Analysis of the channel $\Lambda_b \to \Lambda J/\Psi$

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Analysis of the channel Λ_b

→ ΛJ/Ψ

Ziad Ajaltouni, E. Conte

To cite this version:

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democrite-00024814, version 1 - 5 Oct 2005

LHCb 2005-067, PHYSICS PCCF RI 0509

Analysis of the channel

Λ

_b

→ Λ J/Ψ

Ziad AJALTOUNI

1

_{, Eric CONTE}

2

September 21, 2005

Laboratoire de Physique Corpusculaire de Clermont-Ferrand IN2P3/CNRS Universit´e Blaise Pascal

F-63117 Aubi`ere C´edex FRANCE

Abstract

A first study of the LHCb sensitivity to the decay Λb → Λ(pπ−) J/Ψ(µ+µ−) (including

also Λb → Λ(pπ+) J/Ψ(µ+µ−) ) is presented in this paper. A signal sample of 280,000

events allows to estimate the different efficiencies of this channel. The global efficiency (included first HLT simulation) reachs 0.45% and the annual yield is expected to be about

18×103 _{selected events. A study of the background is performed. For inclusive bb , a B/S}

ratio of 0.30, based on an analysis of 12.8 millions events(DC04v1), has been estimated. Specific background contributions are negligible.

1

ziad@clermont.in2p3.fr 2

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CONTENTS

1 Introduction and motivations

Since its discovery by Cronin, Fitch, Cristenson and Turlay in the year 1964 in the

K0

− K0 _{system[1], CP violation process is always studied in order to improve our}

un-derstanding of symmetry in nature. This phenomenon is well-known in the context of strange and beauty mesons. The use of hyperon particles is another aspect of CP

vi-olation test. We will follow this approach by using beauty baryons such as Λb which

decay particularly into Λ and meson vector. As CP conjuguate channels Λb and Λb have

different final states, a direct CP violation process can be put into evidence by measuring asymmetry parameter or CP conjuguate observables.

On another side, we are interested into Time Reversal (TR) violation process. Ob-viously, the famous CPT theorem in Quantum Field Theory involves a violation of TR symmetry with the same intensity than CP violation. But it is possible to put a limit on this process independently of CP violation. The results of CPLear experiment in the year

1999[2] agree with this statement. That’s why analysis of Λb → Λ vector meson can be

done for performing both CP violation and TR violation tests. This second aim presents a supplementary difficulty : the non-existence of a T observable due to the ”antiunitary” nature of TR operator[3]. So the method is based on searching for T-odd observables which sign changes by TR transformation. A non vanishing mean value of these variables could be a sign of TR violation if interaction in the final states are negligible. In the opposite case, these interactions must be determined.

This study will be performed in the context of LHCb experiment. We must

deter-mine the performance of LHCb detector for reconstructing channels like as Λb → Λ vector

meson . It is important to notice that it is the first time that Λ and Λb particles are

reconstructed with the LHCb detector simulations, and it represents a real challenge for tracking system. In fact, Λ particles are characterized by a great life-time and most of them decay beyond the vertex locator detector. This case is similar to the reconstruction

of K0

s meson which life-time is three times smaller than Λ particle one.

The first ”member” of the Λb → Λ vector meson family is the channel Λb → Λ J/Ψ

and its DaVinci analysis is presented in this paper. A sample of 277,000 signal events

has been generated and it contains both channels Λb → Λ J/Ψ and Λb → Λ J/Ψ . The

assumed visible Branching-Ratio (BR) is (4.7 ± 2.8) × 10−4_{[4]. We obtain a global BR}

of 20.6 × 10−6 _{by requiring Λ and J/Ψ decay respectively into pπ}− _{(63.9%) and into}

µ+

µ−_{{γ}(6.76%) with a possible radiative emission. Finally, the authors assert that the}

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2 Strategy and analysis tools

Concerning the generation of the preceding decay, no particular dynamics has been introduced up to now. We have begun to perform a dynamics model based on the Jacob-Wick-Jackson helicity formalism and on the computation of hadronics matrix elements by the OPE techniques. Main results are gathered in our previous publications [5], [6] and [7]. We are intent on implementing this model into Gauss software, notably EvtGen code. Signal events are generated in a cone centered around the z axis and with an angle of 400 mrad which covers the LHCb detector acceptance (300-350 mrad). This condition avoids generating irrelevant events which cannot be reconstructed by the apparatus. In Pythia, the ratio of beauty mesons generated in the 400 mrad over those generated in 4π

is varying from (34.69±0.04)% to (34.77±0.18)%[8]. For Λb particles, we have considered

the classical value of 34.71%. The proximity of these values is due to the b(b) quark which gives its momentum to the beauty hadrons (dominant quark).

The present analysis has been made with the help of LHCb tools : DaVinci v12r12 and LoKi v3r13p1. It includes three algorithms, each one associated to one resonance selection. One simple algorithm will be used for selecting all J/Ψ particles whatever their origin is. The Λ particle selection is performed by another algorithm, independently of

J/Ψ reconstruction. This selection is based on K0

s reconstruction code performed by

Yuehong Xie[9]. A last code is dedicated to the selection of Λb particles by requiring that

at least one J/Ψ candidate and one Λ candidate have been reconstructed.

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3 Detection and Reconstruction Efficiencies

3.1 Λ and Λ absorption

Because of its life time of (2.632 ± 0.020) × 10−10_{s[4], most of the Λ particles decay}

beyond the vertex locator. This statement is reinforced for Λ particles coming from the

Λb decay(a secondary vertex). This feature involves that about 10% of Λ or Λ interact

with the detector matter (RICH subdetector for instance). These events are lost for the analysis and decrease the statistics. Table 1 gives distributions of Λ and Λ originating

from a Λb by using only Monte-Carlo informations.

generated not interacting with matter % interacting Λ

Λ 142,525 128,295 9.98%

Λ 137,475 123,007 10.52%

Total 280,000 251,302 10.25%

Table 1: Number of Λ and Λ which are absorbed by matter

We can notice that as much Λ as Λ interact with detector matter while more absorbed Λ should be expected. The understanding of this phenomenon has been provided by the Geant4 conceptors. The most possible explanation is that the interaction rate of Λ and Λ depend on their energy and, at high energies, the cross-sections become usually identical. Therefore, this process must be taken into account for the test of CP symmetry.

3.2 Tracking setup

The generic reconstruction program aims to find all tracks in the event which leave sufficient hits in the subdetectors. According to LHCb convention[10], we can define five kind of tracks but only tracks used in this analysis are described (figure 1):

• Long tracks go through the full tracking setup from the VELO to the T stations. This kind of tracks has a good reconstruction efficiency of 94% provided their mo-mentum higher than 10 GeV/c. The ghost rate for B signal tracks is about 3% owing

to their high PT.The momentum resolution δp/p varies from 0.35% (few GeV/c) to

0.55% (140 GeV/c).

• Upstream tracks go only through the VELO and TT stations. The reconstruction effiency has been estimated around 75% with a ghost rate of 15%. Owing to the small fraction of upstream tracks, the momentum resolution δp/p is about 15%. • Downstream tracks go only through the TT and T stations. The test of their

performance has been carried out with K0

s decay. In the reconstruction algorithm,

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3.3 Track repartition

than 5 GeV/c with a momentum resolution δp/p of 0.43% (estimated with a sample

of pions among them pions coming from K0

S decay). Upstream track TT VELO T1 T2 T3 T track VELO track Long track Downstream track 0 0 −0.2 −0.4 −0.6 −0.8 −1.0 −1.2 2 4 6 8 _z_[m] By [T]

Figure 1: LHCb track conventions[10]

3.3 Track repartition

In the case of J/Ψ, the LL track combination is dominating with a high ratio of 92.3%. That’s why, only long tracks are selected and the others are rejected.

For Λ particles, we have a specific repartition of tracks which are represented in figure 2b. This pie chart has been achieved by identifying reconstructed particles by Monte Carlo informations.

As we can notice for Λ (Λ) particles, DD combinations are dominating (with 55% for

Λ orginated from Λb decay) because main decays occur beyond the VELO. The other

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3.4 Definition of Reconstructible and Reconstructed particle

Gathering these four combinations gives us 96.7% of Λ which could be selected.

The Λ track repartition can be compared to the K0

s one in figure 2a (realized with

a sample of 280,000 B0

d → K 0

s J/Ψ events). The pourcentage of each class is almost

the same for both the two channels, while a reduction of 4% of LL combinations can be noticed for Λ particles. We can explain this similarity by remarking that about 25% of the non reconstructed Λ decay beyond the TT chamber (z > 2400mm).

Figure 2: Repartition of track combinations repartition for K0

s particles (in B

0 d →

K0

s J/Ψ)(left) and for Λ particles (right)

3.4 Definition of Reconstructible and Reconstructed particle

First of all, definition of a reconstructible and reconstructed particles is recalled. We limit it to charged particles[10][11].

A stable Monte Carlo particle (MCParticle) is reconstructible if this particle has hitted several tracking subdetectors. This criterion depends on the nature of the track according to the table 2.

VELO TT each T station

Long 3r+3φ clusters X 1x+1stereo clusters

Upstream 3r+3φ clusters 3 clusters X

Downstream X 3 clusters 1x+1stereo clusters

Table 2: Conditions for a MCParticle to be reconstructible

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3.5 Detection and Reconstruction efficiencies

A decaying particle is reconstructible or reconstructed if all final state particles are respectively reconstructible or reconstructed.

3.5 Detection and Reconstruction efficiencies

The number of reconstructible or/and reconstructed events are summed up and shown in tables 3, 4 and 5 for the different nature of particles appearing in the decays. From these data, detection efficiency(normalized to the 4π angle) and reconstruction efficiency

for Λb (Λb) can be deduced.

µ±

J/Ψ

nb rec’ible particles 352,777 122,430

nb rec’ed particles 354,982 123,659

nb rec’ible & ed particles 345,359 118,158

Table 3: Number of reconstructible/reconstructed J/Ψ (any origin)

p(p) π±

Λ (Λ)

nb rec’ible particles 217,893 133,769 110,778

nb rec’ed particles 178,263 81,745 60,165

nb rec’ible & ed particles 174,269 77,108 57,594

Table 4: Number of reconstructible/reconstructed Λ (any origin)

µ± _J/Ψ _p(p) _π± _{Λ (Λ)} _Λ

b (Λb)

nb rec’ible particles 314,987 108,882 110,799 73,250 63,495 37,681

nb rec’ed particles 316,862 109,920 95,557 50,343 39,234 24,088

nb rec’ible & ed particles 308,378 105,095 94,254 48,106 37,883 22,629

Table 5: Number of reconstructible/reconstructed Λb

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4 Identification

4.1 Elements of the identification process

Experimental setup of the LHCb identification[10][11] is composed of three sub-detectors: the two RICH detectors, the Calorimeter system and the Muon detector. Calorimeter provides separation between electromagnetic particles (electron and photon)

and hadrons. The muon detector is dedicated to the identification of µ± _{particles. Using}

Cherenkov Ring technique, the RICH detectors can identify charged hadrons according to their momentum and helps to the separation between leptons and hadrons.

The identification is better for long tracks than for short tracks. Indeed, long tracks go through these three subdetectors whereas downstream tracks may not hit the RICH1. The worst case concerns Upstream tracks which can hit only the RICH1 detector and do not reach calorimeter and the muon chambers. For this kind of tracks, the identification procedure is restricted.

In the analysist point of view, informations given by the identification detectors are synthesized in a log-likelihood function. There is one log-likelihood function for each subdetector but only the product of these three is used.

L(µ) = LRICH_{(µ) × L}CALO_{(non e) × L}M U ON_(µ)

L(p) = LRICH(p) × LCALO(non e) × LM U ON(non µ)

L(π) = LRICH(π) × LCALO(non e) × LM U ON(non µ)

The identification of a particle is performed by setting a threshold on likelihood func-tion ratio between two hypothesis or equivalently on difference of log-likelihood fucfunc-tions. Usually, the pion hypothesis is taken as a reference and in the case of proton-pion sepa-ration, the delta log-likelihood is given by the following formula :

∆Lpπ = ln

L(p)

L(π) = lnL(p) − lnL(π)

In this case, we can put a threshold to this parameter in order to discriminate protons and pions. Indeed, high positive value is associated to the tracks which the proton hypothesis is the most checked. On the contrary, pion hypothesis is dominating for negative values of the delta log-likelihood.

4.2 Muon identification

In the signal sample, muon subdetector information is available for all particles re-constructed and associated to Monte-Carlo muon particles. But 11.2% of those do not hit this subdetector and only RICH information is used for their identification. In order

to reduce contamination, the ∆ ln Lµπ value is maintained to -15 in the preselection and

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4.3 Proton and pion identification -1000 -80 -60 -40 -20 0 20 40 60 80 100 500 1000 1500 2000 2500 3000 2 10 × N . E n tr ie s / 1

Figure 3: ∆ ln Lµπ for µ (red) and π (green) tracks

∆ ln Lµπ ǫ(µ) ǫ(π → µ) rate of lost µ

particles

-15 6.8% 93.2% 1.3%

-8 8.5% 91.5% 1.6%

Table 6: Muon contamination depending on ∆ ln Lµπ value

ǫ(µ) = nb particles identif ied muon associated to MC muon

nb particles identif ied muon

ǫ(π → µ) = nb particles identif ied muon associated to MC pion

nb particles identif ied muon

4.3 Proton and pion identification

For the reconstruction of Λ(Λ) particles, we must identify proton and pion parti-cles. In the CombinedParticleMaker configuration, the exclusive identification mode is selected. Therefore, only one identity is given for each ProtoParticle. We specified that the proton identification has priority.

The threshold for the ∆ ln Lpπ of Long and Downstream tracks are chosen in order

to maximize the number of LL and DD Λ(Λ) combinations. According to table 7 and 8, the prescription used is 6 for these tracks.

In another side, Upstream tracks ∆ ln Lpπ occur only in LU combinations in our

se-lection. Bad resolution on the identification of Upstream tracks gives a tight sprectrum

of ∆ ln Lpπ (figure 6). We cannot choose the treshold which maximizes the number of

LU Λ(Λ) candidates because too many protons could be identified as pions. For limiting

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4.3 Proton and pion identification than 6.

In the case of LU combinations, 90% of Upstream tracks are pions. The requirement of this feature can be a powerful criterion for the selection. In the following sections, we

only keep this kind of combinations which will be noticed ”LU∗”. This asymmetry does

not appear in the case of LD combinations.

The study of the final state identification is not completed and other points must be taken into account in the next revision :

• We could constrain other ∆ ln L parameters

• Effects of the inclusive mode in the CombinedParticleMaker configuration • Achieve a better identification of proton and pion

• Optimize the threshold for LU combinations

ǫ(p) = nb particles identif ied proton associated to MC proton

nb particles identif ied proton

ǫ(π → p) = nb particles identif ied proton associated to MC pion

nb particles identif ied proton

LL combinations : -1000 -80 -60 -40 -20 0 20 40 60 80 100 100 200 300 400 500 600 700 800 900 PROTONS PIONS

Figure 4: ∆ ln Lpπ for p (red) and π (green) Longstream tracks

∆ ln Lpπ ǫ(p) ǫ(π → p) Λ(Λ) could be selected 4 62.50% 37.50% 4,847 5 71.01% 28.81% 4,892 6 76.92% 23.08% 4,897 7 80.70% 19.30% 4,883 8 83.38% 16.62% 4,855

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4.3 Proton and pion identification DD combinations : -1000 -80 -60 -40 -20 0 20 40 60 80 100 500 1000 1500 2000 2500 3000 3500 4000 4500 PROTONS PIONS

Figure 5: ∆ ln Lpπ for p (red) and π (green) Downstream tracks

∆ ln Lpπ ǫ(p) ǫ(π → p) Λ(Λ) could be selected 4 54.26% 45.80% 18,615 5 58.31% 41.68% 18,841 6 61.52% 38.48% 19,074 7 64.34% 35.67% 19,071 8 66.85% 33.15% 19,058

Table 8: Downstream proton contamination depending on ∆ ln Lpπ value

LU combinations : -1000 -80 -60 -40 -20 0 20 40 60 80 100 1000 2000 3000 4000 5000 PROTONS PIONS

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4.3 Proton and pion identification ∆ ln Lpπ ǫ(p) ǫ(π → p) Λ(Λ) could be selected -2 6.65% 93.35% 1,975 -1 7.33% 92.67% 2,078 0 8.33% 91.66% 2,235 1 9.45% 90.55% 2,387 2 11.59% 88.41% 2,588

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5 Selection of the final states

In this section and the following one analysis is made by using only signal event sample. The ”background” is made up of fragmentation particles (or their product) and ghosts. The present cuts will be reinforced and new ones will be added when the inclusive

bb and prompt J/Ψ sources will be analyzed.

Moreover, we are trying to reconstruct Λ candidates and J/Ψ candidates whatever

their origin is, before Λb reconstruction. Thus, the Λ and J/Ψ sub-algorithms could be

adapted and used in other channel analysis.

5.1 Selection of muons µ

±

The selection of J/Ψ final states is contained in the preselection code. It requires

each muon particle having a transverse momentum (PT) greater than 250 MeV/c and a

momentum greater than 3 GeV/c. The number of selected and matched muons is 292,071 over the 288,000 events.

5.2 Selection of pions π

±

_{and protons p(¯}

_p)

For Λ final states, criteria depend on the class the tracks and their identity. They are displayed in table 10. Table 11 provides their cumulative efficiencies for proton/pion particles. protons pions L D U L D U minimum PT (MeV/c) 150 200 200 80 100 50 MIP (mm) 0.2 X 0.3 0.2 0.2 0.2 χ2

/nDoF track reconstruction 2 X 3 2 2 2

Table 10: Criteria applied to proton and pion particles

protons pions L D U L D U minimum PT 99.1% 99.6% 97.6% 92.6% 96.7% 99.9% MIP 87.9% X 88.4% 89.9% 96.7% 98.7% χ2 /nDoF track 84.6% X 77.6% 86.1% 90.0% 84.4%

Table 11: Cumulative efficiency of the particle selection

An usual requirement is applied to the transverse momentum of the final states (figure

9). It is well-known that fragmentation particles have a low PT. So selected protons must

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5.2 Selection of pions π± _{and protons p(¯}_p)

Upstream). For pions, the thresholds are respectively 80MeV/c and 100MeV/c for Long and Downstream tracks. For upstream tracks, the generic reconstruction algorithm have

required a PT > 50MeV/c.

The Minimum Impact Parameter (MIP)[11] is a relevant parameter. According to figure 8, the Impact Parameter (IP) is defined as the smallest distance between an ar-bitrary vertex and a particle track (or its extension). As several primary vertices in an event can be reconstructed, a calculation of the IP is made for each primary vertex and the smallest value is called MIP. Figure 10 shows that the requirement on the MIP value is a conservative cut for Longstream and Upstream tracks.

Reconstruction track quality is constrained in order to suppress fragmentation tracks.

Longstream tracks must have a χ2

/nDoF smaller than 3 in order to be selected (figure 11). In the case of Downstream and Upstream tracks, only tracks which have a small

χ2_{/nDoF (< 3 for Downstream and < 5 for Upstream) have been accepted. This}

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5.2 Selection of pions π± _{and protons p(¯}_p) 0 5000 10000 15000 20000 25000 30000 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 1000 2000 3000 4000 5000 6000 7000 MeV/c MeV/c N . E n tr ie s / 1 5 0 M e V / c N . E n tr ie s / 2 5 M e V / c

Figure 7: P and PT of muon(green) and fragmentation particles(black)

particle momentum

IP

reference vertex

Figure 8: definition of the Impact Parameter wrt a vertex

0 50 100 150 200 250 300 350 400 1 10 2 10 3 10 0 50 100 150 200 250 300 350 400 10 2 10 3 10 0 50 100 150 200 250 300 350 400 1 10 2 10 0 50 100 150 200 250 300 350 400 10 2 10 3 10 4 10 0 50 100 150 200 250 300 350 400 10 2 10 3 10 4 10 0 50 100 150 200 250 300 350 400 2 10 3 10 4 10

MeV/c MeV/c MeV/c MeV/c MeV/c MeV/c

N . E n tr ie s / 2 M e V / c N . E n tr ie s / 2 M e V / c N . E n tr ie s / 2 M e V / c N . E n tr ie s / 2 M e V / c N . E n tr ie s / 2 M e V / c N . E n tr ie s / 2 M e V / c

L pions D pions U pions

L protons D protons U protons

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5.2 Selection of pions π± _{and protons p(¯}_p) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2 10 3 10 4 10 5 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 1 10 2 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 10 2 10 3 10 4 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 3 10 4 10 5 10 6 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 10 2 10 3 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 3 10 4 10 5 10 mm mm mm mm mm mm N . E n tr ie s / 0 .0 2 5 m m N . E n tr ie s / 0 .0 2 5 m m N . E n tr ie s / 0 .0 2 5 m m N . E n tr ie s / 0 .0 2 5 m m N . E n tr ie s / 0 .0 2 5 m m N . E n tr ie s / 0 .0 2 5 m m

Figure 10: MIP of proton/pion(green) and fragmentation particles(black)

0 1 2 3 4 5 6 7 8 1 10 2 10 3 10 4 10 0 1 2 3 4 5 6 7 8 1 10 2 10 3 10 4 10 0 1 2 3 4 5 6 7 8 10 2 10 3 10 0 1 2 3 4 5 6 7 8 10 2 10 3 10 4 10 5 10 0 1 2 3 4 5 6 7 8 1 10 2 10 3 10 4 10 0 1 2 3 4 5 6 7 8 3 10 4 10 N . E n tr ie s / 0 .0 4 N . E n tr ie s / 0 .0 4 N . E n tr ie s / 0 .0 4 N . E n tr ie s / 0 .0 4 N . E n tr ie s / 0 .0 4 N . E n tr ie s / 0 .0 4

Figure 11: χ2

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6 Selection of Λb

candidates

6.1 Summary of essential observables

6.1.1 Distance of closest approach beetween two tracks

The Distance of Closest Approach (DCA)[11] is a useful geometrical criterion. The distance d beetween the first measured points of two tracks is calculated. The Distance

of Closest Approach is the projection of this distance on the −→u12 axis, which is normal to

the plane defined by the two particle momentums.

− → d − →_p 1 − →_p 2 −→ u12 = − →_p 1 ×−→p2 |−→p1 ×−→p2 | 6.1.2 Vertexing fitter

The unconstrained vertex fit[12] extrapolates the vertex position without any kine-matics assumption. From measurement, the vertex z position is estimated by requiring the minimum values of x and y variances.

The mass constrained vertex fit[12] imposes two contrains on the vertex extrapolation. The first is geometrical : all tracks should have a common point in space. The second one concerns the invariant mass. For a two body decay, the vertex fitting requires that

the square of the invariant mass, M2_{, must be equal to the square of the sum of the}

momentum p1 and p2 :

M2

= (p1+ p2)2

This tool is available if daughter particles have a width smaller than 1MeV/c2

(it is the case for all particles in the decay chain).

6.2 Selection of J/Ψ candidates

By selecting muon pairs, J/Ψ candidates are obtained but a discrimination between true J/Ψ and combinatorial background must be performed. That is why a sequence of criteria is applied. Table 12 provides the efficiency of this selection.

Preselection code :

• Unconstrained vertex fitting with a χ2

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6.2 Selection of J/Ψ candidates

• Mass window of ± 120 MeV/c2

around true J/Ψ mass (3096.916±0.011) MeV/c2

[4] Selection code :

• Mass constrained vertex fitting with a χ2 _{< 16}

• Distance of Closest Approach (DCA) smaller than 0.1mm

• Mass window of ± 35 MeV/c2 _{around true J/Ψ}

Particle selection 99.5%

Unconstrained vertex fitting. χ2

98.6% Mass constrained vertex fitting. χ2

86.4%

P min 86.4%

DCA (mm) 84.7%

Tight Mass Window 84.5%

Matching efficiency 99.6%

Table 12: Cumulative selection efficiency for J/Ψ candidates

Figure 12 shows that the spectrum of χ2 _{for the unconstrained vertex fitting and the}

mass constrained vertex fitting having a large tail. We require that this parameter must be smaller than 10 for the unconstrained vertex fitting and smaller than 16 for the mass constrain vertex fitting in order to remove a main part of the combinatorics. A refinement of the selection is carried out by imposing a minimal value of 0.1mm on the Distance of Closest Approach between the two muons. Finally, a tight mass window (about four times smaller than preselection one) is applied. The role of this cut will be put into ev-idence when the mass resolution of the reconstructed J/Ψ will be studied(see section 8.1). Thus the J/Ψ selection efficiency is equal to 84.5%. To estimate the signal contami-nation by combinatorics, we define the matching efficiency as the ratio of the number of matching selected candidates over the total number of selected candidates. The matching efficiency of 99.6% provides a good indication of signal purity.

0 2 4 6 8 10 12 14 16 18 20 1 10 2 10 3 10 4 10 0 20 40 60 80 100 120 140 160 180 200 1 10 2 10 3 10 4 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 1 10 2 10 3 10 4 10 mm N . E n tr ie s / 0 .1 N . E n tr ie s / 1 N . E n tr ie s / 0 .0 1 m m χ2 _unconst. _χ2 _const. DCA

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6.3 Selection of Λ candidates

Λ candidates can be realized by combining selected protons and pions. Major part of the combinatorial background is rejected by requiring a loose mass window of ±100

MeV/c2

around the true Λ mass (1115.683±0.006) MeV/c2

[4]. Tables 13 and 14 summa-rize respectively the constrain cuts and their efficiencies.

LL DD LU∗

LD Loose mass window (MeV/c2

) ±100 ±100 ±100 ±100

3 100 5 20

Mass constrained vertex fitting. χ2

3 200 10 12

PT (MeV/c) 300 700 400 1000

DCA (mm) 0.2 25 0.2 3.5

Tight Mass Window (MeV/c2

) ±4 ±18 ±17 ±8

Table 13: Criteria applied to Λ candidates

LL DD LU∗

LD

Particle selection 69.1% 91.7% 66.7% 76.9%

Loose mass window (MeV/c2

) 68.7% 88.5% 66.7% 76.9%

60.0% 81.2% 57.4% 39.0%

51.3% 67.7% 54.6% 18.7%

PT (MeV/c) 51.0% 66.3% 48.8% 16.9%

DCA (mm) 49.0% 65.8% 46.1% 15.4%

) 48.7% 65.6% 43.2% 15.3%

Matching efficiency 91.2% 88.9% 67.4% 44.1%

Table 14: Cumulative selection efficiency for Λ candidates

The most powerful cut applied to Λ candidates consists in vertex fitting (unconstrained

and mass constrained). The χ2

spectrum can be found in figures 14 and 15. Cuts are

very sharp for LL, LU∗ _{and LD. The high valued threshold for DD class combinations}

(100 for unconstrained and 200 for mass constrained) is due to the lack of hits in the VELO.

According to figure 16, combinatorial background has a low PT with respect to the

signal events. A cut on this observable allows to purify the signal.

The Distance of Closest Approach between protons and pions is a relevant parameter for the Λ selection. The queue of this spectrum (figure 17) is removed by requiring DCA

greater than 0.2mm, 24mm, 0.6mm and 3.5mm for respectively LL, DD, LU∗ _{and LD}

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6.4 Selection of Λb candidates

The selection is finished by imposing a tight mass window with a width depending on the class of the tracks. The justification can be found in the mass resolution section.

A selection efficiency can be deduced for each class of tracks and a matching efficiency (nb matching and selected Λ / nb Λ selected) for Λ with any origin. We can notice that the selection efficiency for DD combination is the highest (65.6%). The matching efficiency is quite good for LL and DD candidates. Nonetheless, table 14 shows clearly that the

contamination is important for LU∗ _{and LD class. This remaining contamination will be}

suppressed by the Λb selection.

6.4 Selection of Λb

candidates

The Λb resonance is reconstructed by using both the two preceding selections. In the

same goal than for Λ selection, a loose mass window of ±150 MeV/c2 _{is applied. We can}

sort Λb candidates by the Λ class of tracks. For simplifying notation, we call, for instance,

a ”DD Λb” a Λb candidate reconstructing by a DD Λ particle. The sequence of criteria

and their efficiency are described in tables 15 and 16.

LL DD LU∗ _LD

) ±250 ±250 ±250 ±250

15 X 15 X

30 150 40 50

) ±50 ±60 ±50 ±50

Table 15: Criteria applied to Λb candidates

LL DD LU∗ _LD

J/Ψ and Λ selection 35.0% 37.5% 32.5% 13.1%

) 35.0% 37.5% 32.5% 13.1%

35.0% X 22.1% X

35.0% 37.5% 32.0% 10.1%

) 35.0% 36.9% 30.6% 10.1%

Table 16: Cumulative selection efficiency for Λb candidates

Cuts on unconstrained vertex fitting and mass constrained vertex fitting are sufficient

to select a good Λb candidate. Figure 18 shows that the first cut is irrelevant for DD and

LD combinations. For LL and LU∗_{, the threshold is maintained to 15. In the case of}

mass constrained vertex fitting, a maximun χ2

is required for all kinds of classes (figure 19). The last (but not the least) constrain is a tight mass window which width will be justified in the resolution section.

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6.5 Selection of the primary vertex

Finally, we can select the primary vertex from which Λb comes, among reconstructed

primary vertices. Figure 13 gives the number of reconstructed primary vertices by event and an average value of 1.3 can be deduced.

0 50000 100000 150000 200000 250000 5 4 3 2 1 0 Nb events

Figure 13: Number of reconstructed primary vertices per event

The primary vertex selection, as suggested by the TDR 2003[10], is used. We kept the

one which minimizes the Impact Parameter of the Λbcandidate. So each Λb candidate has

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6. 5 S ele ct io n of th e p rim ar y ve rt ex 0 5 10 15 20 25 2 10 3 10 4 10 0 50 100 150 200 250 300 350 400 2 10 3 10 4 10 0 5 10 15 20 25 30 2 10 3 10 4 10 0 10 20 30 40 50 60 2 10 3 10 4 10 N . E n tr ie s / 0 .1 2 5 N . E n tr ie s / 2 N . E n tr ie s / 0 .1 5 N . E n tr ie s / 0 .3 LL DD LU∗ _LD

Figure 14: χ2 unconstrained vertex fitting for Λ candidates (green for signal, black for combinatorics)

dd 0 5 10 15 20 25 1 10 2 10 3 10 0 100 200 300 400 500 600 700 800 1 10 2 10 3 10 0 5 10 15 20 25 1 10 2 10 0 5 10 15 20 25 30 35 40 45 50 10 N . E n tr ie s / 0 .1 2 5 N . E n tr ie s / 4 N . E n tr ie s / 0 .1 2 5 N . E n tr ie s / 0 .2 5 LL DD LU∗ _LD

Figure 15: χ2 mass constrained vertex fitting for Λ candidates (green for signal, black for combinatorics)

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6. 5 S ele ct io n of th e p rim ar y ve rt ex 0 200 400 600 800 1000 12001400 1600 18002000 0 5 10 15 20 25 30 35 40 45 0 500 1000 1500 2000 2500 3000 0 10 20 30 40 50 60 70 80 90 0 500 1000 1500 2000 2500 3000 0 50 100 150 200 250 300 350 400 450 0 1000 2000 3000 4000 5000 6000 7000 0 10 20 30 40 50 N . E n tr ie s / 1 0 M e V / c N . E n tr ie s / 1 5 M e V / c N . E n tr ie s / 1 5 M e V / c N . E n tr ie s / 3 5 M e V / c LL DD LU∗ _LD

MeV/c MeV/c MeV/c MeV/c

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6. 5 S ele ct io n of th e p rim ar y ve rt ex 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 100 200 300 400 500 600 700 0 5 10 15 20 25 30 35 40 0 200 400 600 800 1000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 100 200 300 400 500 600 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 N . E n tr ie s / 0 .0 0 5 m m N . E n tr ie s / 0 .1 6 m m N . E n tr ie s / 0 .0 0 7 5 m m N . E n tr ie s / 0 .1 5 m m mm mm mm mm LL DD LU∗ _LD

Figure 17: DCA of Λ candidates (green for signal, black for combinatorics)

dd 0 5 10 15 20 25 30 35 40 45 50 0 20 40 60 80 100 0 50 100 150 200 250 300 350 400 450 500 0 100 200 300 400 500 600 700 800 900 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 40 45 50 0 0.5 1 1.5 2 2.5 3 3.5 4 N . E n tr ie s / 0 .2 5 N . E n tr ie s / 2 .5 N . E n tr ie s / 0 .2 5 N . E n tr ie s / 0 .2 5 LL DD LU∗ _LD Figure 18: χ2

unconstrained vertex fitting for Λb candidates (green for signal, black for combinatorics)

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6. 5 S ele ct io n of th e p rim ar y ve rt ex 0 50 100 150 200 250 0 50 100 150 200 250 0 100 200 300 400 500 600 700 800 0 200 400 600 800 1000 0 50 100 150 200 250 0 10 20 30 40 50 60 0 50 100 150 200 250 1 10 N . E n tr ie s / 1 .2 5 N . E n tr ie s / 4 N . E n tr ie s / 1 .2 5 N . E n tr ie s / 1 .2 5 LL DD LU∗ _LD Figure 19: χ2

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7 Background Studies

The combinatorial background is not the most important source of backgrounds for our analysis. We must take into account the standard inclusive bb events and the prompt J/Ψ events. Then, the analysis will be improved by studying (in a very exhaustive way) background channels which present similar topology to the signal.

7.1 Usual background sources

7.1.1 Sample description

We have used about 20 million inclusive bb events from DC04v1 (Data Challenge 04). Our analysis takes into account two conditions : the bug gerenation problem and the downscaling factor.

• During the production, redondant events have been generated and some random generator ”seeds” have been used several times. Consequently, inclusive bb sample contains a part of dependent events.

• The J/Ψ preselection code does not reduce exactly the background by a factor 1/1000 and has been downscaled during the stripped production. We must include a downscaling factor which varies between 80% and 90% for our preselection. Thus, we can consider a sample of 12.8 millions of inclusive bb for the analysis with a 400mrad requirement ratio of 43.21%. We recall that the cross-section of this production is estimated to σ(pp → bb)=500µb.

Concerning the prompt J/Ψ events, no preselection code is required. This source of

background is typically relevant for our analysis due to charmonia decaying into µ+

µ−

pair. The production mechanism is performed according to table 17.

gg → J/Ψ + ... 37 µb

gg → χ1c(J/Ψ + γ) + ... 21 µb

gg → χ2c(J/Ψ + γ) + ... 51 µb

gg → χ2c(J/Ψ + γ) 67 µb

Total 176µb

Table 17: Quadruple production mechanism of prompt J/Ψ

A sample of 2 million events is used. The 400 mrad generator requirement is estimated to 61.83%. This value (greater than 50%) can be explained by the quadruple production mechanism which can give several prompt J/Ψ events by event.

7.1.2 Selection refinement

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7.1 Usual background sources

• Minimum Impact Parameter of muons > 0.01 mm

• PT > 1050MeV /c for D protons and PT > 1000MeV /c for L protons (in LU∗

combinations only)

• Λb flight angle θf light < 250 mrad, 200 mrad, 250 mrad and 250 mrad for LL, DD,

LU∗ _{and LD combinations respectively}

The threshold used for the two first cuts are justified by figures 21 and 22. A constrain

is applied on the ”flight angle” of the Λbcandidates to reject background. The geometrical

interpretation of this parameter is given in the figure 20. As this parameter must vanish

for a good Λb candidate, an upper limit is set for θf light for each class of tracks (figure

23). Primary vertex −→ PΛ_b Λb vertex θf light

Figure 20: definition of the Λb flight angle

This refinement has an immediate consequence on the selection efficiency. The final

selection efficiency reaches 26.2%instead of 34.4%. The matching efficiency remains almost the same : 95%.

7.1.3 B/S ratio estimation

In order to calculate the ”so-called” B/S ratio, the formula giving both the Signal and Background annual yields is recalled. Annual signal yield can be calculated by the following way :

S = Lint_year × σ(pp → bb) × 2 × f (b → Λb) × BRvisible × Θ4π ×

Nselected

Ntotal

where :

• Lint

year nominal annual integrated luminosity = L × ∆t = 2 × 10

39

cm−2

with luminosity L = 2 × 1032_cm−2_.s−1 _{(2009) and LHC running time ∆t = 10}7_{s a}

year

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7.2 Specific background sources

• factor 2 takes into account Λb and Λb production

• Θ4π : 400mrad generator requirement ratio = 34.71%

For the background annual yield calculation, another parameter must be introduced : Θwindow. This parameter is the ratio of the Λb tight mass window to the Λb loose mass

window (the present analysis indicating a value of 60/140). Due to the lack of statistics,

we assume background distribution flat in the loose mass window. By the factor Θwindow,

we bring this distribution into the tight mass window.

B_bb = Lint_year × σ(pp → bb) × Θ4π × Nselected Ntotal × Θwindow BJ/Ψ= Lintyear × σ(pp → J/Ψ) × Θ4π × Nselected Ntotal × Θwindow

In the case of inclusive bb background, only one event remains in the loose mass

window. Assuming we have 0.43 event in the tight mass window, a B/S ratio of 0.30

has been derived. On another side, no prompt J/Ψ remains in the loose mass window. Nota Bene : The DC04v2 stripping is not yet finished. But the first 21 millions of DC04v2 inclusive bb events have been used. After the selection, only one event remains in the tight mass window and it is refused by L0 trigger.

7.2 Specific background sources

We have considered channels with the following topology : ”beauty hadrons → J/Ψ(µ+_µ−₎

X”. These decay modes provide backgrounds where the J/Ψ is produced in a secondary vertex (complementary analysis to prompt J/Ψ background). As J/Ψ particles are per-fectly reconstructed by the algorithm, the contribution of other channels which do not contain charmonium can be negligible.

Thus, the most important channel of this type is B0

d → J/Ψ(µ+µ−)Ks0(π+π−). The

main part of K0

s is reconstructed as DD combinations and the Ks0 reconstruction

algo-rithm is a model for Λ selection. Contamination can occur if a pion of the K0

s decay

is identified as a proton or if a K0

s decay pion is combined with a proton coming from

fragmentation. Other channels such as B0

s → J/Ψ(µ+µ−)Φ(K+K−) could be relevant.

Table 18 gathers the main results of the specific background study. It shows clearly

that this kind of source is harmless for the analysis of Λb. This work must be completed

by taking into account non negligible channels such as Λb → Λ vector meson.

Decay channel Assumed visible BR Nb of used events B/S ratio

B0

d → J/Ψ(µ+µ−) Ks0(π+π−) 19.8 × 10−6 365,500 0.005

B0

s → J/Ψ(µ+µ−) Φ(K+K−) 31.0 × 10−6 466,000 0.002

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7. 2 S p ec ifi c b ac k gr ou n d so u rc es 0 0.02 0.04 0.06 0.08 0.1 0 5 10 15 20 25 30 35 N . E n tr ie s / 0 .0 0 0 5 m m proton PT mm

Figure 21: MIP of muons (green for signal, black for prompt J/Ψ)

dd 0 500 1000 1500 2000 2500 3000 0 5 10 15 20 25 30 35 40 0 500 1000 1500 2000 2500 3000 0 2 4 6 8 10 12 N . E n tr ie s / 1 5 M e V / c N . E n tr ie s / 1 5 M e V / c MeV/c MeV/c

Figure 22: PT of downstream protons and long protons (LU∗ combinations only) (green for signal, black for prompt J/Ψ)

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7. 2 S p ec ifi c b ac k gr ou n d so u rc es 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 1 10 2 10 3 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 1 10 2 10 3 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 1 10 2 10 3 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 1 10 N . E n tr ie s / 0 .0 1 ra d N . E n tr ie s / 0 .0 1 ra d N . E n tr ie s / 0 .0 1 ra d N . E n tr ie s / 0 .0 1 ra d LL DD LU∗ _LD

rad rad rad rad

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8 Resolution

After the selection, 5836 Λb (1460 LL, 3982 DD, 314 LU, 80 LD) remain. From these

events, resolution can be computed for several physics observables : mass, momentum, vertex and life-time of the reconstructed resonances. Nonetheless, LU and LD combina-tions are not enough numerous for a good resolution estimation.

8.1 Mass resolution

Figure 24 shows a spectrum of the Λ mass resolution (e.g. difference between re-constructed invariant mass and the true Λ mass). The spectrum of LL mass resolution

is a thin peak with σ = 1MeV /c2

, while DD spectrum is larger with σ = 6MeV /c2

. This difference (owing to momentum resolution of Long and Downstream tracks) had

been hightlighted for K0

s resonance (LL : σ = 4MeV /c2, DD : σ = 7MeV /c2). A

resolu-tion of 7MeV /c2

has been estimated for LU combinations (12MeV /c2

for LU K0

s). The

lack of LD combinations data invokes the spectrum is irrelevant. The sum of these dif-ferent contributions give a resulting resolution (figure 26) which has not a gaussian shape.

The mass resolution of 10MeV /c2

for J/Ψ is similar to the mass resolution of J/Ψ

coming from the channel B0

d → Ks0 J/Ψ.

In the case of Λb, the spectra of figure 25 have not the same difference in width as Λ.

The resolution varies from 13MeV /c2 _{for LL to 22MeV /c}2 _{for LU. Thus, the resulting}

spectrum have a resolution of 17MeV /c2

.

8.2 Momentum resolution

The momentum resolution spectrum of Λ and Λb are respectively represented by

figures 27 and 28. They have been obtained after applying the unconstrained fitting to resonance decay vertices. The lower part of the DD combination spectrum is larger than LL combination spectrum and two gaussian fits are necessary to estimate the resolution. This resulting Λ has a momentum resolution of 153MeV /c (core resolution of 73.6MeV /c)

and Λb has a momentum of 266.0MeV /c (core resolution of 177.0MeV /c). These results

are essential because they give elements of explanation for the vertex and the proper time resolution.

8.3 Vertex resolution

The difference between z-position of the Λ reconstructed vertex and the Λ MC vertex has been plotted in figure 30. For LL and LU combinations, a tight peak around 0 arises from the continuum of spectrum. For DD combinations, the peak is less distinct. These graphics show that a major part of Λ vertex has not been well extrapolated by the un-constrained vertex fitting tool.

Λb vertex has not been deduced from Λ and J/Ψ momenta. As J/Ψ decays into µ+µ−

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8.3 Vertex resolution

of this method is that Λ can profit by the good extrapolation of J/Ψ vertex. According to figure 31, the Vz core resolution is about 150µm.

The primary vertex has almost the same resolution (50µm) of the one given in the TDR 2003 (44µm).

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8. 3 V er te x re so lu tio n -25 -20 -15 -10 -5 0 5 10 15 20 25 0 100 200 300 400 500 600 700 800 -25 -20 -15 -10 -5 0 5 10 15 20 25 0 50 100 150 200 250 300 -25 -20 -15 -10 -5 0 5 10 15 20 25 0 20 40 60 80 100 120 140 160 -25 -20 -15 -10 -5 0 5 10 15 20 25 0 10 20 30 40 50 60 N . E n tr ie s / 0 .2 5 M e V / c 2 N . E n tr ie s / 0 .2 5 M e V / c 2 N . E n tr ie s / 0 .5 M e V / c 2 N . E n tr ie s / 1 M e V / c 2 LL Λ DD Λ LU Λ LD Λ 0.93 ± 0.01 5.96 ± 0.04 6.61 ± 0.13 2.15 ± 0.08

Figure 24: Mass resolution of Λ for each class of tracks

dd -1000 -80 -60 -40 -20 0 20 40 60 80 100 10 20 30 40 50 -1000 -80 -60 -40 -20 0 20 40 60 80 100 20 40 60 80 100 -1000 -80 -60 -40 -20 0 20 40 60 80 100 5 10 15 20 25 -1000 -80 -60 -40 -20 0 20 40 60 80 100 2 4 6 8 10 12 14 16 18 20 22 N . E n tr ie s / 1 M e V / c 2 N . E n tr ie s / 1 M e V / c 2 N . E n tr ie s / 5 M e V / c 2 N . E n tr ie s / 1 0 M e V / c 2 LL Λb DD Λb LU Λb LD Λb 12.9 ± 0.3 17.6 ± 0.3 21.5 ± 1.0 15.3 ± 1.8

Figure 25: Mass resolution of Λb for each class of tracks

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8. 3 V er te x re so lu tio n -40 -30 -20 -10 0 10 20 30 40 0 200 400 600 800 1000 1200 1400 -25 -20 -15 -10 -5 0 5 10 15 20 25 0 200 400 600 800 1000 1200 -1000 -80 -60 -40 -20 0 20 40 60 80 100 20 40 60 80 100 120 140 160 N . E n tr ie s / 0 .4 M e V / c 2 N . E n tr ie s / 0 .2 5 M e V / c 2 N . E n tr ie s / 1 M e V / c 2 J/Ψ Λ Λb 10.20 ± 0.03 16.8 ± 0.2

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8. 3 V er te x re so lu tio n -10000 -800 -600 -400 -200 0 200 400 600 800 1000 10 20 30 40 50 60 70 80 -10000 -800 -600 -400 -200 0 200 400 600 800 1000 20 40 60 80 100 120 -10000 -800 -600 -400 -200 0 200 400 600 800 1000 5 10 15 20 25 30 35 40 45 -10000 -800 -600 -400 -200 0 200 400 600 800 1000 5 10 15 20 25 N . E n tr ie s / 1 1 M e V / c N . E n tr ie s / 1 0 M e V / c N . E n tr ie s / 6 7 M e V / c N . E n tr ie s / 1 3 3 M e V / c 62.8 ± 3.3 92.9 ± 3.3 76.9 ± 4.2 176.5 ± 4.6 199.8 ± 12.2 144.9 ± 23.9 LL Λ DD Λ LU Λ LD Λ

Figure 27: Momentum resolution of Λ for each class of tracks

dd -15000 -1000 -500 0 500 1000 1500 10 20 30 40 50 -15000 -1000 -500 0 500 1000 1500 20 40 60 80 100 120 -15000 -1000 -500 0 500 1000 1500 10 20 30 40 50 -15000 -1000 -500 0 500 1000 1500 2 4 6 8 10 12 14 16 18 20 22 24 N . E n tr ie s / 1 7 M e V / c N . E n tr ie s / 1 5 M e V / c N . E n tr ie s / 1 0 0 M e V / c N . E n tr ie s / 2 0 0 M e V / c 153.0 ± 8.3 234.9 ± 7.6 177.3 ± 7.2 273.3 ± 6.1 271.4 ± 19.8 295.2 ± 43.0 LL Λb DD Λb LU Λb LD Λb

Figure 28: Momentum resolution of Λb for each class of tracks

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8. 3 V er te x re so lu tio n -10000 -800 -600 -400 -200 0 200 400 600 800 1000 20 40 60 80 100 120 140 160 180 200 220 -15000 -1000 -500 0 500 1000 1500 20 40 60 80 100 120 140 160 N . E n tr ie s / 1 0 M e V / c N . E n tr ie s / 1 5 M e V / c 73.6 ± 2.9 153.3 ± 3.3 177.0 ± 5.7 266.8 ± 4.8 Λ Λb

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8. 3 V er te x re so lu tio n -4000 -300 -200 -100 0 100 200 300 400 10 20 30 40 50 -4000 -300 -200 -100 0 100 200 300 400 5 10 15 20 25 30 35 40 45 -4000 -300 -200 -100 0 100 200 300 400 2 4 6 8 10 12 14 16 18 20 22 -4000 -300 -200 -100 0 100 200 300 400 0.5 1 1.5 2 2.5 3 3.5 4 N . E n tr ie s / 4 m m N . E n tr ie s / 4 m m N . E n tr ie s / 8 m m N . E n tr ie s / 1 6 m m 3.9 ± 20.2 137.8 ± 11.8 57.8 ± 2.1 4.4 ± 21.6 98.4 ± 27.0 LL Λ DD Λ LU Λ LD Λ

Figure 30: Vz resolution of Λ for each class of tracks

dd dd -4 -3 -2 -1 0 1 2 3 4 0 50 100 150 200 250 300 350 400 450 -4000 -300 -200 -100 0 100 200 300 400 20 40 60 80 100 -0.50 -0.4 -0.3 -0.2 -0.1 -0 0.1 0.2 0.3 0.4 0.5 50 100 150 200 250 N . E n tr ie s / 0 .0 4 m m N . E n tr ie s / 4 m m N . E n tr ie s / 0 .0 0 5 m m 0.149 ± 0.004 0.203 ± 0.004 71.8 ± 2.1 4.1 ± 20.0 0.0502 ± 0.0007 J/Ψ = Λb Λ Primary vertex

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9 Trigger role

LHCb trigger system is a technically advanced and crucial part of the detector ac-quisition system. It makes an on-line selection of events and reduces the data flow from 40MHz to 200Hz. From DaVinci v12r11, the three levels of trigger are simulated and efficiencies for the studied channel have been calculated as it is shown in table 19.

Level Nb of triggered events Efficiency

L0 5,426 ǫL0 = 93%

L1 4,275 ǫL1 = 79%

HLT 3,804 ǫHLT = 89%

Table 19: Efficiency for each trigger level

ǫL0= Nb of L0 triggered events Nb of selected events ǫL1= Nb of L1 triggered events Nb of L0 triggered events ǫHLT = Nb of HLT triggered events Nb of L1 triggered events

For understanding theses values, we must analysis the response of each level. For the High Level Trigger (HLT), the specific algorithm selection for our channel will be described. We will avoid entering into technological details of the trigger system.

9.1 L0 and L1

[L0 decision] = [Electron] OR [Photon] OR [Hadron] OR [local π0

] OR [global π0

] OR [Mu1] OR [MuS]

[L1 decision] = [Generic] OR [Mu] OR [DiMu] OR [J/Ψ] OR [Photon] OR [Electron]

For simplifying, an event is triggered by the level 0 if it satisfies two conditions. First, the total transerve energy deposed in the calorimeter system must overrun a specified

threshold. Then L0 trigger looks for the ET highest electron, photon, hadron and π0

candidates but also the two pT highest muons. A simply threshold is applied for each

candidate and the event is accepted if one candidate satisfies a L0DU criterion. Figure 32a shows the different tresholds which has been stepped over. The dominating

tresh-olds are in the decreasing order ”muS” (a requirement on the sum of the two highest PT

muons) and ”mu1” (a requirement on the highest PT muon). There are essentially muons

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9.2 High Level Trigger 0 1000 2000 3000 4000 5000 6000 MuS Mu1 Pi0G Pi0L Hadron Photon Electron Nb events 0 500 1000 1500 2000 2500 3000 3500 Electron Photon J/Psi Dimu Mu Generic Nb events

Figure 32: L0 (left) and L1 (right) triggered components from Λ decay have only a small contribution.

Concerning the L1 decision, a generic algorithm is runned at the beginning. It uses mainly the transverse momentum of tracks in order to extract events containing beauty hadrons. According to figure 32b, this contribution is by far the most dominating. More-over, L1 trigger has a specific algorithm which uses signatures releaved by L0 trigger : muon, photon and electron candidates. If one of them satisfies L1 specific requirements, the event is keeped. In our case, the presence of muons in the signal allows to increase our efficiency from 67% to 78%. The three criteria concerning muon particles are :

• ”mu” criterion : muon PT is constrained

• ”dimuon” criterion : two muons (whatever their charges are) are combined.

Invariant mass and Impact Parameter are constrained : M > 500MeV /c2

(MJ/Ψ=

3.1GeV /c2_{) and IP > 0.05mm.}

• ”J/Ψ” criterion : invariant mass of two muons must be in the range ±500MeV /c2

around J/Ψ mass or in the range ±500MeV /c2

around B0

d mass

9.2 High Level Trigger

The figure 33 is dedicated to the HLT process. Its selection is more complicated because the system can almost access to all measures. An event is accepted if it has been selected by the HLT generic algorithm and if one of the four streams (inclusive b → µ,

Dimuon, D∗ _{and exclusive selections ) has satisfied specified conditions. For the channel}

Λb → Λ J/Ψ , the component ”Dimuon” is dominating because the algorithm requires a

dimuon with a mass above 2.5 GeV /c2_{. Muon contribution appears also in the component}

”inclusive b → µ” which constrains the PT and the Impact Parameter of these particles.

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9.2 High Level Trigger 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Exclusif D* Dimuon B inclusif Generic Nb events 0 500 1000 1500 2000 2500 3000 3500 B-> Jpsi X Bd->Mu Mu K* B->Mu Mu Bs->Phi Gamma Bs->Phi Phi Bs->Ds h Bd->D* Pi Bd->D0 K* B->h h D* Nb events

Figure 33: HLT triggered components (left) and the exclusive selection (right)

[HLT decision] = [Generic] AND ( [B inclusif] OR [DiMu] OR [D∗

] OR [Exclusif] )

Among HLT exclusive selection, a selection is based only on the research of a J/Ψ candidate which come from a secondary vertex. The algorithm is described by the table

34. Foreseen at the beginning for the B0

d → J/Ψ Ks0 channel, it is adjusted to our

channel. Thus, it is useless to write a proper HLT exclusive selection for Λb. This idea is

reinforced by the fact that only long tracks are reconstructed at this stage.

muons PT > 500MeV

IP/σ > 2.0

J/Ψ |Mrec− Mtrue| < 50MeV /c2

χ2

< 50 IP/σ > 1.0

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10 Global efficiency and annual yield

From the numerous results of the preceding sections, we can compute a global effi-ciency which is defined by the following formula. (In our case, the tagging effieffi-ciency is

supposed equal to 1 because Λb and Λb final states are different.)

ǫglobal = ǫdet× ǫrec× ǫsel× ǫtrig

In table 20, a comparison is etablished between our results and those of similar channel analysis, extracted from TDR 2003[10]. As HLT simulation has been implemented in the

software in the year 2005, we define an intermediate global efficiency ǫ′ _{which does not}

take account of HLT efficiency.

Channel ǫdet ǫrec ǫsel ǫL0+L1 ǫ′tot ǫHLT ǫtot

B0 d → J/ΨΦ 7.6% 82.5% 41.6% 64.0% 1.67% B0 d → J/ΨKs0 6.5% 66.5% 53.5% 60.5% 1.39% Λb → J/ΨΛ 4.7% 60.0% 26.2% 73.6% 0.53% 88.9% 0.47% B0 s → J/Ψη 10.1% 69.6% 10.1% 64.8% 0.46%

Table 20: Comparison between different channels analysis

This table shows that the channel Λb → Λ J/Ψ has the lowest detection and

re-construction efficiency. It can be explained by the fact that 10% of Λ(Λ) are absorbed by the detector matter. Moreover, Λ(Λ) have a big life-time and some events are lost. The selection efficiency is an average value. Although, we have a proton in the final

state, the efficiency is lower than K0

s(π+π− final state) and can be explained by a bigger

contribution of DD combinations which resolution is worse than LL one. Concerning the trigger levels L0 and L1, we must take into account that simulation has been improved since the publication of TDR 2003. We could consider that all these channels have the same efficiency due to the presence of J/Ψ particles.

From the global efficiency of 0.47%, the estimation of the annual yield is equal to

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11 Conclusion and Perspectives

A first analysis of the channel Λb → Λ J/Ψ has been performed. Difficulties and

con-venients of the channel reconstruction have been highlighted. Indeed, a big part of Λ final states are reconstructed as Downstream tracks which consequence is the deterioration of momentum resolution and fitting vertex accuracy. But the presence of the J/Ψ particles in the decay helps us to suppress background and provides a good trigger efficiency.

LHCb detector performance for the study of this channel has been quantified. The

global efficiency is estimated to 0.47% i.e. 19,000 Λb and Λb by year are expected. This

statistics makes possible our physics goals. Furthermore, the purity of the signal is rela-tively good. Indeed, the matching efficiency of the signal reachs 95% and the B/S ratio is about 0.30 for inclusive bb events. Others specific background sources are negligible.

In spite of these interesting results, this analysis is not completely achieved and some points must be optimized :

• The identification of final states should be refined. It is important to study the consequence of a better identification on the results of the analysis.

• With the arrival of DC04v2, we hope a better and unbiaised estimation of B/S ratio for inclusive bb .

• Life-time resolution must be improved

This analysis can be extended to the case where J/Ψ particles go into e+_e−_{. But it}

could also be considered as the starting point of Λb → Λ vector meson channels. The

vector meson could be, for instance, ρ(π+

π−_{) or Φ(K}+

K−_{). But, the absence of J/Ψ}

particles in the decay chain should involve a lower global efficiency. In fact, a preliminary calculation is needed for these new channels in order to know if the statistics should be sufficient for testing CP and T symmetries.

12 Acknowledgements

(46)

REFERENCES

References

[1] J. H. Christenson, J. W. Cronin, V. L. Fitch and R. Turlay. CP violation discovery. Physics Review Letters 13, 1964.

[2] CPLEAR collaboration. CERN-EP/99-51. 1999.

[3] Albert Messiah. Quantum Mechanics. Elsevier Science, 1961. ISBN 0720400422. [4] Particle Data Group. Particle Physics Booklet. Review of Particle Physics, July

2004.

[5] Z.J. Ajaltouni, E. Conte. Time-Odd Observables and CP Violation in Lambdab Decays (I) Angular analysis of Lambdab decays into Lambda l+l- and Lambda h+h-. LHCb-2004-040, 26 May 2004.

[6] Z.J Ajaltouni, E. Conte and O. Leitner. Λb decays into Λ-Vector. Physics Letters B

614, pages 165–173, 2005.

[7] Z.J Ajaltouni, E. Conte and O. Leitner. Testing CP symmetry and Time Reversal

in Λb Physics with LHCb. LHCb Production and decay models WG proceeding, 30

June 2005.

[8] LHCb Computing team. Data File in Production. Technical report, May 2003.

[9] Y. Xie. K0

s reconstruction. LHCb-2003-088, 21 August 2003.

[10] LHCB collaboration. LHCb TDR Reoptimized Detector. CERN, Geneva, 9 september 2003. CERN/LHCC 2003-030, ISBN 92-9083-209-6.

[11] P. Koppenburg. DaVinci - The LHCb analysis program page. 2005. http://lhcb-comp.web.cern.ch/lhcb-comp/Analysis/default.htm.

Analysis of the channel $\Lambda_b \to \Lambda J/\Psi$

HAL Id: in2p3-00024814

http://hal.in2p3.fr/in2p3-00024814

Analysis of the channel Λ_b

→ ΛJ/Ψ

Ziad Ajaltouni, E. Conte

To cite this version:

democrite-00024814, version 1 - 5 Oct 2005

Analysis of the channel

Λ

b

→ Λ J/Ψ

Ziad AJALTOUNI

, Eric CONTE

September 21, 2005

Contents

1

Introduction and motivations

2

Strategy and analysis tools

3

Detection and Reconstruction Efficiencies

3.1

Λ and Λ absorption

3.2

Tracking setup

3.3

Track repartition

3.4

Definition of Reconstructible and Reconstructed particle

3.5

Detection and Reconstruction efficiencies

4

Identification

4.1

Elements of the identification process

4.2

Muon identification

4.3

Proton and pion identification

5

Selection of the final states

5.1

Selection of muons µ

5.2

Selection of pions π

and protons p(¯

p)

6

Selection of Λb

candidates

6.1

Summary of essential observables

6.2

Selection of J/Ψ candidates

6.3

Selection of Λ candidates

6.4

Selection of Λb

candidates

6.5

Selection of the primary vertex

7

Background Studies

7.1

Usual background sources

7.2

Specific background sources

8

Resolution

8.1

Mass resolution

8.2

Momentum resolution

8.3

Vertex resolution

9

Trigger role

9.1

L0 and L1

_b

_{, Eric CONTE}

_{and protons p(¯}

_p)