CAPÍTULO V PRESENTACIÓN, ANÁLISIS Y DISCUSIÓN DE RESULTADOS
5.1. Presentación de resultados
5.1.2. Proceso de implementación de las NIIF en Motorperú
There are two assumptions made when using the recoil method: the first is that theBreconstruction efficiency is well modeled by the Monte Carlo simulations of generic B decays and continuum events. The hadronic Btag re-
construction efficiencies defined in Eqs (7.4.4) and (7.4.3) depend on the decay rates ofB-meson decays to final state included in the reconstruction. Some of them are poorly known and hence theBtag reconstruction efficiencies de-
termined on simulated samples need to be validated or cal- ibrated using the real data sample. The second is that for analyses with few reconstructed particles from the signal B, the extra energy used to discriminate signal from back- ground events is also well-modeled. These assumptions can be checked by using control samples which test both the tagB reconstruction efficiency and the description of ex- tra energy in a fully-reconstructed event. BothBABARand Belle use double-tagged samples, in which bothBmesons are fully reconstructed either in semileptonic or hadronic final states, as such a control.
The crosscheck using the double-tag approach was first applied byBABAR(Aubert,2004y), using double semilep- tonicB decays. For the semileptonicBtag technique de-
scribed in Section 7.4.2 this means the reconstruction of two oppositely charged and non-overlappingB→D0ν X
candidates with little other detector activity. BothBABAR
and Belle have also used “hybrid double-tags”, where one B is reconstructed in a hadronic final state while the second B is reconstructed in a semileptonic final state (B → D(∗)ν). These samples vary in size, depending
on the final states used, but given a semileptonic tag re- construction efficiency (quoted byBABAR) of∼0.7% and a hadronic tag efficiency of∼ 0.2%, one expects to find approximately 50 semileptonic double-tagged events per fb−1, 30 hybrid tags per fb−1, and 4 hadronic double- tagged events per fb−1. Given the large datasets of theB Factories, and the expected dataset at future super flavor factories, these are significant samples which can be used as important cross-checks of the assumptions in the recoil method.
The double-tagged events have two important features. The first is that one expects na¨ıvely the yield to be propor- tional toε2
tag, which is the basis of the cross-check of the
tag efficiency. The second is that the complete reconstruc- tion of both B mesons creates an environment in which the extra energy in a given event should represent the ef- fect of energy deposits unassociated with the B decays themselves. This latter feature is an important ingredient in the cross-check of the extra energy modeling in signal events, where it is also assumed that all detected particles associated with theBdecays have been reconstructed.
The cross-check of the tag efficiency is currently only used in the semileptonic approach, and only by BABAR. The early approach to the double-tag sample (Aubert, 2006a) made two assumptions. Given an efficiency, εtag,
for reconstructing one of the twoBs in an event in a se- mileptonic final state, the number of double tags (N2) is
given simply by
N2=ε2tag×NB+B− (7.4.5)
whereNB+B−is the number of chargedB pairs originally
produced by the BFactory or generated in Monte Carlo simulations. The tag efficiency cross-check was performed by taking the ratio of the above equation in data and in MCsimulation and assuming that the double-tag sample is dominated by charged B mesons so that NB+B− can-
cels, yielding the correction factor (ctag) for the tagging
efficiency in MC, ctag= εdata tag εMC tag = Ndata 2 NMC 2 . (7.4.6)
While MCstudies of the double-tags suggest that the con- tamination from neutralB decays, or other backgrounds, is very small, the second assumption - that the reconstruc- tion of the firstBdoes not bias the reconstruction of the second - is not addressed. The closeness of the correction to 1.0, as cited byBABAR, does suggest that also the sec- ond assumption is essentially correct.
A second approach to the efficiency correction attempts to address some of the potential deficiencies of the first method outlined above. In the alternative approach (Au- bert,2007a), the data/MCcomparison is performed using the ratio of single-tagged to double-tagged events. If the efficiency of reconstructing the first tag is εtag,1 and the
efficiency of reconstructing the second tag is εtag,2, then
the single-tag and double-tag yields,N1andN2, are given
by
N1=εtag,1×NB+B− (7.4.7)
N2=εtag,1×εtag,2×NB+B−. (7.4.8)
The ratio of the two cancels some of the common factors, yielding the following quantity to be determined in both data and MCsimulations,
εtag,2= N 2
N1
(7.4.9)
BABARdetermines the number of single-tagged events by subtracting the combinatorial component under theD0
mass distribution using an extrapolation of events from theD0mass sideband. This leaves a sample of events con-
taining correctly reconstructed events, mis-reconstructed events from neutralBsemileptonic decay, and events from e+e− → cc continuum background events with real D0
mesons paired with a combinatorial lepton. The correc- tion to the tag efficiency is assumed to be equal for either the first or second tag, and is computed from the data and MCas, ctag= εdata tag,2 εMC tag,2 = N data 2 /N1data NMC 2 /N1MC (7.4.10) The correction is computed using only events in which the D0 meson in the first B
tag decays into the K−π+ final
state. This is cross-checked using a sample in which the D0meson from the first tag decays into theK−π+π−π+
final state only, yielding complementary results.
In both of the above methods, and across several it- erations of semileptonic recoil-based analyses,BABARhas found the correction to be very close to 1.0. This sug- gests both that the assumptions in the above two meth- ods are largely accurate, and also that existing simulations of these and the background decays are adequate for the purposes of modeling the decays. The correction has an associated systematic error, which is typically determined by propagating the statistical uncertainty due to the finite sample sizes of the double-tag and single-tag samples. The uncertainty of the correction is about4%.
Belle (Sibidanov,2013) uses fully reconstructed events to calibrate the efficiency of the NB-basedBtagreconstruc-
tion. One of the produced B mesons is reconstructed as hadronicBtagwhile the otherBmeson is reconstructed in
the semileptonic decay modeBsl→D(∗)ν. The number
of double tagged events is therefore given by: N(BtagBsl) =NBB× B(Btag→f)εBtag→f×
B(Bsl→D(∗)ν)εBsl, (7.4.11)
where B(Btag → f)εBtag→f is the product of branching fraction and reconstruction efficiency of the specific decay Btag →f andB(Bsl→D(∗)ν)εBsl is the corresponding
product for the semileptonically decayingBmeson, which is well modeled in the simulation. The correction factor for Btag →f is then obtained by measuring the ratio of
the numbers of reconstructed double tagged events in real data and MCsamples
cf
tag=
Bdata(B
tag→f)εdataBtag→f
BMC(B tag→f)εMCBtag→f = N data(B tagBsl) NMC(B tagBsl) · NMC BBB MC(B sl→D(∗)ν) Ndata BB B data(B sl→D(∗)ν). (7.4.12) In this method of the Btag efficiency calibration it is as-
sumed that theBsl→D(∗)ν modes are well modeled in
the MC sample and hence theεdata
Bsl = ε MC
Bsl. The overall
correction factor (averaged over allBtag modes) is found
(GeV) ECL E 0 0.5 1 Number of events 0 50 100 150 200 250 300 350 (GeV) ECL E 0 0.5 1 (data/MC) events Ratio of N 0 0.2 0.4 0.6 0.8 1 1.2 1.4
Figure 7.4.5. Extra energy distribution for double-tagged
B+
tagB−slevents (left plot), where the semileptonically decaying B meson is reconstructed in theD∗0
−ν decay mode. Black
and red data points show the distribution obtained in data and in a sample of simulated events, respectively. The right plot shows the ratio of the two distributions fitted with a lin- ear function. Belle internal, from the Adachi (2012b) analysis.
to be around 0.7 and consistent between differentBsl de-
cay modes. The total uncertainty of the calibration is es- timated to be4.2% forBtag+ and4.5% forB0
tag.
The second application of the double-tagged sample is to test the modeling of extra particles left in the detec- tor after bothB mesons have been reconstructed. In the case of signal events, this typically means that the tagB is reconstructed up to any neutrinos in the final state (as in semileptonic tags), and that the signalBis also recon- structed up to possible neutrinos in its final state. After reconstruction of bothB mesons the remaining particles left in the event are assumed to come from several sources: neutrals, such as photons, which arise from the electron- positron beams but not the interaction point; some low momentum charged particles associated with interactions between the beam and the beampipe; neutral clusters from hadronic showering in the calorimeter which fail to asso- ciate with a track; and detector noise. These sources would typically lead to a few extra neutral particles left in a sig- nal event in about20-30% of the reconstructed events.
Double-tagged events are used to test the simulation of these extra neutral particles by fully reconstructing both Bmesons either semileptonically, hadronically, or in a hy- brid configuration. An example of the use of the double- tags to test the extra energy simulation is the Belle col- laboration’s hadronic-tagged search forB+→τ+ν
τ. Belle
constructs a hybrid double-tag sample (one hadronic B and one semileptonicBper event in the sample), and as- sumes that the extra neutral clusters remaining in these events comes from the same sources as in signal events. They compare the extra energy in data and MC (Fig. 7.4.5) and use the difference as a variation on theirp.d.f. model for signal events.Comparisons show that existing detector simulations at the B Factories handle the vari- ety of sources of extra neutral clusters fairly well, even in moderate to high multiplicity final states ofBdecay.
7.5 Summary
B-meson reconstruction is crucial for the broad physics program performed at Belle andBABAR. All of the tech- niques presented in this chapter utilize unique constraints provided by the experimental setup ofBFactories. They either improve the resolution (e.g. mES and ΔE versus
B-meson invariant mass in full hadronic reconstruction), increase reconstruction efficiency (partial reconstruction) or make possible studies ofB-meson decays with multiple neutrinos in the final state (recoil reconstruction). Some of the B reconstruction methods presented herein were already used by experiments prior to Belle and BABAR. Others, in particular recoil techniques using fully- or semi- exclusive B-meson reconstruction, were pioneered in the BFactories era and proved invaluable to access rare pro- cesses where the kinematics of the signalB meson could not be fully constrained. Together with background dis- crimination (seeChapter 9)B reconstruction techniques have been constantly improved over the past ten years which has enabled studies of less clean modes and in- creased sensitivity to rare decays.
Chapter 8
B-flavor tagging
Editors:
Juerg Beringer (BABAR) Kazutaka Sumisawa (Belle) Additional section writers: Robert Cahn, Simone Stracka
8.1 Introduction
The goal ofB-flavor tagging is to determine the flavor of a B meson (i.e. whether it contains abor a b quark) at the time of its decay. At the B Factories, flavor tagging is needed for most measurements of time-dependent CP asymmetries and B meson mixing. As will be discussed inChapter 10, these measurements usually require full re- construction of the decay of one of theBmesons (referred to asBrecor “signal”B), measurement of the decay time
difference Δtbetween the twoBmeson decays, and flavor tagging of the otherB meson (referred to asBtag in the
following).
At the B Factories, in contrast to hadron colliders, B meson pairs are produced in isolation (apart from any initial-state radiation), since there is no “underlying event” and the fraction of events with multiplee+e−interactions
(“pile-up”) is negligible. Therefore, if aBrecdecay is fully
reconstructed, the remaining tracks in the event can be assumed to come from the Btag decay. In this case fla-
vor tagging is to a good approximation independent of the specificBrecdecay mode reconstructed (but of course
still depends on whether decays of B0/B0, B+/B− or, when running at the Υ(5S),B0
s/B0s are tagged), and the
flavor tagging performance can be measured using fully reconstructed flavor-specificBrecdecays. For inclusive re-
construction of the signalB, flavor tagging in general de- pends on the specificBrecreconstruction since the remain-
ing tracks in the event cannot be unambiguously assigned to either theBrecorBtag meson.
The tagging of neutralB0/B0mesons fromΥ(4S) de-
cays assuming a fully reconstructedBrec decay is the pri-
mary use case for flavor tagging at the BFactories. This is the situation considered in the following.
Flavor tagging relies on the fact that a large fraction ofB mesons decay to a final state that is flavor specific, i.e. to good approximation, can only be reached either through the decay of a b quark, or through the decay of a b quark. Because of the large number of decay chan- nels, full reconstruction of a sufficiently large number of flavor-specific Btag decays is not feasible. Instead inclu-
sive techniques are employed that make use of different flavor-specific signatures ofB decays. For example, in se- mileptonic decaysB0→D∗−+ν the charge of the lepton
unambiguously identifies the flavor of the decayingBme- son as long as the lepton can be clearly associated with the
semileptonicBdecay and does not come from a secondary Dmeson decay.
The flavor tagging algorithms developed byBABARand Belle proceed in two stages. In the first stage, individual flavor-specific signatures are analyzed, each of which pro- vides a signature-specific flavor tag that by itself could be used for flavor tagging. In the second stage, the results from the first stage signatures are combined into a final flavor tag. Both stages rely on multivariate methods in order to optimally combine all available information.
The outline of this chapter is as follows. After defining the relevant quantities characterizing the performance of B-flavor tagging and discussing the choice of tagging cat- egories, the different sources of flavor information and the corresponding discriminating variables are reviewed. Sec- tion 8.6 describes the specific flavor tagging algorithms used by the BABAR and Belle experiments and quotes the performance of these algorithms. The method used to measure the flavor tagging performance is described elsewhere (see Section 10.6).
8.2 Definitions
The figure of merit for the performance of a tagging algo- rithm is the effective tagging efficiencyQ,
Q=εtag(1−2w)2, (8.2.1)
whereεtagdenotes the fraction of events to which a flavor
tag can be assigned, and the mistag probabilityw is the fraction of events with an incorrectly assigned tag. The term
D= 1−2w (8.2.2) is called the dilution and is the factor by which measured CP and mixing asymmetries are reduced from their physi- cal values due to incorrectly assigned flavor tags. The def- inition of Q is motivated by the fact that the statistical uncertaintiesσ on such asymmetry measurements gener- ally scale approximately as (see Section 8.4)
σ∝ √1
Q. (8.2.3)
Tagging efficiencies and mistag fractions are not a pri- ori the same for tagging B0 and B0 decays because the
detector performance may not be completely charge sym- metric. Therefore the averages
εtag= εB 0+ε B0 2 (8.2.4) w= wB0+wB0 2 (8.2.5) and differences Δεtag=εB0−ε B0 (8.2.6) Δw=wB0−w B0 (8.2.7)
are defined where the subscript refers to the true decay. For example, wB0 refers to the fraction of neutral Btag mesons that decay asB0but are tagged asB0.
8.3 Tagging categories
The effective tagging efficiency Q can be improved (and hence the statistical uncertainty of a measurement de- creased) by grouping events into mutually exclusive tag- ging categories according to their mistag probabilities w (or dilutionsD). For tagging categoriescwith fractions of eventsεc, dilutionsDc, total tagging efficiencyε=
cεc
and average dilutionD=cεcDc/εone finds
Q= c εcD2c =εD 2+ c εc(Dc−D)2. (8.3.1)
Thus the resultingQ is always larger or equal to the one obtained when all events are treated as a single category. One gains most from dividing events into categories when the differences in dilution (or mistag fraction) between categories can be made large. However, the characteris- tics and any systematic effects, such as correlations with the tag vertex resolution, tag-side interference (see Sec- tion 15.3.6), or background levels, are expected to be de- termined by the different flavor-specific signatures. For this reason one would prefer a grouping of events accord- ing to different signatures over a category definition based onw.
The mistag probability w that can be achieved for a given set ofBtagdecay modes is determined by the flavor-
specific signatures present in these decays. Fortunately, the mistag probabilities of different flavor-specific signa- tures tend to be different. For example, in semileptonic decays the charge of a reconstructed high-momentum elec- tron or muon gives a much better indication of the correct tag than the charge of a low momentum pion (“slow pion”)