Listado de divergencias o desvíos recurrentes

In this section the tagging algorithms developed byBABAR

and Belle are discussed. In both experiments these algo- rithms have been improved greatly during the lifetime of the experiment, resulting in a substantial performance in- crease. In the following only the final versions of the tag- ging algorithms are discussed.

8.6.1 Multivariate tagging methods

TheBABARand Belle tagging algorithms both use multi- variate methods:BABARuses an artificial neural network, while Belle’s tagger is based on a multi-dimensional look- up table. Both algorithms provide not only a flavor tag but also an estimated mistag probability for each event.

Both tagging algorithms were trained using large sam- ples of simulated events. Imperfections in the simulation of particle decays (e.g. due to incomplete knowledge of branching fractions) or detector response may lead to in- accurate estimates of the per-event mistag probability by the tagging algorithm. Therefore both algorithms use the estimated per-event mistag probabilities only when sepa- rating events into tagging categories. For each category, w and Δw are measured using a sample of events where the signalB decays into a self-tagging decay mode (Bflav control sample, see Section 10.6). As a result, inaccuracies in the simulation of the training sample can only lead to a non-optimal tagging performance but will not introduce any systematic errors. The loss in tagging performance that results from using tagging categories rather than per- event mistag probabilities was found to be small both for theBABARand the Belle tagging algorithms.

8.6.2 Systematic effects

Systematic effects associated with tagging are discussed inChapter 15; only a brief overview is given here. As dis- cussed above, by using tagging categories whose w and Δw are measured on data, systematic effects that could arise from imperfections in the tagging algorithm or its training are replaced by the statistical uncertainties of the measurements ofwand Δw. The remaining systematic ef- fects associated with flavor tagging arise from

– potential differences in the tagging performance for sig- nal events and for the Bflav control sample used to measurewand Δw, and

– tag-side interference (see Section 15.3.6).

8.6.3 Flavor tagging in BABAR

TheBABARtagging algorithm (Aubert,2005i,2009z; Lees,

2013c) is a modular, multivariate flavor-tagging algorithm that analyses charged tracks on the tag side in order to provide a flavor tag and a mistag probabilityw. The flavor ofBtagis determined from a combination of nine different flavor-specific signatures, which include charged leptons, kaons, pions andΛbaryons (see Section 8.5).

For each of these signatures, properties such as charge, momentum, and decay angles are used as input to a spe- cific neural network (NN) or “sub-tagger”. Three sub- taggers are dedicated to charged leptons, making use of identified electrons (Electron), muons (Muon) and kine- matically identified leptons (Kin. Lepton). The Kaon sub- tagger combines the information from up to three kaons into a single tag. Slow pions are used both by a dedi- cated slow pion sub-tagger (Slow Pion) and in correla- tion with kaons (K-Pi). The Max p* sub-tagger analyzes high-momentum particles. The correlation of fast and slow particles is exploited by the FSCsub-tagger. The Lambda sub-tagger looks atΛbaryons.

These sub-taggers are combined by a single final neu- ral network (BTagger) that is trained to determine the correct flavor ofBtag. Based on the output of this NN and the contributing sub-taggers, each event is assigned to one of six mutually exclusive tagging categories. The overall structure of the BABARtagging neural network is shown in Figure 8.6.1.

Figure 8.6.1.Schematic overview of theBABARtagging algo-

rithm. Each box corresponds to a separate neural network.

The use of sub-taggers dedicated to specific signatures allows one to keep track of the underlying physics of each event and simplifies studies of systematics. For ex- ample, events with an identified electron or muon from a semi-leptonicBtagdecay can be separated from other de- cays and assigned to the Lepton tagging category. The Lepton category does not only have a low w but also more precisely reconstructed Btag vertices, is less sensi-

tive to the bias from charm on the tag side, and is im- mune to the intrinsic mistagging associated with doubly

Cabibbo-suppressed decays (see tag-side interference in Section 15.3.6).

The training and validation of each of the sub-tagger NNs is based on the Stuttgart Neural Network Simulator (Zell et al., 1995). Extensive studies have been performed for each sub-tagger, including a wide search for the most discriminating input variables. NN architectures and the number of training cycles are optimized to yield the most efficient flavor assignment. The NNs are feed-forward net- works with one hidden layer. The weights and bias values of the logistic activation functions are optimized during training using standard back-propagation.

The NNs are trained using a simulated sample of about 500,000 B0_B0 _{pairs in which one meson (B}

rec ) decays to a π+_π− _{final state while the other (B}

tag) decays to any possible final state according to known or expected branching fractions. Half of this sample is used for training the NN, while the other half is used as a test sample for an unbiased evaluation of the performance. Each sub-tagger is trained separately before the training of the BTagger network.36

Details of the architecture of the different neural net- works used by the BABARtagging algorithm are given in Table 8.6.1. For each of the nine sub-taggers and for the final BTagger NN the table lists all input variables and the training target. Some of the sub-taggers are trained to separateB0 _fromB0 _{decays, while others are trained} to discriminate true from fake signatures.

The outputyBTaggerof the final BTagger NN is mapped to values between−1 (for a perfectly taggedB0_{) and +1} (B0_{). The distribution of this output for theB}

flavcontrol sample is shown in Figure 8.6.2. Excellent agreement is observed between data and simulation.

The estimated probabilitypof a correct tag assignment is given by the BTagger NN output

p= 1−w= (1 +|yBTagger|)/2, (8.6.1) and the probability of a givenBtag being aB0is

pBtag=B0= (1 +yBTagger)/2. (8.6.2)

The correctness of these probabilities can be checked with theBflav control sample. For example, one can plot the probability of observing a B0 _{on the B}

flav side as a function of the estimated probability pBtag=B0. Tak-

ing into account the time-integrated mixing probability χd= 0.1862±0.0023 (Beringer et al. (2012)), one expects

for a perfectly trained tagging algorithm

pBflav=B0 = (1−2χd)pBtag=B0+χd (8.6.3)

= (1−2χd)(1 +yBTagger)/2+χd. (8.6.4) 36

Simultaneous training of all sub-taggers and the BTagger NN has been shown not to result in a significantly better clas- sification performance.

As can be seen from Figure 8.6.3, the probabilities ob- tained from the BTagger NN output are in very good agreement with the expectations for both data and sim- ulation. Nevertheless, as discussed in Section 8.6.1, these estimated probabilities are only used to separate events into tagging categories.

Fraction per 0.02 0.01 0.02 0.03 0.04 0.05 MC Data BTagger y -1 -0.5 0 0.5 1 Data - MC 0 0.002

Figure 8.6.2.Distribution of the output of the final BTagger

NN (yBTagger) on theBflavcontrol sample for data and simu- lation, using the fullBABARdata sample. A contribution of up to 22% from combinatorial background is subtracted in each bin based on a fit to themESdistribution. The difference be- tween data and simulation (with statistical uncertainties added in quadrature) is also shown.

The tagging algorithm assigns each event to one of six hierarchical and mutually exclusive tagging categories: Lepton,Kaon I,Kaon II,Kaon-Pion,PionorOther. The name given to each category indicates the dominant physics processes (or sub-tagger) contributing to the fla- vor identification. For most categories, this classification is based onyBTagger. For theLepton category, which sin- gles out events with a cleanly identified primary lepton, additional cuts are made on the output of the electron or muon sub-taggers. Over 95% of events in theLeptoncat- egory contain a semileptonicBtagdecay. The definition of the tagging categories is summarized in Table 8.6.2.

The final version of the BABAR tagging algorithm37 (Lees,2013c) achieves an effective tagging efficiencyQ= (33.1±0.3)% on the fullBABARdata set. The breakdown of this performance into the different tagging categories is shown in Table 8.6.3.

37

Improvements in the particle identification algorithms used for the final version of the BABAR tagging algorithm (Lees, 2013c) lead to a higher Q value of (33.1±0.3)%, compared toQ≈31% achieved by the previous version (Aubert, 2005i). The tagging algorithm itself did not change.

Table 8.6.1.Overview of the neural networks used by theBABARBTagger and its sub-taggers. For each sub-tagger the network architecture is shown in the second column according to the notationNinputs:Nhidden nodes:Noutputs. The input variables are

listed in the third column while the fourth column describes the goal of the NN training. (Sub-)Tagger Network architecture Discriminating input variables Training goal

Electron 4:12:1 q,p∗,EW

90, cosθmiss ClassifyB0versusB0

Muon 4:12:1 q,p∗,EW

90, cosθmiss ClassifyB0versusB0

Kin. Lepton 3:3:1 p∗,EW

90, cosθmiss Recognize primary leptons

Kaon 5:10:1 (qLK)1, (qLK)2, (qLK)3,nK_S0,Σp⊥ ClassifyB

0

versusB0

Slow Pion 3:10:1 p∗, cosθπT,LK Recognize slow pions fromD∗±decays

Maxp∗ 3:6:1 p∗,d0, cosθ Recognize directBdaughters

K–Pi 3:10:1 (qLK), SlowPion tag, cosθK,π RecognizeK-πpairs fromD∗±decays

FSC 6:12:1 cosθSlowFast, pSlow∗ , p∗Fast, cosθSlowT,

cosθFastT,LKSlow

Recognize fast-slow correlated tracks Lambda 6:14:1 MΛ,χ2, cosθΛ,sΛ,pΛ,pproton RecognizeΛdecays

BTagger 9:20:1 All of the above tags ClassifyB0

versusB0

Table 8.6.2.Definition of tagging categories for theBABARflavor tagging algorithm. Events with|yBTagger|<0.1 are classified

asUntaggedand are not used to extract time-dependent information from data.

Category Definition

Lepton (|yElectron|>0.8 or|yMuon|>0.8) and|yBTagger|>0.8

Kaon I |yBTagger|>0.8

Kaon II 0.6<|yBTagger|<0.8

Kaon-Pion 0.4<|yBTagger|<0.6

Pion 0.2<|yBTagger|<0.4

Other 0.1<|yBTagger|<0.2

Table 8.6.3.Performance of the finalBABARtagging algorithm on data. Category εtag(%) Δεtag(%) w(%) Δw(%) Q(%) ΔQ(%)

Lepton 9.7±0.1 0.2±0.2 2.1±0.2 0.2±0.5 8.9±0.1 0.1±0.4 Kaon I 11.3±0.1 −0.1±0.2 4.1±0.3 0.2±0.6 9.6±0.1 −0.1±0.4 Kaon II 15.9±0.1 −0.1±0.2 13.0±0.3 −0.2±0.6 8.7±0.2 0.0±0.5 Kaon-Pion 13.2±0.1 0.4±0.2 23.0±0.4 −1.3±0.7 3.9±0.1 0.5±0.3 Pion 16.8±0.1 −0.3±0.3 33.3±0.4 −2.7±0.6 1.9±0.1 0.6±0.2 Other 10.6±0.1 −0.5±0.2 41.8±0.5 5.9±0.7 0.28±0.03 −0.4±0.1 Total 77.5±0.1 −0.3±0.5 33.1±0.3 0.7±0.8

The contribution of each of the nine sub-taggers to the overall tagging performance can be evaluated in two ways: – the absolute effective tagging efficiency obtained by

using only one sub-tagger (Qabs);

– the incremental effective tagging efficiency (Qincr), de-

fined as the improvement inQassociated with adding a single sub-tagger on top of all the others.

Table 8.6.4 shows Qabs and Qincr for the nine sub-

taggers. In most events multiple flavor tagging signatures are present and contribute to the final tag as can be seen from the fact thatQincris small for most sub-taggers. The

exception is the Kaon sub-tagger which is the only tagger whose presence is essential to maintain a high tagging per-

formance. The fact that in most cases several sub-taggers contribute to the final tag helps to ensure the robustness of the tagging algorithm.

8.6.4 Flavor tagging in Belle

The flavor tagging method used by Belle (Kakuno,2004) is based on a multi-dimensional look-up table. A schematic diagram of the algorithm is shown in Figure 8.6.4.

The algorithm provides two parameters as the flavor tagging outputs:qdenoting the flavor ofBtag(+1 forB0, −1 for B0_{), and r is an expected flavor dilution factor}

Table 8.6.4. Contribution of the nine sub-taggers to the BABARtagging algorithm for the version of the algorithm used in 2004. The final version of the algorithm has the same architecture of the sub-taggers and BTagger but uses an improved kaon identification, leading to a slightly larger tagging performance. The determination ofQabs on data was made using the Bflav

control sample, assuming a time-integrated mixing probability ofχd= 0.182 and correcting for background. See text for the

definition ofQabsandQincr.

Sub-tagger Qabson MC (%) Qabson data (%) Qincron MC (%)

Electron 6.1±0.1 5.0±0.2 1.14 Muon 4.0±0.1 3.3±0.2 1.0 Kin. Lepton 2.9±0.1 2.6±0.2 0.36 Kaon 18.8±0.1 18.3±0.4 9.91 Slow Pions 5.2±0.1 6.1±0.4 0.47 K-Pi 9.3±0.1 10.0±0.4 0.25 Maxp∗ 11.0±0.3 9.7±0.5 0.06 FSC 6.0±0.1 6.6±0.4 0.08 Lambda 0.3±0.1 0.2±0.1 0.38 ) 0 B = flav p (B 0.2 0.4 0.6 0.8 1 MC Data Expected ) / 2 BTagger (1 + y 0 0.2 0.4 0.6 0.8 1 Residuals_-0.02 0 0.02

Figure 8.6.3. Probability of observing a fully reconstructed

B0

on theBflavside as a function of the probabilitypBtag=B0= (1 +yBTagger)/2 of having aB0 on theBtagside. The dotted

line shows the dependence expected for a perfectly trained tag- ging algorithm. The solid points are from the fullBABARBflav

control sample, the open circles are obtained from simulation. A contribution of up to 22% from combinatorial background is subtracted in each bin based on a fit to themESdistribution.

The residuals with respect to the expectation are shown at the bottom.

to unity for an unambiguous flavor assignment (w 0). In order to obtain a high overall effective tagging effi- ciencyQ, an estimated flavor dilution factor is assigned to each event based on multiple discriminants. Using a multi- dimensional look-up table prepared from a large sample of simulated events and binned by the values of the discrim-

Slow pion Kaon Lepton

Information on charged tracks

Lambda

Track-level look-up tables

Flavor information "q" and "r" Event-level look-up table

q.r (q.r)K/Λ q.r Select track with largest "r" Calculate combined "q.r" Select track with largest "r"

Figure 8.6.4. Schematic diagram of Belle’s two-stage flavor tagging algorithm. See the text for the definition of the param- eters “q” and “r”.

inants, the signed probability,q·r, is given by q·r= N(B

0_)−N(B0₎

N(B0_{) +}N₍B0₎, (8.6.5)

whereN(B0_{) andN(B}0_{) are the numbers ofB}0 _andB0

in the corresponding bin of the look-up table.

The flavor tagging algorithm proceeds in two stages: the track stage and the event stage. In the track stage, each pair of oppositely charged tracks is examined to sat- isfy criteria for theΛ-like particle category. The remaining charged tracks are sorted into slow-pion-like, lepton-like and kaon-like particle categories. Thebflavor and its di- lution factor of each particle,q·r, in the four categories is estimated using the discriminants shown in Table 8.6.5.

In the second stage, the results from the first stage are combined to obtain the event-level value ofq·r. From the lepton-like and slow-pion-like track categories, the track with the highest r value from each category is chosen as the input to the event level look-up table. The flavor dilu- tion factors of the kaon-like andΛ-like particle candidates are combined by calculating the product of the flavor dilu- tion factors in order to account for the cases with multiple

Table 8.6.5. Discriminants used in the Belle tagging algo- rithm.

(Sub-)Stage Variables Number of bins Lepton q, eorμ,L , p∗, θlab, Mrecoil, p∗miss 31680

Kaon q, n K0 S , p∗, θ lab,LK 19656 Lambda q, n K0 S, MΛ, θΛ, Δz 32

Slow pion q, plab, θ_lab,cos_θπT,Le 7000 Event (q·r) _,(q·r)_{K/Λ ,}(q·r)_πs 16625

s quarks in an event. The product of flavor dilution fac- tors gives better effective efficiency than taking the track with the highestr. Using the flavor dilution factorrdeter- mined from MonteCarlo (MC) simulation as a measure of the tagging quality is a straightforward and powerful way of taking into account correlations among various tagging discriminants.

By using two stages, the look-up tables can be kept small enough to provide sufficient statistics for each bin. Four million B0_B0 _{MC events are used to generate the}

particle-level look-up tables. To reduce statistical fluctu- ations of the r values in the particle-level look-up tables, the r value in each bin is calculated by including events in nearby bins with small weights. The event-level look-up table is prepared using MC samples that are statistically independent of those used to generate the track-level ta- bles to avoid any bias from a statistical correlation be- tween the two stages. Seven millionB0_B0_{MC events are}

used to create the event-level look-up table. The perfor- mance of individual tagging categories as obtained in MC simulation is shown for illustration in Table 8.6.6.

Table 8.6.6. Performance of sub-taggers in the Belle flavor tagging algorithm in terms of effective tagging efficiencyQabs

in simulated events.

Sub-tagger Qabson MC

Leptons 12%

Kaons andΛ’s 18%

Slow Pions 6%

All tagged events are sorted into seven subsamples ac- cording to the value of r: 0 ≤ r ≤ 0.1, 0.1 < r ≤ 0.25, 0.25 < r ≤ 0.5, 0.5 < r ≤ 0.625, 0.625 < r ≤ 0.75, 0.75 < r ≤0.875 and 0.875 < r ≤ 1. For each subsam- ple l, the corresponding average wrong tag fraction wl

is determined. For events with r ≤ 0.1, there is negligi- ble flavor discrimination available and w0 is set to 0.5.

For the other six subsamples, the average wrong tag frac- tions wl (l= 1,6) are measured directly from data using

samples of semi-leptonic (B0 _{→ D}∗−+_{ν) and hadronic}

(B0 _{→ D}(∗)−_π+ _{with D}∗−_ρ+_{) B meson decays. These}

decays are fully reconstructed and the flavor of the asso- ciated B mesons is tagged. A total of 1461983 events are used to evaluate the performance of the tagging algorithm. An effective tagging efficiency ofQ= (30.1±0.4)% is ob-

tained. The wrong tag fractions, differences and tagging efficiencies for each subsample are shown in Table 8.6.7.

The average value ofrfor each region (rl) and the mea-

sured wrong tag fraction (wl) should satisfyrl1−2wl

if the MC simulation used for constructing the look-up tables simulates genericBdecays correctly. The degrada-

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