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Register a new userThe Axion Mass from 5D Small Instantons
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We calculate a new contribution to the axion mass that arises from gluons propagating in a 5th dimension at high energies. By uplifting the 4D instanton solution to five dimensions, the positive frequency modes of the Kaluza-Klein states generate a power-law term in the effective action that inversely grows with the instanton size. This causes 5D small instantons to enhance the axion mass in a way that does not spoil the axion solution to the strong CP problem. Moreover this enhancement can be much larger than the usual QCD contribution from large instantons, although it requires the 5D gauge theory to be near the non-perturbative limit. Thus our result suggests that the mass range of axions (or axion-like particles), which is important for ongoing experimental searches, can depend sensitively on the UV modification of QCD.
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We examine the contribution of small instantons to the axion mass in various UV completions of QCD. We show that the reason behind the potential dominance of such contributions is the non-trivial embedding of QCD into the UV theory. The effects from instantons in the partially broken gauge group appear as fractional instanton corrections in the effective theory. These will exhibit unusual dependences on the various scales in the problem whenever the index of embedding is non-trivial. We present a full one-instanton calculation of the axion mass in the simplest product group models, carefully keeping track of numerical prefactors. Rather than using a t Hooft operator approximation we directly evaluate the contributions to the vacuum bubble, automatically capturing the effects of closing up external fermion lines with Higgs loops. This approach is manifestly finite and removes the uncertainty associated with introducing a cutoff scale for the Higgs loops. We verify that the small instantons may dominate over the QCD contribution for very high breaking scales and at least three group factors.
We present a new mechanism to relax the initial misalignment angle of the QCD axion and raise the cosmological bound on the axion decay constant. The QCD axion receives a contribution from small UV instantons during inflation, which raises its mass to the inflationary Hubble scale. This makes the axion start rolling down its potential early on. In the scenario, the standard model Yukawa couplings of quarks are dynamical, being of order one during the inflationary era and reducing to their standard model values once it ends. This means that after inflation the contribution of the small instantons is suppressed, and the axion potential reduces to the standard one from the usual IR instantons. As a result, when the axion starts to oscillate again after inflation, the initial misalignment angle is suppressed due to the dynamics during inflation. While the general idea of dynamical axion misalignment has been discussed in the literature before, we present in detail the major bottleneck on the mismatching between the minima of the axion potentials during and after inflation, and how it is circumvented in our scenario via the Froggatt-Nielsen mechanism. Taking into account of all the constraints, we find that the axion decay constant could be raised to the GUT scale, $10^{15}$ GeV, in our scenario.
We show that axions interacting with abelian gauge fields obtain a potential from loops of magnetic monopoles. This is a consequence of the Witten effect: the axion field causes the monopoles to acquire an electric charge and alters their energy spectrum. The axion potential can also be understood as a type of instanton effect due to a Euclidean monopole worldline winding around its dyon collective coordinate. We calculate this effect, which has features in common with both nonabelian instantons and Euclidean brane instantons. To provide consistency checks, we argue that this axion potential vanishes in the presence of a massless charged fermion and that it is robust against the presence of higher-derivative corrections in the effective Lagrangian. Finally, as a first step toward connecting with particle phenomenology and cosmology, we discuss the regime in which this potential is important in determining the dark matter relic abundance in a hidden sector containing an abelian gauge group, monopoles, and axions.
It is a common belief that the last missing piece of the Standard Model of particles physics was found with the discovery of the Higgs boson at the Large Hadron Collider. However, there remains a major prediction of quantum tunnelling processes mediated by instanton solutions in the Yang-Mills theory, that is still untested in the Standard Model. The direct experimental observation of instanton-induced processes, which are a consequence of the non-trivial vacuum structure of the Standard Model and of quantum tunnelling in QFT, would be a major breakthrough in modern particle physics. In this paper, we present for the first time a full calculation of QCD instanton-induced processes in proton-proton collisions accounting for quantum corrections due to both initial and final state gluon interactions, a first implementation in an MC event generator as well as a basic strategy how to observe these effects experimentally.
The axion mass receives a large correction from small instantons if the QCD gets strongly coupled at high energies. We discuss the size of the new CP violating phases caused by the fact that the small instantons are sensitive to the UV physics. We also discuss the effects of the mass correction on the axion abundance of the Universe. Taking the small-instanton contributions into account, we propose a natural scenario of axion dark matter where the axion decay constant is as large as $10^{15text{-}16}$GeV. The scenario works in the high-scale inflation models.
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