open_problems:strong_cp_puzzle
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | Last revision Both sides next revision | ||
|
open_problems:strong_cp_puzzle [2018/05/05 12:59] jakobadmin |
open_problems:strong_cp_puzzle [2020/04/02 22:14] 95.91.224.105 fixed typos |
||
|---|---|---|---|
| Line 6: | Line 6: | ||
| The strong CP puzzle is the observation that in the [[models:standard_model|standard model]] nothing forbids that [[models:standard_model:qcd|strong interactions]] violate [[advanced_notions:cp_symmetry|CP symmetry]] but so far such a CP violation by strong interactions was never observed. | The strong CP puzzle is the observation that in the [[models:standard_model|standard model]] nothing forbids that [[models:standard_model:qcd|strong interactions]] violate [[advanced_notions:cp_symmetry|CP symmetry]] but so far such a CP violation by strong interactions was never observed. | ||
| - | The puzzle is regarded as a deep and interesting since upon closer inspection there are possibly two sources how strong interactions could violate CP symmetry. These two sources come from completely different sectors and thus its somewhat a mircale that they cancel exactly. | + | The puzzle is regarded as a deep and interesting since upon closer inspection there are possibly two sources how strong interactions could violate CP symmetry. These two sources come from completely different sectors and thus it's somewhat a mircale that they cancel exactly. |
| One possible source comes from the nontrivial structure of the [[advanced_notions:quantum_field_theory:qcd_vacuum|ground state of the theory of strong interactions]] (QCD). | One possible source comes from the nontrivial structure of the [[advanced_notions:quantum_field_theory:qcd_vacuum|ground state of the theory of strong interactions]] (QCD). | ||
| Line 84: | Line 84: | ||
| If at least one quark were massless, the Lagrangian would have a chiral symmetry $u \to e^{i\alpha \gamma_5} \Psi$. Such a chiral rotation shifts the $\theta$ parameter: $\theta \to \theta + c \alpha$. When at least one quark is massless, we can perform one completely arbitrary chiral rotation and hence eliminate $\theta \to 0$. | If at least one quark were massless, the Lagrangian would have a chiral symmetry $u \to e^{i\alpha \gamma_5} \Psi$. Such a chiral rotation shifts the $\theta$ parameter: $\theta \to \theta + c \alpha$. When at least one quark is massless, we can perform one completely arbitrary chiral rotation and hence eliminate $\theta \to 0$. | ||
| - | However, when all quarks do have mass, we can't choose the phase $\alpha$ arbitrary. Instead, it is fixed by the requirement that we must get a real mass for the quarks. Hence $\alpha$ is not an arbitrary parameter and $\theta$ can not be shifted to zero. Of course, it is possible that $\alpha$ happens to be exactly the right value to set $\theta$ to zero. However, there is no reason why this should be the case and this is the strong CP problem. Why should this seemingly unrelated, but fixed parameter $\alpha$ exactly cancel the bare parameter $\theta$? | + | However, when all quarks do have mass, we can't choose the phase $\alpha$ arbitrarily. Instead, it is fixed by the requirement that we must get a real mass for the quarks. Hence $\alpha$ is not an arbitrary parameter and $\theta$ can not be shifted to zero. Of course, it is possible that $\alpha$ happens to be exactly the right value to set $\theta$ to zero. However, there is no reason why this should be the case and this is the strong CP problem. Why should this seemingly unrelated, but fixed parameter $\alpha$ exactly cancel the bare parameter $\theta$? |
| A chiral rotation shifts $\theta$, because a chiral rotation is basically a change of basis, i.e. a relabelling of the quark fields. Such changes of basis are accompanied by a Jacobian. In this case, the Jacobian is proportional to $F \tilde F$ and thus shifts $\theta$. | A chiral rotation shifts $\theta$, because a chiral rotation is basically a change of basis, i.e. a relabelling of the quark fields. Such changes of basis are accompanied by a Jacobian. In this case, the Jacobian is proportional to $F \tilde F$ and thus shifts $\theta$. | ||
open_problems/strong_cp_puzzle.txt · Last modified: 2020/04/10 19:51 by 71.46.88.3
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
