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Determination of quantum numbers for several excited charmed mesons observed in $B^- \to D^{*+} \pi^- \pi^-$ decays

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Abstract

A four-body amplitude analysis of the $B^- \to D^{*+} \pi^- \pi^-$ decay is performed, where fractions and relative phases of the various resonances contributing to the decay are measured. Several quasi-model-independent analyses are performed aimed at searching for the presence of new states and establishing the quantum numbers of previously observed charmed meson resonances. In particular the resonance parameters and quantum numbers are determined for the $D_1(2420)$, $D_1(2430)$, $D_0(2550)$, $D^*_1(2600)$, $D_2(2740)$ and $D^*_3(2750)$ states. The mixing between the $D_1(2420)$ and $D_1(2430)$ resonances is studied and the mixing parameters are measured. The dataset corresponds to an integrated luminosity of 4.7 $fb^{-1}$, collected in proton-proton collisions at center-of-mass energies of 7, 8 and 13 TeV with the LHCb detector.

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Distribution of (a) $m( K ^- \pi ^+ \pi^+_{\rm s})-m( K ^- \pi ^+ )+m_{D^0}^{\rm PDG}$ and (b) $ D ^{*+} \pi ^- \pi ^- $ invariant masses for candidates after the selection on the $\chi^2/\mathrm{ndf} $ from the fit to the $ B ^- $ decay tree.

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Mass distribution for $ D ^{*+} \pi ^- \pi ^- $ candidates after the selection $\cal R >0.5$. The full (red) line is the result from the fit while the dotted (blue) line describes the background. The vertical dashed lines indicate the signal region.

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Dalitz plot distribution for $ B ^- \rightarrow D ^{*+} \pi ^- \pi ^- $ candidates in Run 2 data.

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Distribution of $m( D ^{*+} \pi ^- )_{\rm low}$ for the total dataset.

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Definition of the angles (a) $\theta_H$, (b) $\theta$ and (c) $\gamma$ .

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Two-dimensional distribution of $\cos \theta_H$ vs. $m( D ^{*+} \pi ^- )_{\rm low}$. The vertical lines indicate the positions of the $ D_1(2420)$ and $ D^*_2(2460)$ resonances.

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Distribution for low/high-purity selection (filled black/open red points) for (a) $m( D ^{*+} \pi ^- )_{\rm low}$ and (c) $\cos \theta$. Signal-subtracted distributions for (b) $m( D ^{*+} \pi ^- )_{\rm low}$ and (d) $\cos \theta$ with superimposed fit curves described in the text.

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Interpolated efficiency as a function of $\log(m( D ^{*+} \pi ^- )/\text{ Me V} )$ and $\cos \theta$ for (a) Run 1 and (b) Run 2 data. The line indicates the regions where $\log(m( D ^{*+} \pi ^- )/\text{ Me V} )$ is taken as $\log(m( D ^{*+} \pi ^- )_{\rm low}/\text{ Me V} )$ (left side of the line) and as $\log(m( D ^{*+} \pi ^- )_{\rm high}/\text{ Me V} )$ (right side of the line).

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(a) Magnitude and (b) phase of the $1^+S$ amplitude from the QMI method. The red circles indicate the mass bin where the complex amplitude has been fixed.

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(a) Magnitude and (b) phase of the $J^P=0^-$ amplitude from the QMI method. The red circle indicates the mass bin where the complex amplitude has been fixed. The curves are the result from the fit described in the text.

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(a) Magnitude and (b) phase of the $J^P=1^-$ amplitude from the QMI method. The red circle indicates the mass bin where the complex amplitude has been fixed. The curves represent the Breit--Wigner function describing the $ D^*_{1}(2600)$ resonance.

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(a) Magnitude and (b) phase of the $J^P=1^+D$ amplitude from the QMI method. The red circle indicates the mass bin where the complex amplitude has been fixed. The curves represent the Breit--Wigner function describing the $ D_1(2420)$ resonance.

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(a) Magnitude and (b) phase of the $J^P=2^+$ amplitude from the QMI method. The red circle indicates the mass bin where the complex amplitude has been fixed. The curves represent the Breit--Wigner function describing the $ D^*_2(2460)$ resonance.

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Projections of the fit to Run 2 data from the QMI fitting model. The background contribution is shown in gray. Data are represented with filled dots and the line is the results from the fit.

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Projections of the fit to the total dataset from the QMI fitting model with (a,b) all amplitude contributions and (c) the significant interference terms.

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Legendre polynomial moments $Y_L^0(\cos \theta)$ as functions of $m( D ^{*+} \pi ^- )$ for Run 2 data. The data are represented by filled dots and the superimposed histograms result from the amplitude analysis described in the text.

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Distributions of the Legendre polynomial moments (a) $Y_2^H (\cos \theta_H)$ and (b) $Y_2^{\gamma}(\cos \gamma)$ as a function of $m( D ^{*+} \pi ^- )$ for Run 2 data. The data are represented by filled dots while the superimposed histograms result from the amplitude analysis described in the text. The vertical lines indicate the positions of the $ D_1(2420)$ , $ D^*_2(2460)$ and $ D^*_{1}(2600)$ resonances.

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Animated gif made out of all figures.

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Tables and captions

List of the amplitudes used in the present analysis.

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Resonance parameters from the amplitude analysis. The first uncertainty is statistical, the second systematic. The upper part reports the resonance parameters obtained from the amplitude analysis described in Sec. 7, the lower part those obtained from the mixing analysis described in Sec. 8.3. The labels indicating the spin-parity of $ D_0(2550)$ , $ D^*_{1}(2600)$ , and $ D_{2}(2740)$ resonances are updated, with respect to those reported in Ref. [3], according to the results from the amplitude analysis reported in this work. The $ D^*_2(2460)$ parameters are fixed to the world averages.

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Fit results from the amplitude analysis for the model where the $J^P=1^+S$ and $J^P=0^-$ amplitudes are described by QMI. The first uncertainty is statistical, the second systematic.

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Absolute systematic uncertainties on the fractions (in %) (top), and phases (bottom) for the model where the $J^P=1^+S$ and $J^P=0^-$ amplitudes are described by QMI.

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Systematic uncertainties contributions to the measured mass and width (in MeV) of the different resonances contributing to the $ B ^- $ decay.

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Relationship between the Legendre polynomial moments $Y_L^0$ and spin amplitudes. In the column describing the interfering amplitudes, the left side amplitude is intended to interfere with any of the amplitudes listed on the right side.

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Comparison of the resonance parameters measured in the present work with previous measurements. The first uncertainty is statistical, the second systematic.

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Fit results from the amplitude analysis for the model where the $ D_1(2430)$ and $ D_0(2550)$ resonances are described by relativistic Breit--Wigner functions. The first uncertainty is statistical, the second systematic.

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Fit results from the mixing model. The first uncertainty is statistical, the second systematic.

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Summary of the measurements of the branching fractions. The first uncertainty is statistical, the second systematic, the third is due to the uncertainty on the measurement of the $B^- \rightarrow D^{*+} \pi^- \pi^-$ absolute branching fraction. A comparison with measurements obtained by the Belle collaboration [4] is shown.

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Created on 06 December 2019.