Search for the $X(4140)$ state in $B^{+}\to J/\psi \varphi K^{+}$ decays with the D0 detector

We investigate the decay $B^{+}\to J/\psi \varphi K^{+}$ in a search for the $X(4140)$ state, a narrow threshold resonance in the $J/\psi \varphi$ system. The data sample corresponds to an integrated luminosity of $10.4{\mathrm{fb}}^{-1}$ of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ collected by the D0 experiment at the Fermilab Tevatron collider. We observe a mass peak with a statistical significance of 3.1 standard deviations and measure its invariant mass to be $M=4159.0\pm 4.3(\text{stat})\pm 6.6(\text{syst})\mathrm{MeV}$ and its width to be $\mathrm{\Gamma }=19.9\pm 12.6{(\text{stat})}_{-8.0}^{+3.0}(\text{syst})\mathrm{MeV}$.

Figure 1

(a) Invariant mass distribution of $B^{+}\to J/\psi \varphi K^{+}$ candidates after the $1.005<M(\varphi )<1.035\mathrm{GeV}$ requirement. The fit of a Gaussian signal with a second-order Chebyshev polynomial background is superimposed. The vertical green lines define the $B^{+}$ signal region. (b) Invariant mass distribution $M({\mu }^{+}{\mu }^{-})$ after the $B^{+}$ and $\varphi$ mass window requirements.

Figure 2

(a) Invariant mass distribution of $\varphi$ candidates after the $B^{+}$ mass requirement $5.23<M(B^{+})<5.33\mathrm{GeV}$ and in the $B^{+}$ sidebands. (b) Invariant mass distribution of $\varphi$ candidates after the $B^{+}$ mass requirement. The fit of a relativistic $P$-wave Breit-Wigner function (RBW) with the world-average width of 4.26 MeV, convoluted with a Gaussian resolution of 3 MeV taken from simulations, with a second-order Chebyshev polynomial background is superimposed. The vertical green lines define the $\varphi$ signal region.

Figure 3

(a) Background-subtracted invariant mass distribution of $J/\psi K$ pairs after the mass requirements $5.23<M(B^{+})<5.33\mathrm{GeV}$ and $1.005<M(K^{+}{K}^{-})<1.035\mathrm{GeV}$. (b) Invariant mass of the same pairs under the $J/\psi \pi$ hypothesis.

Figure 4

Invariant mass distribution $M(J/\psi {\pi }^{+}{\pi }^{-})$ before the $\psi (2S)$ veto. The fit assumes a Gaussian $\psi (2S)$ signal with the mean mass set to the world-average value [1] and a free resolution parameter. The arrows indicate the $\pm 2.5$ standard deviation range excluded from the analysis. The background is described by a product of a Landau function and an exponential.

Figure 5

Invariant mass distribution $M(J/\psi \varphi )$ after the mass requirements $5.23<M(B^{+})<5.33\mathrm{GeV}$ and $1.005<M(K^{+}{K}^{-})<1.035\mathrm{GeV}$. The background is estimated from the $B^{+}$ sidebands. (b) Difference between the distributions of the signal and normalized background.

Figure 6

Invariant mass distributions of $B^{+}\to J/\psi \varphi K^{+}$ candidates in two selected intervals of $M(J/\psi \varphi )$. Superimposed are the fits of a Gaussian signal (solid blue lines) with a second-order Chebyshev polynomial background (dashed red lines), with the signal and background shape parameters constrained to the results of the fit in Fig. 1, and allowing for the signal yield to vary.

Figure 7

The $B^{+}\to J/\psi \varphi K^{+}$ signal yield per 30 MeV resulting from fits in 17 $M(J/\psi \varphi )$ bins defined in the text, corrected for acceptance. Note that the second and third bins have widths of 15 MeV, and the points are normalized to the counts per 30 MeV as the rest of the bins. (a) Fit allowing for no $J/\psi \varphi$ resonance and assuming a three-body phase-space (PHSP) [1]; (b) allowing for a Breit-Wigner $X(4140)$ signal with an unconstrained mass and width and with a resolution of 4 MeV; (c) allowing for two Breit-Wigner resonances where the natural width of the second is set to 30 MeV. The resonance contributions, the three-body phase-space contribution, and the total fit are also shown.

Figure 8

Relative efficiency as a function of $M(J/\psi \varphi )$ due to kinematic acceptance, reconstruction efficiency, and resolution.