The shape of the $B_s^0\rightarrow D_s^{*}\mu^+\nu_{\mu}$ differential decay rate is obtained as a function of the hadron recoil using protonproton collision data at a centreofmass energy of 13 TeV, corresponding to an integrated luminosity of 1.7 fb$^{1}$ collected by the LHCb detector. The $B_s^0\rightarrow D_s^{*}\mu^+\nu_{\mu}$ decay is reconstructed through the decays $D_s^{*}\rightarrow D_s^{}\gamma$ and $D_s^{}\rightarrow K^K^+\pi^$. The differential decay rate is fitted with the CapriniLellouchNeubert (CLN) and BoydGrinsteinLebed (BGL) parametrisations of the form factors, and the relevant quantities for both are extracted.
Schematic overview of the $ B ^0_ s \rightarrow D ^{*}_ s \mu ^+ \nu _\mu $ decay, introducing the angles $\theta_{D_s}$ , $\theta_{\mu}$ and $\chi$. 
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Distribution of the reconstructed $ D ^_ s \gamma $ mass, $m( D ^_ s \gamma )$, with the fit overlaid. The fit is performed constraining the $ D ^_ s $ mass to the worldaverage value [16]. The signal and background components are shown separately with dashed red and dotted green lines, respectively. 
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Distribution of the corrected mass, $m_{\rm corr}$, for the seven bins of $ w$ , overlaid with the fit results. The $ B ^0_ s \rightarrow D _{ s 1}(2460)^ \tau ^+ \nu _\tau $ and the $ B ^0_ s \rightarrow D _{ s 1}(2460)^ \mu ^+ \nu _\mu $ components are combined in $ B ^0_ s \rightarrow D _{ s 1}(2460)^ \ell^+ \nu _\ell $ . Below each plot, differences between the data and fit are shown, normalised by the uncertainty in the data. 
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Distribution of (top right) $\chi$, (bottom left) $\cos(\theta_{D_s} )$ and (bottom right) $\cos(\theta_{\mu} )$ integrating over $w$ and the other decay angles from data (black points) compared to the distribution from simulation with their relative size extracted from the fit to the corrected mass. The $ B ^0_ s \rightarrow D _{ s 1}(2460)^ \tau ^+ \nu _\tau $ and the $ B ^0_ s \rightarrow D _{ s 1}(2460)^ \mu ^+ \nu _\mu $ components are combined in $ B ^0_ s \rightarrow D _{ s 1}(2460)^ \ell^+ \nu _\ell $ . The uncertainties on the templates, indicated by the hashed areas in the figures, are a combination from all templates. 
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$\Delta$ $\chi^2$ contours for the scaled parameters $a_1^f/a_0^f$ versus $a_2^f/a_0^f$. The black cross marks the bestfit central value. The solid (dashed) contour encloses the $\Delta$ $\chi^2$ = 2.3 (6.17) region. The observed shape is due to the applied unitarity condition, see Eq. ???. 
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Unfolded normalised differential decay rate with the fit superimposed for the CLN parametrisation (green), and BGL (red). The band in the fit results includes both the statistical and systematic uncertainty on the data yields. 
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Total efficiency as a function of $ w_{\rm true}$ , including the acceptance of the LHCb detector as well as the reconstruction and selection efficiencies. 
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$\Delta$ $\chi^2$ contours for the scaled parameters $a_1^f$ versus $a_2^f$. The black cross marks the bestfit central value. The solid (dashed) contour encloses the $\Delta$ $\chi^2$ = 2.3 (6.17) region. The observed shape is due to the applied unitarity condition, see Eq. 11. 
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Comparison between the $ w$ spectrum measured in this paper to the normalised $\Delta\Gamma/\Delta w $ spectra inferred from the CLN and BGL parametrisations in Ref. [7]. 
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Animated gif made out of all figures. 
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Binning scheme used for this measurement. Only the upper bound for each bin is presented. The lower bound on the first bin corresponds to $w=1$. 
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Fraction of the unfolded yields corrected for the global efficiencies, $N^{\mathrm{unf}}_{\mathrm{corr}}$, for each $ w$ bin. Also shown in this table is the breakdown of the systematic and statistical uncertainties on $N^{\mathrm{unf}}_{\mathrm{corr}}$. These are shown as a fraction of the unfolded yield. 
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Correlation matrix for the unfolded data set in bins of $ w$ , including both statistical and systematic uncertainties. 
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Summary of the systematic and statistical uncertainties on the parameters $\rho^2$, $a_1^f$ and $a_2^f$ from the unfolded CLN and BGL fits. The total systematic uncertainty is obtained by adding the individual components in quadrature. 
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Results from different fit configurations, where the first uncertainty is statistical and the second systematic. 
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Covariance matrix for the unfolded data set in bins of $ w$ , including both statistical and systematic uncertainties in units of $10^{5}$. 
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Response matrix, containing the migration from $ w_{\rm true}$ to $w$ bins together with the total efficiency in units of $10^{4}$. 
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Fit inputs used for the BGL fit, taken from Ref. [17] and Ref. [24]. 
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Supplementary material full pdf 
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This ZIP file contains supplementary material for the publication LHCbPAPER2019046. The files are: supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps, *.C : The figures in various formats 
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Created on 20 February 2021.