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A light DM model for large $B \to K + \mbox{invisible}$ and $K \to π+ \mbox{invisible}$ decays and its implications for $B_s-\bar B_s$ mixing and neutron EDM

Xuan Hong, Xiao-Gang He, Ming-Wei Li

TL;DR

This paper proposes a UV-complete light dark matter scenario to account for potential excesses in $B^+\to K^+\nu\bar{\nu}$ and $K^+\to\pi^+\nu\bar{\nu}$ decays by replacing neutrino pairs with a light DM pair $\phi\phi$ within a Type-III two-Higgs-doublet model. The authors derive the resulting $\phi\phi$-quark effective interactions and identify a minimal Yukawa sector that can reproduce the needed Wilson coefficients, then analyze the model’s implications for $B_s-\bar B_s$ mixing and neutron EDM. They find that mass splittings between the neutral scalars $H$ and $A$ can yield sizable, testable shifts in $\Delta m_s$, while CP-violating phases in the Yukawas can generate EDMs, with potential cancellations between neutral and charged Higgs contributions allowing compatibility with current bounds. The work provides a concrete, testable framework linking rare meson decays to high-scale Higgs dynamics and low-energy precision observables.

Abstract

We present a light dark matter model with sizable invisible rare meson decays to accommodate possible larger than standard model (SM) predictions for both $B^+\to K^+ν\barν$ by Belle II and $K^+\toπ^+ν\bar ν$ by NA62. Since the emitted neutrinos are unobserved, the excesses may be due to light dark matter pairs in the final states. We show that it is possible to realize this by a UV-complete model based on a two Higgs doublet model. The neutral spin-zero Higgs bosons (scalar or pseudoscalar) mediating dark matter interaction, can also produce some effects at low energies which modify the SM predictions significantly. In particular we find large testable consequences for $B_s - \bar B_s$ mixing due to splitting of scalar and pseudoscalar masses, and also neutron EDM. We find that there is a cancellation due to exchange of neutral spin-zero particle for neutron EDM in general, but QCD running will lift this cancellation.This is generally true for any neutral Higgs contributions. However, we find that such a cancellation does not happen for charged scalar contribution. The allowed CP violating phase in the Yukawa sector can produce a neutron EDM experimental bound.

A light DM model for large $B \to K + \mbox{invisible}$ and $K \to π+ \mbox{invisible}$ decays and its implications for $B_s-\bar B_s$ mixing and neutron EDM

TL;DR

This paper proposes a UV-complete light dark matter scenario to account for potential excesses in and decays by replacing neutrino pairs with a light DM pair within a Type-III two-Higgs-doublet model. The authors derive the resulting -quark effective interactions and identify a minimal Yukawa sector that can reproduce the needed Wilson coefficients, then analyze the model’s implications for mixing and neutron EDM. They find that mass splittings between the neutral scalars and can yield sizable, testable shifts in , while CP-violating phases in the Yukawas can generate EDMs, with potential cancellations between neutral and charged Higgs contributions allowing compatibility with current bounds. The work provides a concrete, testable framework linking rare meson decays to high-scale Higgs dynamics and low-energy precision observables.

Abstract

We present a light dark matter model with sizable invisible rare meson decays to accommodate possible larger than standard model (SM) predictions for both by Belle II and by NA62. Since the emitted neutrinos are unobserved, the excesses may be due to light dark matter pairs in the final states. We show that it is possible to realize this by a UV-complete model based on a two Higgs doublet model. The neutral spin-zero Higgs bosons (scalar or pseudoscalar) mediating dark matter interaction, can also produce some effects at low energies which modify the SM predictions significantly. In particular we find large testable consequences for mixing due to splitting of scalar and pseudoscalar masses, and also neutron EDM. We find that there is a cancellation due to exchange of neutral spin-zero particle for neutron EDM in general, but QCD running will lift this cancellation.This is generally true for any neutral Higgs contributions. However, we find that such a cancellation does not happen for charged scalar contribution. The allowed CP violating phase in the Yukawa sector can produce a neutron EDM experimental bound.
Paper Structure (7 sections, 39 equations, 3 figures)

This paper contains 7 sections, 39 equations, 3 figures.

Table of Contents

  1. Introduction
  2. A type-III two Higgs doublet model realization
  3. constraints on the minimal model parameters
  4. Implications for $B_s-\bar{B}_s$ mixing and neutron EDM
  5. Effects on $B_s-\bar{B}_s$ mixing
  6. Effects on neutron EDM
  7. Conclusions

Figures (3)

  • Figure 1: $\Delta m_s^{NP}$ as a function of $m_H/m_A$ at different $\lambda_3$. The red dashed lines represent $-0.465\pm 0.630\ \mathrm{ps}^{-1}$ respectively. Left panel: $m_H=0.5\ \mathrm{TeV}$. Right panel: $m_H=1\ \mathrm{TeV}$.
  • Figure 2: The contribution of u and d quark to neutron EDM due to the neutral Higgs divided by $\mathrm{tan}\theta^{qq}$ as a function of $m_H/m_A$ at different $\lambda_3$. The solid lines represent d quark contribution and the dashed lines represent u quark contribution. Left panel: $m_H=0.5\ \mathrm{TeV}$. Right panel: $m_H=1\ \mathrm{TeV}$.
  • Figure 3: Left panel: The contribution of u and d quark to neutron EDM due to the neutral Higgs divided by $\mathrm{tan}\theta^{qq}$ as a function of $\lambda_3$ with $m_H/m_A = 1.05$ . Right panel : The contribution of u and d quark to neutron EDM due to the charged Higgs divided by $\mathrm{tan}\theta^{qq}$ as a function of $\lambda_3$. The solid lines represent d quark contribution and the dashed lines represent u quark contribution.