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Current experimental upper bounds on the dipole moment give an upper bound of <math>d_N < 10^{-26} \text{e}\cdot</math>cm, which requires <math>\bar \theta < 10^{-10}</math>. The angle <math>\bar \theta</math> can take any value between zero and <math>2\pi</math>, so it taking on such a particularly small value is a fine-tuning problem called the strong CP problem.
==Proposed
The strong CP problem is solved automatically if one of the quarks is massless.<ref>{{cite journal|last1=Hook|first1=Anson|date=2019-07-22|title=TASI Lectures on the Strong CP Problem and Axions|url=https://pos.sissa.it/333/004/pdf|journal=Proceedings of Science|volume=333|doi=10.22323/1.333.0004|arxiv=1812.02669|access-date=2021-12-02}}</ref> In that case one can perform a set of chiral transformations on all the massive quark field to get rid of their complex mass phases and then perform another chiral transformation on the massless quark field to eliminate the residual θ-term without also introducing a complex mass term for that field. This then gets rid of all CP violating terms in the theory. The problem with this solution is that all quark masses are known to be massive from experimental matching with [[lattice QCD|lattice calculations]]. Even if one of the quarks was essentially massless to solve the problem, this would in itself just be another fine-tuning problem since there is nothing requiring a quark mass to take on such a small value.
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