A light DM model for large $$B \rightarrow K + \text{ invisible }$$ and $$K \rightarrow \pi + \text{ invisible }$$ decays and its implications for $$B_s-\bar{B}_s$$ mixing and neutron EDM

Abstract We study the implications for $$B_s - \bar{B}_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>-</mml:mo> <mml:msub> <mml:mover> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mi>s</mml:mi> </mml:msub> </mml:mrow> </mml:math> mixing and the neutron electric dipole moment (EDM) in a light dark matter model with sizable invisible rare meson decays to accommodate the recent possible deviations from Standard Model (SM) predictions observed in $$B^+\rightarrow K^+\nu \bar{\nu }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>B</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mi>ν</mml:mi> <mml:mover> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math> by Belle II and $$K^+\rightarrow \pi ^+\nu \bar{\nu }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mi>ν</mml:mi> <mml:mover> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math> by NA62. Given that the neutrinos in these decays escape detection, they can be replaced by other invisible final states. Based on effective operator analysis, it has been proposed that branching ratios for $$B^+\rightarrow K^+ +\text{ invisible }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>B</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>+</mml:mo> <mml:mspace/> <mml:mtext>invisible</mml:mtext> <mml:mspace/> </mml:mrow> </mml:math> and $$K^+\rightarrow \pi ^+ +\text{ invisible }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>+</mml:mo> <mml:mspace/> <mml:mtext>invisible</mml:mtext> <mml:mspace/> </mml:mrow> </mml:math> can naturally be larger than the SM predictions due to the emission of light dark matter pairs. We demonstrate that this scenario can be realized within a UV-complete two-Higgs-doublet model (2HDM) where neutral Higgs bosons mediating dark matter interactions induce significant low-energy effects especially for $$B_s-\bar{B}_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>-</mml:mo> <mml:msub> <mml:mover> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mi>s</mml:mi> </mml:msub> </mml:mrow> </mml:math> mixing and neutron EDM. Within the allowed parameter space, we find non-negligible contributions to $$B_s - \bar{B}_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>-</mml:mo> <mml:msub> <mml:mover> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mi>s</mml:mi> </mml:msub> </mml:mrow> </mml:math> mixing. For the neutron EDM, there is a cancellation due to the exchange of neutral spin-zero particles, but QCD renormalization group evolution will lift this cancellation which in fact is generally true for any neutral Higgs contribution. However, we demonstrate that such a cancellation does not occur for charged scalar contributions. Ultimately, the allowed CP-violating phases in the Yukawa sector can generate a neutron EDM at a level consistent with the current experimental bound.