Small instantons and the strong CP problem in composite Higgs models

Topic

natural sciences

Frequently Asked Questions (FAQ)

What is the Strong CP problem? The Strong CP problem is a puzzle in particle physics that stems from the observation that the strong force, which governs the interactions between quarks, does not seem to violate CP symmetry (a combination of charge conjugation and parity) as much as expected. This is perplexing because the Standard Model of particle physics contains terms that could lead to significant CP violation in the strong force. The question then arises: why is the observed CP violation in the strong force so small?
What are the traditional solutions to the Strong CP problem? Two main solutions have been proposed: Massless Up Quark: This solution suggests that the up quark, one of the fundamental building blocks of matter, is massless. This would introduce a symmetry that makes the Strong CP phase unphysical. However, lattice QCD calculations indicate a non-zero up quark mass, seemingly ruling out this solution. Peccei-Quinn Symmetry and the Axion: This solution proposes the existence of a new symmetry, known as the Peccei-Quinn symmetry. This symmetry is spontaneously broken, leading to the emergence of a new particle called the axion. The axion interacts with the strong force in a way that dynamically cancels out the Strong CP phase.
How do small instantons affect the Strong CP problem in traditional solutions? Both traditional solutions assume that non-perturbative effects contributing to the up quark mass or the axion potential primarily arise from large instantons in the infrared (IR) energy scale. However, if small instantons in the ultraviolet (UV) energy scale also contribute significantly, it can drastically alter the expectations for these solutions.
Why are small instanton effects typically suppressed? Small instanton effects are typically suppressed due to two main factors: Asymptotic Freedom of QCD: The strength of the strong force decreases at high energies (UV) due to asymptotic freedom. This makes the suppression factor associated with instantons, κs = e^(-2π/αs), very small in the UV where the strong coupling constant, αs, is small. Small Yukawa Couplings: The contribution of small instantons is also suppressed by the product of Yukawa couplings of all quarks. Since these couplings are small in the Standard Model, the overall suppression is significant.
How do composite Higgs models enhance small instanton contributions? Composite Higgs models, particularly those employing partial compositeness, offer a unique setting where both suppression factors can be overcome: Running of the Strong Coupling: These models often introduce many new colored fermions to provide partners for all Standard Model fermions. These additional fermions modify the running of the strong coupling constant, making it grow strong again in the UV. This enhances the instanton suppression factor, κs. Anarchic Yukawa Couplings in the UV: In composite Higgs models, the effective Standard Model Yukawa couplings can be anarchic and of order one in the UV. This mitigates the suppression due to small Yukawa couplings, allowing for larger contributions from small instantons.
Can the up quark mass be generated entirely from small instantons? Yes, in composite Higgs models, it’s possible to generate the entire up quark mass from small instanton contributions. This occurs because the up quark Yukawa coupling, which is zero in the deep UV, can be generated by instanton effects around a specific energy scale where these effects become unsuppressed. This scenario naturally solves the Strong CP problem, as the CP-violating phase can be rotated away in the deep UV where the up quark mass is absent.
What implications do small instantons have for the axion solution? In composite Higgs models with an axion, small instanton contributions can significantly modify the axion potential, leading to an axion mass much larger than the traditional QCD axion. The axion mass can be as large as 10 TeV, opening up a vast unexplored parameter space that is not ruled out by existing experimental constraints.
How robust is the solution to the Strong CP problem in composite Higgs models against the effects of higher dimensional operators? The solution is robust if the only sources of flavor symmetry breaking are the left-handed mixings and Planck-scale suppressed operators. However, if the flavor symmetry is broken at a lower scale, such as the compositeness scale, then additional constraints on the model parameters are required to ensure that the solution to the Strong CP problem is not spoiled. Paper: [https://inspirehep.net/literature/search?q=aps]

Significance

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