A measurement of the shape of the differential decay rate and the associated IsgurWise function for the decay $\Lambda_b^0\to\Lambda_c^+\mu^\overline{\nu}$ is reported, using data corresponding to $3 fb^{1}$ collected with the LHCb detector in protonproton collisions. The $\Lambda_c^+\mu^\overline{\nu}$(+ anything) final states are reconstructed through the detection of a muon and a $\Lambda_c^+$ baryon decaying into $pK^\pi^+$, and the decays $\Lambda_b^0\to\Lambda_c^+\pi^+\pi^\mu^\overline{\nu}$ are used to determine contributions from $\Lambda_b^0\to \Lambda_c^{\star+}\mu ^\bar{\nu}$ decays. The measured dependence of the differential decay rate upon the squared fourmomentum transfer between the heavy baryons, $q^2$, is compared with expectations from heavyquark effective theory and from unquenched lattice QCD predictions.
(a) The ln(IP/mm) distribution and (b) $p K ^ \pi ^+ $ invariant mass for $\Lambda ^+_ c $ candidate combinations with a muon. The red (dasheddotted) curves show the combinatorial $\Lambda ^+_ c $ background, the green (dashed) curves the $\Lambda ^+_ c $ from $\Lambda ^0_ b $ and the bluesolid curves the total yields. 
Fig1a.pdf [20 KiB] HiDef png [206 KiB] Thumbnail [67 KiB] *.C file 

Fig1b.pdf [21 KiB] HiDef png [219 KiB] Thumbnail [69 KiB] *.C file 

The mass difference $m(p K ^ \pi ^+ \pi ^+ \pi ^ )m(p K ^ \pi ^+ )$ added to the known $\Lambda ^+_ c $ mass, $m_{\rm PDG}(\Lambda ^+_ c )$ [14], for candidates with $p K ^ \pi ^+ $ invariant mass within $\pm$20 MeV of the known $\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 $\Lambda ^+_ c $ instead of $\pi ^+ \pi ^ $. The signal fits are identified as follows: (a) for $m<2700$ MeV, the $\Lambda_ c (2595)^+ $ as magenta dashed line, and the $\Lambda_ c (2625)^+ $ as green longdashed line, (b) for $m>2700$ MeV, the $\Lambda_ c (2765)^+ $ as magenta dashed line, and the $\Lambda_ c (2880)^+ $ as green longdashed line. 
Fig2a.pdf [22 KiB] HiDef png [253 KiB] Thumbnail [83 KiB] *.C file 

Fig2b.pdf [20 KiB] HiDef png [220 KiB] Thumbnail [74 KiB] *.C file 

The spectra (a) $dN_{\rm meas}/dw$ before unfolding and (b) $dN_{\rm u}/dw$ after unfolding, for the decay $\Lambda ^0_ b \rightarrow \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. 
Fig3a.pdf [14 KiB] HiDef png [90 KiB] Thumbnail [39 KiB] *.C file 

Fig3b.pdf [13 KiB] HiDef png [78 KiB] Thumbnail [35 KiB] *.C file 

(a) The IsgurWise function fit for the decay $\Lambda ^0_ b \rightarrow \Lambda ^+_ c \mu ^ \nu$ with a Taylor series expansion in $(w1)$ up to second order. The black dots show the data and the solid (blue) line shows the fitted function with the secondorder 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. 
Fig4a.pdf [14 KiB] HiDef png [107 KiB] Thumbnail [40 KiB] *.C file 

Fig4b.pdf [14 KiB] HiDef png [128 KiB] Thumbnail [47 KiB] *.C file 

Comparison between the fit to the seven experimental data points using either the Lattice QCD calculation of Ref. [19], shown as grey 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. 
Fig5.pdf [16 KiB] HiDef png [135 KiB] Thumbnail [51 KiB] *.C file 

Animated gif made out of all figures. 
PAPER2017016.gif Thumbnail 
Predictions for the slope at zero recoil of the baryonic IsgurWise function $\xi _B$. The evaluation from Ref. [21] includes firstorder corrections in HQET. 
Table_1.pdf [53 KiB] HiDef png [47 KiB] Thumbnail [8 KiB] tex code 

Measured raw yields for the four $\Lambda_ c ^{\ast +} \mu ^ \overline{\nu } _\mu $ final states and the inclusive $\Lambda ^+_ c \mu ^ \overline{\nu } _\mu X$. 
Table_2.pdf [50 KiB] HiDef png [122 KiB] Thumbnail [18 KiB] tex code 

Summary of the values for the slope and curvature of the IsgurWise function with different parameterizations. The quoted uncertainties are statistical only. The models marked with "*" have only the slope at zero recoil as a free parameter, thus the curvature is derived from the fitted $\rho^2$. 
Table_3.pdf [38 KiB] HiDef png [42 KiB] Thumbnail [7 KiB] tex code 

Summary of the systematic uncertainties on the slope parameter $\rho^2$. The total uncertainty is obtained by adding the individual components in quadrature. 
Table_4.pdf [56 KiB] HiDef png [113 KiB] Thumbnail [18 KiB] tex code 

Masses of the relevant form factor poles in the physical limit (in GeV). 
Table_5.pdf [50 KiB] HiDef png [40 KiB] Thumbnail [7 KiB] tex code 

Measured normalized yields $dN_{\rm corr}(\Lambda ^0_ b \rightarrow \Lambda ^+_ c \mu ^ \overline{\nu } _\mu )/d q^2 $ . 
Table_6.pdf [34 KiB] HiDef png [192 KiB] Thumbnail [25 KiB] tex code 

Covariance matrix of the measured normalized yields ${\rm Cov}[dN_{\rm corr}(\Lambda ^0_ b \rightarrow \Lambda ^+_ c \mu ^ \overline{\nu } _\mu )/d q^2 $] . 
Table_7.pdf [27 KiB] HiDef png [93 KiB] Thumbnail [14 KiB] tex code 
Created on 23 February 2019.Citation count from INSPIRE on 23 February 2019.