Measurement of the shape of the ${\mathrm{\Lambda }}_b^0\to {\mathrm{\Lambda }}_c^{+}{\mu }^{-}{\overline{\nu }}_{\mu }$ differential decay rate

A measurement of the shape of the differential decay rate and the associated Isgur-Wise function for the decay ${\mathrm{\Lambda }}_b^0\to {\mathrm{\Lambda }}_c^{+}{\mu }^{-}{\overline{\nu }}_{\mu }$ is reported, using data corresponding to $3{\mathrm{fb}}^{-1}$ collected with the LHCb detector in proton-proton collisions. The ${\mathrm{\Lambda }}_c^{+}{\mu }^{-}{\overline{\nu }}_{\mu }(+\mathrm{anything})$ final states are reconstructed through the detection of a muon and a ${\mathrm{\Lambda }}_c^{+}$ baryon decaying into $p{K}^{-}{\pi }^{+}$, and the decays ${\mathrm{\Lambda }}_b^0\to {\mathrm{\Lambda }}_c^{+}{\pi }^{+}{\pi }^{-}{\mu }^{-}{\overline{\nu }}_{\mu }$ are used to determine contributions from ${\mathrm{\Lambda }}_b^0\to {\mathrm{\Lambda }}_c^{*+}{\mu }^{-}{\overline{\nu }}_{\mu }$ decays. The measured dependence of the differential decay rate upon the squared four-momentum transfer between the heavy baryons, $q^2$, is compared with expectations from heavy-quark effective theory and from unquenched lattice QCD predictions.

Figure 1

(a) The ln(IP/mm) distribution and (b) $p{K}^{-}{\pi }^{+}$ invariant mass for ${\mathrm{\Lambda }}_c^{+}$ candidate combinations with a muon. The red (dashed-dotted) curves show the combinatorial ${\mathrm{\Lambda }}_c^{+}$ background, the green (dashed) curves show the ${\mathrm{\Lambda }}_c^{+}$ from ${\mathrm{\Lambda }}_b^0$, and the blue-solid curves show the total yields.

Figure 2

The mass difference $m(p{K}^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-})-m(p{K}^{-}{\pi }^{+})$ added to the known ${\mathrm{\Lambda }}_c^{+}$ mass, $m_{\mathrm{PDG}}({\mathrm{\Lambda }}_c^{+})$ [14], for candidates with $p{K}^{-}{\pi }^{+}$ invariant mass within $\pm 20\mathrm{MeV}$ of the known ${\mathrm{\Lambda }}_c^{+}$ mass in candidate semileptonic decays for the entire $w$ range: data are shown as black dots, the combinatoric background is shown as a blue solid line, and the gray histogram shows the WS spectrum, obtained by combining a ${\pi }^{+}{\pi }^{+}$ or ${\pi }^{-}{\pi }^{-}$ pair with ${\mathrm{\Lambda }}_c^{+}$ instead of ${\pi }^{+}{\pi }^{-}$. The signal fits are identified as follows: (a) for $m<2700\mathrm{MeV}$, the ${\mathrm{\Lambda }}_c(2595{)}^{+}$ as a magenta dashed line and the ${\mathrm{\Lambda }}_c(2625{)}^{+}$ as a green long-dashed line; (b) for $m>2700\mathrm{MeV}$, the ${\mathrm{\Lambda }}_c(2765{)}^{+}$ as a magenta dashed line and the ${\mathrm{\Lambda }}_c(2880{)}^{+}$ as a green long-dashed line.

Figure 3

The spectra (a) $d{N}_{\mathrm{meas}}/dw$ before unfolding and (b) $d{N}_{\mathrm{u}}/dw$ after unfolding, for the decay ${\mathrm{\Lambda }}_b^0\to {\mathrm{\Lambda }}_c^{+}{\mu }^{-}{\overline{\nu }}_{\mu }$. The latter spectrum is then corrected for acceptance and reconstruction efficiency and fitted to the IW function ${\xi }_B(w)$ with the procedure discussed in the text.

Figure 4

(a) The Isgur-Wise function fit for the decay ${\mathrm{\Lambda }}_b^0\to {\mathrm{\Lambda }}_c^{+}{\mu }^{-}\nu$ with a Taylor series expansion in ($w-1$) up to second order. The black dots show the data, and the solid (blue) line shows the fitted function with the second-order Taylor series expansion model. The vertical scale is in arbitrary units. (b) The correlation between slope ${\rho }^2$ and curvature ${\sigma }^2/2$; the three ellipses correspond to the $1\sigma$, $2\sigma$, and $4\sigma$ contours.

Figure 5

Comparison between the fit to the seven experimental data points using either the lattice QCD calculation of Ref. [19], shown as gray points with a shaded area corresponding to the binned $1\sigma$ theory uncertainty, or a single form-factor fit in the $z$-expansion, shown as the solid blue curve. The data points, modulo a scale factor, are shown as black points with error bars.