A $U(1{)}_{(B-L{)}_3}$ model for dark matter and the $B^{+}\to K^{+}\nu \bar{\nu }$ excess reported by Belle II

Abstract

We explore the $U(1{)}_{(B-L{)}_3}$ gauge symmetry under which only third generation fermions are charged. The cancelation of the $[U(1{)}_{(B-L{)}_3}{]}^3$ anomaly requires a chiral fermion, ${\chi }_L$, singlet under the gauge group but charged under $U(1{)}_{(B-L{)}_3}$. This chiral fermion can play the role of thermal dark matter with a relic abundance set via the freeze-out scenario through the annihilation to pairs of the third generation fermions. In the quark mass basis, the new gauge boson will have off-diagonal couplings to the $b$ and $s$ quarks which can lead to a new contribution to $B^{+}\to K^{+}{\nu }_{\tau }{\bar{\nu }}_{\tau }$. We discuss the relevant bounds from the LHC searches for a new gauge boson, dark matter searches, electroweak precision data, ${\rm Y}$ decay, the CKM matrix and the $B_s^0-{\bar{B}}_s^0$ mixing. We entertain the possibility of explaining the $B^{+}\to K^{+}\nu \bar{\nu }$ excess recently reported by Belle II within this model.

Comments: 24 pages, 4 figures; v2: references added, typos corrected