Relating theta_QCD to neutron EDM How do I relate the topological $\theta_\text{QCD}$ parameter to the electric dipole moment (EDM) of the neutron?
I am very familiar with chiral perturbation theory.  I just need to know how to take $\theta_\text{QCD}$ into account.
Any good sources?
 A: The phenomenological relevant parameter is not the coefficient of the topological term $\theta_{QCD}$ but the combination:
$$\theta\equiv\theta_{QCD}+\sum _q Arg \{ m_q\}$$
since one may transform the first term into the second through field redefinitions. I do not know the precise derivation of the relation between $\theta$ and the neutron's electric dipole moment $\mathcal{D}$, but a good estimate is the following. (Sorry if this is not enough for you but it could be interesting for other readers).
$\mathcal{D}$ must vanish if either the up quark or the down quark were massless and if $\theta$ were zero. Moreover, $\mathcal{D}$ has dimensions of electric charge times length and must be suppressed by $\Lambda_{QCD}$. An expression which verifies the previous requirements is:
$$\mathcal{D}\approx {\hbar \, \theta \,e\over \Lambda_{QCD}^2} \frac{m_u \cdot m_d }{m_u + m_d } $$
The experimental constraint on $\mathcal{D}$ is: $$| \mathcal{D}|< 6 \cdot 10^{-26}e \cdot \mbox{cm}$$
giving rise to:$$\theta \lesssim 5\cdot10^{-10}$$
which is in agreement with the constraint reported.
