Probing scalar and pseudoscalar new physics using rare kaon decays

TL;DR

This work investigates how scalar and pseudoscalar new physics can be probed with rare kaon decays using a minimal EFT framework with Wilson coefficients $C_S$ and $C_P$. It analyzes charged modes $K^+\to \pi^+ \ell^+\ell^-$ and neutral modes $K_{L,S}\to \mu^+\mu^-$ and $K_L\to \pi^0 \ell^+\ell^-$, presenting two illustrative scenarios: A with $\delta C_P=0$ and B with $\delta C_S=-\delta C_P$. Current data from $K^+\to \pi^+\ell^+\ell^-$ constrain $|C_S|$ to roughly $\mathcal{O}(3-5)$, while $K_L\to \mu^+\mu^-$ and $K_S\to \mu^+\mu^-$ provide complementary, correlation-driven constraints under the two scenarios. The paper emphasizes the complementarity of charged and neutral kaon channels and the potential reach of NA62, the LHCb upgrade, and KOTO-II to uncover or tightly constrain scalar/pseudoscalar NP, contingent on reducing long-distance uncertainties in the theoretical predictions.

Abstract

Rare kaon decays provide sensitive tests of new physics. In this work, we focus on scalar and pseudoscalar operators, analysing the $K\to π\ell^+\ell^-$ and $K\to \ell^+\ell^-$ decays. We highlight the complementary role of different modes: $K^+\toπ^+\ell^+\ell^-$, in particular the forward-backward asymmetry in the muon channel as a clean probe of scalar effects, the stringent constraints from $K_L\to μ^+μ^-$, and the discovery potential of future measurements of $K_S\to μ^+μ^-$ and $K_L\to π^0 \ell^+\ell^-$. The interplay between charged and neutral modes underscores the complementarity of NA62, the LHCb upgrade, and KOTO-II.

Figures (6)

• Figure 1: BR($K_L\to \mu^+\mu^-$) with both sign for LD on the left and only LD:+ on the right.
• Figure 2: BR($K_L\to \mu^+\mu^-$) vs BR($K_S\to \mu^+\mu^-$) as a function of $\delta C_{S}^\mu$. Zoomed version on the right.
• Figure 3: BR($K_L\to \mu^+\mu^-$) with both sign for LD on the left and only LD:+ on the right.
• Figure 4: BR($K_L\to \mu^+\mu^-$) vs BR($K_S\to \mu^+\mu^-$) as a function of $\delta C_{S}^\mu = -\delta C_{P}^\mu$. Zoomed version on the right.
• Figure 5: BR($K_L\to \pi^0\ell^+\ell^-$) as a function of $\delta C_{S}^\mu$.