Dark photon relic dark matter production through the dark axion portal

We present a new mechanism to produce the dark photon ($\gamma'$) in the early universe with a help of the axion ($a$) using a recently proposed dark axion portal. The dark photon, a light gauge boson in the dark sector, can be a relic dark matter if its lifetime is long enough. The main process we consider is a variant of the Primakoff process $f a \to f \gamma'$ mediated by a photon, which is possible with the axion--photon--dark photon coupling. The axion is thermalized in the early universe because of the strong interaction and it can contribute to the non-thermal dark photon production through the dark axion portal coupling. It provides a two-component dark matter sector, and the relic density deficit issue of the axion dark matter can be addressed by the compensation with the dark photon. The dark photon dark matter can also address the reported 3.5 keV $X$-ray excess via the $\gamma' \to \gamma a$ decay.Comment: 10 pages, 8 figures, Version accepted by PR

Portal Connecting Dark Photons and Axions

The dark photon and the axion (or axion-like particle) are popular light particles of the hidden sector. Each of them has been actively searched for through the couplings called the vector portal and the axion portal. We introduce a new portal connecting the dark photon and the axion (axion--photon--dark photon, axion--dark photon--dark photon), which emerges in the presence of the two particles. This dark axion portal is genuinely new couplings, not just from a product of the vector portal and the axion portal, because of the internal structure of these couplings. We present a simple model that realizes the dark axion portal and discuss why it warrants a rich phenomenology.Comment: Version accepted for publication in Phys. Rev. Let

Improved Regret Bounds of (Multinomial) Logistic Bandits via Regret-to-Confidence-Set Conversion

Logistic bandit is a ubiquitous framework of modeling users' choices, e.g., click vs. no click for advertisement recommender system. We observe that the prior works overlook or neglect dependencies in $S \geq \lVert \theta_\star \rVert_2$, where $\theta_\star \in \mathbb{R}^d$ is the unknown parameter vector, which is particularly problematic when $S$ is large, e.g., $S \geq d$. In this work, we improve the dependency on $S$ via a novel approach called {\it regret-to-confidence set conversion (R2CS)}, which allows us to construct a convex confidence set based on only the \textit{existence} of an online learning algorithm with a regret guarantee. Using R2CS, we obtain a strict improvement in the regret bound w.r.t. $S$ in logistic bandits while retaining computational feasibility and the dependence on other factors such as $d$ and $T$. We apply our new confidence set to the regret analyses of logistic bandits with a new martingale concentration step that circumvents an additional factor of $S$. We then extend this analysis to multinomial logistic bandits and obtain similar improvements in the regret, showing the efficacy of R2CS. While we applied R2CS to the (multinomial) logistic model, R2CS is a generic approach for developing confidence sets that can be used for various models, which can be of independent interest.Comment: 32 pages, 2 figures, 1 tabl