Heavy QCD axion in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>s</mml:mi></mml:math> transition: Enhanced limits and projections
Sabyasachi Chakraborty, Manfred Kraus, Vazha Loladze, Takemichi Okui, Kohsaku Tobioka
Abstract
We study a ``heavy'' QCD axion whose coupling to the standard model is dominated by $aG\stackrel{\texttildelow{}}{G}$ but with ${m}_{a}\ensuremath{\gg}{m}_{\ensuremath{\pi}}{f}_{\ensuremath{\pi}}/{f}_{a}$. This is well motivated as it can solve the strong $CP$ problem while evading the axion quality problem. It also poses interesting challenges for its experimental search due to its suppressed couplings to photons and leptons. Such axion with mass around a GeV is kinematically inaccessible or poorly constrained by most experimental probes except $B$-factories. We study $B\ensuremath{\rightarrow}Ka$ transitions as a powerful probe of the heavy QCD axion by performing necessary 2-loop calculations for the first time, together with some improvement on the existing analysis strategy. We find some of the existing limits are enhanced by at least an order of magnitude. We also demonstrate that the bounds are robust against unknown UV physics. For forthcoming data sets of the Belle II experiment, we provide a projection that ${f}_{a}$ of a few TeV is within its future reach, which is relevant to the quality problem.