Difference between revisions of "Relativistic Differential Cross-section"

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<center><math>d\sigma=\frac{1}{F}|\mathcal{M}|^2 dQ</math></center>
 
<center><math>d\sigma=\frac{1}{F}|\mathcal{M}|^2 dQ</math></center>
  
dQ is the invariant Lorentz phase space factor and F is the flux of incoming particles
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dQ is the invariant Lorentz phase space factor  
  
  
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<center><math>dQ=(2\pi)^4\delta^4(p_1 + p_2 - p_1^' - p_2^')\frac{d^3p_1^'}{(2π)^3 2E_1^'}\frac{d^3p_2^'}{(2π)^3 2E_2^'}</math></center>
  
<center><math>dQ=(2\pi)^4\delta^4(p_1 + p_2 - p_1^' - p_2^')\frac{d^3p_1^'}{(2π)^3 2E_1^'}\frac{d^3p_2^'}{()^3 2E_2^'}</math></center>
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and F is the flux of incoming particles
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<center><math>F=2E_1 2E_2(|\vec {v}_1-\vec {v}_2|</math></center>
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The invariant form of F is
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<center><math>F=4\sqrt{(\vec {p}_1 \cdot \vec {p}_2)^2-(m_1m_2)^2}</math></center>
  
  
  
 
<center><math>\frac{d\sigma}{d\Omega}=\frac{1}{64\pi^2 s} \frac{\mathbf p_f}{\mathbf p_i}|\mathcal {M}|^2</math></center>
 
<center><math>\frac{d\sigma}{d\Omega}=\frac{1}{64\pi^2 s} \frac{\mathbf p_f}{\mathbf p_i}|\mathcal {M}|^2</math></center>

Revision as of 15:42, 1 July 2017

[math]d\sigma=\frac{1}{F}|\mathcal{M}|^2 dQ[/math]

dQ is the invariant Lorentz phase space factor


[math]dQ=(2\pi)^4\delta^4(p_1 + p_2 - p_1^' - p_2^')\frac{d^3p_1^'}{(2π)^3 2E_1^'}\frac{d^3p_2^'}{(2π)^3 2E_2^'}[/math]


and F is the flux of incoming particles


[math]F=2E_1 2E_2(|\vec {v}_1-\vec {v}_2|[/math]


The invariant form of F is


[math]F=4\sqrt{(\vec {p}_1 \cdot \vec {p}_2)^2-(m_1m_2)^2}[/math]


[math]\frac{d\sigma}{d\Omega}=\frac{1}{64\pi^2 s} \frac{\mathbf p_f}{\mathbf p_i}|\mathcal {M}|^2[/math]