Evidence for a $B_s^0{\pi }^{\pm }$ State

We report evidence for a narrow structure, $X(5568)$, in the decay sequence $X(5568)\to B_s^0{\pi }^{\pm }$, $B_s^0\to J/\psi \varphi$, $J/\psi \to {\mu }^{+}{\mu }^{-}$, $\varphi \to K^{+}{K}^{-}$. This is evidence for the first instance of a hadronic state with valence quarks of four different flavors. The mass and natural width of this state are measured to be $m=5567.8\pm 2.9{(\mathrm{stat})}_{-1.9}^{+0.9}(\mathrm{syst})\mathrm{MeV}/c^2$ and $\mathrm{\Gamma }=21.9\pm 6.4{(\mathrm{stat})}_{-2.5}^{+5.0}(\mathrm{syst})\mathrm{MeV}/c^2$. If the decay is $X(5568)\to B_s^{*}{\pi }^{\pm }\to B_s^0\gamma {\pi }^{\pm }$ with an unseen $\gamma$, $m\mathbf{(}X(5568)\mathbf{)}$ will be shifted up by $m(B_s^{*})-m(B_s^0)\sim 49\mathrm{MeV}/c^2$. This measurement is based on $10.4{\mathrm{fb}}^{-1}$ of $p\overline{p}$ collision data at $\sqrt{s}=1.96\mathrm{TeV}$ collected by the D0 experiment at the Fermilab Tevatron collider.

Figure 1

Invariant mass distribution of $J/\psi \varphi$ candidates. The signal region and two sideband regions are indicated. The solid curve presents the fit results to the function, modeled by a sum of a third-order polynomial to describe the combinatorial background and a Gaussian to describe the $B_s^0$ signal. The dotted curve shows the combinatorial background.

Figure 2

The combined background for the $m(B_s^0{\pi }^{\pm })$ distribution described in the text and the fit to that distribution with the $\mathrm{\Delta }R<0.3$ cone cut and without the cone cut.

Figure 3

The $m(B_s^0{\pi }^{\pm })$ distribution together with the background distribution and the fit results (a) after applying the $\mathrm{\Delta }R<0.3$ cone cut and (b) without the cone cut.

Figure 4

The $m(B_s^0{\pi }^{\pm })$ distribution resulting from fits of the $B_s^0$ signal to $m(J/\psi \varphi )$ in twenty mass intervals of $(B_s^0{\pi }^{\pm })$ candidates described in the text. The solid line shows the result of the fit. The dashed line shows the contribution of events due to the $B_s^0$ background from simulations. There is no non-$B_s^0$ background.