- #1

maximus123

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I've tried finding the invariant mass of the positron and pion as followsFor the decay [itex]p\rightarrow e^+\pi ^0[/itex] show that the energy of the pion in the proton’s rest

frame (i.e., the lab frame) is

[itex]E_{\pi}=\frac{m_p^2+m_{\pi}^2-m_e^2}{2m_p}[/itex]

[itex]M^2=(E_e+E_{\pi})^2-(\mathbf{p_e}+\mathbf{p_{\pi}})\\[/itex]

[itex]=E_e^2+E_{\pi}^2+2E_eE_{\pi}-p_e^2-p_{\pi}^2-2\mathbf{p_ep_{\pi}}\\[/itex]

[itex]=m_e^2+m_{\pi}^2-2(E_eE_{\pi}+\mathbf{p_ep_{\pi}})\\[/itex]

[itex]=m_e^2+m_{\pi}^2-2(E_eE_{\pi}+p_ep_{\pi}\textrm{cos}\theta)\\[/itex]

**At this point I cannot see how to get any closer to the given answer. Any help with how to proceed from here, or advice on where I may have already gone wrong, would be greatly appreciated.**

[itex]m_e^2+m_{\pi}^2-2(E_eE_{\pi}+p_ep_{\pi}\textrm{cos}\theta)=m_p^2[/itex]

[itex]m_e^2+m_{\pi}^2-2(E_eE_{\pi}+p_ep_{\pi}\textrm{cos}\theta)=m_p^2[/itex]

Thanks