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I try to calculate the squared amplitude of the following self energy digram :

where se is massless Dirac fermion , and vrm is massless right handed neutrino. x is a scalar with mass m ..

I wrote the nominator of this process as:

N = ## \bar{u}(p) (1-\gamma_5) (p\!\!\!/ +k\!\!\!/ ) (1+\gamma_5) u(p) \to p\!\!\!/ (1-\gamma_5) (p\!\!\!/ +k\!\!\!/ ) (1+\gamma_5) \to p\!\!\!/ (1-\gamma_5) (p\!\!\!/ +k\!\!\!/ ) \to p_\alpha \gamma^\alpha (1-\gamma_5) (p_\alpha \gamma^\alpha + k_\beta \gamma^\beta ) \to p_\alpha p_\alpha \gamma^\alpha \gamma^\alpha +p_\alpha k_\beta\gamma^\alpha \gamma^\beta - p_\alpha \gamma^\alpha \gamma_5 p_\alpha \gamma^\alpha - p_\alpha \gamma^\alpha \gamma_5 k_\beta \gamma^\beta ##

I don't know how the first term as ## p_\alpha p_\alpha \gamma^\alpha \gamma^\alpha ## can be calculated or the third term .. also I don't know how ## P.K## which comes from the second term can be calculated from the process kinematics ? while ## P^2 =0 ## and ## K^2 = m_\chi^2##

Note that: the momentums of the particles in the Feynman diagram are se(p), vrm(p+k) and x(k)

Also the "x se vrm " vertices come from these Lagrangian terms:

## y (\bar{\nu_R^c} \chi s + \bar{s} \chi \nu_R^c ) ## (where s-> se, ##\chi ## -> x and \nu -> vrm)

Thanks ..

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# I How to calculate self energy Feynman diagram like that

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