Quantcast
  • 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.

News

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

Attributions

(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 ...

  Axion mass generation and EW scale

+ 3 like - 0 dislike
451 views

Suppose we have largangian of QCD axion below PQ scale:

$$
L_{a} = \frac{1}{2}\partial_{\mu}a\partial^{\mu}a - C_{G}\frac{a}{f_{a}}G \wedge G + C_{\gamma}\frac{a}{f_{a}}F_{EM}\wedge F_{EM} + L_{SM},
$$​

where $G$ denotes gluon field strength, $\wedge$ denotes contraction with Levi-Civita tensor, $L_{SM}$ is SM lagrangian, $C_{G/\gamma}$ denote constants which depend on properties of underlying theory. 

People say that axion acquires mass during QCD phase transition. For demonstrating that they redefine quark fields via local chiral rotation,

$$

q \to e^{iC_{G}\gamma_{5}\frac{a}{6f_{a}} }q, \qquad (0)

$$

Which eliminates $aG\wedge G$ coupling, but obtain "modified" mass and kinetic terms for quark fields,

$$
L_{SM} \to \in L_{aq} = \bar{q}^{i}_{L}e^{iC_{G}\gamma_{5}\frac{a}{3f_{a}}}M_{ij}q^{j}_{R} + h.c. + L_{\text{kinetic}} \qquad (1)
$$​

In a time of QCD phase transition, $\bar{q}^{i}_{L}q^{j}_{R} = v\delta^{ij}$, so from Eq. $(1)$ we obtain axion potential $V_{a} = -m_{a}^2f_{a}^2\left( 1 - cos\left(\frac{a}{f_{a}}\right)\right)$, which contains axion mass term.

My question is following. Redefinition $(0)$ also generates axion interaction with EW sector. EW sector also has spontaneously symmetry breaking scale. So why axion mass doesn't arise at EW phase transition? I.e., why there is no term

$$
L_{aHH} = e^{ic\frac{a}{f_{a}}}H^{\dagger}H + h.c.,
$$

which generates axion mass at EW scale?

asked Nov 23, 2015 in Theoretical Physics by NAME_XXX (1,060 points) [ revision history ]
retagged Jan 1, 2016 by Dilaton.admin

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:
p$\hbar$ysicsOver$\varnothing$low
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
...