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Analysis of the resonant components in $\overline{B}^0_s \to J/\psi\pi^+\pi^-$

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Abstract

The decay Bs->J/\psi\pi+\pi- can be exploited to study CP violation. A detailed understanding of its structure is imperative in order to optimize its usefulness. An analysis of this three-body final state is performed using a 1.0/fb sample of data produced in 7 TeV pp collisions at the LHC and collected by the LHCb experiment. A modified Dalitz plot analysis of the final state is performed using both the invariant mass spectra and the decay angular distributions. The \pi+\pi- system is shown to be dominantly in an S-wave state, and the CP-odd fraction in this Bs decay is shown to be greater than 0.977 at 95% confidence level. In addition, we report the first measurement of the J/\psi\pi+\pi- branching fraction relative to J/\psi\phi of (19.79 +/- 0.47 +/- 0.52)%.

Figures and captions

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

feyn1.pdf [87 KiB]
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(a) Invariant mass spectrum of $J/\psi K^+K^-$ for candidates with $m(K^+K^-)<1050$ MeV. The data has been fitted with a double-Gaussian signal and linear background functions shown as a dashed line. The solid curve shows the sum. (b) Background subtracted invariant mass spectrum of $K^+K^-$ for events with $m(K^+K^-)<1050$ MeV. The dashed line (barely visible along the $x$-axis) shows the S-wave contribution and the solid curve is the sum of the S-wave and a P-wave Breit-Wigner functions, fitted to the data.

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JpsiKK.pdf

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

fitmass.pdf [41 KiB]
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fitmass.pdf

Background subtracted $\chi$ distribution from $\overline{ B }{} ^0_ s \rightarrow J/\psi \pi^+\pi^-$ candidates.

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bkgsubchi.pdf

Distribution of $m(J/\psi \pi^+)$ for $\overline{ B }{} ^0_ s \rightarrow J/\psi \pi^+\pi^-$ candidate decays within $\pm20$ MeV of $\overline{ B }{} ^0_ s $ mass shown with the (blue) solid line; $m(J/\psi \pi^+)$ for wrong-sign $J/\psi \pi^+\pi^+$ combinations is shown with the (red) dashed line, as an estimate of the background.

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m-jpsipi.pdf

Distribution of $s_{23}\equiv m^2(\pi^+\pi^-)$ versus $s_{12}\equiv m^2(J/\psi\pi^+)$ for $\overline{ B }{} ^0_ s $ candidate decays within $\pm20$ MeV of $\overline{ B }{} ^0_ s $ mass.

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dalitz-1.pdf

Parametrized detection efficiency as a function of $s_{23}\equiv m^2(\pi^+\pi^-)$ versus $s_{12}\equiv m^2(J/\psi\pi^+)$. The scale is arbitrary.

effmod[..].pdf [582 KiB]
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effmodel_patrick.pdf

Projections of invariant mass squared of (a) $s_{12}\equiv m^2(J/\psi \pi^+)$ and (b) $s_{23}\equiv m^2(\pi^+\pi^-)$ of the MC Dalitz plot used to measure the efficiency parameters. The points represent the MC generated event distributions and the curves the polynomial fit.

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eff.pdf

Distributions of (a) $\cos\theta_{J/\psi}$, (b) $\cos\theta_{KK}$ for $J/\psi\phi$ background subtracted data (points) compared with the MC simulation (histogram).

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cos_theta.pdf

Projections of invariant mass squared of (a) $s_{12}\equiv m^2(J/\psi \pi^+)$ and (b) $s_{23}\equiv m^2(\pi^{\pm}\pi^{\pm})$ of the background Dalitz plot.

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xy_bkgnew.pdf

The $\cos\theta_{J/\psi}$ distribution of the background and the fitted function $1+\alpha\cos\theta_{J/\psi}+\beta \cos^{2}\theta_{J/\psi}$.

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bkg_cosH.pdf

Dalitz fit projections of $m^2(\pi^+ \pi^-)$ fit with 3R+NR for the preferred model. 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. The normalized residuals in each bin are shown below, defined as the difference between the data and the fit divided by the error on the data.

mpipi-[..].pdf [82 KiB]
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mpipi-fits2-single.pdf

Dalitz fit projections of (a) $s_{12}\equiv m^2(J/\psi \pi^{+})$ and (b) $\cos \theta_{J/\psi}$ fit with the 3R+NR preferred model. 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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8R1-R3.pdf

Background subtracted and acceptance corrected $\cos \theta_{J/\psi}$ helicity distributions fit with the preferred model: (a) in $f_0(980)$ mass region defined within $\pm90$ MeV of 980 MeV ($\chi^2$/ndf =39/40), (b) in $f_2(1270)$ mass region defined within one full width of $f_2(1270)$ mass ($\chi^2$/ndf =25/40), (c) in $f_0(1370)$ mass region defined within one full width of $f_2(1370)$ mass ($\chi^2$/ndf = 24/40). The points with error bars are data and the solid blue lines show the fit from the 3R+NR model.

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2JPsi2_all.pdf

Background subtracted and acceptance corrected $\cos \theta_{\pi\pi}$ helicity distributions fit the preferred model: (a) in $f_0(980)$ mass region defined within $\pm90$ MeV of 980 MeV ($\chi^2$/ndf =38/40), (b) in $f_2(1270)$ mass region defined within one full width of $f_2(1270)$ mass ($\chi^2$/ndf = 32/40), (c) in $f_0(1370)$ mass region defined within one full width of $f_2(1370)$ mass ($\chi^2$/ndf =37/40). The points with error bars are data and the solid blue lines show the fit from the 3R+NR model.

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2PP2_all.pdf

Background subtracted and acceptance corrected $\cos \theta_{\pi\pi}$ helicity distributions fit the preferred model: (a) in $[-90,0]$ MeV of 980 MeV ($\chi^2$/ndf =41/40), (b) in $[0,90]$ MeV of 980 MeV ($\chi^2$/ndf =31/40)

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2sol2_all.pdf

The $\pi^+\pi^-$ mass dependence of the spherical harmonic moments of $\cos \theta_{\pi\pi}$ after efficiency corrections and background subtraction: (a) $\langle Y^0_0\rangle$, (b) $\langle Y^0_1\rangle$, (c) $\langle Y^0_2\rangle$, (d) $\langle Y^0_3\rangle$, (e) $\langle Y^0_4\rangle$, (f) $\langle Y^0_5\rangle$, (g) $\langle Y^0_6\rangle$, and (h) $\langle Y^0_7\rangle$. The points with error bars are the data points and the solid curves are derived from the 3R+NR preferred model.

2SPH.pdf [102 KiB]
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2SPH.pdf

Detection efficiency of $\overline{ B }{} ^0_ s \rightarrow J/\psi\pi^+\pi^-$ as a function of $s_{23}\equiv m^{2}(\pi^+\pi^-)$.

jpsipi[..].pdf [34 KiB]
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jpsipipieff.pdf

Animated gif made out of all figures.

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Tables and captions

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

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Models used in data fit.

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Breit-Wigner resonance parameters.

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Table_3.pdf

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

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Table_4.pdf

Fit fractions (%) of contributing components for the preferred model. For P- and D-waves $\lambda$ represents the final state helicity. Here $\rho$ refers to the $\rho(770)$ meson.

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Table_5.pdf

Fit fractions (%) of contributing components from different models for the alternate solution. For P- and D-waves $\lambda$ represents the final state helicity. Here $\rho$ refers to the $\rho(770)$ meson.

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Table_6.pdf

Fit fractions (%) of interference terms for both solutions of the 3R+NR model.

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Table_7.pdf

Fit results from the 3R+NR model for both the preferred and alternate solutions. $\phi$ indicates the phase with respect to the $f_0(980)$. For the $f_2(1270)$, $\lambda$ represents the final state helicity.

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Normalized fit fractions (%) for alternate and preferred 3R+NR models and the ratio $R$ (%) relative to $\overline{ B }{} ^0_ s \rightarrow J/\psi\phi$. The numbers for the $f_2(1270)$ refer only to the $\lambda=0$ state.

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Table_9.pdf

Relative systematic uncertainties on $R$(%).

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Table_10.pdf

Changes due to modified acceptance function.

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Table_11.pdf

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