Evidence for an $\eta_c(1S) \pi^-$ resonance in $B^0 \to \eta_c(1S) K^+\pi^-$ decays

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LHCb-PAPER-2018-034
EP-2018-245
arXiv:1809.07416 [PDF]

(Submitted on 19 Sep 2018)
EPJC
Inspire 1694990

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Abstract

A Dalitz plot analysis of $B^0 \to \eta_c(1S) K^+\pi^-$ decays is performed using data samples of $pp$ collisions collected with the LHCb detector at centre-of-mass energies of $\sqrt{s}=7, 8$ and $13$ TeV, corresponding to a total integrated luminosity of $4.7 \text{fb}^{-1}$. A satisfactory description of the data is obtained when including a contribution representing an exotic $\eta_c(1S) \pi^-$ resonant state. The significance of this exotic resonance is more than three standard deviations, while its mass and width are $4096 \pm 20 ^{+18}_{-22}$ MeV and $152 \pm 58 ^{+60}_{-35}$ MeV, respectively. The spin-parity assignments $J^P=0^+$ and $J^{P}=1^-$ are both consistent with the data. In addition, the first measurement of the $B^0 \to \eta_c(1S) K^+\pi^-$ branching fraction is performed and gives $\displaystyle \mathcal{B}(B^0 \to \eta_c(1S) K^+\pi^-) = (5.73 \pm 0.24 \pm 0.13 \pm 0.66) \times 10^{-4}$, where the first uncertainty is statistical, the second systematic, and the third is due to limited knowledge of external branching fractions.

Figures and captions

Feynman diagrams for \subref{B2etacKstar} $B^0 \rightarrow \eta_cK^{*0}$ and \subref{B2ZK} $B^0 \rightarrow Z_c^-K^+$ decay sequences.	Fig1a.pdf [24 KiB] HiDef png [32 KiB] Thumbnail [6 KiB] *.C file
	Fig1b.pdf [150 KiB] HiDef png [57 KiB] Thumbnail [13 KiB] *.C file
Distribution of the $ p $ $\overline p $ $ K ^+$ $\pi ^-$ invariant mass. The solid blue curve is the projection of the total fit result. The components are shown in the legend.	Fig2.pdf [38 KiB] HiDef png [257 KiB] Thumbnail [86 KiB] *.C file
Distribution of the $ p $ $\overline p $ invariant mass in (left) linear and (right) logarithmic vertical-axis scale for weighted $ B ^0 \!\rightarrow p \overline p K ^+ \pi ^- $ candidates obtained by using the sPlot technique. The solid blue curve is the projection of the total fit result. The full azure, tight-cross-hatched red and dashed-black line areas show the $\eta _ c $ , $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ and NR $ p $ $\overline p $ contributions, respectively.	Fig3a.pdf [22 KiB] HiDef png [290 KiB] Thumbnail [76 KiB] *.C file
	Fig3b.pdf [21 KiB] HiDef png [606 KiB] Thumbnail [96 KiB] *.C file
Results of the 2D mass fit to the joint [$ m( p \overline p K ^+ \pi ^- )$, $ m( p \overline p )$] distribution for the (a) Run 1 $ m( p \overline p K ^+ \pi ^- )$ projection, (b) Run 1 $ m( p \overline p )$ projection, (c) Run 2 $ m( p \overline p K ^+ \pi ^- )$ projection, and (d) Run 2 $ m( p \overline p )$ projection. The legend is shown in the top left plot.	Fig4a.pdf [21 KiB] HiDef png [273 KiB] Thumbnail [89 KiB] *.C file
	Fig4c.pdf [20 KiB] HiDef png [238 KiB] Thumbnail [76 KiB] *.C file
	Fig4b.pdf [21 KiB] HiDef png [246 KiB] Thumbnail [84 KiB] *.C file
	Fig4d.pdf [20 KiB] HiDef png [241 KiB] Thumbnail [78 KiB] *.C file
SDP distributions used in the DP fit to the Run 2 subsample for (a) combinatorial background and (b) NR $ B ^0 \!\rightarrow p \overline p K ^+ \pi ^- $ background.	Fig5a.pdf [20 KiB] HiDef png [158 KiB] Thumbnail [58 KiB] *.C file
	Fig5b.pdf [19 KiB] HiDef png [153 KiB] Thumbnail [58 KiB] *.C file
Background-subtracted (top) DP and (bottom) SDP distributions corresponding to the total data sample used in the analysis. The structure corresponding to the $K^*(892)^0$ resonance is evident. The veto of $ B ^0 \!\rightarrow \eta _ c K ^+ \pi ^- $ decays in the $\overline{ D }{} {}^0$ region is visible in the DP.	Fig6a.pdf [17 KiB] HiDef png [239 KiB] Thumbnail [125 KiB] *.C file
	Fig6b.pdf [17 KiB] HiDef png [229 KiB] Thumbnail [122 KiB] *.C file
$ B ^0 \!\rightarrow \eta _ c K ^+ \pi ^- $ signal efficiency across the SDP for the (a) Run 1 and (b) Run 2 samples.	Fig7a.pdf [20 KiB] HiDef png [216 KiB] Thumbnail [66 KiB] *.C file
	Fig7b.pdf [20 KiB] HiDef png [217 KiB] Thumbnail [66 KiB] *.C file
Projections of the data and amplitude fit using the baseline model onto (a) $ m( K ^+ \pi ^- )$, (c) $ m(\eta _ c \pi ^- )$ and (e) $ m(\eta _ c K ^+ )$, with the same projections shown in (b), (d) and (f) with a logarithmic vertical-axis scale. The veto of $ B ^0 \!\rightarrow p \overline p \overline{ D }{} {}^0 $ decays is visible in plot (b). The $ K ^+ \pi ^- $ S-wave component comprises the LASS and $K^*_0(1950)^0$ meson contributions. The components are described in the legend at the bottom.	Fig8a.pdf [23 KiB] HiDef png [166 KiB] Thumbnail [57 KiB] *.C file
	Fig8b.pdf [24 KiB] HiDef png [426 KiB] Thumbnail [83 KiB] *.C file
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	Fig8d.pdf [26 KiB] HiDef png [919 KiB] Thumbnail [122 KiB] *.C file
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	Fig8g.pdf [13 KiB] HiDef png [136 KiB] Thumbnail [35 KiB] *.C file
Projections of the data and amplitude fit using the nominal model onto (a) $ m( K ^+ \pi ^- )$, (c) $ m(\eta _ c \pi ^- )$ and (e) $ m(\eta _ c K ^+ )$, with the same projections shown in (b), (d) and (f) with a logarithmic vertical-axis scale. The veto of $ B ^0 \!\rightarrow p \overline p \overline{ D }{} {}^0 $ decays is visible in plot (b). The $ K ^+ \pi ^- $ S-wave component comprises the LASS and $K^*_0(1950)^0$ meson contributions. The components are described in the legend at the bottom.	Fig9a.pdf [23 KiB] HiDef png [163 KiB] Thumbnail [56 KiB] *.C file
	Fig9b.pdf [24 KiB] HiDef png [400 KiB] Thumbnail [82 KiB] *.C file
	Fig9c.pdf [24 KiB] HiDef png [250 KiB] Thumbnail [82 KiB] *.C file
	Fig9d.pdf [26 KiB] HiDef png [624 KiB] Thumbnail [102 KiB] *.C file
	Fig9e.pdf [24 KiB] HiDef png [252 KiB] Thumbnail [82 KiB] *.C file
	Fig9f.pdf [24 KiB] HiDef png [325 KiB] Thumbnail [82 KiB] *.C file
	Fig9g.pdf [13 KiB] HiDef png [129 KiB] Thumbnail [36 KiB] *.C file
Comparison of the first four $ K ^+ \pi ^- $ Legendre moments determined from background-subtracted data (black points) and from the results of the amplitude fit using the baseline model (red triangles) and nominal model (blue triangles) as a function of $ m( K ^+ \pi ^- )$.	Fig10a.pdf [22 KiB] HiDef png [175 KiB] Thumbnail [57 KiB] *.C file
	Fig10b.pdf [23 KiB] HiDef png [186 KiB] Thumbnail [63 KiB] *.C file
	Fig10c.pdf [22 KiB] HiDef png [191 KiB] Thumbnail [65 KiB] *.C file
	Fig10d.pdf [22 KiB] HiDef png [190 KiB] Thumbnail [65 KiB] *.C file
Comparison of the first four $\eta _ c \pi ^- $ Legendre moments determined from background-subtracted data (black points) and from the results of the amplitude fit using the baseline model (red triangles) and nominal model (blue triangles) as a function of $ m(\eta _ c \pi ^- )$.	Fig11a.pdf [23 KiB] HiDef png [206 KiB] Thumbnail [67 KiB] *.C file
	Fig11b.pdf [23 KiB] HiDef png [213 KiB] Thumbnail [74 KiB] *.C file
	Fig11c.pdf [23 KiB] HiDef png [205 KiB] Thumbnail [71 KiB] *.C file
	Fig11d.pdf [23 KiB] HiDef png [202 KiB] Thumbnail [69 KiB] *.C file
Comparison of the first four $\eta _ c K ^+ $ Legendre moments determined from background-subtracted data (black points) and from the results of the amplitude fit using the baseline model (red triangles) and nominal model (blue triangles) as a function of $ m(\eta _ c K ^+ )$.	Fig12a.pdf [22 KiB] HiDef png [206 KiB] Thumbnail [68 KiB] *.C file
	Fig12b.pdf [23 KiB] HiDef png [215 KiB] Thumbnail [73 KiB] *.C file
	Fig12c.pdf [23 KiB] HiDef png [212 KiB] Thumbnail [72 KiB] *.C file
	Fig12d.pdf [22 KiB] HiDef png [209 KiB] Thumbnail [71 KiB] *.C file
2D pull distribution for to the baseline model.	Fig13.pdf [22 KiB] HiDef png [167 KiB] Thumbnail [58 KiB] *.C file
2D pull distribution for to the nominal model.	Fig14.pdf [22 KiB] HiDef png [167 KiB] Thumbnail [58 KiB] *.C file
Animated gif made out of all figures.	PAPER-2018-034.gif Thumbnail

Tables and captions

Relative systematic uncertainties on the ratio $R$ of Eq. \eqref{ratio}. The total systematic uncertainty is obtained from the quadratic sum of the individual sources.	Table_0.pdf [24 KiB] HiDef png [43 KiB] Thumbnail [6 KiB] tex code
Yields of the components in the 2D mass fit to the joint [$ m( p \overline p K ^+ \pi ^- )$, $ m( p \overline p )$] distribution for the Run 1 and 2 subsamples.	Table_1.pdf [53 KiB] HiDef png [46 KiB] Thumbnail [7 KiB] tex code
Resonances included in the baseline model, where parameters and uncertainties are taken from Ref. \cite{PDG2016}. The LASS lineshape also parametrise the $ K ^+ \pi ^- $ S-wave in $ B ^0 \!\rightarrow \eta _ c K ^+ \pi ^- $ NR decays.	Table_2.pdf [52 KiB] HiDef png [79 KiB] Thumbnail [12 KiB] tex code
Complex coefficients and fit fractions determined from the DP fit using the nominal model. Uncertainties are statistical only.	Table_3.pdf [55 KiB] HiDef png [89 KiB] Thumbnail [14 KiB] tex code
Significance of the $Z_c(4100)^-$ contribution for the systematic effects producing the largest variations in the parameters of the $Z_c(4100)^-$ candidate. The values obtained in the nominal amplitude fit are shown in the first row.	Table_4.pdf [54 KiB] HiDef png [59 KiB] Thumbnail [9 KiB] tex code
Rejection level of the $J^P=0^+$ hypothesis with respect to the $J^P=1^-$ hypothesis for the systematic variations producing the largest variations in the parameters of the $Z_c(4100)^-$ candidate. The values obtained in the nominal amplitude fit are shown in the first row.	Table_5.pdf [54 KiB] HiDef png [56 KiB] Thumbnail [8 KiB] tex code
Fit fractions and their uncertainties. The quoted uncertainties are statistical and systematic, respectively.	Table_6.pdf [54 KiB] HiDef png [113 KiB] Thumbnail [19 KiB] tex code
Branching fraction results. The four quoted uncertainties are statistical, $ B ^0 \!\rightarrow \eta _ c K ^+ \pi ^- $ branching fraction systematic (not including the contribution from the uncertainty associated to the efficiency ratio, to avoid double counting the systematic uncertainty associated to the evaluation of the efficiencies), fit fraction systematic and external branching fractions uncertainties, respectively.	Table_7.pdf [55 KiB] HiDef png [78 KiB] Thumbnail [12 KiB] tex code