# Peculiar aspects of the Standard Model and indirect probes of New Physics

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## Overview of the analysis

The BR of a given decay is proportional to the total number of observed signal events NB(s) and inversely proportional to the total number NB(s) of B0 (s) produced. Taking into account an efficiency factor sig describing the effects due to the detector acceptance as well as the whole selection process, the following relation holds BRsig = −1 sig Nsig NB(s) . (3.1) The goal of the analysis is thus to select in the collected dataset those events being potentially the B0 (s) ! μμ decays, count them and convert through relation (3.1) in a value for the BR. To do that the number of B0 (s) mesons in the dataset must be extracted and the efficiency factor sig must be computed. The total number of B mesons in the sample is proportional to the integrated luminosity L through the relation NBq = L · b¯b · fq · q , (3.2) where
• b¯b is the b¯b pair cross section
• fq is the hadronization fraction, i.e. the fraction of b-quarks hadronizing into a Bq meson.
• q is an efficiency factor due to the detector acceptance.
In the analysis presented here, nevertheless, the total number of B(s) is obtained in a different way. In particular eq. (3.1) is used for some normalization channels of already well known BR. By inverting this relation the value of NB(s) is obtained as a function of the number NNorm of normalization channel events present in the dataset. More explicitly, the relation between the BR and the number of observed signal events Nsig is: BRsig = Norm sig BRNorm NNorm is the ratio of the hadronization probabilities for a b-quark into the signal and the decaying B meson in the normalization channel. The normalization factor Norm has been defined as the conversion factor between the observed number of signal events and the signal BR. The particular form of eq.(3.3) motivates the choice of the normalization channels. In particular they are chosen in order to be as much as possible similar to the signal, both with respect to the topology and the particle content of the final state. In such a way, possible systematics and biases in the reconstruction, trigger, and selection processes cancel out in their ratio. In addition these channels must be precisely measured. The analysis proceeds in two steps: the B0 (s) ! μμ candidate selection is achieved through a preliminary loose selection followed by a refined selection based on the output of a Multi Variate Analysis (MVA) classifier (see e.g. Ref.). This first selection aims to remove as many obvious background events as possible while keeping a very high signal efficiency, in order to increase the sensitivity S which is defined as S = Np N + B (3.4) where N and B are the number of signal and background events respectively. In order to avoid any further removal of signal events from the sample, the selected events are classified with respect to two independent variables: the invariant mass of the di-muon system mμμ and a variable describing the geometry of the event. This variable is the output of a second MVA classifier using kinematical and topological variables related to the signal candidate. The B0 ! μ+μ− and the B0 s ! μ+μ− signal yields are extracted through a simultaneous unbinned extended maximum likelihood fit in the mμμ variable in eight bins of the output of the MVA classifier. If an excess of signal candidate events is observed, its significance is evaluated. If this is greater than 3 a value for the BR is measured, if not, the observed pattern of events is compared with the expected one for several BR hypotheses and an upper limit on the BR is computed.

### Signal features

between the two proton beams, which will be referred to as the Primary Vertex (PV). Thanks to its large lifetime (see Tab.3.1) it flies inside the VELO for 1cm before decaying into the two μ of the final state. The signature of a B0 (s) ! μμ decay in an event is thus the presence of two tracks identified as muons forming a good Secondary Vertex (SV) well displaced with respect to any other PV in the event; the sum of the momenta of the two tracks must be collinear with the direction defined by the B0 (s) production and decay vertexes, and the invariant mass of the two tracks mμμ must be compatible with the one of the B0 s or B0 mesons. classification rely on requirements on the quality of the reconstructed vertex formed by the two muons and the topology of the reconstructed B0 (s) ! μμ candidates, the following two normalization channels are chosen.
• B+ ! J/ (! μμ)K+: which, like the B0 (s) ! μμ signal, contains two muons coming from the same vertex in the final state;
• B0 ! ±K which, being a 2-body decay, has the same topology of the B0 (s) ! μμ signal.

#### Trigger selection

At the trigger level, events featuring the presence of a B0 (s) ! μμ decay candidate are selected by the following trigger requirements (see Sec.2.3.3):
• at the L0 level the high transverse momentum (pT ) of the muons coming from a B decay is exploited. In particular the following two triggers are used:
– L0Muon.
– L0Dimuons.
• at the HLT1 level the trigger selection relies on the single muon trigger Hlt1TrackMuon or the di-muon triggers Hlt1DiMuonLowMass and Hlt1DiMuonHighMass.
• the HLT2 trigger is based on Hlt2DiMuonBmm for the signal. For the B+ ! J/ K+ the Hlt2DiMuonJPsi is used (except for the last 470fb−1 for which the Hlt2DiMuonDetached is used), while for the B ! hh(0) the Hlt2Topo2Body, Hlt2B2hhX and Hlt2B2hh decisions are used.

Optimization of the input variables set and tuning parameters

One of the main improvements of the analysis presented here with respect to the previous ones consists in the use of an improved MVA classifier. To this extent, a larger sample of background combinatorial MC generated events has been generated. This sample corresponds to an integrated luminosity 50 fb−1 (to be compared with the sample used for the previous rounds of the analysis, equivalent only to 0.5fb−1). In term of number of events, 90164 generic MC b¯b ! μμX events have been used as a proxy for background, while 683671 B0 s ! μμ MC generated events for signal. BDT input variables. The classifier used for the previous B0 (s) ! μμ analysis was trained using the following set of nine input variables:
• the B candidate meson proper time ( ),
• the impact parameter of the B (IP(B)),
• the transverse momentum of the B candidate (pT (B)),
• the B candidate isolation based on the CDF definition (ICDF (B)) , i.e. , ICDF = pT (B) pT (B) +P track2cone pT (track) (3.10) where the ‘’cone” is defined by the relation q 2 + 2 < 1.0 (3.11) being and the difference in pseudorapidity and coordinate of the given track with respect to the B candidate,
• the minimum impact parameter significance of the muons with respect to any primary vertex (IP2(μ)),
• the distance of closest approach of the two muons (DOCA),
• the isolation of the two muons (defined in Appendix A) with respect to any other track in the event (I(μ)),
• the minimum transverse momentum of the two muons (minpT (μ)),
• the cosine of the angle between the muon momentum in the di-muon rest frame and the vector perpendicular to the plane defined by the B direction and the beam axis (“polar angle”).

Signal yield and limit extraction

Once the BDT classifier has been defined, the selected events are classified in a 2 dimensional plane according to the output of the BDT classifier and the invariant mass mμμ, as shown in This lower boundary is chosen to exclude all backgrounds coming from the b cascade decays b ! c(! μX)μX0. The number of observed signal B0 ! μμ and B0 s ! μμ events in the dataset is extracted through a simultaneous unbinned likelihood fit in the invariant mass projection in eight BDT bins. In particular, for each BDT bin, the observed pattern of events is fitted with a function ftot(mμμ) = NbkgFbkg(mμμ) + NB0FB0(mμμ) + NB0  FB0  (mμμ) , (3.13) where Nbkg,B0,B0 and Fbkg,B0,B0  (mμμ) are the yields and the invariant mass PDFs of the background, the B0 ! μμ, and B0 s ! μμ events respectively. The functions Fbkg,B0,B0 s (mμμ) are normalized to one, i.e. Z Fbkg,B0,B0 s (mμμ)dmμμ = 1 . (3.14) To perform the fit, the knowledge of the functions Fbkg,B0,B0 s (mμμ), as well of the eventfraction in each BDT bin, is required. In the following the definition and calibration of the BDT and invariant mass PDFs will be shown, both for signal and the different sources of background. The BDT binning has been optimized  in order to reach the highest sensitivity for the SM signal. The eight BDT bins have the following boundaries: 0.0, 0.25, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 and are characterized by different signal purities, and the last bins will be the most sensitive ones.

1 Introduction and motivations
1.1 Successes and limitations of the Standard Model
1.1.1 The Standard Model of elementary particles physics
1.1.2 Peculiar aspects of the Standard Model and indirect probes of New Physics
1.1.3 Limits of the Standard Model
1.1.4 Flavor observables and the NP scale: the “Flavor Puzzle”
1.2 B0 (s) ! `¯` decays
1.2.1 The effective hamiltonian for B0 (s) ! `¯`
1.2.2 B0 (s) ! `¯` observables
1.2.3 SM predictions
1.2.4 B0 (s) ! `¯`: current bounds
1.3 Current anomalies in B-meson decay observables and hints of NP in third generation
1.4 Conclusions
2 The LHCb detector
2.1 The LHC accelerator complex
2.2 The b¯b production cross section at LHC
2.3 The LHCb detector
2.3.1 The tracking system
2.3.2 The Particle Identification
2.3.3 The Trigger system
2.4 Conclusions
3 B0 (s) ! μ+μ−
3.1 Overview of the analysis
3.1.1 Signal features
3.1.2 Trigger selection
3.1.3 Loose selection
3.1.4 Tight selection
3.2 BDT optimization
3.2.1 Introduction to Boosted Decision Trees
3.2.2 Optimization of the input variables set and tuning parameters
3.2.3 Correlation with the invariant mass
3.2.4 The final BDT classifier
3.3 Signal yield and limit extraction
3.3.1 Signal PDF calibration
3.3.2 Backgrounds PDF calibration
3.3.3 Normalization
3.3.4 Results
3.4 Combination with the CMS result
3.5 Interpretation of the results.
3.6 LHCb prospects for the next Runs of the LHC
3.7 Preparing current analysis improvements
3.7.1 The ZVtop algorithm
3.7.2 Definition of Isolation Variables using ZVtop
3.7.3 Combination of isolation variables
3.7.4 BDT classifier with new isolation variables
3.7.5 Study of the background composition of events falling in last BDT bin .
3.7.6 Pointing related variables
3.7.7 Conclusions
3.8 Conclusions
4 B0 (s) ! +−
4.1 B0 (s) ! +− at LHCb
4.1.1 The ! 3 decay
4.1.2 The (3, 3) final state analysis
4.2 Candidate reconstruction
4.2.1 Preselection
4.2.2 Background composition after preselection
4.2.3 Background characterization
4.2.4 Analysis strategy
4.2.5 Signal MC generated samples
4.3 Tight selection
4.4 Normalization
4.5 Full reconstruction of B0 (s) ! +(! 2+−¯ )−(! 2−+ ) events
4.5.1 The one-dimensional case
4.5.2 The real case
4.5.3 A new approach
4.5.4 Calculations
4.5.5 Choice of the ”right” solution
4.5.6 approximation
4.5.8 Conclusion and prospects
4.6 BDT classification
4.6.1 BDT distributions