University of Groningen

First observation and amplitude analysis of the B- -> D+K-pi(-) decayAaij, R.; Adeva, B.; Adinolfi, M.; Affolder, A.; Ajaltouni, Z.; Akar, S.; Albrecht, J.; Alessio, F.;Alexander, M.; Ali, S.Published in:Physical Review D

DOI:10.1103/PhysRevD.91.092002

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Citation for published version (APA):Aaij, R., Adeva, B., Adinolfi, M., Affolder, A., Ajaltouni, Z., Akar, S., Albrecht, J., Alessio, F., Alexander, M.,Ali, S., Alkhazov, G., Cartelle, P. A., Alves, A. A., Amato, S., Amerio, S., Amhis, Y., An, L., Anderlini, L.,Anderson, J., ... LHCb Collaboration (2015). First observation and amplitude analysis of the B- -> D+K-pi(-)decay. Physical Review D, 91(9), [092002]. https://doi.org/10.1103/PhysRevD.91.092002

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First observation and amplitude analysis of the B− → DþK−π− decay

R. Aaij et al.*

(LHCb Collaboration)(Received 11 March 2015; published 5 May 2015)

The B− → DþK−π− decay is observed in a data sample corresponding to 3.0 fb−1 of pp collisiondata recorded by the LHCb experiment during 2011 and 2012. Its branching fraction is measured to beBðB− → DþK−π−Þ ¼ ð7.31� 0.19� 0.22� 0.39Þ × 10−5 where the uncertainties are statistical, system-atic and from the branching fraction of the normalization channel B− → Dþπ−π−, respectively. Anamplitude analysis of the resonant structure of the B− → DþK−π− decay is used to measure thecontributions from quasi-two-body B− → D�

0ð2400Þ0K−, B− → D�2ð2460Þ0K−, and B− → D�

Jð2760Þ0K−

decays, as well as from nonresonant sources. The D�Jð2760Þ0 resonance is determined to have spin 1.

DOI: 10.1103/PhysRevD.91.092002 PACS numbers: 13.25.Hw, 14.40.Lb

I. INTRODUCTION

Excited charmed mesons are of great theoretical andexperimental interest as they allow detailed studies of QCDin an interesting energy regime. Good progress has beenachieved in identifying and measuring the parameters ofthe orbitally excited states, notably from Dalitz plot (DP)analyses of three-body B decays. Relevant examplesinclude the studies of B− → Dþπ−π− [1,2] and B̄0 →D0πþπ− [3] decays, which provide information on excitedneutral and charged charmed mesons (collectively referredto as D�� states), respectively. First results on excitedcharm-strange mesons have also recently been obtainedwith the DP analysis technique [4–6]. Studies of promptcharm resonance production in eþe− and pp collisions[7,8] have revealed a number of additional high-massstates. Most of these higher-mass states are not yetconfirmed by independent analyses, and their spectroscopicidentification is unclear. Analyses of resonances produceddirectly from eþe− and pp collisions do not allowdetermination of the quantum numbers of the producedstates, but can distinguish whether or not they have naturalspin parity (i.e. JP in the series 0þ; 1−; 2þ; � � �). The currentexperimental knowledge of the neutral D�� states issummarized in Table I (here and throughout the paper,natural units with ℏ ¼ c ¼ 1 are used). The D�

0ð2400Þ0,D1ð2420Þ0, D0

1ð2430Þ0 and D�2ð2460Þ0 mesons are gen-

erally understood to be the four orbitally excited (1P) states.The experimental situation as well as the spectroscopicidentification of the heavier states is less clear.The B− → DþK−π− decay can be used to study neutral

D�� states. The DþK−π− final state is expected to exhibit

resonant structure only in theDþπ− channel, and unlike theCabibbo-favored Dþπ−π− final state does not contain anypair of identical particles. This simplifies the analysis ofthe contributing excited charm states, since partial-waveanalysis can be used to help determine the resonances thatcontribute.One further motivation to study B− → DþK−π− decays is

related to the measurement of the angle γ of the unitaritytriangle defined as γ ≡ arg ½−VudV�

ub=ðVcdV�cbÞ�, where Vxy

are elements of the Cabibbo-Kobayashi-Maskawa (CKM)quark mixing matrix [10,11]. One of the most powerfulmethods to determine γ uses B− → DK− decays, with theneutral D meson decaying to CP eigenstates [12,13]. Thesensitivity to γ arises due to the interference of amplitudesproportional to the CKM matrix elements Vub and Vcb,associated with D̄0 and D0 production respectively.However, a challenge for such methods is to determinethe ratio of magnitudes of the two amplitudes, rB, that mustbe known to extract γ. This is usually handled by includingD-meson decays to additional final states in the analysis. Bycontrast, in B− → D��K− decays the efficiency-correctedratio of yields of B− → D��K− → D−πþK− and B− →D��K− → Dþπ−K− decays gives r2B directly [14]. Thedecay B− → D��K− → Dπ0K− where the D meson isreconstructed in CP eigenstates can be used to search forCP violation driven by γ. Measurement of the first two ofthese processes would therefore provide knowledge of rB inB− → D��K− decays, indicating whether or not a competi-tive measurement of γ can be made with this approach.In this paper, the B− → DþK−π− decay is studied for the

first time, with the Dþ meson reconstructed through theK−πþπþ decay mode. The inclusion of charge-conjugateprocesses is implied. The topologically similar B− →Dþπ−π− decay is used as a control channel and fornormalization of the branching fraction measurement. Alarge B− → DþK−π− signal yield is found, correspondingto a clear first observation of the decay, and allowinginvestigation of the DP structure of the decay. The

*Full author list given at the end of the article.

Published by the American Physical Society under the terms ofthe Creative Commons Attribution 3.0 License. Further distri-bution of this work must maintain attribution to the author(s) andthe published article’s title, journal citation, and DOI.

PHYSICAL REVIEW D 91, 092002 (2015)

1550-7998=2015=91(9)=092002(24) 092002-1 © 2015 CERN, for the LHCb Collaboration

amplitude analysis allows studies of known resonances,searches for higher-mass states and measurement ofthe properties, including the quantum numbers, of anyresonances that are observed. The analysis is based on adata sample corresponding to an integrated luminosityof 3.0 fb−1 of pp collision data collected with theLHCb detector, approximately one third of which wascollected during 2011 when the collision center-of-massenergy was

ffiffiffis

p ¼ 7 TeV and the rest during 2012 withffiffiffis

p ¼ 8 TeV.The paper is organized as follows. A brief description of

the LHCb detector as well as reconstruction and simulationsoftware is given in Sec. II. The selection of signalcandidates is described in Sec. III, and the branchingfraction measurement is presented in Sec. IV. Studies ofthe backgrounds and the fit to the B candidate invariantmass distribution are in Sec. IVA, with studies of the signalefficiency and a definition of the square Dalitz plot (SDP)in Sec. IV B. Systematic uncertainties on, and the resultsfor, the branching fraction are discussed in Secs. IV Cand IV D respectively. A study of the angular moments ofB− → DþK−π− decays is given in Sec. V, with results usedto guide the Dalitz plot analysis that follows. An overviewof the Dalitz plot analysis formalism is given in Sec. VI,and details of the implementation of the amplitude analysisare presented in Sec. VII. The evaluation of systematicuncertainties is described in Sec. VIII. The results and asummary are given in Sec. IX.

II. LHCb DETECTOR

The LHCb detector [15,16] is a single-arm forwardspectrometer covering the pseudorapidity range 2 < η < 5,designed for the study of particles containing b or c quarks.The detector includes a high-precision tracking systemconsisting of a silicon-strip vertex detector [17] surround-ing the pp interaction region, a large-area silicon-stripdetector located upstream of a dipole magnet with abending power of about 4 Tm, and three stations ofsilicon-strip detectors and straw drift tubes [18] placed

downstream of the magnet. The polarity of the dipolemagnet is reversed periodically throughout data taking. Thetracking system provides a measurement of the momentum,p, of charged particles with a relative uncertainty that variesfrom 0.5% at low momentum to 1.0% at 200 GeV. Theminimum distance of a track to a primary vertex, the impactparameter (IP), is measured with a resolution ofð15þ 29=pTÞ μm, where pT is the component of themomentum transverse to the beam, in GeV. Different typesof charged hadrons are distinguished using informationfrom two ring-imaging Cherenkov detectors [19]. Photon,electron and hadron candidates are identified by a calo-rimeter system consisting of scintillating-pad and pre-shower detectors, an electromagnetic calorimeter and ahadronic calorimeter. Muons are identified by a systemcomposed of alternating layers of iron and multiwireproportional chambers [20].The trigger [21] consists of a hardware stage, based on

information from the calorimeter and muon systems,followed by a software stage, in which all tracks withpT > 500ð300Þ MeV are reconstructed for data collectedin 2011 (2012). The software trigger line used in theanalysis reported in this paper requires a two-, three- orfour-track secondary vertex with significant displacementfrom the primary pp interaction vertices (PVs). At leastone charged particle must have pT > 1.7 GeV and beinconsistent with originating from the PV. A multivariatealgorithm [22] is used for the identification of secondaryvertices consistent with the decay of a b hadron.In the offline selection, the objects that fired the trigger

are associated with reconstructed particles. Selectionrequirements can therefore be made not only on the triggerline that fired, but also on whether the decision was due tothe signal candidate, other particles produced in the ppcollision, or a combination of both. Signal candidates areaccepted offline if one of the final-state particles created acluster in the hadronic calorimeter with sufficient trans-verse energy to fire the hardware trigger. These candidatesare referred to as “triggered on signal” or TOS. Events thatare triggered at the hardware level by another particle in theevent, referred to as “triggered independent of signal” orTIS, are also retained. After all selection requirements areimposed, 57% of events in the sample were triggered bythe decay products of the signal candidate (TOS), while theremainder were triggered only by another particle in theevent (TIS-only).Simulated events are used to characterize the detector

response to signal and certain types of background events.In the simulation, pp collisions are generated using PYTHIA

[23] with a specific LHCb configuration [24]. Decays ofhadronic particles are described by EVTGEN [25], in whichfinal-state radiation is generated using PHOTOS [26]. Theinteraction of the generated particles with the detector andits response are implemented using the GEANT4 toolkit [27]as described in Ref. [28].

TABLE I. Measured properties of neutral D�� states. Wheremore than one uncertainty is given, the first is statistical and theothers systematic.

Resonance Mass (MeV) Width (MeV) JP Ref.

D�0ð2400Þ0 2318� 29 267� 40 0þ [9]

D1ð2420Þ0 2421.4� 0.6 27.4� 2.5 1þ [9]D0

1ð2430Þ0 2427�26�20�15 384þ107−75 �24�70 1þ [1]

D�2ð2460Þ0 2462.6� 0.6 49.0� 1.3 2þ [9]

D�ð2600Þ 2608.7� 2.4� 2.5 93� 6� 13 natural [7]D�ð2650Þ 2649.2� 3.5� 3.5 140� 17� 19 natural [8]D�ð2760Þ 2763.3� 2.3� 2.3 60.9� 5.1� 3.6 natural [7]D�ð2760Þ 2760.1� 1.1� 3.7 74.4� 3.4� 19.1 natural [8]

R. AAIJ et al. PHYSICAL REVIEW D 91, 092002 (2015)

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III. SELECTION REQUIREMENTS

Most selection requirements are optimized using theB− → Dþπ−π− control channel. Loose initial selectionrequirements on the quality of the tracks combined toform the B candidate, as well as on their p, pT and χ2IP, areapplied to obtain a visible peak in the invariant massdistribution. The χ2IP is the difference between the χ2 of thePV reconstruction with and without the considered particle.Only candidates with an invariant mass in the range 1770 <mðK−πþπþÞ < 1968 MeV are retained. Further require-ments are imposed on the vertex quality (χ2vtx) and flightdistance from the associated PVof the B and D candidates.The B candidate must also satisfy requirements on itsinvariant mass and on the cosine of the angle between themomentum vector and the line joining the PV underconsideration to the B vertex (cos θdir). The initial selectionrequirements are found to be about 90% efficient onsimulated signal decays.Two neural networks [29] are used to further separate

signal from background. The first is designed to separatecandidates that contain real Dþ → K−πþπþ decays fromthose that do not; the second separates B− → Dþπ−π−signal decays from background combinations. Both net-works are trained using theDþπ−π− control channel, wherethe SPLOT technique [30] is used to statistically separateB− → Dþπ−π− signal decays from background combina-tions using the D (B) candidate mass as the discriminatingvariable for the first (second) network. The first networktakes as input properties of theD candidate and its daughtertracks, including information about kinematics, track andvertex quality. The second uses a total of 27 input variables.They include the χ2IP of the two “bachelor” pions (i.e. pionsthat originate directly from the B decay) and propertiesof the D candidate including its χ2IP, χ2vtx, and cos θdir,the output of the D neural network and the square of theflight distance divided by its uncertainty squared (χ2flight).Variables associated with the B candidate are also used,including pT, χ2IP, χ

2vtx, χ2flight and cos θdir. The pT asym-

metry and track multiplicity in a cone with a half angleof 1.5 units of the plane of pseudorapidity and azimuthalangle (measured in radians) around the B candidate flightdirection [31], which contain information about the iso-lation of the B candidate from the rest of the event, are alsoused in the network. The neural network input quantitiesdepend only weakly on the kinematics of the B decay. Arequirement is imposed on the second neural networkoutput that reduces the combinatorial background by anorder of magnitude while retaining about 75% of the signal.The selection criteria for the B− → DþK−π− and B− →

Dþπ−π− candidates are identical except for the particleidentification (PID) requirement on the bachelor track thatdiffers between the two modes. All five final-state particlesfor each decay mode have PID criteria applied to prefer-entially select either pions or kaons. Tight requirements are

placed on the higher-momentum pion from the Dþ decayand on the bachelor kaon in B− → DþK−π− to suppressbackgrounds from Dþ

s → K−Kþπþ and B− → Dþπ−π−decays, respectively. The combined efficiency of the PIDrequirements on the five final-state tracks is around 70%for B− → Dþπ−π− decays and around 40% for B− →DþK−π− decays. The PID efficiency depends on thekinematics of the tracks, as described in detail inSec. IV B, and is determined using samples of D0 →K−πþ decays selected in data by exploiting the kinematicsof the D�þ → D0πþ decay chain to obtain clean sampleswithout using the PID information.To improve the B candidate invariant mass resolution,

track momenta are scaled [32,33] with calibration param-eters determined by matching the measured peak of theJ=ψ → μþμ− decay to the known J=ψ mass [9].Furthermore, a fit to the kinematics and topology of thedecay chain [34] is used to adjust the four-momenta ofthe tracks from the D candidate so that their combinedinvariant mass matches the world average value for the Dþmeson [9]. An additional Bmass constraint is applied in thecalculation of the variables that are used in the Dalitzplot fit.To remove potential background from misreconstructed

Λþc decays, candidates are rejected if the invariant mass of

theD candidate lies in the range 2280–2300 MeV when theproton mass hypothesis is applied to the low-momentumpion track. Possible backgrounds from B−-meson decayswithout an intermediate charm meson are suppressed bythe requirement on the output value from the first neuralnetwork, and any surviving background of this type isremoved by requiring that the D candidate vertex isdisplaced by at least 1 mm from the B-decay vertex.The efficiency of this requirement is about 85%.Signal candidates are retained for further analysis if they

have an invariant mass in the range 5100–5800 MeV. Afterall selection requirements are applied, fewer than 1% ofevents with one candidate also contain a second candidate.Such multiple candidates are retained and treated in thesame manner as other candidates; the associated systematicuncertainty is negligible.

IV. BRANCHING FRACTION DETERMINATION

The ratio of branching fractions is calculated from thesignal yields with event-by-event efficiency correctionsapplied as a function of square Dalitz plot position. Thecalculation is

BðB− → DþK−π−ÞBðB− → Dþπ−π−Þ ¼ NcorrðB− → DþK−π−Þ

NcorrðB− → Dþπ−π−Þ ; ð1Þ

where Ncorr ¼ PiWi=ϵi is the efficiency-corrected yield.

The index i sums over all candidates in the data sampleand Wi is the signal weight for each candidate, which isdetermined from the fits described in Sec. IVA and shown

FIRST OBSERVATION AND AMPLITUDE ANALYSIS OF … PHYSICAL REVIEW D 91, 092002 (2015)

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in Figs. 1 and 2, using the SPLOT technique [30]. Each fitis performed simultaneously to decays in the TOS andTIS-only categories. The efficiency of candidate i, ϵi, isobtained separately for each trigger subsample as describedin Sec. IV B.

A. Determination of signal and background yields

The candidates that survive the selection requirementsare comprised of signal decays and various categories ofbackground. Combinatorial background arises from ran-dom combinations of tracks (possibly including a realDþ → K−πþπþ decay). Partially reconstructed back-grounds originate from b-hadron decays with additionalparticles that are not part of the reconstructed decaychain. Misidentified decays also originate from b-hadrondecays, but where one of the final-state particles has beenincorrectly identified (e.g. a pion as a kaon). The signal(normalization channel) and background yields areobtained from unbinned maximum likelihood fits to theDþK−π− (Dþπ−π−) invariant mass distributions.Both the B− → DþK−π− and B− → Dþπ−π− signal

shapes are modeled by the sum of two Crystal Ball

(CB) functions [35] with a common mean and tails onopposite sides, where the high-mass tail accounts for non-Gaussian reconstruction effects. The ratio of widths of theCB shapes and the relative normalization of the narrowerCB shape are constrained within their uncertainties to thevalues found in fits to simulated signal samples. The tailparameters of the CB shapes are also fixed to those found insimulation.The combinatorial backgrounds in both DþK−π− and

Dþπ−π− samples are modeled with linear functions; theslope of this function is allowed to differ between the twotrigger subsamples. The decay B− → D�þK−π− is a par-tially reconstructed background for DþK−π− candidates,where the D�þ decays to either Dþγ or Dþπ0 and theneutral particle is not reconstructed. Similarly the decayB− → D�þπ−π− forms a partially reconstructed back-ground to the Dþπ−π− final state. These are modeled withnonparametric shapes determined from simulated samples.The shapes are characterized by a sharp edge around100 MeV below the B peak, where the exact position ofthe edge depends on properties of the decay including theD�þ polarization. The fit quality improves when the shape

) [MeV]-π-π+D(m5200 5400 5600 5800

Can

dida

tes

/ (5

MeV

)

1

10

210

310Data

Total

Signal

Comb. bkg.−π−K* +( )D→−B

−π−π+*D→−B

LHCb

) [MeV]-π-π+D(m5200 5400 5600 5800

Can

dida

tes

/ (5

MeV

)

1

10

210

310Data

Total

Signal

Comb. bkg.−π−K* +( )D→−B

−π−π+*D→−B

LHCb

FIG. 1 (color online). Results of the fit to the B− → Dþπ−π− candidate invariant mass distribution for the (left) TOS and (right) TIS-only subsamples. Data points are shown in black, the full fitted model as solid blue lines and the components as shown in the legend.

) [MeV]-π-K+D(m

5200 5400 5600 5800

Can

dida

tes

/ (5

MeV

)

1

10

210

DataTotalSignalComb. bkg.

−π−π* +( )D→−B−π−K+

sD→−B−π−K+*D→−B

LHCb

) [MeV]-π-K+D(m

5200 5400 5600 5800

Can

dida

tes

/ (5

MeV

)

1

10

210

DataTotalSignalComb. bkg.

−π−π* +( ) D→−B−π−K+

sD→−B−π−K+*D→−B

LHCb

FIG. 2 (color online). Results of the fit to the B− → DþK−π− candidate invariant mass distribution for the (left) TOS and (right) TIS-only subsamples. Data points are shown in black, the full fitted model as solid blue lines and the components as shown in the legend.

R. AAIJ et al. PHYSICAL REVIEW D 91, 092002 (2015)

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is allowed to be offset by a small shift that is determinedfrom the data.Most potential sources of misidentified backgrounds

have broad B candidate invariant mass distributions, andhence are absorbed in the combinatorial backgroundcomponent in the fit. The decays B− → Dð�Þþπ−π− andB− → Dþ

s K−π−, however, give distinctive shapes in themass distribution of DþK−π− candidates. For Dþπ−π−candidates the only significant misidentified backgroundcontribution is from B− → Dð�ÞþK−π− decays. The mis-identified background shapes are also modeled with non-parametric shapes determined from simulated samples.The simulated samples used to obtain signal and back-

ground shapes are generated with flat distributions in thephase space of their SDPs. For B− → Dþπ−π− and B− →D�þπ−π− decays, accurate models of the distributionsacross the SDP are known [1,2], so the simulated samplesare reweighted using the B− → Dþπ−π− data sample; thisaffects the shape of the misidentified background compo-nent in the fit to theDþK−πþ sample. Additionally, theDþand D�þ portions of this background are combined accord-ing to their known branching fractions. All of the shapes,except for that of the combinatorial background, arecommon between the two trigger subsamples in each fit,but the signal and background yields in the subsamples areindependent. In total there are 15 free parameters in the fitto theDþπ−π− sample: yields in each subsample for signal,combinatorial, B−→Dð�ÞþK−π− and B−→D�þπ−π− back-grounds; the combinatorial slope in each subsample; thedouble CB peak position, the width of the narrower CB,the ratio of CB widths and the fraction of entries in thenarrower CB shape; and the shift parameter of the partiallyreconstructed background. The result of the Dþπ−π− fit isshown in Fig. 1 for both trigger subsamples and gives acombined signal yield of approximately 49 000 decays.Component yields are given in Table II.There are a total of 17 free parameters in the fit to the

DþK−π− sample: yields in each subsample for signal,combinatorial, B− → D�þK−π−, B− → Dþ

s K−π− andB− → Dð�Þþπ−π− backgrounds; the combinatorial slopein each subsample; the same signal shape parameters asfor the Dþπ−π− fit; and the shift parameter of the partiallyreconstructed background. Figure 2 shows the result of theDþK−π− fit for the two trigger subsamples that yield a totalof approximately 2000 B− → DþK−π− decays. The yields

of all fit components are shown in Table III. The statisticalsignal significance, estimated in the conventional way fromthe change in negative log-likelihood from the fit when thesignal component is removed, is in excess of 60 standarddeviations (σ).

B. Signal efficiency

Since both B− → DþK−π− and B− → Dþπ−π− decayshave nontrivial DP distributions, it is necessary to under-stand the variation of the efficiency across the phase space.Since, moreover, the efficiency variation tends to bestrongest close to the kinematic boundaries of the conven-tional Dalitz plot, it is convenient to model these effectsin terms of the SDP defined by variables m0 and θ0 whichare valid in the range 0 to 1 and are given for the DþK−π−

case by

m0 ≡ 1

πarccos

�2mðDþπ−Þ −mmin

Dþπ−

mmaxDþπ− −mmin

Dþπ−− 1

�and

θ0 ≡ 1

πθðDþπ−Þ; ð2Þ

where mmaxDþπ− ¼ mB− −mK− and mmin

Dþπ− ¼ mDþ þmπ− arethe kinematic boundaries ofmðDþπ−Þ allowed in the B− →DþK−π− decay and θðDþπ−Þ is the helicity angle of theDþπ− system (the angle between the K−- and the Dþ-meson momenta in the Dþπ− rest frame). For the Dþπ−π−case, m0 and θ0 are defined in terms of the π−π− mass andhelicity angle, respectively, since with this choice only theregion of the SDP with θ0ðπ−π−Þ < 0.5 is populated due tothe symmetry of the two pions in the final state.Efficiency variation across the SDP is caused by the

detector acceptance and by trigger, selection and PIDrequirements. The efficiency variation is evaluated for bothDþK−π− and Dþπ−π− final states with simulated samplesgenerated uniformly over the SDP. Data-driven correctionsare applied to correct for known differences between dataand simulation in the tracking, trigger and PID efficiencies,using identical methods to those described in Ref. [5]. Theefficiency functions are fitted with two-dimensional cubicsplines to smooth out statistical fluctuations due to limitedsample size.

TABLE II. Yields of the various components in the fit to theB− → Dþπ−π− candidate invariant mass distribution.

Component TOS TIS-only

NðB− → Dþπ−π−Þ 29 190� 204 19 416� 159

NðB− → Dð�ÞþK−π−Þ 807� 123 401� 84

NðB− → D�þπ−π−Þ 12 120� 115 8551� 96Nðcomb bkgdÞ 784� 54 746� 47

TABLE III. Yields of the various components in the fit to theB− → DþK−π− candidate invariant mass distribution.

Component TOS TIS-only

NðB− → DþK−π−Þ 1112� 37 891� 32

NðB− → Dð�Þþπ−π−Þ 114� 34 23� 27

NðB− → Dþs K−π−Þ 69� 17 40� 15

NðB− → D�þK−π−Þ 518� 26 361� 21Nðcomb bkgdÞ 238� 38 253� 36

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The efficiency is studied separately for the TOS andTIS-only categories. The efficiency maps for each triggersubsample are shown for B− → DþK−π− decays in Fig. 3.Regions of relatively high efficiency are seen where alldecay products have comparable momentum in the B restframe; the efficiency drops sharply in regions with a low-momentum bachelor track due to geometrical effects. Theefficiency maps are used to calculate the ratio of branchingfractions and also as inputs to the DþK−π− Dalitz plot fit.

C. Systematic uncertainties

Table IV summarizes the systematic uncertainties on themeasurement of the ratio of branching fractions. Selectioneffects cancel in the ratio of branching fractions, except forinefficiency due to the Λþ

c veto. The invariant mass fits arerepeated both with a wider veto (2270–2310 MeV) andwith no veto, and changes in the yields are used to assign arelative systematic uncertainty of 0.2%.To estimate the uncertainty arising from the choice of

invariant mass fit model, the DþK−π− mass fit is varied byreplacing the signal shape with the sum of two bifurcatedGaussian functions, removing the smoothing of the non-parametric functions, using exponential and second-orderpolynomial functions to describe the combinatorial back-ground, varying fixed parameters within their uncertaintiesand varying the binning of histograms used to reweight thesimulated background samples. For the Dþπ−π− fit thesame variations are made. The relative changes in the yields

are summed in quadrature to give a relative systematicuncertainty on the ratio of branching fractions of 2.0%.The systematic uncertainty due to PID is estimated by

accounting for three sources: the intrinsic uncertainty ofthe calibration (1.0%); possible differences in the kinemat-ics of tracks in simulated samples, used to reweight thecalibration data samples, to those in the data (1.7%); thegranularity of the binning in the reweighting procedure(0.7%). Combining these in quadrature, the total relativesystematic uncertainty from PID is 2.1%.The bins of the efficiency maps are varied within

uncertainties to make 100 new efficiency maps, for bothDþK−π− and Dþπ−π− modes. The efficiency-correctedyields are evaluated for each new map and their distribu-tions are fitted with Gaussian functions. The widths of theseare used to assign a relative systematic uncertainty on theratio of branching fractions of 0.8%.A number of additional cross-checks are performed to

test the branching fraction result. The neural network andPID requirements are both tightened and loosened. Thedata sample is divided by dipole magnet polarity and yearof data taking. The branching fraction is also calculatedseparately for TOS and TIS-only events. All cross-checksgive consistent results.

D. Results

The ratio of branching fractions is found to be

BðB− → DþK−π−ÞBðB− → Dþπ−π−Þ ¼ 0.0720� 0.0019� 0.0021;

where the first uncertainty is statistical and the secondsystematic. The statistical uncertainty includes contribu-tions from the event weighting used in Eq. (1) and fromthe shape parameters that are allowed to vary in the fit [36].The world average value of BðB− → Dþπ−π−Þ ¼ ð1.07�0.05Þ × 10−3 [9] assumes that BþB− and B0B̄0 are pro-duced equally in the decay of the ϒð4SÞ resonance. UsingΓðϒð4SÞ → BþB−Þ=Γðϒð4SÞ → B0B̄0Þ ¼ 1.055 � 0.025

Eff

icie

ncy

00.00020.00040.00060.00080.0010.00120.00140.00160.00180.002

'm

' θ

00.10.20.30.40.50.60.70.80.9

1LHCb Simulation

Eff

icie

ncy

00.00010.00020.00030.00040.00050.00060.00070.00080.00090.001

'm

'θ

0

0.20.30.40.50.60.70.80.9

1LHCb Simulation

FIG. 3 (color online). Signal efficiency across the SDP for (left) TOS and (right) TIS-only B− → DþK−π− decays. The relativeuncertainty at each point is typically 5%.

TABLE IV. Relative systematic uncertainties on the measure-ment of the ratio of branching fractions for B− → DþK−π− andB− → Dþπ−π− decays.

Source Uncertainty (%)

Λþc veto 0.2

Fit model 2.0Particle identification 2.1Efficiency modeling 0.8Total 3.0

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[9] gives a corrected value of BðB− → Dþπ−π−Þ ¼ð1.01� 0.05Þ × 10−3. This allows the branching fractionof B− → DþK−π− decays to be determined as

BðB− →DþK−π−Þ ¼ ð7.31� 0.19� 0.22� 0.39Þ× 10−5;

where the third uncertainty is from BðB− → Dþπ−π−Þ.This measurement represents the first observation of theB− → DþK−π− decay.

V. STUDY OF ANGULAR MOMENTS

To investigate which amplitudes should be included inthe DP analysis of B− → DþK−π− decays, a study of itsangular moments is performed. Such an analysis is par-ticularly useful for B− → DþK−π− decays because reso-nant contributions are only expected to appear in the Dþπ−combination, and therefore the distributions should be freeof effects from reflections that make them more difficult tointerpret.The analysis is performed by calculating moments from

the Legendre polynomials PL of order up to 2Jmax, whereJmax is the maximum spin of the resonances considered.Each candidate is weighted according to its value ofPLðcos θðDþπ−ÞÞ with an efficiency correction applied,and background contributions subtracted. The results forJmax ¼ 3 are shown in Fig. 4 for the Dþπ− invariant massrange 2.0–3.0 GeV. The distributions of hP5i and hP6i arecompatible with being flat, which implies that there are nosignificant spin-3 contributions. Considering only contri-butions up to spin 2, the following expressions are used tointerpret Fig. 4:

hP0i ∝ jh0j2 þ jh1j2 þ jh2j2; ð3Þ

hP1i∝2ffiffiffi3

p jh0jjh1jcosðδ0−δ1Þþ4ffiffiffiffiffi15

p jh1jjh2jcosðδ1−δ2Þ;ð4Þ

hP2i ∝2ffiffiffi5

p jh0jjh2j cos ðδ0 − δ2Þ þ2

5jh1j2 þ

2

7jh2j2; ð5Þ

hP3i ∝6

7

ffiffiffi3

5

rjh1jjh2j cos ðδ1 − δ2Þ; ð6Þ

hP4i ∝2

7jh2j2; ð7Þ

where S-, P- and D-wave contributions are denoted byamplitudes hjeiδj (j ¼ 0; 1; 2 respectively). The D�

2ð2460Þ0resonance is clearly seen in the hP4i distribution ofFig. 4(e). The distribution of hP3i shows interferencebetween spin-1 and -2 contributions, indicating the pres-ence of a broad, possibly nonresonant, spin-1 contributionat lowmðDþπ−Þ. The difference in shape between hP1i and

hP3i shows interference between spin 1 and 0 indicatingthat a broad spin-0 component is similarly needed.

VI. DALITZ PLOT ANALYSIS FORMALISM

A Dalitz plot [37] is a representation of the phase spacefor a three-body decay in terms of two of the three possibletwo-body invariant mass squared combinations. In B− →DþK−π− decays, resonances are expected in them2ðDþπ−Þ combination; therefore this and m2ðDþK−Þare chosen to define the DP axes. For a fixed B− mass,all other relevant kinematic quantities can be calculatedfrom these two invariant mass squared combinations.The complex decay amplitude is described using the

isobar approach [38–40], where the total amplitude iscalculated as a coherent sum of amplitudes from resonantand nonresonant intermediate processes. The total ampli-tude is then given by

Aðm2ðDþπ−Þ; m2ðDþK−ÞÞ

¼XNj¼1

cjFjðm2ðDþπ−Þ; m2ðDþK−ÞÞ; ð8Þ

where cj are complex coefficients giving the relativecontribution of each intermediate process. TheFjðm2ðDþπ−Þ; m2ðDþK−ÞÞ terms contain the resonancedynamics, which are composed of several terms and arenormalized such that the integral of the squared magnitudeover the DP is unity for each term. For a Dþπ− resonance

Fðm2ðDþπ−Þ; m2ðDþK−ÞÞ ¼ RðmðDþπ−ÞÞ × Xðj~pjrBWÞ× Xðj~qjrBWÞ × Tð~p; ~qÞ;

ð9Þ

where the functions R, X and T are described below, and~p and ~q are the bachelor particle momentum and themomentum of one of the resonance daughters, respectively,both evaluated in the Dþπ− rest frame.The XðzÞ terms, where z ¼ j~qjrBW or j~pjrBW, are Blatt-

Weisskopf barrier factors [41] with barrier radius rBW, andare given by

L ¼ 0∶ XðzÞ ¼ 1;

L ¼ 1∶ XðzÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffi1þ z201þ z2

s;

L ¼ 2∶ XðzÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiz40 þ 3z20 þ 9

z4 þ 3z2 þ 9

s;

L ¼ 3∶ XðzÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiz60 þ 6z40 þ 45z20 þ 225

z6 þ 6z4 þ 45z2 þ 225

s; ð10Þ

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092002-7

where z0 is the value of z when the invariant mass is equalto the pole mass of the resonance and L is the spin ofthe resonance. For aDþπ− resonance, since the B− mesonhas zero spin, L is also the orbital angular momentumbetween the resonance and the kaon. The barrier radius,

rBW, is taken to be 4.0 GeV−1 ≈ 0.8 fm [5,42] for allresonances.The terms Tð~p; ~qÞ describe the angular probability

distribution and are given in the Zemach tensor formalism[43,44] by

) [GeV]−π+D(m2 3 4

/ (0

.054

GeV

)⟩ 0P⟨

0

0.1

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) [GeV]−π+D(m2 3 4

/ (0

.054

GeV

)⟩ 1P⟨

-0.02

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610×

(b)LHCb

) [GeV]−π+D(m2 3 4

/ (0

.054

GeV

)⟩ 2P⟨

-0.04-0.02

00.020.040.060.08

0.10.120.140.16

610×

(c)LHCb

) [GeV]−π+D(m2 3 4

/ (0

.054

GeV

)⟩ 3P⟨

-30

-20

-10

0

10

20

30

310×

(d)LHCb

) [GeV]−π+D(m2 3 4

/ (0

.054

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)⟩ 4P⟨

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610×

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) [GeV]−π+D(m2 3 4

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)⟩ 5P⟨

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25

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) [GeV]−π+D(m2 3 4

/ (0

.054

GeV

)⟩ 6P⟨

-15

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0

5

10

15

310×

(g)LHCb

FIG. 4 (color online). The first seven Legendre-polynomial-weighted moments for background-subtracted and efficiency-correctedB− → DþK−π− data (black points) as a function of mðDþπ−Þ in the range 2.0–3.0 GeV. Candidates from both TOS and TIS-onlysubsamples are included. The blue line shows the result of the DP fit described in Sec. VII.

R. AAIJ et al. PHYSICAL REVIEW D 91, 092002 (2015)

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L ¼ 0∶ Tð~p; ~qÞ ¼ 1;

L ¼ 1∶ Tð~p; ~qÞ ¼ −2~p · ~q;

L ¼ 2∶ Tð~p; ~qÞ ¼ 4

3½3ð~p · ~qÞ2 − ðj~pjj~qjÞ2�;

L ¼ 3∶ Tð~p; ~qÞ ¼ −24

15½5ð~p · ~qÞ3 − 3ð~p · ~qÞðj~pjj~qjÞ2�;

ð11Þwhich are proportional to the Legendre polynomials,PLðxÞ, where x is the cosine of the angle between ~p and~q (referred to as the helicity angle).The function RðmðDþπ−ÞÞ of Eq. (9) is the mass line

shape. The resonant contributions considered in the DPmodel are described by the relativistic Breit-Wigner (RBW)function

RðmÞ ¼ 1

ðm20 −m2Þ − im0ΓðmÞ ; ð12Þ

where the mass-dependent decay width is

ΓðmÞ ¼ Γ0

�qq0

�2Lþ1

�m0

m

�X2ðqrBWÞ; ð13Þ

where q0 is the value of q ¼ j~qj for m ¼ m0. Virtualcontributions, from resonances with pole masses outsidethe kinematically accessible region of the phase space, canalso be modeled by this shape with one modification:the pole mass m0 is replaced with meff

0 , a mass in thekinematically allowed region, in the calculation of theparameter q0. This effective mass is defined by the ad hocformula [5]

meff0 ðm0Þ ¼ mmin þ ðmmax −mminÞ

×

�1þ tanh

�m0 − mminþmmax

2

mmax −mmin

��; ð14Þ

where mmax and mmin are the upper and lower limits of thekinematically allowed range, respectively. For virtual con-tributions, only the tail of the RBW function enters theDalitz plot.Given the large available phase space in the B decay, it is

possible to have nonresonant amplitudes (i.e. contributionsthat are not from any known resonance, including virtualstates) that vary across the Dalitz plot. A model that hasbeen found to describe well nonresonant contributions inseveral B-decay DP analyses is an exponential form factor(EFF) [45],

RðmÞ ¼ e−αm2

; ð15Þ

where m is a two-body (in this case Dπ) invariant massand α is a shape parameter that must be determined fromthe data.Neglecting reconstruction effects, the DP probability

density function would be

Pphysðm2ðDþπ−Þ; m2ðDþK−ÞÞ

¼ jAðm2ðDþπ−Þ; m2ðDþK−ÞÞj2RRDP jAj2dm2ðDþπ−Þdm2ðDþK−Þ ; ð16Þ

where the dependence of A on the DP position has beensuppressed in the denominator for brevity. The complexcoefficients, given by cj in Eq. (8), are the primary resultsof most Dalitz plot analyses. However, these depend on thechoice of normalization, phase convention and amplitudeformalism in each analysis. Fit fractions and interference fitfractions are also reported as these provide a convention-independent method to allow meaningful comparisons ofresults. The fit fraction is defined as the integral of theamplitude for a single component squared divided by thatof the coherent matrix element squared for the completeDalitz plot,

FFj ¼RR

DP jcjFjðm2ðDþπ−Þ; m2ðDþK−ÞÞj2dm2ðDþπ−Þdm2ðDþK−ÞRRDP jAj2dm2ðDþπ−Þdm2ðDþK−Þ : ð17Þ

The fit fractions do not necessarily sum to unity due to thepotential presence of net constructive or destructive inter-ference, described by interference fit fractions defined fori < j only by

FFij ¼RR

DP 2Re½cic�jFiF�j �dm2ðDþπ−Þdm2ðDþK−ÞRR

DP jAj2dm2ðDþπ−Þdm2ðDþK−Þ ;

ð18Þ

where the dependence of Fð�Þi andA on the DP position has

been omitted.

VII. DALITZ PLOT FIT

The LAURA++ [46] package is used to perform the Dalitzplot fit, with the two trigger subsamples fitted simulta-neously using the JFIT method [47]. The two subsampleshave separate signal and background yields, efficiencymaps and background SDP distributions, but all parameters

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of the signal model are common. The likelihood functionthat is used is

L ¼YNc

i

�Xk

NkPkðm2i ðDþπ−Þ; m2

i ðDþK−ÞÞ�; ð19Þ

where the index i runs over Nc candidates, while kdistinguishes the signal and background components whereNk is the yield in each component. The probability densityfunction for signal events, Psig, is given by Eq. (16) wherethe jAðm2ðDþπ−Þ; m2ðDþK−ÞÞj2 terms are multiplied bythe efficiency function described in Sec. IV B. The massresolution is approximately 2.4 MeV, which is much lowerthan the width of the narrowest contribution to the Dalitzplot (∼50 MeV); therefore, this has negligible effect on thelikelihood and is not considered further.The signal and background yields that enter the Dalitz

plot fit are taken from the mass fit described in Sec. IVA.Only candidates in the signal region, defined as �2.5σaround the B signal peak, where σ is the width of the peak,are used in the Dalitz plot fit. Within this region, in the TOSsubsample the result of the B candidate invariant mass fitcorresponds to yields of 1060� 35, 37� 6, 26� 8 and16� 4 in the signal, combinatorial background,Dð�Þþπ−π−and Dþ

s K−π− components, respectively. The equivalentyields in the TIS-only subsample are 849� 30, 39� 6,5� 5 and 9� 3 candidates. The contribution fromD�þK−π− decays is negligible in the signal window.The distributions of the candidates in the signal regionover the DP and SDP are shown in Fig. 5.The SDP distributions of the Dð�Þþπ−π− and Dþ

s K−π−

background sources are obtained from simulated samplesusing the same procedures as described for their invariantmass distributions in Sec. IVA. The distribution of com-binatorial background events is modeled by consideringDþK−π− candidates in the sideband high-mass range5500–5800 MeV, with contributions from Dð�Þþπ−π− in

this region subtracted. The dependence of the SDP dis-tribution on B candidate mass was investigated and foundto be negligible. The SDP distributions of these back-grounds are shown in Fig. 6. These histograms are used tomodel the background contributions in the Dalitz plot fit.Using the results of the moments analysis of Sec. V as a

guide, the nominal Dalitz plot fit model for B− → DþK−π−

decays is determined by considering several resonant,nonresonant and virtual amplitudes. Those that do notcontribute significantly and that do not aid the stability ofthe fit are removed. Only natural spin-parity intermediatestates are considered, as unnatural spin-parity states do notdecay to two pseudoscalars. The resulting signal model,referred to below as the nominal DP model, consists of theseven amplitudes shown in Table V: three resonances, twovirtual resonances and two nonresonant terms. Parts ofthe model are known to be approximations. In particularboth S- and P-waves in the Dπ system are modeled withoverlapping broad structures. The nominal model gives abetter description of the data than any of the alternativemodels considered; alternative models are used to assignsystematic uncertainties as discussed in Sec. VIII.The free parameters in the fit are the cj terms introduced

in Eq. (8), with the real and imaginary parts of thesecomplex coefficients determined for each amplitude in thefit model. The D�

2ð2460Þ0 component, as the referenceamplitude, is the exception with real and imaginary partsfixed to 1 and 0, respectively. Fit fractions and interferencefit fractions are derived from these free parameters, as arethe magnitudes and phases of the complex coefficients.Statistical uncertainties for the derived parameters arecalculated using large samples of simulated pseudoexperi-ments to ensure that nontrivial correlations are accountedfor. Several other parameters are also determined from thefit as described below.In Dalitz plot fits it is common for the minimization

procedure to find local minima of the likelihood function.To find the global minimum, the fit is performed many

]2) [GeV-π+D(2m

5 10 15 20

]2)

[GeV

-K

+D(2

m

5

10

15

20

25

LHCb

'm0 0.2 0.4 0.6 0.8 1

'θ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

LHCb

FIG. 5. Distribution of B− → DþK−π− candidates in the signal region over (left) the DP and (right) the SDP. Candidates from bothTOS and TIS-only subsamples are included.

R. AAIJ et al. PHYSICAL REVIEW D 91, 092002 (2015)

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times using randomized starting values for the complexcoefficients. In addition to the global minimum of thelikelihood, corresponding to the results reported below,several additional minima are found. Two of these have

negative log-likelihood (NLL) values close to that of theglobal minimum. The main differences between secondaryminima and the global minimum are the interference patternsin the Dπ S- and P-waves, as shown in Appendix A.

Ent

ries

0

0.5

1

1.5

2

2.5

3

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Ent

ries

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ries

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Ent

ries

0

0.1

0.2

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0.4

0.5

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0.7

'm0 0.2 0.4 0.6 0.8 1

'θ0

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Ent

ries

00.20.40.60.811.21.41.61.82

'm0 0.2 0.4 0.6 0.8 1

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Ent

ries

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'm0 0.2 0.4 0.6 0.8 1

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1LHCb Simulation

FIG. 6 (color online). Square Dalitz plot distributions used in the Dalitz plot fit for (top) combinatorial background, (middle)B− → Dð�Þþπ−π− decays and (bottom) B− → Dþ

s K−π− decays. Candidates from the TOS (TIS-only) subsamples are shown in the left(right) column.

TABLE V. Signal contributions to the fit model, where parameters and uncertainties are taken from Ref. [9]. Stateslabeled with subscript v are virtual contributions.

Resonance Spin DP axis Model Parameters

D�0ð2400Þ0 0 m2ðDπÞ RBW m ¼ 2318� 29 MeV, Γ ¼ 267� 40 MeV

D�2ð2460Þ0 2 m2ðDπÞ RBW

Determined from data (see Table VI)D�

Jð2760Þ0 1 m2ðDπÞ RBWNonresonant 0 m2ðDπÞ EFF

Determined from data (see text)Nonresonant 1 m2ðDπÞ EFFD�

vð2007Þ0 1 m2ðDπÞ RBW m ¼ 2006.98� 0.15 MeV, Γ ¼ 2.1 MeVB�0v 1 m2ðDKÞ RBW m ¼ 5325.2� 0.4 MeV, Γ ¼ 0.0 MeV

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The shape parameters, defined in Eq. (15), for thenonresonant components are determined from the fit todata to be 0.36� 0.03 GeV−2 and 0.36� 0.04 GeV−2 forthe S-wave and P-wave, respectively, where the uncertain-ties are statistical only. The mass and width of theD�

2ð2460Þ0 resonance are determined from the fit toimprove the fit quality. Since the mass and width of theD�

Jð2760Þ0 state have not been precisely determined byprevious experiments, these parameters are also allowed tovary in the fit. The masses and widths of theD�

2ð2460Þ0 andD�

Jð2760Þ0 are reported in Table VI.The spin of theD�

Jð2760Þ0 state has not been determinedpreviously. Fits are performed with all values up to 3, andspin 1 is found to be preferred with changes relative tothe spin-0, -2 and -3 hypotheses of 2ΔNLL ¼ 37.3; 49.5and 48.2 units, respectively. For comparison, the value of2ΔNLL obtained from a fit with the D�

1ð2760Þ0 stateexcluded is 75.0 units. The alternative models discussedin Sec. VIII give very similar values and therefore do notaffect the conclusion that the D�

Jð2760Þ0 state has spin 1.The values of the complex coefficients and fit fractions

returned by the fit are shown in Table VII. Results for theinterference fit fractions are given in Appendix B. The totalfit fraction exceeds unity mostly due to interference betweenthe D�

0ð2400Þ0 and S-wave nonresonant contributions.The consistency of the fit model and the data is evaluated

in several ways. Numerous one-dimensional projections(including several shown below and those shown in Sec. V)show good agreement. A two-dimensional χ2 value isdetermined by comparing the data and the fit model in100 equally populated bins across the SDP. The pull, i.e.the difference between the data and fit model dividedby the uncertainty, is shown with this SDP binning in

Fig. 7. The χ2 value obtained is found to be within the bulkof the distribution expected from simulated pseudoexperi-ments. Other unbinned fit quality tests [48] also showacceptable agreement between the data and the fit model.Figure 8 shows projections of the nominal fit model and

the data onto mðDπÞ, mðDKÞ and mðKπÞ. Zooms areprovided around the resonant structures on mðDπÞ inFig. 9. Projections of the cosine of the helicity angle ofthe Dπ system are shown in Fig. 10. Good agreement isseen between the data and the fit model.

VIII. SYSTEMATIC UNCERTAINTIES

Sources of systematic uncertainty are divided into twocategories: experimental and model uncertainties. Thesources of experimental systematic uncertainty are the signaland background yields in the signal region, the SDPdistributions of the background components; the efficiencyvariation across the SDP, and possible fit bias. The consid-ered model uncertainties are, the fixed parameters in theamplitude model, the addition or removal of marginalamplitudes, and the choice of models for the nonresonantcontributions. The systematic uncertainties from each sourceare combined in quadrature.

TABLE VI. Masses and widths determined in the fit to data,with statistical uncertainties only.

Resonance Mass (MeV) Width (MeV)

D�2ð2460Þ0 2464.0� 1.4 43.8� 2.9

D�Jð2760Þ0 2781� 18 177� 32

TABLE VII. Complex coefficients and fit fractions determined from the Dalitz plot fit. Uncertainties are statisticalonly.

Isobar model coefficients

Resonance Fit fraction (%) Real part Imaginary part Magnitude Phase

D�0ð2400Þ0 8.3� 2.6 −0.04� 0.07 −0.51� 0.07 0.51� 0.09 −1.65� 0.16

D�2ð2460Þ0 31.8� 1.5 1.00 0.00 1.00 0.00

D�1ð2760Þ0 4.9� 1.2 −0.32� 0.06 −0.23� 0.07 0.39� 0.05 −2.53� 0.24

S-wave nonresonant 38.0� 7.4 0.93� 0.09 −0.58� 0.08 1.09� 0.09 −0.56� 0.09P-wave nonresonant 23.8� 5.6 −0.43� 0.09 0.75� 0.09 0.87� 0.09 2.09� 0.15D�

vð2007Þ0 7.6� 2.3 0.16� 0.08 0.46� 0.09 0.49� 0.07 1.24� 0.17B�v 3.6� 1.9 −0.07� 0.08 0.33� 0.07 0.34� 0.06 1.78� 0.23

Total fit fraction 118.1

'm0 0.2 0.4 0.6 0.8

' θ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-6

-4

-2

0

2

4

6

LHCb

FIG. 7 (color online). Differences between the data SDPdistribution and the fit model across the SDP, in terms of theper-bin pull.

R. AAIJ et al. PHYSICAL REVIEW D 91, 092002 (2015)

092002-12

The signal and background yields in the signal region aredetermined from the fit to the B candidate invariant massdistribution, as described in Sec. IVA. The uncertainty oneach yield (including systematic uncertainty evaluated as inSec. IV C) is calculated, and the yields varied accordinglyin the DP fit. The deviations from the nominal DP fit resultare assigned as systematic uncertainties.

The effect of imperfect knowledge of the backgrounddistributions over the SDP is tested by varying the histo-grams used to model the shapes within their statisticaluncertainties. For Dð�Þþπ−π− decays the ratio of the D�þ

and Dþ contributions is varied. Where applicable, thereweighting of the SDP distribution of the simulatedsamples is removed.

) [GeV]-π+Dm(2 3 4 5

Can

dida

tes

/ (40

MeV

)

0

50

100

150

200

250

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v0B*

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FIG. 8 (color online). Projections of the data and amplitude fit onto (a) mðDπÞ, (c) mðDKÞ and (e) mðKπÞ, with the same projectionsshown in (b), (d) and (f) with a logarithmic y-axis scale. Components are described in the legend.

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(c) the D�1ð2760Þ0 region. Components are as shown in Fig. 8.

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2ð2460Þ0 region and (c) the D�1ð2760Þ0 region. Components are as shown in Fig. 8.

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The uncertainty related to the knowledge of the variationof efficiency across the SDP is determined by varying theefficiency histograms before the spline fit is performed. Thecentral bin in each cell of 3 × 3 bins is varied by itsstatistical uncertainty and the surrounding bins in the cellare varied by interpolation. This procedure accounts forpossible correlations between the bins, since a systematiceffect on a given bin is also likely to affect neighboringbins. The effects on the DP fit results are assigned assystematic uncertainties. An additional systematic uncer-tainty is assigned by varying the binning scheme of thecontrol sample used to determine the PID efficiencies.Systematic uncertainties related to possible intrinsic fit

bias are investigated using an ensemble of pseudoexperi-ments. Differences between the input and fitted values fromthe ensemble for the fit parameters are found to be small.Systematic uncertainties are assigned as the sum in quad-rature of the difference between the input and output valuesand the uncertainty on the mean of the output valuedetermined from a fit to the ensemble.Systematic uncertainties due to fixed parameters in the fit

model are determined by varying the parameters withintheir uncertainties and repeating the fit. The fixed param-eters considered are the mass and width of the D�

0ð2400Þ0resonance and the Blatt-Weisskopf barrier radius, rBW. Themass and width are varied by the uncertainties shown inTable V and the barrier radius is varied between 3 and5 GeV−1 [5]. For each fit parameter, the difference com-pared to the nominal fit model is assigned as a systematicuncertainty for each source.The marginal B�0

v component is removed from the modeland the changes in the other parameters are assigned asthe systematic uncertainties. Dalitz plot analysis of B̄0

s →D0Kþπ− revealed that a structure atmðD0KþÞ ∼ 2.86 GeVhas both spin-1 and spin-3 components [4,5]. Althoughthere is no evidence for a spin-3 resonance in this analysis,the excess at mðDþπ−Þ ∼ 2.76 GeV could have a similarcomposition. A putative D�

3ð2760Þ resonance is added tothe fit model, and the effect on the other parameters is usedto assign systematic uncertainties.The EFF line shapes used to model the nonresonant

S- and P-wave contributions are replaced by a power-lawmodel and the change in the fit parameters used as asystematic uncertainty. The dependence of the results onthe effective pole mass description of Eq. (14) that is usedfor the virtual resonance contributions is found by using afixed width in Eq. (12), removing the dependency on meff

0 .The total experimental and model systematic uncertain-

ties for fit fractions and complex coefficients are summa-rized in Tables VIII and IX, respectively. The contributionsfor the fit fractions, masses and widths are broken down inTables X and XI. Similar tables summarizing the systematicuncertainties on the interference fit fractions are given inAppendix B. The largest source of experimental systematicuncertainty on the fit fractions is due to the efficiency

variation. For the model uncertainty on the fit fractions, theaddition and removal of marginal components and variationof fixed parameters dominate. In general, the modeluncertainties are larger than the experimental systematicuncertainties for the fit fractions and the masses and widths.Several cross-checks are performed to confirm the

stability of the results. The data sample is divided intotwo parts depending on the charge of the B candidate, thepolarity of the magnet and the year of data taking. Selectioneffects are also checked by varying the requirement on theneural network output variable and the PID criteria appliedto the bachelor kaon. A fit is performed for each of thesubsamples individually and each is seen to be consistentwith the default fit results, although in some cases oneof the secondary minima described in Appendix A becomesthe preferred solution. To cross-check the amplitude model,the fit is repeated many times with an extra resonance withfixed mass, width and spin included in the model. Allpossible mass and width values, and spin up to 3, wereconsidered. None of the additional resonances are found tocontribute significantly.

TABLE VIII. Experimental systematic uncertainties on the fitfractions and complex amplitudes.

Isobar model coefficients

Resonance

Fitfraction(%)

Realpart

Imaginarypart Magnitude Phase

D�0ð2400Þ0 0.6 0.03 0.02 0.02 0.06

D�2ð2460Þ0 0.9 � � � � � � � � � � � �

D�1ð2760Þ0 0.4 0.03 0.03 0.01 0.08

S-wavenonresonant

1.5 0.03 0.03 0.02 0.04

P-wavenonresonant

2.1 0.03 0.05 0.03 0.05

D�vð2007Þ0 1.3 0.03 0.04 0.04 0.07

B�v 0.9 0.22 0.02 0.03 0.11

TABLE IX. Model uncertainties on the fit fractions and com-plex amplitudes.

Isobar model coefficients

Resonance

Fitfraction(%)

Realpart

Imaginarypart Magnitude Phase

D�0ð2400Þ0 1.9 0.28 0.13 0.15 0.51

D�2ð2460Þ0 1.4 � � � � � � � � � � � �

D�1ð2760Þ0 0.9 0.03 0.03 0.03 0.08

S-wavenonresonant

10.8 0.17 0.15 0.20 0.11

P-wavenonresonant

3.7 0.34 0.68 0.12 0.95

D�vð2007Þ0 1.5 0.56 0.77 0.05 0.60

B�v 1.6 0.09 0.08 0.07 0.27

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IX. RESULTS AND SUMMARY

The results for the complex coefficients are reported inTables XII and XIII in terms of real and imaginary parts andof magnitudes and phases, respectively. The results for the

fit fractions are given in Table XIV and the results for theinterference fit fractions are given in Appendix B. The fitfractions for resonant contributions are converted intoquasi-two-body product branching fractions by multiplyingby BðB−→DþK−π−Þ¼ð7.31�0.19�0.22�0.39Þ×10−5,as determined in Sec. IV D. These product branchingfractions are shown in Table XV; they cannot be convertedinto absolute branching fractions because the branchingfractions for the resonance decays to Dþπ− are unknown.The masses and widths of theD�

2ð2460Þ0 andD�1ð2760Þ0

are determined to be

mðD�2ð2460Þ0Þ ¼ ð2464.0� 1.4� 0.5� 0.2Þ MeV;

ΓðD�2ð2460Þ0Þ ¼ ð43.8� 2.9� 1.7� 0.6Þ MeV;

mðD�1ð2760Þ0Þ ¼ ð2781� 18� 11� 6Þ MeV;

ΓðD�1ð2760Þ0Þ ¼ ð177� 32� 20� 7Þ MeV;

where the three quoted errors are statistical, experimentalsystematic and model uncertainties, respectively. Theresults for the D�

2ð2460Þ0 are within 2σ of the worldaverage values [9]. The mass of the D�

1ð2760Þ0 resonanceis similarly consistent with previous measurements. Themeasured width of this state is larger than previousmeasurements by 2 to 3 times the uncertainties. Futurestudies based on much larger data samples will be requiredto better understand these states.The measurement of BðB− → DþK−π−Þ corresponds to

the first observation of this decay mode. Therefore, theresonant contributions to the decay are also first observa-tions. The significance of the B− → D�

1ð2760Þ0K− obser-vation is investigated by removing the correspondingresonance from the DP model. A fit without theD�

1ð2760Þ0 component increases the value of 2ΔNLL by75.0 units, corresponding to a high statistical significance.Only the systematic effects due to uncertainties in the DPmodel could in principle significantly change the conclu-sion regarding the need for this resonance. However, inalternative DP models where a Dπ resonance with spin 3 isadded and where the B�

v contribution is removed, the shift

TABLE XI. Breakdown of model uncertainties on the fitfractions (%) and masses (MeV) and widths (MeV).

NominalAdd/rem

Alt.models

Fixedparams Total

D�0ð2400Þ0 8.3� 2.6 2.0 0.1 0.2 1.9

D�2ð2460Þ0 31.8� 1.5 1.3 0.2 0.4 1.4

D�1ð2760Þ0 4.9� 1.2 0.8 0.1 0.3 0.9

S-wavenonresonant

38.0� 7.4 4.8 4.5 5.4 10.8

P-wavenonresonant

23.8� 5.6 2.6 2.1 3.0 3.7

D�vð2007Þ0 7.6� 2.3 0.6 0.1 1.4 1.5

B�v 3.6� 1.9 0.7 1.0 1.1 1.6

mðD�2ð2460Þ0Þ 2464.0� 1.4 0.5 0.1 0.1 0.5

ΓðD�2ð2460Þ0Þ 43.8� 2.9 0.8 1.4 0.6 1.7

mðD�1ð2760Þ0Þ 2781� 18 6 6 1 11

ΓðD�1ð2760Þ0Þ 177� 32 16 9 1 20

TABLE X. Breakdown of experimental systematic uncertain-ties on the fit fractions (%) and masses (MeV) and widths (MeV).

NominalS/Bfrac. Eff. Bkg.

Fitbias Total

D�0ð2400Þ0 8.3� 2.6 0.2 0.5 0.1 0.3 0.6

D�2ð2460Þ0 31.8� 1.5 0.2 0.8 0.0 0.2 0.9

D�1ð2760Þ0 4.9� 1.2 0.2 0.2 0.1 0.2 0.3

S-wave nonresonant 38.0� 7.4 0.7 0.5 0.4 1.2 1.5P-wave nonresonant 23.8� 5.6 1.0 1.6 0.7 0.5 2.1D�

vð2007Þ0 7.6� 2.3 0.7 1.0 0.3 0.3 1.3B�v 3.6� 1.9 0.3 0.3 0.2 0.8 0.9

mðD�2ð2460Þ0Þ 2464.0� 1.4 0.1 0.1 0.0 0.2 0.2

ΓðD�2ð2460Þ0Þ 43.8� 2.9 0.3 0.3 0.0 0.4 0.6

mðD�1ð2760Þ0Þ 2781� 18 1 4 0 2 6

ΓðD�1ð2760Þ0Þ 177� 32 3 1 2 5 7

TABLE XII. Results for the complex amplitudes and their uncertainties. The three quoted errors are statistical,experimental systematic and model uncertainties, respectively.

Isobar model coefficients

Resonance Real part Imaginary part

D�0ð2400Þ0 −0.04� 0.07� 0.03� 0.28 −0.51� 0.07� 0.02� 0.13

D�2ð2460Þ0 1.00 0.00

D�1ð2760Þ0 −0.32� 0.06� 0.03� 0.03 −0.23� 0.07� 0.03� 0.03

S-wave nonresonant 0.93� 0.09� 0.03� 0.17 −0.58� 0.08� 0.03� 0.15P-wave nonresonant −0.43� 0.09� 0.03� 0.34 0.75� 0.09� 0.05� 0.68D�

vð2007Þ0 0.16� 0.08� 0.03� 0.56 0.46� 0.09� 0.04� 0.77B�v −0.07� 0.08� 0.22� 0.09 0.33� 0.07� 0.02� 0.08

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in 2ΔNLL remains above 50 units. The alternative modelsalso do not significantly impact the level at which theD�

1ð2760Þ0 state is preferred to be spin 1. Therefore, theseresults represent the first observation of the B− →D�

1ð2760Þ0K− and the measurement of the spin of theD�

1ð2760Þ0 resonance.In summary, the B− → DþK−π− decay has been

observed in a data sample corresponding to 3.0 fb−1 ofpp collision data recorded by the LHCb experiment. Anamplitude analysis of its Dalitz plot distribution has beenperformed, in which a model containing resonant contri-butions from the D�

0ð2400Þ0, D�2ð2460Þ0 and D�

1ð2760Þ0

states in addition to both S-wave and P-wave nonresonantamplitudes and components due to virtual D�

vð2007Þ0 andB�0v resonances was found to give a good description of the

data. The B− → D�2ð2460Þ0K− decay may in the future be

used to determine the angle γ of the CKM unitarity triangle.The results provide insight into the spectroscopy of charmmesons, and demonstrate that further progress may beobtained with Dalitz plot analyses of larger data samples.

ACKNOWLEDGMENTS

We express our gratitude to our colleagues in the CERNaccelerator departments for the excellent performance ofthe LHC. We thank the technical and administrative staff atthe LHCb institutes. We acknowledge support from CERNand from the national agencies: CAPES, CNPq, FAPERJand 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 andSER (Switzerland); NASU (Ukraine); STFC (UnitedKingdom); NSF (USA). The Tier1 computing centresare supported by IN2P3 (France), KIT and BMBF(Germany), INFN (Italy), NWO and SURF (TheNetherlands), PIC (Spain), and GridPP (UnitedKingdom). We are indebted to the communities behindthe multiple open source software packages on which wedepend. We are also thankful for the computing resourcesand the access to software R&D tools provided by YandexLLC (Russia). Individual groups or members have receivedsupport from EPLANET, Marie Skłodowska-Curie Actionsand ERC (European Union), Conseil général de Haute-Savoie, Labex ENIGMASS and OCEVU, RégionAuvergne (France), RFBR (Russia), XuntaGal andGENCAT (Spain), and the Royal Society and RoyalCommission for the Exhibition of 1851 (United Kingdom).

APPENDIX A: SECONDARY MINIMA

The results, in terms of fit fractions and complexcoefficients, corresponding to the two secondary minima

TABLE XIII. Results for the complex amplitudes and their uncertainties. The three quoted errors are statistical,experimental systematic and model uncertainties, respectively.

Isobar model coefficients

Resonance Magnitude Phase

D�0ð2400Þ0 0.51� 0.09� 0.02� 0.15 −1.65� 0.16� 0.06� 0.50

D�2ð2460Þ0 1.00 0.00

D�1ð2760Þ0 0.39� 0.05� 0.01� 0.03 −2.53� 0.24� 0.08� 0.08

S-wave nonresonant 1.09� 0.09� 0.02� 0.20 −0.56� 0.09� 0.04� 0.11P-wave nonresonant 0.87� 0.09� 0.03� 0.11 2.09� 0.15� 0.05� 0.95D�

vð2007Þ0 0.49� 0.07� 0.04� 0.05 1.24� 0.17� 0.07� 0.60B�v 0.34� 0.06� 0.03� 0.07 1.78� 0.23� 0.11� 0.27

TABLE XIV. Results for the fit fractions and their uncertainties(%). The three quoted errors are statistical, experimental sys-tematic and model uncertainties, respectively.

Resonance Fit fraction

D�0ð2400Þ0 8.3� 2.6� 0.6� 1.9

D�2ð2460Þ0 31.8� 1.5� 0.9� 1.4

D�1ð2760Þ0 4.9� 1.2� 0.3� 0.9

S-wave nonresonant 38.0� 7.4� 1.5� 10.8P-wave nonresonant 23.8� 5.6� 2.1� 3.7D�

vð2007Þ0 7.6� 2.3� 1.3� 1.5B�v 3.6� 1.9� 0.9� 1.6

TABLE XV. Results for the product branching fractionsBðB− → RK−Þ × BðR → Dþπ−Þ (10−4). The four quoted errorsare statistical, experimental systematic, model and inclusivebranching fraction uncertainties, respectively.

Resonance Branching fraction

D�0ð2400Þ0 6.1� 1.9� 0.5� 1.4� 0.4

D�2ð2460Þ0 23.2� 1.1� 0.6� 1.0� 1.6

D�1ð2760Þ0 3.6� 0.9� 0.3� 0.7� 0.2

S-wave nonresonant 27.8� 5.4� 1.1� 7.9� 1.9P-wave nonresonant 17.4� 4.1� 1.5� 2.7� 1.2D�

vð2007Þ0 5.6� 1.7� 1.0� 1.1� 0.4B�v 2.6� 1.4� 0.6� 1.2� 0.2

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discussed in Sec. VII are compared to those of the global minimum in Table XVI. The main difference between the globaland secondary minima is in the interference pattern in the Dπ P-waves, while the third minimum exhibits a differentinterference pattern in the Dπ S-wave than the global minimum and has a very large total fit fraction due to strongdestructive interference.

APPENDIX B: RESULTS FOR INTERFERENCE FIT FRACTIONS

The central values and statistical errors for the interference fit fractions are shown in Table XVII. The experimentalsystematic and model uncertainties are given in Tables XVIII and XIX. The interference fit fractions are common to bothtrigger subsamples.

TABLE XVI. Results for the fit fractions and complex coefficients for the secondary minima with 2NLL values 2.8 and 3.3 unitsgreater than that of the global minimum of the NLL function.

Resonance Fit fraction (%) Real part Imaginary part Magnitude Phase

2ΔNLL 0 2.8 3.3 0 2.8 3.3 0 2.8 3.3 0 2.8 3.3 0 2.8 3.3

D�0ð2400Þ0 8.3 9.6 84.4 −0.04 −0.03 −1.38 −0.51 −0.55 −0.72 0.51 0.55 1.56 −1.65 −1.62 −2.66

D�2ð2460Þ0 31.8 31.5 34.9 1.00 0.00 1.00 0.00

D�1ð2760Þ0 4.9 4.6 5.5 −0.32 −0.30 −0.30 −0.23 −0.24 −0.26 0.39 0.38 0.40 −2.53 −2.46 −2.42

S-wave nonresonant 38.0 36.2 4.6 0.93 0.89 −0.33 −0.58 −0.60 0.15 1.09 1.07 −0.36 −0.56 −0.59 2.71P-wave nonresonant 23.8 22.6 −31.9 −0.43 0.83 −0.84 0.75 0.15 0.45 0.87 0.85 0.96 2.09 2.96 2.65D�

vð2007Þ0 7.6 7.1 11.9 0.16 −0.38 −0.28 0.46 −0.29 −0.51 0.49 0.48 0.58 1.24 −2.49 −2.07B�v 3.6 1.0 25.0 −0.07 −0.16 −0.31 0.33 0.09 0.79 0.34 0.18 0.85 1.78 2.61 1.94

Total fit fraction 118.1 112.6 198.3

TABLE XVIII. Experimental systematic uncertainties on the interference fit fractions (%). The amplitudes are (A0) D�vð2007Þ0, (A1)

D�0ð2400Þ0, (A2) D�

2ð2460Þ0, (A3) D�1ð2760Þ0, (A4) B�

v, (A5) nonresonant S-wave, and (A6) nonresonant P-wave. The diagonal elementsare the same as the conventional fit fractions.

A0 A1 A2 A3 A4 A5 A6

A0 1.3 0.0 0.0 0.4 0.6 0.0 2.6A1 0.6 0.0 0.0 0.4 0.6 0.0A2 0.9 0.0 0.3 0.0 0.0A3 0.4 0.2 0.0 0.7A4 0.9 1.1 1.2A5 1.5 0.0A6 2.1

TABLE XVII. Interference fit fractions (%) and statistical uncertainties. The amplitudes are (A0) D�vð2007Þ0, (A1) D�

0ð2400Þ0, (A2)D�

2ð2460Þ0, (A3) D�1ð2760Þ0, (A4) B�

v, (A5) nonresonant S-wave, and (A6) nonresonant P-wave. The diagonal elements are the same asthe conventional fit fractions.

A0 A1 A2 A3 A4 A5 A6

A0 7.6� 2.3 0.0� 0.0 0.0� 0.0 2.4� 0.9 4.8� 1.3 0.0� 0.0 −14.2� 5.3A1 8.3� 2.6 0.0� 0.0 0.0� 0.0 −1.6� 0.7 18.1� 2.6 0.0� 0.0A2 31.8� 1.5 0.0� 0.0 −2.3� 0.6 0.0� 0.0 0.0� 0.0A3 4.9� 1.2 2.0� 0.8 0.0� 0.0 −9.6� 2.9A4 3.6� 1.9 −6.7� 2.3 −11.1� 3.6A5 38.0� 7.4 0.0� 0.0A6 23.8� 5.6

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TABLE XIX. Model systematic uncertainties on the interference fit fractions (%). The amplitudes are (A0) D�vð2007Þ0, (A1)

D�0ð2400Þ0, (A2) D�

2ð2460Þ0, (A3) D�1ð2760Þ0, (A4) B�

v, (A5) nonresonant S-wave, and (A6) nonresonant P-wave. The diagonal elementsare the same as the conventional fit fractions.

A0 A1 A2 A3 A4 A5 A6

A0 1.5 0.0 0.0 0.1 1.4 0.0 1.1A1 1.9 0.0 0.0 1.7 4.8 0.0A2 1.4 0.0 0.5 0.0 0.0A3 0.9 0.6 0.0 3.4A4 1.6 2.8 0.4A5 10.8 0.0A6 3.67

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L. Zhang,3 Y. Zhang,3 A. Zhelezov,11 A. Zhokhov,31 and L. Zhong3

(LHCb Collaboration)

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil3Center for High Energy Physics, Tsinghua University, Beijing, China

4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France

6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France

8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot, CNRS/IN2P3, Paris, France9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany

10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

12School of Physics, University College Dublin, Dublin, Ireland13Sezione INFN di Bari, Bari, Italy

14Sezione INFN di Bologna, Bologna, Italy15Sezione INFN di Cagliari, Cagliari, Italy16Sezione INFN di Ferrara, Ferrara, Italy17Sezione INFN di Firenze, Firenze, Italy

18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy19Sezione INFN di Genova, Genova, Italy

20Sezione INFN di Milano Bicocca, Milano, Italy21Sezione INFN di Milano, Milano, Italy22Sezione INFN di Padova, Padova, Italy

23Sezione INFN di Pisa, Pisa, Italy24Sezione INFN di Roma Tor Vergata, Roma, Italy25Sezione INFN di Roma La Sapienza, Roma, Italy

26Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland27AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science,

Kraków, Poland28National Center for Nuclear Research (NCBJ), Warsaw, Poland

29Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania30Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia

31Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia32Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia

33Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia34Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia

35Institute for High Energy Physics (IHEP), Protvino, Russia36Universitat de Barcelona, Barcelona, Spain

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37Universidad de Santiago de Compostela, Santiago de Compostela, Spain38European Organization for Nuclear Research (CERN), Geneva, Switzerland39Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

40Physik-Institut, Universität Zürich, Zürich, Switzerland41Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands

42Nikhef National Institute for Subatomic Physics and VU University Amsterdam,Amsterdam, The Netherlands

43NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine44Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine

45University of Birmingham, Birmingham, United Kingdom46H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom47Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom

48Department of Physics, University of Warwick, Coventry, United Kingdom49STFC Rutherford Appleton Laboratory, Didcot, United Kingdom

50School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom51School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom

52Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom53Imperial College London, London, United Kingdom

54School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom55Department of Physics, University of Oxford, Oxford, United Kingdom56Massachusetts Institute of Technology, Cambridge, MA, United States

57University of Cincinnati, Cincinnati, OH, United States58University of Maryland, College Park, MD, United States

59Syracuse University, Syracuse, NY, United States60Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil (associated with

Institution Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil)61Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China (associated with

Institution Center for High Energy Physics, Tsinghua University, Beijing, China)62Departamento de Fisica, Universidad Nacional de Colombia, Bogota, Colombia (associated with

Institution LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,CNRS/IN2P3, Paris, France)

63Institut für Physik, Universität Rostock, Rostock, Germany (associated with Institution PhysikalischesInstitut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany)

64National Research Centre Kurchatov Institute, Moscow, Russia (associated with Institution Institute ofTheoretical and Experimental Physics (ITEP), Moscow, Russia)

65Yandex School of Data Analysis, Moscow, Russia (associated with Institution Institute of Theoretical andExperimental Physics (ITEP), Moscow, Russia)

66Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC, Valencia, Spain (associated withInstitution Universitat de Barcelona, Barcelona, Spain)

67Van Swinderen Institute, University of Groningen, Groningen, The Netherlands (associated withInstitution Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands)

aAlso at Università di Firenze, Firenze, Italy.bAlso at Università di Ferrara, Ferrara, Italy.cAlso at Università della Basilicata, Potenza, Italy.dAlso at Università di Modena e Reggio Emilia, Modena, Italy.eAlso at Università di Milano Bicocca, Milano, Italy.fAlso at LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain.gAlso at Università di Bologna, Bologna, Italy.hAlso at Università di Roma Tor Vergata, Roma, Italy.iAlso at Università di Genova, Genova, Italy.jAlso at Scuola Normale Superiore, Pisa, Italy.kAlso at Università di Cagliari, Cagliari, Italy.lAlso at Politecnico di Milano, Milano, Italy.mAlso at Universidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil.nAlso at AGH - University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków,Poland.

oAlso at Università di Padova, Padova, Italy.pAlso at Hanoi University of Science, Hanoi, Viet Nam.qAlso at Università di Bari, Bari, Italy.

FIRST OBSERVATION AND AMPLITUDE ANALYSIS OF … PHYSICAL REVIEW D 91, 092002 (2015)

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rAlso at Università degli Studi di Milano, Milano, Italy.sAlso at Università di Roma La Sapienza, Roma, Italy.tAlso at Università di Pisa, Pisa, Italy.uAlso at Università di Urbino, Urbino, Italy.vAlso at P.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia.

R. AAIJ et al. PHYSICAL REVIEW D 91, 092002 (2015)

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