Search for lepton flavor violation decay \tau \to l l l l=e,\mu at BaBar

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TUDI DI

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_CIENZE

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Search for Lepton Flavor Violation

decay

_τ

−

_{→ ℓ}

−

_ℓ

+

_ℓ

−

_{ℓ = e, µ at B}

A

B

AR

Dissertazione di Dottorato in Fisica - XXI ciclo

Candidato:

Dr. Alberto Cervelli

Relatore: Coordinatore:

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Introduction

The Standard Model (SM) is one of the most tested and verified physical theories of all time, present experimental observations are consistent with SM expectations. On the other hand SM can not explain many physical observations: the cosmological observations possibly infer the presence of dark matter which is clearly beyond the SM expectations; the SM Higgs model, while explaining the generation of fermion masses, can not explain the hierarchy problem and a non natural fine tuning of SM is needed to cancel out quadratic divergences in the Higgs boson mass.

New physics (NP) beyond SM should hence be investigated: rising the energy above NP processes thresholds, and detecting new particles or new effects not predicted by the standard model directly, is one of the possible approaches; another approach is to make precision measurements of well known processes or looking for rare processes which involve higher order contribution from NP processes, this approach need higher luminosities with respect to the previous approach but lower beam energies.

Search for Lepton Flavor Violation (LFV) in charged lepton decays is promising: neutrino physics provides indeed a clear and unambiguous evidence of LFV in the neutral lepton sector via mixing processes [1], which have been observed for the first time by the Homestake collaboration. We expect LFV in the charged sector as well, both in µ and τ sector, but current experimental searches for LFV processes did not find any evidence for those processes [2, 3], and more results are expected to come from new experiments in the coming years [4, 5].

LFV processes are allowed in the SM, with the light neutrino matrix (mν) as the only

source of LFV, but in this case these decays are predicted to have rates well below any

realistic experiment sensitivities, with expected branching fraction (B) ∼ O(10−40_{) for}

τ → µγ. Any observation of higher BF for LFV processes in charged lepton sector would provide a clear evidence for physics beyond the SM.

τ sector is particularly promising for this exploration since most of the NP models predict couplings proportional to a positive power of the incoming lepton mass, making LFV decay rates much bigger for the τ sector with respect to the µ sector. Many models

predict LFV for τ → µγ and τ−_{→ ℓ}−_ℓ+_ℓ− _{with ℓ = e, µ well within present experimental}

sensitivities, with B ∼ O(10(−7) _{− 10}(−10)_{). A quick overview of the models predicting}

LFV at high rates is presented in Chap. 1.

The B-factories recorded in the last ten years the biggest τ -pair data sample ever

produced, BA_BAR having recorded a sample of ∼ 5 · 108 τ -pairs. The amount of data

available consent to the B-factories to reach the highest sensitivities, among the present experiments, to the LFV processes we are interested in. In Chap. 2 we will describe in

detail the BA_BAR _apparatus.

The goal of the work described in the following is to search for the LFV decay τ−

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ℓ−_ℓ+_ℓ− _{using an integrated luminosity of 472 fb}−1

collected by BA_BARdetector. In chapter

3 and 4 event selection and background estimation procedure will be presented, and in Chap. 5 the systematics associated to the measurement is described.

The present best Upper Limits (UL) for τ−_{→ ℓ}−_ℓ+_ℓ− _{at 90% confidence level has}

been published by BELLE collabration [6] using a sample consisting in 535 fb−1 with

measured B < (2.0 − 4.1)10−8_{. The results obtained during this thesis work will be}

presented in Chap. 6 along with future prospects at higher luminosity Super-B factories which has been proposed in the last years [5, 7].

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Chapter 1 LFV in

τ decays

In this chapter we a brief overview of models in different frameworks: SM extensions in neutrino sector, super-symmetric (SUSY) models, and grand unified theories (GUT) models, is presented. A particular attention is devoted to models predicting high rates

for τ−_{→ ℓ}−_ℓ+_ℓ− _{decay. A complete review of theoretical models predicting LFV can be}

found in [8].

1.1 Standard Model expectations

Neutrino mixing is a well known and studied phenomenon, which provides evidences of LFV in the neutral sector in the SM. An occurrence of LFV phenomena would be also

expected in the charged sector: the allowed Feynman graphs involving τ−_{→ ℓ}−_ℓ+_ℓ−

de-cays are shown in Fig. 1.1. Since all processes leading to LFV in charged leptons are at least one-loop diagrams, due to the strong mass suppression coming from W boson mass, and the need for neutrino mixing [1], these processes are expected to lead to very small B.

Figure 1.1: Two examples of SM allowed diagrams for LFV decay, a one loop diagram on the left and a box diagram on the right side.

At present no explicit calculation for SM τ−

→ ℓ−_ℓ+_ℓ− _{decay has been made. In}

[9]-[10] τ → µγ decay has been analyzed, with an expected B of O(10−40_{) if we consider the}

same diagrams for τ−

→ ℓ−_ℓ+_ℓ−

as a τ → µγ, with a virtual photon converting in two

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to consider also other way to get a neutrino-less final state with three leptons, but we expect the B to be beyond the present, and probably future, experimental sensitivities. Given the small B expected in the SM any observation of LFV in τ sector is a clear hint of physics beyond the SM, and a great probe to understand the flavor sector of NP models.

1.2 Standard Model extensions

Many models, consisting of non supersymmety (non-SUSY) extensions of the SM, predict higher rates for LFV. The main sectors which could lead to an enhancement of LFV are basically two: the neutrino sector, and the Higgs sector. Extension in the neutrino sector provide larger amplitudes for flavor changing neutral currents in the neutral and charged lepton sectors. On the other hand extension in the Higgs sector, especially Little Higgs models [11], predict larger amplitudes for Higgs mediated box diagrams.

1.2.1 SM with right handed Majorana Neutrinos

The SM can be extended by adding additional NR right-handed neutrinos νR along with

the NL left-handed neutrinos νL already present in the SM. The mass matrix M can be

written as a (NL+ NR) × (NL+ NR) matrix, with a see-saw block form [12]:

M = µ 0 mD mT D mM ¶ (1.1)

where mD and mM represents Dirac-neutrino and Majorana-neutrino mass matrices,

re-spectively. The submatrices present in the M matrix share a similar structure with

the light neutrino matrix mν. The (NL+ NR) eigenstates correspond to the Majorana

neutrino masses.

Present observation of neutrino mixing and measurement of the neutrino masses put

a bound on the lightest neutrino mass, mν,light < 1 eV. This bound put strong constraints

on M-matrix eigenvalues, so that we need a |mD| ≪ |mM| hierarchy, which suppresses the

heavy-to-light neutrino mixing, in order to predict the small neutrino masses observed.

This model has [13] two CP-violating phases (δ1, δ2) so that the Dirac and Majorana

can take the form:

mD = µ a beiδ1 ceiδ2 d ¶ , mM =µM1 0 0 M2 ¶ (1.2)

where M1 and M2 are the masses of the Majorana heavy neutrinos (M2 > M1) (we

consider a 2-family problem). It is possible to calculate the largest possible LFV B for

τ → ℓγ and for τ−

→ ℓ−_ℓ+_ℓ− _{for given M}

1 and M2 [14].

In this model τ → µγ and τ → µµµ are expected to have B of O ≤ 10−9_{and O ≤ 10}−10

respectively. On the other hand τ → eγ and τ → eee are expected to have much smaller B since present experiments indicate the mixing angle between the third and first family is almost zero, and are strongly suppressed with respect to τ → µ transitions. Branching

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Figure 1.2: Maximal B for τ → µγ (solid line) and τ → µµµ (dashed line) for a fixed

ratio M1/M2 = 0.1 (left) and M1/M2 = 0.5 (right)

1.2.2 SM with left-right neutral isosinglets

SM neutrino sector can be extended also with the introduction of an equal number NR of

left-handed (SLi) and right-handed (νRi) neutral singlet [14]-[13]. In this model the mass

matrix M is such that the lepton number is conserved, with lepton mixing still possible.

M =   0 mD 0 mT D 0 mTM 0 mM 0   (1.3)

M is a (NL+ ÑR) × (NL + ÑR)-dimensional matrix, where ÑR = 2NR. The

see-saw restriction mν light < m2D/m2M does not apply in this scheme [15]: although not

limited by the bounds on the light neutrino mass, this models has constrains arising from the smallness of heavy-to-light neutrino mixing parameters, which introduce a hierarchy

|mD| < |mM|. This model features NL mass-less neutrinos, however non zero masses can

be obtained introducing perturbation in the mass matrix.

The sub-matrices for M, as defined in Eq.1.3, can be taken of the form

mD = µ a beiξ ceiξ _d ¶ , mM =µM1 0 0 M2 ¶ (1.4)

where ξ is the CP-violating phase. Since NL are massless, τ LFV decay rates will be

affected neither by light neutrino mass bounds nor the requirement of maximal (νµ− ντ,

νµ − νe) and minimal (ντ − νe) mixing angles, as observed in solar and atmospheric

neutrino experiments.

The τ → µ rates are suppressed in comparison to τ → e because the upper bound for the mixing to additional neutrino singlets, as the ones introduced earlier, is smaller for

µ with (sνe

L)2 < (s

νµ

L )2. The upper bounds for τ → eγ and τ → eee B are O ≤ (10−8)

and O ≤ (10−9_{) respectively [14]. Decays involving τ → µ processes are suppressed by a}

factor (sνe

L)2/(s

νµ

L)2 ∼ 0.4. Branching fractions for τ → eγ and τ → eee as a function of

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Figure 1.3: Maximal B for τ → eγ (solid line) and τ → eee (dashed line) for a fixed ratio

M1/M2 = 0.1 (left) and M1/M2 = 0.5 (right)

1.2.3 SM with Higgs triplet

The see-saw mechanism ascribe the smallness of observed neutrino masses to the large

scale of the unobserved right-handed neutrinos (NR). A mass scale of the NR reduced

to the order of a few TeV, would require neutrino mass terms of the order of the MeV: this low energy see-saw mechanism can be implemented with Left-Right symmetric (LR) models [16] with an Higgs triplet representation [12].

In LR theories H_L,R±± mediate τ−

→ ℓ−_ℓ+_ℓ− _{at a tree level, with an effective Fermi}

interaction for the 4 charged leptons. In this model we expect τ → ℓγ decays to arise

from loop contribution and hence expect τ−

→ ℓ−_ℓ+_ℓ−

≫ τ → ℓγ which contrast with

most model expectation, where usually no tree level interaction for τ−

→ ℓ−_ℓ+_ℓ− _is

present.

The 4 lepton interaction is proportional to h⋆

τ ihjk/M_H2±±

L,R

, where hij are the Yukawa

couplings between two lepton families i, j. The hij depend on charged lepton sector

mix-ing matrix, which is unknown, thus they can not be predicted with the present knowledge on neutrino oscillation. 10-14 10-13 10-12 10-11 BR(µ+→e+γ) 10-17 10-15 10-13 10-11 10-9 10-7 BR(τ+→µ−µ+µ+) BR(τ+→e−e+e+) (a) 10-14 10-13 10-12 10-11 BR(µ+→e+γ) 10-17 10-15 10-13 10-11 10-9 10-7 BR(τ+→µ−e+e+) BR(τ+→e−e+µ+) (b) 10-14 10-13 10-12 10-11 BR(µ+→e+γ) 10-17 10-15 10-13 10-11 10-9 10-7 BR(τ+→e−µ+µ+) BR(τ+→µ−e+µ+) (c)

Figure 1.4: Branching ratios for τ−

→ ℓ−_ℓ+_ℓ−

decays against B(µ → eγ)

As shown in Fig. 1.4 τ−

→ ℓ−_ℓ+_ℓ−

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decays. The maximum predicted B are of O(10−9_{) for τ}− _{→ µ}−_µ+_µ− _{and τ}− _{→ µ}+_e−_e− [17], although only observing all of the six channels it would be possible to decide which set of hypotheses for the mixing matrix is correct.

1.3 SM with Little Higgs and T-parity

A group of non supersymmetric models including LFV are represented by Little Higgs models. The Little Higgs with T-Parity (LHT) [18] model in particular predicts rates for LFV processes within experimental reach [18]. In LHT model a two-stages spontaneous symmetry breaking is present, the first of the two breaking points is at f > 500 GeV while the second breaking v happens at the TeV scale. The symmetry breaking introduces new gauge bosons, and the theory predicts new scalar and vector particles, both new gauge bosons and particles are predicted to be light enough to be discovered in forthcoming accelerators, and there is a dark matter candidate.

Little Higgs models without T-parity predict LFV B similar to those predicted by SM, however by introducing T-parity where the presence of mirror leptons with masses of ∼ 1T eV , and new flavor violating interaction can change SM expectations for as much as 40 orders of magnitude, with predicted rates for LFV decays well inside the present experimental sensitivity.

The LHT predicts larger B for τ−

→ ℓ−_ℓ+_ℓ−

than for τ → ℓγ decays, this behavior, while common for many non supersymmetric SM extension, represent a clear distinction

with supersymmetric models, where τ− _{→ ℓ}−_ℓ+_ℓ− _{come only through loop diagrams,}

and generally it is suppressed with respect to τ → ℓγ processes. As shown in Fig. 1.5

the expected ratio between Bℓi → eee/Bℓi → eγ , with ℓi = e, µ, is O(10), assuming

f > 1 TeV. by measuring both Bs it would be easy to distinguish between LHT and minimal supersymmetric models (MSSM) [18]

Figure 1.5: B for µ → eγ versus Bµ → eee in the LHT model (blue dots) and for MSSM (red dots). The gray region is the region not yet explored by the present experiments.

The µ decays already provide strict constraints to the LHT model, these constraints however still allow B within the present experimental reach for τ LFV decays, and makes this model particularly interesting as a possible extension of the SM.

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1.4 Supersymmetric SM extensions

Super-symmetric (SUSY) models allow LFV processes at observable rates , in particular

the minimal super-symmetric models (MSSM) predict rates as high as O(10−9_{). As in}

the SM extensions the two main sources of LFV arise from the lepton sector via see-saw mechanisms, and Higgs sector. Interestingly the predicted B for these two classes of models have much different correlation between different processes, and hence the ratios between different channel B[19]-[20], can give clear hints on which model is underlying in the process.

1.4.1 SUSY with See-saw

The low energy SUSY extensions of SM expect LFV and CP-violating interactions orig-inating from the misalignment between fermion and sfermion mass eigenstates. The ab-sence of deviations from SM expectations in LFV and CPV processes observed at present experiments suggest only a minor misalignment. Understanding why LFV and CPV are suppressed is one of the most sought after questions in low energy SUSY, and it can be answered by high luminosity machines with precision measurements in the heavy flavor quark and lepton sectors.

Assuming a seesaw mechanism with three heavy right-handed neutrinos, the misalign-ment between the lepton and slepton sector comes from the Yukawa couplings between left- and right-handed neutrinos, with the latter being a potential source for large LFV B. Low energy observables from neutrino sector can not be used to understand the neu-trino Yukawa matrix which depend on the yet unobserved heavy right-handed neuneu-trinos couplings. This is not true in the quark sector where Yukawa couplings depend only on quark masses and Cabibbo-Kobayashi-Maskawa couplings, and so while CPV processes can be predicted with small errors, in the LFV the predictions depend strongly on the assumption made on the masses and coupling of the right-handed neutrinos.

By making assumptions on right-handed neutrino masses, we can reduce the number of free parameters in the model and it is possible to make prediction on LFV B. Assuming degenerate right-handed neutrino masses, LFV depends on an orthogonal matrix R which

is a complex mixing matrix that can be parametrized using three complex angles θj =

xj + iyj. B for µ → eγ and τ → µγ are shown in Fig. 1.6 for both degenerate and not

degenerate right-handed neutrino masses.

In case of non-degenerate right-handed neutrino masses, we assume M1 ≪ M2 ≪ M3,

with M1 = 1010GeV, and x1 ∼ x2 ∼ nπ. The experimental upper bound on B(µ → eγ),

constrain the mass of the heaviest right-handed neutrino M3 [21]. The expected B and

the constrain on the B are shown in Fig. 1.7.

More stringent constraints can be obtained observing the ratios between different LFV observables. In this way the study of one channel would limit the free parameters of LFV mechanism for the other channels. In Fig. 1.8 correlation induced by type I seesaw mechanism for µ → eγ and τ → µγ is shown. These bounds are independent on the mass hierarchy assumption made on the right-handed neutrino masses.

All the results above were obtained in the case of a real R matrix. In conclusion if LFV processes are going to be observed the ratio between the LFV observables would provide unique insight on the source of LFV mechanism.

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Figure 1.6: LFV expected B as function of yj for fixed MR = 1012GeV for hierarchical

(red) and degenerate (green) neutrino masses. The values of xj are scattered on 0 < xj <

2π

Figure 1.7: B(µ → eγ) as function of M3| cos(θ2)|2. The scattered points are the expected

B obtained varying the seesaw parameters in their allowed ranges. The solid and dashed lines represent the present and near future experimental sensitivity.

1.4.2 Higgs-mediated SUSY

Another possible large source of LFV mechanisms comes from the SUSY Higgs sector, like in non-SUSY SM extensions: if slepton mass matrices have lepton flavor violating entries, and the effective Yukawa interaction includes non-holomorphic couplings, Higgs-mediated LFV amplitudes are necessarily induced [19]. As for non-SUSY extensions LFV observables have different predictions in Gauge and Higgs mediated processes [19]-[25].

Models predicting more than one Higgs doublet allow flavor violating couplings be-tween neutral Higgs and fermions. Such couplings would predict rates for LFV processes

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Figure 1.8: B(µ → eγ) and B(τ → µγ) in MSSM [22] for hierarchical (triangles), quasi-degenerate neutrinos quasi-degenerate neutrinos (diamonds), and hierarchical light and heavy neutrino masses. The present experimental upper limits [23]-[24] are shown as solid lines.

larger than the present experimental bounds. Assumptions on the Yukawa structure of the model have to be done, in order to suppress Higgs coupling contributions. We can assume a discrete symmetry to allow only a single higgs doublet to couple with a given fermion type, in this case tree-level flavor changing neutral currents will not be present.

Processes like ℓi → ℓjγ, with a discrete symmetry for the Yukawa matrix, can be only

mediated by loop Higgs exchanges, while ℓi → ℓjℓkℓk receive contribution also from tree

level Higgs exchanges, leading to larger rates for τ−_{→ ℓ}−_ℓ+_ℓ−_{than τ → ℓγ. On the other}

hand if the main contribution comes from gauge-boson loops (i.e. W), it becomes larger

than one loop Higgs contribution and B(ℓi → ℓjγ) becomes larger [26]. Predictions for

τ−_{→ ℓ}−_ℓ+_ℓ− _{and τ → ℓγ B as a function of the Higgs boson mass are shown in Fig.1.9.}

1.4.3 SUSY Grand Unified Theories

SUSY embedded into grand unification theories (GUT), such as minimal SU (5) model, or SO(10) model constitutes another class of models predicting LFV mechanisms. In particular in SU (5) GUT predictions for LFV processes can be obtained introducing only

3 free parameters in the theory: the triplet Mass MT, the SUSY breaking scale BT, and

a coupling constant λ. The phenomenological predictions for SU (5) GUT are interesting for B-factories and forthcoming SuperB-factories. Assuming the mixing parameter in

neutrinos to be θ13= 0, LFV is privileged in τ sector with B(τ → µγ)/B(µ → eγ) ∼ 300.

If we consider the case θ13= 0.2, the previous ratio drops to ∼ 2. Other LFV processes

are correlated to ℓi → ℓjγ in a model-independent way, assuming SM couplings only. in

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Figure 1.9: Branching ratios for τ → µX and τ → eX processes, where X = γ, η, ee, µµ,

as a function of Higgs mass mH

10−6 10−5 10−4 10−3 10−15 10−14 10−13 10−12 10−11 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−5 Non−perturbative Present µ → e B R µ→ eγ τ→ µγ τ→ eγ µ→ e in Ti Present τ → µγ Present τ → eγ Present µ → eγ Future µ → eγ Future τ → µγ , τ → eγ MT= 109GeV , BT= 20 TeV , s13= 0 m1 = 0 eV (N H ) m1 = 0 .3 eV (Q D ) λ 10 −6 10−5 10−4 10−3 10−15 10−14 10−13 10−12 10−11 10−10 10−9 10−8 10−7 10−6 Non−perturbative B R µ→ 3e Present µ → 3e Present τ → 3e Present τ → 3µ , τ → µe+e− Future µ → 3e τ→ 3e τ→ µe+e− τ→ eµ+_µ− Future τ → 3ℓ τ→ 3µ MT= 109GeV , BT= 20 TeV , s13= 0 λ 10−6 10−5 10−4 10−3 10−15 10−14 10−13 10−12 10−11 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−5 Non−perturbative B R Present µ → e µ→ eγ τ→ µγ τ→ eγ µ→ e in Ti Present τ → µγ Present τ → eγ Present µ → eγ Future µ → eγ Future τ → µγ , τ → eγ m1 = 0 eV (N H ) m 1 = 0 .3 eV (Q D ) λ MT= 109GeV , BT= 20 TeV , s13= 0.2 10−6 10−5 10−4 10−3 10−15 10−14 10−13 10−12 10−11 10−10 10−9 10−8 10−7 10−6 Non−perturbative B R µ→ 3e Present µ → 3e Present τ → 3e Present τ → 3µ , τ → µe+e− Future µ → 3e τ→ 3e τ→ µe+e− τ→ eµ+_µ− Future τ → 3ℓ τ→ 3µ MT= 109GeV , BT= 20 TeV , s13= 0.2 λ

Figure 1.10: Left panels: predicted B for ℓi → ℓjγ as function of coupling constant y.

Right panels: predicted B for ℓi → ℓjℓkℓk as function of coupling constant y. The gray

region gray is excluded by perturbability request. The green region is excluded by the

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1.5 Comparison among models

As described previously different models predict different B for τ−

→ ℓ−_ℓ+_ℓ− _{decays. In}

Tab. 1.1 are reported the expectations for the model described.

Table 1.1: Upper limits for τ −→ lll in different theoretical scenarios.

Model BR Reference

BSM SM + right heavy Majorana ν < 10

−10 _[14]

SM + left-right neutral isosinglets _{∼ 10}−9 _[14]

SUSY

MSSM + right heavy Majorana ν _{∼ 10}−9 _[27]

left-right SUSY _{∼ 10}−10 _[27]

SUSY + neutral Higgs 10−10_{− 10}−7 _[28]

SUSY + Higgs triplet _{∼ 10}−7 _[29]

MSSM + universal soft SUSY breaking _{∼ 10}−9 _[30]

MSSM + non-universal soft SUSY breaking _{∼ 10}−6 _[31]

Other Technicolor _{∼ 10}−8 _[32]

The theoretical models outlined in the previous sections all predict LFV up to the present experimental sensitivity. On the other hand the mechanism leading to LFV decays are similar and make difficult to distinguish one model from the others with a single observable measured. Although it is possible to have a clear understanding on the model underlying the LFV by looking at the ratios of the B for different processes, which are almost parameter-independent in the models presented. In Tab. 1.2 are reported the ratios predicted by some of the aforementioned models [18].

Table 1.2: Ratios between LFV processes in different models

Ratio SM + Seesaw LHT MSSM (no Higgs) Higgs + MSSM

B(τ → µµµ)/B(τ → µγ) 0.1 0.4-2.3 _{2 · 10}−3 _0.06-0.1 B(τ → eµµ)/B(τ → eγ) ∼ 0.01 0.3-1.6 _{2 · 10}−3 _0.02-0.04 B(τ → eee)/B(τ → eµµ) 1.3-1.7 5 0.3-0.5 B(τ → µµµ)/B(τ → µee) 1.2-1.6 0.2 0.08-0.15 B(τ → eee)/B(τ → eγ) 0.1 0.4-2.3 0.01 0.01 B(τ → µee)/B(τ → µγ) ∼ 0.01 0.3-1.6 0.01 0.01

1.6 Present Status on Flavor Violating

τ Decays

B-factories operating around Υ (4S) resonance can be also considered τ -factories. At

the center of mass energy of √s = 10.58 GeV the cross section for τ -pair production is

στ τ = 0.92nb, for comparison it is only 20% less than the B ¯B production cross section

σB ¯B = 1.15nb. BABAR and BELLE thus recorded the largest samples of τ ’s presently

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channels may be classified in three broad classes τ → ℓγ, τ−_{→ ℓ}−_ℓ+_ℓ−_{, and τ ℓh, where} ℓ is either a muon or an electron, and h is an hadronic system (i.e. π, η, K, etc.).

The different classes of LFV decay channel have different experimental signatures and different background contributions, nonetheless the analysis strategy is similar, due to the clear environment of the B-factories. Analysis are performed using a blinded-analysis method, the event selection is optimized using only Monte Carlo (MC) generated events . Real data are only considered at the end of the optimization process (unblinding procedure). The background expectation is obtained directly on MC or can be found with more sophisticated methods, with multivariate analysis tools or by fitting data distributions, in a two-dimensional mass-energy plane.

The Data-taking at BA_BAR ended last year after recording 530 fb−1 of data, while

BELLE is continuing its data-taking and having integrated 895 fb−1 at the moment,

the combined data samples exceed one billion of τ -pairs. Analysis of the samples for both experiments are ongoing and so far there is no evidence for LFV in either exper-iment.Depending on channel the upper limits at 90% confidence level are ranging from

10−7 _{to 10}−8_{, for single experiment.}

Assuming that no signal event is observed, when the number of expected background

events Nbgdis large, the upper limit for the number of observed events at 90% confidence

level can be calculated as N90

UL = 1.64pNbgd, on the other hand if Nbgdis of the order

of O(1), N90

ULcan be obtained using Cousin and Higland method [33], which gives in the

case of Nbgd = 0 an expectation NUL90 = 2.4. The B upper limit can be calculated as:

B90U L= N90 UL 2εNτ τ = N 90 UL 2εLστ τ (1.5)

where Nτ τ = Lστ τ is the number of tau pairs produced, L is the integrated luminosity

and στ τ is the τ -pair production cross section. The most recent results for LFV searches

in τ decays is summarized in Tab.1.3.

Based on the analyses searching for LFV decays a reliable estimate for the achievable sensitivities for future generation B-factories which will provide integrated luminosities up to 150 times the present ones, can be made. Sensitivity of future experiments is defined as the expected UL at 90% confidence level, obtained assuming that no signal has been observed. Depending on the expected backgrounds the sensitivity may approach two possible asymptotic behaviors:

• if the expected background is of O(1) event, while the efficiency is the same, the

UL on the B for the process under study is BU L

90 ∝ L−1. This behavior is expected

for some τ−_{→ ℓ}−_ℓ+_ℓ− _{channels (i.e. τ}− _{→ e}+_µ−_µ−_);

• if the expected background is more than few units, while retaining the same

effi-ciency as previous analysis we expect the sensitivity to scale as ∝√L.

It should be noted that the two regimes stated above represent the limits for improve-ment in the sensitivity at future experiimprove-ments obtained without changing the selection method. A new analysis approach may change the efficiency, and hence the sensitivity, but such improvements are hard to predict, as they depend on many unknown parameters (i.e. machine backgrounds, detector acceptance, track reconstruction, etc.). In Tab. 1.4

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Table 1.3: Present upper limits for LFV processes in τ decays. BA_BAR _BELLE τ−_→ _BU L 90 (10−8) L fb−1 B90U L(10−8) L fb−1 e−_γ _1.2 535 [34] 1.2 232 [24]-[35] µ−_γ _4.5 _4.5 e−_e+_e− _4.3 376 [36] 3.6 535 [6] µ−_e+_e− _8.0 _2.7 µ+_e−_e− _5.8 _2.0 e−_µ+_µ− _5.6 _4.1 e+_µ−_µ− _3.7 _2.3 µ−_µ+_µ− _5.3 _3.2 e−_π0 ₈ 401 [37] 13 339 [38] µ−_π0 ₁₂ ₁₁ e−_η _9.2 ₁₆ µ−_η _6.5 ₁₅ e−_η′ ₁₆ ₂₄ µ−_η′ ₁₃ ₁₄ e−_K S 3.3 469 [39] 5.6 282 [40] µ−_K S 4.0 4.8 e−_ρ _4.3 451 [39] 6.3 543 [41] µ−_ρ _0.8 _6.8 e−_K⋆ _5.6 _7.8 µ−_K⋆ ₁₆ _5.9 e−_K¯⋆ _4.0 _7.7 µ−_K¯⋆ _6.4 ₁₀ e−_ω _3.1 _7.3 µ−_ω ₁₈ ₁₃

Table 1.4: Expected UL at 90% confidence level at Super-B factory. Results shown

represent the expectation for 75 ab−1 in the assumption of no signal found.

Channel sensitivity B(τ−_{→ e}−_γ) _{2 · 10}−9 B(τ− → µ−_γ) 2 · 10−9 B(τ− _{→ µ}−_µ+_µ−₎ _{2 · 10}−10 B(τ− _{→ eee)} _{2 · 10}−10 B(τ− → µ−_η) 4 · 10−10 B(τ− _{→ e}−_η) _{6 · 10}−10

are reported the expected sensitivities at the Super-B factory, a future high luminosity B-factory.

In the near future, with the increase of luminosity expected at Super-B factories, τ−_→

ℓ−_ℓ+_ℓ− _{channels become even more interesting, the absence of irreducible backgrounds}

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same scaling for the sensitivities is not expected in τ → ℓγ processes where initial state radiation and radiation in the final state for τ → µν ¯ν decays constitute an irreducible

background, and making the sensitivity ∝√L.

LFV searches in τ−_{→ ℓ}−_ℓ+_ℓ− _{can become the most sensible channel to NP in τ as}

the data sample increase above 75 ab−1, even if the NP model leading to LFV decay

suppresses τ−

→ ℓ−_ℓ+_ℓ−

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Chapter 2 The B

A

B

AR

Experiment at SLAC

BA_BAR _{[42]is a 4π detector, operating at the interaction region of the PeP-II asymmetric}

e+_e−_{collider [43]. The B}_A

BAR experiment was designed and built by a large international

collaboration in order to provide the cleanest environment possible for the reconstruction and study of rare processes involving heavy flavors: the physics program consisting in the study of CP-violation in B systems, bottom and charm decays, τ physics, and search for

rare processes. The detecting period for BA_BAR is now over and the detector and storage

ring are going through their decommissioning and dismantling period.

In this chapter we will describe the main features and performances of PeP-II and

BA_BAR.

2.1 The PeP-II

e

+

e

−

Collider

PeP-II is an asymmetric e+_e−_{collider optimized for CP-Violation studies in B sector that}

has stopped its operations in April 2008. It was most of the time producing events around

the Υ (4S) resonance corresponding to a center of mass (CM) energy of √s = 10.58 GeV,

in the last period of data-taking an energy scan towards lower energies has been performed studying region of the other vector resonances of the Υ system, in Fig. 2.1 the resonance system is shown.

The effective cross section for Υ (4S) at √s = 10.58 GeV is about 1.05 nb, this cross

section is about one third lower than the peak cross section due to the beam energy spread (i.e. about 3-6 MeV), and initial state radiation. A B-factory is also a τ -factory

producing almost the same number of τ -pairs as B ¯B pairs, the cross section for τ -pair

production being στ τ = 0.92 nb, making BABAR one of most suitable experiments to

study rare τ decay processes. The other main physics processes happening at PeP-II

interaction region are light quark pair production (u¯u, d ¯d, s¯s), commonly referred as

uds processes, charm couple production, di-muon production, and BhaBha scattering. In Tab. 2.1 the effective cross for all the main processes is reported, the BhaBha cross section is divergent at small angles and the reported value considers the Bhabha falling into the detector acceptance, which means tracks with polar angles, measured in the laboratory

frame, comprised between 18◦ _{and 131}◦_.

About 10% of data were taken with a CM energy 40 MeV lower than the Υ (4S) peak, these off-peak data, may be used to study in detail all the physics processes not involving B meson decays, since the energy is under production threshold for B-pair production.

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Figure 2.1: Cross section as a function of the CM energy for the first four S-wave Υ resonances. The larger width for the 4s resonance is due to the fact that it is the only

one above threshold for B ¯B production

Table 2.1: Effective cross section for the main physics processes at PeP-II interaction

region around Υ (4S). Bhabha angular differential cross section is integrated between 18◦

and 131◦ _{in the laboratory frame.}

Process σ(nb) τ τ 0.92 B ¯B _{1.05 (peak ∼ 3.6)} uds 2.09 c¯c 1.35 BhaBha 25.5 µµ 1.16

The off-peak data are particularly interesting for the study of rare processes, as LFV in τ decays, where the understanding of all the background contribution is crucial for the estimation of the UL.

PeP-II is an asymmetric e+e− _{collider. The electron beam, circulating in the High}

Energy Ring(HER), has an energy of 9.0 GeV and collides with a 3.1 GeV positron beam,

circulating in the Low Energy Ring (LER), resulting in a boost for the CM of βγ ∼ 0.56

in the laboratory frame. The choice of a boosted CM made it possible for BA_BAR _to

distinguish the decay vertexes of the B’s produced in Υ (4S) decays, permitting to study time-dependent CPV in the B system. A schematics of the PeP-II layout is shown in Fig. 2.2, and accelerator parameters are reported in Tab. 2.2.

Electrons and positrons are injected in the two rings at the collider energies by after being accelerated in the 3 Km long linear accelerator (LINAC) and accumulated in the

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Figure 2.2: Overview of the PeP-II accelerator Table 2.2: PeP-II accelerator parameters

Parameter Design August 2007

Energy HER/LER ( GeV) 9.0/3.1 9.0/3.1

Current HER/LER (A) 0.75/2.15 1.87/2.90

Bunch length (mm) 15 _{11 − 12}

Peak Luminosity (1033_cm−2_s−1₎ _3.0 _12.0

Integrated Luminosity ( fb−1month−1) 3.3 20

PeP-II 2.2 Km long rings.In proximity of the interaction region, the beams are focused by four quadrupole magnets (Q1, Q2, Q3, Q4 as shown in Fig. 2.6) , and a pair of samarium-cobalt permanent dipoles (B1) located at ±21 cm from the interaction point (IP) which permit to the particle bunches to collide head-on. The B1 dipoles and Q1

quadrupoles operates inside the field of the BA_BAR superconducting solenoid, while the

other quadrupoles are located outside the field.

The interaction region is enclosed in a water-cooled beam pipe made of two thin layers of beryllium with a water channel in between, with the outer radius is about 28 mm. To attenuate synchrotron radiation, the inner surface of the beam pipe is gold-plated. The total thickness of the beam pipe section, at normal incidence, corresponds to 1.06% radiation lengths.

The BA_BAR apparatus is installed around the beam pipe at the interaction region.

2.1.1 Beam Parameters Measurements

Two machine parameters are critical for the study of rare processes as LFV in τ decays: the luminosity and the energy of the two beams. A good luminosity measurement is crucial in order to be able to have a good estimation of the actual number of τ -pair produced, on the other hand a small beam energy spread, in absence of radiation in the initial state or in the decay, permit to have a smaller spread in the energy of produced τ ’s resulting in a higher sensitivity to neutrino-less decay.

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Luminosity Monitoring

PeP-II and BA_BAR _{have different and independent ways to measure the machine}

luminos-ity. PeP-II uses an high rate sampling of BhaBha scattering during on-line operations,

BA_BAR derives the absolute luminosity off-line from QED processes, primarily by

us-ing e+_e− _{scattering, and µ}+_µ− _{pair production. The best estimate of the relative error}

on luminosity is 0.8% for data taken before Summer 2003 and 0.5% for the remaining data [44].

Beam Energy

The mean energies of the two beams are calculated from the total bending strength and the beam orbits, including the effects of off-axis fields and steering magnets. The systematic uncertainty on the calculation of the absolute energies of the beam is estimated to be 5 − 10 MeV for PeP-II, while the relative energy setting is known with a 1 MeV precision. The energy spread is different in LER and HER being 2.3 MeV and 5.5 MeV respectively. In order to record data close to Υ (4S) peak the observed ratio between

B ¯B and lepton pair production is monitored online, with a 2.5% change in the B ¯B rate

corresponding to a 2 MeV change in the CM energy at the resonance peak. Unfortunately in this way it is not possible to know the sign of the energy change. To know the absolute error for the beam energy, momentum of fully reconstructed B mesons constrained with

the known B meson mass are used. An absolute error of 1.1 MeV is obtained for 1 fb−1,

this error is equally limited by the error on B meson mass and detector resolution.

2.1.2 PeP-II performances

PeP-II started to deliver data to BA_BARdetector in 1999 and as already mentioned ended

its operational period April 2008, recording a total integrated luminosity of 531 fb−1

including about 54 fb−1 off-peak data, 433 fb−1 recorded on-peak, and 44 fb−1 collected

at other resonances (namely Υ (3S) and Υ (2S)). BA_BAR recorded luminosity is shown in

Fig. 2.3. ] -1 Integrated Luminosity [fb 0 100 200 300 400 500 Delivered Luminosity Recorded Luminosity Recorded Luminosity Y(4s) Recorded Luminosity Y(3s) Recorded Luminosity Y(2s) Off Peak

BaBar_{Run 1-7} PEP II Delivered Luminosity: 553.48/fb BaBar Recorded Luminosity: 531.43/fb BaBar Recorded Y(4s): 432.89/fb BaBar Recorded Y(3s): 30.23/fb BaBar Recorded Y(2s): 14.45/fb Off Peak Luminosity: 53.85/fb

As of 2008/04/11 00:00

2000 2001 2002 2003 2004 2005 2006 2007 2008

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As can be seen in Tab. 2.2, PeP-II surpassed its design performances, both in term of instantaneous luminosity (by a factor 4) and daily integrated luminosity (by a factor 6)[43]-[45]. The increase in instantaneous luminosity is mainly due to the increase in beam currents and improved focusing and a better control of beam orbits. A major improvement in PeP-II operation has been achieved between December 2003 and March 2004 with the implementation of a new procedure called trickle injection. Before the implementation of trickle injection PeP-II operated in series of 40-minute fills during which the colliding beams coasted: it took three to five minutes to replenish the rings

between two fills, and during the filling time, the BA_BAR data acquisition system had to

be turned off for detector safety due to the high backgrounds caused by the injection. The trickle injection on the other hand permitted a virtually uninterrupted data-taking period with the LINAC continuously injecting new particles with small injection at small rates (up to 10Hz in the HER and 20Hz in the LER). This novel method of injection allows an increase in the integrated luminosity between 20% and 30%, (Fig.2.4 moreover the continuous injection made the beam more stable making easier machine operation and a very important overall reduction of beam losses. After a beam loss approximately 15 minutes are needed to refill the ring with no data taking possible for detector safety reason.

Figure 2.4: Comparison between the best 8-hour period of data-taking for three different period of data taking. Top panel: no trickle, middle panel: trickle only in LER, bottom panel: trickle on both LER and HER.

2.2 The B

A

B

AR

Detector

The BA_BAR detector was designed and optimized to study CPV in the B meson systems,

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achieve the goals of performing accurate event reconstruction there are many features needed:

• a large and uniform acceptance, in particular down to small polar angles relative to the boost direction, to avoid particle losses. Although the boost is small this generate an asymmetric detector design even in the innermost tracking systems like for the SVT;

• excellent detection efficiencies for charged particles down to very small momenta, threshold being about 60 MeV/c;

• good vertex reconstruction and precise momentum measurement resolution, uniform in the kinematic range comprised between 60 MeV/c and 4 GeV/c;

• identification of electrons and muons over a wide range of momentum, great π − µ separation even at low momenta using information both from inner trackers and dedicated particle identification sub-detector;

• highly efficient, selective trigger system with redundancy so as to avoid significant signal losses and systematic uncertainties.

Other technical issues have been addressed in order to handle high collision rates and the machine induced backgrounds and radiation doses

• low noise electronics and data acquisition system both flexible and stable;

• an on-line computing and network system that can control, process, and store the expected high volume of data;

• detector components that can tolerate significant doses of radiation and operate under high background condition.

The BA_BAR _{detector (Fig. 2.6) has been designed and built by a large international}

collaboration of international institution from twelve different countries that shared the responsibilities of designing and building the various subdetectors. Details on the

sub-systems constituting the BA_BAR _{detector will be given in the next sections.}

An overview of the polar (θ) angle coverage for the different sub-detector, their

seg-mentation, and performance is given in Tab. 2.3. The BA_BAR _{detector is constituted}

by nested sub-detector: inside superconducting magnet, which produces an axial 1.5 T field, going from the innermost to the outermost detector, lay a five-layer silicon ver-tex tracker (SVT), a drift chamber (DCH) for charged particle detection and momenta

measurement, a ring-imaging ˇCerenkov detector (DIRC), for charged particle

identifica-tion, and a CsI(Tl) crystal electromagnetic calorimeter (EMC), for electron and photon momenta measurement and identification. Given the asymmetric design of PEP-II the EMC is designed asymmetrically, with an end-cap extending its coverage downstream of the HER, where many of the collision products emerge. Outside of the magnet field, the instrumented flux return (IFR) is composed of 18 layers of steel, which increase thickness

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Table 2.3: Overview of coverage, segmentation and performance of BA_BAR sub-detectors. C, B, and F notations indicate central barrel, backward and forward sectors respectively. All performance reported consider 1 GeV/c particle except when otherwise specified.

System θ coverage (◦₎ _Channels _Layers _Segmentation _Performance

SVT [20.1, 150.2] 150 K 5 _{50 − 100 µm r − Φ} σd0 = 55µm 100 − 200 µm z σz0 = 65µm DCH [17.2, 152.6] 7104 40 6-8 mm σΦ = 1 mrad drift distance σtg(λ) = 0.001 σPt/Pt= 0.47% σ(dE/dx) = 7.5% DIRC [25.5, 141.4] 10752 1 _{35 × 17mm}2 _σ θC = 2.5 mrad r∆Φ × ∆r per track EMC-C [27.1, 140.8] _{2 × 5760} 1 _{47 × 47mm}2 _σ E/E = 3.0% EMC-F [15.8, 27.1] _{2 × 820} 1 _{47 × 47mm}2 _σ Φ = σθ = 3, 9% mrad IFR-C [47, 123] 22K + 2K 19+2 20-38 mm 90% µ efficiency IFR-F [20, 47] 14.5K 18 28-38 mm 6-8% π mis-id IFR-B [123, 154] 14.5K 18 28-38 mm (1.5-3.0 GeV/c)

moving outwards, with in between 19 planes of resistive plate chambers (RPCs) or lim-ited streamer tubes (LSTs). IFR allows muon identification and in particular helps π/µ separation.

The average momentum of particles in τ−

→ ℓ−_ℓ+_ℓ− _{is around 1 GeV/c, the errors}

on the tracking resolution is dominated by Coulomb multiple scattering, rather than the intrinsic tracking resolution. Thus particular care was given to keep the material, in the active region of the detector, to a minimum. Fig.2.5 shows the material in unit of radia-tion length for each sub-detector, each curve represents the radiaradia-tion length transversed before the particle reach the first active layer of a particular sub-detector. During the

whole data-taking period for the BA_BAR detector many efforts were made to get the

subsystem to work beyond their design performance. In particular novel software recipes were implemented to improve tracking and particle identification capabilities, which are

crucial to the τ−

→ ℓ−_ℓ+_ℓ− _{search we are going to perform. In the following sections we}

will describe the general performances of the sub-detectors, while an in-depth description of the software methods adopted for this particular analysis will be described in Chap 3.

2.3 The Silicon Vertex Tracker

The SVT provides precise measurement of the decay vertexes and of the charged particle trajectories in the region near the interaction point. The mean vertex resolution along the z-axis for a B meson decay is less than 80 µm, making it possible to undergo preci-sion measurement of time-dependent CP asymmetry; a 100 µm resolution in the x − y transverse plane is necessary to reconstruct the decays of the τ leptons.

The choice of five layers of double-sided silicon strip sensors allow a complete tracking reconstruction even in the absence of DCH informations. The SVT also provides the only

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)

θ

Cos(

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0

Material / X

10

-2

10

-1

1 EMC

DIRC

DCH

SVT

Figure 2.5: Overview of the material in front of each sub-detector, in units of radiation length, as a function of polar angle

mean for tracking particles with low transverse momenta (pT) with momenta that cannot

be measured in the drift chamber, like soft pions coming from D∗ _{decays, and for particle}

produced in high multiplicity τ decays, as may happen in τ−

→ ℓ−_ℓ+_ℓ− _decays.

The SVT provides also useful information for particle identification for both low and high momentum tracks. For low momenta (less than 300 MeV/c) the SVT dE/dx mea-surement is the only information available; when the momentum of the track is more than 500 MeV/c, the DIRC uses the tracking informations from the SVT to achieve its

resolution on the ˇCerenkov angle measurement.

The five layers of SVT are built of of 300µm thick, double-sided microstrip detectors

[46]. The total active silicon area is 0.96 m2 _{and the material traversed by particles}

moving normally with respect to the detector is 4%. The geometrical acceptance is 90%.

The active part of the detector consists of high resistivity n− _{bulk implanted with p}+

strips on one side, and orthogonally-oriented n+ _{strips on the other side. The detectors}

are operated in reverse mode at full depletion with bias voltages lying in 25 − 35 V range. The strip readout pitch is different among the layers and varies from minimum of 50 µm up to a maximum of 210 µm.

The detectors and the readout electronics are assembled in mechanical units called modules. The three inner layers have “cylindrical” shape and are composed of six modules each. They are placed around the interaction region, with radial distance of 3.3, 4.0, and 5.9 cm from the beam axis (Fig. 2.7). The detectors in the outer two layers, composed of 16 (the fourth) and 18 (fifth) modules have been assembled to reduce the incident angles of particles coming from the interaction region, the layers have distinctive arc-shapes, and the barrel modules are placed at radii of 122.7 and 14.6 cm from the beam axis,

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/6 ,2558 K K 2&,3*9.(8-.*1) +47).7( .3897:2*39*) +1:=7*9:73 .+7 '&77*1 8:5*7(43):(9.3, (4.1 8.1.(43;*79*= 97&(0*7 8;9 JKZKIZUX)2 S ' 6 6 6 ':(0.3,(4.1 9IGRK ('('8)UUXJOTGZK9_YZKS _ _^ ` +47<&7) *3)51:, (7>4,*3.( (-.23*> *1*(9742&,3*9.( (&147.2*9*7 *2( )7.+9(-&2'*7 )(- (-*7*304; )*9*(947 ).7( .+7 *3)(&5 S ('('8)UUXJOTGZK9_YZKS _ ^ ` 9IGRK ,2558 )(-).7( .+7'&77*1 *&79-6:&0* .841&947 *&79-6:&0* 9.*)4<3 .+7(>1.3)7.(&175(X *2( 8;9 HZYF\F^XJHYNTS 8:5*7(43):(9.3, (4.1

Figure 2.6: Lateral (top panel) and front (bottom panel) views of the BA_BAR _detector.

as well shown in Fig. 2.7. Full azimuthal coverage is obtained by partially overlapping

the adjacent modules, the modules are either tilted in the Φ plane by 5◦ _{(layers 1-3) or}

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polar angle coverage is 20.1◦ _{< θ}

LAB < 150.2◦ .

Beam Pipe 27.8mm radius Layer 5a Layer 5b Layer 4b Layer 4a Layer 3 Layer 2 Layer 1 580 mm 350 mrad 520 mrad e e- + Beam Pipe Space Frame Fwd. support cone Bkwd. support cone Front end electronics

Figure 2.7: Front (top) and lateral (bottom) view of the SVT layout.

Performances

Hit efficiency and resolution

The overall efficiency for the SVT detector, after excluding the only 5 defective readout section out of the 208 constituting the detector is measured to be about 96%.

Fig. 2.8 shows the spatial hit resolution in z and r − Φ for the five SVT layers, as a function of the track angle of incidence on the silicon wafer plane . The resolution is determined by looking at the distance of the hit in the wafer plane and the reconstructed track trajectory of high momentum tracks. The uncertainty contribution is subtracted to obtain the hit resolution, which varies between 15 − 50 µm.

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Layer 1 Layer 3 Layer 5 Layer 2 Layer 4 (a) angle (degrees) angle (degrees) z Resolution ( µ m) angle (degrees) angle (degrees) φ Resolutiion ( µ m) (b) Layer 1 Layer 2 Layer 3 Layer 4 Layer 5

Figure 2.8: SVT hit resolution in z (left) and Φ (right) coordinates in µm.

Tracking efficiency and track parameter resolution In order to estimate the track

detection efficiency the pion spectrum obtained from data is compared with its MC prediction [42]. Efficiency is estimated to be 20% for particles with momenta up to 50 MeV/c, rapidly increasing to over 80% at 70 MeV/c.

The tracks can be identified by five parameters (d0,Φ0, ω,z0, and tg(λ)), determined at

the track point of closest approach (POCA) to the z axis, and the error matrix associated

to the five parameters. d0 and z0are the distances from the interaction region in the (x, y)

plane and z axis respectively. Φ0 is the angle between transverse component of the vector

tangent to the track and the x axis. λ is the angle between the vector tangent to the track and the transverse plane. ω is the curvature of the track, this quantity is signed, and incorporates the information on the charge of the track. All parameters, except ω, have

errors dominated by SVT intrinsic resolution, while pT resolution and hence the error

on ω is dominated by DCH resolution. Fig. 2.9 shows the resolution for all parameters determined from calibrations using cosmic rays with transverse momenta above 3 GeV/c.

In Fig. 2.10 [47] d0 and z0 resolutions are shown as a function of pT.

0 400 800 Tracks –0.2 0 0.2 –0.2 0 0.2 ∆z₀ (mm) –4 0 4 ∆tanλ (10-3) ∆d₀ (mm) ∆Φ₀ (mrad) a) b) –4 0 4 c) d)

Figure 2.9: Distribution of the differences between the fitted cosmic tracks in the two halves of the SVT.

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Transverse Momentum (GeV/c) σ (mm) σz0 σd0 0 0.1 0.2 0.3 0.4 0 1 2 3

Figure 2.10: Impact parameter resolution in high multiplicity hadron decay as a function of transverse momentum, both in the transverse plane and along the z-axis.

In order to study the parameter resolution online, the tracks present in the detectors

are fitted to the same vertex , and d0 and z0 are calculated with respect to the common

vertex. The contribution from the vertex error are accumulated and fitted for, and

removed from the resolution errors. Resolution for d0 and z0 are estimated to be 25 µm

and 40µm respectively, in good agreement with the cosmic ray expectations.

Particles of low momentum can only be identified through dE/dx in silicon. The particle ID information for those tracks rely only comes from the measurement of the specific ionization loss dE/dx obtained looking at the total charge deposited in the active silicon region. The measurement can be reliably made for tracks with at least 4 hits in the SVT. The SVT dE/dx distribution is shown in Fig. 2.11 [48]. The resolution achieved is about 14% for minimum ionizing particles (MIP), and a 2σ separation between kaon and pions for tracks with momenta up to 500 MeV/c.

2.4 The Drift Chamber

The main tracking sub-system is the DCH chamber, that allows the reconstruction of the

tracks with transverse momenta above pT ∼ 200 MeV/c, providing the measurement of

the curvature of the particle’s trajectory inside the 1.5 T magnetic field generated by the

superconducting BA_BAR solenoid. The DCH is designed also to measure the coordinate

along z-axis, with a ∼ 1 mm resolution. The good resolution in the longitudinal coordi-nate is needed to match properly SVT and DCH tracks and projecting the track to the DIRC and EMC.

For tracks with low momenta the DCH provides information over dE/dx which can be used for particle ID purposes, allowing a good K/π separation for transverse momenta up to ∼ 700 MeV/c, the DCH particle ID capabilities are complementary to the DIRC in barrel region, while it is the only mean of particle ID in the backward and forward direction where DIRC coverage is incomplete.

The DCH provides also real-time information used in the charged particle trigger as described in Sec.2.8

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e µ π K p d Momentum (GeV/c) dE/dx (a.u) -10 0 10 20 30 40 50 60 70 10-1 1 10

Figure 2.11: Ionization energy loss measured in the SVT as function of track momentum. Vertical scale is arbitrary

Detector Layout

The DCH design is illustrated in Fig.2.12, it consists of a 280 cm-long cylinder located outside the PEP-II support tube [49]. The inner radius is 23.6 cm and the outer is 80.9 cm. The tracking volume was designed with the center of the DCH being displaced by 36.7 cm in the forward direction, to cope with the PeP-II asymmetric boost, thus increasing the acceptance for charged particle going forward.

The drift systems consist of 7104 hexagonal cells, arranged in 40 concentric layers. Each cell consist of one sensitive wire and six field wires, as shown in Fig. 2.13. The field wires are at ground potential while high positive voltage is applied to the sensitive wires. The layers are grouped in 4 super layers, shown in Fig. 2.13. Super layers are also used for a quick local segment finding in the first step in L1 trigger pattern recognition. In order to be able to measure the z position of the hit two different types of wire were used: the type A, parallel to the z-axis, provides the position in x − y plane, while the longitudinal position is obtained with wires placed at small angles with respect to the z-axis.

Low mass materials and reduced thickness has been chosen in the design to limit the

effect of Coulomb multiple scattering on the momentum measurement of low pT particles.

The 40 layers provide up to 40 position measurements for particles with pT > 180 MeV/c.

The material within the chamber has been minimized (0.2% X0) using low-mass field

wires and an helium based gas mixtures. The gas mixture is reported in Tab.2.4. A resolution of around 7% has been achieved also for dE/dx using the helium-isobutane

mixture. The inner wall has been kept thin (0.28% X0) in order to maintain high precision

in the pT resolution and minimize backgrounds due to photon conversion. The outer wall

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IP

236

469 1015

1358 Be

1749

809

485

630

68

27.4

464 Elec–

tronics

17.2 e–

_e+

Figure 2.12: DCH layout, the asymmetric position of the center of the chamber is clearly visible. Sense Field Guard 0 Stereo 1 Layer 0 Stereo 1 Layer 0 2 0 2 0 2 0 3 0 4 0 4 45 5 45 5 47 6 47 6 47 6 48 7 48 7 50 8 -52 9 -54 10 -55 11 -57 12 0 13 0 13 0 14 0 14 0 15 0 16 4 cm

Sense Field Guard Clearing

Figure 2.13: DCH cell layout (left) and superlayer structure (right)

Detector Performances

Tracking efficiency and resolution

DCH reconstruction efficiency has been measured using control samples of multi-track events. The absolute drift chamber tracking efficiency is determined as the fraction of all tracks detected in SVT which are also reconstructed in DCH, since the two sub-detectors can actually reconstruct tracks independently. At the design voltage of 1960V the mean

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Table 2.4: DCH gas admixture properties at atmospheric pressure and 20◦_C

Parameter Value

Mixture H2:C4H10 80:20

Radiation Length 807 m

Primary Ions (MIP) 21.2/cm

Drift velocity 22µm/ns

Avalanche gain _{3 × 10}4

Lorentz angle 32◦

dE/dx Resolution 6.9%

reconstruction efficiency is 98±1% [42]. Due to aging and radiation damage the operating voltage was lowered during later period of data-taking, resulting in an efficiency drop of 2% in efficiency. The dependence of tracking efficiency on polar angle and momentum is shown in Fig. 2.14.

Figure 2.14: Tracking efficiency as a function of transverse momentum (left) and polar angle (right)

The transverse momentum resolution is related to the track curvature (ω) in the magnetic field, and it is measured by studying cosmic ray events [50]. The data are well fitted by a linear function

σpT

pT = (0.13 ± 0.01) · pt% + (0.45 ± 0.03)%

(2.1)

where pT is measured in GeV/c. The contribution proportional to pT comes from finite

spatial measurement resolution, and dominates at high pT. The constant term dominates

at low pT and is due to multiple scattering in the material.

dE/dx resolution

The specific ionization loss for charged particles is derived by measuring the charge de-posited by the traversing particle in each drift cell, by making ad average from the lowest 80% energy deposits measured. In Fig. 2.15 the distribution of the reconstructed dE/dx

(35)

from the drift chamber as a function of the particle momentum. The superimposed Bethe-Bloch curves have been determined using different control samples for each particle specie. The resolution achieved for dE/dx measurement is 7.5%, as shown in Fig. 2.15, limited by the number of samplings and the Landau fluctuation. A 3 σ K/π separation can be achieved for momenta up to 700 MeV/c [50].

104 103 10–1 ₁ ₁₀ e µ π K p d dE/dx Momentum (GeV/c) 0 100 200 300 -0.4 0 0.4

(dE/dx_meas.– dE/dx_exp.) / dE/dx_exp.

Tracks

Figure 2.15: Energy loss resolution: on the left dE/dx resolution as a function of particle momentum, on the right difference between measured and expected dE/dx for Bhabha electrons.

2.5 Detector of internally reflected ˇ

Cherenkov

radi-ation

Particles with pT ≥ 700 MeV/c cannot be identified using only the dE/dx informations

coming from the inner tracker detectors. A special ˇCherenkov (DIRC) is the main particle

identification system in BA_BAR _{it allows k/π separation of 3σ or greater for tracks with}

momenta ranging from 500 MeV/c up to 4.2 GeV/c.

Detector Layout

The DIRC is a novel design ring-imaging ˇCherenkov detector, it is based on the principle

that the light angle is conserved in the reflection on a flat surface [51]. In Fig. 2.16 the schematics of the DIRC detector is shown.

The material used both as a radiator and as light guides in the DIRC, is synthetic silica (its refraction index being n = 1.473) fused in 144 bars with rectangular cross section. The bars are 17mm thick, 35mm wide and 4.9 m long, they are arranged in a 12-sided polygonal barrel section, with each side made up of 12 bars. The azimuthal coverage of the system is 94% while it covers only 83% of the polar angle in the CM

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~2 m

~5 m

Quartz Bar Sector

Plane Mirror (12) Hinged Cover (12) PMT Module

Standoff Cone

Figure 2.16: Schematics of DIRC radiator bars and detection region

thick, leaves room for a large tracking volume, which allows to achieve precise momentum resolution, and allows to build a compact electromagnetic calorimeter with a high angular resolution.

The bars have also a high internal reflection coefficient, greater than 0.9992 per bounce, making optimal light guides. A charged particle traversing the silica bar

gen-erates a ˇCherenkov light cone of angle 2θC with its axis along the particle direction,

cosθC = 1/βn. For particles with β = v/c ∼ 1, some photons will be reflected inside

the tube and transported to wither one or both ends of the bar. To avoid any losses or having detectors at both ends of the detector, a mirror, perpendicular to the bar axis was placed at the forward end of the bars, and it reflected incident photons towards the backward end of the detector, where the light detection system was installed.

Once photons are guided to the backward region, they emerge into an expansion region (Fig.2.17), filled with 6000 liters of purified water. A fused silica wedge, located at the end of each bar reflects photons at large angles reducing the required detection surface. The light detection system has arrays of densely packed photomultiplier’s tubes (PMTs), each of it surrounded by reflecting cones, which capture light otherwise lost by the PMT.

The expected ˇCherenkov light pattern in the expansion region is a conic section, whose

opening angle is the ˇCherenkov angle θC, modified by the refraction of the purified water

outside the silica window.

Detector performance

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Mirror 4.9 m 4 x 1.225m Bars glued end-to-end Purified Water Wedge Track Trajectory 17.25 mm Thickness (35.00 mm Width) Bar Box PMT + Base 10,752 PMT's Light Catcher PMT Surface Window Standoff Box Bar

{

1.17 m

Figure 2.17: Schematics of the radiator and detection system of the DIRC

σθC =

σθC,γ

pNγ

(2.2)

where θC,γ is the single photon angle resolution and Nγ is the number of ˇCherenkov

photons detected.

The single photon resolution is estimated using di-muon events control samples, and it is measured to be 10.2 mrad, as shown in Fig.2.18. The main contribution on the photon resolution come from the detector geometry (bar size and distance between the wedge and PMTs) and from the spread on the photon production angle.

The number of photons detected varies as a function of the track polar angle, as shown

in Fig.2.19, ranging from a minimum of about 20 for θ ∼ 90◦_{, to over 50 photons when}

the track is going towards the forward or backward direction. The detection of more photons by particles with large dip angles is because more material is traversed by the particle, resulting in a higher photon yield, and the angle of emission is such that the number of photon internally reflected by the bars is higher. This feature is particularly

useful in BA_BAR thanks to the forward boost of the CM in the laboratory frame, with

more particle boosted at large dip angles. A bump is present at θ ∼ 90◦ _{because light}

coming from both forward and backward direction is collected around that angle, the drop in the collected photons for tracks going in the backward direction is due to the absorption in the silica bar.

The combination of the ˇCherenkov photon angle distribution, the angular distribution

of detector photon, and the polar angle distribution of charged track yields an average

σθC of about 2.5 mrad, for di-muon events. A similar resolution is found for Kaons and

pions using control samples from charm meson decay (D∗±

→ D0_π±_{, with D}0 _{→ K}±_π∓₎

reconstructed in data, where K±_/π∓ _{are identified exploiting the charge correlation with}

the π± _{coming from D}∗± _{decay. The single track resolution from single tracks as a}

Search for lepton flavor violation decay \tau \to l l l l=e,\mu at BaBar

U

NIVERSIT `

A DEGLI

S

TUDI DI

P

ISA

F

ACOLT `

A DI

S

CIENZE

M.F.N.

Search for Lepton Flavor Violation

decay

τ

−

→ ℓ

−

ℓ

+

ℓ

−

ℓ = e, µ at B

A

B

AR

Dissertazione di Dottorato in Fisica - XXI ciclo

Dr. Alberto Cervelli

Contents

Introduction

Chapter 1

LFV in

τ decays

1.1

Standard Model expectations

1.2

Standard Model extensions

1.2.1

SM with right handed Majorana Neutrinos

1.2.2

SM with left-right neutral isosinglets

1.2.3

SM with Higgs triplet

1.3

SM with Little Higgs and T-parity

1.4

Supersymmetric SM extensions

1.4.1

SUSY with See-saw

1.4.2

Higgs-mediated SUSY

1.4.3

SUSY Grand Unified Theories

1.5

Comparison among models

1.6

Present Status on Flavor Violating

τ Decays

Chapter 2

The B

A

B

AR

Experiment at SLAC

2.1

The PeP-II

e

e

Collider

2.1.1

Beam Parameters Measurements

2.1.2

PeP-II performances

2.2

The B

A

B

AR

_{ACOLT `}

_{A DI}

_CIENZE

_τ

_{→ ℓ}

_ℓ

_ℓ

_{ℓ = e, µ at B}

_e+