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Observation of the ${B^0 \to \rho^0 \rho^0}$ decay from an amplitude analysis of ${B^0 \to (\pi^+\pi^-)(\pi^+\pi^-)}$ decays

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Abstract

Proton-proton collision data recorded in 2011 and 2012 by the \lhcb experiment, co\-rres\-pon\-ding to an integrated luminosity of 3.0\invfb, are a\-na\-lysed to search for the charmless ${B^0 \to \rho^0 \rho^0}$ decay. More than 600 ${\B^0 \to (\pi^+\pi^-)(\pi^+\pi^-)}$ signal decays are selected and used to perform an amplitude analysis from which the ${B^0 \to \rho^0 \rho^0}$ decay is observed for the first time with 7.1 standard deviations significance. The fraction of ${B^0 \to \rho^0 \rho^0}$ decays yielding a longitudinally polarised final state is measured to be $\fL = 0.745^{+0.048}_{-0.058} ({\rm stat}) \pm 0.034 ({\rm syst})$. The ${B^0 \to \rho^0 \rho^0}$ branching fraction, using the ${\B^0 \to \phi K^*(892)^{0}}$ decay as reference, is also reported as ${\BF(B^0 \to \rho^0 \rho^0) = (0.94 \pm 0.17 ({\rm stat}) \pm 0.09 ({\rm syst}) \pm 0.06 ({\rm BF})) \times 10^{-6}}$.

Figures and captions

Reconstructed invariant mass spectrum of (left) $ (\pi ^+\pi ^-)(\pi ^+\pi ^-)$ and (right)$(K^+K^-)(K^+\pi^-)$. The data are represented by the black dots. The fit is represented by the solid blue line, the $ B ^0$ signal by the solid red line and the $ B ^0_ s $ by the solid green line. The combinatorial background is represented by the pink dotted line, the partially reconstructed background by the cyan dotted line and the cross-feed by the dark blue dashed line.

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Helicity angles for the $ (\pi ^+\pi ^-)(\pi ^+\pi ^-)$ system.

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Background-subtracted $M (\pi ^+\pi ^-) _{1,2}$, $\cos\theta_{1,2}$ and $\varphi$ distributions. The black dots correspond to the four-body background-subtracted data and the black line is the projection of the fit model. The specific decays $B^0\rightarrow \rho^0\rho^0$ (brown), $B^0 \rightarrow \omega \rho^0$ (dashed brown), $B^0\rightarrow VS$ (dashed blue), $B^0 \rightarrow SS$ (long dashed green), $B^0\rightarrow VT$ (orange) and $B^0 \rightarrow a_1^{\pm}\pi^{\mp}$ (light blue) are also displayed. The $B^0\rightarrow \rho^0\rho^0$ contribution is split into longitudinal (dashed red) and transverse (dotted red) components. Interference contributions are only plotted for the total (black) model. The efficiency for longitudinally polarized $B^0\rightarrow \rho^0\rho^0$ events is $\sim$5 times smaller than for the transverse component.

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Animated gif made out of all figures.

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Tables and captions

Yields from the simultaneous fit for the 2011 and 2012 data sets. The first and second uncertainties are the statistical and systematic contributions, respectively.

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Amplitudes, $A_i$, $ C P$ eigenvalues, $\eta_i$, and mass-angle distributions, $f_i$, of the $ { B ^0 \rightarrow (\pi ^+\pi ^-)(\pi ^+\pi ^-) }$ model. The indices ${ijkl}$ indicate the eight possible combinations of pairs of opposite-charge pions. The angles $\alpha_{kl}$, $\beta_{ij}$ and $\Phi_{kl}$ are defined in Ref. [38].

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Results of the unbinned maximum likelihood fit to the angular and two-body invariant mass distributions. The first uncertainty is statistical, the second systematic.

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Relative systematic uncertainties on the longitudinal polarisation parameter, $ f_{\rm L}$ , and the fraction of $ B ^0 \rightarrow \rho^0\rho^0$ decays in the $ { B ^0 \rightarrow (\pi ^+\pi ^-)(\pi ^+\pi ^-) }$ sample. The model uncertainty includes the three uncertainties below.

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Supplementary Material [file]

Supplementary material full pdf

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This ZIP file contains supplemetary material for the publication LHCb-PAPER-2015-006. The files are: Supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps : The figures in variuous formats

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Created on 27 April 2024.