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I have done some studies trying to understand the relation between the QCD theta angle and neutron electric dipole moment.

General, the QCD vacuum produces the term

[tex] L_{\theta} = \theta g_s^2\: G_a^{\mu\nu} \, G^a_{\mu\nu} [/tex]

this I can derive! I have studied Srednicki ch 93, Ramond (journeys beyond SM) ch. 5.6 and Axions : theory, cosmology, and experimental searches ch 1

Now we will generate a similar term with the inclusion of massive quarks, with "paramter"

[tex] \text{Arg}\, \text{Det}\,M [/tex]

where M is a (in general) complex mass matrix for the quarks, thus the "total theta" reads:

[tex] \tilde{\theta} = \theta _{QCD} + \text{Arg}\, \text{Det}\,M [/tex]

I have also understood that if the quarks are massless, then the QCD theta is not a physical parameter due to redefinition of dummy variable in the Path Integral (thanks to the anomalous U(1)_A symmetry).

Now my quest is to understand how this QCD-theta affects the Electric Dipole moment of the Neutron.

From reading Srednicki, the angle which gives a contribution to that is the angle from the complex mass matrix! See eq. 94.10, and not the total theta!

I mean, WHY should the theta in eq. 94.10 be the same as in the Path Integral eq. 94.1?

So my question is, how does the QCD theta affect el-dip-mom of the neutron?

the "other books", (the ones listed above) and Burgess and Moore (standard model - a primer) says that it should be [tex] \tilde{\theta} = \theta _{QCD} + \text{Arg}\, \text{Det}\,M [/tex] that comes in to the electric dipole moment....

Thank you in advance

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# QCD theta angle and Neutron electric dipole moment

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