# Measurement of the shape of the $\Lambda_b^0\to\Lambda_c^+ \mu^- \overline{\nu}_{\mu}$ differential decay rate

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## Abstract

A measurement of the shape of the differential decay rate and the associated Isgur-Wise 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 proton-proton 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 four-momentum transfer between the heavy baryons, $q^2$, is compared with expectations from heavy-quark effective theory and from unquenched lattice QCD predictions.

## Figures and captions

 (a) The ln(IP/mm) distribution and (b) $p K ^- \pi ^+$ invariant mass for $\Lambda ^+_ c$ candidate combinations with a muon. The red (dashed-dotted) curves show the combinatorial $\Lambda ^+_ c$ background, the green (dashed) curves the $\Lambda ^+_ c$ from $\Lambda ^0_ b$ and the blue-solid curves the total yields. Fig1a.pdf [20 KiB] HiDef png [206 KiB] Thumbnail [163 KiB] *.C file Fig1b.pdf [21 KiB] HiDef png [219 KiB] Thumbnail [168 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 long-dashed line, (b) for $m>2700$ MeV, the $\Lambda_ c (2765)^+$ as magenta dashed line, and the $\Lambda_ c (2880)^+$ as green long-dashed line. Fig2a.pdf [22 KiB] HiDef png [253 KiB] Thumbnail [210 KiB] *.C file Fig2b.pdf [20 KiB] HiDef png [220 KiB] Thumbnail [182 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 [88 KiB] *.C file Fig3b.pdf [13 KiB] HiDef png [78 KiB] Thumbnail [78 KiB] *.C file (a) The Isgur-Wise function fit for the decay $\Lambda ^0_ b \rightarrow \Lambda ^+_ c \mu ^- \nu$ 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. Fig4a.pdf [14 KiB] HiDef png [107 KiB] Thumbnail [93 KiB] *.C file Fig4b.pdf [14 KiB] HiDef png [128 KiB] Thumbnail [122 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 [124 KiB] *.C file Animated gif made out of all figures. PAPER-2017-016.gif Thumbnail

## Tables and captions

 Predictions for the slope at zero recoil of the baryonic Isgur-Wise function $\xi _B$. The evaluation from Ref. [21] includes first-order corrections in HQET. Table_1.pdf [53 KiB] HiDef png [47 KiB] Thumbnail [24 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 [52 KiB] tex code Summary of the values for the slope and curvature of the Isgur-Wise 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 [21 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 [55 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 [20 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 [63 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 [43 KiB] tex code

Created on 17 August 2019.Citation count from INSPIRE on 20 August 2019.