# 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. Fig1a.pdf [22 KiB] HiDef png [342 KiB] Thumbnail [241 KiB] *.C file Fig1b.pdf [21 KiB] HiDef png [287 KiB] Thumbnail [216 KiB] *.C file Helicity angles for the $(\pi ^+\pi ^-)(\pi ^+\pi ^-)$ system. Fig2.pdf [7 KiB] HiDef png [79 KiB] Thumbnail [41 KiB] *.C file 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. Fig3a.pdf [24 KiB] HiDef png [474 KiB] Thumbnail [377 KiB] *.C file Fig3b.pdf [22 KiB] HiDef png [324 KiB] Thumbnail [240 KiB] *.C file Fig3c.pdf [19 KiB] HiDef png [228 KiB] Thumbnail [189 KiB] *.C file Animated gif made out of all figures. PAPER-2015-006.gif Thumbnail

## 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. Table_1.pdf [49 KiB] HiDef png [66 KiB] Thumbnail [36 KiB] tex code 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]. Table_2.pdf [70 KiB] HiDef png [98 KiB] Thumbnail [42 KiB] tex code Results of the unbinned maximum likelihood fit to the angular and two-body invariant mass distributions. The first uncertainty is statistical, the second systematic. Table_3.pdf [65 KiB] HiDef png [164 KiB] Thumbnail [76 KiB] tex code 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. Table_4.pdf [81 KiB] HiDef png [47 KiB] Thumbnail [20 KiB] tex code

## Supplementary Material [file]

 Supplementary material full pdf supple[..].pdf [125 KiB] 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 Sup1a.pdf [22 KiB] HiDef png [349 KiB] Thumbnail [255 KiB] *C file Sup1b.pdf [22 KiB] HiDef png [351 KiB] Thumbnail [256 KiB] *C file Sup2.pdf [21 KiB] HiDef png [296 KiB] Thumbnail [220 KiB] *C file

Created on 11 July 2020.