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Measurement of resonant and $CP$ components in $\overline{B}_s^0\to J/\psi\pi^+\pi^-$ decays

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Abstract

The resonant structure of the decay $\overline{B}_s^0\to J/\psi\pi^+\pi^-$ is studied using data corresponding to 3 fb$^{-1}$ of integrated luminosity from $pp$ collisions by the LHC and collected by the LHCb detector. Five interfering $\pi^+\pi^-$ states are required to describe the decay: $f_0(980),f_0(1500),f_0(1790),f_2(1270)$, and $f_2^{\prime}(1525)$. An alternative model including these states and a non-resonant $J/\psi \pi^+\pi^-$ component also provides a good description of the data. Based on the different transversity components measured for the spin-2 intermediate states, the final state is found to be compatible with being entirely $CP$-odd. The $CP$-even part is found to be $<2.3$% at 95% confidence level. The $f_0(500)$ state is not observed, allowing a limit to be set on the absolute value of the mixing angle with the $f_0(980)$ of $<7.7^{\circ}$ at 90% confidence level, consistent with a tetraquark interpretation of the $f_0(980)$ substructure.

Figures and captions

Leading order diagram for $\overline{ B }{} ^0_ s $ decays into $J/\psi \pi^+\pi^-$.

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feyn1.pdf

Definition of helicity angles. For details see text.

helAng[..].pdf [26 KiB]
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helAngles-ss.pdf

Distributions of the BDT classifier for both training and test samples of $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi^+\pi^-$ signal and background events. The signal samples are from simulation and the background samples are from data.

overtr[..].pdf [86 KiB]
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overtrain_BDT_new.pdf

Invariant mass of $J/\psi \pi^+\pi^-$ combinations. The data have been fitted with double Crystal Ball signal and several background functions. The (red) solid curve shows the $\overline{ B }{} ^0_ s $ signal, the (brown) dotted line shows the combinatorial background, the (green) short-dashed line shows the $B^-$ background, the (purple) dot-dashed curve is $\overline{ B }{} ^0 \rightarrow J/\psi \pi^+\pi^-$, the (light blue) long-dashed line is the sum of $\overline{ B }{} ^0_ s \rightarrow J/\psi\eta'$, $\overline{ B }{} ^0_ s \rightarrow J/\psi\phi$ with $\phi\rightarrow \pi^+\pi^-\pi^0$ backgrounds and the $\Lambda _b^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K^- p$ reflection, the (black) dot-long dashed curve is the $\overline{ B }{} ^0 \rightarrow J/\psi K^- \pi^+$ reflection and the (blue) solid curve is the total.

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Distribution of $m^2(\pi^+\pi^-)$ versus $m^2(J/\psi\pi^+)$ for all events within $\pm20$ MeV of the $\overline{ B }{} ^0_ s $ mass peak.

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Distributions of (a) $m(J/\psi \pi^+)$ and (b) $m(\pi^+\pi^-)$ for $\overline{ B }{} ^0_ s \rightarrow J/\psi \pi^+\pi^-$ candidate decays within $\pm20$ MeV of the $\overline{ B }{} ^0_ s $ mass. The (red) points with error bars show the background contribution determined from $m(J/\psi \pi^+\pi^-)$ fits performed in each bin of the plotted variables.

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mjpsipi-data.pdf
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mpp-data.pdf

Distribution of the angle $\chi$ for the $J/\psi \pi^+\pi^-$ simulation sample fitted with Eq. (10), used to determine the efficiency parameters.

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chi_acc.pdf

Second order polynomial fit to the acceptance parameter $a(m^2_{hh})$ used in Eq. 11.

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cosH_acc.pdf

Projections of invariant mass squared of (a) $m^2(J/\psi \pi^+)$ and (b) $m^2(J/\psi \pi^-)$ of the simulated Dalitz plot used to measure the efficiency parameters. The points represent the simulated event distributions and the curves the polynomial fit.

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effx.pdf
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effz.pdf

Parameterization of the detection efficiency as a function of $\cos\theta_{\pi^+\pi^-}$ and $m(\pi^+\pi^-)$. The scale is arbitrary.

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acc3.pdf

Distribution of $\cos\theta_{J/\psi}$ of the other background and the fitted function $1+\alpha\cos^2\theta_{J/\psi}$. The points with error bars show the background obtained from candidate mass fits in bins of $\cos\theta_{J/\psi}$.

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Projections of (a) $\cos\theta_{\pi\pi}$ and (b) $m(\pi^+\pi^-)$ of the total background. The (blue) histogram or curve is projection of the fit, and the points with error bars show the like-sign combinations added with additional $\rho^0$ background.

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coshh-bkg.pdf
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Distribution of $\chi$ of the total background and the fitted function. The points with error bars show the like-sign combinations added with additional $\rho^0$ background.

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chi_bkg.pdf

Projections of (a) $m(\pi^+\pi^-)$, (b) $\cos\theta_{\pi\pi}$, (c) $\cos \theta_{J/\psi}$ and (d) $\chi$ for 5R Solution I. The points with error bars are data, the signal fit is shown with a (red) dashed line, the background with a (black) dotted line, and the (blue) solid line represents the total.

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5RSol1.pdf

Projections of (a) $m(\pi^+\pi^-)$, (b) $\cos\theta_{\pi\pi}$, (c) $\cos \theta_{J/\psi}$ and (d) $\chi$ for 5R+NR Solution II. The points with error bars are data, the signal fit is shown with a (red) dashed line, the background with a (black) dotted line, and the (blue) solid line represents the total.

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Distribution of $m(\pi^+\pi^-)$ with contributing components labeled from 5R Solution I.

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Distribution of $m(\pi^+\pi^-)$ with contributing components labeled from 5R+NR Solution II.

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S-wave (a) amplitude strength and (b) phase as a function of $m(\pi^+\pi^-)$ from the 5R Solution I (open) and 5R+NR Solution II (solid), where the widths of the curves reflect $\pm1\sigma$ statistical uncertainties. The reference point is chosen at 980 MeV with amplitude strength equal to 1 and phase equal to 0.

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amp.pdf
ph.pdf [34 KiB]
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The $\pi^+\pi^-$ mass dependence of the spherical harmonic moments of $\cos \theta_{\pi\pi}$ after efficiency corrections and background subtraction: (a) $\langle Y^0_0\rangle$ ($\chi^2$/ndf =78/70), (b) $\langle Y^0_1\rangle$ ($\chi^2$/ndf =37/70), (c) $\langle Y^0_2\rangle$ ($\chi^2$/ndf =79/70), (d) $\langle Y^0_3\rangle$ ($\chi^2$/ndf =42/70), (e) $\langle Y^0_4\rangle$ ($\chi^2$/ndf =43/70), (f) $\langle Y^0_5\rangle$ ($\chi^2$/ndf =35/70). The points with error bars are the data points and the solid curves are derived from the model 5R Solution I.

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shy5.pdf

The $\pi^+\pi^-$ mass dependence of the spherical harmonic moments of $\cos \theta_{\pi\pi}$ after efficiency corrections and background subtraction: (a) $\langle Y^0_0\rangle$ ($\chi^2$/ndf =73/70), (b) $\langle Y^0_1\rangle$ ($\chi^2$/ndf =36/70), (c) $\langle Y^0_2\rangle$ ($\chi^2$/ndf =72/70), (d) $\langle Y^0_3\rangle$ ($\chi^2$/ndf =43/70), (e) $\langle Y^0_4\rangle$ ($\chi^2$/ndf =41/70), (f) $\langle Y^0_5\rangle$ ($\chi^2$/ndf =34/70). The points with error bars are the data points and the solid curves are derived from the model 5R+NR Solution II.

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Animated gif made out of all figures.

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Tables and captions

$ C\!P$ parity for different spin resonances. Note that spin-0 only has the transversity component $0$.

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Possible resonance candidates in the $\overline{ B }{} ^0_ s \rightarrow J/\psi \pi^+\pi^-$ decay mode and their parameters used in the fit.

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Fit $\rm -ln\mathcal{L}$ and $\chi^2/\text{ndf}$ of different resonance models.

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Fit fractions (%) of contributing components for both solutions.

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Non-zero interference fraction (%) for both solutions.

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Fitted resonance phase differences ($^\circ$).

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Other fit parameters. The uncertainties are only statistical.

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Absolute systematic uncertainties for Solution I.

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Absolute systematic uncertainties for Solution II.

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Fit fraction ranges taking $1\sigma$ regions for both solutions including systematic uncertainties.

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Created on 09 December 2018.Citation count from INSPIRE on 18 December 2018.