Dear all(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# QCD theta angle and Neutron electric dipole moment

**Physics Forums | Science Articles, Homework Help, Discussion**