- #1

kaksmet

- 83

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Can anyone see what's 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

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: