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Constraints on models for the Higgs boson with exotic spin and parity in $\boldsymbol{VH\rightarrow Vb\bar{b}}$ final states

We present constraints on models containing non-standard model values for the spin $J$ and parity $P$ of the Higgs boson, $H$, in up to 9.7~fb$^{-1}$ of $p\bar{p}$ collisions at $\sqrt{s} = $ 1.96~TeV collected with the D0 detector at the Fermilab Tevatron Collider. These are the first studies of Higgs boson $J^{P}$ with fermions in the final state. In the $ZH\rightarrow \ell\ell b\bar{b}$, $WH\rightarrow \ellνb\bar{b}$, and $ZH\rightarrow ννb\bar{b}$ final states, we compare the standard model (SM) Higgs boson prediction, $J^{P}=0^{+}$, with two alternative hypotheses, $J^{P}=0^{-}$ and $J^{P}=2^{+}$. We use a likelihood ratio to quantify the degree to which our data are incompatible with non-SM $J^{P}$ predictions for a range of possible production rates. Assuming that the production rate in the signal models considered is equal to the SM prediction, we reject the $J^{P}=0^{-}$ and $J^{P}=2^{+}$ hypotheses at the 97.6$\%$ CL and at the 99.0$\%$ CL, respectively. The expected exclusion sensitivity for a $J^{P}=0^{-}$ ($J^{P}=2^{+}$) state is at the 99.86$\%$ (99.94$\%$) CL. Under the hypothesis that our data is the result of a combination of the SM-like Higgs boson and either a $J^{P}=0^{-}$ or a $J^{P}=2^{+}$ signal, we exclude a $J^{P}=0^{-}$ fraction above 0.80 and a $J^{P}=2^{+}$ fraction above 0.67 at the 95$\%$ CL. The expected exclusion covers $J^{P}=0^{-}$ ($J^{P}=2^{+}$) fractions above 0.54 (0.47).