# Strong CP problem, electric dipole moment, and fate of the axion

### Submission summary

 Authors (as Contributors): Gerrit Schierholz
Submission information
Date accepted: 2022-04-06
Date submitted: 2022-01-28 14:20
Submitted by: Schierholz, Gerrit
Submitted to: SciPost Physics Proceedings
Proceedings issue: XXXIII International Workshop on High Energy Physics (Hard Problems of Hadron Physics: Non-Perturbative QCD & Related Quests)
Ontological classification
Specialties:
• High-Energy Physics - Theory
Approach: Theoretical

### Abstract

Three hard problems! In this talk I investigate the long-distance properties of quantum chromodynamics in the presence of a topological theta term. This is done on the lattice, using the gradient flow to isolate the long-distance modes in the functional integral measure and tracing it over successive length scales. It turns out that the color fields produced by quarks and gluons are screened, and confinement is lost, for vacuum angles |theta| > 0, thus providing a natural solution of the strong CP problem. This solution is compatible with recent lattice calculations of the electric dipole moment of the neutron, while it excludes the axion extension of the Standard Model.

Published as SciPost Phys. Proc. 6, 011 (2022)

### Submission & Refereeing History

Submission scipost_202201_00039v1 on 28 January 2022

## Reports on this Submission

### Anonymous Report 1 on 2022-3-27 (Invited Report)

• Cite as: Anonymous, Report on arXiv:scipost_202201_00039v1, delivered 2022-03-27, doi: 10.21468/SciPost.Report.4784

### Strengths

1- one of the most important problems of the strong interections theory is addressed
2- nice short introduction into the problem
3- the powerful tool of the gradient flow is used to address the strong CP problem
4- the string tension is computed from the lattice data for the gradient flow coupling $\alpha_{GF}$.
5- impressive comparison of the nonperturbative beta function with the perturbative one is provided to show how the perturbative beta function gradually approaches the nonperturbative one with increasing order

I see none

### Report

The paper is addressing one of the most important unsolved problems of the strong interections theory, the strong CP problem. SU(3) gluodynamics in lattice regularization is considered. In the Introduction a short and useful review of the problem is presented. The author uses the gradient flow to study the long-distance (small momenta) modes. The lattice configurations are produced at small enough lattice spacing to be sure that the finite cutoff effects are suppressed. The finite volume effects are kept under controle due to use of three different volumes. The gradient flow coupling $\alpha_{GF}(\mu)$ is computed numerically and $1/\mu^2$ dependence is clearly demonstrated in Fig.2. This numerical result allows to compute the string tension with value 445(19) MeV impressively close to common expectations.
In Section 3 the results for nonzero $\theta$ are presented. The lattice configurations are splitted into disconnected topological sectors after the gradient flow is applied. This allows to determine the topological charge distribution $P(Q)$ at $\theta=0$ and then compute the running coupling at nonzero $\theta$ via the discrete Fourier transformation (4). The outcome is that the the running coupling constant gets screened at long distances. While at short distances the $\theta$ term has no effect on the coupling constant. It is then concluded that confinement is limited to $\theta=0$. It is furthermore concluded via glueball correlator computations that the theory has no finite mass gap for nonzero $\theta$. The important conclusion made is that the color fields produced by quarks and gluons are screened for nonzero $\theta$ and this limits the vacuum angle to $\theta = 0$ at macroscopic distances. Thus any strong CP violation at the hadronic level is ruled out.
In my opinion the paper presents very important results on the strong CP problem obtained via numerical simulations of lattice gluodynamics and it definitely deserves to be published.

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• grammar: excellent