\pi^2E_2}[/tex]

    However, this is the right answer, which should be
    [tex]\int d\Omega \frac{|p_1|}{16\pi^2E_{CM}}[/tex]


    All ideas greatly appreciated
     
    Last edited: Jul 1, 2010
  2. jcsd
  3. Jul 1, 2010 #2
    Problem sovled. Misstake was that E_2 is a function of E_1 so I cannot directly use the delta function. Taking this into account the correct answer is obtained.
     
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