Observation of the B0→ρ0ρ0 decay from an amplitude analysis of B0→(π+π−)(π+π−)decays

Physics Letters B 747 (2015) 468–478 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Observation of the B0→ρ0ρ0decay from an amplitude analysis of B0→(π+π−)(π+π−)decays .LHCb Collaboration a r t i c l e i n f o a b s t r a c t Article history: Received 26 March 2015 Received in revised form 18 May 2015 Accepted 10 June 2015 Available online 15 June 2015 Editor: M. Doser Proton–proton collision data recorded in 2011 and 2012 by the LHCb experiment, corresponding to an integrated luminosity of 3.0fb −1, are analysed to search for the charmless B0→ρ0ρ0decay. More than 600 B0→(π+π−)(π+π−)signal decays are selected and used to perform an amplitude analysis, under the assumption of no CP violation in the decay, from which the B0→ρ0ρ0decay is observed for the first time with 7.1 standard deviations significance. The fraction of B0→ρ0ρ0decays yielding a longitudinally polarised final state is measured to be fL=0.745+0.048 −0.058(stat) ±0.034(syst). The B0→ρ0ρ0branching fraction, using the B0→φK∗(892)0decay as reference, is also reported as B(B0→ρ0ρ0)=(0.94 ±0.17(stat)±0.09(syst)±0.06(BF)) ×10−6. ©2015 CERN for the benefit of the LHCb Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 1. Introduction The study of Bmeson decays to ρρ final states provides the most powerful constraint to date for the Cabibbo–Kobayashi– Maskawa (CKM) angle α≡arg (VtdV∗ tb)/(VudV∗ ub)[1–3]. Most of the physics information is provided by the decay B0→ρ+ρ−as measured at the e+e−colliders at the ϒ(4S)resonance [4,5],1for which the dominant decay amplitude, involving the emission of a Wboson only (tree), exhibits a phase difference that can be interpreted as the sum of the CKM angles β+γ=π−αin the Standard Model. The subleading amplitude associated with the exchange of a Wboson and a quark (penguin) must be determined in order to interpret the electroweak phase difference in terms of the angle α. This is realised by means of an isospin analysis involving the companion modes B+→ρ+ρ0[6,7] and B0→ρ0ρ0[8, 9].2In particular, the smallness of the amplitude of the latter leads to a better constraint on α. The BaBar and Belle experiments reported evidence for the B0→ρ0ρ0decay [8,9] with an average branching fraction of B(B0→ρ0ρ0)=(0.97 ±0.24)×10−6[8,9]. Despite small observed signal yields, each experiment measured the fraction fL of decays yielding a longitudinally polarised final state through an angular analysis. The Belle Collaboration did not find evidence for polarisation, fL=0.21+0.22 −0.26 [9], while the BaBar experiment measured a mostly longitudinally polarised decay, fL=0.75+0.12 −0.15 [8]. These results differ at the level of 2.0 standard deviations. The 1Charge conjugation is implicit throughout the text unless otherwise stated. 2ρ0stands for ρ0(770)throughout the text. large LHCb data set may shed light on this discrepancy. In addition, LHCb may confirm the hint of B0→ρ0f0(980)decays reported by Belle [9]. Measurements of the B0→ρ0ρ0branching fraction and longitudinal polarisation fraction at LHCb can be used as inputs in the determination of α[2,3]. This work focuses on the search and study of the B0→ (π+π−)(π+π−)decay in which the two (π+π−)pairs are selected in the low invariant mass range (<1100 MeV/c2). The B0→ρ0ρ0is expected to dominate the (π+π−)mass spectrum. The (π+π−)combinations can actually emerge from S-wave nonresonant and resonant contributions or other Por D-wave resonances interfering with the signal. Hence, the determination of the B0→ρ0ρ0yields requires a two-body mass and angular analysis, from which the fraction of the longitudinally polarised final state can be measured. The branching fraction is measured relative to the B0→ φK∗(892)0mode. The B0→φK∗(892)0decay, which results in four light mesons in the final state, is similar to the signal, thus allowing for a cancellation of the uncertainties in the ratio of selection efficiencies. 2. Data sets and selection requirements The analysed data correspond to an integrated luminosity of 1.0fb −1and 2.0fb −1from pp collisions recorded at a centre-ofmass energy of 7TeV, collected in 2011, and 8TeV, collected in 2012, by the LHCb experiment at CERN. The LHCb detector [10,11] is a single-arm forward spectrometer covering the pseudorapidity range 2 <η<5, designed for the study of particles containing bor cquarks. It includes a highhttp://dx.doi.org/10.1016/j.physletb.2015.06.027 0370-2693/©2015 CERN for the benefit of the LHCb Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. LHCb Collaboration / Physics Letters B 747 (2015) 468–478 469 precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region [12], a large-area siliconstrip detector located upstream of a dipole magnet with a bending power of about 4Tm, and three stations of silicon-strip detectors and straw drift tubes [13] placed downstream of the magnet. The tracking system provides a measurement of momentum, p, of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV/c. The minimum distance of a track to a primary vertex, the impact parameter, is measured with a resolution of (15 +29/pT)μm, where pTis the component of the momentum transverse to the beam, in GeV/c. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov (RICH) detectors [14]. Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers [15]. The online event selection is performed by a trigger [16], which consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction. In this analysis two categories of events that pass the hardware trigger stage are considered: those where the trigger decision is satisfied by the signal b-hadron decay products (TOS) and those where only the other activity in the event determines the trigger decision (TIS). The software trigger requires a two-, threeor fourtrack secondary vertex with large transverse momenta of charged particles and a significant displacement from the primary pp interaction vertices (PVs). At least one charged particle should have pT>1.7GeV/cand is required to be inconsistent with originating from any primary interaction. A multivariate algorithm [17] is used for the identification of secondary vertices consistent with the decay of a bhadron. Further selection criteria are applied offline to reduce the number of background events with respect to the signal. The (π+π−)candidates must have transverse momentum larger than 600 MeV/c, with at least one charged decay product with pT> 1000 MeV/c. The two (π+π−)pairs are then combined to form a B0candidate with a good vertex quality and transverse momentum larger than 2500 MeV/c. The invariant mass of each pair of opposite-charge pions forming the B0candidate is required to be in the range 300–1100 MeV/c2. The identification of the final-state particles (PID) is performed with dedicated neural-networks-based discriminating variables that combine information from the RICH detectors and other properties of the event [14]. The combinatorial background is further suppressed with multivariate discriminators based on a boosted decision tree algorithm (BDT) [18,19]. The BDT is trained with simulated B0→ρ0ρ0(where ρ0→π+π−) events as signal sample and candidates reconstructed with fourbody mass in excess of 5420 MeV/c2as background sample. The discriminating variables are based on the kinematics of the Bdecay candidate (Bp Tand the minimum pTof the two ρ0candidates) and on geometrical vertex measurements (quality of the B candidate vertex, impact parameter significances of the daughters, Bflight distance significance and Bpointing to the primary vertex). The optimal thresholds for the BDT and PID discriminating variables are determined simultaneously by means of a frequentist estimator for which no hypothesis on the signal yield is assumed [20]. The B0meson candidates are accepted in the mass range 5050–5500 MeV/c2. The normalisation mode B0→φK∗(892)0is selected with similar criteria, requiring in addition that the invariant mass of the (K+π−)candidate is found in a range of ±150 MeV/c2around the known value of the K∗(892)0meson mass [21] and the invariant mass of the (K+K−)pair is in a range of ±15 MeV/c2centred at the known value of the φmeson mass [21]. A sample enriched in B0→(K+π−)(π+π−)events is selected using the same ranges in (π+π−)and (K+π−)masses to estimate the background with one misidentified kaon. The presence of (π+π−)pairs originating from J/ψ, χc0and χc2charmonia decays is vetoed by requiring the invariant masses Mof all possible (π+π−)pairs to be |M−M0| >30 MeV/c2, where M0stands for the corresponding known values of the J/ψ, χc0and χc2meson masses [21]. Similarly, the decays D0→K−π+ and D0→π+π−are vetoed by requiring the corresponding invariant masses to differ by 25 MeV/c2or more from the known D0 meson mass [21]. To reduce contamination from other charm backgrounds and from the B0→a+ 1(→ρ0π+)π−decay, the invariant mass of any three-body combination in the event is required to be larger than 2100 MeV/c2. Simulated B0→ρ0ρ0and B0→φK∗(892)0decays are also used for determining the relative reconstruction efficiencies. The pp collisions are generated using Pythia [22] with a specific LHCb configuration [23]. Decays of hadronic particles are described by EvtGen [24]. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [25] as described in Ref. [26]. 3. Four-body mass fit The four-body mass spectrum M(π+π−)(π+π−)is fit with an unbinned extended likelihood. The fit is performed simultaneously for the two data taking periods together with the normalisation channel M(K+K−)(K+π−)and PID misidentification control channel M(K+π−)(π+π−)mass spectra. The four-body invariant mass models account for B0and possible B0 ssignals, combinatorial backgrounds, signal cross-feeds and background contributions arising from partially reconstructed b-hadron decays in which one or more particles are not reconstructed. The B0and B0 smeson shapes are modelled with a modified Crystal Ball distribution [27]. A second power-law tail is added on the high-mass side of the signal shape to account for imperfections of the tracking system. The model parameters are determined from a simultaneous fit of simulated signal events that fulfil the trigger, reconstruction and selection chain, for each data taking period. The values of the tail parameters are identical for the B0and B0 smesons. Their mass difference is constrained to the value from Ref. [21]. The mean and width of the modified Crystal Ball function are free parameters of the fit to the data. The combinatorial background in each four-body spectrum is described by an exponential function where the slope is allowed to vary in the fit. The misidentification of one or more final-state hadrons may result in a fully reconstructed background contribution to the corresponding signal spectrum, denoted signal cross-feed. The magnitude of the branching fractions of the signal and control modes as well as the two-body mass selection criteria make these signal cross-feeds negligible, with one exception: the misidentification of the kaon of the decay B0→(K+π−)(π+π−)as a pion yields a significant contribution in the M(π+π−)(π+π−)mass spectrum. The mass shape of B0→(K+π−)(π+π−)decays reconstructed as B0→(π+π−)(π+π−)is modelled by a Crystal Ball function, whose parameters are determined from simulated events. The yield of this signal cross-feed is allowed to vary in the fit. The measurement of the actual number of reconstructed B0→(K+π−)(π+π−)events multiplied by the data-driven estimate of the misidentification efficiency is consistent with the measured yield. The partially reconstructed background is modelled by an ARGUS function [28] convolved with a Gaussian function accounting 470 LHCb Collaboration / Physics Letters B 747 (2015) 468–478 Fig. 1. Reconstructed invariant mass spectrum of (left) (π+π−)(π+π−)and (right) (K+K−)(K+π−). The data are represented by the black dots. The fit is represented by the solid blue line, the B0signal by the solid red line and the B0 sby 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. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Table 1 Yields from the simultaneous fit for the 2011 and 2012 data sets. The first and second uncertainties are the statistical and systematic contributions, respectively. Decay mode Signal yields 2011 Signal yields 2012 B0→(π+π−)(π+π−)185 ±15 ±4 449 ±24 ±7 B0→(K+π−)(π+π−)1610 ±42 ±5 3478 ±62 ±10 B0→(K+K−)(K+π−)1513 ±40 ±8 3602 ±62 ±10 B0 s→(π+π−)(π+π−)30 ±7±171±11 ±1 B0 s→(K−π+)(π+π−)40 ±10 ±396±14 ±6 B0 s→(K+K−)(K−π+)42 ±10 ±366±13 ±4 for resolution effects. Various mass shape parameterisations are examined. The best fit is obtained when the endpoint of the ARGUS function is fixed to the value expected when one pion is not attributed to the decay. The other shape parameters of the ARGUS function are free parameters of the fit, common to the two data taking periods. The floating width parameter of the signal mass shape is constrained to be equal to the width of the Gaussian function used in the convolution. Fig. 1 displays the M(π+π−)(π+π−)and M(K+K−)(K+π−) spectra with the fit results overlaid. The signal event yields are shown in Table 1. Aside from the prominent signal of the B0→ (π+π−)(π+π−)decays, the decay mode B0 s→(π+π−)(π+π−) is observed with a statistical significance of more than 10 standard deviations. The statistical significance is evaluated by taking the ratio of the likelihood of the nominal fit and of the fit with the signal yield fixed to zero. A systematic uncertainty due to the fit model is associated to the measured yields. The dominant uncertainties arise from the knowledge of the signal and signal cross-feed shape parameters determined from simulated events. Several pseudoexperiments are generated while varying the shape parameters within their uncertainties, and the systematic uncertainties on the yields are estimated from the differences in results with respect to the nominal fit. 4. Amplitude analysis An amplitude analysis is used to determine the vector–vector (VV) contribution B0→ρ0ρ0by using two-body mass spectra and angular variables. The four-body mass spectrum is first analysed with the sPlot technique [29] to subtract statistically the background under the B0→(π+π−)(π+π−)signal. For the two-body mass spectra, contributions from resonant and non-resonant scalar (S), resonant vector (V) and tensor (T) components are considered in the amplitude fit model through complex mass propagators, M(mi), where the label i =1, 2are the first and second pion pairs, which are assigned randomly in every decay since they are indistinguishable. The P-wave lineshape model comprises the ρ0meson, described using the Gounaris– Sakurai parameterisation Mρ(mi)[30], and the ωmeson, parameterised with a relativistic spin-1 Breit–Wigner Mω(mi). The D-wave lineshape Mf2(mi)accounts for the f2(1270), modelled with a relativistic spin-2 Breit–Wigner. The S-wave model includes the f0(980)propagator Mf(980)(mi), described using a Flatté parameterisation [31,32], and a low-mass component. The latter includes the broad low-mass resonance f0(500)and a non-resonant contributions, which are jointly modelled in the framework of the K-matrix formalism [33] and referred as M(ππ)0(mi). Following the K-matrix formalism, the amplitude for the low-mass π+π− S-wave can be written as A(m)∝ˆ K 1−iρˆ K,(1) with ˆ K≡ˆ Kres +ˆ Knon-res =m0(m) (m2 0−m2)ρ(m)+κ,(2) ρ(m)=2q(m) m,(3) where κis measured to be −0.07 ±0.24 from a fit to the inclusive π+π−mass distribution and m0and are the nominal mass and mass-dependent width of the f0(500), as determined in Ref. [34]. The functions ρ(m)and q(m), defined in Ref. [33], are the phase space factor and the relative momentum of a pion in the ρ0 centre-of-mass system. By convention, the phase of the M(ππ)0(mi) mass propagator is set to zero at the ρ0nominal mass. The signal sample is described by considering the dominant amplitudes of the signal decay. The B →VV component contains the B →ρ0ρ0and B0→ρ0ωamplitudes. The B →VS component accounts for B0→ρ0(π+π−)0and B0→ρ0f0(980)amplitudes and the B →VT contribution is limited to the purely longitudinal amplitude of the B0→ρ0f2(1270)transition. Because of the broad natural width of the a± 1particle, a small contamination from the decays B0→a± 1π∓remains in the sample. This contribution with a± 1→ρ0π±in S-wave is considered along with its interference with the other amplitudes. This is done by introducing the CP-even eigenstate from the linear combination of individual amplitudes of the decays B0→a+ 1π−and B0→a− 1π+, as defined in Ref. [35]. The contribution of the decays B0→ ωω, B0→f0(980)f0(980), B0→ωS, B0→ωT, B0→f2(1270)S, B0→f2(1270)f2(1270)and B0→(ρ0f2(1270)),⊥are assumed LHCb Collaboration / Physics Letters B 747 (2015) 468–478 471 Fig. 2. Helicity angles for the (π+π−)(π+π−)system. to be negligible, where the and ⊥subindices indicate the parallel and perpendicular amplitudes of the decay. The choice of the baseline model was made prior to the measurement of the physical parameters of interest after comparing a set of alternative parameterisations according to a dissimilarity statistical test [36]. The differential decay rate for B0→(π+π−)(π+π−)decays at the B0production time t=0is given by d5 dcosθ1dcosθ2dϕdm2 1dm2 2 ∝4(m1,m2) 11  i=1 Aifi(m1,m2,θ 1,θ 2,ϕ) 2 ,(4) where the variables θ1, θ2and ϕare the helicity angles, described in Fig. 2, and 4is the four-body phase space factor. The notations of the complex amplitudes, Ai, and the expressions of their related angular distributions, fi, are displayed in Table 2. The mass propagators included in the fifunctions are normalised to unity in the fit range. For the CP conjugated mode, B0→(π+π−)(π+π−), the decay rate is obtained under the transformation Ai→ηiAi, where ηiis the CP eigenvalue of the CP eigenstate i, shown in Table 2. The untagged time-integrated decay rate of B0and B0to four pions, assuming no CP violation, can be written as d5( +) dcosθ1dcosθ2dϕdm2 1dm2 2 ∝ 11  j=1 i≤j Re[AiA∗ jfif∗ j](2−δij)(1+ηiηj)4(m1,m2), (5) where δij =1 when i =jand δij =0otherwise. The efficiency of the selection of the final state B0→ (π+π−)(π+π−)varies as a function of the helicity angles and the two-body invariant masses. To take into account variations in the efficiencies, four event categories kare defined according to their hardware trigger decisions (TIS or TOS) and data taking period (2011 and 2012). The acceptance is accounted for through the complex integrals ωk ij =(θ1,θ 2,ϕ,m1,m2)fif∗ j(2−δij) ×4(m1,m2)dcosθ1dcosθ2dϕdm2 1dm2 2,(6) where fiare the functions given in Table 2 and the overall efficiency. The integrals are computed with simulated events of each of the four considered categories, selected with the same criteria as those applied to data, following the method described in Ref. [38]. The coefficients ωk ij are used to determine the efficiency and to build a probability density function for each category, which is defined as Sk(m1,m2,θ 1,θ 2,ϕ) =11 j=1i≤jRe[AiA∗ jfif∗ j](2−δij)(1+ηiηj)4(m1,m2) 11 j=1i≤jRe[AiA∗ jωk ij](1+ηiηj). (7) The four event categories are used in the simultaneous unbinned maximum likelihood fit which depends on the 19 free parameters indicated in Table 3. Systematic effects are estimated by fitting with the angular model and ensemble of 1000 pseudoexperiments generated with the same number of events as observed in data. The biases are for the parameters of interest consistent with zero. A systematic uncertainty is assigned by taking 50% of the fit bias or the uncertainty on the rms when the latter is bigger in order to account for possible statistical fluctuations. Several model related uncertainties are envisaged. The B0→ a± 1π∓angular model requires knowledge of the lineshape of the a± 1meson. The a± 1natural width is chosen to be 400 MeV/c2. The difference to the fit results obtained by varying the width from 250 to 600 MeV/c2is taken as the corresponding systematic uncertainty. In addition, a systematic uncertainty is obtained by introducing the CP-odd component in the fit model of the decay amplitude B0→a± 1π∓by fixing the relative amplitudes of B0→a+ 1π− and B0→a− 1π+components to the values measured in Ref. [39]. Table 2 Amplitudes, Ai, CP eigenvalues, ηi, and mass-angle distributions, fi, of the B0→(π+π−)(π+π−)model. The indices ijkl indicate the eight possible combinations of pairs of opposite-charge pions. The angles αkl, βij and kl are defined in Ref. [37]. Aiηifi A0 ρρ 1Mρ(m1)Mρ(m2)cosθ1cos θ2 A ρρ 1Mρ(m1)Mρ(m2)1 √2sinθ1sin θ2cos ϕ A⊥ ρρ −1Mρ(m1)Mρ(m2)i √2sinθ1sin θ2sin ϕ A0 ρω 11 √2[Mρ(m1)Mω(m2)+Mω(m1)Mρ(m2)]cosθ1cos θ2 A ρω 11 √2[Mρ(m1)Mω(m2)+Mω(m1)Mρ(m2)]1 √2sinθ1sin θ2cos ϕ A⊥ ρω −11 √2[Mρ(m1)Mω(m2)+Mω(m1)Mρ(m2)]i √2sinθ1sin θ2sin ϕ Aρ(ππ)0−11 √6[Mρ(m1)M(ππ)0(m2)cosθ1+M(ππ)0(m1)Mρ(m2)cosθ2] Aρf(980)−11 √6[Mρ(m1)Mf(980)(m2)cosθ1+Mf(980)(m1)Mρ(m2)cosθ2] A(ππ)0(ππ)01M(ππ)0(m1)M(ππ)0(m2)1 3 A0 ρf2−15 24 Mρ(m1)Mf2(m2)cosθ1(3cos2θ2−1)+Mf2(m1)Mρ(m2)cos θ2(3cos2θ1−1) AS+ a1π11 √8{ijkl}1 √3Ma1(mijk)Mρ(mij)[cos αkl cosβik +sin αkl sinβik cos kl] 472 LHCb Collaboration / Physics Letters B 747 (2015) 468–478 Table 3 Results of the unbinned maximum likelihood fit to the angular and two-body invariant mass distributions. The first uncertainty is statistical, the second systematic. Parameter Definition Fit result fL|A0 ρρ |2/(|A0 ρρ |2+|A ρρ |2+|A⊥ ρρ |2)0.745+0.048 −0.058 ±0.034 f |A ρρ |2/(|A ρρ |2+|A⊥ ρρ |2)0.50 ±0.09 ±0.05 δ−δ0arg(A ρρ A0∗ ρρ )1.84 ±0.20 ±0.14 Fρ(ππ)0|Aρ(ππ)0|2/(|A0 ρρ |2+|A ρρ |2+|A⊥ ρρ |2)0.30+0.11 −0.09 ±0.08 Fρf(980)|Aρf(980)|2/(|A0 ρρ |2+|A ρρ |2+|A⊥ ρρ |2)0.29+0.12 −0.09 ±0.08 F(ππ)0(ππ)0|A(ππ)0(ππ)0|2/(|A0 ρρ |2+|A ρρ |2+|A⊥ ρρ |2)0.21+0.06 −0.04 ±0.08 δ⊥−δρ(ππ)0arg(A⊥ ρρ A∗ ρ(ππ)0)−1.13+0.33 −0.22 ±0.24 δ⊥−δρf(980)arg(A⊥ ρρ A∗ ρf(980))1.92 ±0.24 ±0.16 δ(ππ)0(ππ)0−δ0arg(A(ππ)0(ππ)0A0∗ ρρ )3.14+0.36 −0.38 ±0.39 Fρω (|A0 ρω|2+|A ρω|2+|A⊥ ρω|2)/(|A0 ρρ |2+|A ρρ |2+|A⊥ ρρ |2)0.025+0.048 −0.022 ±0.020 fρω L|A0 ρω|2/(|A0 ρω|2+|A ρω|2+|A⊥ ρω|2)0.70+0.23 −0.60 ±0.13 fρω |A ρω|2/(|A ρω|2+|A⊥ ρω|2)0.97+0.69 −0.56 ±0.15 δω 0−δ0arg(A0 ρω A0∗ ρρ )−2.56+0.76 −0.92 ±0.22 δω −δ0arg(A ρω A0∗ ρρ )−0.71+0.71 −0.67 ±0.32 δω ⊥−δρ(ππ)0arg(A⊥ ρω A∗ ρ(ππ)0)−1.72 ±2.62 ±0.80 F0 ρf2|A0 ρf2|2/(|A0 ρρ |2+|A ρρ |2+|A⊥ ρρ |2)0.01+0.04 −0.02 ±0.03 δ0 ρf2−δρ(ππ)0arg(A0 ρf2A∗ ρ(ππ)0)−0.56 ±1.48 ±0.80 FS+ a1π|AS+ a1π|2/(|A0 ρρ |2+|A ρρ |2+|A⊥ ρρ |2)1.4+1.0 −0.7+1.2 −0.8 δS+ a1π−δρ(ππ)0arg(AS+ a1πA∗ ρ(ππ)0)−0.09+0.30 −0.36 ±0.38 Another source of uncertainty originates in the modelling of the low mass (π+π−)S-wave lineshape. The f0(500)mass and natural width uncertainties from Ref. [34] and the uncertainty on the parameter that quantifies the non-resonant contribution are propagated to the angular analysis parameters by generating and fitting 1000 pseudoexperiments in which these input values are varied according to a Gaussian distribution having their uncertainties as widths. The root mean square of the distribution of the results is assigned as a systematic uncertainty. The same strategy is followed to estimate the systematic uncertainties originating from the ρ0, f0(500)and ωlineshape parameters. The uncertainty related to the background subtraction method is estimated by varying within their uncertainties the fixed parameters of the mass fit model and studying the resulting angular distributions and two-body mass spectra. The difference to the fit results is taken as a systematic uncertainty. An alternative subtraction of the background estimated from the high-mass sideband is performed, yielding compatible results. The knowledge of the acceptance model described in Eq. (6) comes from a finite sample of simulated events. An ensemble of pseudoexperiments is generated by varying the acceptance weights according to their covariance matrix. The root mean square of the distribution of the results is assigned as a systematic uncertainty. The resolution on the helicity angles is evaluated with pseudoexperiments resulting in a negligible systematic uncertainty. The systematic uncertainty related to the (π+π−)mass resolution is estimated with pseudoexperiments by introducing a smearing of the (π+π−)mass. Differences in the parameters between the fit with and without smearing are taken as a systematic uncertainty. Table 4 details the contributions to the systematic uncertainty in the measurement of the fraction of B0→ρ0ρ0signal decays in the B0→(π+π−)(π+π−)and its longitudinal polarisation fraction. The final results of the combined two-body mass and angular analysis are shown in Fig. 3 and Table 3. The fit also allows for Table 4 Relative systematic uncertainties on the longitudinal polarisation parameter, fL, and the fraction of B0→ρ0ρ0decays in the B0→(π+π−)(π+π−)sample. The model uncertainty includes the three uncertainties below. Systematic effect Uncertainty on fL(%) Uncertainty on P(B0→ρ0ρ0)(%) Fit bias 0.10.8 Model 3.66.2 B0→a1(1260)+π−1.21.1 S-wave lineshape 3.46.1 Lineshapes <0.1 0.1 Background subtraction 0.10.5 Acceptance integrals 2.74.5 Angular/Mass resolution 0.81.5 the extraction of the fraction of B0→ρ0ρ0decays in the B0→ (π+π−)(π+π−)sample, defined as P(B0→ρ0ρ0)=3 j=1i≤jRe[AiA∗ jωij] 11 j=1i≤jRe[AiA∗ jωij],(8) which is P(B0→ρ0ρ0)=0.619 ±0.072(stat)±0.049(syst). The B0→ρ0ρ0signal significance is measured to be 7.1 standard deviations. The significance is obtained by dividing the value of the purity by the quadrature of the statistical and systematic uncertainties. No evidence for the B0→ρ0f0(980)decay mode is obtained. The fraction of longitudinal polarisation of the B0→ρ0ρ0 decay is measured to be fL=0.745+0.048 −0.058 (stat)±0.034 (syst). LHCb Collaboration / Physics Letters B 747 (2015) 468–478 473 Fig. 3. Background-subtracted M(π+π−)1,2, cosθ1,2and ϕdistributions. 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 B0→ρ0ρ0(brown), B0→ωρ0(dashed brown), B0→VS (dashed blue), B0→SS (long dashed green), B0→VT (orange) and B0→a± 1π∓(light blue) are also displayed. The B0→ρ0ρ0contribution 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 polarised B0→ρ0ρ0events is ∼5 times smaller than for the transverse component. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 5. Branching fraction determination The branching fraction of the decay mode B0→ρ0ρ0relative to the decay B0→φK∗(892)0can be expressed as B(B0→ρ0ρ0) B(B0→φK∗(892)0) =λfL·P(B0→ρ0ρ0) P(B0→φK∗(892)0)×N(B0→(π+π−)(π+π−)) N(B0→(K+K−)(K+π−)) ×B(φ →K+K−)B(K∗→K+π−) B(ρ0→π+π−)2,(9) where the factor λfLcorrects for differences in detection efficiencies between experimental and simulated data due to the polarisation hypothesis of the B0→ρ0ρ0sample, P(B0→ρ0ρ0)and P(B0→φK∗(892)0)are the fractions of B0→ρ0ρ0and B0→ φK∗(892)0signals in the samples of B0→(π+π−)(π+π−)and B0→(K+K−)(K+π−)decays, respectively. The quantities N(B0→ (π+π−)(π+π−)) and N(B0→(K+K−)(K+π−)) are the yields of B0→(π+π−)(π+π−)and B0→(K+K−)(K+π−)decays as determined from a fit to the four-body mass distributions, weighted for each data-taking period by the efficiencies of the signal and normalisation channels obtained from their respective simulated data. Finally, B(φ →K+K−), B(K∗(892)0→K+π−)and B(ρ0→ π+π−)denote known branching fractions [21]. The product λfL·P(B0→ρ0ρ0)is determined from the amplitude analysis to be 1.13 ±0.19(stat)±0.10(syst). This quantity is mainly related to the modelling of the S-wave component, and dominates the systematic uncertainty of the parameters of interest. The fraction of B0→φK∗(892)0present in the B0→ (K+K−)(K+π−)sample is taken from Ref. [40]. A 1% systematic uncertainty is added, accounting for differences in the selection acceptance for Pand S-wave contributions. The amounts of B0→(π+π−)(π+π−)and B0→ (K+K−)(K+π−)candidates are determined from the four-body mass spectra analysis and their associated statistical and systematical uncertainties are propagated quadratically to the branching fraction uncertainty estimate. The limited size of the simulated events samples that meet all selection criteria result in a systematic uncertainty of 1.7% (2.6%) on the measurement of the relative branching fraction for the 2011 (2012) data-taking period. The impact of the discrepancies between experimental and simulated data related to the B0meson kinematical properties is 0.6% (1.2%). The efficiencies of the particle-identification requirements are determined from control samples of data with a systematic uncertainty of 0.5%, mostly originating from the limited size of the calibration samples. An additional 1% systematic uncertainty on the tracking efficiency is added accounting for different interaction lengths between πand K. The relative branching fraction is measured to be B(B0→ρ0ρ0) B(B0→φK∗(892)0)=0.094 ±0.017(stat)±0.009(syst). (10) The agreement between the results obtained in the two datataking periods is tested with the best linear estimator technique [41] yielding compatible results. The average branching fraction of B0→φK∗(892)0as determined in Ref. [21] does not take into account the correlations between systematic uncertainties due to the S-wave modelling. Instead, we average the results from Refs. [42–44] including these correlations to obtain B(B0→φK∗(892)0) =(1.00 ±0.04 ±0.05) × 10−5. Using this value in Eq. (10), the branching fraction of B0→ ρ0ρ0is B(B0→ρ0ρ0) =(0.94 ±0.17(stat)±0.09(syst)±0.06 (BF)) ×10−6, where the last uncertainty is due to the normalisation channel branching fraction. Using the B0→ρ0ρ0branching fraction, the ρ0f0(980)amplitude, a phase space correction and assuming 100% correlated uncertainties, an upper limit for the B0→ρ0f0(980) decay, at 90% confidence level, is obtained B(B0→ρ0f0(980)) ×B(f0(980)→π+π−)<0.81 ×10−6. (11) 6. Conclusions The full data set collected by the LHCb experiment in 2011 and 2012, corresponding to an integrated luminosity of 3.0fb −1, is analysed to search for the B0→ρ0ρ0decay. A yield of 634 ± 28 ±8 B0→(π+π−)(π+π−)signal decays with π+π−pairs in the 300–1100 MeV/c2mass range is obtained. An amplitude analysis is conducted to determine the contribution from B0→ρ0ρ0 decays. This decay mode is observed for the first time with a significance of 7.1 standard deviations. In the same π+π−pairs mass range, B0 s→(π+π−)(π+π−)decays are also observed with a statistical significance of more than 10 standard deviations. The longitudinal polarisation fraction of the B0→ρ0ρ0decay is measured to be fL=0.745+0.048 −0.058 (stat)±0.034(syst). The measurement of the B0→ρ0ρ0branching fraction reads 474 LHCb Collaboration / Physics Letters B 747 (2015) 468–478 B(B0→ρ0ρ0) =(0.94 ±0.17(stat)±0.09(syst)±0.06 (BF)) ×10−6, where the last uncertainty is due to the normalisation channel. These results are the most precise to date and will improve the precision of the determination of the CKM angle α. The measured longitudinal polarisation fraction is consistent with the measured value from BaBar [8] while it differs by 2.3 standard deviations from the value obtained by Belle [9]. The branching fraction measurement is in agreement with the values measured by both BaBar [8] and Belle [9] Collaborations. The evidence of the B0→ρ0f0(980)decay mode reported by the Belle Collaboration [9] is not confirmed, and an upper limit at 90% confidence level is established B(B0→ρ0f0(980)) ×B(f0(980)→π+π−)<0.81 ×10−6. Acknowledgements We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); INFN (Italy); FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FANO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). The Tier1 computing centres are supported by IN2P3 (France), KIT and BMBF (Germany), INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom). We are indebted to the communities behind the multiple open source software packages on which we depend. We are also thankful for the computing resources and the access to software R&D tools provided by Yandex LLC (Russia). 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Molina Rodriguez 60, S. Monteil 5, M. Morandin 22, P. Morawski 27, A. Mordà 6, M.J. Morello 23,t, J. Moron 27, A.-B. Morris50, R. Mountain 59, F. Muheim 50, K. Müller 40, M. Mussini 14, B. Muster 39, P. Naik 46, T. Nakada 39, R. Nandakumar 49, I. Nasteva 2, M. Needham 50, N. Neri 21, S. Neubert 11, N. Neufeld 38, M. Neuner 11, A.D. Nguyen 39, T.D. Nguyen 39, C. Nguyen-Mau 39,q, V. Niess 5, R. Niet 9, N. Nikitin 32, T. Nikodem 11, A. Novoselov 35, D.P. O’Hanlon 48, A. Oblakowska-Mucha27, V. Obraztsov 35, S. Ogilvy 51, O. Okhrimenko 44, R. Oldeman 15,e, C.J.G. Onderwater 67, B. Osorio Rodrigues 1, J.M. Otalora Goicochea 2, A. Otto38, P. Owen 53, A. Oyanguren 66, A. Palano13,c, F. Palombo 21,u, M. Palutan 18, J. Panman 38, A. Papanestis 49, M. Pappagallo 51, L.L. Pappalardo 16,f, C. Parkes 54, G. Passaleva 17, G.D. Patel 52, M. Patel 53, C. Patrignani 19,j, A. Pearce54,49, A. Pellegrino 41, G. Penso 25,m, M. Pepe Altarelli 38, S. Perazzini 14,d, P. Perret 5, L. Pescatore 45, K. Petridis 46, A. Petrolini 19,j, E. Picatoste Olloqui 36, B. Pietrzyk 4, T. Pilaˇ r48, D. Pinci 25, A. Pistone 19, S. Playfer 50, M. Plo Casasus 37, T. Poikela 38, F. Polci 8, A. Poluektov 48,34, I. Polyakov 31, E. Polycarpo 2, A. Popov 35, D. Popov 10, B. Popovici 29, C. Potterat 2, E. Price 46, J.D. Price 52, J. Prisciandaro 39, A. Pritchard 52, C. Prouve 46, V. Pugatch 44, A. Puig Navarro 39, G. Punzi 23,s, W. Qian 4, R. Quagliani 7,46, B. Rachwal 26, J.H. Rademacker 46, B. Rakotomiaramanana 39, M. Rama 23, M.S. Rangel 2, I. Raniuk 43, N. Rauschmayr 38, G. Raven 42, F. Redi 53, S. Reichert 54, M.M. Reid 48, A.C. dos Reis1, S. Ricciardi 49, S. Richards 46, M. Rihl 38, K. Rinnert 52, V. Rives Molina 36, P. Robbe 7,38, A.B. Rodrigues 1, E. Rodrigues 54, J.A. Rodriguez Lopez 62, P. Rodriguez Perez 54, S. Roiser 38, V. Romanovsky 35, A. Romero Vidal37,∗, M. Rotondo 22, J. Rouvinet 39, T. Ruf 38, H. Ruiz 36, P. Ruiz Valls 66, J.J. Saborido Silva 37, N. Sagidova 30, P. Sail 51, B. Saitta 15,e, V. Salustino Guimaraes 2, C. Sanchez Mayordomo 66, B. Sanmartin Sedes 37, R. Santacesaria 25, C. Santamarina Rios 37, E. Santovetti 24,l, A. Sarti18,m, C. Satriano 25,n, A. Satta24, D.M. Saunders 46, D. Savrina 31,32, M. Schiller 38, H. Schindler 38, M. Schlupp 9, M. Schmelling 10, B. Schmidt 38, O. Schneider 39, A. Schopper 38, M.-H. Schune 7, R. Schwemmer 38, B. Sciascia 18, A. Sciubba 25,m, A. Semennikov 31, I. Sepp 53, N. Serra 40, J. Serrano 6, L. Sestini 22, P. Seyfert 11, M. Shapkin 35, I. Shapoval 16,43,f, Y. Shcheglov 30, T. Shears 52, L. Shekhtman 34, V. Shevchenko 64, A. Shires 9, R. Silva Coutinho 48, G. Simi 22, M. Sirendi 47, N. Skidmore 46, I. Skillicorn 51, T. Skwarnicki 59, N.A. Smith 52, E. Smith 55,49, E. Smith 53, J. Smith 47, M. Smith 54, H. Snoek 41, M.D. Sokoloff 57,38, F.J.P. Soler 51, F. Soomro 39, D. Souza 46, B. Souza De Paula 2, B. Spaan 9, P. Spradlin 51, S. Sridharan 38, F. Stagni 38, M. Stahl 11, S. Stahl 38, O. Steinkamp 40, O. Stenyakin 35, F. Sterpka 59, S. Stevenson 55, S. Stoica 29, S. Stone 59, B. Storaci 40, S. Stracka 23,t, M. Straticiuc 29, U. Straumann 40, R. Stroili 22, L. Sun 57, W. Sutcliffe 53, K. Swientek 27, S. Swientek 9, V. Syropoulos 42, M. Szczekowski 28, P. Szczypka 39,38, T. Szumlak 27, S. T’Jampens 4, M. Teklishyn 7, G. Tellarini 16,f, F. Teubert 38, C. Thomas 55, E. Thomas 38, J. van Tilburg 41, V. Tisserand 4, M. Tobin 39, J. Todd 57, S. Tolk 42, L. Tomassetti 16,f, D. Tonelli 38, S. Topp-Joergensen 55, N. Torr 55, E. Tournefier 4, S. Tourneur 39, K. Trabelsi 39, M.T. Tran 39, M. Tresch 40, A. Trisovic 38, A. Tsaregorodtsev 6, P. Tsopelas 41, N. Tuning 41,38, A. Ukleja28, A. Ustyuzhanin 65, U. Uwer 11, C. Vacca 15,e, V. Vagnoni 14, G. Valenti 14, A. Vallier 7, R. Vazquez Gomez 18, P. Vazquez Regueiro 37, C. Vázquez Sierra 37, S. Vecchi 16, J.J. Velthuis 46, M. Veltri 17,h, G. Veneziano 39, M. Vesterinen 11, J.V. Viana Barbosa 38, B. Viaud 7, D. Vieira 2, M. Vieites Diaz 37, X. Vilasis-Cardona 36,p, A. Vollhardt 40, D. Volyanskyy 10, D. Voong 46, A. Vorobyev30, V. Vorobyev 34, C. Voß 63, J.A. de Vries 41, R. Waldi 63, C. Wallace 48, R. Wallace 12, J. Walsh 23, S. Wandernoth 11, J. Wang 59, D.R. Ward 47, N.K. Watson 45, D. Websdale 53, A. Weiden 40, M. Whitehead 48, D. Wiedner 11, G. Wilkinson 55,38, M. Wilkinson 59, M. Williams 38, M.P. Williams 45,