Study of the [Formula: see text] and [Formula: see text] decays with the ATLAS detector

Abstract

The decays [Formula: see text] and [Formula: see text] are studied with the ATLAS detector at the LHC using a dataset corresponding to integrated luminosities of 4.9 and 20.6 fb[Formula: see text] of pp collisions collected at centre-of-mass energies [Formula: see text] TeV and 8 TeV, respectively. Signal candidates are identified through [Formula: see text] and [Formula: see text] decays. With a two-dimensional likelihood fit involving the [Formula: see text] reconstructed invariant mass and an angle between the [Formula: see text] and [Formula: see text] candidate momenta in the muon pair rest frame, the yields of [Formula: see text] and [Formula: see text], and the transverse polarisation fraction in [Formula: see text] decay are measured. The transverse polarisation fraction is determined to be [Formula: see text], and the derived ratio of the branching fractions of the two modes is [Formula: see text], where the first error is statistical and the second is systematic. Finally, a sample of [Formula: see text] decays is used to derive the ratios of branching fractions [Formula: see text] and [Formula: see text], where the third error corresponds to the uncertainty of the branching fraction of [Formula: see text] decay. The available theoretical predictions are generally consistent with the measurement.

Fig. 1

Feynman diagrams for $B_c^{+}\to J/\mathit{\psi }{D}_s^{(\ast )+}$ decays: a colour-favoured spectator, b colour-suppressed spectator, and c annihilation topology

Fig. 2

Distributions of a $cos{\mathit{\theta }}^{\ast }(D_s^{+})$ and b $cos{\mathit{\theta }}^{\prime }(\mathit{\pi })$, where ${\mathit{\theta }}^{\ast }(D_s^{+})$ and ${\mathit{\theta }}^{\prime }(\mathit{\pi })$ are two angular variables defined in Sect. 3. The distributions are shown for data sidebands (black dots) and MC simulation of $B_c^{+}\to J/\mathit{\psi }{D}_s^{+}$ signal (red solid line) and $A_{00}$ (green dotted line) and $A_{\pm \pm }$ (blue dashed line) components of $B_c^{+}\to J/\mathit{\psi }{D}_s^{\ast +}$ signal. The distributions are obtained after applying all selection criteria except the ones on the plotted variable. The MC distributions are normalised to data

Fig. 3

The mass distribution for the selected $J/\mathit{\psi }{D}_s^{+}$ candidates. The red solid line represents the projection of the fit to the model described in the text. The contribution of the $B_c^{+}\to J/\mathit{\psi }{D}_s^{+}$ decay is shown with the magenta long-dashed line; the brown dash-dot and green dotted lines show the $B_c^{+}\to J/\mathit{\psi }{D}_s^{\ast +}$ $A_{00}$ and $A_{\pm \pm }$ component contributions, respectively; the blue dashed line shows the background model. The uncertainties of the listed fit result values are statistical only

Fig. 4

Mass distribution of the a $J/\mathit{\psi }$ and b $D_s^{+}$ candidates after the full $B_c^{+}\to J/\mathit{\psi }{D}_s^{(\ast )+}$ selection (without mass constraints in the cascade fit) in the mass window of the $B_c^{+}$ candidate $5900\mathrm{MeV}<m(J/\mathit{\psi }{D}_s^{+})<6400$ MeV. The spectra are fitted with a sum of an exponential and a modified Gaussian function. The uncertainties of the shown $J/\mathit{\psi }$ and $D_s^{+}$ yields are statistical only

Fig. 5

The projection of the likelihood fit on the variable $|cos{\mathit{\theta }}^{\prime }({\mathit{\mu }}^{+})|$, where the helicity angle ${\mathit{\theta }}^{\prime }({\mathit{\mu }}^{+})$ is the angle between the ${\mathit{\mu }}^{+}$ and $D_s^{+}$ candidate momenta in the rest frame of the muon pair from $J/\mathit{\psi }$ decay, for a the full selected $J/\mathit{\psi }{D}_s^{+}$ candidate dataset and b a subset of the candidates in a mass range $5950\mathrm{MeV}<m(J/\mathit{\psi }{D}_s^{+})<6250$ MeV corresponding to the observed signal of $B_c^{+}\to J/\mathit{\psi }{D}_s^{\ast +}$ decay. The red solid line represents the full fit projection. The contribution of the $B_c^{+}\to J/\mathit{\psi }{D}_s^{+}$ decay is shown with the magenta long-dashed line (it is not drawn in b because this contribution vanishes in that mass range); the brown dash-dot and green dotted lines show the $B_c^{+}\to J/\mathit{\psi }{D}_s^{\ast +}$ $A_{00}$ and $A_{\pm \pm }$ component contributions, respectively; the blue dashed line shows the background model

Fig. 6

The mass distribution for the selected $B_c^{+}\to J/\mathit{\psi }{\mathit{\pi }}^{+}$ candidates. The red solid line represents the result of the fit to the model described in the text. The brown dotted and blue dashed lines show the signal and background component projections, respectively. The uncertainty of the shown signal yield is statistical only

Fig. 7

Comparison of the results of this measurement with those of LHCb [10] and theoretical predictions based on a QCD relativistic potential model [3], QCD sum rules [4], relativistic constituent quark model (RCQM) [5], BSW relativistic quark model (with fixed average transverse quark momentum $\mathit{\omega }=0.40$ GeV) [6], light-front quark model (LFQM) [7], perturbative QCD (pQCD) [8], and relativistic independent quark model (RIQM) [9]. The uncertainties of the theoretical predictions are shown if they are explicitly quoted in the corresponding papers. Statistical and systematic uncertainties added in quadrature are quoted for the results of ATLAS and LHCb.