• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  How do we know $\theta_\mathrm{QCD} \ne \pi$?

+ 7 like - 0 dislike

Strong CP violation happens when the theta term gives a complex phase, but there are two values where the effect is real, $\theta=0$ which gives no phase for instantons, or $\theta=\pi$, which gives a -1 phase for each instanton. Do we know we are at 0, not at $\pi$?

For instance, do we have lattice simulations or other theoretical estimates for the $\pi$ version of QCD showing disagreement with the hadron spectrum? This might not be easy, as there is a sign problem.

asked Sep 15, 2014 in Theoretical Physics by Ron Maimon (7,720 points) [ revision history ]

1 Answer

+ 5 like - 0 dislike

This question is considered at the end of the paper by Crewther, Di Vecchia, Veneziano and Witten :


They argue that to go to $\theta_{QCD} =0$ to  $\theta_{QCD} = \pi$ is equivalent to change the sign of one of the masses of quarks, for example $m_u$ (this step uses the usual relation between chiral rotation and $\theta$-term). Then they look for quantities sensible to the sign of $m_u$. A natural choice is $m_d - m_u$, that you can expect to show up in the difference of masses  between the neutral kaon anf the positively charged kaon. Indeed, they use a formula obtained by current algebra techniques at $\theta_{QCD} =0$ relating this difference of masses to $m_d - m_u$ (formula (23) of the paper). For $\theta_{QCD}= \pi$, the same formula should be true with $m_u$ replaced by $-m_u$ (formula (24) of the paper). Comparison with experimental masses of kaons excludes the case $\theta_{QCD} = \pi$ (roughly, the smallness of the difference of masses between the neutral and the positively charged kaons suggests that $\theta_{QCD}$ is around 0 rather than around $ \pi$).

answered Sep 16, 2014 by 40227 (5,140 points) [ revision history ]
edited Sep 16, 2014 by 40227

Aren't masses always supposed to be positive? 

Is that link stable and permanent? I'd like to import the paper for review, and Dashen's paper linked as 6 in the references. Thanks, this is interesting. I figured some sort of SVZ/Veneziano-Witten thing would estimate it, but I didn't know it was considered.

Maybe a better link is http://cds.cern.ch/record/133382 which is a page of the CERN Document server, so I guess stable and permanent, where one can find a link to the pdf.

Dirac fermions in 3+1d can have complex masses and still be unitary.

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights