I am also grateful to the other members of the Υ(5S) group, as well as the entire Belle collaboration. This thesis reports a measurement of the branching fraction (BF) for the decay B0s →ϕγ and searches for the decay Bs0 →γγ in high-energy e+e− collisions with Υ(5S) energy. This chapter concludes with a brief discussion of the current status of the decay values Bs0 → ϕγ and Bs0 → γγ.
This chapter concludes with a brief discussion of the possible implications of the results of these analyses.
The Standard Model of Particle Physics
For local U(1) symmetry (e.g. the electromagnetic field), when we introduce a space-time dependence of ψ(ψ7→e−iχ(x,t)ψ), the Lagrangian is no longer invariant. The term LH represents the Higgs Lagrangian, which is required to account for the masses of the fermions and gauge bosons. The symmetry of the vacuum (or ground state) is spontaneously broken by the choice of a particular VEV.
When a symmetry is thus broken, i.e. the symmetry is valid in the Lagrangian but not for the ground state of the system is said to be a.
Flavor Changing Neutral Current Processes
They are strongly suppressed via the GIM mechanism [14] and the loop factors in the SM. The ηparameter is the complex phase parameter responsible for the CP violation in the SM. We observe non-zero non-diagonal elements in the CKM matrix, indicating that generation-changing charged currents are possible in the SM.
Because of the large suppression in the SM, FCNC decays are ideal places to look for evidence of new physics.
Renormalization and Effective Field Theory
Physics of distances smaller than R−1 (i.e. contributions from scales higher than R or the high energy interactions) are contained in the Wilson coefficients Ci and those of distances larger than that (i.e. the low energy interactions) are charged by the operators. The above set of operators is typical of any consideration of the interaction between QCD and electroweak effects. The Wilson coefficients will generally depend on the mass of the particles that were integrated from it.
On the other hand, the calculation of operators (and thus matrix elements) requires non-perturbative calculations, since they involve long-range contributions.
Analysis Methods
Exclusive Reconstruction Method
An AB-meson decaying to an exclusive final state is reconstructed by measuring the energy and momentum of all long-lived decay products (π±, K±, e±, µ± and γ) and choosing intermediate states with a certain invariant mass. Theoretical calculations of decay rates for exclusive processes require the calculation of the decay rate to a specific hadronic final state. The matrix element of the lepton flux can be calculated explicitly, and the hadronic flux can be expressed by meson form factors.
Since these shape factors describe strong interaction effects, they must be calculated using non-perturbative models such as light cone QCD sum rules or vector meson dominance, for each individual configuration of initial and final state.
Inclusive Reconstruction Method
The Eγ spectrum is then binned and associated fits are performed to obtain BF values for each bin. With large statistics and efficient background rejection techniques, the cutoff on Eγ can be relaxed to reduce model dependence. B(B →Xs) =B(b→s) +O(1/m2b) (1.45) The leading term in the expansion is modeled by the decay of the free b quark and corresponds to the free quark matrix element⟨s| Qi|b⟩, which can be calculated perturbatively.
Power corrections (O(1/m2b)) describe the difference between initial b quarks and B mesons which causes an estimated suppression of the decay rate of the order of 1.5% [26].
Semi-Inclusive Reconstruction Method
The electron beam is generated by evaporating electrons from the filament and the positrons are produced by firing an extension of the electron beam at the target, producing electron-positron pairs. The pivot point is chosen as the thread position of the innermost hit in the CDC. The schematic diagram Belle Detector 39 of the Cherenkov counter and its modules are shown in Figure 2.14 and Figure 2.15, respectively.
It also includes systematic effects such as the uncertainty in the calibration of the light output of the crystals. An important part of the Belle experiment is the trigger and the data acquisition system (DAQ). The visible energy (Evis) is the sum of the 'good track momenta' and the 'good photon'.
The sum of calorimeter energies (Esum), i.e. the sum of energies of "good clusters" in ECL must satisfy 0.18 < Esum/√. In addition to these 16 moments, we have,. pT: the sum of the transverse amount of all visible particles and the "apparent mass missing from the event", defined as:. The file contains all the information needed to perform the analysis, e.g. network parameters and all weights.
In this chapter, we present a brief overview of the maximum likelihood (ML) fitting procedure used to derive the signal yield in real data. In statistics, the term 'estimation' means a precise and accurate procedure, leading to a result (for example, the value of a parameter of a distribution) that may be imprecise, but where the degree of inaccuracy is known [92]. The fit details are listed in Table 4.22 and the fit graphs are shown in Figure 4.18.
In that table, the ratio between PID efficiency in data and MC (i.e. the relative PID efficiency between data and MC) is given as a function of 'p' and 'cos(θ)'. The systematic uncertainty about the number of Bs0 is therefore the squared sum of the uncertainties in LΥ(5S)int , σbΥ(5S)¯b and fs.
Chapter Summary
Study of rare decay was also one of the primary motivations of the Belle experiment. In this chapter we discuss about the Υ(nS) resonances, the KEKB accelerator, the Belle detector, data acquisition system, triggering, processing and skimming of the data sample. At the first three resonances, the Υ(nS) system can only decay with the destruction of b and ¯b as shown in Figure 2.2.
Thus, the variety of hadronic events at the Υ(5S) resonance, as shown in Figure 2.3, is richer than that at the Υ(4S) CM energy.
The KEKB Accelerator
It consists of 2 storage rings: a high energy ring (HER) for electrons and a low energy ring (LER) for positrons, and a linear accelerator (LINAC). The electron and positron beams are then accelerated to the desired energies before being injected into the storage rings. The two beams move in opposite directions and collide at the interaction point (IP) where the Belle detector is located.
The energies are set so that the CM energy is equal to the mass of the Υ(nS) resonances. The two beams do not collide head-on, but with a small crossing angle of 22 mrad. The nonzero crossing angle reduces the luminosity and also the CM energy by about 1 MeV (0.01%);
To handle the light loss, since January 2007, the clusters have been tilted by two superconducting radio frequency cavities known as scratch cavities [58], installed in each ring to collide the clusters with a maximum overlap as shown in Figure 2.6. Due to asymmetric beam energies, the Υ(4S) quasi-bound state particles are produced with a Lorentz boost of. The distance between the decay angles of the two B mesons (∆z) can be measured with an angle detector with a resolution of 100µm.
The Belle Detector
- Beam Pipe and the Silicon Vertex Detector (SVD)
- Central Drift Chamber (CDC)
- Aerogel Cherenkov Counter (ACC)
- Time of Flight Counters (TOF)
- Electromagnetic Calorimeter (ECL)
- Extreme Forward Calorimeter (EFC)
- K L 0 and Muon Detector (KLM)
The Belle Detector 33 coordinate system used in the Belle detector: It is important to define the coordinate system used in the Belle detector to help describe each of the subdetectors. This is best illustrated by the coverage of the polar angle θ, as shown in Table 2.1. The measured signal height and operating time provide information about the energy deposition and the distance from the sensor wire.
It works on the principle that a particle moving faster than light inside a medium (vlight=c/n) emits Cherenkov light, where is the refractive index (RI) of the medium. Therefore, simultaneous measurements of the momentum of the charged particle in the CDC allow the identification of the different charged particles in the ACC. The RIs of the airgel in the barrel region were chosen based on the polar angles and range between 1.010 to 1.028.
The information on time of flight (T) measured using the TOF counter and momentum (p) measured using SVD and CDC provides a measure of the mass of. Given the magnitude of the magnetic field, a charged particle must have a momentum greater than 0.54 GeV/c to reach the TOF counter. The angular coverage of ECL is the same as CDC, which allows matching charged tracks with clusters of hits on CDC.
Its full-angle coverage allows improving the sensitivity of processes such as B+ → τ+ντ and providing labeling information for γγ physics. However, due to the fluctuations of this shower, a useful measurement of its energy is not possible.
Trigger and the Data Acquisition System (DAQ)
Here, LK and Lπ are the probabilities that the track comes from a kaon and pion, respectively. The thrust axis is defined as the direction that maximizes the sum of the longitudinal momentum of the decaying particles.1. )0 so. After training, unknown samples (ie, validation samples) are fed into the network and it separates the signal and background events based on the training.
Refer to Appendix B for plots of the correlation matrices of the input variables and the NeuroBayes target for the Bs0→γγ and B0→K0∗γ analysis. For training, we used 2/3 of the available MC sample remaining after applying all selection criteria. 3For the decomposition B0s→ϕγ,ϕ→K+K−, the helicity angle is defined as the angle between Bs0 and any of the daughters (K+orK−) in the rest frame.
The details of the actual data fits are presented in Table 4.8 and the resolution corrections obtained from the fit are presented in Table 4.9. This chapter provides a brief introduction to the systematic uncertainties and their impact on the results of the analyses. The multiplicative uncertainties do not affect the signal yield and signal significance of the decay channel, but affect its BF.
The additive uncertainties reduce the signal significance of the observed peak and change the BF of the decay. It is calculated as the squared sum of the systematic uncertainties in the photon reconstruction, kaon identification, tracking efficiency, CNB cut and the MC statistics. In this section we present the functional form of some of the functions we used to model the signal and background PDFs.
