Measurement of the B0 -->pi l nu Form-Factor Shape and Branching Fraction, and Determination of |Vub| with a Loose Neutrino Reconstruction Technique

We report the results of a study of the exclusive charmless semileptonic decay, B -->pi l nu, undertaken with approximately 227 million BBbar pairs collected at the Upsilon(4S) resonance with the BaBar detector. The analysis uses events in which the signal B decays are reconstructed with an innovative loose neutrino reconstruction technique. We obtain partial branching fractions in 12 bins of q2, the momentum transfer squared, from which we extract the f+(q2) form-factor shape and the total branching fraction BF(B0 -->pi l nu) = (1.46 +- 0.07(stat) +- 0.08(syst)) x 10^-4. Based on a recent unquenched lattice QCD calculation of the form factor in the range q2>16 GeV^2, we find the magnitude of the CKM matrix element |Vub| to be (4.1 +- 0.2(stat) +- 0.2(syst) +0.6-0.4(FF)) x 10^-3, where the last uncertainty is due to the normalization of the form factor.

(Dated: November 5, 2018) We report the results of a study of the exclusive charmless semileptonic decay, B 0 → π − ℓ + ν, undertaken with approximately 227 million BB pairs collected at the Υ (4S) resonance with the BABAR detector. The analysis uses events in which the signal B decays are reconstructed with an innovative loose neutrino reconstruction technique. We obtain partial branching fractions in 12 bins of q 2 , the momentum transfer squared, from which we extract the f+(q 2 ) form-factor shape and the total branching fraction B(B 0 → π − ℓ + ν) = (1.46 ± 0.07stat ± 0.08syst) × 10 −4 . Based on a recent unquenched lattice QCD calculation of the form factor in the range q 2 > 16 GeV 2 , we find the magnitude of the CKM matrix element |V ub | to be 4.1 ± 0.2stat ± 0.2syst +0. 6 −0.4 FF × 10 −3 , where the last uncertainty is due to the normalization of the form factor.
PACS numbers: 13.20.He, 12.15.Hh,12.38.Qk,14.40.Nd A precise measurement of |V ub |, the smallest element of the CKM matrix [1], will constrain the description of weak interactions and CP violation in the Standard Model. The rate for exclusive B 0 → π − ℓ + ν decays [2] is proportional to |V ub f + (q 2 )| 2 , where the form factor f + (q 2 ) depends on q 2 , the momentum transfer squared. Values of f + (q 2 ) for B 0 → π − ℓ + ν decays are provided by unquenched lattice QCD (LQCD) calculations (HPQCD [3], FNAL [4]), presently reliable only at large q 2 (> 16 GeV 2 ), by light cone sum rules (LCSR) calculations [5], based on approximations only valid at small q 2 (< 16 GeV 2 ), and by the ISGW2 quark model calculations [6]. Uncertainties on these calculations dominate the errors on the computed values of |V ub |. The QCD theoretical predictions are at present more precise for B 0 → π − ℓ + ν than for other exclusive B → X u ℓν decays, where X u stands for any charmless meson. Experimental data can be used to discriminate between the various calculations by precisely measuring the f + (q 2 ) shape, thereby leading to a smaller theoretical uncertainty on |V ub |.
Values of |V ub | have previously been extracted from B 0 → π − ℓ + ν measurements by CLEO [7], BABAR [8,9] and Belle [10]. In this letter, we present measurements of the partial branching fractions (BF) ∆B(B 0 → π − ℓ + ν, q 2 ) in 12 bins of q 2 using an innovative loose neutrino reconstruction technique. This leads to more precise values of the total BF B(B 0 → π − ℓ + ν) and of the f + (q 2 ) form-factor shape, which supersede those of our previous untagged measurement [8]. We combine the values of ∆B(q 2 ) with recent form-factor calculations [3, 4, 5] to obtain a value of |V ub |.
The data set used in this analysis contains approximately 227 million BB pairs corresponding to an integrated luminosity of 206 fb −1 collected at the Υ (4S) resonance with the BABAR detector [11] at the PEP-II asymmetric-energy e + e − collider, and of 27.0 fb −1 integrated luminosity of data collected approximately 40 MeV below the Υ (4S) resonance (denoted "offresonance data"). To estimate the signal efficiency, and the signal and background distributions, we use a detailed Monte Carlo (MC) simulation of generic BB and uu/dd/ss/cc/τ + τ − "continuum" events as well as B 0 → π − ℓ + ν signal events. Signal MC events are produced by the FLATQ2 generator [12] and are reweighted to reproduce the Becirevic-Kaidalov (BK) parametrization [13] of f + (q 2 , α, c B ) where the values of the shape and normalization parameters, α and c B , are taken from Ref. [8].
We reconstruct B meson candidates using π ± and ℓ ∓ tracks together with the event's missing momentum p miss as an approximation to the signal neutrino momentum. The decay of the second B meson is not explicitly reconstructed. The neutrino four-momentum P miss ≡ (| p miss |, p miss ) is inferred from the difference between the momentum of the colliding-beam particles p beams , and the sum of the momenta of all the charged and neutral particles detected in a single event p tot , such that p miss ≡ p beams − p tot . Compared with the tagged analyses in which the two B mesons are explicitly reconstructed [9,10], the neutrino reconstruction approach yields a lower signal purity but a significant increase in the signal reconstruction efficiency. The present loose neutrino reconstruction technique also increases the signal efficiency substantially with respect to the previous untagged approach by avoiding the tight neutrino quality cuts [7,8] which ensure that the neutrino properties are well taken into account when computing q 2 = (P ℓ + P ν ) 2 . In this analysis, we calculate instead the momentum transfer as q 2 = (P B − P π ) 2 , where the ambiguity in the direction of the B meson is handled by use of the method described in Ref. [14]. In this way, the value of q 2 is unaffected by any mis-reconstruction of the rest of the event. We obtain a q 2 resolution of σ = 0.52 GeV 2 for the signal candidates in which the pion candidate track truly comes from a B 0 → π − ℓ + ν decay (91% of the total). We correct for the reconstruction effects on the q 2 resolution by applying an unregularized unfolding algorithm to the measured q 2 spectrum [15].
To separate the B 0 → π − ℓ + ν signal from the backgrounds, we require two well-reconstructed tracks associated with a lepton-pion pair. The electron (muon) tracks are required to have momenta greater than 0.5 (1.0) GeV in the laboratory frame to avoid misidentified leptons and secondary semileptonic decays. We ensure that the momenta of the lepton and pion candidates are kinematically compatible with a real B 0 → π − ℓ + ν decay. This requires that a geometrical vertex fit of the two charged tracks gives a χ 2 probability greater than 0.01 and that the angle between the Y and B momenta in the Υ (4S) frame takes a physical value: | cos θ BY | < 1, where the pseudo-particle Y is defined by its four-momentum P Y ≡ (P π +P ℓ ). Most backgrounds are efficiently rejected by q 2 -dependent cuts on the helicity angle θ ℓ of the W boson [12], on the angle between the thrust axes of the Y and of the rest of the event, on the polar angle associated with p miss , and on the squared invariant mass of P miss . We reject B 0 → π − µ + ν candidates with Y mass close to the J/ψ mass to avoid J/ψ → µ + µ − decays. Non-BB events are suppressed by requiring the ratio of second to zeroth Fox-Wolfram moments to be smaller than 0.5, and by cuts [16] on the number of tracks and clusters. Radiative Bhabha and two-photon processes are rejected by vetoing events containing a photon conversion and by requiring ( p tot ·ẑ)/E tot < 0.64 and ( p tot ·ẑ)/E tot > 0.35 for candidates in the electron and positron channels, respectively, where the z axis is given by the electron beam direction. We reduce the remaining backgrounds with the variables ∆E = ( s is the total energy in the Υ (4S) frame. Only candidates with |∆E| < 1.0 GeV and m ES > 5. 19 GeV are retained. When several candidates remain in an event after these cuts, the candidate with cos θ ℓ closest to zero is selected. This rejects 30% of the combinatorial signal candidates while keeping 97% of the correct ones. The signal event reconstruction efficiency varies between 6.7% and 9.8%, depending on the q 2 bin.
The B 0 → π − ℓ + ν signal yield is obtained as a function of q 2 by performing a two-dimensional extended maximum-likelihood fit [17] on m ES , and ∆E in each bin of q 2 . The data samples in each q 2 bin are divided into four categories: B 0 → π − ℓ + ν signal, other b → uℓν, other BB, and continuum backgrounds. These four types of events have distinct structures in the two-dimensional m ES -∆E plane. We use the m ES -∆E histograms obtained from the MC simulation as two-dimensional probability density functions (PDFs). The yields of the signal, b → uℓν background and other BB background, subdivided in twelve, three and four q 2 bins, respectively, are extracted from a nineteen-parameter fit of the MC PDFs to the experimental data. The continuum background is corrected to match the off-resonance data control sample and is fixed in the fit. The number and type of fit parameters were chosen to provide a good balance between reliance on simulation predictions, complexity of the fit and total error size. m ES and ∆E fit projections for the experimental data are shown in Fig. 1 in two ranges of q 2 corresponding to the sum of eight bins below and four bins above q 2 = 16 GeV 2 . We obtain 5072±251 events for the total signal yield, 9867 ± 564 events for the b → uℓν background, 33341 ± 409 events for the other BB backgrounds, and 9299 ± 450 events for the continuum yield. The fit has a χ 2 value of 423 for 389 degrees of freedom.
Numerous sources of systematic uncertainties and their correlations among the q 2 bins have been investigated. The uncertainties due to the detector simulation are established by varying within bounds given by control samples the tracking efficiency of all charged tracks, the particle identification efficiencies of signal candidate tracks, the calorimeter efficiency (varied separately for photons, K 0 L and neutrons) and the energy deposited in the calorimeter by K 0 L mesons. The reconstruction of these neutral particles affects the analysis via the neutrino reconstruction. The uncertainties due to the generatorlevel inputs to the simulation are established by varying, within errors [18], the BFs of the background processes b → uℓν, b → cℓν, D → Xℓν and D → K 0 L X as well as the BF of the Υ (4S) → B 0 B 0 decay. The B 0 → π − ℓ + ν, B → ρℓν, B → Dℓν and B → D * ℓν form factors are varied within bounds given by recent calculations [19] or measurements [14,18,20]. The heavy quark parameters used in the simulation of non-resonant b → uℓν events are varied according to Ref. [21]. We assign an uncertainty of 20% to the final state radiation (FSR) corrections calculated by PHOTOS [22,23]. Finally, the uncertainties due to the modeling of the continuum are established by varying its q 2 , m ES , and ∆E shapes and total yield within their errors given by comparisons with the offresonance data control sample. The high statistics provided by our technique allow us to show that there is good agreement between data and simulation for the critical variables in signal depleted, signal enhanced, b → uℓν enhanced and continuum control samples. Consistent results are obtained either by dividing the final dataset into sub-samples or using modified binnings or modified event selections.
The partial BFs are calculated using the observed signal yields, the unfolding algorithm and the signal efficiencies given by the simulation. The total BF is given by the sum of the partial BFs, thereby reducing the sensitivity of the signal efficiency to the uncertainties of the f + (q 2 ) form factor. We compute the covariance matrix for each source of uncertainty and use these matrices to calculate the errors on the total BF. The fit and systematic errors are given in Table I for five ranges of q 2 . The complete set of fit and systematic uncertainties of the partial and total BFs as well as their correlation matrices are given in Ref. [24]. Our value of the total BF, (1.46 ± 0.07 stat ± 0.08 syst ) × 10 −4 , is comparable in precision to the world average prior to our result [18]: (1.35 ± 0.08 stat ± 0.08 syst ) × 10 −4 . The systematic error is due in large part to the detector efficiency. The systematic errors arising from the BFs and form factors of the backgrounds have been reduced with respect to previous untagged measurements by the many-parameter fit to the background yields in the 12 bins of q 2 .
The ∆B(q 2 ) distribution is displayed in Fig. 2 together with theoretical predictions. We modify the measured q 2 distribution to remove FSR effects, in order to allow a direct comparison with the theoretical predictions which do not include such effects (this procedure is referred to as "No FSR" in Ref. [24]). We obtain the f + (q 2 ) shape from a fit to this distribution. The χ 2 function minimized in the f + (q 2 ) fit uses a PDF based on the twoparameter BK parametrization. It is defined in terms of the ∆B(q 2 ) covariance matrix to take into account the correlations among the measurements in the various q 2 bins. The fit gives α = 0.52±0.05 stat ±0.03 syst , compared to our previous untagged measurement α = 0.61±0.09 [8] (statistical error only) as well as a value of |V ub f + (0)| = (9.6 ± 0.3 stat ± 0.2 syst ) × 10 −4 from the fit extrapolated to q 2 = 0, with P (χ 2 )=65%. This value includes a 67%  4], LCSR calculations [5], and the ISGW2 quark model [6]. anti-correlation between the shape and normalization parameters, α and c B , and can be used to predict [25] rates of other decays such as B → ππ.
In summary, we have measured the partial B 0 → π − ℓ + ν branching fractions in 12 bins of q 2 using a loose neutrino reconstruction technique. We obtained the most precise measurement to date of the B(B 0 → π − ℓ + ν) and |V ub f + (0)|, as well as a detailed description of the f + (q 2 ) shape. This shape can be compared with various theoretical predictions and, in particular, shows that the ISGW2 model can be ruled out. From the most recently published unquenched LQCD calculation [3], we obtain We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and kind hospitality.