R EFERENCES
CHAPTER 4. ANALYSIS OVERVIEW 29
4.3.1 Signal MC sample
Signal MC samples are used to optimize the analysis procedure with the full detector simulation. Espe-cially, the estimation of the reconstruction efficiency is crucial to calculate the actual number of signal events from reconstructed signal yields.
Signal MC sample of B ! Xs`+` is produced separately from three components, B ! K`+` , B !K⇤`+` , and non-resonantB!Xs`+` . Samples ofB !K`+` andB!K⇤`+` are produced using an EvtGen model of BTOSLLBALL [59], which utilizes a Light Cone Sum Rule approach to estimate theB !K(⇤) form factors. Those of non-resonantB!Xs`+` rely on the BTOXSLL model, in which the di-lepton mass spectrum is generated according to [60] and then the two lepton momentum is generated according to [61]. Mass of the non-resonant Xs is required to be larger than 1.1 GeV/c2. Expressions for the Wilson coefficients and power corrections are taken from [35] and the detailed formulae are taken from [62] and [63]. In the hadronization of non-resonantXswhich is performed by the PYTHIA [55] [56], the partons (s-quark andu-/d-quark) are turned into two to ten hadrons which can be excited states such asK⇤and then they are distributed according the allowed phase space.
Since the reconstruction efficiency depends on the multiplicity and momentum of final state particles, the fragmentation of non-resonant Xs should be corrected by using real data and uncertainties of the measurement of the fragmentation should be included in the systematic uncertainty. Since parameters in the EvtGen model can also change the momentum of final state particles, the e↵ect on the reconstruction efficiency from these variation of these parameters. Moreover, the value of the transition point, mXs >
1.1 GeV/c2, which is same with the previous [2] is arbitrary and should be taken into account as systematic uncertainty. It will be described in Section 8.5.
These three components are mixed according to the SM predictions of branching fractions [42] [35]
which are shown in TABLE 2.2 and TABLE 2.4. Due to the photon pole contribution, electron modes have larger branching fractions than muon modes for K⇤ and non-resonant Xs. We have used the SM prediction of B ! (K, K⇤, Xs)µ+µ on muon modes as well as electron modes applying a cut of Me+e >0.2 GeV. The branching fraction of K and K⇤ modes are assumed to be 0.35⇥10 6 and 1.19⇥10 6. That of non-resonantXsis assumed to be 2.61(= 4.15 0.35 1.19)⇥10 6. The uncertainty on the branching fraction has to be also taken into account as systematic uncertainty. The detail will be described in Section 8.5.
According to the MC samples, the fraction of theXscovered by this study (TABLE 4.1) is 63.0%. If the fraction of states containingKL0 is taken to be equal to that containingKS0, the missing fraction is 16.9%. Figure 4.1 shows theMXs distribution of the signal MC samples.
4.3.2 Background MC sample
To establish background suppression forB!Xs`+` , two kinds of hadronic MC samples are produced.
One is the continuum events,e+e !qq(q=u, d, s, c), and the other isBB (B0B0 andB+B ) events.
Decay process of these samples are simulated generically according to the recent measurements results.
The number of background MC samples corresponds to an integrated luminosity of 5 ab 1.
30 4.3. MONTE-CARLO SIMULATION SAMPLE
0.5 1 1.5 2 2.5 3
[GeV]
MXs
0 50 100 150 200 250 300
Entries / 20 MeV
distribution M
XsK
0) π (w/o π K1
0) (w/ π K1π
0) (w/o π K2π
0) (w/ π K2π
0) (w/o π K3π
0) π (w/
π K3
0) (w/o π K4π
0) (w/ π K4π
S) 3K (at most 1K0
S) 3K (more than 1K0
π0 including 2 K5π Baryon Others
distribution M
XsFIG 4.1: MXs distribution for generated signal MC samples. The histograms are scaled to the 200 fb 1. Decay modes ofXs are separated by color code of histogram.
Chapter 5
Reconstruction
5.1 Particle selection
Charged particles are selected from tracks (reconstructed with CDC, SVD and PXD) originating from the interaction point (IP) by requiring dr <0.5 cm and |dz|<2.0 cm, wheredr anddz is distance between a track and IP in the plane to the beam axis and along the beam axis, respectively. Type of the charged particles is identified using the particle identification information obtained by the sub detector systems.
Electron candidates are required to satisfy
• p >0.4 GeV/c
• P IDe>0.9
where p is the momentum and P IDe is the likelihood ratio defined in Section 3.4. The momentum selection, p > 0.4, is required so that the track can reach the ECL. Due to the light mass, electrons often emit bremsstrahlung photons and loose energy. The energy is recovered by adding four momenta of photons within 0.05 rad cone around the electron to the electron’s four momenta.
Muon candidates are required to satisfy
• p >0.7 GeV/c
• P IDµ >0.9
The momentum selection,p >0.7 GeV/cis required so that the track can reach the KLM.
Kaon and pion candidates are selected by requiring P IDK > 0.6 and P ID⇡ > 0.4, respectively.
Additional selection on the number of hits in CDC, nCDCHits, is required to ensure the CDC dE/dx infromation: nCDCHits>20.
TheKS0 candidates are reconstructed from two oppositely charged tracks requiring a mass selection, 0.3< M⇡+⇡ <0.7 GeV/c2. Kinematics of these tracks are calculated by assuming the pion mass. Neither particle identification nor impact parameter cuts are applied on these tracks. Since the four momenta of tracks are calculated at the closest position to the IP, the sum of the four momenta of daughters shifts from the true four momenta ofKS0. To correct the di↵erence, the kinematics of daughters are recalculated at the vertex position ofKS0, which is called the vertex fit. After the vertex fit, the following criteria are applied on KS0 candidates: 0.4876< MK0
S <0.5076 GeV/c2 and significanceOfDistance>50, where MKS0 is the mass ofKS0 calculated after the vertex fit andsignificanceOfDistanceis the significance of distance from the vertex to IP. The variable significanceOfDistance is applied to reject many candidates that arise from random pion tracks originating from the interaction region. Figure 5.1 shows the reconstructed invariant mass MKS0 ofKS0!⇡+⇡ in the MC samples.
The⇡0 candidates are formed by combining two photons which are reconstructed from ECL clusters inside the CDC acceptance (17 <✓ <150 ). In addition, the candidates are required to satisfy the following criteria to reduce background photon issued by beam backgrounds: clusterNHits>1.5 and [clusterReg== 1 andE >0.080 GeV] or [clusterReg== 2 andE >0.030 GeV] or [clusterReg== 3 and E >0.060 GeV], whereclusterReg is the ECL region of a cluster, 1:forward, 2:barrel, 3:backward.
The energy threshold is optimized for each region of ECL and clusterNHits is sum of weights of all
32 5.2. XS RECONSTRUCTION
0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 2] [GeV/c
π
-π+
M
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Frequency density
FIG 5.1: MK0
S distribution ofKS0!⇡+⇡ in the MC samples.
crystals in an ECL cluster. For non-overlapping clusters,clusterNHitsis equal to the number of crystals in the cluster. This, however, can be a non-integer value, when energy splitting among nearby clusters.
Finally,⇡0candidates are required to satisfy the following selection, 0.120< M <0.145 GeV/c2, 1.5<
<1.5 rad,↵ <1.4 rad where is di↵erence of between two gammas and↵ is the angle between two gammas. In the low momentum region, there are a lot of fake⇡0candidates which degrades the signal-to-background ratio. Momentum requirement on ⇡0 candidates is applied to be more than 0.4 GeV/c. Figure 5.2 shows the reconstructed invariant massM of⇡0! in the MC samples.
0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 2] [GeV/c
γ
Mγ
0 0.01 0.02 0.03 0.04 0.05
Frequency density
FIG 5.2: M distribution of⇡0! in the MC samples.
The particle selection criteria are summarized in Table 5.1.
5.2 X
sreconstruction
The hadronic systemXs is reconstruced with sum-of-exclusive approach. The twenty final states listed in TABLE 4.1 are adopted asXscandidates. To suppress combinatorial backgrounds, the invariant mass of Xs is required to be smaller than 2.2 GeV/c2: MXs <2.2 GeV/c2. Figure 5.3 shows the reconstructed invariant mass MXs in the signal MC samples.
5.3 B reconstruction
TheB meson produced as a BB pair is reconstructed by combiningXs and an electron pair or a muon pair. Two independent kinematic variables, which are the beam constraint mass Mbc and the energy