I am doing a project on electric dipole moments in supersymmetry. My background is in high energy physics, so I am having trouble fully grasping the nuclear interactions. Part of that includes understanding the CP and T violating interactions on a hadronic scale.

The effective Langrangian used in this case is the following:

$\mathcal{L} \propto \bar{e}i\gamma_5 e\bar{\psi}_N\left( C_S^{(0)}+C_S^{(1)}\tau_3\right)\psi_N + \bar{e} e\bar{\psi}_Ni\gamma_5\left( C_P^{(0)}+C_P^{(1)}\tau_3\right)\psi_N - \epsilon_{\mu\nu\alpha\beta}\bar{e}\sigma^{\mu\nu} e\bar{\psi}_N\sigma^{\alpha\beta}\left( C_T^{(0)}+C_T^{(1)}\tau_3\right)\psi_N + \dots$

Here $\psi_N$ is a relativistic nucleon field, $\tau$ is the isovector of the Pauli matrices and $C_{S,P,T}$ are the coefficients I am asking about.

My question is: What do the different coefficients $C_S, C_P$ and $C_T$ mean/represent exactly?

What I do know is: these are the scalar-pseudoscalar, pseudoscalar-scalar and tensor interaction respectively. I can see this in the Lagrangian, but I am struggling with the deeper meaning. I have done my master research in high energy physics, so atomic physics is not my strongest part. I have read articles that talk about these terms as relevant for short-range ($C_S$) and long-range interactions ($C_T$), or spin-independent ($C_S$) vs spin-dependent ($C_T$), or in relation to electric dipole moments of molecules (where $C_S$ is relevant for paramagnetic systems and $C_T$ for diamagnetic systems).

I would love to understand this better. How do I see what these different terms represent, and why they contribute (mostly) to specific systems? Could anybody explain this, or help me find papers that also explain the basics? Thanks a lot!


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