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A new heavy $Z'$ vector boson provides a possible explanation for the neutralcurrent B anomalies. Various $U(1)'$ gauge groups have been proposed andstudied. In this paper, we explore a new type of $U(1)'$ gauge symmetryinspired by fundamental composite Higgs models with hyperfermions. It is alsothe first attempt to connect such a $Z'$ boson with a solution to the hierarchyproblem. The $U(1)'$ symmetry is identified as the quantum number of thedifference between the Standard Model fermion number and hyperbaryon number,written as $SM-HB$. This type of $U(1)'$ gauge symmetry is naturally broken insome fundamental composite Higgs models, which leads to a TeV-scale $Z'$ boson.We present a concrete example based on the minimal fundamental composite Higgsmodel with $SU(4)/Sp(4)$ coset, where the $Z'$ boson is the only state belowthe compositeness scale beside the composite Higgs. We also show that if the$U(1)'$ symmetry is third-generation-philic, written as $SM_3-HB$, thecorresponding $Z'$ boson can explain the neutral current B anomalies. The modelintroduces the composite Higgs and the $Z'$ boson from the same symmetrybreaking scale, so Higgs physics and flavor physics are now connected. Afterconsidering all the experimental constraints and theoretical preferences, wefound that there is still a natural parameter space for $SU(4)/Sp(4)$fundamental composite Higgs model with $N_{HC}=2$, which can be probed in thenear future.

Explaining the $R_{K^{(*)}}$ anomalies in a Fundamental Composite Higgs Model with Gauged $U(1)_{SM_3-HB}$