The light invisible boson in FCNC decays of B and $$B_c$$ mesons

<jats:p>In this paper, we study the FCNC decay processes of <jats:italic>B</jats:italic> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$B_c$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> meson, in which one invisible particle is emitted. Both the spin-0 and spin-1 cases are considered. The model-independent effective Lagrangian is introduced to describe the coupling between the light invisible boson and quarks. The constraints of the coupling coefficients are extracted by experimental upper limits of the missing energy in <jats:italic>B</jats:italic> meson decays. The bounds are used to predict the upper limits of branching fractions of corresponding <jats:inline-formula><jats:alternatives><jats:tex-math>$$B_c$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> decays, which are of the order of <jats:inline-formula><jats:alternatives><jats:tex-math>$$10^{-6}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> or <jats:inline-formula><jats:alternatives><jats:tex-math>$$10^{-5}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> when final meson is pseudoscalar or vector, respectively. The maximum branch ratios are achieved when <jats:inline-formula><jats:alternatives><jats:tex-math>$$m_\chi \approx 3.5$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>χ</mml:mi> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>3.5</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>–4 GeV, where <jats:inline-formula><jats:alternatives><jats:tex-math>$$m_\chi $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>χ</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> is the mass of the invisible particle.</jats:p>