Recent BABAr Results
We present herein the most recent B AB AR results on direct asymmetry measurements in , on partial branching fraction and asymmetry measurements in , on a search for decays, on a search for lepton number violation in modes and a study of and decays.
The decays and (with ) are flavor-changing neutral-current (FCNC) processes that are forbidden in the Standard Model (SM) at tree level. They occur in higher-order processes and are described by an effective Hamiltonian that factorizes short-distance contributions in terms of scale-dependent Wilson coefficients  from long-distance contributions expressed by local four-fermion operators that define hadronic matrix elements,
Figure 1 shows the lowest order diagrams for these FCNC decays. In , the electromagnetic penguin loop dominates. The short-distance part is expressed by the effective Wilson coefficient . Through operator mixing at higher orders, the chromomagnetic penguin enters whose short distance part is parameterized by . In modes, the penguin and the box diagram contribute in addition whose short-distance parts are parametrized in terms of and , the vector and axial-vector current contributions of these diagrams. Physics beyond the SM introduces new loops and box diagrams with new particles (e.g. a charged Higgs boson or supersymmetric particles) as shown in Fig. 2 (left, middle). Such contributions modify the Wilson coefficients and may introduce new diagrams with scalar and pseudoscalar current interactions and in turn new Wilson coefficients, and . To determine , , and precisely, we need to measure many observables in several radiative and rare semileptonic decays, which potentially can probe new physics at a scale of a few TeV.
Lepton-number-violating decays are highly suppressed in the SM and may need new physics processes. Figure 2 (right) shows a annihilation diagram into in which the neutrino mixes into an antineutrino producing like-sign leptons that are forbidden in SM interactions. Such processes require Majorana-type neutrinos that are absent in the SM .
The decays and also involve FCNC processes that are mediated by gluonic penguin loops included in (see Eqn. (1)). Here, the short-distance contributions are parameterized by the Wilson coefficients , , and , while the long-distance contributions involve the operators , , and . Figure 3 shows the lowest-order diagrams for these decays. New physics loops depicted in Fig. 2 may also contribute here. These charmless vector vector decays involve three amplitudes. In the transversity frame, these are the longitudinal amplitude (S-wave), the transverse amplitude (P-wave) and the parallel amplitude (D-wave). For measuring violation, they need to be known.
In chapter 2, we present new B AB AR measurements of the direct asymmetry in using a semi-inclusive analysis. We extract the ratio of Wilson coefficients from a measurement of the difference in asymmetries between charged and neutral decays. We also show asymmetry measurements for decays. In chapter 3, we present our branching fraction and asymmetry measurements of decays using a semi-inclusive analysis. In chapter 4, we summarize our branching fraction upper limits on and . In chapter 5, we summarize our results on searches for lepton number violation in exclusive modes. In chapter 6, we present our results on the charmless vector vector decays and and in chapter 7 we end with concluding remarks. Note that B AB AR performs all analyses blinded meaning that results are sealed until selection criteria and fitting procedures are finalized.
2 Measurement of Violation in
In the SM, the branching fraction is calculated at next-to-next-to-leading order (up to four loops) yielding for photon energies in the center-of-mass (CM) frame [7, 8]. For larger values of , the prediction depends the shape of the of the spectrum, which is modeled in terms of a shape function  that depends on the Fermi motion of the quark inside the meson and thus on the quark mass. Since the shape function is expected to be similar to that determining the lepton-energy spectrum in , precision measurements of the spectrum help to determine more precisely [10, 11, 12]. The measurement of also provides constraints on the charged Higgs mass [13, 14].
Experimentally, the challenge consists of extracting signal photons from those of and decays, copiously produced in continuum (with ) and processes that increase exponentially at smaller photon energies. One strategy consists of summing exclusive final states. In a sample of events collected with the B AB AR detector [15, 16] at the PEP-II asymmetric storage ring at the SLAC National Laboratory, we reconstruct 38 exclusive final states containing one or three kaons with at most one , up to four pions with at most two s and up to one . We require photon energies in the CM frame of . Previously, we published total and partial branching fractions . Here, we focus on the measurement of direct asymmetry, which is defined by
For this analysis , we select 16 self-tagging modes, ten 111. and six final states222.. We maximize the signal extraction using a bagged decision tree with six input variables. This improves the efficiency considerably with respect to the standard selection where and are the beam energy and meson energy in the CM frame, respectively. To remove continuum background, we train a separate bagged decision tree using event shape variables. For each mass bin, we optimize the sensitivity where is the signal (background) yield using loosely identified pions and kaons. To extract , we fit the beam-energy-constrained mass simultaneously for -tagged and -tagged events where is the B momentum in the CM frame. After correcting the raw for detector bias determined from the sideband below the signal region, we measure () , which agrees well with the SM prediction of at 95% confidence level (CL)  and which supersedes the old B AB AR measurement . Though this result is the most precise single direct measurement, the uncertainty is sufficiently large to allow for new physics contributions in . Figure 4 (bottom part) shows our result  in comparison to the Belle measurement . The asymmetry difference between and decays, , is very sensitive to new physics since it originates from the interference between the electromagnetic and the chromomagnetic penguin diagrams in which the latter enters through higher-order corrections. Calculations yield 
where is the hadronic matrix element of the interference, predicted to lie in the range 17 190 . In the SM, vanishes since and are real. However in new physics models, these Wilson coefficients may have imaginary parts yielding non-vanishing [22, 23, 24]. From a simultaneous fit to and modes, we measure from which we obtain the constraint -1.64 6.52 at 90% CL. This is the first measurement and first constraint on .
Figure 5 (left) shows the of the fit as a function of . The dependence on is not parabolic indicating that the likelihood has a non-Gaussian shape. The reason is that is determined from all possible values of . In the region , a change in can be compensated by a change in leaving unchanged. For positive values larger (smaller) than 2.6 (0.2), increases slowly (rapidly) since remains nearly constant at the minimum value (increases rapidly). For negative values, starts to decrease again, which leads to a change in the shape. Figure 5 (right) shows as a function of .
In the fully inclusive analysis, involves contributions from and that cannot be separated on an event-by-event basis. Therefore, we define here as
We tag the flavor of the non-signal flavor by the lepton charge in semileptonic decays. Using a sample events, we measure after correcting for charge bias and mistagging . Figure 4 (top part) shows all measurements from B AB AR [25, 26, 27], Belle  and CLEO , which all agree well with the SM prediction [22, 30].
3 Study of Decays
Using a semi-inclusive approach, we have updated the partial and total branching fraction measurements of modes ( or ) with the full B AB AR data sample of events. We reconstruct 20 exclusive final states: , , , , , with recoiling against or . After accounting for modes, and Dalitz decays, the selected decay modes represent 70% of the inclusive rate for hadronic masses . Using JETSET fragmentation  and theory predictions [33, 34, 35, 36, 37, 38], we extrapolate for the missing modes and those with . We impose the requirements and for () modes. We define six bins of the momentum-squared transferred to the dilepton system and four bins in hadronic mass . Table 1 shows the defined ranges of these bins.
|0||1.0 – 6.0||1.00 – 2.45|
|1||0.1–2.0||0.32– 1.41||1||0.4 – 0.6|
|3||4.3–8.1||2.07 –2.6||3||1.0 –1.4|
|4||10.1 –12.9||3.18–3.59||4||1.4 – 1.8|
|5||14.2 –||3.77 –|
To suppress and combinatorial background, we define boosted decision trees (BDT) for each bin separately for and modes. From these BDTs, we determine a likelihood ratio () to separate signal from and backgrounds. We veto and mass regions and use them as control samples. We measure in six bins of and four bins of . We extract the signal in each bin from a two-dimensional fit to and . As examples, Figs. 6 and 7 show the and distributions for modes in bin and for modes in bin , respectively. Clear signals are visible both in the and distributions. Figure 8 shows the differential branching faction as a function of (left) and (right) . Table 2 summarizes the differential branching fractions in the low and high regions in comparison to the SM predictions [34, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47]. In both regions, the differential branching fractions are in good agreement with the SM predictions. These results supersede the previous B AB AR measurements  and agree well with the measurements from Belle .
The direct asymmetry is defined by
|Mode||B AB AR||SM||B AB AR||SM|
|1 – 6||1 – 6|
We use 14 self-tagging modes consisting of all modes and modes with decays to a to measure in five bins. Due to low statistics, we have combined bins and . Figure 9 shows the asymmetry as a function of . The SM prediction of the asymmetry in the entire region is close to zero [50, 51, 52, 53]. In new physics models, however, may be significantly enhanced [54, 55]. In the full range of , we measure , which is in good agreement with the SM prediction. The asymmetries in the five bins are also consistent with zero.
4 Search for Decays
In the SM in lowest order, modes are also mediated by the electromagnetic penguin, penguin and box diagrams. However, they are suppressed by with respect to the corresponding decays. In extensions of the SM, rates may increase significantly . Using events, we recently updated the search for modes and performed the first search for modes . The SM predictions lie in the range – and – where the large ranges result from uncertainties in the form factor calculations [56, 58, 59] and from a lack of knowledge of form factors , respectively.
We fully reconstruct four and four final states by selecting and recoiling against or . We select leptons with , recover bremsstrahlung losses, remove conversions and require good particle identification for and . We select photons with and impose and mass constraints of and , respectively. For the final state, we require to remove asymmetric background that peaks near one. We veto and mass regions and use four neural networks (NN) to suppress combinatorial and continuum backgrounds, separately for and for modes. The NNs for suppressing background use 15 (14) input distributions for () modes, while those for suppressing continuum use 16 input distributions for both modes. For validations of the fitting procedure and peaking backgrounds, we use pseudo-experiments and the vetoed and samples.
For and , we perform simultaneous unbinned maximum likelihood (ML) fits to and distributions for and modes separately. We include the mode in the fit to extract the peaking background contribution in the modes by reconstructing the as a . For , we perform simultaneous unbinned ML fits to and distributions, again for and modes separately. In addition, we perform fits for the isospin-averaged modes and , lepton-flavor-averaged modes , and and both isospin- and lepton-flavor-averaged modes .
We see no signals in any of these modes and set branching fraction upper limits at 90% CL. Figure 10 shows them in comparison to results from Belle  and a measurement of from LHCb . For , our branching fraction upper limit is the lowest and so far only B AB AR has searched for modes. The present branching fraction upper limits lie within a factor of two to three of the SM predictions.
5 Search for Lepton Number Violation in Decays
In the SM, lepton number is conserved in low-energy collisions. However, in high-energy and high-density interactions, lepton number may be violated . Many models beyond the SM predict lepton number violation (LNV) with rates  that may be accessible already in present data samples. These models also predict Majorana-type neutrinos  for which particles and antiparticles are identical. Via oscillation of a neutrino into an antineutrino, lepton-number violating decays become possible such as depicted in Fig. 2 (right). The observation of atmospheric neutrino oscillations confirms hat neutrinos carry mass  but we do not know if any Majorana-type neutrinos exist. However, lepton number violation is also a necessary condition to explain the observed baryon asymmetry in the universe .
Using the full B AB AR data set of events collected at the peak, we have searched for lepton number violation in 11 decays333 and and where or . . We select events with more than three charged tracks of which two are identified as like-sign leptons having a combined momentum less than in the laboratory frame. We remove and from photon conversions. We define sufficiently wide mass regions around the ), ) and ) mesons to allow reasonable modeling of backgrounds. We combine the and candidates with the two leptons to form a candidate. We remove combinations with an invariant mass close to that of the as the may be a misidentified from . The misidentification rate is about 2%.
For each signal mode, we construct BDTs to discriminate signal from and backgrounds using nine inputs consisting of event shape variables, kinematic observables, flavor tagging and the proper decay time. If more than one candidate is found, we choose the one with the smallest in the fit to the B decay vertex. We perform a simultaneous unbinned ML fit to , and the BDT output distributions. For the , and final states, we include the and mass distributions, respectively. The background PDFs consist of an Argus function  for , first- or second-order polynomials (for modes) or a Cruijff444The Cruijff function is a centered Gaussian with different left-right resolutions and non-Gaussian tails: . function (for modes) for , a non-parametric kernel estimation KEYS algorithm  for the BDT output and a first-order polynomial plus a Gaussian function for the resonance masses. The corresponding signal PDFs consist of a Crystal Ball function  for , a Crystal Ball function plus a first-order polynomial (for modes with s) for , the simulated distribution in form of a histogram for the BDT output and for the masses two Gaussians, a relativistic Breit-Wigner function and a Gounaris-Sakurai function , respectively. We checked the fit procedure with a simulated background sample having the same size as the on-resonance data sample. We further performed a blinded fit to the on-resonance data sample confirming that the background distributions agreed with the background PDFs. Selection efficiencies vary between 6% and 16% depending on the final state.
Figures 11 and 12 show projections of the fit on the discriminating variables for and , respectively. Table 3 summarizes our results. In all 11 modes, the data are consistent with combinatorial background. We see the highest significance of in . We set Bayesian upper limits on the branching fraction at 90% CL using a flat prior (see Tab. 3). The additive systematic uncertainty that includes contributions from the PDF parameterization, fit biases, background yields and efficiencies is mode dependent between 0.2 and 0.7 events. The total multiplicative uncertainty on the branching fraction is 5% or less. The branching fraction upper limits at 90% CL lie in the range 1.5 – 26 where the lowest limit is set in the mode. Figure 13 summarizes all results of lepton-number-violating B decays from B AB AR , Belle , LHCb  and CLEO  including results for  and . All limits are set at 90% CL except for LHCb whose limits are set at 95% CL.
6 Study of and Decays
The longitudinal polarization fraction in charmless vector vector decays poses a puzzle. In tree-dominated decays like and , is nearly 100% while in decays with dominant penguin contributions like , is around 50% . Are there large transverse SM contributions that reduce [78, 79, 80, 81, 82, 83] or is this caused by new physics [82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94]? Thus, it is interesting to investigate other charmless vector vector decays such as the so far not-observed modes and . In the SM, the branching fractions are expected to be of the order of for and for . The SM predicts longitudinal polarization fractions of for both modes [93, 94]. Charmless vector vector modes are also well suited to measure the Unitarity Triangle angle [96, 97]. The Scan Method group has determined – contours from a fit to measured branching fractions, longitudinal polarizations and asymmetries using all observed charmless vector vector decays . The decay amplitudes of each mode are expressed in terms of tree, color-suppressed tree, gluonic penguin, singlet penguin, electroweak penguin and -annihilation/- exchange amplitudes. For decays involving s, SU(3) breaking is taken into account. All contributions up to order are considered where (Cabibbo angle), since the leading amplitude is already at order . Figure 14 shows the 90% CL – contour determined from the fit.
Using the full B AB AR data sample of events, we reconstruct the -daughter candidates via their decays with and . If multiple candidates exist, we select the one for which the probability of a fit to the two vector meson masses is smallest. The combinatorial background from collisions dominates. We use a tight selection on the angle between the thrust of the signal candidate in the rest frame and that of the rest of the event, requiring ) for and decay modes. Furthermore, we define a Fisher discriminant based on four shape and kinetic variables as inputs. We perform an extended unbinned ML fit to extract the signal and background yields from the data. We define the PDF as a product of six individual PDFs including , , , masses and helicity angles of the two vector mesons and the decay angle between the in the dipion rest frame and the flight direction:
where the last term is not present in . For signal, we use a sum of two Gaussians for and , a two-piece normal distribution for , relativistic Breit-Wigner functions for the distributions, each convolved with two Gaussians to account for detector resolution. We parameterize the helicity angles by the angular distribution:
convolved with a resolution function for each angle. Thus for signal, the PDF is factorized as . For the angles , the PDFs are distributions. For combinatorial background, we use an Argus function  for , a second-order polynomial for