Constraints on models for the Higgs boson with exotic spin and parity in 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 $ZH\rightarrow \ell\ell b\bar{b}$,$WH\rightarrow \ell\nu b\bar{b}$,and$ZH\rightarrow \nu\nu b\bar{b}$ 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$\mathrm{\%}$ CL and at the 99.0$\mathrm{\%}$ CL, respectively. The expected exclusion sensitivity for a $J^P=0^{-}$ ($J^P=2^{+}$) state is at the 99.86$\mathrm{\%}$ (99.94$\mathrm{\%}$) 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$\mathrm{\%}$ CL. The expected exclusion covers $J^P=0^{-}$ ($J^P=2^{+}$) fractions above 0.54 (0.47).