Study of the decay $B_s^0\to J/\psi f_2^{\prime }(1525)$ in ${\mu }^{+}{\mu }^{-}{K}^{+}{K}^{-}$ final states

We investigate the decay $B_s^0\to J/\psi K^{+}{K}^{-}$ for invariant masses of the $K^{+}{K}^{-}$ pair in the range $1.35<M(K^{+}{K}^{-})<2\mathrm{GeV}$. The data sample corresponds to an integrated luminosity of $10.4{\mathrm{fb}}^{-1}$ of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ accumulated with the D0 detector at the Fermilab Tevatron collider. From the study of the invariant mass and spin of the $K^{+}{K}^{-}$ system, we find evidence for the two-body decay $B_s^0\to J/\psi f_2^{\prime }(1525)$ and measure the relative branching fraction of the decays $B_s^0\to J/\psi f_2^{\prime }(1525)$ and $B_s^0\to J/\psi \varphi$ to be $R_{f_2^{\prime }/\varphi }=0.19\pm 0.05(\mathrm{stat})\pm 0.04(\mathrm{syst})$.

Figure 1

(a) Invariant mass of the $B_s^0$ candidates as a function of $M(K^{+}{K}^{-})$ as well as (b) and (c) one-dimensional projections. The observed structure is consistent with a decay $B_s^0\to J/\psi K^{+}{K}^{-}$ proceeding through $f_2^{\prime }(1525)$ or $f_0(1500)$ mesons. (d) Invariant mass of the $B_s^0$ mesons as a function of $M(K^{+}{K}^{-})$ for the simulated decay $B_s^0\to J/\psi f_2^{\prime }(1525)$ as well as (e) and (f) one-dimensional projections.

Figure 2

Distribution of the invariant mass $M({\pi }^{+}{\pi }^{-})$. The solid and dashed vertical lines represent the world-average mass and the natural width of the $f_0(1500)$ meson [1], respectively.

Figure 3

(a) Invariant mass of the $B_s^0$ candidates versus $M(K^{+}{K}^{-})$ for simulated decay $B^0\to J/\psi K_2^{*}(1430);K_2^{*}\to {\pi }^{\pm }{K}^{\mp }$, with the pion assigned the kaon mass, as well as (b) and (c) one-dimensional projections. (d) $K\pi$ $\mathcal{S}$-wave contribution [9] to the decay $B^0\to J/\psi K^{\pm }{\pi }^{\mp }$, with the pion assigned the kaon mass as well as (e) and (f) one-dimensional projections.

Figure 4

Invariant mass of $B^0$ mesons from the simulated decay $B^0\to J/\psi K_2^{*}(1430)$, $K_2^{*}(1430)\to K^{\pm }{\pi }^{\mp }$, where the pion is assigned the kaon mass, for a sampling of different $M(K^{+}{K}^{-})$ ranges. The distributions are fitted with a sum of two Gaussian functions with free masses, widths, and normalizations.

Figure 5

Invariant mass of $B^0$ mesons from the simulated $K\pi$ $\mathcal{S}$-wave contribution [9] to the decay $B^0\to J/\psi K^{\pm }{\pi }^{\mp }$, where the pion is assigned the kaon mass, for a sampling of different $M(K^{+}{K}^{-})$ ranges. The distributions are fitted with a sum of two Gaussian functions with free masses, widths, and relative normalizations.

Figure 6

Invariant mass of $B_s^0$ mesons from the simulated decay $B_s^0\to J/\psi f_2^{\prime }(1525)$ for a sampling of different ranges of $M(K^{+}{K}^{-})$. The distributions are fitted with a sum of two Gaussian functions with free masses, widths, and relative normalization.

Figure 7

Invariant mass of the $B_s^0$ candidates with $1.45<M(K^{+}{K}^{-})<1.6\mathrm{GeV}$. Curves show (a) the result of the fit allowing for a free $B_s^0$ signal yield (dashed-dotted lines) and a background composed of a $3:2$ mixture of $B^0\to J/\psi K^{\pm }{\pi }^{\mp }$ decays with the $K^{\pm }{\pi }^{\mp }$ system in the $J=0$ and $J=2$ states (dashed lines) and a combinatorial component described by a linear function (dotted lines), and (b) the result of the fit assuming the same background model but setting the $B_s^0$ signal rate to zero.

Figure 8

Invariant mass of candidates for the decay $B_s^0\to J/\psi K^{+}{K}^{-}$ in a sampling of different $M(K^{+}{K}^{-})$ ranges. Each fit uses a template derived from the $B_s^0$ signal simulation, a combination of the templates for the decays $B^0\to J/\psi K_J^{*}(1430)$, $K_J^{*}(1430)\to K^{\pm }{\pi }^{\mp }$, $J=1$, 2, as shown in Figs. 4 and 5, and a linear function describing the combinatorial background. The fit is performed in the range $5.25<M(J/\psi K^{+}{K}^{-})<5.7\mathrm{GeV}$, used to avoid the steeply falling background from multibody decays of $B$ mesons at lower masses and the steeply rising background from decays $B^{\pm }\to J/\psi K^{\pm }$ at higher masses. Neither the $B_s^0$ signal nor background components are constrained to positive values in order to obtain unbiased results for rates close to zero.

Figure 9

Invariant mass distribution of the meson pair from the $B_s^0$ candidates in the mass range $5.4<M(J/\psi K^{+}{K}^{-})<5.6\mathrm{GeV}$, under the $K^{\pm }{\pi }^{\mp }$ hypothesis. The curve shows the fit of a relativistic Breit-Wigner $J=2$ resonance at a fixed mass of 1.43 GeV and with a floating width, over a background described by a second-order polynomial function.

Figure 10

The $B_s^0$ signal yield as a function of $M(K^{+}{K}^{-})$ obtained from the fits shown in Fig. 8. The outer and inner error bars correspond to the statistical uncertainties with and without systematic uncertainties added in quadrature.

Figure 11

Definition of the decay angles ${\theta }_H$, ${\varphi }_H$, and $\psi$ in the helicity basis for the sequential decay $B_s^0\to J/\psi X$, $J/\psi \to {\mu }^{+}{\mu }^{-}$, $X\to K^{+}{K}^{-}$.

Figure 12

Angular dependence of the detection and event selection acceptance of the decay $B_s^0\to J/\psi f_2^{\prime }(1525)$ from simulations as a function of (a) $\cos {\theta }_H$, (b) ${\varphi }_H$, and (c) $\cos \psi$. The acceptance is found to be independent of the angle ${\varphi }_H$. For $\cos {\theta }_H$ and $\cos \psi$, we fit the acceptance dependence with symmetric fourth-order polynomial functions.

Figure 13

The $B_s^0$ mass distribution in five intervals of $|\cos \psi |$ as shown. The fits assume a two-Gaussian $B_s^0$ signal template and a background composed of a reflection of the $B^0\to J/\psi K^{\pm }{\pi }^{\mp }$ decay and a linear component. There is a steeply falling background from multibody decays of $B$ mesons at lower masses and a steeply rising background from decays $B^{\pm }\to J/\psi K^{\pm }$ at higher masses. These backgrounds are particularly acute for $\cos (\psi )>0.8$ making it impossible to obtain a reliable fit in this region.

Figure 14

The $|\cos \psi |$ distribution for the decay $B_s^0\to J/\psi X$, $X\to K^{+}{K}^{-}$ in the range $1.45<M(K^{+}{K}^{-})<1.6\mathrm{GeV}$. The curves are best fits assuming pure $J=0$ (dashed line), pure $J=1$ (dashed-dotted line), and pure $J=2$ (solid line).

Figure 15

The $M(K^{+}{K}^{-})$ distribution from the simulation of the decay $B_s^0\to J/\psi f_2^{\prime }(1525)$ fitted by the relativistic Breit-Wigner function [1].

Figure 16

Fit to the $B_s^0$ yield versus $M(K^{+}{K}^{-})$ as obtained in Fig. 10. The full fit to $B_s^0\to J/\psi K^{+}{K}^{-}$ includes a $f_2^{\prime }(1525)$ signal described by a relativistic Breit-Wigner and nonresonant constant term for the $\mathcal{S}$ wave. The outer and inner error bars correspond to the statistical uncertainties with and without systematic uncertainties added in quadrature.

Figure 17

Invariant mass distribution of $B_s^0$ candidates with $ct>200\mu \mathrm{m}$ for events in the mass range $1.01<M(K^{+}{K}^{-})<1.03\mathrm{GeV}$. A fit to a sum of a double Gaussian $B_s^0\to J/\psi \varphi$ signal (dashed-dotted line), a quadratic combinatorial background (dotted line), and the reflection of the decay $B^0\to J/\psi K^{*}(892)$ (dashed line) is used to extract the $B_s^0$ yield.